PAR1�Ђ�BL��AT=Convolutional neur�twork-based regression for depth predic7� in digital holography Tomoyoshi Shimobaba Takashi Kakue $�IIto arXiv:1802.00664v1 [] 2 Feb 2018 Graduate School of Engineering Grad��6xT with millimeter preciA\ �bDms. Index Terms—F�,r� , multiplA=��,�r��H I. I NTRODUCTION J, is a�miEB!�AJLtechnique because ituXsi�4aneously measu��%Hamplitude and phase!Ymz, }�m A�ta�d}� (3D).�].Z�,sensor [1]. J�!�$be applied%�< microscopic [2]�(d>]ic -y) to ma<�[3]�6in 3D �oR*1�J*rded HG�+ SubsequenA�aq���i�� lcule�atiM[. WhenmxLthe angular spectruma�a[4]� .\c Y hperform�,Mfollow!� equa'�:     (1) uz (x, y) = F −1 F uhDH(µ, ν) , where AF?E�q`complex U� in ]�$ed plane a��zI�Tthe  operators F · y �re(4 Fourier trans!(i�j�e,�a!^ively.恚h*er func!5�|j� . Without�n!r1I( ’s>RinQ; , in��F��ޭ6��2� k� ��Zs} � para�(s1qdetec��j� by�#���,4s. A number ofB�d>�$y have bee! �aint�tya6���e� � �?a!��J-E�$, [10]. 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C ONCLUS%�Y. 4;�)me�Z#i3V�approxi�&lyam43a�� 5  aA��&�+ �9�� F� �a��(E&�.=�L U)H�?f�H� a f�R�Ѕfa (Az$� "p �� /8��,��s is :A� s ed6q �Fu  Iti �%lso�ful%J1D�)A)� larg�-�-fucs� [�Q1"4 H%H%� =�m,pt�E2l�� �!M�Ui *of.,t&�f1).�7��38� �� !�CNF�I�Z�V�XI�Xis 5mm. ACKNOWLEDGMENT,!�par�ly�or �4JSPS KAKENHI Gl N�#�16K00151. R EFERENCES [1] T.-C. Poon,N�'�� ree-"valW(play: Princ�$)�A!(c{s. Sp�( er So#ce & BA�"0Media, 2006. ?($M. K. Kim,� :X�nZ)EB2a(,  Jour� of Photon�"A�TEnergy, pp. 018 005– �10. [3!$ Nakatsuji%K0tsu�-a�F! viewpoint "c�g p�)-shif�4synthetic apereeB� �%L�,a@Ds, vol. 47, no. 19 �(D136–D143�\08. [4] J. W. Goodman, I�%du�Qto~%;. Rober  nd C�p0ny PublishersY,5. [5] Y. Ha�Q. Yue% "$U�A�e�n��vof\in-� :�m%�O��munQJ, �283 �6 �,929–931, 2)� 6] Za�n, N. Ch A !�E.�LaIe Autof��}al scg�~Nb�on�&�E��inu@�8vTe@Dime&y1I/. �al Socie�&America�5 �\DT4A–4. [7] S. JIAO, P%�M. Tsa6.�$J.-P. Liu,A Zou,�X%�Enh�d �5iC�� r�� dLp $%IEEE T�)ron Ind�JI@cEZ 17. �'��!Dhanenberg, B. Kemp�.D�,rks!�!SG. Von B`�2�&�p�$e�"� *�,!�p7"+,� live � e�� �_:�I�F�7a� D182eDa�9]!� Lieb� �M. Uns��ȅ�q$ fres�1ws�)K� et-spa�2 criterV1�JOSA A �21iF12E], 2424–2430�Af10]!�$Memmolo, C!Jte,�P*zo,a^FinizioE�FerraroEl B. JavidIp!��%asN�Ld,< l� �tretched9܍2le��+36 �0� 194�� 1947eX 1. [�I�%fet-,� Beng�Ae�; ourville,K$"5. MIT�ssQ 6. �#e!"5��Kuwata%6Hom�:T. Takah5tDNagahama, M. Sano,a�DHasegawa, R. Hiray#>K�3%| Shiraki e�.e C&iB�$f + page :>!�!Mca1 memorR�I�5-g2�� 7327–73IKe�13]��Muram�?EMW. Oo � ItohE0!~OchiaI0 Deep�:�GgAd ng 3&� �_, a binary-we$ edg uter-gene�Y2A1D \SIGGRAPH Asia 2017 Poste�ACMa 17, p. 29A*4�u-J�8B. Zhao, H. Im,�mMi�s�C.a$ Casta R& jY. Endo:-Y� m]a:yx T. Nishi� BWe�3di�Masudaqm ��encoderm\N"�'��<��� qJ13��FeIF.H7�Z�%IPT.A�N�%�Pn����� abiliu%�*4 B;�!͏*%�m4�(� � e�)W2 � 18� FR#:M� �2��.�N" �I�8in European Con8#�iomg6al-�"� J� � . 104140Ka�9]�Griffa�A�ub)�P. Peron� C&�%&  8gory �setE�200�20%RݻC �T��kur��N. Oke:?a A.G��e@i5 �T�oE�g ut> al�%� L �� c++:T � =. 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Apz�ix?�W��q �D!g[5)�� / &{�c R )b��1e|al�KO� [35]� "I [~gJ $ΓR βTk v�:$Tk u ds: 2�r %�let�x1 + n��Ung� abov� sum�/�&� al I��`= Z r 1/r |∇u| dx+ Ω2 β|!� | dsy,(A.1) ΓR %-|��zQ :.%��@���>ZU4���TP�a �L� ��R^�fRM]:x� ri4� moa6.�A!gD",=9hA�enM�) 2 ds�n� � V�b�eSB ofB�wE�rmCo�r �e ��?\�7��� ��������$Z Z 1+n 2nƨn�B (DII���) !�}��> f !� 2) dx + 2TA uMA�%䡪�Z� Vdiv� �qV!<�4���!Zdi -~U�s�1n)���2q &9lyiN� "m ��l ?M5a%v^� ?d��" R q∇!uA�in��p��H��%�!3)+D�M u∈V kqkM kukVcK�� �8  �ho�|M = L���@&�� nFAO5HṼ = {�,V : u|��= 0}:R ̃,� =[�V]EK so R�0 � �� � >2a�! inf0B. �q�:M̃!Lr0�%��� ]3P!O4) A�ngA�+A6���ep ��CA<qBA�� ��7��*90 case of the �Iinf-sup condition in [35]. Thus, (2.5) is well posed and has a unique solu=�L. REFERENCES [1] Department of Defense World Geodetic System 1984: Its definiQ k rela Hships with local ge BsB�s, Tech. Rep. NGA TR8350.2, U.S. NaGlal Geospatial-Intelligence Ay, �Gvi�Tin 2004. [2] M. F. AdaohA parallel maximal independ�4set algorithm,HxProceedings 5th copper mountain!�fer� !��6�A�.�p4est: Sر��K�$mesh refin��o� ests��octrea�>�Z�3 (2011�10A�113An10�Q Cai,A_Nonaka,e. Bell�HE. Griff�K A. Donev,}11�coQtm-volume1�mP%�munic�dn%�i! al Physic��6�4�26�297. [11%�HCanuto, P. GervasioIf3]!alornford,%B. MartinTA�avaD�RankenE�(M. Le Brocq%f,M. Gladstone!J. Pay A� . Ng �W.� Lipscomb, ��a�,M� I� model!S$of marine �us.^�232ED2M�52!549A�4�^DamanJ. Hr!z A. Ouazzi �EATrek, A monolithic fem->%�$nonisother� comp�i���*�� geneish!a�lZ�228a��G386�388%�5�}Devil��nd!x Mund��A�pseudou��s!y� (ptic proble� j.zS�wst� �� 9�31�34�16�O.…}F. Fisch��XEE< �High-O8я�I2o Fluid F�vol. 9�LCambridge Monographs!�mRl �� al .d ?Uni��+P!�,[ , UKe~�7�Durufl � GrobI`4P. Joly, Influ� f Gaus�M �-Lobatto quadrature rules on the accuracy�a &ila� lqU��� ��9 time domaa�"� %s%U� �vdifZ  equ% s, 2�U�526–5��8�iC. Eisen: %_H�Q Walk!� Choo�;� forca� term��aQ,exact Newton �, j�)�Ix7� 6�1�3%�9�Elm��V. How!� J. 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ReferH[�s [1] J. S. Birman, Mapping class groups !J�T"�>hip�lKg',�R m. P꜐Appl. Math. 22 (1969), 213–238. [2]:|D. R.4Chillingworth,�G home�?y p�? a non-oric�bl(T��X, Proc. Camb. Philos. S71�072), 437–44�3]HB. A. Epstein, CurvCA$2-manifold)i�rNActa �115]<66), 83-107. [4]!`$Gervais, P.ĝ!Y0central exten N�mJ�4, Trans. Amer. t �348y9y309�3132. [56~AR[_�UNt0a punctured s-`\ Topology 40 (2001), no.�O70!�D725. [6] L. Harer,.�oA?9�AN��F� s, Invent-, 72, 221 239! 83) [7]!�HatchWKV$urston, A xOA7P 9Z��a�4� . . 1 w0A�21E�!�8EWL. Johnsye�tru%Q\wTorelli) . I.9�bF�fI, Ann.�BI{ҝ11E8�S!�aU2!�44A 9B�.�%iGm�London [Sa7,Stud. Texts I�L90). [10] M. KorkmazZ@ofa�9V�Tr%WY�RZin term� Artin)�$s, Algebr. �E�. 1�A�7!U114�2]AYB��,Lickorish, H���sb!.�two�T�!f2�i�5EY6!�30i�AY13VxO�L�,2b+�Y>+ {6�+65), 6A�6� 4] F. LuoBEfGsA� R��Lett. 4a�497), 735–739!P5]P� moriA� in^ da9J��^�a6��E8��4B. Szepietowsku�no]ۙ Bull�ti�Fra�f143AI1!Wm�5�25�[17eQ Stukbb&��F2l}G Fund� 18iD� 11A3147�Z���39 [182�[. C2kI�A�level 2N=!TEϹ?Yd6> 16�12!W6�>8�>21�Wajnryba�+J�n��Q{, Israel!'I�4 8%�5E}\74. (Ryoma Kobayashi) De�Xcef G�jl Educ�,, Ishikawa N al Colleg{ITechnB , Tsubata2\, 929-0392, Japan E-mail/jress: k� r�@i lD-nct.ac.jp (Genki ��>��e�Wc� okyo Ins� t��.�HOhokayama, Meguro, 2152-8551^���8i.g.aa@m.titech �` "�A (1.4 + )-approxi�,on algorithmq+$ 2-Max-Duo�_Tblem∗† Yao Xu1 , Yu�Chen2,0Guohui Lin‡@Tian Liu3 , Taibo�4,dDPeng Zhang‡5 1 6�C�^Y Sci| , Univers�NAlberEdmont* \ T6G 2E8, Canada. {xu2,t�,g� }@ua @ca:z2�8Hangzhou Dianzi�� 8, Zhejiang 3100PtChina. chenyong@hdu.edu.cn Key�oF��(High Confid� Softw#eU$ies (MOE),27 *, Schoola�HElectronic Engineer!F��)Ter9SPeking 9Z. 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I� �M�8e�AA��2%�d�*�=out�!on `s�4Ta4u+�fH<{">� NO� %�z��onM��(o�*r���=Ela�obserO"Y**2�# �)��"%�>xiJOI7�-��"n�.f La�:we hopC.�e�heA��0} E�sN�4�7p�3Hic rule-of-thumb unVL� (by academicOoryCfact,oA�+; framework� �R:� A3M richEjexhib#7a natud%,D3>to�=�T�%�� �!�um�Ma wide a���� ip�D 2�T@REFERENCES Anton,\ ,ard, 1988, C|VusE� AT!(8Geometry 3rd Ed�><(John Wiley & So�$,New York, NY10eng��$William P.i94, D*�':=�@h&GU$data, Jour� of Finan_' Plane=7(0S 171-180. N{2006, B�a.xœ 'lay� ake'�� y#I!�ri� clients, � J�819(8), 44-51. B�8hett, David M.,�7, DynaAaa&�EZ �.j &� s: .@A�Eal61ym.=N�,20(12), 68-8�ox,!�rge E.!�8Gwilym M. Jenki!졣 Gregory Ch insel1� Se*SEHsis FoQ��?Conh6WP,(ice Hall, EC6w"@$Cliffs, NJA[,radley, Step��Arnoldo�Hax�lThomas L�gnanti�77,�Jld Math�/$al Program� (Add�! -WesA�Publish�C�!ny, Re. , MA�`igham, Eugene F., Michael�EhrhardtE8}.Q�ManagIfTh�o% P�?e 12thyySouth�o,CENGAGE Leara , MVQ, O01harlsa� Josh�|Herbst, Kailin Liu, Laura P. Lut�!�e�(Rekenthaler� 9, T�At-_ s)�/!H0 paper: Indus�71ey (Mo�j(P, Inc., Chicago, IL).H, J., Gr02Gardnu�Yuan-An{ 5H,!-�(e debate: S�)t�fund y sO m%pd "to"{" D"}�? (RussM , I���s, Sea?, WACooE�Philip L�arla= Hubb�o�4Daniel T. WalzA�98AQ"#��: Choo��.S�R� {-us�S , AmCn�Zoci'�I&- �ors�W410(3), 16–21!���2011, Pf 2Z-s:|N�Vo �������4��448-60. Damodar�Aswath.K Data� �H�DSS!xBf[&s (New ��, University,��<) 2:SA� A.��ve$zS�'aG 13, #�&�a,ome: An Adap_���  B/A.H�/Li�7i�DݣX01(1), 124-135e Fede{A�rve Bank!;Minnea�]s, }\!Z 1913}\Pa� nt, 1#www.m6fed.org/�w5y_� E�/tuer/�^/��V.cfm>��ke��, W� D. L���G �[ ]�4 nt� a"� $8$ low-yield�@ld�y6(6�� 6-55. Guy� Jona�T���c�w)�&=�o�.��re�aI '�' YU: �W"?.�Nz7(JM$54-62. INGm�z�da]A��"&E�QO�cipant�  JV �-:gs: Exa�ng)�p� )n E07.� wndB-,u,graphics8.ny�$s.com/packa�8/pdf/tdf_white_� .pdf> Irl� Gord�^0Joseph Tomlin�20t]= i������/anl�h�T economics2�I1�� 118-128. �NU� EE>!dUt�F�[&J�- A��Frs For DQ|�"@? 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Our MDGN network-produced descrip{4s, as displayeB8Fig. 5-(a3) and 6�, maintain more important details tha���e ones generated with the poly-phase down-sampling technique [19], even after image compression. The differences between these pairs of2�( are exhibi�in ��4:�H4), from which it c%i observed�t!� propo!�)�� tends to JOURNAL OF LATEX CLASS FILES 11 F!k6 �visual�arisonAd �t _ s for (d)�2. (a1put im!*(left �!s(enlargement7Dred line boxed regA� of iG` (right), (a2) multiple dY> cre%� by a��K3ZKY,by�5Z.�B4) � �iAue5* ce bM aE�%in �A�%�F1l~B3%5)zcoI�a>h h�6b& � 3); (b-f)2V:Vs, where�0(b1-f1, b2-f2)�4(b4-f4, b5-f5)E�� side:PiOs, (b3-fm�(b6-f6<cV� ��|1-b3) MDB1a(27.808/0.824/0.232(s �31.319(61/0.463(c)!b4-b6 @b A43'25FA67622A c1-c �2a(28.5{83&6�526@5F� c4-c �2b@7�3� @ A,31.60�85�@ d1-d �3�64z82f @El31.28:8502� d4-d �3�70 82,@ !A5Z5� �; (e1-e �4a(29.24!{84�@ 29.4T>� e4-e � @7�N@7z2@; (f1E<Ours-��(32.04D6>� 3.09�88J �, (f4EtD(31.91!}87�229UD3. S88!�458AD). (Nota���� .�selefrepres� a part��s�&d��$correspond��ful� solu�9m like��;4 real  size�} (a2-� half of �f ’s+a�ile allJ��im hav�e sam Za��K) keep>.�dista��a��A� has less �u�� %.rva� . Further���> fs)8o:u�� to highlight obvious feature pixel���2Xin order�Uprotec�zkeyDs�Crefor ��=)!� gof lossy6]alwayH 8 kept, although!Iy�JH possibly badly smo!�d%Bcontamin��0ion, as shown�"X 5E!~[ . T!�F�Q3��BA ��I' been!�F� eEx. FroE�se figur�&�clez  sWtqi� R�aR��w" :< lookY nAalLE�AtM� .��n eAYF �sɓ-MDB4a, ��b b,Qour��#  ebetm performe1t� :a. AmongA!sex, both~4aj�b e��a�an��3a,* �3b� chs %xin, 5-(b-e�W9� e). 1� abov� jective� B\ s,.�onclud� ,it’s very &� to em� ��$n signific� aextu���(irdly, we u�j��to enhA�A:s24�� rest� them!!be re"� ]:of� �1�2  . Be�\� wo �|n~ algorithm� provided A�r��y:/. MoreovAY��" � � SSIM1�bin�oge��� _�N� m�or1Fn � make s���;� eZE�(diverse, bu��y� she��el����s�2 R EFERENCES [1] Y. Wang, A. Reibman,e�,S. Lin, “MJ�q�!�!�o del�,y,” Proceea�s1��IEEE, vol. 93, no. 1, pp. 57–70, 2005. [2] V. Goyalb�a. ing:URion meet�^e1��y Sig�2�ssASMagazine �18 �5 �74–��2001. [3] K. Viswanatha, E. Akyol�UK. Ro!�“CoAH�human�}Psystem characteristicf� Circuit�xS=% Video T��ology, ET24 �8, AT(1390–1394�4. [5]�Liu�C�uEaE��!�two-st!�N�8 scalar quantizew9�Bc LS s �16 �4)� 253–256�09. [6E�(VaishampayaiDemaG�2� � �erfTf,39 �3 �L821–834, 1993. [7]�S.,E�amchandr�V.:��... Z1-�7I�912�� 2007�3���M. Or��d,V�.% ^ i� ue pairwisA~rrelaS ns� fv B�)�aJaR��35!�36e��14] I��jic%�J. Woods%�Concate��N2� �ofw -��cble��!� ia� ternejal Confe� �>� New YorkY\5%zpM� taniiH. Garg� Wire� ~ t mis� )f�2O s �  [16]7892012345<2<2<2<with pri� �+ DCTs� ”�I.+ 6+� medi4,Expo, Lausan�Aug. 20a� -�.� � IP�%�>�0 15)���3� 3��(5. T. Tillo�Grang��G. Olm6�2F�́�!�5�LagH� �W alloc�@b� BIBL -�67 683%�7�B�A novel�*D � ��.k(JPEG2000 de�`r�I�B�  L6� mi� 90.  92004.�]Foi�z Katkovnik�(K. Egiazaris “Point�Ype-adap���AQp-qualit�noi�! deblock!�of grayA~� olor)��ReB���   1395 4 � 7. H�M`M. Ng �T. 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Pa�letti,(DÃűrfler�$Bullo, “��Q�� i>�`N��,s,” IEEE Tcf�onM AutoQ ��fHh, vol. 58, pp. 2715–2729,��3. [2] Y�q$, E. Garon/v$. Casavola �B� nopoli��xdata in%ion��"P �C*� �wirp- � / � in D6�� C�(CDC)�0 49th �Conb�y�20��X5967– 5972. [3] C. Kw%W. Liu �I. Hwang�S"m.tT���6��}�ealthf!h��p%�in Am�rn�!��(AC �3�3)�83344–3349. [4E^8Miao, Q. Zhu, MAojic � G. J ppas�Co�-aFc5��Y��1�E�F�4 Ey53rd Ann�7F�4 �85776–5781. [5!�-Z. Bai]V. Gup��“On k.� �8�B\��a�06�: g"�`.� #B�q.�9�4%� � 3029!�034. [6� �e�2�a�2�URin.�cI�QL6�l �/f���fY5�5)�19e�00.�|1.�'�#�� 0 10 1�J��l� 0 ,P����l.O05 [7] �>árdenA�S. Amin,!:LY. HuexC !> S. SastryEƩ#yl��s�ol  : RiskIess* ,]�WYdponseQ�P�9ea#rAc@6th ACM SymposiumSI��6a� (IFA!��5pt�[�. YY��Ross,T��toA�b�M� $s, Ninth EX3Orls�,, FL, USA: A�zmic P�Uc.!Z0%Z42] H. Nijmeije$Jda�)_(r Schaft, N"(oa�3�m�4. New York: Sp�� 1990�3]�8Guo, D. Shi, K.{JohansK�alL �$p�?�var�MmoH�mp>tAi >- Q� of N�7 m,6 4, no.�U��)� *�Y �� Gustaf � Adap�V F����C� DeY+i��W  Sussex, CW�est!)Eng!�:!n Wil� nd S��LTD%�%L5]!<Cheolhye�Y. Scot�nd!VInseoke�R&CPafeL�<�unmann&ircraft�jF� m�i& Jour Dof Aeros D.I:b!P!\2� 4ͭA6]A$I. Urbina,a�A #raldo, �ea�dN. O. Ti>�hau˱J. Va��e1 FaisalI�{R� ndell�1H�ndber L�!�a�&�AJ� I{x Y�ry15Ein�F>� 2016�vIGSACA� o��xe��~&A�.qs "$CCS ’16,TɁ$1092–110%Q7JQG^NZ;%e .e*-NMhS.B SurvM��6t/� � s�=)N��� o�Q:L$ NIST Stan��Re16�ɢWebsi!�2, , Data�� N$�16-? N@ala1tit�R�� m�4T�� ology, Ga�Usburg Me�89] �O8]!$C�1!"R� tta�Robust��-B��,Fault Diagno� D:�.�K Po�A��any�� orpo�,dE �$ K. Watana�;nda^ M. H4@lblau� �d�i��# ��$k�3.6 ii.C&o���aB�eAIChE �$�e�198�0] T.Ha,�y%6De�cof Digiep2� �U. Cambri�WUni��"��. [)L. Lju�=ndoGlad,)�!Nh)vZ��ew՟(Cliffs: PTR[n��Ha�F199( 22��J�B trö� Bqten�e,�Q -M�ledn (^ Ed.-:Q-Saddle R� , NJ��PM; ice- I��199823]sAG<so� J�oSf�K՞F�h: :c197�24� &�E9�S�3 tes��-35Cal"��e�$Ann. 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Ac��f���:ОI��"7ank�FE��edler!JEskin�9 Larsen, E�S nden� uQMG�Drguli|�G. Prasa *(their inter�uest in this project and several insightful conversations. 2. Notation and preliminary lemmas Q Let T be a finite set /let kv �local field for all v ∈ T ; define kT = v∈T kv as �$e introduc��. We endow kT with the norm | · | = maxv∈S v where is a 2on�� each�. 2.1.a|-algebraic groups. A Q variety QN$ M (resp:A M) is�formal!�� of �Mv kvFwRv%( 6( �Dies). The usual no!54s from element!��leometry e.g. regular maps, r%�al>4point etc. are-�(d fiberwise%�0will use thes!� �!�Tout further remarks. T%�P4two topologies!�M(kT ),%= Hausdorff$yA�Zariski�0make it clearA4n referring toZ> Hence, ifA�a �A� stat%N we do!i give W8Wpartic%V Ay!d�n!$ one whichA!be�$consideredA�F�.e}Mib kT -E� . An1� e 6= gei)DNa Xof class A if g = (gv )IgTis diagonalizable overj,%sa8.��lcomponent gv has eigenvalues �!�4integer powers�=uniaizer ̟q 0. Given a sub�]B ⊂�we�i$hBi denoteJclosed (��eJ<) %-�[ generated by B. MEASURE RIGIDITY FOR SOLVABLE GROUP ACTION 5 2.2. Pseudo-parabolic subg�0L�)�.of positA4`characteristic. Suppose M!�aA nec�k)�)�`(λ : Gm →Q \non central homomorphismu�)�. D�v(−λ(a) =  −15�aE; k × . Asa8[Sp98, §13.4] ��0[CGP10, Ch. 2App. C],1�PM (λ)J�s-* of Mxm)�th!��s x�M suc��at%�map �x�,extends to a!��GaAto Mi5W+ �bI1�Aal�!� �,� �P�� |�!�e a�fgoe� 0��-�E�of�image λ!�I�$d − by Z �(. Similarly-� �%�)mYwe�u DA�W ?�]( multiplicaEuiGm act�e0Lie(M) via λIca�we s.���1�Ie� �EW±1bmay!f$identified�\!vspacesA�a�� cor�Jond���zero,y=A�neg � � . It!Nshown inn�se�soM� 2�BT78]��atU ± Z���k-Q�%M. Moreau,1���]s�Ms�!|pr"maps×-�aPAk5� k-isy�Z�$ies. A pse6��,�pIM���cRu,k A$��some λE�bov��e $I��maximal,��,qrunipot�1ks� {M,5�4Def. 2.2.1]. W-�rec�{eܑ Prop* 1.8(3)] t!�>G$(2.1) + Waci !T1�!_ !]) 1Hn�8y�3) ADWM (s)E� ±EB.w3. 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C�����i3en� ({gnZ��'� \(N�E�Ͱ]+.JbyM }*�zuw φ �� }0_�M2� by#�,iJ�o 3�`]�#y2O �� l�2�UFf �� ity "];"$^���-�*�8)�� s,D*k !�BK���1��#n�Tak�!%�e�atjE@� R�2�OB|�~gy�� Wr �zMz�/vuA3Y��;Gj� :�+)�at *>� .j.\�*�!h&�6gn5� �je� �V'E�6  s&�,!�u�>� sNq.� = ! x. 1�)!�Z�each mdoos��^Z� vn%m ℓn6S ((����/͚5�e�BOmmSo�q��-�(eV@ �_>�I 2a�(�* ,�$i. PŸb_�ty�ejM /6N 2�-'8�2�1��$!N J&�ӡ�G��/m 2��,(2�fEnd"q 7a�&�+� x1:�'<@Cu!��+ 6.9�A�"% n���'�in2H {6� ��@lT = v∈T lv ⊂� kT where lv = kv if v 6= w and lw = (k ′ )q for some q = pn , moreover, q depends only on the weights of the action of S by conjugation, (2) aPnected lT -subgroup F4�[RkT /lT (G) so that F(lT ) ∩ Γ is Zariski dense in F, (3) a point x = g0 Γ ∈ X, such tLµA�the Σ-invariant probability Haar measure�`closed orbit Σx with Σ i F + (λ)(2�)g0−1 %} •wJure�D$ respect t�Pe Hausdorff topology,!�?g<@defined in (2.2) !�0a non central%]xhomomorphism λ : Gm → F. Mor-�g0-d)_!,smallest set!�form M%�ΓMTM�anmsub!Oety5�µ(0X/Γ) > 0. Proof. IndeedY(above asserA<s are!�v �|course�pC DTheorem 1.1. We giI A�P detailed discussion e!+TsakR�Fcompleteness. MEASURE RIGIDITY FOR SOLVABLE GROUP ACTION 31 In view�Woin beginning#,§6, we have4following. (a)�Ie�lT ⊂a�asO(1ymi;U which!�.6.1) is-�D-split, unipotent,^y�of.~. W�,us replace GI�.��@�SU�G, see�!� By Step 2� the N�b b= aZ4 , E,�0minimal dimen%�u� �E := EE� �Z, �!Zf1�AnpA�es.�@a�1 m�,E/E��g�~� ,E�ov�BFi:�!,E. 1<5��<c) �:(Σ-ergodic ���$����> Σx,i���E�-(F�). �� !D:= hWE+ (s), WE− i. NotA\at�vm;!� -8Eg0%L��2�8&.i5fore, Fxa?]� , lTqLa)�]!�m^$b) satisfy-aimex!t�m0. The final c!M+� we nōo showw)A= Σ. E� firs!at since��E�� �� ρ(SU �A,is toge! )}1h5 n�fa\�K U implies�� Q In u36.18)�t��g%�at�LE. Hence, − WH (s)�u�Ee�.%+!<riKHa�9, i4Σa3wasi�ed.  32 AMIR MOHAMMADI AND ALIREZA SALEHI GOLSEFIDY 7I�8arithmetic case�Tt!:U�e=vide B�escripE�o� �s FEVΣ in�uA�tmFe7b� by fixaZ�qiKe( global funi[field�a��ite�|�s K��Lput Y G= Gv , v∈T �  Gv�-G(Kv i�KvS�� 5 4of K at v. Den��by OT'ring �� -integer�%K%zlet Γ �fi�index+ %�[ G(OT�9Q Put�= ��� us��in.�,(particular,�a�kT��� Kv� all� ��t F).IN�s a�(2), haP � ��.>] = G(k� Let M d)4)U-�%_ onen%�ident M����0 ofv n Ge<n�  K2� � [Sp98,�t(11.2.4(ii)]�I.7� !+6G=:��T . Rec!K����ω�3.1��=0M%L M equals !u�a%a��a��he standa���.%k�. (M)1�Ң&\ ei���(K 3 or�= 2, 3,AnE���8absolutely almo� �*e�*ore�M* 1ype A. ���N $, our goal% o �/biTstructI`��q  (7< D′�""z1�I�,�G!`Q�is���.i <{M∗i : 1 ≤ ir}.6K-f. S�My%!y .�ee! ��  r Y r.� 2) M= i=14��!A�2�%�Lre exists a separabltw Ki /��*� NB9� 2�,C-�, M̌i ," �= R f(0). Qbi σi,j p { }E" different�X2�b,is naturally�� fied)�}E aA�&JF&}�6 ⊕Cvi��unA�.1Q�of� J Kj�3Q5M* ��2� f�⊕α∈�`%3%�, E = Eα�� ` (4|� �^�.�,�J��Õ�f� j.ain%� (⊕� ) q!DQ2 7.2 occup�Agres� *u E�4us briefly out��I$trategy. 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REFERENCES [1] Qi Chen, Bing Xue, Lin Shan�%ݮngjieȪng,�6.h�%G�s�of tic .��� SymbxR& ~" Struct%�( Risk Minim Q.cN6e�K ��6 ov�^c�"w?g��) Ca\en#�pACM, 709–716. [2] Agoston E* �Márk"'��02. A �2no*+2w ! �FMo~���ECf�02 �.�.n� (CEC 2002), Vol. 58. 2–587. [3] :� %&��13�lan�,"� !�c&//ixUtic�"�%�Cxlea�t�_Aof&�� �A:  . Sp+30er, 73–84. ��:�6� �̚ F�� �5"y�� izE� a&� J�-�pr܎�41!m2. [5Blf�Q(n(�%�5��KqG� MZ#ne: A Fe&��6m0A%se+ A"�x Insp#mby F�R�mUIsin Arty ��Intellige. Lea�e@e5iW er S9�ceM�9273. 9�0280–285. [6z,0Joana B. Melo� d̃oc�B.!�reiras%@ 2. R� U| technique�g.�lrol�z�.��2�18�{�[7B��7. An E�cE}a A�*�AA�Ov.`�"a`�': S �1J�A$Sach{.,Ph.D. Disser�$on. D Kt� of ^r� Rr�ݛ [8B��:M1.��j��C#�ol�� i�ΑQQ�.Ҵe15th P8�u�!��|hZ�: Z�f� (EPIA�?`1). [9] Michael Kommenda, Affenzell��PBogdan Burlacu, Gabri7ronbeRo�b Step� M WinklerE$4 a:t�P�/v)M=�*s�+&4^+a�an�Pk�6U� AnnuaZ�Zy�8.�-136��136�/10] Johnh�oza[�i��2�"�A��6�s���jNaSj�()lex Adap�4 Sys�) (1 ed.9ZMIT� ss. � Ibrahim U�!�0�n E4(u�E�Garye�a��Y�.�.�*!��&<. 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(12) O� �hand,V9� X   P^R R�P�E[p]AL > γ9f�- 9p9 P |.�|@%w0.5H Gr6(2/3)!�.f(!�0.5| >]  13 ES�V " Bennet.��A8 >!—se�in�Tce, (Pollard, 2015, Pr{ 15)—a get41 %W JB5 !2P !a>a& ++ <!6%@Q 1.54γ/(9a�<2_26 &, &(11f12 (13�ge�(A�Z��E� 942 ] γ∈[(3/2��(9/4)ν� �(�γ�e�3) n oe0�} + 2p �a$!X 3 �u &�ν!(��u0.9ν ŵN!F't t�Vp u� γ 32 u2 �):3$�� γQ AWraU6�'�%W#��l�&displayL ut�'is�GAB  1/3 2/3z����(2�'1)!@%�u /6 ,��2*a#&W:�2jMarkov� ���A1<&!v!�2F#!(k�*� v� sup PM kF � J/Y��"Z!�T�P kF i=0,1  EEp#F I�!�&$� NowCteq*#\ ψ = arg�8∈{0,1} F i 2 >�"�"E �� [F ]�(%45 >�!�j"� �(ψoiaF i�2LpFN��" M/α�{ ;�F6;�riangl &�again,a a%�1���π �o#>��!� iR)�6P,��α Yi/a l> α M  O RI��&�9?�Nα!��#.�M�iU�6KK esuln�"a dir� icEa�< 2.2 in � (�) & d"p��j�). 4#!''>J��0ψ ∗ satisfT (x�� 0.772� n x ^ 0, 1  14v:"�$usR� 6 Qµ *�y�  µl(0,��2� P(σ!� 2 µ�/n�QλJ0,∞)e λ(d"A� λ-m�$!�NXs�#a~,   �X�N, �$ dZ0�$2  dv (Xay1� XI�1�$2n  n sC ε oX�ε e��$=1+ 1+29&��R�qt!�� t�/�cZ \J^KL(!k��! e� (dX�s. 2n Nw2nNe 9:�p��� Xn �k µk�µ/��@.� A�=�1+ e =W µε�% , 2k�!(σ k! k∈Ny�s  L!&2 9 s s � W�t&�2n2& 2n �2S& = 2 2W&J7.�h sL ,A�&1  >�&= n6R@. ACKNOWLEDGMENTS^author�nk4nonym�/re�0�8his/her carefulPo Cp#a$fruitful s�s�Hs. #?��be�n�'�.�9eC proj��xLabex MMEDII (ANR11-LBX-0023-011e work�o#� w R9�)riL grant Inv�sse�,s d’Avenirm-11IDEn03/ � Ecodec/AN-LA�47++4EFERENCES Bick�P. J.% HRitov, Y. (1988). E�/ g�d"�d�ty deri,ves: Sharp bD0ofh)"V/�m] . Sankhy:�q4E Jour of SSs, Se�A�61-200�l50(3):381–393. Birgé, L.�=7). Mi sel2a���pro,es, v03e V 55�Lec�@Notes–Monograph �8, pages 32–64�stitut�SMathemat .��Beachwood, Ohio, USA. Boucheron, S., Lugosi, G.,Massart,!� (2013). C"�* I�i!�8A Nonasymptotic!do�) �5�r%H. OUP Oxford. Brown%=(D., Carter,A�V., L� M. �(Zhang, C.-H)m4A0quival[a"r!pQ)-�ion, p�5�E�gNwhite �~*, drift. Ann.1Np., 32(5):2074–2097. Butucea�SComte, F �9). A!�!�  & ��xA ��Y *�s. Z$poulli, 15(1):69–98. Cai, T.��9I!�%7M���- nonconvex*&spaces. F2):55A�576~�5�&�9�V F�3%�31a� 2343ҏ 5 z46�(4^�a quadra=�>� 34�298A@325z#1��!ng�7e hyp��J hermA� poly�&I��=��4a!�smo�8Yz>� 39!�101!�1041. ͵, Oa�omming��L.�2G e�BEm1�nmA�N9sq "%c$eF�45��923A�5A��YR�:� �VerzélX0N ���i�*�s&�7�@. ArXiv e-prints, (:1611.097442P%�%@S �a!Curve �stA`on� nonp�8Lric goodness-of-fit $ing�j� . Pla��In�( (162:20–42��!�R*67]]a�p-.�)&]f��a)%>�>2�]cb"2� ight�5f4�Nstenc0v�)���contex24 high.� i�7:�40e�667a�69�咪�Bq -�!4^ i� nullu�i�;�8via a N(��O0regression. E�r J.�T7:146–190. Donoho, D)cLiu, R� !�On�� o%�Lh7 Func��$als. Technre8 (Un�81� (California,��keleyQ partk �M� ics)f, 2Y Y2�L � Nussbaum,O(1990� ��9U�(�^�&1 �p� , 6��4290 – 323. E=ovicha E�.�199�>�"F:.�a:�*3RelN4 F� , 98��26�$75. Golubeg �nLevit,�� An oracle(roa�o^�F�A�a"I @ 6� Mz �%9�(, 13(01):39�e0408. Grama, I)0B�# A&d _8� � :44zed�m� s.&jL 1L111!M1i�14. Ings� Y.�Kutoya��Y.� Fa;N2���>Ajng�� ?4At'� � �II1��(45. IvanoffAz, Pic F��RivoirV�g��U��loE+�- !`&0�.o y M�#ne Lear8"Res� , 17(55):A�46. 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Acknowledg��s:�pro�receisfu%�n,European Uni' s Ho# 2020u*� innoc^gramm!k(der grant a�2��$ No 640891�"g�� y a�Im�of �YCorpo���� do~"on'GPU� A+�x!�a�����11 Re��#,[1] K. Chatf�,LSimonyan, A. Vedaldi�,A. Zisserman�tur�devilA� the /: Delv��U"in�&"neQ LIn BMVC, 2014. [2] D�@en, X. Cao, L. Waq$F!|e$nd J. Sun.&�facA�vis�: A�!Pmul�n  ECCVo2. �"J. De^W. Do R� cher{Li%x(L. Fei-Fei.�ne� �v4 hier!�� m1�x� � CVPR�09. [4]�\onahue, Y. Jia, O. Vinya�J. Hoffm!�N. Zh%E. Tz��$T. Darrell�caf: A)|�$9w#v%�'Ar generic v�a`< � ICML�815. [5] M. Eitz%Hildeb��,� BoubekeurI9Mj$a.�B!d-�G: B���bagi��s� crip�%. TVCG�1. [6�!(ayD ndyHow do� ��Ps?A�SIGGRAPHUA7E�� �eo92 .^t 1�� e analysit in} %d. JourD&G  InstitX Elec�4al Engineers-P�!$III: Radio%Com*~ ,�'x93 (26):429–441, 1946. [8] G.A(Ha�n,A=$Srivastavae�0Krizhevsky, IaStskevA�!DR.�'2� 0a back-propag%���� �U � 1990a95 ��$L. Bottou,!(B. Or�.K. Mü$. Effice�hg. N2] s: Trick�vF 0trade, pages �8936 �i,!:SU�S. GongѠ2�by&�"�+�"�+�)�"�3� 12�aa4,��T�j Hosp� �Y��!��Free-�!M�>�J�,��K����18]wLu, C�i,a`Su��S. Ca��M2� odelaa e��onic  ��$ ��q�-Ai+ D�'!�0�9e�A. Olsh<�6eldA� J. E".!�-cl(+ p��AI/a y ��p3"cod�6;. NKe�]9�]20]�Ouy� T� Z�X. Li. C�7-modal� QS : beyong �e1�MTA�  1� G. Schnei� !�(T. Tuytelaa�W%>n)6-drL�f�.�,I�S#  As� � 2E 7 b6* V�R��*� �< `>� L2 E�23] PA�usasM.A4Fonseca. GeomeV 5aE� clipb/Mw&~ "�  of�A�*q !;�- �&TA�((2):71–83�824) Stol�a�0 MasciAGomeziD��$chmidhuber��eG-!�l7��g�at-o&% feed�+�MY/ion)���1�5]a�R L. KE��YI�I=� 3d�'pZ �I$2� N��  pr*� 504.03504!,)�6�Yin, Q� X"� �C�u. Icdar�3 g1�1��K.�Ν�2OIn / 6 Docu�AquRY� DAR ��[27%�D. Zei�( R. Fergus� Cz�L �&6<�5%� E2�8]�|tnickL,D. Parikh. 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Let us sayI�a.�al�%a�ri6 set Q (=o�5 ) of “pH s”cIn�B!~a sub<X �i�'a0Y ,7 ”; !Q� F)KQ E�$itself. (TOqu:Ct�aGu��,lso��`taEto!- �ly�aS%��2s:2)correspo�%�7�/:6H�;%% ehend.) S5a���9Nexh73 !�P2xA�X��f-(ws:%�q 0 = x,QD,for m ≥ 0 =qma.�) `da5@ qm+1 = F(qm ) if)6∈ Y ;  , �IQAj� ��aZ F�f�im steps,A�duc!�=o�q m . C�"!�Y� (�MyG�ve& in aF�.Hq�)�Cam({A!ZZ��isTa)ny�DnR+�6�6ba�2� �(��er�inY*m��%�4A� x"uN2((��! nu��&�0�25q:%�!R2�m� C�,(Q, X, Y, F)e,leH:1M P & 0 , XYF 0 ); P�s CA+Ee is auv σ2w NtalXi� \�x.8� 8se�Y ,�1�;t Q if xE�XM�:-!:U2�?]� sequE0x =e, q1 ,9 in C�3,en σ (q0 ),�(q1 �d���� K� :ciazOx�Sq0!HJ in P��Q if C!v 9�P�y) x, P!�m$y 0 "i�re τ (oy.� Y@p2  (� 3),!ah X� !p�ex��.R*�.� 92b]�™�"��4]Bfa�� g�8of (pre��|5 6 CHAPTER 1. 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Ht�!$� a� b.8�i��E0cQ�*j0 "��J ��"&2 [E�Ia&� *=�v^�� & R;�Kv-�wis%� 96 �� BibliD@phy [Bloom & Esik�3]� ve L. and Z.0ikAe)�� o!F� E al Log�6fVCve��ab EATCS Mon �Wl Ke)�#uWSciF�M�o�>��� J. S�ric �,, 55(3):1252!26)<0. [Kasangian & &5�a�#fano !!�Sebasti.9���IT�u� JA%؉e � InT�!�(al Joint Co��o�3�P� O�Softw�9DevelopAT (TAPSOFT/CAAP ’91),m� 493%�eۺeh �B�$, pages 21%�40N�AK1b8b�8Tre �aR�y!ZN9m�y�Sy�0.;A�omo� 1488-�q%2��$ 237–248r�0halil] Wafaa Z E"Fu9al ��s. PhD!�sis, S��l���= S��s�,�.�" ydne\ t >z.�OVhAn� e��ve"��=n Zj, II. RAIRO Iۦ�T́or., 27(6):503–522E&3A&%+a�2a>1����G^�r�Go!3.Re۷ 92-46, ) ��q26qb>q=��g4g=��g leen�36E��C. . G���v.O9of :��DAnn., 112:727–74%J|36. 97 98 BIBLIOGRAPHY [Klin���Paul [/(meta-enviro=s�1g�+ ym��'� CM T��x o��n�v EngineR�PMethodology, 2(2):176aD01%�E nuth�O 6] D(�d E. Ų��h�: ��p�F� h[ �tmՀ(CM, 9(9):65Ar654l66. LE��EditorA �73J�hA�VA�� � !@. Addison–WesleEn7.�84JWL�9� LmfJouX�e@ 2):9!�11%984. Re �as Chap5 4AA[�92]�92n�2�N�P 27� CSLI� � . Ce���������L�%�� %�!�e�a�5y�/"� ofБr`�AKE"����ν9}�A"� {\5. [Lawvere] F. William . Per�`l�$ctron�mun~-. [Mac�a� 71] Saund� ieQ! WorkaF��ianNA 197�<Manin� 7] Yu.I�nina�C�!�Naq NS New York!77�2)S W.M. !eF��.X 8(7):44aX4�pSWichau� ~ Chr��an  . UnRB$marque àa�poSZ  sur R in� iU� par � � et� (C. R. Acad.) . P�, 309:43�437�87 0Pair & Quèr!�68]CA]A.. Dé0r ét��bi�  régulu����� Co�l, 13:56�593�68��abadini >�$Nicoletta #�R O&;�!Rdo� | utom\�� et�zpproach�x>urO �ProughRj efYns�wort 93-7N 3�, :�a]J�,B@ f  AnK��� �:!N"v�. �"\3-8��b�� ��� ofQin�t1�A�$ M. Nivat,A�0Rattray, T. R|�ANGa2y, e�s,�yic.�.Q  Techn�� (AMAؓ�93),�9 }in&� Third 2� 6� ��q,�E shop� �!iׇpa� 3 334,*� !)Tw��- Nebl��M�FY~�6�� A�;LKN� ��,�xp!�i., 6:1�139�6. 2ǪF{Una t�xɗa@hegli alberi. 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Vapnik, V.,!G�n�$})��al�X�ses, er, ©Spx!(<1999. Cherkassky\�Ma, Y gP(%WS"%%of� P���No!�Es�,�!b(< regression”. MNI\s, vol., 17, pp. 113-126�`Suykens, J. A. K., Gestel�TAm raba$$$0D., Moor, B.D�"Vandew�&!$“Least s�(b� Worldv'tific�,2. ANDRÉS M�TENARO DAZA, S., CARLOS� GERMÁN CM�53=NIn �[s-S �V� M�6nes R5H, Oriented, U�( Gial�'$CrossValid%��) , Dyna, y:.,79, Nro. 171)sX23-30. Medellin, Februa�*2� Carlos!�Coello"r <, Gary B. LamontDavid34van Veldhuizen": “E*�)&5� SolN Multi-Obj+ Pr�A�Y�D2007. D. N. Wilke.!�Analy�0o�.��(JT ��Y Ma� 's Dissera_on,��ShPretoria, 2005. Khalil A.S.�~An InvC'L o�to6�*St� )of !�tic. a[S4- �slli�aJ ArE�zj&h01). Kennedy J., Spears W.M �Match�x"��".U AnY$er�6 tal (���P� �y SomeE�:�� %�modalD���r$W�)n-C�a�D�* 15thex3��hun C, Qinghua M, Shuqiang L �Re,on mJ iJ.A+, � k Ma�% Fo� ” .*Ap�9�� Soft u� i" 148, a_ 607-612�012. Guo Z., W� H., Liu Q� "�%6 � � LPP EV./by� a�© y�.)e�/ViMd A&Ms�,1zi�http://7 He.yahoo.com. Xie, G)w��f*�wA0Sh�a+]"'B�"-��� ��e�!k&-�e on$trol, Auto�- nd S�. E*�.h(CASE), pp.1-4., 30-31 July�1. Hu!� C.; L an T �R��"F:wavelet�1VIA`G, Eigh�&.�-�A�N��al-�)^(ICNCATJui Y �p� al%A�3!�roachs1orI� )�6��=9~Sym�)um on �DConsume� Co%� (IS3���52 - 55Q�L�|�� Chih- Chi L,he(“A hybrid�� by"A-e-bEEf�-e&�-� MARSa' [2� 2� 23� 2� 2� 2� 2� [2 !SVR�X �1�E�ELSEVIERf/i� Q�I��B!Jrdo, D.:�� erval �64-2 Fuzzy Logic� sE�Ag#g��] A�summariyqarbit�' o�uniY,in �Ket�; A���Sal� U/(UKCIMc@ 12th UK Workshop��. 1-7.�OchotorehC.N. � Robuk F&tra�,��f�de-7tre*_ AJ*Q j�� y�.�H& Economics (CIFEr)�8�$Yi X., JinDFengbin L. & Shouy�W �Ensem�, ANNsrGAuS� Day-ah�7�WE-exch�-efs Bg2�J>�1R�IXs,�( 6"�1�96-114��3. 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Gramacki, A�4J., Andrzejews LW.: Probability dens func�Hs for calculating a�Daggregates. Founda 4of Compu 1�nd Decision Sciences 35(4), 223–240�10) 13��>eengard, L., Strain, J.: The fast gauss transform. SIAM Journal�j@tic and Statistic%e�l12(1), 79–94 (1991) 14. Hap, Kamber!�$: Data Min%�Concepts_ Techniqu!�`Morgan Kaufmann Series in DDanagement Systems Aj6) 15|�rris, M.: Optimizing parallel reduc!h� in CUDA. http://developer.download.nvidia.com/co�le/cuda/1_1/Website/projects/Z /doc@. 16. Hendriks, H!im,E�Consist�!� effi!�tUJestimE . InEnceedings!�a2003 int} c2 IMEal)�cep$Its Applics- ICCSAS�: Part I, vol. LNCS 2667, pp. 388–397. Springer%�@3) 17. Higham, N.Qwaccuracy� floi point sum�I�.�. � 14, 78A�799Ehf$8. Ioannid�T|Y., Poosala, V.: Histogram-based}yaI0of set-valued�t answersfh5th�r Bases)/$174–185 a'89) 19. JagadishAVAoudas!50, MuthukrishnaMS6�,acik, K.C uel, T.: E� al h�$s with qua��guarantealAP VLDB �275�L86�48) 20. 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A PPENDIX�Proof� Lemma 3.2�1��s�λ�DfS-or�deriva!8 ψλ′ 1 ,λ2i��(1&�simplif��s ′7 ,λ � =D4A λ�× x4�L + 2(D2 /4 + H 2 )x2c3/16D 4!- 2 . ;DM )2 + *�  ( O"�� $ Then√w%�8!%�!a�s)z�d���k *�a�1t%VED�H,��$s�� > if �\ −D�} � �� ≤ 0,B/P0]%� (18):� > 0,cj�2[�[B�XD/2]. &j�y< �,a����H > 0��a�cma2cl���Ak,λUd s monotonrl*Bx"de Z!�- �:M,�0],1���>�����A�ξ)0en both x∗� ��)�� >�e�e�a*x!A�.29).QesecondEfe�E�I��g%j\0)E. �m� (19)R 0,!�]A�� �] azx.�0�Q��d.�� �B.��.� 3.1 .NeeH6�iAt"rdirec� q]��,�;not��EzN�-�-,��� � (9)�ind� unique|#� . S6�&nZ�q?��gB�K 2(� e id�mca�Ek�= Ek ({IW �}A�$T Qk (0). 2� ����$o���(4)�met%x 1�P 2-��a~he��α% a}�& (MD.A�I �.�" "�9)%�1x%���!�$wo���sm�$-'}�J ξ��En��8-X!��'!& e *6 �\soL&s �E�19v"Mr�a%?ξ�� s τ#� ��τ :�2t �� �be5��" ity B�� comb~$E�7 !wrx(f$isu�m� . CZ� 4.2 �%&e�Vn�%J)a]P3�F� 6� must�uM��us�l1�a $to adopt a*�".0 )#�c2 stayeOa"& R&�\a cer �(�imIcn�* Ii.e|lo�* (Qu sIQ! , sia�[ ' ER Z ^ H "#4. Sup`)E�6�!VwR�# � �� �ŦC2� x�%0AVA���Q��t%−x)R 1)U)!��2.m �Ws�&a��U ���b�"�)��o��>"% )aBwn�9)�+�n!�"&A,5��H2� &��:�!(��?"ξ) &� ��+T� f�oT iz� F�f=��A��set x� pos�, id� !�� V6��!�'�Fmm���P3)��ay�>ceb(5)Fp'thu��,ts. R EFERENCES [1] S. Bi, C. K�% R. Zha�,“Wire�Ve�mmu� � ,: Opportunit1*A�ch�8nges,” IEEE C5�. Mag., vol. 53, no. 4, pp. 117–125, Apr. 2015. [2] Y. Ze�$B. ClerckxJ� bi���&als ��w2�Imis� �Ti(.� �65 �X5, pp. 2264–2290, May�L7. [3] J. Xu, L. LiuJ�Multi MISO beam7a��s�taneou| -~in$%t%e%� �ferB�Signal�& cess�2 �18%t< 4798–4810, Se�014. [4 �k2Ene� .��one-bi�/edback� -N �� N�20 �@5370–5381, Oct.!X�5]QF��.�!I�%P5�e "�$�Z�M��.pA�6�50, Feb�A�6]]��0E. Bayguzina,eAav�mR�%�f�Z54)�23)5<6313–6328, Dec�6. [755,=�a�T.A�Lim �Qfce�uE!� un�d aer=$vehicles: �� .� �5 �%[42uH�8��Th�put��i$aJUAV� � relafY��M��Fu0 � 1M498!i4996, .i9]a� Xie,A�ShiT�S�H. D. Sh�2i%uMakA�$sensor net4s immortal: AnM�-renew� pproach%�Y�EE2  �u /ACM� Netw�al�y6)~174� 1761�2. [10%� Shu,�8Yousefi, P. Che��J �Gu,�e��$K. G. 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Hodgkin�LE{x�vA.F�?52) A G5sv� S=pesembra�d[S!�7�app8�'�@��o�3d�Qo)�e.2L�=E�@, August 28, 17:4%+ 500-5� KoYL n, T�88�I*�du� I/�_ X s* 3-16!p�$��M 82)6DI:kFN)i�]em�#!3l!�iv,� m� a�C,!�>��rJx+!yA���7 9:8)\2554-2558. Arshavsky, Y.�� Gelf!�(�� 2G�0o�%xq}israelmg 9e{ bio_�"/ae_biomed� }u20 "N3!�}�B:eBF cU�aOm, �tznd:"�!�ern1I&: , p��( 147-175. EWgz66) Atom�Or�d|w�W roac 3The�� al B) �-ton: "��*� .uMI� 7) R��i���Ic��s_ F&sburgN,ébec: É �s Orbis��) 83 � rö�� � 1 Is Life?w�� Asp k� Li3Ceb Cambn�:  J�2�03  ever�6w�9�In�Bu(Ed�qA�� Behavio]8Y����`, LNAI 2684. .B��lsman&e�436�18 s�h#&�:a�� [""�5�*e� �gomena "A�2��)�!ZU�:�R.l.+(Gef� Klir, !6� �Se?Qa� M��E����)���/"� "�, Febr�)��. xv-lx� ullo�WPit�g 943��K\�Xcus�!� imman�҈e��a�City, BF}t�Rf 2�Bi��, 5)�115-133..� 1999��tZ�*A Spooky��#c  DuboQ  %ZCASYS,:a&� A�N� P���C���V 99, L� : CHAOS1 . 6. 3-47.� 20106�%��*: 39� 3-!�� �5%�_AeW%ode>o�2��sm i�7, F�X%�!K* al Biolog��y, 2. New York: Academic Press. Ellis, G.F.R. (2012) Recognising Top-Down Causation. 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[6]A�BunAk,AR)W)�M�G%�mea GhQd��}it�: F�2ds:lD!'nad�5OS��zIn/l0 Through Datanresf3, PhD��sP����0R. de Wolf, Aq�i�p"P| sic~ >D�/����!#u�M, J., 28:41e 49-6�2~���ab�"gn2�!<o:rP5�1 q5%�2!�!�! 3wL..�> } �mSu�Z�Kn"�xnd)�Engine�y, 19:3�7), 370��83. 3Uxl �8 TAG:2c1 *c1Y�t�-z rRk!tag SNPs)ku� 21:8}%73E�736! 5] H�/ loni�;H��Schulz��� tru�7� empi��z,�%unsch8er6 icht��(dem Institu�n̈r Psyo0ogie, 1(1977)�6��Amuc�q)���data. BrH^h�M��aa. q ., 3;81A6��18��.S!�nsoli, K. Darby-Dowman, G. Geleijnse,\Korst� Pauws, H&� ��ach ���quE xc�.I3=�6�YV�ER.,%4�b!28� �:a SantoBF+d��>�L. Antun}]f�s>wi� 19th � �q�-�,dx��ystems�%6, 68A�690 [1�_O. DudasE. Hart- (G. Stork, P�j rn C:�s�e�X, Wiley4ss� ces��20]!�FeleR3t, Evo{o'sI�DNA"/s:*d�:*;lihood!�r!�o Mole�rS, 1��Ej368a�7arXkDO. Gascuel, BIONJ:�Q Bv�NJ&P �sa s\  model��[cee,�.� . �., ᅁ�1�� 22]�H. Hu�B�ct,.8 b^7e{t� a au�z!ISt�| N | .!�3:2��(6), 254–2�023] S.C. 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E"�Q,e: � A�q��a�(αβ� + γδy 3 )&�Egisg ��isa+yWseF at: O/ 1"� = βI � α�2�" δ�h ��γ�3 Ii,HM�% "&�*mG_9�Wbe9� m�&�&�s CH{H yc!Hc B!3@$A!Aa^L� �?��L�#� m��� ��i� :Ԟ ���� A"�Kf&| �{�ݼ2k,&� �" d 2k B��PO09Lk&� �a�eJPT&�!8$ 2k (A∗cZLk��Vi5b!wU�:osG. U�O:]��:� dap��e*& !�5F i�`<Lt/UI�dI ��e=�22�y�ɏ6�'��� B bH�]�N>:@F��3 a : M -Zc���Y�!�= S m& S n (B��#. m+n=2k���x�pAnV��h �oh�9 � �$: iα b o �0( α⊗b �>Ubc�9,��ich&3��s��\ �(%.-!�2&.�~VH�!-mVp^VHHEeF���dyJ�_b,=�:) T⊗ Lk = S m (V ∗ ) S n (B�qLk−m . (3.10) m+n=2k Now we recall that the algebra of classical covariants of the space of binary cubics S 3� is+R8GL(V )−equivaSL polynomial maps f :2H → S�, i.e.,Z OinMeleme �  S (S 3�)!)%'N = S20S(L−11O(,. Hence by )J eachN$� suitably adapted to our situation will give rise 8a TPI. For this!�ne;Hhe following definiC : D \ 3.9 Let E be a vector s!�0, let α ∈ I+andPS k5!%E. Then�^Lp�a.� func!� . In�basis!`(3.6)!�Hhave Tm (xe1 + ye2 A��(a + f )x + (e + d)y , in other words, Tm =,ǫB .ǫ2 .I�_�= i (e+d)e1 −(a+f )e2 and  = ∧ 8,  -(T! 9 _ F{e2E/(.F)deg(f )abaY2)��%y%�e51r l)!0bidegree (k, J ) (s�� ). We nowioHexplicit formulæ ferea s on!�whichE�obtaiI� taka�0 f in!�12icJ) of a b�X [19]. The simplest exa �^lE��� DiscA^A]�L2 (corresponding to n = 4, m = 0, k = 2 �0)A��gives �}TE�)[:! `o��1d4, 2) 1^7)% �1Wmula) �econd��Id�.�E=��6��A�3,�1F�:6.10 Ifm��.f⊗ di�\e i�Bity� fine p̃3^+ )+ by '(ma�−8Qm )e. 2�6�7P − 32f ade + 24bde2 2  cf a cf 2 �8a2 de=40f a38E2� ! 85 j2 /16D2 FP$8bd3 + 8becf a3:��Ze�83) Remark 3.11��erm��A>$coordinate[3]��)e= 81x2B^�y�M,��)-� �@ dualAc (e1 ,�)en��Xtheir Eq.[6] (p 4483). �5" e.^of7  wo remain�N .a twis � cubic Q�5 B. 15 2�12����� �of V �� x, y�:I�`i�Vis <����Q = Q1 ��� �����1���  µ��i"2&&i�l���Hessian�$Q1 : ∂ 2   2 µ(Q) E� ..xA� �y 2 ∂y ��6�(e quadratic�r H does not �������9M�kM+ofm�| � �6p ( 6a/+ ae@4e} 12bd 24eb)x2 +. 36bc 8f d + 4a %8aa�D$e)yx +(16di�16eh12a 92aՁ4d2 )y 2�z��4) 29�G=�&� f�4Poisson bracke% Q1�µ: G)�!�Q �µ!� �-�y(y xV�I� I�\��6�S:�  23 3� 144bf�372b%�96�+!�!f36b-�4�0!� 08b )�64f��a x3  + #)� 288b��T��88beY�!�2E2A-e %�5)�`ac��16bcf�|1�Q� 72bd2 yx2| 72a2 � 12ad�48�%448��< � dz−28�t8��=24f��cA��e Aux   !+dc!72eM� 144e �36dV96ɥ108c2b!3d3�64e 48d2Y3 N.� se "�s� &� unde e a0 a�� a鱵� Ja�unt��)2� g onlyzlSL�aq$is means t� atղ to slight��$Eisenstein&Psatisfi�Ehe�.to 2<. Propos� 3.13�  valu�?J/ s� L, Id, µ, G at any v�V �y5J�L 16 × 27Disc(Q)Q(v)A+�p(v)3 =!�e}�of. A ? !8forward consequD�@5�{i- eq%/ jw �µ��G!�I �new� . 16 QEDBf4��: 6�2Piw �2& S.9F8  2 !Cm r : A�� ݏ =�U��+ �Kaa� 6� �U 36bd� −36"% 1�C "a��41m ��"(  2 d2� 6) ���e R < ��5 ��248 ; 12cV< 2.>�6 "�� U)�!e Inv"� .� !Z&3 6, 3%� Invm = 1�G=�54 6� V� ?�a3 cd�� e J bc2 �96b2 c�1 f +4!% 1Me30 ef 08-s ;bce2 +2at� �]7,2abd4 4abe4�aada�8a(>�> ��2 ���8?�4iJ8�4���s 6a��MEfy �3�+ 2a4 cdD!7p3��E���Ja%A 6bcd!J�6��ef 2 I�7)��6aP� t3& +�ce?a L 2 bcm ![�2��b � )3 .*� 5�� 2� 1:U2�� �� F� &} 6�contrast����,j p̃�i quarh iE e�� uctu�onstantR &�V.� in� ��`Inva�sex]xi� on��v"�<[3]. 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Egly,�A�"�� !� v = x�,2�ɲ� � �*(aU be)x2 + (�bc)xye�cf/�� Dm �l� + bd D2y >L�eac{.LNotice�if c0zf =�e�%*i�D� Dm .9�Tobserved an analogous �� erty� cubes)/4“twofold sym� ya�orA�B([2], p. 225daTthcom![pap%a]llA�estig����rbitraryU,-dimensional� A�Ddetail. 18 4 M: eic: ��ec� the >� 4.1Ésumé%Wcompari�EOAgresul$f Anan’i![ d Mironov�6�B i\s ���ip�!s n o Ac��m s.t.� 6= 0�� Rs!�F � U st =:V∃n a�9�.rF 6≡ 0� �F���(4.20)�especi�t�m=� s M��/], M �A. CN�鬁�1B �b�u!nverse���@true (Appendix A)d&�#�� N����c��Oe�A�!�e*r"8�"fundal alau�m>m3!a raceat� e �4 i�2� ,s p2 , p3 p3�= �   � , p = ,� � !�?"� well&��� d&� !�!&tak���!es��F�6Q�3�|iђE���noA� ons:, ν̂!�= ( ��);�FQm!��splitt�hfield!L���.�upn%l�of 7ext�os);e$,3. 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QED The following theorem shows that many of the solutions 8Eisenstein equa are in0�> image of ζ. In fact, as we will show in Corollary 7.7, it turgut �a-~Zc�o� 7.4 ��Ts : Ac3 /SL(V ) → Γ�his given by n o Im(ζs )|Ac5= Γ∗6D= (A, B, D, C) ∈6Vts.t. D 6= 0 . 3 Proof. We spl� he ph into two lemmas correspond%�,o whether C No X. L1 7.5 Let�0�6�.!%�(re exists m�!! such)t� ([m]-2 ) = �0). � ByQ%yD6.5 (2), (3.1) and 2)Arm p̃3 A2 B = , Disc(Qm| D .  D2  ItM�M�F� (c , p̃2 [,!(.��e5Y6:Y5�6Ybe)�C)�!�g N�]Tbg1%Vj�9OInvm C!]3!W fO.g 46 =�3.17, 27%!Q3 + 4!a2 =�h,24 36 Inv2m Ahence.5 A D l 2 +4viE�byY@2 this reduces to:8 27 B  A 2VFM< U B 3! 3 � 4 6 3 CN�.aC a but since�$hypothesis�A2! B 3. C 2% I,�get�I���!�e+6@E̡� C.gA� mape,: A3st��N$surjectiveN��s it remain!��ܥ���2� cont'�i ∗ 2�\6Cu�0Vc0. First note qζ(m)>9impliA:ha�U�e fundamental cubic Qm has a multiple root U�\ m admits at least one v�=V�;m(v, v)�Upropor�Dal to v. Motivated�lE�observ�@, let u�nsider��nf%M4form m(e1 , e1%�a m(e��e2d m(m( ee1 + f# , wh��$a, d, e, f�F. Us�s (3.7�dc���y�ńis��ivalent�,(d−2e)2 (a f )�0. ChooVd = 2�e = 1!GdE0A&-xic%  table��2N��!�we now]�if m(ZYsatisfA3Bi��B�%�is)�.=F�. From!X13�$6�%1-l"H N� >r�� = 72(a%�)(a�� !{,(ǫ1 ∧ ǫ2)�A ,2!�−36-2F.B ,�; = 4*3 6+� C , 47 ISB%�C-Cy!9., @constraint 4(−BD$(4 × 27)2�.H . One easily check��!�aA��F2A�� ! )�4e linear syste�, B AB[� 9o72C �.3'9a2. A�6� :�m �A@N�(. To comple�� EPe\  only �\pointsP2^whichB j�M:e 0,). (Recs �,BV��  bN�d�-.) For�,%�n�1:�J�c.�2 , 2 cB�Zbwe ob�|aA�27c6��@��B%,�` = 0,�Q�4 taking c= A  �5��� � ��� ia�e x -�(paper.Assum2F,algebrai!�,y closed we � )�ζs)n embedd; Q� 4−moduli spac� s��A� muta� 0-dimensional ys o� he' ersurfE2� in a four.B vector u. Fur� more,!  “pro�i��on”��� s exactlI�B�G B��P2H[3]Uo%h also�C!�=s�U bothaS3 ac�5of k�5T of1Htw2<2X5Hcan b�oughtV&mpgf�4e�6�$of generic�h.e�insta� !L(Acst:Γ� "T)�re “!(at infinity!��!�h*Jix “�.�” oyZ�$. 48 Th)�(7.8 Supposej��ie �coY�$diagram: � �  /2�H F F ✤ ✍ ✌✌  . #�F& toto+ R+ _ pπ % !~c� qW.'$Φ|Sing(M) 2: � ❝ ❜ � �� �� ❫ � �� �� � ��� ❩ � ❢ ❡ �l,✤ ❨ ❳ �%%��  + ζg - ����/ e [4�� c eCardano / r��A�- N�� P(.� ) A" �5 )❲�j G!� ❲  ♣ � %X�0 ♣ J ✎✎4Φ +' 7j� = Ψ$%�∼6�<❲�!�gL  4 � 3-��� Y � X ��_!+ 2 xζs�a � PF >�%/!T )y�  %* 5 � 5=F1"�5mQ2  >% (.7 � pif.*.� c( /PE ,{!q 'M 26.B)� �  =�)�4M K� ζ gne !�/ A�)�A�7 ��AWΓq.6�AE)A (  h$♥♥ I i ># ν̂'N  Ψ3 A�=U{P�BK U� & >w + 2 v " F> n 1.ŧN�6��biNon; 29g918��%M2;�a.<3<q�2��RT272# FV4V �V:� 2 )�5. !g:�=�!����.�2x �PS .&6W̃3Y�ru� markP �Kfront�. �Q involve ly"��{&9 �; back L4J| a� sYf,prove part 1J 2. S�ity� � maps was 8d� &N4 over a�0bitrary fieldy9yo 8�inEF`�s�&J, [m′ Z6�=� .Is>�y 6C)nby den ion, �(m)� "� � )*p!�(�-�)"+ f (7.46)   FADno non-trivial ext s�osA$m5e:12' (3|at 98=:8.M�5~Bzg ,Mb!�at:&J* = U3E5�����,�� ζg . ′H��*m�!Q   thenP*#��  )]k,�B(s 4.19, 4.2I� 4.24i�[m�5B �e0}. �e.4�.6\b0:�r&halready1�a�9߁ J���N (4.2h$we have Φ%�A�1�, ΦRG�� , (cf [3]) Φ1�[m8y4y0!�.��Won�V[3])�Φ�u�eATi:���AQ� G ; (as �5B q�;is*��.i��s)�ap�j�IRz���m, �/��st2��˱ e��c�n Zi/M�)��o 9� $)�!�>g^"Pg� Q��D(= g · m. O �r h%� ��=:�B��~2��YP^�)�Is3�� 1 ����7) If&%k.2�.f��b��]�= 6�.ro�=�<(see Appendix A)I�mE��9)�"� v to�M� ajT>4 1 (two types)6 2 (�e�� ). 1 eD�muI� s sameHB� a��a>��[�,zAX&�F�ce�&6�!l�{&�9� 2 )%7(e′,′be base# V . We de6by ,+ ?ǫ @ A�6� dual U. Dy e αe;Fr"by }� ea�e �50 (i)�ν, ν AÁ0$F \ { 12 }�c�!�*6 9��q���YE;%,� = 21� + ν E�2P1eA�6m; C Y-H _b�!If.kZ�%�sfyE�6a0�y5i�2*. (ii) C�E!E0 �� � � �1 +bB JE�,-�)Z!d Y->�7z7Q��, λU�A����^�λE�FV�Γλ!0!MjW]�OnO% a�: SC!�]^�we�x� �#=!��9ѧA.1).��!��6)<7��−18(2�l$�� 1)(ν +.)�kA|j9E�oE�)2r2r9q2�q /� =k.kB2Fd, . Substitut�_���` � 1/α�E� solv/�Kws above�> s α?.)� !/2�NInv′<V/B�3� n α�1�is���α2 as�� mapp�VfV�b g�!�Q�g"!� �?, isomorphism��$determinan�!�A: J'"%)�!=lOMq:� �-J�:&� � b��a�n� ��i)qwM�]�!7λ��(A� I�M� �$ have�)=�λ.��µ����,e unique squa�roo�λ/�i# )HµI . ItC B $ghtforward"& .9^ �$BZ fµA-�is]�\TA���!�*�O*c ���Finally,� � 56)A��� U_ 5B i!at! A�ŧequ: Rfac %at W=�a�!z�os�;",s`-  �4)�GJ Φ[3]).�&51 ~ D)-�m�s�o��!��bin~ quadraticH m:3 8 .� iU Q Ac ,� &$ D Ydiscriq�q%6o� Lm � )3.18) �%s-'on�~2!seE�^�'AcD ="�%V* 1�6< , �o%�left 7o%�-1× " 4(g1 ,g2 ) m(u�& = g1 m(g2%�u, v:Restric�[� e�,he��ly_ed s g 7q(g, g)�rec� Fof . (2.3!@t>�- �not j�� �in�.�)ic.�'� !� � Ɂ%#ssociata�o mU AcD %R} D$�**3 D̂�8%�>!!�/( ��) wit��e6.ofKdee&ate:�s S�V� )n.d.�. 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BD IZ );=�)�� .j � A� �M�R� ForC%nes� aA%|�"�� Pu5l2�E * yv)2�l-scalar-� C�( polynomial� nish.� 3&� 3jy mU,>Y �2ARurH�6�N:�� kf� � �)o�6� ��=*"� 8*�,��� is very�, ilar��R-!� ,a�7�""9 4� antere�gF2VFz%�.� d amongs�Z�Qas be�X .�"�2�H  ;�G d R�F�x�r gH&dA.5*( �yen�%narticle6  aF�"R�2mMCnecessarX*�Qui�"�a . 5�I��� B �>�Fu:"\ � Z*= yx2E�= 22)�v"y 3A�V?:� �� �e267 P,Xf7 B DW+δ� = δe1aB+B 0� F .8 δ��{�f� .2z� 3: ��Q" 6lBRefer98s [1] J.-P. SerWV$Cohomologi!�loisienne. Berlin: Springer-Verlag, 1994. [2] M. �,/Hig�c���&8s. i: A new vie�&ga:�4�*�� aliz]s.,�$Ann. Math.sct 159 (2004) no. 1, 217–250. �F0A. Z. Anan’qWnd$E. Mironov��E�"xW��22)1O� Ca� n. A� 28�0 ��J`481–4488. [4] B. PeirceoL�[at7iI K_ Am. J�$4 (1881) 9�D29. [5] T. LuchianRAJ� real/> _��2,8divisR2of ;(..)g0. şti. Univ ,�Al. I. Cuza# Iaşi, nEH.,{,̧. I 4, No.%�0-38 (1958)., . [6] L� rkus�Q"�:difE�A�#0�7d�iJ2%�] Stud. 45w60) 185A13. [7]�Burduj-:T#G���.O:�X%N%- 1P1- S!-in! u%20al. i. cuza i9,se!,';!,ia 31,.$l., 102-10�85)2<85. [8] S. 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A� "��%��  N6DT! j��j�geN� �via)~�~)  li�I�dBB j�as�.XE�c� t`?!1�� �������5"�<=o%J%�C 7"�t%5�as�'� FA.TA�� generaliz��A��l�`�verdi�A�Lo A�al��6���E�B `^l%rZ �!0%>�to!�W6�� like��M��2�. We hop��N� B )b� %A�Q�� A��&� %i%��)�I@e&cais JHX 8. REFERENCES [1] [234l5] F.S. Gharehchopogh, I. M�b, S.R.�dO9�A New�)�MM^��L TravU0ng Salesman P���,"JntRrZ"��6�O }”, ZZf Adv��e��in�uA�*�d\ & Technology (IJARCET),kfRIssue Dpp. 352-358, Febru�Y�ZZJ.IK|d=HApproach�6<a�1; S�: A1:�Z=�. DescW Gradients!, b,Man�FPublic S�8IH%lYCommun�g95ies!7 MPIC573�g15 1-9, Dece*F2012. ZgN��Q{1 Zp95�pChaos�ory!5Va�^vaS?e IPSQO-7,IM 9-44!*v-Dec-N=-DM. Farahmandian, "a�UM�v�&BVv�BS�yZk": J�ifA)igAp:�iA1 5) 12  Sept.$lJ. Kennedy, R.C. Eberhart, "62���tcee��T�� IEEE6� Con�Pon NeaNetms �81942-1948, 1995]8��^��^$[6] [7] [8��9] [1012��14 56)1314192072723] [262�D."0D��n&3a�mn honey�^ swar�,nu�L͑�$e/�KReW%P TR06, Erciyes UniverZZ,2�Facul�jNAj D" j,�9 5. X���9�N�b-IK`�h"Ii�R� Lu� P�eQP8. P. Lucic, D. 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In: Joint European Conf. on Machine Learning and Knowledge Discovery in Databases, Springer, pp 440–456 Grosskreutz H, Boley M, Krause-Traudes M (2010) S � � ��Celection analysis: a case study in descriptive data mining. In: Int.�Di- 4 Science, Spri�|57–71 Huan J, Wang W, Prins J !~3) Effi@t k, of frequent)w aphs�the presl< of isomorphism.�3rd IEEE>�ata M�, ,!^H549–552 Kabán A�T12) Non-parametric det-84of meaningless!^tance�@high dimensional !?. StatEV�Is and Computing 22(2):375–385 Klösgen W (1996) Explora: A multipatternImstrategy�IP assi�t% Adv�kUY��-}D, American AssociaE0A= Arti!�(al Intellig!�%L2%L2716�2002) %m% task) $methods: SB�: dev z Q�� Handbook!���J�x, Oxford University Press, Inc.�354!��61 Lavrač N, Kavšek B, Flach P, Todorovski L �4)J�P with cn2-sd. Journal�Ma:pResearch 5(Feb):153–188 Lem%�dh F, Atzmueller M, Puppe FE�86) Fast exhausta�sBN� nuQHal target concepts.)�i%IKU'y� 30(3):711a�862 Li G, Zaki Me��SamplA�u�A^!�mal bool�#pI�s:a�ory% applicImin clA�f ��1):18�`225 Mehlhorn K, Sanders P!7�� AlgorithmI�ELtstructures: The basic toolbox.�ܑ� & Busin� PMedia Parthasarathy S5 , Ogihara!� Dwarkadas��1999)A�remental!  interac!� s� ce%Gn�� Proc. 8th+.!�,f. on Inform)F!{ymanagd, ACME�25%+(58 PasquierA�pBastide Y, Taouil R, Lakhal L��9V�as�0rules !\g closed itemset latticee��sys  24!�2�46 Piet!�BF,A�,bbe A, Dzeroa���10R� in ranked%�,e an2ito gene �enrich!��j)cprefer�� le��0workshop (PL �oP at ECML PKDD, vol 10%c!a$18 Schmidt�Hapfelme!n A, M}�erneczky!q Kurz Drzezga K��r S (u��erpre�M,pet scans byY�dami�HA���MK6� dEia �a��.!swl�AM.]S2�1��T170 23 Song H, KullA�A,Kalogridis Ga��5V� pR r scoS ER)�JoBs -�onFe�J� in��bNx 92410 Uno T, AsaiUchidaa Arimura H�� An e"�a�^�9e�|a!� m �A�transa� !�� �I��Com޹�p &/  pp 16�� 1 Webb GIe�5) Opus::� dmissible:�$unordered ɚ. ��o &�"�� 3:43A�465�2001)��a�)si�%!$ic variabl�:m�of�) 7th�� SIGKDD:�9�n���38�g388 Wrob 1997)!%6�e -rel�Tal_of�l-�EuA�,an SymposiumA�� ciples3 vl=�8 pp 78–87 A.!ofG0Theorem 3 In %���prLThm. 3, let us start�noA� thatE�funEu�[ ��@ of Eq. 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For (/ .;) �m2 ) ∈ ∆ we define a representation of GL2 (C) in the space of functions on C by   x11 x12 ϕ(t) = Tµ1 , �;�, �2 x21 x22   x + tx  x 12 22 −1+��2 k �1<2 det 11 (x11 +tR) =ϕ\   �l 1/2+�k P′2 . We consider .�@ C ∞ -smooth fu� ϕ o�5� ′ ϕ(−t� )N�!��µ2 is:f(at 0. These:�s form��<(nonunitary) principal series. It is convenient to complexifyB,Lie algebra 9�, gl2!�C ≃ ⊕ . Un)(8is isomorphism,V operatorsT!K.gactAIour:�A@ d + !91/2 +E� ), dt d =!�tt! −E�6' 6FE3 "2 K +.J# MA . d U�!MV" F.� L11 � 82 = (1.8) L212911  12 L Formally,a�Dhave duplicated exa�se�<(1.2)–(1.3). 7T10)l(11) If Re�!\�) = 0, !^i�4(1.12) 2 the�:!T�c812�A~M�!�0L . Denote by�vtemperedA# setA.iLuplesz�, iE�ado��Da countable familyS� Rσ,σ′!oGL4�� in 2 L�u*    B 7i9=mA=A + XC)��(B D)A�0D   1−σk ��A B�2+2σ� ×i�Q|�$ . C D  v"z �-U.J : L2�→2 by A!�i J5 � (��+ � . �1 I!�is way��getfhUb= n9G �=�  2 in =�: Uσk%� !��)��f�!D��1�!� ×%��%k8 �=%4. 1.8Ey��] yWe wish9 writee�act�pa�*� glE{6  6  !4�JdeaposiT�|�+0��dard gen&Z ob0 and 0 ���EklE k��$spectively`� `��shift Q� s V1��: �z�H��2�L =2(+ 1"b .+ ; V1a��¶XLU a.X, !similaruC s V2%V2u��� 0�2 .��ne/@ ���% � ��7 � �Cσ*  V V ;@ �$� ∂s 1>t � j�n%M∂IV��eb�� (V )- (VEe� ; = v%+ �Z� �G9 �q� �~�n V1 + V2d:�t>sA�+D����r�B$ V . V + =J�R�s%X`�t 1 E14 = E 14 E32 E 32� Calcul�s 2.1e ��res ��(. Lemma 2.1�  K(·)��an integ! q3 �ε1 ε2k isكiu�r6�8A; , :0) = ZZZ  F u%�tv, s stv w, (v + w u−3� 1 //Qw2T2 du dv dw. = R3 (2.1��2F C0���R)�% 녨is�u� p taken over a bounded domain.9 :l���q fw A@>A, 2 �� fixed%) ,it has a merpcR tinu �to� whol��� �>G with poc on%�hyper��� A�a=k 8>w5 k@ �� 2, .L(see, e.g., [4], §I� 4 9 Proof. By�����"� !�&A� � ψ� ,dt = R = ZRR) .FDF  , x1AR,r )ϕ3�8.�I:−�×O ,12 ] Zx22!\Z)PMd d%dzdd~dt. xB=2 �eE/ rior a]� pass fro� vari� s eF�to new 'ue# w, s)ted= �    �t6� u 0 1 s =a$2) 0 1 v w% �or/=y�j =J� := v $e�m&0Jacobi matrix�_t� "I�4is triangular,�L <��s |u|�� iamseFC�:� %�22 u =%W!�2��v $w = , s= .E ". WPso�!�:h!+w. Aft�he changN=�we�e to ZZ~!� ms dt, R2� ���{ ��. A&JF�X<m��R4 \ {V�$0}. So, ac� aY�vA� ����!(= w + sv ar� ntaiA�in�6 �6 T!�implies%�,second claimIe l��H.  2.2. Preliminar 4marks. Below Fr otes F : �nJ!& lso,�11 F 2 etc. XW :=e �jv+x1I1y4.J�� =!?+ w ~4Partial deriva� pF!bi F�� �+ s��� �u#�t��s ++2 A2AvFA 2 2 F, w 10�_3)�F45�and!�-�vt�� G��os.−�(IZ=.+t )�notic� Hat  y ν//δ �� (2.6�7) = ν!\ %+1(,2.3. 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Pte. Ltd., Hackensack, NJ, 2008. [4n�. G. Oku�>A�VPestov, IJ��TB6s, 6I5D33%�L9), 63–76. [5] R.Z!�zyakovaEFAЂas, Fund.I , 219!�1�245A51. [6c EA�king, G.�y (revism4c"�=��ion), Heldermann Verlag, Berlin, 1989. [7] S.P. FrankMh"�k��>�>:�57!65A�0Ea15. [8]!� Gruenhage� ized)v� 0s, In: K. Kun�&DJ. E. Vaughan(Eds.�andbooka�setAt[�n";orth-HE5�<Am�5dam�4, 42!�50!\D9] J.A. Guthrie, A.c" j*� s�Fe!7Q*10!�110. :PH.J. Junnila, Z. Yun,V8iH�7;σ-2F 8pre5Ka2k-�u�U�192�9EL09AL%�11] Li, F. Liy"d�_Liu, N�xke f�.F.Jk80E�%�86�Z8�2]Nd�>a�S2� �f76(2014E^�c3A��evQ�-ca�!" s-maah Adv.Aʩ�$(China), 2��,96), 548–5eq14W�8Y. Tanaka, Poin.�5�9NG] q�� F: 59%��7!�8�Q15] V.I� lykh-�8L.B. Shapiro, P�ia�ac�dI8 "."s, �+O s, 3e�8!�5y62!M6�[Ayrk�0Oj Amer*�� oc. TransS , 8�6A|19a 27a7] P. 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S� ger _jce & B�7� Media, �gD|1w�(ndA\ VadhA� “C� &� �la�I: Toward de�� ?͗Procees�q�thirtie�nn��ACM sݧ�10�?u�.&�h98-;3�f44!�11%0 Roth%�;-^  arra��^;�ir>�4crisscross err��rre�}!ں:37)�2��L328 –336, mar 1991of2ofn4Kcrs���New� teri^ RDa] "�8m��!!2�=.1E�6hA�.MX=no.Q�53��548uA�hE.�B��^)�!ze�e�>r`%`Pro&$(y Peredachi��sBe��q=1I�16A 85. Ӌ �&E'A�TDSee\�k Sn_SphNPiece S���|hess Azlan Iqbal1 ABSTRACT Auto? c��s� �$or puzzl�{o ��typ�&��� es�J�!�t� ng��z�@tLEs,%�tim�  ��cular p��I�� �on,]R�d�u u!�zLest;/;al leg�&� a�g9trul�XH��� &{G�b�Jo&� ��Bs%� D8 �GB�co"�.s�V�g�mith. So� desbc!�5 %�wTuc�fully� �8exa�Xng ‘merely’ 100,000!�sbF-�Aa� oret!� �&�/YS(100 billion�N��HH� y@��Hpproach!6d���vi%:Aperhaps��essive� �� rticle, I�G .ethodevalA#Ej%y�Z6%� �IUa�b00orIgpermuC � . WhrLm*zgitself}�lreadyA &qw�M�c�\ ��]\2+ y!&�I�_regarz$�%�bo?i[Us�E�documentz� etf� "� . 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MC6�.ei�XenM�i�{��Ō%�is-��X�Vmy �YxA9)1A�فe DigiAtSynap�rNe~ySu�i(te (DSNS) t"�jmFis �relevanߝ� J4\�'�8tegNedA*d!Ua�XƦ(�� �`/v 2016r��.Pd ��a����%q<���A�P( 08 Ia viewno�;earlier.�.�A�:4�|A *�� issu�^E%�oi�q% at I% founq�re!� fis��ng�x-��,��r �m>F�,y'�b�_lyeq��n�raccRY�&&g�pb�Nj .-? s'w�h�$ exponenti���%� -pus��l��hyR�%�A�s!��Wn9�"MX500�\ �� �Xq,(Lomonosov T��WA*1�A"Y i�pA ��!ϑ�B�/a�XB� + �,ay, KQRBvkqr��e]?%�o��LVV� n�m j�"�Q!�advK!�%� �*d6cu,}5or�mX"��swc\8e�� �e��o ��~ny E!{�i2 A�q�o7w%B�lm�‘j, diA��cQ� AC�} {�aI�i�N even�̡h�  x%ly�mB<was�����6a, � L1a6B7 boutT� !"`G�s% -�e a����mX�  (e=h!�O@NYsn!�2�sO-��O ugg� ��1-�j ��,��� e’��G�(G��, I��q��*� beh�My4!�:?��Vi�%iP01 ogicmfru��6��@i-�help 1un}(i��@���/��e�� ��*� � R<e8 ct�%0 �=m ��a9&Q�di��'r"� �.�]METHOD��Y�I2)o� ns��4 ; ��2� ��obj� �Pb�>� 4� B� an2�-�� �k��Urst il�rN!��Dept t us=eph<I�K�ba banana�ba�l�-�4ran�{~ six `���f&ZV(put 1 Colle>�C�s�J*� .�sU�t(i Tenaga Na�vlKKt�$rajaya, Ja�4KRAM-UNITEN, 4�t Kaj�Selangor��nDia. Email: azlan@u2+$n.edu.my 2�`2y�� ͱ{"��p�‘F\eck�@orap�eAi!�movS Alae-��r7oR!�%� �����I�6�squar�̉<  (нin�3l!� ty-f�S8�tched� 7ڛglek?�!�-cr�� ���pm�.V\be � � +AH" ULŒ�nZ��T� �o{+si� �)Z"s ������J"_ 0' 9w!��a�L�u�� &� %���v��E1�e d.�g�cpK a���*�:� �<?�9� I �ond(�����d�lisp:��1 orig�02Z. S� �!6��~ E��ec�J �k!�ba��w�2� U !$&a!8#tcus r��r�I� [%�r�� b� Vnan���bQ,a��wfive 6<� �up��e�� 4i.e. 6 x 5 x 4�*20�qu6� &"  ��had� �s�Z�Y|)յxA7�a�e�6�?&e1n 2Aha~#� thXat�RF *� y i��:�lbJIas� %�%� "�on� : 8 x 7 x=(x 3 (A")��} 8) / (3! x 2!) (2[!{=-4) = 1,68Zv� �aFD �9VVtr���^n r !=�s�YEI3�^ 2.1 Q T� Case�=R��ARa�AT/� Jkn!�j�su��eK!�Jmf9KNNNNv�v.� l 6pyQw�G�a�\Q : 64!�321x 60A�98 / 4!A�30,�$400,320 unJ�%a seemAvk-B plauI �6|0��!.v�-��en� "����VhAw6�]/j-�esep�Ear 0.025% of�E]&we� �=�N�� ookIe'.�KRR (i��s),s-�bqoin�.a j�n1&�A*.A���d$C 1�!�&� �i�B5R�b\J%�� %2 �7Zq��on of pieces would be useful using the method just described. The calculation is therefore: 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 / (4! x 2!) = 3,717,978,909,000 unique combinations. Incidentally, such a posit�Hwas indeed composed�Xautomatic chess problem+�r, Chesthetica (Friedel, 2017). Three convent�� were also applied, namely, no cooks, hecks andapture�!5| first or key move. Clearly find!�|not only a legal forced mate but �done that abides by all sai!n�@is more difficult6n)� any posit!Oi �0universe of n �4 trill%.4s. Regardless,�number7% � needed toAtexamined�=� (Y� DSNS!droach)%�Daround 120,000 or x� 0.0 323%}A�,search space!�i%�v%(somU�(perspective%�Hscale about how eff  the ]REo!�ap �!g!�perhaps>m!_ suchMt%gs ca,!o$principle,! ULed in a given amount�8ime. A ‘systeE� ’ bruteI#�of O�i�thm� cMp(be futile elfor t!+AZ partA.arI binaE$of �EP. 3 CONCLUSIONS TheA�h �al�proi�Ebis \le can�u�to�cA�e total6Usible U^1$ se%#m��!�� in reason�its�$licability!�E�eiof �cDis typically deterI�i�fte!3e- are!�randomly!�plaa�oi\ boarE�A�program �u= E1��E35ore���0be generated A{tes >���)�eyma�(r experimen�(o know. FurA1 work=�\ea might include developAgo1�Cs!�50� raw5��nts�]j%�.p s so=yQ+a$ ared with p�Ed. Addei!%,A�u��Z or puzzA�e�ersk��b� p,against each �,by benchmark!their��EHA� S baA�IsM-E�.�$ sizes, as�DM�+pleM� in s��on 2.1A6isA�e��i�aI��)M setsA�e%�or� $, which do�lhavmist�0endgame table��ˑ��Cnever will. REFERENCES Iqbal, M. A. B. M. (2008). A Discrete Computa�K al A�s Mode��8 a Zero-sum Per� Infor��4on Game, Ph.D.�rsis, Fa��y� a er Scienc��.@0Technology, U��m�PMalaya, Kuala Lumpur, dsia. https://goo.gl/zg6hVA�A., Guid!t, Colton, S., Krivec, J., Azma a� Haghighi,!1(2016xe Digi��Synap�,Neural Substa� : A New A�~to ���Lal Creativity, 1st Ei8, SpringerBrief�Cogni�)>C) I���Fal Publishing, Switzerland. eBook ISBN 978-3-319-28079-0, Softcover IF"�8-3, Series ISSN 2212-6023. DOI: 10.1007/BY. Shor!�pre�t: !��://arxiv.org/abs/1507.07058 Lomonosov TY�!�2A���N#.Y tb7.�mok.com/1-site FrG F.RK Four Kna�Xs vs Queen Challenge II� \sBase News, Hamburg, GerH(, 2 OctoberI�://en �a��(post/four-k n-vs-qn-cnD-2 *QGROUP ACT῰ WITH COMMENSURATED SUBSETS, WALLINGS AND CUB p arXiv:1302.5982v2 [] 13 AugD H6 YVES CORNULIER AE�,ct. 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S3W) AjD�ic EAo!�o Z�� ��E6 ix�s g,<�E!� �x�Aa % �l)!�MA +n�=y=Z�/I�� {��2.���+�u8����n��dm��6�as"> _)>a��/-�u�!�&.on}�� 2J2mWpdoJa66" wu�0 dM (g, h) = `#(gM△ hM). Note that istcontinuous, but does not defin+pe topology of S(X, M) since iG/�Hausdorff (for #(X) ≥ 3); however tVL is n d by&familp�pseudo-distances dN when N ranges o[Dsubsets commensura�lo M. We have dM (g, h) = ℓ0 −1h), withylength � 0;�#(M △ gM). Proposition 4.D.2. The act9/ onTpM !,is faithful,=�� and metrically proper. Moreover,�linjective homomorphism αp :1�, → Isom(� ul) has a closed image, namel)tset Ξ �of afEiso�!jf�AD preservI'A(of points i�(, {0, 1}), �Dwhose linear part Gs� � conep As([0, ∞[). !vof.�the~�q!k\equivariantly identified9� �4 indicator fun%�s�eleme�of Comm%�. Sem!�9�A�n ,,a'follow�at�abb . Another!sequeep A if both M%QiI�p �8 are infinite, A( �)Ec5�)G tranA�ve.�5F . If M or>jA� g4 it still hold �2{�{e�%�ame orb�}%|,, by an argu!� left to=Lreader. 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T�yhe Sageev graph associated to (G, X, A, σ) is the component of Sel(X, ≤, σ) containing principal ultraselections. The 2w is connecy@by definition andmedianPropos 7.H.3; �a] of G0�$inuous. ItTains an isometric copy2@@set of translatesA, with !ym 7(difference  . Remark �,5. Actually,1]L[Sa95] directly cubued Z{ u6'�� link �-%�Ds was brought out Qr!"4Chepoi [Che]. !m poin�< view given here%*loser!�tha%0Nica [Nic]. D!�8e CommσA (X) aI � subsets M!04X commensurateTA�such _8M c = σ(M); it�a!�-�U]NSI]=E[. �.6 cAe� ed a!29�!� embedded�%6W�,!/LemmaEKT2. In general, finding�)�E�2"��,E� amounts!FL“small” invarianE� �-�su �E��. H!�C\ can, among others, mean)�A4 �is lo) ePe, or% underly�cubis )-di!�ional. A!� stru�,�&um0n adde� WG!� well�rlnonzero. abel � . S� )nH 1�A�d0�p� y G-.�+� of XF n o�"� AA)fixed�Ρ�M�q&PHFK; fix a��DA r {0}. For N ⊂d nd x X, e 1aN (x�equalA�a!� )N%Z0Z wise�Jn�s,1aM − 1agM�2� 1-cocycle!G�,%8�h� !�$the vanish��of>c is aI$boundary, t  ha;form f�gf a� � o. Hma*& h =� G-"I$. So N = {)X : h!# = a}�2,Write PN +��� , wfŸ�6B rtI7 9?pf2?�^F9 , soAnd!�r�"5e![ thuCis2XBz 3vR. Equ"* : (i) G��  ; (ii)M�Bc 9oo�is %�ed78"&  cell�$"R �yN�i!ԅ�=� d!s (we ow in)�-*� cu&S es)�vт�nonemptV�has aa�ed�_`; 72 YVES CORNULIER (Nrb !��N� A6� ; (v5X.B�B��5K�nA�[ Ki) (i"mpas��A� endo5��wact%a��) Z�)���H��G� Schreier �G/H �t mm1p �iW r R.:;��"� �] 6Y�wnd & "� ��A�G-%r# Y,� ) -�. (ixQ�&s=�q  (�q 6q ,%� � �. �.9�n;� �ZZX) = 0� �m�  1 im�t� entail� "= c�A⇔ (i v) vix). One��i:� i)I�Viv�!�!�t�� (�  4.E.1�1.��QvR.92�3.B.3��v M�  t��7.G�(��⇒�VDc6�.� G.4` us���T ��xui�⇐6RL>%�2M�' !�!j6=�!��p6 ,of Gerasimov] th)�(� � 3) &fI.4� >i3(x� �Z)not@ rH an FL un�9. Whil? e!of�'r ove+gatu R i�*� L� T, X ���}bQ��|C"� M B� ,u�Ri�)rea`at M E�an� ��U does� . hold. Mor��,/n ≥ 2,4 k G = Z/nZuZ �X� } redu!uFleton. SDG���, ��Oy FW. Oi�i�han44straightforwarGat�� R�>�!1�(�i1� �of 0 endomorphism� �)�) hom�E, ZX�be�tudied�� [Ho78]. 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How�� ! hang�$A"�econd!� and E%cerA�ly�Gx+ motiv)e�ri%XE���$nlthelesc��%�coQnt�=�inmnWo* ��9�FWirA i!�latti'[Cor3�"involv� o�0echnical issuuc�'%[inuity���no�"y�#res!"in §4.C�,!isliz)!�o remov�1�daH&�"s,I�in7 ca)�5�] sI�%y%&�ise� simila� m�}&((sAIeaj j $R"It/'cooked�s��#(alE� taut� !C).xt2 s!thoug�#$correspond�� �� (�� a)��s�h��ndVTs (!�times 1�m#s �"�sS�in�y( �  a!Kp�$ tate�-asJ�a�\#ly extra�)9��nai�a�AJBad��� c�� (incluc'a ��8 5.A.3(1)) seem��be�TMHwB specif^ td A~.@&���"I^�ayLs� !A!sbinator� rpretI�*h@kl��&R 7.E.6. By.6 #a ofD4FD:RIaA(� -�'sQ$1|%���aP$of-�.- ��l(z act -fd [CaS1�3.12],��TPierre-Emmanuel Caprac�$ Frédéq+Haglu�+nde�e)"Aio�to ��� !{ argu1� adapSto�vid���wl��M�of>� (E8,I�.�+�E�-��)Y癚A�%�brief>K�*� ques� “� class�F�1�adm� cofor��~?” U,7, Q1]E�Z(�)Ity would�be FW’�is ���ni��to deal����p .. �. Anywa�6ne�'es9op#�>Hqu)���a�Z wn r��(<Mba �A�� (B#�5�!� A 5�)Q> term� s�M.���`� ty b��eC s� ..k� thanz c%XexpectI! 2�:g!7.I.3 "}'o�y.� ,: ��d%%F�eI?��6 ssen�*Z.AXe�eFcha��r��kx)%r�  ew (&�!.D�(x)!� as"�  $t may�Rm^ f+"s!�, ##E4mJAWa�t 6A�aͥA�of�-eA�Wn�-� oreQ� yclicAig�3 app"t%of Exam��6.A.7p new..� 8!LrA�!�A�.V.S9.� m!" comfor\ B dec��whe o �-.{ 6.C.5 aq�r�"2yq�ton%T3G 1; h hais � �"���,made earlier- e��b�.ai�EOHaagerup¥�n��per̈́�fa�� .� (or 9walls)��Abh�$ ideri�Qa �,�0 nineC .3ps  [Hag].]k�mphasi�+new��uni� :h , VD(Γ))�hopefueq� 8 relev�/in�� $exts. Ref52�>s [ABJLMS] G. Arzhantseva, M. Bridson, T. Januszkiewicz, I. LeaN! A. Minasy0@J. Swiatkowski. I3)�g �"� �k-Geom. Ta t. 13 (2009) 1229–1263. [AO] >� D. Osajdaqly�&����0�{ Ivi�%� UF � y. J�Av0 7(3)�15), 38�406�W] � kemann%6 Walter. U� nega��7&�O anadrpMath. 33 (4) (1981) 862–871l l] R� perin. L:9 �x �1n trendy TSnatsh��th. 93, 261–265, 1982. [BC] A. BarnhiC18nd I. Chatterji��es(T)_ u� FW&�5A�Guido�" booka�cour C*(� ��Indira.lEnseign � (2) 54!�08)�. �, 3A)89.�[$[BH] 75 .�$A. Haeflig!� “M�5s[(? e���ve curva�”. Sp@er-Verlag, Berlin!b99!bpHV] B. Bekka, P. de la Harpe,|8Valette. Kazhda�a�%c(T). NewM7 Mono�H 11, Cambridge Univ!�ess. 2008�JS]�ozejkoN�R� atzi!u�Coxetf!oups do�0.�2S Oper� �& y 19E�-�0(6!�67�Lee�Bergmq'nd H. Le�3 a. S�!s�)o norm{ eULAlgebra 127, 80–97v9)f i] Y!�njamini,a�L h uss.��)� nonlinear"L8al analysis. Vo�� Ameriu3a� emat  Socie�#I quium Pubs 48,v:� i nce, RJ,!�0�PP] L�� ailovsky,�Pas� k, CAaeE�S�097B�� �M �Lo��Proc.�q�S123!M9�$no. 8, 228!� 2295�V �art��$B. VirágSna�5 ty via ra��ks. Duke%G%�130(1) � 5) 3��5��BW] N!�=5�� D. Wk(�)�' c�r� &F7�r`!��z4(3f12), 84�85a� CaS] P-E.2WM.` . RankF id�iJ^����Fun� �d21��,2011) pp. 85��89��(CCJJV] P.-A�� erix�mCow��@$Jolissaint ul0nd2LGi�( �B�Egg�/��!I� s, vE�097. Birkhäu�9��( Basel, 200� DH] .3E�Drutu �F�]g���>� c �me{;gpH:. AdvQ�225�10� 2, 88�?92�he] V%>poi. 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Jackson�pCmpFotFl@t). 50: 51: 52: .�, ANY) :.� NOP;2�Seq% �6�Fp)6=ITE=!3%06C)z.�!#>Y', ɨ3: 54: 55: 56: 57: 58: conforms no { e | S-�t |.w, t) } }!��9: 60: } Theory and Practice of Logic Programming 15 Appendix B Example Symbol Table Qualifiers ParallelFSMs left left left left v, Name ADD ANY !7�R DIV EQ FALSE GE GT INT LE LT MUL NEG NEQ NOP NOT OR SUB TRUE a e e’ e’’ e’ 4 i n op s s’t5g Acta;Mapion Asn e" i E�� Event Expr ITE Kind, Arity η, 0 ���x� �H �, 2� 2 µ 30 1 3 .(vr.Ac!�s&(.DetFSMWith2,MachTwoState )�Non P right����J� 2���iuPInit IntOp Reach Seq )A$Sub Trans �� U�! Vare#�� $eFoo s1 s2�Q����, Table B 1. ��tHof composite model ��DCntrs in Figure 5.F�u �, 1e!iK1 3  *i�σa�. au 6i��q ~�<���� 16 :PReferences Aiken, A.ŝ�CMurphy, B. R. 1991. Implementing Regular Tree Expressions. In FPCA 15� Springer-Verlag, 427–447. Alvaro, P., Marczak, Wr|, Conway, N., Hellerstein, J. M.0ier, D.,�|Sears, R. 2010. Dedalus: DatalogA! Time - pace� X. 262–281. Barnett, M) Schulte,�$2003. RuntLverifica�A� .NET cont��Ps. Journal of Systems 4oftware 65, 3,!^|$08. Bisztr�� Heckel, R �Ehrig, H�09. Cmionality�Me�4��@s. Electr. Notes � @lut. Sci. 236, 5–19. Börg!aEm5. Abs� �� ��0ines: a unifyA view�e�s a�ut�� of s% � design frameworks. Ann. Pure Appl. Logic 133, 1-!)4!)17!�oronatA�A 6(Mesegu�J�9. RewriE�k Semantic)�V:�VE A�,ASE. 18–33!(��:zA�4An algebraic swHfor MOF. Formal Asp9�(22, 3-4, 26�$296. CabotA�(, ClarisóYRieraaA�(7. UMLtoCSP!� toolptheo.� of0 /OCL1�us!�con!�int pr"� %%54a�548� rdelli, L�/7. M�4TheE� uterAt�y  Enginee�)4 Handbook. 220!g223� rtey^ , Lyngsø�$de Moor, O�12�=nthesi�graph!� card�$s from DSL � PLDI. 121a 32. DesaiI`$Gupta, V.,B ,aK., QadeAi8S., Rajamani, Sn ��Zuf�dy!�p 2013. P: safe asynchronous e� -driven�min)n �3�3��TlI Disk�Zrito�A 8. Und�<and!�!oimprovHUML package merge. ��*)�i0 7, 4, 443��867. Gurevich, Yp!{�S4: A Perspectiv)�A�Pot�BalE -. E�,0. HaemmerleI��Fages, Fb06.� ulesA� Pro�� RevidVICLP. 4!�55. He����, Leij��_�0van IJzendoor����Helium,elearn!Haskel�  �:��0Hermenegildo,�>A1@Puebla, G., Bueno�I@López-Garcı́a� 5� tegrated m{( debugging,2� Loptimiz�ii�a��interpre��(�!�Ciao ��0preprocessor)��_�Pi� . 58��2, 11�)4!�0orváth, Á�ergmann �R I � Varr��D� ExperiW al assess �*combi%y0pattern match!���Dtegies with viatraa�TTT 12�@1A23� udak%b$1996. BuiletDomain-Specific Embedded LanguA|. ACM-},Surveys 28. S�Bjørner�!kS2@011. Canonical&F ypes!�E� (Tech "Commu ��s). 7a}83FzKaA,E., DahlweidA� , Seifert��I, SantaT1�CH(nents, plat9�(possibiliti��Ltowards generic autoc ��DA� EMSOFT. 3a��>%= �.6 2�H etec)o-�% Error� � ara�_L1�ICպ)VMoDELS��(14. Jouaulta�%�Béziv�J66. KM3��DSL � etam` 2��$FMOODS. 17Ar@185. NienaltowskiAy, MeyAB �Ostroff���32� @ sconcur� y+ 6+1��30a�\318. Sangiovanni-Vincent� A. LAhuk��ͥ,Sztipanovits�, YEI��A�$Mathaikutt�� �5 in��n E�@aRepresen�n� digm��P-Level�aig!=EEE D & Tesa�E�)s 26,& 54–69.�E7 Simko�� Lind, ri �Hndovszky, T., Neema��I�>A�3.6�4 of Cyber-Physe�yPI�� &t - I��ion%f3si . InU�4EO487%lz�Y Wazny)�!�StuckfP.Y�A Fra^ %Exten��A� � �~DFLOPS. 47–64. �����E,*6әCd*a~WinBioinfTools: ormatics P for Windows High Per$�Ince Computing Server 2008 A Joint Project between Microsoft Egypt, Cairo M�Innovation Center, and arXiv:0905.0586v1 [cs.MS] 5 Mayv�9 Nile University Mohamed Abouelhoda Hisham M ∗ �April 9, 2018 Abstract Open source b%,5t!5 runn!under MS5,are rto find� those 655^$PC cluster>8almost non-exis!g|. This is despite the fact that OisD0popular operaI�@ system used among life scientists. Therefore, we introduce in th� nitiativetI=E4, a%$kit contai%#(a number of:L NL�Au �u . It�an�1�< code package, w��,rs and devel!s can sh!��add to. 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We also tClour colleagues, Dr. Sen Wang \tepheno Rosa, Shuyu Lin,0hai Xie, Bo Y3L Jiarui Gan, Zhihua L`Ronald Clark, Zihang Lai,��R their help, and Prof. Hongkai Wen at University of Warwick for useful discussions F!!,usage of GPU!putati�� resources. References [Bloesch et al. 2015] B X, M.; Omari, S.; Hutter � A Surve�Indoor � Pos���� N�y, Pedestrians ��COMMUNICATIONS SURVEYS & TUTORIALS 15(3):1281–129��4Hausdorff 2007� !@ M!d07. Gait dynamics, fractal �$falls: FinA� mea�ine�deA_ fluctu�7e)&�!�!¡)evA�W.-p.!8 Pandya, P.; Xu� ; Zhoui- chepers��A��M�,al Object-Ba�1A� h toY�Ph>  DM6(. ICLR 1:15!�17A Karl�6] � Soel��Bay��a�0van der Smagt�a[,6. Deep VariE]al80s Filters: Un��u�of Statem�Shu6OShu, Y* h�K�; He,  Cha'J%� 5. Last-M��)�S.I� 6� 21st Ann2!Z�  ayunA�S E�Mob�: , 51�;2Ax Skog�0] A\a9̈ndel!�; Nila�, J.-O� Rantakok� 0. Zero-vR�&4— an algo- )�e�6mPt: Lbio-medical engineerA�$57(11):265� 2666A_"� �4].� h N.; Hinton, G.; Krizhevsky��; Sutsk� I �4 Salakhutdinov��� 4. 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For example, [[λk. S(:= GT (λd.g{d/k}) yW1 W2 �:= FW ([�) (). To underu rela�between�4filter domainsa�sec0 types, it�|convenient to formally introduce?\environments associating os;variablZx : d|4k : e where d %oe `K. We let Πfil denote an.q!|QΘ)F"i(. As usual,�� occurr�i%( 2��should be distinct from each other. DY A.4�6$typ`judge!) �, �,⊢s T : τ >IL this8as se are Π%0$Θ satisfyd!�follow ree!�dE�Hs: (i) Supposed tha�Tis x1 :d1 , x2 :d2 , .<, xm :dm , 37 c �=+�is!� A-Q σ T >WmM%T σ iIa memberRQ� i . (ii) :�%�is k1 :enk2 :e.kkn :en )�N��@m��LκMκ>N κn I��κ^�e �i) Π!�2�4holds. Similar{IV4 sorts. Propos%� A.5. To q2{�uze wi�)4A*sMz = Π5ndM��= Θξ in a natural manner. Namely,Yakemr$if ξ(x) =2� ke�+Y�� : τe�[[T�� ⊥ � σ �� κ K�� ⇐⇒V �,V �: a�> T :τ Q: �d W :σ K : κ. Next two p9�\s establish subject redu�\/expans�38target calculus�(η-3P, we have only a weakA$mA�bX>.6�Msi� T →�� by βh%�n!�m F�5r:L�� n�ofcM� modelaqsound�xregard�,β-�xr%*Lsince Fa ◦ Ga = id�. T,�K.  :+7r�=e ��4I�(1) Ifb�,:5 >s. (2?Tis�se�!� some>� , so-T .�NWe � GW (d)as ↑{a<���L|�M �`d}. He!Q.6 ⊆ d. So2{( preserves )uas%Uq does�!� caseA�Dλx. W x. Specific6,�,W has atomic! e α��n6 i Q4provided with �Ssa)6$e. Howevera cana stitut��6a B,an arbitrary{ .�94En both ��e�!��!K,single W may # wo oA�r1� ��s�apply �u ��$repeatedly!-needed1�η=w5��$ability. O�� hand,a3 (Fa MdEm9K [,!baul%� Dń,!_^� actu!�Q� Now�J@characterize solv ��nL izz >��!k &e� adap�Usults��[5]�7our setz > 8. Term Ta\ �le!b���Yif!"W �� τ sucA�) 2�A� fo:�I%� n�'�#EU assuA�]� ia$ least one2�bwisA��no deriv� s> dpA_>9.9�FF)���� "53, all of� �� not� tain��ω5<H]q%�emphasA<1A :yL excep% $e lowermos��A�9 t�a�co�}( 38 Refer�`s [1] A. W. Appel, Compilr��Continu)f<, Cambridge Univ���ty Press, 1992. [2] Z. M. Ariola, Harrbelin),(A. Sabry, A�0e-theoretic f�m�T delimited��THigher-Order Symbolic ��Cut. 22(3):233–273, 2009. [3] F. Barbanera, M. Dezani-Ciancaglini, a!DU. de’Liguoro, I�0"un��a� s: Syntax semantics4T .�$119(2):202�30%45. [4]!&P�endregt,qLambda C, , Its.mSmStudies�ULogic�AF5T� Mathema� Vola�4103, Revised E6 ,, North-Holl�U1984. �yH6�M. Coppo)�ZUA l � !I�(completenes�!Wa�igc , J.5� �<, 48(4):931–94%M83. [6]!�Bergera\H. Schwichtenberg, An inA���� evalI� fun� ale��d�� ,, Proceeding�a�0 Sixth Annual�� um on �!�I�A�cia�X, LICS ’91, Amsterdam)�Ne� !~s, Ju� 19(pages 20E�11, IEEEEN1. [7]!�-�D.b�4M. Zacchi, Typ�]ori���ms)�D∞ -.�A�I� �., 72A�85–116�D87. [8] T. Crolarda�conflubλ-1S�q�a catch/throw mechanism, J. Func.!y0gram. 9(6):62n647n9a�89] P.-L. CurienQH���ua>�fcomput�u>�EFif!�$CM SIGPLAN� n2al Con�O!���xal�$ming, ICFP!�00�xO�ky,a�LWadler, eds., Montre�,Canada, Sep.��0,1��� 43, ���@2000. [10] R. Dav�aaF. Pfen����te��A�=al effec� 6�=�1�&- on�P.������708R�1!�$ de GrooteAf CPS-trans� λµUuR� 19thB�lloqum�Tre�jAlgebra !gPrE�)�CAA%�,94, S. Tison!�`., Edinburgh, U.K., AprilE�44, Lecture Not c>2 787Q ej99, Sp�AE199��12Fsi�e��!K��9 lE�SecondB1�A�/d6�iAk Applices, TLCAA�95E�DJlG. 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Mav�raޯ wald�XI�Q>�K.n*�9�BD L�@smW1M�9iW58�5 SeptI�e�2�#76� � new"&�euTZ1F�*-S��q1�M�A@79�R79�'0��8]"�W. Xi�Mnd��"� ��!? tq̥��6@3� $�}��I�X ����10e 1089�3!Q9]A���L. Ko� � X. Y� J��of i ple-in��o��L vvmp�-�w�H �T R� 0, Sonar & NavDn��%�6�72��738�A$20]����J�� polarimet�&u���� :� ~��+�8� 96࡝��S��KĦFunda�:al�<StJ���� &� :**��* H9� ��m�%M2]�1%>��e~� A�I�enh�9�p�7erties :�"�9-�E�  vM3�E���p. 53%)53�920"j� S. B<@!�A.��$SteinhardtLA ��s��=n��ame��@�K"l �s&�,^2�,>3 ce� I^��^al Processing, vol. 43, no. 9, pp. 2164–2175, September 1995. [24] A. De Maio, S. M. Kay, and�Farina, “On the invariance, coincidence, 2Hstatistical equival of<�H unifying framework� 6���in homogeneous plus structured interferA�part i: M�m>XY�V Y�J�4- 1)� 2894a� 906, JuneA�6! 8] ——%�^�9�E���- �i: DeA�$ors designᢅB�9%�29!�� 20 �9E� Klemm, Pr�;Lples of Space-Time Aqwy*.� Ra�8, Sonar, Naviga�#E�Avionicsa�02. [30nNitzberg)Tpplic 5of)�Hum likelihood estim!y�ic.�matrices2&p����2a1Aeros��Electr� Systems��16M4I312A2127, 198��(31] C. Hao,2) G. FogliaiDG. Giunt��8Knowledge-basedy:u�4: Joint exploi��on!)clutte�'d s� ��< 11 [36] [37] 89401234] [456:48950] [58Paa��ter N σd ρ1 f1 CN R1 [dB] ρ2 f2 2 h Case 1 (L = 1) 13 0.15 0.8285 30 - (2 (2R(20 0.9@05$ TABLE I: ��s setting. Fig. 1: Block diagram!D(a two-stage9q archia� ure -w���i�a��@ classifier. 100 90 Percene$of Correctm��N!�H5] 80 70 60 50 AIC c GIC ( =!  D4) Asymptotic BIC TIC 40!D(20 10 0 15  25  35" 45�mZm506qK (a) H��1.)!1��:�2�40 ��(b2�21�)%!K ��4]�(aR��a�$properties��B_  Lea�2�10��P489– 1493, October �� P. Stoica��P. Babu�}�]�exponentially embedded family (eef) rule �model orp se�/ion�� 19, * ,551–554, S" 2012.:�Y. Selef �-:�$: A reviewahinq � criter�9rulvfMagazine��26 5  36–47��4�,�@ J. Li1b� �)��Q(generalized.�r� ̒s*�:,�!sQ,7�797.)�S."k 0A. H. NuttallɺP(Baggenstoss�i��& ple � al �%jE�Y B>�2I�t 36��371�m5. K. ��urnham%�D.�A�son, I�&{ e�� Infer[ , A Pr�cal I�)-TheoreWAu�, 2nd ed. New York, USA: Springer-Verlag, 2� R.��Bh-li�Y. Dow�eWS����� )�@of an autoregress���oed by a�;!� 4akaike’s fpe��%�Bioikam�% �54 551� 077. H. Bozdog��n }�E��kJ�$on (aic): AI���ori�ialy�xt�*m�Psych:�52�73M�45A�70�087. N. SugiurX Furth alyst5c data%>1* s.�93�!� finite co� � %NCommuni�mD S� gs EG �Method�7I�m�1a�26�78. C�`Hurvich�C. Tsa�IRM o ��series2� A. Neat)�J. E. C� augh%+A�bayesia�"� �Pon: background, derive�ba& )�WIREsAlpuA^`.^^ �!�p.F��03, M� ��2.��M. Reid���$eigenvalue-i� !�2dY!� SIAM Re ~3Y 3E�3.h� 7. M�Goldstei� Redu���,pseudoinvers&a h�t!NF�x� Mathec�Co5+ �2��pp. 71�;7o JulyA�4��DL. Van Trees, Opti�Array*P  (��� q�~ and Modul%э, P�PIV). John Wiley & Son"Ke�Abadi�J.��Magnus!�,trix Algebraʼn щ8: Cambridge Uni!;p P�8,��5.&��c23.#8�{6{s[2J���d2�4�2: Pcc � us Ke�Study F��� A (prim�second��).B�90�Z^��d:d)_!G.qK�����P~.��.��z!� r A�V��.��)�.�uN%���!^.qK%�2x#����J�. �V�J9�5v,2��,��v3vv16vB (6� only���F���!(80��^��U+6��J4F70 !�/��GJi���"!Z�&�ؚ+�'�"12�|�|�|Z|%M!R.��&30��1MzP��a �DZDF���A]�QSV��iJi�vM!�Z[ 6v�:/b�JJ�(F_^�4: 6::�meach *. assum��ߥxK2�  �E^d'y p ��!c xs arXiv:1703.03010v2 [] 26 NovI 7 �Abbott� Hume $Osin AbstY We add� 5follow�natur�"�2{ � �2�: Given�0roup G, a sub H ≤ nd,!"L Ha2�P, when is it possible*� d it an-� whole �G V( >y difPt)2k? Wkdoes su� f �eserv�!ter�ng!yoriginal�8H? We begin by \liz@ thisE%G!pf:# con�8of�induced[whn,behaves well),H!.hyperbo�2in�TMoreover, we show that:a0s can be used!fchaA#erizeba1�s.� also obta�<results! elem_q mena!�E#Ts. 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Thus it makes sens%�-2  a.{ elementsn!&,. The follow!�51�8summarizes some<ary'A�eIF!= ich Y immediaEmz in GI�*� X ife��TO C�d2Tof left���s (�lM(2)�4�lusion ��`G gives rise to a quasi-i���Qembed%�N, _.��dC,X )�λ}Λ��ere "is!# cor�onR���o!(see ]82.18). Further,!#^��<_"G .���sa�at�=a of Y���ifAF�>�!I��>PX!�vcIn pa� ular!�is�i6.�i�is I�.� . W�ul� pl! “�:�” �“*� g� m%i� 7 �0above. Moreov!�we ha 60Lemma�.9i�X, Y ��wo:h�:F,6� such2�bsymMRdiffer� X4Y!�)��n:E��e��on�f�DY . 24 Proof. 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In seek���nalogous �!� Artin �s,!�g�/!O��as ) s: D�3� 7��� ��gto!L�QhwG ��� ��Qb��T2) hsi��j i�Ohsji whb� no �(y/a3 a��i�` h2�' :X�e��V�9��T��.�2�¸4Conjecture 7.3� ~),�3 � � �.�t(at a node k��(AΓ ∼ = A80. 8. Acknowl,u T�A8work was suppor�u� �he RTG grant NSF/DMS-1148634. We would also like to� n( University�motiva�this r ReferJs �p4 Michael Barot%�XRobert J. Marsh. Reflec�[5 presen�s aris!6(from clusteG�gebras. arXiv: 1112.2300v2, 2013. [Cha06] Ruth Charney. A�trodu s to r� -angled A �. ^,math/0610668^@06. [FN61] R. Fox�(L. NeuwirthE� braid �s�QA$$andinavica� Hges 119–126, 1961bo ( A. Felikso� @P. Tumarkin. Coxe!%9�Df ir quot4 �@ 1307.0672=?@FZ02] Sergey Fomi �LAndrei Zelevinsky. C:� I: Fy �s.!� Amer)L. Soc., 15:497–529%V2�Z03�uvinite � classific�. Invent � 4:63%s�00A34GM14] Joseph G�� B�B=�"Ger��Q� 1408.5267�14. [Qiuc Y. Qiu. 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AcAl�{�As.e�@thank Syamantak D0r help�� disc��on"� M�P. References [1] Ali��$ahverdi, Jzs! ND Gupta�q�a�d ra� ����"T LIPIcs-Leibniz InternQ� Proc�@1&I���_cs, vol=�66.A lT&Dagstuhl M0-Zentrum fuer=k!017. [7] José�,rea, Alberto!@chetti-Spaccamela�T@nnik Matuschke, LeHStougie, Ola Svenss�\8Víctor Verdugo�� o�[$. Strong l���>O *n:jGn unrel��}2M��%al!;�F�0, 154(1-2):30a:0328, 2015. [8>Vi��p�Q!�/ usQ�rade-offB����we��"�3�E. O�s-`��LJ](s, 44(4):46A�473%�@6. [9] Friedrich &�:��Gennady �:4. Carathéodor�[)n�}cl" n�< 34(5):564–568�ak8[10] Paul C GilC�4Ralph E Gomory��j!pr5��ja�[I�o!`stock)j2!�, 9�84!85�z 61. B) Michel X�)�Thomas �)ß. P"*U*r.�)���Vn#I.@$it5�*|a�Aru�E twenty-f֝anne� ACM-�N symposiu�1 Discre��"& , pa�� 830–839��!o14�L2] Raymond Hemmecke,!�uel Ond1L Lyubov Romanchuk. Ny 1�.�in cubicM�fQ �1��7���13] D�$ S HochbaunDavid B�oy"Y�d!6O�!�R�,t� �� prac ��2:� 4ACM (JACM), 34�?14A�162��8� 14] Klaus�9. An ept� �ۙ��@�� ors:zn milp ��x��MDa]BD&��r��)�.lQ 9�s, 24r 457–485%�0A56� , Kim-ManA$aV�Cloɡhe ga���*ZE.�؆spars&L�&� e 43rd:�C�:quM�Automa� LanguA� �P�X, ICALP 2016, July 11-1 �6,A�$e, Italy, I�72:A��166E5Felix}d�n-* =�e�* E~A�D"\ Con� � 1\ �^q�15��170. Spgzer%�6!�7a�vi Kann� ,Minkowski’�nvex boda~�AA�E>e� ��.}�'"� sa"�U , 12. 41�44'�m,8] Dušan Knr�@Martin Kouteckỳq1meetsZ� �}. arXiv� ���0Xiv:1603.0261�^0)9]�2$drik W LenL J��a%6�)�[Z"j&�'s.�8�T538��4� 83. 3�x[20� exaH Mäck!�mJ$Malatyali,�helm Mey(�ufԺ Heid� 4Sören RiecherL<^von"� �]�e_W��hop�"����D��Stur�i542�53:z @21] Clyde L MonmaEY(Chris N PotI Aa�s��f&W ��!��T"�X 6�Ji , 41a 981–993��P 22]�D��Onne�K+�?opt���w . Zu Le��D A�2Mu�$al Societye��[23l ansr Dalekamp, René Sit��L, Suzanne Van Der StA66* R Ank 6 Zuyl�[f B�u�y2& ����$1�129�%�4] Pe_%Schuurm6�ndN�. 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IV. /NCLUSION��pa�/m5Eied=��!�r�k�\%�dA� v. G75an &n� I^ 6 |I�y  �I��B&�BBZdW� na�!��&!M��Z5,6�EjM� )���IBJ YJin=t�Wa�n  �b ive JM&�� ~at!6< . ourQPto U%2A� k)Z/n��<�'�!&�I�e<p�Mc�XEA��DeVF:�%Y�1u�iih7&%6!��$�T'_�EB�)J�A�&�*of%"�=Q-?� ��!8�%��Bhe JmMsu@ipH�H�J~c,coincid!A_!xa"� �capac3 Mn:�_(��1�(fb/;{ n bea�e�h!�. Fut� work�,ay�r��I8Rim�ant)�)Y�Q-su3�,fD ��(-X���*�!&%|iBM��>is ��'focused�_o�bcre2i*Vs�*����z2g� ousmelM�we limi�3 f&��qu�)on�th�3s��. �g(a>3;70lan�5vna[.9"�JU)�!� D�0�E1��9�A�is� helpe�y.�&V�jing�.e�)�ls<as"-*H0"*ZC s. CsD+ /[1n 6Yi�) uragAuavenu�arc"hG��x!��A��B k� lo@*%�*.B2�. R EFERENCES [1] B. Chor, O. Goldrei~4E. Kushilevitz_ M. Sudan,�PBt6���,�(in IEEE AnnZ3Sym�u�e Found&%%C�(er Sc�S@1995, pp. 41–50vm 0 [2�>�6����Journal!r!\ACM (JACM), vol. 45, no.�I�$965–981,�08. [3] K. Efr� ko%E3-��^Insubexpon�k��1a�.Y��!s))X ing, 2009)QL39–44. [4] Z. Dvir%SApi�2-S���-��Sub-P"Y7[mu�b�b�Z�1-�577!�84. [On�5]. Avail�=�: http://doi.acm.org/10.1145/2746539. 46 [5] N.A�Shah,!l V. Rashmi Ramcy$rA�AP."Kumu`�I�cy- r�!nd�R�6Net� 201�1j��people.eecs.berkeley.edu/∼ nihar/public%Qs/ secu,.pdf [6n��K��“Xextra bi��Ten�w�fes>vn� in 2014i�Intern�al6�I*I, June>I�4856–890. [7]APR. Blackburn, T. Etzi�\�M%�P�Ps!�IR� � I`"�- 5lexOBlow� ��#%Á�1u�� (ISIT)�7 �14�1��[8]�Tajeddy;4S. El RouayhebewrVAMDa$d[&nR�� �A�6��ly!6�1��14a�Q(�D�R.BB�A.� � .�{(�*dK up[n)i��� ^�$908–1912! 1] H?� d�A. Jaf�{�8"� of��I�FIa�>Z8Nt�63�m�407� 4088a�I�%� 2] ——Ee>�robus;ivb%)q%gEg!�E�Ei j��9oryYU6Banawa5< Ulukm�B�r��A:�20a�i�$ 1609.0813�14r�ƱE�9 m�:�*t�{a� �uref^6+ et a"a ��>�893A�89E5ŕ"e�sn ��3 B�(,�rte��n ve R��2.nlI~J� B> ��@��264��265��7]!�Fazeli, Vardy� E. Yaakob �)�T. xE�*R� headeQ)�5i�2' 2� F�B�, (2852–2856!�8]�4uang,!� Chen � J. L �Py&3T s: F �Q�+?H/F^!�acYm effi� ނ�fi� �� �6cJ�6 Netz"� ER�jes (NCA)��0-�7� 8�9]�0Sathiamoorthy�Asteris,�`4Papailiopoulos%�G. Dimak"R. Vada!�S�11 D. BQ akure�XOR�@elephants: Novel ��E�Ibig%1�,Proc. 39th V�uL&D0B�Endowu ,A�3I�32��33�20] F.!�$MacWilliamnN A. 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B1d�[h�2w so�Mm���&���isel-%%� 10 D�l��/�1^ڡ�� @FW5#�slo �� MmE� 19� W %h�>6h6� ic�#s_>i��%=i2b�� �G�f-!A s&aU:�)(+e*�&o)�5 fZT speedup�`%�$. 7. N��*��+&��2�he@� x s: CF�+��1arxy*x�7��� Q(a)m0� �a%)�*7{1*�/�4)qp.�>.�BE���� �3AmR�1�~�Y (dpA�� �1�{�*a�y,�2^*� ay} ]*v" �wA���(�)SeqT!��: "�1, s us� k�� �p1w��p��1u�&�h��fp�;"�22)(�+2) �!ps'fp2�B(�,5 $5)��^ Rw1q?�to�f_qmE e, u T r!�, (x,y,�68(dp(2),dp(1)); 4 I1�x2+ �-x+�-2"2V"+2; op��(redSBSSA std(\); S1T[1]=t-2 S1[2]=y2+2x+2y3]=xy14]=x2>)� S!O2pO> S2; S2Q+2 Q -2x-Q2 Q-2xQ2 Qcn| ��.~ �d�s� yNat�&V�iKEFRean pZk ,��i�s: > l�lV�1,� mg>-�g!x// CRAB�(*D� )S)�G)�chinrem�(l��(; > Gp1; Gp)�2+1 %U+xt+yt)�xt )�yt��B11��� v:Y`�>��!�2�I �2:�M�M�IR/ hard�Y1&����p J�&�' {��mReϡ�t}. Fur�mo�X�/�Fclgzxt��'J8�f�&A'#p��h hang[ &� b;0� ^q�"��$ @B�rin�' ; �!6o pul#�e��]�s �!m"+�+s. /*F�ingE�h */ > �8�0f�>y^imap(r,A�"2eintvecet5, 13;��j =qCy? j; j��A}j2{j.7jy5/*�:��h0farey(j, 5*13��i&f�!b� ezg�� al�F�/sii+Z�J Aao��/ ifI9]� �K�B skip6�',"*� 2,�z�r n . H`*�� ��ML]A'* �E�s�" (0,a�(Z&>��. = a2+1Y G =IG s, j%��Z t(G,$a"ify2); //�z%� enP��N�ey�U G[1]=y2+dax+ay G[2]=xy+ax+1 G[3]=x2tThus we get the same result asone"(mentioned a +Hbeginning. 8. Imple$a&@ and Timings We ided Algorithm 3 in Singular �\library nfmodstd.lib [4]S| compared its performance agains �m �of [10,x1] m }vt(� comm�isStd),�9 ! std,�0Magma [5, 12]#H GroebnerBasis. For T,!`added tXminimal polynomial f toZlgiven input ideal I (conside!as an in a E(ring over a.\)�!^u!��reduce�̈� b�L e + hf i w.r.t. K �2�P%weX of[ ��e = hHi 12 DEREJE K. BOKU, WOLFRAM DECKER, CLAUS FIEKANDHREAS STEENPASS ExaAi, Min. deg. I!$ Poly.A xmi I1 m1 2 I2 m2 5 I3a m3 7 I3b P4 m4 6 I5 m5 12 I6 m63<7 m7 8 I8 m8 7 %�UE 1 moA+ E�StE %� 1 c. 32 �^241.98 1.51 1.24 0.37 0.22 0.13 error 70.55 19.59 4.79 1.89 0.61 0.90 143.79 9.34 3.27 0.51 314.00 11212.00 1118.78 97.43 19.23 265.53 9163.38 567.03 686.01 99.41 2061.95 3321.28 256.58 430.23 71.47 2.93 8931.13 197.20 47.54 24.26 8.99 0.90 2044.08 195.41 8.54 1.87 - 15477.87 15274.97 4787.49 92.99 23.89 Table 1. Total running times in seconds for I�A�aA�2�M�}DE�s withE�$correspondBJ�via5�%�,I�Ie Q , usF1VeAores whe$pplicable �Z�A�a�� Im�\n algebraic number field� J�(f . Note th��FBour[��His internally linkec exis%mFG��1��[10].� lhave nine benchmark problems�� demonstra�e superi�y! �new a�[d(see appendix). The cyclic-2C�F n vari!m4s has become aF� for><$ technique�������replac��(coefficient-�!N��4 by a random e�N!&Q(a) M!{.� -��,�e�ɧ XI6GA.=S�M�5u 5uXare chosen from [2, 11]�W s I1E�I2. '],p�4I7 11]��2l1$2>�%�J�aq elec��!�!�i�s,cD: m1 = a2 + 1 , m25 + 23,7 − 7a + 346(-4 3J&N5&12<,5a11 + 24a100115a9 + 551a8<2640a7 + 12649a6e(4:m24a\�6r�57 a 16a7*\a5P5� 13a39A13a�7 � m8G>0 ��10 h. W�respecta�theseJs,�� ings!��ddu%�by��< 4.0.2E7�U� V2.21-2 on a Dell PowerEdge R720 machi� �ith two Intel Xeon E5-2690 CPUs, 16�m� 32 thread��H total, 2.9-3.8 GHz)192 GBa�ru� �H Gentoo Linux opera��system. �h? �summariz� n T�j 1.2}.�a�%8 did not finish��(in 12 hoursa �71 dicaA��>dash (-).� ll ta� cases�y, also occupi� Dn excessive amount! �>memory, more GRÖBNER BASES OVER ALGEBRAIC NUMBER FIELDS 13��an 100!\�kpoint��n* �Vrup�it. All2B in s��. We us��e� re� dverse lexicographical orde� (dpCSs )�-all�5s. In�>6�)0�k8of primes whichI�!\�Rl��1 of �� 2 de��sA΁�J��@ ��t3 �; star!A� 10 uon� 9 �f25�onA�E eA�tim! ~heavily) the splitE�behavi��J&modul� � � . Fi �opt� �gy%btM� still und� ctA],research. Re��8.1!� &st��e�,no parallel !�i!f��� � �@$hm-�works+ R( )9refor��co��!�-�AH �us� &!{ only. F�4m�)�eA�M�SM�a�_s0 %�3 p� w��in(pariso��� |~�.[Howa , �aa5e %G!�"�"� VeYdmuch faster. 9. Acknowledg�s� $would like��8ank Gerhard Pfi;%�Lmany fruitful discus!�s!�8ferences [1] W. Adam���v��Includ�O*=��lgemo��renamedA7� ��8subsequent rele� . [5E�Bosma,!�Cannon! PlayA�)�i�x bra  I Duser language. J. 6=@ 24(3-4):235–262997)�u� al_!���– A��r �-�E*�Unm? www.���8.uni-kl.de. [8]2�%.�}'i:�R'Y contribu!s� Olaf Ba@nn, Christoph Los� !� Hans> 5tBerlin,<  extenaD1| -|9]�Hashemi6o:k,)Steenpas` nd S.idel.��mi�,>l�,u!|S!� method)���10] NA�reA�9I$.�P8izE�c�2a�>�846(6):672–684!11�>Ml roe1"�:A ElIaJWV� �s. In���� softw4A� ICMS!� 6. S�dAi�A>alAM gres{ ma�F8, Castro Urdial!CSpaA.SepteD1–3�gProcee Hs, pages 99–109. Yt2- [ �(Group� �G�A�/ SN y�� m^.�0s.usyd.edu.aum3]��Tra o�9��tra'!)W$P. Gianni,e or,%�o'A� �ic.�,, volume 358ABLectureC� � er S�ce1&12��138. 1989�4/ von zur G!�FJ._ �er ua��. CambriUni�ity P!�, >r 2013. 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A�6&�0�- scer��Ifi�%2�E���N��  start��U$nd'68s23 T5$s (T=50) re T�� jlhe� s��o'ac>!+tt=A0- f T���e�5!A��NaMi)���V!%6�malc� 5;oi�jNK&v�i��FF �1A�F�F> i��O� yn; A=B� [rEg���}�6���"�"12]A� 6  g"K≥6@����-5JK.pe����:[$ evolved u�s��D"$ B AAA�=5 �  (HB ,� e<� � Y>s ( rror barst max minI�� TEk9��� acY�On �� A�>�.s͟�ic"�1�E��Rp 1Y4a(��(��E�s,�""I6��� nd a�+�3-4��+� �&�   ���5�&3� .o�3�'�  2�* .�'ac�Z+%�zF� x%�- |(-��/a .�+�M� 6.#h�)�a “�"��”� p�1��"U��$a�I&�& $E2Z���"�*3A� 62P7 enco�6E (%4a dynam��de`$ . Ev:!ge(#�$�+�" Y2���'as some Q�ep �A�!�e "�- . Fu�3E�should �$� fact�int>)�DE �5r�W"&T )q^iV�he��var1!�"u DA��# � 2* � �be�&��5"&�"�,re-�2`dou�7was&�I6�8of� 63%+ s w!9� see�2 hold ��0%'L2.�.�5F sear9"�, !l�-ure�4q (jz#)%ly�d o+ K>0)a^��N��A�"�5�,�!�onF�  � but �QNKE�s. No�h19�.�'b"� as.H]'m-st#�'�'1 fl� #qr)�8. REFERENCES 1s%P. 3. 4. 5. 6. 7. 8. 9&�6�,��g�0�0�0 ,� ,Zv<�#u�<6�CLUSIONS & FUTURE WORK [1] H. Bhasin & S. Mehta. O� p c� a�����!Y; . 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Limi�B�8urrain,!+2�13>s rankF��<Q�e��A+mC , 30�08m�125�1279. [1�tE�<C. Jutt![�e%uHandbook����Source��ar%�$, Academic�� Oxford, 2���1�*f�M!� renshMt>� by.Ctrans��s, Report ISRN I3S-RR-2007-06-FR,�7)�3]���e.��A"�5�! afte�Cewhite� a���v*%R6��;�e>m� 6H (�9�)���(a�15���7�14J���B�= MoorIn0J. Vandewalle�^�s)�se1�!q2� thir� Zv i�<996 8th EuropeanJ:ConI(ce (EUSIPCOa��0?i�Y��15����O as ank-* $(r1 ,r2 ,.�G ,rn)�e2�{ � �J Jm� 6��2�00qm32em34��16���.aF�AF (.��)���*�TaS�a��� �S>- , 49eN�1 �226. 2271a_7]a�$Ishteva, P. c�PEx Doa��,r � &�  �b!�:� ��F�>5�+ 0� �.eu., ���65Ac 67%��8j���S �HuffeliE 2ITucker%�g .8�7�l�$U, Chemo��%� Intellig[$Laboratory�"s, 10p �11s�5�� 64, X doiV (10.1016/j.cd lab.�n06.006!�9]�G(G. Kolda, OF�H�eESPK�oN J�%Z�]236!43–255 �02��!��W. Bad ��2��'. ���RA w, 51 � G� �4� 50� 21]!��Kj@�zHH. Park� 7 �m�/ RealE' Fu�Mn%�� % Birkhäu�& Bost� 2002v/22�v/[22��� , Nonnega�L2>�n�tU r � f .o�,1�5,�3a�44a�23]�~D.a��M@M�,C. F. V. Loa�� jacobi-t=�1e�A8�u|'2��� 6�-���n�VB��1 123a�24] N%�ikh�S. 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A�� ampl�/�E�nEJ�35.7%�suba�%��6kew)��K �H� ��V�~R�5�6)>�up>1A~����new&<>s�)gBibli��Hy [1] W. Pugh, “U��Q �q�� O ,”��P� �e�ռ 5th �I�r���a|�n� �n SupeRpu �u, ICS ’91, (New York, NY, USA), pp. 341–352, ACM, 1991. [2] N. Kukreja, M. Louboutin, F. Vieira, F. Luporini, M. L�FI G. G��n����:*� OP�#ite"a �6�o�9 CoRR, vo�%�bs/1608.08658, 2016. [3] A. Aho, R. Sethi �J. Ullm��o,ilers: Princ�8 s, TU%� 2�'. Add%U$Wesley ser�]J8� er s����f\�A E�- F�PC�@�any, 198�44] C. Bastoul,�Coh�g$S. Girbal, Sharma �$O. Temam, � �P��� � 6=ne��-)� 209–225�}rl!�4Heidelberg: Sp� er Bx, 2004. [5] D. McCormick, “T�b;1���(�|s.Aۘhttps://github.com/dymcc/ opesci-meng/$/master/��. AZed:!�@7-06-18. [6] K. D��E�@Murphy, V. Volkov%?Willia0+J.=. ter, L. Oq r,��PI'rson,$Shalf, !�K. Yel�a��I��e;2�����/���9�&c,the-artD5�cu. �sj�02008 ACM/IEEE�>j�SCa�(08, (Piscat� , NJ.�,4:1–4:12, T�P�!aX�0!W<7] U. BondhugulaE�Hartono%!Ra�n�jA�!%(P. 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The� resulting schemes which can be either symmetric or non-symmetric in the discretization of diffusive terms, exhibit good accuracy properties. The symm k��@show optimal convergence rates in numerical tests on the scalar c3�c�-d �on equause good �� are observed also for Navier-Stokes Ds basedw�entropy variables. Future work with these�,will be focu Eapply!� themxltwo dimensional viscous flow�@blems to study if;� �B5( carry over6hig!�b s, and tr �o coupleU�m �<particle methods�rarefied �sit)cDs. Appendix A. 1-D^H In�!v%�V�mvn5�Q�8written as ∂F�GU + + =0 �t�x $where `� ρ U =  ρu  , ρ6#�u F $p +(�2 )$(ρe + p)uN S@0  −τ G=  u + q %d8he shear stress%y heat fluxA�l given by τ= 4 ∂u µ , 3 Px The coefficient of CconduE� isH,κ = Prandtla;lber. q = −κ µCp Pr = !+�T�x0γR (γ−1) !%D R^�gaststant�Pr � Y0B. Polyatomic3es�dMaxwell-Boltzmann distribua� fun �discusa+ abov�rrespondea monat [AA��the rAV!specific%'�s�4γ = 53 . Real � like aiC<are mostly compo��o�� �,molecules N2�8O2 have a value-h1.4 eff��vely be+ s dTgas�� intera�energyL such!�s ��erent si�they Tcon5H$s from rot! PdegreesQ8freedom. In ord�getL c!hct2��A��h���:��, addi!�al>�� �!q��i�:ducedAOapproach�8Deshpande [28],pcolli�inRnt �E�C�o11is modi��4to 21 |v|2 + IA"�l!bvBGK��0[9], it is 2 >as 12>ξ 2 ,� = ξ1X�.+ ξK ,[U K de�ng�6(γ. A third��iE�Tuse 1 2 δ |v| + I as 9-h by Perthame [36]; this hassadvantagE}pre�\v!` form!\ �Bqv 2 ��usHH = f ln f [36, 30]%�ͼ adopted�Lgnt��. Not�:�aIF kinea� spli��es &�E�anE�Ki�Q �e�( identical U�re!0no X��w�l�A�to OU�� N��W3wchoic%9Rn�s)�v�� 5I�� [30] Z Z!��1�~1 (IX −uA�I δ )�4Q� �CRT g(ρ, u, T ; v, I) = , α = e dv · e−I dI, δ= 1 e d α(RT )1/�� d + R R ��� 2��momenL L)�V�yield-$rr!oexAa���!@���3 ��W a p2m�6ma� �um"� I una�E�7�Q�va� a� a� ic ɦ�5e I' �xC (21)���)� V�+, s |u|2 u 1!� , ,!A γ 1 2RT!�4RT 29 > An�=�#�t q6B��, e.g., defin�Oq� physe;s, � ignored. ,do not changa��e7 tability * -�NS=qorDG�$i� only�� jump��9�or!�ir deri� �va�pp �i��"V *7 C. KFVSE2�e)��:1-DE�inviscidRi2�� F±� � uA±� B ± � �("� �)�u� &� /2)% 4 p s = u β, *= a�81 ± erf(s)), 2B± =T√ exp(−s2 ) 2 πβ� �� NHF��   A�< τ + 54 βuq β��� � � + 45 βq�G��  ��uA�q% − 32 S�23uq 5 �a��q�a�f� . Re�ces. �[1]!�(Cercignani,e�թU)jits�'lic�s, Appl� maG  �1! �ces, SpringerVerlag, 1988. [2] D. I. Pullin, Di��simul[2�  � ibA!�id��al-�h� , Jou� of Compu|  Pe��Is 34 (2) (1980) 231 – 244. doi:10.1016/0021-9991(80)90107-2. [3] S. M. D% , A se� �-� �aoteU8theory�� �*u@2���s, Tech! <p. NASA TP-2613, �$6). [4] J.!� Mandal, S>���K�vector���Euler5�s,-9er" Fluids 231894) 447%8478)8DOI=<�45-7930(94)90050-7. [5] P. L. Bhatnagar, E.8Gross, M. Krook!Smodel�" �3ces� n gas�(I. Small am�ude pr'chargedE�,neutral one-!ton; systems, A"!sv. 94!c054) 511–525 �A 103/EO4Rev.94.511. [6EY. Chou,A� Baganoff,2��-R�a�Z��,%�E��. � 130�097) 217–230��006/jcph.1996.5579. [7] K. H. Prendergast, K. Xu, N"�,hydrodynamic� gas-�I�F�� 109�$3) 53–66V��3.119a��8�Xu,A�M�nelli,�$Jameson, G{�e volum" ��:F��Se��ai, R. Narasimha (Eds.), Fourteenth I� : Con�+ �N5�Mzini D-"$, Vol. 453�qLec�� lARic�, Berl��1995, pp!;6–1AE30 [95�A2}&. ej3E conn�on� !hficial` sip�/Godunov��fI�H 171 (1) (2001) 289�335. �J�D�Q�(\.6790. [10] T. Ohwada, O��c� �rGof�B�����7�2) 156 ��175u1]�dTorrilhAam��S"� �J�istenc Q�upwin� �5ada�ion–�u� .E IMA ݍYM4Analysis 26 (4)@6) 68A722� 2] We�Reed,!*\R. Hill, Triangular mesh-�� A��,on transport�, �U`LA-UR73-476, Los Alamos S��tA% Laborat��(1973�p13]VCockburn�p-Y. LA�C.-W. Sh, @VB Runge-Kutta lo projM�ZDontinuous Galerkinm� ele �%pco*�8laws III: One-d*����.4 8��89) 90ep�3!i�4:��.��he2��Z����F�� V: M����14aR 998)���24��5) PN. Arnold, F. Brezzi,6�L. D.�N�i� Un��aQqA�sNx �s Aڡ��p8pr�, SIAM&Z �nN�39 (5I�2)��74�17ŀ16]� assiA6 Rebay��>; 6l��JE� solua� oI��"2 f^Z2 ��31"��r�6��2؁����te��7v^i6��u )�E�time-��<�&e� U�)��.)��.�n . 35a�AY244A�246e��8>[�A� 4terior penaltyZ��w�6��-�F2� J�19��198M2742–76�!�9� Oden,� Babuska,� E. Bau�A@6��hpZ��A۹�U�.��1��a=�465�8) 492 519. [20: .��J.�� ��A���N�� �er.�y Mel� ��Engineeu �� (3-�h1999) 31 �34� 21V�9��eJ%�@nD%ia�.~� i~–>��,:� q�!��>� s 4 �-� 20�r19 07}i� 2/fld.338!�2]�EartI:P. HoustAn��`.6fu�ret*��.���y227 (2 �8) 9670d 968e �16/j.jcpb 8.07.01�23] G.E sner�6Lörch�C�,unzFE�y �(on a space-��zan� II. VA("Y3 �m�2�J.h�.mq�.��3�=8) 26���82C �7/ s10915-007-9169-1. 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Without loss, suppose t = s + 1 and let ni = ⌈s/2⌉ for i = 0, 1, 2, 3, 4. If s is even then mij = ni + nj = s for {i, j} ∈ C1 while mij *+ 1 = sfo62�@2 . In this case ! graph G oDe vertices v0 , v1�2�3�4!n6�(positive) five-cycle given by C2 and-hence%�@signed-eliminable)L�@characterization in [2] (see also Corollary 5.3). Similarly, if sh odd,Nn GX nega�ly |.��lC1 . Example 1.5. The followA1�e (shows that U@ (2)�ThUx really does need to be checked!^�all proper subsets of size at least four. CM�� �HA4 arrangement with�Tmultiplicity m defined!Tm0A m02 = m03�12 = 4 M. DIPASQUALE m14 = 1, m04)/�2 )�m3 3. We can �) m lies in�balanceda��e��0ies. There ar!lur!�8 sums around tha�ENs (so!g!notI�o2�|, q = 4). Also, we compute DV(m)�6. From.� )an�8 conclude %�(A4 , m)AD�VsiA� qℓP� E��ia0mI@. However, let usV��%A3!��-.�AU��re U = {}lmg }. Let mUAE!(restricted =Sy; it �-�-z�A�AU !5�l%~� .~i�!��e���,e�!OU !Q 8. S%8 > 0,�i7s from!�ore�(I"(AU!T>���,�.r%Y1w. 2. N1�and pr�=$ries ℓ !%V = K!(pa vector space over a field KA:�c�jtstic zero. A central hyperplanA�ys4A = ∪ni=1 Hi� a un��of 4�sL⊂ V passing througi�origi��$V . In oth�� ords��weE={x�t�., xAu�} �basis��the dual �V ∗%"S = Sym( $) ∼ = K[6T�l ]�,4Hi = V (αHi )\ some choi!Bf linearm &∈ q�,!que up��scaling�$will u�b(language of�nic.� �referr�zto� braid.(� A! AitsaQ}Ps. Name�sup�0G = (VG , EG e��a ~�C��,ordered as V4i�1��vt�}ia�!aK[x�#%� ]. If {vi�&j }E&n edge�*EG� �nCHi��V (xi� xj )�~�6 associat�R��LAG = ∪{i,j}⊂E(G)V. Cle�# is a!&2wof%\ fullFa� %a,  mayAw$identified)8��N��$correspond9�� �� lete 2 Kℓ+1�~�(!W+ 1) 1�. A�,2���pair (A�� of aq�6i��km�<and a map m : {H.T0Hk } → Z≥!�called a ��T%�m ≡��tY �is deno!��Ai�CsiR]�I�A%�M�:�\A 2�(AA�ɏequivalm#inform�!�Aq -labeled %� (G!:!��p6� *6�(A��� mij y�Lfrequently move back�,forth betwee�w�s� ��s@alwaysA�umr at1 GA!esIY�xi�AAb�A��Q8�A��A-� %��y�0their integer �s {0,u�ℓ}. L�W moduleoderiv �A��S!�*o (DerK (S) = A}S∂x�!�? 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Then, it is easy to verify that B 1 px, ηq Ď K, yielding x P K.  When a convex set is defined through a collection of linear inequalities indexed by the unit sphere�, support fun H$at a given -xu0 vector can be interpreted as!= value�@a semi-infinite l �program% follow�(lemma stateH$at under a�Htinuity assumption,�8needs to lie incon!&0cone spanned �$constraint b$are active � point x˚)�is�oluq�!�� >�� Note whe �number2 -.z�is %Il� EjA{/ �:/�,not granted,1f99Dexample shows. Let!U�Hand G “ tx P Rd :U�� 1, @]�ztu0 A�u0 I�� 2u. I�sinceM�also tru � b�BA�0, 1qIPU theR � M  maxtu�:E�Gu!+1,Az(quely attai!��a)��0u0 . Yet, no 98;-M -!mma 5. !#φ be U]ousY�on�!=let Kl5Ae�q�� e�6I u. AA�-@� H. Fo�?�09�%,�t� A P K �thK pu0 q�-&4˚ y. Moreover6C� I�K��G0 • #I ď d, �IY.��@I, imsart-generic��. 2011/�R5 file: TDLS_v2.tex date: February 10, 2017 Brunel, V.-E./Tukey depth level sets �u0�D ÿ uPI 12 λuA��z,some nonnegae�ijs $, A�8I. 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The constraints which where �\ed during W EIGHTcan be 1 4ed by substitu!:,. The remain8.Tneed toA�s)Y�qsimultaneously. ED E LIMINATION k12 : u̇ = rv − qw + Fbx /m k13 : v̇ = −ru + pw + Fby /m k14 : m = Fbz (ẇ C�uPpv) R d10 : u = u̇dt 1 : v = v�s(Fx = m (amx=(g sin θ) s�Fyy +φ cos "3 : Fz"z +", (8) (9) (10�1�2�3�45)%-k14,�AGd11E�.�tstandard rigid-body kinematicsU�( set. s1-s3C measuremeA hfrom a 3axis accelerometer,1�forE� forcAGmponentATis is a dynamic systemM_MCM0by a differenA�� y�#dr. VII. C ONCLUSIONS In tgpap�,SA methods wA�employInPperform fault diagnos�0n large-scale �(s. PreviousA�(ilar works X$presented, �i8graph-theoretica� � to�Iestigate%3 existence�<analy 34redundancy rel�is used�&Hresidual generators!|� :���. Yet, those approaches did not tak��to!� ount� impl%�u issues !��ma�E8either causalit�strica� s, o�!bi problem �"2�� sets�.U� s. W�roduc!�-� �ind� ��,��bl�yF%$of minimumavt, ba!SDon a novel, weight���iaJite)� re-�%A�E�bin0 of a priori a�a poste inAy ) allows us��p �( results in%�� time�appliA�he0po�IT o%�n exa!��,I�I�model� a fixed-w!+UAV� showU�aa mv type%�Ndm�obtainA� depe)�on �specif�$search cri!pa. R EFERENCES [1] M. Blanke, HKinnaert, J. Lunze,�DM. Staroswiecki, Dq�� !eE� -tolerant��<trol, 2nd ed. Sp��ter Berlin Heidelberg, 2006. [2�xFravolini, V. Brunori, G. Campa�$Napolitano�\La Cava, “Structural AaɁZ�AmvE�!!�Gi�ioA1� 3 ed RM�i�lAircraft FDI,” IEEE TransaifA� Aerospace!+0 Electronic S�f�s�9. [3� Krysander/!h,e. a. Aslund�TAn Efficient Algorithm��Fij Ma@al Over"1ed Sub�� ��MA|-Be_5��� R���Man)]Cyberne���d8. [4] R. Izadi-Zamanabadi�1Jal�F!}��ahE)�� with!lici�to.%�a1�mo!��a�Procee�re$4the 2002 AmeriaCoE���ce�t2. [5] T. Boukhobza, F. Hameli�. Simon��A�v.G.��AL para� s id�3fi�q characaz�s��Inter�� al Journa� ��13. [6V/�)A!�-:"�-.#�Co �uEρ�M'tic TestI.in 16th6�� W�hopaPrincipl�� Eis)�<05. [7] K. Murota��a��esematroidsE���sis�>�,!�0. [8]a1 L. Dulmagex< N. S. Mendelsoh)� Cove�{E(:K � Canadian =� Math� , 195A��9%��+�T. Lo# ze l0SaToolA softw� tool ӕ�� �!jco�,x auto͕ �E(in %s0FAC Symposium��Fa8 Dete%�$, Supervis�ϡ�8Safety of Techn�e4sseiǡr,10] H. W. Ku-/ Hungar!��W assign� ��I� Naval Re�j LogiA=):!�@11] C. E. Leisersa\T.| Corm!>atteq�R. Ri� �,Ap�rqa�� � s.� MIT �s ֡d�1�I�e��q3!E. Friskm���]�� �je��[-m�PI� Multiple )� Isolq��x% 21st�y�28�BZ<a;�1A�13]� Flaugergu!�0V. Cocquempot� Baya�� M. Pengov�.���!�FDI: a��i-�, rti/ �-� can��al deA�osi!��A�EX2� 20n*� j���0%��4E0Sv2 ��N���g��� ��v )��y Usg Compu,  Sequ� s W�w�M�  C"= �A� Ega�otive�b�B4 C��4)�5]�Katsill� nd!�Chantl2 “Can� enc1�& cope�2V� �?� in 8� 1997. 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REFERENCES�YH.�G Ngo,�EG. Lars�Eq�T"<Marzet�F “Energy�VFF9��vFw% �C6-�F? ,”�G0N�.�#uD�.AU 61, no. #Sp. 143�6449, AprT-J,JHoydis@G:�Br]��pQebbiG “M�7� @�~UL/DL�H� �u]�0N�:�r� g s doA���?�"�K�nY�Z��i�L�m��3 �2, pp. 1 J171, Feb�3]>�O. EdfoK7F. Tufve:�� 2� �%mE��eR�w�FF�%�[1�52)���G 195��N�4�JLu,A<[PZP�Iwi0�hurstAshikhmi�U R�J�aR“An�viec.�9�:(kef�#χ&%AYG5��f)�Topic� � Isal�# cess��8 ��Tp. 74JM758, Oct%���5�J70ald@��auNFF(^�v��nd�-siN��:')xM� 17, Y� 53�P�5��1999. �Y�AwOzghani!�?�A� ssek,�,On ultra-wid23I�211-bit��O'�uŸ s: P>� j./Y�)�o��EL%~ini�(Int. Sympos�-on Info��orcJfQ!m12EI128��7e�Mo�(R. W. Heath�i%�of���edI�2����[���s� i&8���N��V.63)�3�549�[ 5512Y2�L8]�M Rusu;Y<González-Prelci�^>�� Low .�Ԉ� .^�(�eiQ�ge��=)�~)Ii�,silomar Conf�X ӡ�(� TP�SYm 113�1143. �V"<B*/B�A."K%�Re4C�hybri-� &s�q$.)?� )?�&K���5i�23�a620^E62žDece��7]T�3U�g Bogai7�d����e� Beam����7��� .�Qp: DNJ� �a<ogjJ�q*Global!��mP=f.�L�� 406�� 4071�4]��l�a��Rajagop@�S. 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A�V� S!��>F�ly ": ����K × KA��tE� griyI� �F�i�>���x�� (i, j�� N[1,K]R � ��EQ� : (n) dx<� �1,∑ xv , |ν'$ | v∈ν �Dn (u 'X� L ) + fn ( , R), \� 1, .4, N, (III.1) (N)�Rre C= [>2 z A�� %TS�i��S��!�R2��en�t5� �l�!ec6 * . DEX�R�(m*ak. D��Dn�� DN ]AY RN+A>�v��O� coef�5 s. R3 RP−N 6� 6~���A�l�"�s!w: {× OZ��RE�E4� �>��.'h� �|A�\#� J\]%L%�s -�n�*�}B!� �c�""�a�-@������0#�>'U] /4�>, I�= [ Y� UiJ5� ݥ�!neighbo�%-��: $: dt P= M�mJ�6)Ł�E�dic�J adjaA��)V. G 5�QaB�[D, RE� RP�v)S(p� v� J �n���� Z�^S x(t�fRK×K×N�� T! i�5,w��: + ���i�OFJ�.J�4i, j at time td. While the model captures`dynamics of concentration( all specieH interest, we assumXHat a subset {n1 , .0, no } ⊆ {1N}l�Z(is observab�Xrough: H : RK×K×N → �o : + [0,b] y = H(x), for some b ∈ R+ . For example, �of�$genes in a | network are tagged with fluores!\ reporters. The relativeF<b�corresponding proteins can be inferred by usingj@ce microscopy. We�1�,ed in analyzZ!N-C)��Xrated by system (III.1):,steady state�refore%�8focus on parame� t!�T2>�< behavior, which�<easily checked t)� a runn�(average: K N (n)  ∑ 8| xi, j (t) − $ |< ε, �82) i=1 j=1 n=1JT where 6 = t−T R τ)dτ/T U:T ≤ t%-74 is said to be>= at tia¯, if)e2) holdsYeD0t ≥ t¯. In%�aGQ� pape!@ e wiaqimp!;a} the =�2,a trajectory.� as3. � M�58, and denote it4,H(x(t¯)). Ei. 3.1: WE�0sider a 32 × reacAh(-diffusion Mde0twou�|(i.e. K = 32, N = 2): R (1) d%� dt (2)  $ (1)  = D1 uEU  + R1-�N6� 2 , O2)cO = D2NK��3 E K+ R4 .Mg3)�ThQ��inspia�8from Turing’sJ$MQ%~ is presenm� [22]!��a��-�Lskin pigments of aa�Limal. At a cell (loce� (!)),E2��A �v1, �, dependa�F7�� 3 1A� this vAGLin its neighbors (if!� > 0)IiA�!}2��V 2EVonly, E7)�,. Similarly,Jm����:`�%� f���2� ��R3 6= 0)����- 1!�m��� mapping�� 32×�2�� 32��,1] given by: ���� ���y!� = �m@$. maxm,n � �(simulat�U�E�4random initialAdia��se�.�R = [1,aI12 , 16])�a�erent e�� �,D1>(5.6, 24.5],ai$= [0.2, 20 ED3$1.4, 5.3].eW)@ed��n&�=h�a x ��| points�!shownAPFigure 1e&& t = 50, �W�B ies ��in2H. N����,4$hree casesi^spa!I distribu!LA��2�2�I Y6 has � regularitQ�it�?Hms a “pattern”.���)�use large spots (LS), fine patches (FP))�sm� )SS)�� refer to � b�s:�to!�%� I D3 ,��pec�ly. (a��b(c) t=0 t=5�1 �2�3�4�560 Fig.!��O !E�s"k �[��3)E�.p�R��� �(b)Aq �(c)�E��� (�2�!��Ae�re���� shad red)#�t&H M� �produce�%�1{%��Z��>�$. Problem��G�*�ajd�S�Mded+ %=�1��x ite � ofNX0 ⊂ {  , rang �!8desig2� P = P1 ×� $× PP , Pi H, i = * �P� �e� i�-5LY+ = {yi }i=1,...,N+e�!�ta� ~�pM�bK� >M� − a� do noV�P find.`p∗ Q $P such ∗ E! .I!OM�4S(p ) originat� E�X0�� guarante �oQ*6 �s��a~g�o� Ce�!;4Y+ . To solve ]� �n\erform� teps: • D)�(a mechanism)k deciA�wheth� �n.��1���-3 . DevelopDearch algorithm ov�b��l �4ce!) the !�6Ito-!t. �first�Qp requi��oM� a�A$criptor. T��is goal%�d�new��� logic ��s��superpos� treA��bA{ed%��.�s�itreat%�!? !�e��a!+z A�piΉE new ��%,J����explai� in S��on IVG�n��hN��uc�)c��a4.-��-e'��f��!�}z��L employ machine-lear� techniqu qe> a�� ula A�X�seteB>!e�#secondI�i� synthesF�fB�a��%�2]����d��c2�� a���2�satisfy=agula �tTE�� a{A�� endE�int�% quantitJsem�c>EA�E! das��AXI�ve valu�F@ aIab2I�-I�)�F��AFis2��� V!lA�edM�easa of-iis us *�(fitness fun7A�A�Lrticle swarm optimiz� (PSO)�F�e choi�=PSO�motiv� by�  in�� � ed na� �' bilit%#ope%� irre� � �� spac� � �i�3es�5�� a� � �i� � >��. Final� weAnpos7%� vised, it�$ive proced!Sm��y)����s.�)4 inv $Q applieYA�� e aStwo% an upd0 tetiquntil)�a�.��.�!�fouE�E�is� �dy`user.���REE SPATIAL SUPERPOSITION LOGIC A. QuadE�!���"� I$WeEg2�ofr ��$atrix Ak,k02k�2k eleq as � �k$N>0 . Each%�6�s!��a� regioE�aEM� (o)}!� �tuple q= h z , · �, �i�a�es 5��gB� -�baj�� � �D��|�l b�[0, b], �*Oy ):� %:��� ,[is , ie ; j je ]!o� sub- A�6�el��ng# rows } indi���.���o]E�he colum�6+��j%�je �fi� on 4.1: A��d-t� $Q = (V, R)]�ag ary  [23]YgEy!����eA vertex v%=�V9����of : �� >on R r �VA�V � ��,four childrezonode vi��i���z f. A��i~ leaf��n��eQ��6�� �i��s havJam�fes.� ���2p�s��e7ex quad!?��~� v09I �entireMM�; � v1>'�subM/G}2k−1 }!7Z�V�7:V�� =��{I2 +^`�z$� ; etc. Inz�2e$also label)�edgD!y!&I�a� dira�o%�$��r*��buE@: north west (NW)xrth ea$E), south "�S" "@ (SE). v0 v1 NW$ NE$ Dv5 v8 v6 v7 SWW$  v4 0 +3 v2��$�2. SO $�6  )wv0 |s 7 (bH� 5i�IEsM"(a- A4 D.��2�i_%^ mean&�(µc : V →^ b]��.�e�R����� ��!�9��{�a� llows: 1����� � (v) = (ie�a�+ 1)(���js� �� ∈{i ,·8 ,i∑ s e }×{)=�}\ � j prov� �ex�ed �l% & �Lvar�I�$index c, 1B�c�o.� ���d�f; v:�3: Two%Y�va , vɟ�V! &�� +val whe��m2�! ����ofv u{�� they�!0S � �: va ≡���⇒%^(va ) = b )X��>2��L��� z�� ��� L� abstr�  (v / on)XvA ti.�+� , avoi?in �waM enumeO �2Y�a��lo� � is appro�?�i�Hbyviouss [6[24��Q%� authqaima comb�k�--�o2�!� woul@m o�wise.� 1%�i����6�� ?��_ 6� vNE , vNW�S SW%!�fe�pr� ty4�:m�NE ) +M/NW �S.� SW ) 2�(�4� of: �pro�m��� deribbya��a1%Otelof 63>�2 [number/!!e#t%or�� ��Eg.�A���\$is upper bK �L,∑ki=0 22i �6��)H�s! !��%�worst �� � ariof�A�2u���� � ���s��E�F1 card� Gm�6 �VZequalA�J)�a fullE+co� �t�r Ee.2�  to9?R��A3,�it I�&�max-��g5� |V |��1 + 4�5`6 + 64 = 85. NW,NE,SE,SW �B =1/2 W$ ��v2���9�0�1��145 ��v1;178 v19 C E,NWsSEaxv( 0$ $ sι c $f,.���vg$ s�B a�s2 +�0W�1W s3��� 3. 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Althoug�2ba:��DUM09� �usn�o5���:�� f S(B��B��t wey�!D�}�$I. CONCLUSx^8AND FUTURE WORK���'�Q"!�s2�c�2�8 ) wh#"�-# s �l�3&Y& �?[�h�a�!�H"E=!�!0,��LA�s6d�+h#�e�dRb � $f�hh���T�kU�de�Xio�j��\�, op a)7>�`�y�`b���>&���.*�t ri�"�s%-�� cur�lver� �d)�Y�bite wCoA1!JaccommoaZ(�/�ro!�/ymmet�2nly�in bi� ��E�r�s�s�X�a.{A��fu�G�.^��c��a|> be� ����ba=�xA=f moreZ%ist'Hmo)!�w�a�� {/than jusc�e�+�n�(�%ZBis �*K���loi K�TYA�)}_�i� per`� �� planA@inv�,�g? reasom$�a7f/�p�+�Gy. nd uIu�2“��.�8�ir�d�<�"@D�$ real%C� v;uch�-popgoq of l}q�Z$ng engineeD�qik)�� I�&3gi ticUMA�be�A“tun K@s5�^ circu�&&hj� q@F�` R EFERENCES [1] J. Goldeqr$d H. Yoon,w�H ocysta��8>Znabaena,!s(Curr Opin M�va., vol.g_�no. 6, pp. 623–629, 1998. [2] R. Scherrere�V. Shull��S&�J�p�alCQ��m��on��T:!�4thiopedia rose:s�s]�p�- lets � an J.��� ��t��7 �07�10�X86. [3] C. M. Bishop, P{ Recog5A�Ma>J�e"8. Springer, 200L 4] A. Jai� . Du <J. Mao-�gi�h rk$: A review�IEEE ,UA��y�n7JxBic 0] ing-�22 �4–37�qP00. [5] T. Pavlidis, 1�alN��-Verlag%>H�6%�(C. Veltkamp�(M. HagedoorI{�S�5(-of-the-artAw shap72�t!W�g�Princ��\Visual I*;�R���vl$Tech. Rep.�$99. [7] E.!�EmersM�TemD��"�\gicqin Handb)ofore)�$Computer S+ce:�,mal M�{I�"�9�,!�8van Leeuwen, Ed�rth-Holl!�8Pub. Co./MIT Pr 1990m^�B)�4995–1072. [8��ME�4Clarke, D. Pel�nd O. Gr�[g, �� a. MIT i!"�9E�M.�vE�t\ chem�s"6morpho��siia Philosoph)� 6� ,Royal Societ 2 Lond!�m�m��3a�72, 195�010] B. Julesz � exto��$E�5�dpercep��vtheir h{m(%��NEj��2!k��91–97A7 81. [11]�H DalaI' B. Triggs� Histogram�or-ed grad 2;r human �6�%in#&c.A[ CVPR 2005�Fe�Yc)3 Coa7�0�Vi !�J�M@1, June���5IKh886–893. [12] S. BelongieE�Malik)@$J. Puzicha��Se��Mm�yOb�$� .�U� ,Con!�)w�6!�n� A�|���Tc,lig� �24 � 509–521���2�3]aG. Lowe� �.H��� scal.d3�=�eE�� .����r�q/ r��A�99 � 1150a�157��4%w�J,ss� �P� vig, Arti ��te1�M�hrn Apb�.a��n�_ Ha�R20)�5e� Rizk%�F. FagA0“FIIl-�Bmto ��L� Awsbint Solv�= .CPp�9I� 15th6(C?gA���E�e��f!QlPreV�mp Lisb�+Portug��820-24 September�r. Le/S)S q&� ��-� 5732ٷE<-�31AQ334. 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He, “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel,” IEEE Transactions on Signal Processing, vol. 59, no. 9, pp. 4331–4340, 2011. [10] D. Schmidt, C. Shi, R. Berry, M. Honig, and W. Utschick, “Comparison of distr �beamform�Lalgorithms for MIMO �@ence networks,”��� v��61, pp. 3476– 3489, July 2013. [11] P. Komulainen, A. Tölli, and M. Juntti, “Effective CSI signaling and decentralized beam coordination in TDD multi-cell �system� IEEE��6��@2204–2218, May �D2] D. H. N. Nguyen�( T. Le-NgocE�Sum-rate6zin the � cell �0ple-access chE with .�� .��!�V��WirelI CommunicaA��s �13-�!�$48, Januar%��4!�,3] R. Brandt�,M. 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W BruU V� ttet8antal Rings (Le�?�#mu4cs, 1327), 198� 5.nD�D��!<�,�e�<F���/surfac�Adv�-�� 9Ss 227��1 �2, 80!S829��6j��%�8Nathan Owen Ilt!�Vanis!N13pl\7!ucker �>^�409.3432��4E��7�&rrado De�2 cini�,Elisabetta S3kland, O�!�#etE| e�,..� 41 (1981|1, 57 – 77. 9 8. Alessio D’Aa�<Gunnar Fløystadi�Amin NA�4bakhsh, Resolu�%�B� >! s, pm�1!a�L6). 3 9. Viviana Ene�̈BLFatemeh Mohammadi, M8Iv �torici�A` Hibi9,e ari�Bq"|J!8, European Jour�:of Comb�4Qs -�1F03, 404–421.!T�3T F9HBjørn Møller GrevJ* nd J>���Le�6$!co-RR(�e�K:R��1.04523%]��1,a (3 11. Mark *�B�B&�B, MbjCs,.�� Geo,By 13 (2���4��|0, 12, 25, 27 12. Robin Hartshor!��D��@ory, vol. 257, Sp"er Sci�Rx & Business Media, 2009. 12 13.>Q%DTakayukiE , Dig6buJ" latti�Xbip�#te�F;alexan�'duality5�+96(�2e�05��3, 289��02Q(�4��:���!�3 1�KO Kleppe����>�m.KE�D;�*m.��H�L�me �F���3R� 40�U��246–27!�, 16. Ezra MiE�A�Bernd.P=�a��m�%�>��1��2R�� J�5. �M!��7��ys�Neev<Mike Stillman, S�9E.z(0lexicographic� 5�$9�U��6�<�9���A�35! 46�XD18. 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MNIST. We generate adversarial examples for the ta>�R Model B. In Figure 11, we show original images with ground truth classes 0–9 in ]0diagonal, andMR���,d by stAdv t� ing Lclass of �� ��sHat column. CIFAR-10� (ResNet-32 m!2�2!� %�6��s ��e���� �� ���Table 6%��s� magnitude1>5l, flow regard%hHotal variation (TV)%�4L2 distance onVImage!(compativset, E�, 1��, respectively. These metrics are calculate!� !Wfollow�equ�,s, where n i �number�8pixels: v u all d u1 X X (5) ||∆u(p) −  $q) ||22 + v v D. TV = t n p q∈N)p 4 https://github.com/tensor!T`/cleverhans/tree/master/em /nips17_ } �_!Ieti!z8/dataset 14 J�� L2���F��� (6) Q: Eval)W M%� (!v-R$in bracket!kiasize) -� � TV  L2 N |(299x299) 2.85 × 10−4 ± 7.285 2.11! 5.195 ��0 (28x28) 8.26�3Q4.9c3 5.1`�2!5.632 15 �! 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(��h�a�da  {�ie_�.��OS�i�@�� 1.)>/�P: A6"!a�&� �5� � n Pn (dx, dy) := 1X δ{(Xi ,Yi )} . n iu��LB�A��no EP [·]AMU� | /r4to�rob�6��P . ��] SRL�C�|ak-u��$ v u n  N� 1/2  Ft l (Xi3d� �*8+ λ kβkg̃−a��(2,1) = EPn [5��3�]4√ 7 2 , β)%Iλ�!so-c^� �.�6pre��S "� �r�can.>38d � ���n��<ex6@�"o�sAFv3�aR�&(NNeAJ F ��" � ����xp�Q� �t�V��.C�n��isc Z(ncy, Dc (P,A�[�J��2,"�P���q!,QAmee" P ,��EA(2)A max A�:�r� 1/2E?α−�+�.A P : �$Pn )≤δ (Using this �mrepresentation, which we formulate, together with its logistic regression analogue, in Section 2.2.1 and Secti 2,bHare able to draw thw�llowing insights: I) GSRL can be interpreted as a gam��choose a parameter (i.e. β) and an adversary .hs a “plausible” perturb% of� data N P );g,δ controls �degre�Pn is a�ed�bef Pproduce P . The value|�g�s dicta�by�expec<loss, under EP ,90decision vari%tβ. II)dhset Uδ (Pn ) = {P : Dc (P,�@) ≤ δ} denotest5(of distribuA>Hal uncertainty. It U_25�5e �<�sM!2�lyAprobabilIkmodel-�4are reasonably!ssistent E�H!�� � DRO �r (2)!:os �rol5j regulariz +5� . Intic 4, because λ =!� 1/2 E�0conclude thatdirect �E!�sizu6Lly =NE�shouldA4:��-$M% gM�to � .� s orJ�availE,!K|@considered. IV) Aa;equenc�I)lIII),�^ ndow �e�$estimator %�desir�general5�ro�iesi&=aims ati�A@�� , β��� -Fper�� well��a� pose�:|descripI��#��Y�given�� !-8. Naturally, ita� important!E�st���wA typeee� for���sqmeasuredq�(discrepancy.�4. For example,!opA� no]qk.>��i��(Kullback-Le�0r (KL) diverg!�0. However, KL ha)� limim`E�only AA2�s9Wty�;�s=Vsup!,ed pr��ely o%]]�training%p�,e,therefore po� �i!� ignores=�.e��)�coab have�%�e!�act�:�risk. I � rest1\paper��nswer� f��quA�4ons. First, in�47explaiX nAMeWa�.���M�<��s an OpaSl Trans!X.A�,. 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T���CA>u��f��, be investigE7>�� !nWi�affecAwwhe �number�E�taneous)� �is �m��n��F �, :UM%0�)�d upon!�$fundamenta�K�t����1q b�� 88ir channel gain��thderivi�similaIo [6]. !ybenef�of>��extendI�MIMO )�s,!: re a1 n di��$clusters (aY thus��ed [1] Q. Li, H. Niu, A.T. Papathanassiou,a1� G. Wu, ”5G network capacity:Key elemen!�nd2y8,” IEEE Vehicř�Tq��Iy Magazine, vol. 9, no.1, pp. 71-78, Mar. 2014. [2] E. Bastug, M. Bennis, w M. Debbah�Lie��he Edge:E� RoleA`(Proactive Ca�nga 05G Wireless N ��Communi�%s �August�(3] T.M. Cov�Wnd J.Aa\omas, El-+of In�1�u�<Theory, John Wiley & Sons, New York, U.S.A., 1991. [4] D. Tse%�<P. Viswanath, FuU��sl�2��H, Cambridge Univers�8Press, 2005 [5] �OviedoA00R. Sadjadpour%o�A��0App!\,h for Fair P�a�A�aYINFOCOM!;6 Worksh��n!�4& Beyond Enabl!�U9��!Y Appl1��.aJ����� >��K� to � in M&: SISO S? �N��,E� T/A]<ons on, AcceptedE�ch�87. [7] Z. Ding,!�Fan!\V. Poo)VImpact!��U�� Pair!) 0NonOrthogonal �plem,ss Downlink �mia��n �e��Z��DFuture Issue, 22 Sɡ��5. [8�Ya�B��(N. 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Since Sw ∩#<= T V ∈ D c , ?pZ(T ) ≤ V , it follows from�(b) that :CF 2c _�UQ0E c by 2.6(b) Z�s~TE = FT (N0 ) by 3.14, Nh��a h�U j�. Thus ∆0yf −1~NN (X w� � |J�� U CS��,X, we have (")fS. One!D0n observes (f!�� !D� D(L�cvia@ � (*) holds)!��proof is complete.  Theorem 5.7. Let (L,� , S) be a7per9�!� let N E L #lartial normal subgroup. p (C!�4$N ⊥ are 6/�� /s AJ. !~$Both OL T !��SE6 AA9I!M!KN )m$ if ΣT (F!'����n T0�=.$. 30 (c)�!�� N��g)�0)8suppos!�<at either (f, g)+ D or (g, %�!�! en [$ ] = 1. (d j(L+ ,�-^(n expansion� v for any K%c!mK+!j!�unique ZDE+ (givena1� II.A2) wh� intersectwa� LAequala��K � (N + )!n�=  )+ . PAJ. By 5.6�re@a choic�∆ suche�: A�B�Land, (**) For each X%W*B%�AJ!�X, --�yq e  WIz�o�Dyf�SaF◦$�U�)zassumea>)�,!D5.4�J�K�0generated (asaM�Q� Set K =I�A��)D-�on Y0!�e%Ls O p (NCT (P )) taka� ver all P%��`r . Recursively define YnE4n > 0!��bA�e setlGΠ(w)%�)  W(Yn�=a.��M� ��union� setsd%$I.1.9. NowE�:�AN6�)I [1�Y0 e��!Zc).e��n�A�index=�:�n9�,xF�let wA�g1 , ·  , gk� � � D. 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Ell�enke,A�1� �p7!F�:�f<arXiv:1506.01459)��5v`Manhattan Kansas E-mail a�: A�mak@mA�4ksu.edu 51 �����C,�6����´@�H���^�The Robot Routing Problem for Collecting Aggregate Stochastic Rewards Rayna Dimitrova, Ivan Gavran, Rupak Majumdar, Vinayak S. Prabhu, and Sadegh Esmaeil Zadeh Soudjani1 1 Max Planck Institute for Software Systems, Kaiserslautern, Germany {Rayna,Gavran,Rupak,Vinayak,Sadegh}@mpi-sws.org arXiv:1704.05303v2 [] 17 Jul 2017 Abstract We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The robot routing problem is modeled as a graph whose nodes are stochasA0processes gen�AF,potential reE$P over discrete time. A~ areA ed accordJ to the stUv qh, but at each step, an exis� YsLappears with a givenFbability �edges ino%� encodel(unit-distance) paths betwee 3 pXs’ locations. 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M&�W�S�W p q Cf��� �( 0.5 1 N���/7 TABL�HAF�P�F%��B)I��."�6 . �H 2. OFL�v`Tve|A2�� &;.}�,��"AI3.�^K�&�PJ6%Q�4BN(7 CONCLUS4Y�I\:3f�[�f6q�<2�8�! .�^P��-��oXc3KP&W_�SB��,�9�R_A4��35�*�;. W�R alyzM��a|G�ف(F^s,JRJ���!degrad_e �=�.�U"4 comp�Z�cO�`f=0d�fW�O�>a�F�1|�u(�bgZ2��It!#�O!�&NAoge�\excel�GF���i�n�K.�&vZ".Pm��d�bi:� f�. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 �2gx14 ,WillebraGiHeinz�ITBaksheesh S. Ghuman. F:�^s:�OE�(Z conniR�vXS�XXoday's networks. SAMS p a�_� 2002. Borah, Deva K., David Voel ��Santasri Basu. "Maximum-likelihood �^M^ea}N)3& "�knus��4return photon �2s." Ap�wd �s 45.Zb@06): 2504-2509. SLIlid�dPHarilaos G., et al. "am]Z�� � KcMZONLs E�>� " IEEE6Na�s�qters 12.c$08): 44-46Foa�)sG.)v. ""b�GoL�sQQ$V-s2�`2Q ��i�Q�B�.V��$." Journal!<T�w�v&�a 27.18�c�09): 3965-3973. Ansari, Imran Shafique, Ferkan YilmazI� Mohamed-SNp(Alouini. "I"�[:Y��8:� mixed RF/!��d59�R�mO_IuAC%��cZ� 2.3�L13): 351-354. Aggarw�gMona,�aul Garg �PaPur��D�E�.�e1e�L.�h�_VT� ]�`�~� 32.9�04): 1821-1828�o abu,e�Eb�.2�em"�d��a�tBIM–!d�CJ�d Over S,c�A*�]&�d�|�S;Y�D2;YU��d�5�Personal6Pe s 81-�@5): pp. 1143-1157�����0of DPSK–SIM�� MIMOeW:=d�"a�2� ." �ek-Interucal5�!JeF%w�EFLon3�c��5mL%�� 5176-5180�����5� of R�8-ARd!��-��B$r!��V�쎶F�V���gmpu2 eS6+*Rf 3.5U�$317. T. Isf94 E. Leitgeb, ".|g.� SIM-!��i�)�&�Z )�:O,," 2016 18th:���C&�hon �c�nt)� al N�B( (ICTON), T�lo, Ita�l[�,%�1-�>. N�sUnakŚ�.��NlV�z 8G. K. Varotsos,lS. Tombras, A. D. Tsigopoulo� 0V. Christofil HQ"S[6�AY�Ff���R��� ��16�5z5Urn CircudandUv�H�i�rMOCAST),I$ssaloniki,BA�.;�wP.;�q�, Sharm���.�b5B�2+ a��Y&L`�`��,"O Si�eM[�e'��a�g�a�d]&SPIA%2014 !�%2l(, vol., no.E=333-337!-21 Feb.D. AE,�MEWIslam|,S. P. Majumd/ib�a*r�i }&B 6'� a"� PIN� de�eors),�e�|;f!QbinerI+�5�a�&�3� .�hU)�yah(CIT), Dhaka!15%# 341-3F "�$ V. S.� O. I! richev. "�Q algo�z!��  R�:_ gral6hyperg"�z�b� eRi}A�realizG7!KREDUCE��."Im�UeY symposium�lSymbolicaS� ic!Sputm4. ACM, 1990. I�$ Gradshtey���d�. 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Most�earch,��t� �t�~�,-N!�!N learn�Halgorithm is traine�esQus&!� �f&�J9�T� sett5has blextensi�kied! Aliter!0�e)E� verg��$y guaranten��-�� is clf�o� ��)y�priate)(�pA(s. However,� many1�al situMcwe wish!�%A� 9_� 5_ konA moreM� domaiM��t!za�oJ )|is po!��i�Ao# !O 5,s. Our work,N ed ���,-�Ae b�is1�efur8 supp;u%�Mvresultsh � p� a s&tQ es� �e#�b� J,. Acknowledg5Dr.�( would like%� hankA4 Jacobs School��@Medicine and Biomal SciEf�fac�atA��t�!=8 through institn,al financial��o&(to M. ��) �!0or!|!�S�,firPuth:!䡝8. Apendix A Ond2 bi9 te�2�   2C� A.1 (Isserlis, 1918). Let (Y1 ,Y2 ) L82 0 , σσ121  σ� �2!2 E(Y 2Y  Y :,= 0. 3σi4 , 12Y2 @� @ + 2  1   ��n4i4U Ana�liceV!!�e���1�sH  �µ1�w]!m*�<of X12 CorollaryK- X1 , X�) µ2%�1� 2 DX22a�Cov(X1  � (�� µ1 A). 2��6��3Y B Proofs �1#1. 8By�� e j;l i ) = E�1 k 1H nj nl ∑ E(ℓi,l' >. ∑(n j=1 n −�0l6= j i∈S jJ�8=j A�a1$ult arises��/n = p je�=�jG, . , k.� 8 = (b) Write Σ%∑ ~ � �� �� ),l �:�. 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That�y is, w(P ) is the maximum cardinality of an antichain in P . Suppose now that, with respect to 4, P is a cartesian productU�cN`s, and write P = P1 × P2�.Lt , where each Pi isXCL�$ki . Then ~Lposet-isomorphic to �set:divisors �positive integer m = pk11 −1 pk22 � ptkt �$p1 , p2 , #h, pt are distinct primes. W!p�@ke this identification without further comment. Next, recall that) � d�!� n be%W,ten uniquely!��form d�r11 pr22 � prt 5l( P 0 ≤ riki� 1,@ w i, 1 "t. In �case,m rank��d!�Tdefined as r(d) = ti=1b. Fors�kVK : !�(}8), let Rk denot!>�e1�element%��Ps{$k; clearly6A8�nY� iI�(In fact, it$proved!0[14] %ii*�=a% |Rk |Agis imal nEW\ccurs at k = ⌊K/2⌋, A�0hence, by [2,A�torem 2], we have    s K u!� K 2 L� i�s!!,|P | = Qt !Mki (-A qui�holdsaGn �eve! �d)�ki� 2, sa 4is upper boun%� bestapsible). Stated more concisely� Lemma 4.1�+%FHa partially ordered%5P ,!�.�s ≥�!�tesian!��E����s�:�,�9uxJ6hasH�ܙ,%qK s2q�,2s -vA� P-o�(!p(− 1). We�I聣xonstant b, b := r 2 . π Pro�p0on 4.2. 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(c)E��4��re=����E���Y�2�#�s�#J�#"�$A��`5.1�B�U"�MWF���e��ؑ�.}6� �b*2.�M��h��kik494359���W�2� �6�o&Wa� �4UqR�c� ��G�T� �BFr&f> ~� 11506�@p4}0j�oq�z�>�@=/xeu�. Be 21/5��U�(200/29:� 6��:��E� alph��_-~%�^� 4y��4.�1��� 4�^�K2�pJ� 50/21b�IQ���2���e�.�s29)/�3512 6a� + ,�+.�!4i$��<~%72.� 28090868.*@�K��2���B���2R��I��a 5 ilar argu!m�to2-FL��6�.���5�6'.P� �:aUa�@�A��� (d���5�� �&t"] 6U2��Ae��� � ��r���3a���<$.��S"?>�!6l�>RR 10, ��and the result follows from Table B.1. Thus, we may assume that s ≥ 553. Applying Corollary 4.27, with α = 2/5, yields three cases. √ (i) s2 , s5 ≤ s2/5 . Then d(G) ≤ 5s/(c′ log s) + c1 s/ log s, which is less than or equal tog�515s for s�<, as required. p0(√ (ii) s2( s2/5B��$2b 5/2s/ l�$ + s3/5 + ls, )mPis is no greater thanf6�� when �139:���!&��V��>���2N���w�,P17. (e) r = 6. Here,=�l5.10 Part (i), together withEpxinductive hypothesis, gives d(G%�%DE(s, 2)+1+d(S). UsAcA�<usual bounds on  , t-`0at most ⌊6c-�6s⌋%�!���%]� 1260,l!�!vever S!�one ofoLexceptional cases. 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F.i#�|�k�|��%o 53 Ap$ices A Up��!g� H�3�'(smA��*� b�s�h.�h��colum� �T0BA.!low��`B�l f�**�d%s .+"1 s left.r�Bsu8��Vy�2y d�Al)� f 2-�s (see"E, 1). t1  ctd~��d�!�� � �&@16 211 3 64 96 I% 143A�6 5 20'�2'13 128 1924> 6Z3 1>718 27J13K�4A�52A2825'�5100 4,14l01E�9)514 26 )�57�A� 19776�0)102��7*38_ 6 7�16X 3800�11020r2800772 384 109`�71 7446n2 5��9U�9115�512 14c�82 1437W133819�104307�)203g�9528231h�45 1638(11661!�21��7!�20554685]�5532- �2512)l`�3%w��%�65538��31 2458b�1a��2� �# S�)�491!\� 3 7I ��4Y��/m��2I�27  d f.K~�21E[5 A^�9A9!��4 1966!��2M0641767!C3 ! �74M'$4 3216926AZ�731E�M$4 6308356�P237980)^�1E�!� 5772E[I21E��4�42iRIi 3 151266!mML!n 9522E��3I,!m$431149936  4777|�2�2E�4 9840I�I�22E��91946M1!!3 5758I]�3I]�123549A�32)05 9393534359~: 184804436]>22i 374516!��2 O�2If�5A126�M?�193786�33j 3 428721E�34,7 363767830!�838590�23�108 7163917062E�E��5a�29070� c�2I�aQ795301鉕!A/� 547255i k�6!c 308 ��RF;ls [1] Alperin, J.L. Local Re% enl8E <y. Cambridge Uni�7 ty PO �,, 1986  4 [2] Ar6�s�7I. On*h�9 s. J|tndon Math. Soc. 42 (1967) 137-p<`[3] Babai, L.; Sòs, V.TG?se�2���w� aph��Cayley g. Europe�0 Combin. 6(2)�L85) 101-114. [4] Ben� D.J.:,�sq0Cohomology: V���e�Basic:0�-\\ �F�: G�; GAssocia@�A��s���AH[5] Bosma, W.; Cann!�8J.; Playoust, C�  Magma"�system.!�The�;r �<%'HSymbolic Comput. 24!.P97) 235-265. [6] BrayA^l N.; Holt, D. F.; Roney-Doug� C. M �maxb%�ou�� low-d&'� �;class�)�JK , Lecture]Se�2 4072�2013. [7�Lyant, R.M.; KovácsAt�G�biIG.�.n:Eirrw� linear^ . Qu/�J�7A�46%E85) 385-407. [8]a_=;�PAt�P*�I0, LB> (Stu�LTexts), vol. 45, CUP2��1999. [9:h�a_�;!��;�,28ChainsA�9�in*�71��J��g? 127�<89) 340-352. [10vQ�A�Q$�FIV� `�  up^32. Ex��pal �O817 (2008) 307-3e�11]��wM��Ha urtis� T.; Norta/ S. Pa2arkerA.; Wil�}+$. An ATLAS�2��are�ܭ-Oxford�*,5; reprinted7)�200A� 12] �C.a� Rein��I>�a�or�QM!E�NQ��I,�,ey, New York��8!�3] Dalla��ta,e�Siemonse�On�=�v) �M ly }F�F$des, DesigHCrypt�A4phy 44 nn. 1-3%��43-150�84] de Bruijn, NE�Lvan Ebbenhorst Tengb��nA�a�ruyswijk��O� �� ivis�7�a number. Nieuw Arch. 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These�ar�hms are obtained by setting � = M (a)ij b)klr M (b �aDwhere a = (a1 , a2�3 4 ) and b�b�b�b�b4 ). The trisecant curve D` (X) is def�in Gr(1,!<() ⊂ P5 by%�44×4-minors ofresul�� MA. Satura<�h!N�,%N!Fq2�!Z�,%;i yieldsU(prime idealh �: 2%q q a��2 �+2�, I =|�4n%�13t!��2x��3 @23 14 24 12 34 13�4�2 24��+�3b��q��+ 2q 2 , !!4v�2v�3��2 �2����3�T�+Q−`% , !%A���q!q +%<��46��i � �R%' 23 1�6� �.��m6�2 A ! 2q9���2 �2 �5���+)�>��i.)}e��2�5j�)d From this, we easily findE�4octic equationA��t2} surf� (D(X): x71 xI�2x4 �2+ x1 x6 $2x51 x2 x2�v (�2�3 7M�2x21 x4 ·  ��Hpolynomial uses 136�,165 = 8+3 mo #e�Ldegree eight. 3 ♦��$e past few��s w��Ldevoted to specializechniquea�$at exploit%structu�& f a given��X. Such ?,can be desig�Q�� all entri��@Table 1. 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NJ$�s S: �n 4��s {5V�),. , (xn n )}, n >d��A:�a�_0���={+�f.���rd-�*�, YiDp= a�bi �vi t�di t3 ; �S � [0, 1],��.�1 1,�0$pa0y5�%g+% ��.Dwe1r�c*8��A?�p� ��/li=� s�F4( � � 2"k r"tU�[���wo�}"� * ���d�� � E��YX� �0� �r�1A�is� Easo � ed�W W�!I�.,Yi a�r0by ai = y i b Di c3(yi+�R� yi -(�D�� � Di+1 d'2(y .) + DA "(24) ,a(Ds� ]"�1�)* )�s"�Wtridia,C-�: TD = R&� �, 2 1  1 4  1 4� T=  ��C� �1 M  C �D< (� D1 D2 D3 ADn�� 1 Dn 6A��5���\X����.��  ���� 1*p�\T����r6)w� � y2exkg�3 �my2��.�6���R = 3  y�M �3 � yiP2 .�%VZ��� ��8)�r-�6a� an n�Y�n2�qz$done by an� O(n) algorithm [32], and in general it is this kind of2which use6$order to f,4the inverse ofmatrix Tc�Eq. (26). However, as we will show, an analytical formulaN]xT can be obtained. Let us consi�(he n × n nDngular tridiagonal �|   a 1 b1  c1 a2 b2 2��.  M= c.^*���40 bn−1  c an T68such a ��written!24[37]:  (P )i+j bi .bj θi(φj+1 /θn ( Mij =  <cj:. c 4θ Dφi<8 if i 6 j, (29) �> wherepA1�, by solving !�precurrence equation θi = ai=� − b �2 ,E/2, �\, n, (30) with θ0 = 1E�θ1[1 . Then˾��φoai<�+� c .���n��1��1��1� φn+� �φn�n .%��ui.i9)�nota 0efficient way^f�aJ�. mb itQAe� to deduce_�i!�q�. Apply!�Eqsa�9, 30%p31)_ �6),a�getA� √ s �2!�43) +(2+ 3) E�AQ s 6=!�,2 (32) θs =7A��� 5� D� A�3+2W^�(d�(  [ Z� �1+U�� <� [�+NZ��1, 2 φ� (33)J2�n nf��−^��$1. 2 Defin!qHinv as inv(s, k) =� 1)s+k θse@φkm� , 7a4) �>E$explicitly.*�� carr%�Hout some elementary� ebra%�i� i�>}�1!&$α† /α) �(h (k+1) ln + ( � / (s+k  + n lnH.�� α e + !pβ A%� `/α)n β� � %��3 = 2/ � =2 3+N#�3 %�.!<@5) α=2 + From ��,ein Z�s (�ifA� k,�}Tsk =k, s) > ko6)u7) Thu� e co�Hs Ds are given by DAs n X T!�$ sk Rk , s��,�&^P8) k=1 Now that all�2e�<have been determ�\ �$parametric�¥��"Hinterpolated points��be ri (tA�{xiA�x�M xi ) t, Y!@} . (39) EliminaE�] yj ��A0th polynomial}Dnormal cubic splinl be   x%�xi ,  � [xi , �0]. (40) Pi (x�Yi Arxi��.��� �in� whol $terval [x1Yn ]!� P T  [ g!��4�6�i!��O�, +has)�promoted�k(a dual func�N (see}module6��+mo� � !Tadi5 erial))\(derivatives!H an arbitr�kf = f (� , x)%�any5H� 2 , � ll�P ′ (f!�8�,! calcuE;5���f!Lits �form. S��xamplei presenAvin Se) $4. 3.3 D!!0Runge–Kutta��� � R1 following� in� differentA[U{(ODE) f��E� F (t, f,  )42iniDcon)~�s!Et0 A`�f�G 9v0 . � �g` be a9��d�� 2 way e�f (1�)���g!o�t re5 AM blem� wantETddress�.� 6� AAcomposEEA(Q��T�g�����,%�iz!Xan y9$ion method�� U S6y���eriŗ l data. NJ thel�8we recommend uso� bologyY1A_L[13, 22] instead, unI6.|� betw�nodes2,� ![requir�  8 J{4thAVer � On&) ost of� � ��sA� numer �l&S ODE)�he:��M%O@ [32, 33, 38]. In zto=bMmE,M�E� �g �f��MK� ! � �^iz)� 4th 6y �( (RK4). Put��x2�Kj, x% f , u1eI�G�2e �xq u2>�� is*��RK4ppro� �sAA��x� �h� %|(t). :����A� of f��}��8real variable t��rk4uAm!����r�� k��g mod Pad�.� is  f˜��{�t1��.�t) ��3)ţ]� � fEQ�� �,ũ, namely gũ),e��b�nstruc�x� ,Eq. (19). 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Rs!Ts [1] W. Clifford, Pre,5 ry sketch�bia;ernA�%Hoc. London MathematO0�L Society 1 (1-4) (1873) 381–395. [2] E. Pennestrı̀, R. Stefanelli, Linear�%8E�"�0o3�a � �bers, Multibody System Dynamics 18 (2007) 323��44. [3] H. Leuck, H.-H. Nagel, Auto�.�%� facilitat���-.�in�)�ti�-a�"ba�road vehH-� r�,, IEEE Compu�1?Con�ce onVi�U�Pat!� Recogb� 2 (5) (1999) 2360. [4] D. Piponij��$, C++ temp65�s'��(�m�, Jour�<of Graphics, GPU .�G,Tools 9 (4) !m 4) 4!��5!�45] J. A. Fike, 0lonso (Eds.),�De!�p�3A}Hyper-�Nu%�E�Exact S��D"�' C͝Y�ee���pa�P49th AIAA Aerospace S�es Mee��h, Orlando FL, USA, 2011. [6e0HYu, M. Blair, DNAD,��*�fol��abAof���3���U�9� PhysA�Commun�184!dH13) 1446–1452. [7%hN. Ly�(, C. B. Mol� �N�3B��nal+A� s, SIAM9�n A%!ysis 4Av,67) 202–21A{8]a�E. Row!M s, T. Lib�I.!A Daniak P. G(�Higher-�3y���e47!�� >�in�7, E.�M�&��3���105!0�1!/9]A�,Griewank, Onf�42��P&+ ming� �c]��UApp��E:Iria�T K. Tanabe, eds., Kluw! DordrechtiNe�)F( 1998. [10]!GKnowla�R. 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Given φ, ψ ∈ Out(Fn ) and a proper `dfactor system F that is ± <preserved by φ Cψ,�gilamina0pairs Λ± φ{L (φ yΛ � kD fill Fn , suppose( the follow� hold: (1)��are both fully irreducible rel F . + − + (2) {Λ−��,� � } ∩ {�$� } = ∅;�$(3) Either fof�b�� C�<nongeometric, or9%� h)�i is $ above� Then0Tre exists M ≥ 1 such)Pfor any integers m, n&�M;\ outer automorphisms φm%� ψ n%�Tly generate a rank twoUq�(m , φn i <YD�� !��0nontrivial ξ%��hoE{9isb�AJhas a>Y!�I�EJξ � ills-�I�if5� Λφ^�!n Λξ�.�D. Remark. In a morAA�s!�(ted contextained i%� proofA6|(9, we shall#�v!^strA�rE clusa�sayA�!E , af!�furEpincreasM, eacheU5 )Fn�4absolute sense� of. Th�@ult breaks naturae.nto%�cases.!kCase 1:u�]�eg24]co�%isO< exactly matches!{.,�$of [Gho16,FPorem 7.3]. Our work hA��i9ref!�just to�verifyU hypothesi�!KR, which Eat��Љ����(��e��)e�(independentMa�Defin�\ 7.2]. 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(SK �m>��$`�� S omitY�!k� Finequ�� �:�falseK we �j�p m�$ef� �n��dUa � ǫ ���a��ǫRG�) ����[&��EB�dare�q"N�o�Q�An:u2`�U+'X�pro�Sy. 7 By��}7��W��e��ed�5!g�ZE� Lh��.Ub a`�c�)�M�!� &N�jb���s���'U&=(� ��i�%���; ng& ���,� A�'� � �i��TZ01]�_W\ M��=�u��r >��UV I /2,h�d!���]ght3��in�!�7y llot� >mi�OO&de�u�:{h!�� � hig:I���Povұ��!�"d�A�0a �Ue:ex)k "��)DE� chal�3�e'I!�fN!*�Tr-�a�i  1k/2�K��end�Kdj@� 3ool�&[0��e��-;"hopr���� ��!�ich���e��5>� �K (!4�r! �N�n��:X�6�Ad�b]����s* �gQlM���B-0,2� s (�4a_at��"d�Bi��)��M��m0#��c �bB + mQA�eco%W$�wekis!;s #no�A���e���a!���[Coh00v�%�AS�uof��A'�l!1 �>\*"�4it���f�7& '4l<ynamic, streamin��g and distributed settings as well [Ber09, HKN14, HKN16]. A (β, ǫ)-hopset is a (small) set of edges F , so that every shortest path has a corresponding β-hops path, whose weight is at most 1 + ǫ larger. √ We compute the approximate clusters in the large scales as follows. First we sample ≈ n vertices √ (those in Ak/2 ), and compute approximate n-hops shortest paths from all the sampled vertices. Next we √ apply a (β, ǫ)-hopset on the graph induced by these sampled vertices, where β ≤ 2Õ( log n) and ǫ ≈ 1/k4 . (A pair of sampled vertices is connected in this graph if and only if one is reachable from the other via an √ approximate nAT-boundA��h]-8.) An efficient2�lalgorithm to construct such )38s is given by [A�X6, EN16a]. We shall use%�DionA��[ *\, since it facilitates mh�sa�(er β, whenA� k is $. (There a0lso some addie0al propertiesr� from�taJmak�m more�ven%in� textGroua� . See SeclL 2.) This enables us)9R>� u>�o _>1,we need onlyAm step�explora|�@each source u, usa�again �(the overlap=AFinally,iextend I appr:��E ther} by initia!e�an^��ampled=exQ hop-�2�aA≈ n1q orig�� i�(inA $t, one canAX� �multi- �PQ�X�c%�),8of [Nan14]). Th!�(rrectness f��M�<with high probabA�y, A��y�A=should b��cluaginM�JH4C̃(u), has ei%Nu or aQ%E��ex�in-A�U2.�!Kit � threshold�r enterE �nR�must be�� carefuE6c �E�at�rte�rwill e join�in ordeE8guaranteadatAG trees <indA��b!�4nnected (whichA�Hclearly crucial forq��)�e I�hand,!e�sur t no�particip�ha�oo many �. Unli�$ exact TZ q��,NDs generaI, do not have�.��. Ap�fRE7ourX��e�.28induces increas��tretch)�analysi�� simila%m]� A�TZ05], )J�ist�=k ite�=searchA%!]aU(”right”%��A+ pay a�oraN,1 + O(ǫ) inma�ofH�s��j, butbtunate�vkA�et��c�allow�D�t��suѦly�� ǫ,U��iM��-+ accumul%�to a�!$ve o(1). F��ae� level,%�%��aI�2^ose�@[LP13a, LP15]. In!q theyi��a varian%��TZ-�C scheme1� ��� error!�4��estim���sI,main differe�Eis�?ine �l!�u.� � 3a],idea waųbuild��pannera^������ ices�a�reI�k numb8�f� . So aq� ��be "|aᥧ��H �, and���V��ed!�jentire�"!is=��n�nYA<ers�(- Dtorage requirement�s� 2��}% know!�x ��5�.L”delayeGhe starD ��c. � ��k/2�Xroughly l0 = (k/2) · (aflog D/�nɽ%(�y�� J%!�y�z�V!�� ~i(tE�in Al0 )��.e�>Q��t��%aq�er H�=%�5� �o!� reA�� �1�How!l�,.21���h '��may%���bY�41−l0 /k 5 �KqM�<.��D!L4!b nD)1)zsY��r0 mca�of���s� ows � avoi�-�memoryJX`1I$is oblivio F|�et�,le significaA�� ���nq�.� range. SE HB�n or�\al!C)run R�i��latter ��de�t8s. 1.2 Organiz�{ Aft!�T ng!�" �-� tool� app��in/�3x describ)"no�A�aF; Meshow � "a �s6O in ae��m�Ё(�ef � 4, we dem� ate \�hQN�� c� usedi5ک�}�gI�t� r�5��!vN� G. "� =5�6>B>���\. 2 Preliminaries Let GA�<V, E, w) be a we��ed �aq&���assum!�Dat w : E → {1, .P, poly(n)} (without t��9�p!�e�re� v loga` ic dependſ� aspect ��%(ata��8uctures’ size�.� s). ��Di9 diameA� of G��ae e 2�j��)A�Tre 1. Denote (t) by dGZi� metric��G �dG��t��s:0�!��a�(ab� noaSonьn%Jis a d�� � dG (u, v)%��length�a path��ua7�v�at� at most t��u�(� Z= ∞!���yBM�G�m9 thanI ). 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SIAM!�!~ut., 3%G�4I��5I: ��N�:GE��OP5Neiman�G�IC%B�hopǩ�;>����A.�e�57������j� ɝ�� ��!}�1�B|F���O^���E �a� optima"s0� M�: E͢�eh�;ct����!� 2016z�� Z���@0, Chicago, IL�_��5-2E����� 23��244�q)GK�p4Mohsen Ghaffar�,Fabian Kuhn.21Q^cut=��jIn.*�m$a7- 2%�2v5�, �u�Q@Jerusalem, Israel�\14-18�3..Q�R�1���5%��|GKP98] Juan A. Garay, Shay Kutt�en, and David Peleg. A sublinear time distributed algorithm for minimum-weight spanning trees. SIAM J. Comput., 27(1):302–316, 1998. [GP03] Cyril Gavoille a>��Compact� localized2��Ddata structures. D�� ?�Luting, 16(2-3):111–120, 2003. 26 [HKN14] Monika Henzinger, Sebastian Krin�)D�Xnupon Nanongkai. Decremental single-source shortest paths on undirected graphs in near-li)��oGupdate%�x. In 55th IEEE Annual SymposiumU4Foundations of%?�<uter Science, FOCS 2014, Philadelphia, PA, USA, October 18-21!%, pages 146!<55 . %7�6�7%7XA deterministic almosttEc�d9�6�$ approxima!�6o� 6o%9$Proceeding%the 48th1G$ACM SIGACT6RTheory9MEM STOC!FD6, Cambridge, MA, %CJune 15@6,-@ 489–498%@\6. [IW14] Taisuke IzumiE]xRoger Wattenhofer. Time lower b!��sa�2 !,dance oracles. In Principle�}, Systems - 1! InternE= al ConferI5OPODIQ7hCortina d’Ampezzo, Italy,a�(ember 16-19�4..z1 60–7UH< [KP98] Shay Ku�� id�� Fast��r�� conse�ion!�,small k-domi�ng setsJ applic�s. J. A��s, 28���4��6��XLP13a] Christoph Lenze �@Boaz Patt-Shamir. �ro�q table6���u� � messaT%�2�Jq2�A|L’13, Palo Alto, CAm�I|-4, 20$i�38��39��13. ��b^���D.x Effi�@6}�s��e��c%� with limi�� bandwidthe|e].�f���PODC �|Montreal, QC, Canada, July 22-24El�3Q_ 375–382  ��5^��Z�partialEseWest�o�oI6SIn Fc�%�5���H2015, Donostia-San ђ$́n, Spain1 1 - 23��51 153���6) �5- �6� Perso�communmDe�6 N�PRO��,BWJ{.���compute�e�qSEai�u?!!�Nan�K�DJ�.C�5!ƕ�Lwe�sedJ?� 2�J��,e��84, New York, NYm�May 3!�e��0)�4, i�56A�57 !X�NRS12] Nicolas Nisse, Ivan Rapaport,! 0 Karol Suchan2� -J� of eu�-Q schemeygener_ chordal��. ��.m��.L4., 444:17–27E �2�Pel00�22@.�u�: A L� tty-sensitive Approach. Society%�Industra�and A��ed Mathe�cs,^� 2000���2���PB�preserv!,label - �/Graph) (y, 33(3):16!(176, March mR00] .k�� Vi�' Rubinovi�A � -tAy.�� th� %�lexit�� a(�3 ^� 2}. B� 30(5):142�442�3!-$27 [PU89J���Eli Upfal. A trade-off between space �Qo�c)�Mt�)SACM, 36!J51�| 530, 1989!�SDP��xAtish Das Sarma, Michael Dinitz�U8Gopal PandurangaV�.\�o)L��sketchi network6L Y�/5):30� �3J �Z SHK+ 12] B��tStephan Holzer, Liah Kor, Amos man, B��,F��&" �J. .uverif��E�hardnes .O2J341�123��126� \2. [TZ01] Mikkel Thorupk Uri Zwick�A� Q u_� >� , Thirteenth � �A� 2Garallel*� uArchite, SPAAI01��0, J�2001.kA�TZ06r�����x�e%MEP�o� j CM, 52c x��0�A 4of���Tdem 3 √ Let X ⊆ V be a� '�vertices so that each v ∈ V is sampled to X independently�Aprobabil�N1/ n.oTDefine V ′ = A ∪ XI^no�l� high2F�DB = 4 n ln n ≥ | G| (si� it�given�r |A| ≤ 2 :).!Jly�� same prepAss��teps aŮ�Ss 3.3.1 � s as d�Hd here, to obtain a�� G′�on 4satisfyd$(13). ˆ C�.�SPTŏ l� first ��to�b�e�Pvalues (d(v), ẑ(v))C1� ′ 1�$. √Every ex in-�A ��ias its\<as (0, v), while 0 /�� $(∞, ⊥)a�xnduct β = min{2Õ( log n) , ( (O(k) } iter� �'<Bellman-Ford roo' at A:�e�1�, �ex �)5!\$ˆ < d(u), broadcast � pair>0�tA�e entire)�I� if uM�!�has w-�(u!+ !z then uK%s!v *ˆ !V�toas(w F� G, -�. (Recki%��dgeD fun of G !�erI�l� r is� virt��g_i#by� 1 augQedI�hhopset o%��:4√ 2.) The nu�of�m(nds require�"7u 4is (n1/2+1/(2k�D) · ~$%�@ by Lemma 1 this � also ��B��it takes%nQ+O(�A· β)"� a;%72�Uxs. Exten�Ja�to V . A \end!�β:.U�:�QgknowsA,J�iq�A�. 2�E��eH =!d {duvMf�}^a ,A�4 v∈V (40) X e�A� u) = i�A`.}�!�he_imizer�F:�z +��� d inAK�o��\1.) Analysis. We assume i�e�nt%DhClaim 3 hold (which happensI�>>). For1 let z))�Aa��a�E�s��dGe�zu ! A). S�n,we performedz�� ��� �.A!m�z �A�!�we hava�at0�� ��i��h5). 28 Consider now some�� e6� � ^�O�bS.�in-�a�left h�U%�5)%f s, a�LfacA� �B��P implies (2) (B) ˆ��d%T�va�!Rv, A) )nN��eA) . AE�% G !�Az�r� �h:���:� cas� at hH%�B,�(2)!jge � �� duzi�zA�2,(1 + ǫ)d(B)�L+ 0 = ��.i`0u G Otherwise��>��byU�'e exi��)�� !d�o�:v!�G from u��zu ? ��v!\� BQ�5́� v�ˆ ��=a9�� �%�.�%Ȟ*�! =2A�<u, zu ) . 29 �����C,�6����ܵ@��������NON-LEFT-ORDERABLE SURGERIES ON 1-BRIDGE BRAIDS arXiv:1711.11389v1 [math.GT] 30 Nov 2017 SHIYU LIANG Abstract. Boyer, Gordon, and Watson [BGW13] have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in S 3 can produce large families of L-spaces, it is natural to examine the conjecture on these 3-manifolds. Greene, Lewallen, and Vafaee [GLV16] have proved that all 1-bridge braids are L-)�Iknots. In this paper, we consider three families of 1-bridge braids. First5,alculate the\ group!�d peri!�al sub . W-n verify9co1�- �H cases by applying g8criterion [CGHV! developed-$ChristiansAo@Goluboff, Hamann,A8 Varadaraj, whe! ey �ied�sam%`jecture for certain twist(orus %SV$ generaliz!� �a i� W13]'$[IT15]. 1!�4troduction c )| “hat”��s�4of Let Y be a F �s!h�e� denote! �HF(Y Heegaard Floer homology, as defined �$OS04b]. Th�0llowing resulE�Xshown by d (Y ) ≥ |H1 �; Z)|. As a space with minimal Ozsváth A�Szabó%t a]: rk HFj���nqV i� as f� s: Defini!E0 1. A closed,AZ nect 4orientable 3-mmh YR.`�f i�a ^f �!�propert5= 2� ��IPinterest!U that�s might!�cha�2erEAby`m�theirF��sA�ich seem�fbe unrea��dZ. RecalleT)I�E%J2V�2!V(non-triviali� G!?Fed 6L if�re existE@trict total orderq�<a�G w�is Gpinvariant, i.e., g < h ⇒ f  0f h, ∀f, g,�� G. A�8identity elemen%~alwayA;a�&symbol 1A�. A� the s >, ≤iZA�hav��Le usual meaning. In �� , Bo^�mak >9q��A indicate!2coE��betweeu �q.sil��o%v�i2(� �{ C�h3 ( �, .�]). An �x i� L-i�if%=onl�xP 2010 Mathematics Sub�z Classif!@ion. 57M25 (20F60 050). Key word�d phr�8�.F�,:� , Dehn su��,y. 1 2 S.�Fig���1�((4, 2, 1)-12�,�sEX�B&. Sin�Na�(vide large .J��s,�� natu�PtoA�ii!2�can��b���o���m �conceptA*an 1���a~ need�7simpl�$our discus��2�4E.<�KaIS 3E�P�U(admits some.J� .� yield�D:�has ba �.�.@YPies. For instance, itZK�suffic�-ly-�M"!I�2�s in [��,�D<orem 14]. Our go��a�u !(to �J  another!� ilar ��y!�!S�s)� speca>��J willA worked ona�6��=�a��i� studA5by BeA��Gabai!� [Ber�Gab90],  ?a Q�subseIb broad�(1aB � �<.� s ([GLV16���T� "Řed^�5 5a�* ��o�� soli�(rus D2 × S� s a 6M�(is isotopic!� a un��!�Two arcs ρ ∪ τ such� •�� ∂(j�)RK ���( transversec0each meridian> =ptŇ Z��F!_ idge�&�L(perly embeda�inI� N onala��k �pt.�positiv�ρ \�K!?��sensekno%Zq�� 1D� 6Q 6D& \supporT inE =�com�8from a genus-1 "�splitt"of� . To pres��� ih, let Bω = hσ1 , σ2 , · @ω−1 |σi σi+1 =  , 1 ≤ i@ω − 2, σj σk2k * j, k.-�1, |j7k|_2i � !l)C�v ω sA,i�^ �gives0 i, i + 1 a r[ $-hand half��EE_�se_ comp3 )h8A�a . It��s �’s c2�U��F5!��.��(�C, ProIl on 2.3])   every>*in%��i�R<form B(ω, t + m b) =F�, mm�hM' �1of NB��(A"A Uσb )N�M3 )t+mE� Ae, I!�b.�C�t/A7 m � Z. Wd ��7 �eu�ca�%B F����i��rL ��aaPlink. J.��,S. 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M���� a�)p)Vb��yE (maybe�H a�$e(+e� �T"5�?=�Wa�dofj�:J!0�n\}�? A[%�_� X>G��D%A�}�YQ�RU19d,)�� {|:��BD�? M����ts�;���nyl�-4$A-�y��-E�:i�.�6N Y9�>��? �.�_tar�Csll KR��X × R� ph�"&���f�s1�C.m�t7Is&� prop^d�q�?�:se�  perhfa�2�F*{�t�o&0 of MA+lis’�,errx�� a wa���r!�ia�horosp"W K��5���9PjV0�HG��)]$.t ! � Td.��)�lces [BHS] Behrstock, J.; Hag!(M; Sisto, A ��xin hier�|ly�F boli���epr��LarXiv:1704.04271. [BrTonk, M.; Schramm, O. E5r�GromovJ^� Geom�enct. A�� 10 (2000)�7(. 2, 266306p F] B��, Noel;��,, Benson Fil�Y-inC+�7~i�y� manifoJ��(N cuc�uh�ran̘ mer. Math$T,c. 350 (1998 �48, 33933405. [��, Eskin, Alex:����)w��Q=)�&w�> . J. B��!# 1997 �$3, 653692.�� Drutu,�~nelia |ys6a7- �-m5Dt<�emiZ � �of.�\�.2�� ^�327388!%2#B��5)�N��.�s5,�%s. R,�12�2, 32136A�F]6Aw2��yJ,latJ � �. I5�R�Lett. 4�1�t5, 705717. [FN] Fisher, David;��'�angB$��-&B�, pm�<, http://front.mA�Pucdavis.edu/1512.0728A�,Fo] Foertsch}omas BN�� z/�al uDA;�;� warp�K�r>��3m��.���cN��3��2M�$7, 2089209�G]�Q(, Mikhael Ii�1��y�g��ic ob�- nee8á�In\M�alMS�gh���o)wc(ians, Vol. d�t (Warsaw, 1983), 385392, PWN, $4. [H] Hua� Jing5 To2�Ir�,in CAT(0) cu�JlexAH�P-�� ��410.819!�'�HKleiner, Bruce; Lee�rnhard"ұ�2��7�uL�  �F�R8st. Hau�j Ét�F Sci. Publ�3No. 86U�115197 ��8) [KL2]�����W ��( ��Invent�163�N�6MJ�+ 7676 30~�$[Kn] Knapp�thony}� beyo�g3!I�ion. Se� e�E�IXin��eEXxs, 140. Birkhuser Boston, Inc.,MAA��02. xviii+812 pp. ISBN: 08176-4259-AL] Leu�3A�E$O@�u*#��fF,N�� F�V�`4, 863873. [LMR] Lubotzky� $ander; Moz�1HShahar; Raghunathan= S� word�,Riemannian m�D�s�#�|�՜�x I��� A�91Ee55I#�W܊ ] Mo��$Lee; Sagee�k chah; Why�*Kevin���a�4�(trees II: F�@ depth Bass-Serre ". MemJ�214�11M�100�8N]�um�%R�lɸz}8zX�J;�rI�8. [P] Pansu, Pi� Mtri�0 de Carnot-CaS�odory e*]�t�V�J�e�Msy?w8 un. 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Also, based on�second ��,an write b =HL,   a 0 c 0 e !L4�. Therefore, � 2−!+nd%K�2�z1 . It \be show|at N 2�8 0 b 0 d 0 fvz � �1 Pz [L , L ] 0 z1 z1 [LA(L2 ] ��1W���It!O0easy to checkE>% rank(�2)64 1 1 2 ) < E�� 0 �!u  2 %�ll)∈ C%�4z1 = 2. Hence,r$necessary !��iA �is propo!�(in [17] (asI  byU: (33))0Xnot satisfied. Furtherm!�fl�o detect�isolate.fault f1Auusing<approach in [36]x4CW1∗ ∩ CW2 A� Since L1)�1 6! ker C,TinvokW4lgorithm (26),e obtains W^ = L1�bL2IR2R��8span{[0, 1]T } .��� N�!s � also:\ In o!] wordsG91can!�be-[ede�-]�d�9Q)~Dion filter (8), if%restrict��9!to�� case with M = C (or H = I), accord%] -requiredR ults� . Finally�Nis nowm�a�,demonstratedI�� �% � both)�sA7and f2�ourY�Hmethodology. Toward�is endv�7I 1 �L�� SQ#21 (t�V�i1��inite unobservability subspace containing���T A^�) �qR�s��T a�0 0�U� D2 =��s, ��y�(30). 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However, below w� �1 ufficientJ ��qthe.��[U_�,I\(as well as n�sti%ll՛ d. 1) (Con� �2 �h�)� 9 ��B��.� P HB2� �01�.&� = �1ŧ�4/�+� � 1 �ҥx|2K!�U�A� Theorem 5!cE��md. 0 1A:B`��22��Ga��_ ��l6U !�S � jR � >R� �,����N��3) (O. 9��)#f���7.��"�  Sx N ,� �Lai������ =�0To summarize,!{�t�O�s�[on!ahav� velop�� nd presen�a��u�c��!��� of����"! Dan Inf-D frameworke�AL time �2a~0by utilizing "0 � � �s%� ved*� ;V���J���E@wasD � ��O�= E��providede�36�77]5�]�n6����ig}�Bis. r� 3 ���abo�ere�cer� ѯ �!��m� i�B�re�� ap���i�cap of �a�!� �ŏ�s��asf��� !���-� suc�|fully. V. S IMULATION R ESULTS I�isQ��,A���y6m�!� �� A�a two-line parallel heat exchanger �� [8!� 49]. Spec�}� we verif[ &�!VXEz!QM�A4!�previou�D�|"� �f��s�J0)s under�� !ANpar�0state measure]$ scenarios� is�cto)realizan!Yropri@sel�`�"�Poutput matrix C). 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"�.�sP*u2no" )e I� Aa� ���)g#in�AYif� = (3��3i%51, 3, 3�6�n � = (4,�5E ��=Q>lso, P��* Ns,∞ =!K�.&�f,�5^~in")�Lemma�-�%(H corol/QK �C y 5�i�he>���2����.��V��$�V1� irRn�,}�. is A&V!Ydifi�B�* ��y��C.**:MZ��Th�8�!X�i�I�s� }Xvalen]L(i}(u��W �R�. (ii)�+(W B�1�C5A2F��3:���W DE�(kF �.A0�= Wz43�U>K�ᩍ!7& �1R?  % �S�$s III)IV�ɉF�& ���-"? �I� i"}�pL7�Gs� maj / arriD@��c&<engA�XR EFERENCES [1] R. Iser�9, F��-��no�4 s:��i��6�f.� ��to toler9/Mri-MDX\06. [2] P. D. Christofid`/Non��rob:7�6ro�+&� s: M�EH*� �z�IhJ-re�%on!�+N��S.��@1. [3] A. Baniame�Y�@K. Khorasani, “%���a�N issio>�v�A"Cs:Jite.�*�a� ,”��2012 A�cana�%Con�L�y8pp. 5894–5899!ZT12. [4] N. H. El-Farra�S. Gh� sala�AcU0or-����rC)�f;��<KZR�(AIChE Journt8vol. 53, no. 6,�(1518–1537�07. [5E .�Aaoutidis��RB R�I � Chem�' engine�[sci�,�� ��1 �85�,05, 1998. [6eF. Cur��(H. Zwart, A�'�%��t0( .��mC�Kory �21. Text��A9Q ed M"�Ns, Q�-Verlag , New Yor� 4995. [7] M. Krk(�0A. 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Sur�"�)s absj��Y�m:�CTA*�x�aA, 1-66���J.��<S�JEBS���S.�(Thev�&�v &Son�ew York.qVa -P.,>�,E., Sergi, D)3 4. E�=�p� dialog@ �co�e�E�m0$. PNAS, 10�4333-7. �C.M%>68)�3�D*�80 As A Queue S� xZ�i�/Ope@ ons"r(, 16, 307-3���U E.Tm57A�Y�<�?yF�aQ�Ccs�A� Review�,6, 620-630. &<pm��4�KA�huBv s. P Q A, 338E��-e!&��S%�(Teslyuk A.BM Shchur, LAx 2006��aC�O� 9��o*G�k2L E=web:��{B� er N�� s. K&�x0V.V., Kakushoz��,"/x!`�LAS$inoh, M., p. ������b�W2�6�mڡ7$74, 37-53. *�xl�ey ���2����,š.�!� * �Kex " Opto&� s, ��ruaą�"160 Processing, �41, 81-90. Luce, R.D., 1986. Response Times. Their Role in Inferring Elementary Mental Organization, Oxford University Press. New York. McDonald, J.B. and Xu, J.Y., 1995. A GeneralizaX< of the Beta of  First>LSecond Kind. Journal2�Econometrics, 66, 133-152. Mitzenmacher, M., 2003. A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Mathematics, 1, 226–251. Newman, M.E.J., 2005. a8laws, Pareto di\� xZipf's&H. Contemporary Phys�h46, 323-351. Oliveira, J.G.%<8Barabasi, A.-L.% 5. Darwin"4 Einstein corrE&xdence patterns. Nature, 437, 12jTSakamoto, Y., Ishiguro)j�(Kitagawa, GQ�( Akaike inf!K%�@criterion statist԰KTK Scientific. Tokyo. Scalas, E., Kaizoji, T irchl1�Hub 8J., Tedeschi, A �X6 (in press). Waiting ta8 between orders� tradesa!$double-auc�markets.-�4a A. Sheskin, iu97ee HandbookA� ParaI�_ Nonp�S1Lal Procedures, CRC P�X. Boca Raton, FL. Solow!�@R., Costello, Ch.� Ward)�I�Tes �he I~A�lModel for Discrete Size Data� AmericanIhalist, 162, 685-689. Stouff!w4D.B., Malmgren��A<Amaral, L.A.N., i\Comments on “The origi� burst%�( heavy tail%�dhuman dynamics”. arXiv:piX/0510216 . van Zandt, TiRatcliff�� 95.2~mimick�of rea)�A&8 data: Single-p!� ss m!Cs, -�8er variability,�mixaDA2 sych��Xic Bulletin & Review, 2a��O-54. ֤�VOLATILITY ESTIMATION FOR STOCHASTIC PDES USING HIGH-FREQUENCY OBSERV5tS B Y M ARKUS B IBINGER† ANDPTHIAS T RABS∗,† )W�1710.03519v1 [] 10 Oct 2017 Philipps-Universität Marburg%��U2�HamD Abstract We study��9GA��TonE�<bolic, linear, s�� e�, stocha�F,tial diA��Kal equ�x<s (SPDEs) observ�(a mild solue�on a dq grid�EA�space�P�high-frequency regime is considered where� mesh� ��The XI6Tle goes to zero. 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P ROOF. Since (∆i X)2 (y) = X ∆i xk ek (y) k>1 2 = X 3xk l e'Xel (y), k,l we obtain%�Pfollowing variance-co , structure o��ies (38)�<different pointsj�:  CR��  n   eϑ1 /ϑ2 (y1 +y2 ) X X �1 )2 ��% Cov() 9�,!�j-%(j xl ) , = En2 i,j=1%+![,while other 9Ps vanish by orthogonaA�L. A careful analysis!;;9S0s yields that-���  =�$ (Ai,k + B �C�)�l (Ci,l ), (Aj , �C�)%Bj�C)  BC,l dNk AE, C�A% + E[ ] ΣB,l += ij  ij ji ij \k >�l>�l > ΣBC B>�� e� ..iΣ 8� ��.BW��DenotaTCξ := supk λk E[hξ,aKi2ϑ ],e8resul0sum!��(first terms�4bounded by n 1E�A�);BW� Q}< k,l>1 n X = 1 6 Cξ2 X   (��e−λlA<n �..�E�'�(��+-$)(i+j−2)E� Var �ϑl iϑ i � X Zd�2��� vu��)2��ar�� Zb�AP :e� 6 2!�2 . nu nYt 26 BIBINGER AND TRABS Repea)�@everal steps from%�proofeȀPropositions 3.1 and 3.2, we see a� also9crossI0 are asymptot� ly small:UA�E�DC,l  E[A A ] Σ +6�i,k j,kA�U�ZBQEIJX W�1i�5�Au  XAaCξ  42 σ   X ���  %�2�Y�E�k 6� e!� p √ ×!�41/2 1i6=j 2 |j? i|6�i + aV82 πϑ2  X  22��U� <a5Uj + + O�RL2n ) + σ 2 1i=j λl�|∆ X  n =O 2 (i + j)−3/2 |i�j| �+�n5/2 = \5/2 n )A�� T\fore,�&�VB� n�%>�q��!m��(6c�B���+�\6U2N9 !.� � (40) ֩;ver alli' k = lH0 induceT "� part�uorder%Ae�is thus>h0negligible at��:$. 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REFERENCES Bagchi, A.E�,Kumar, K. S.0li�A�� fac7>modele` est r�&��se�(Kohlmann, M e0Tang, S., edi�N, Mathe�u<,oO0nce: Workshop�hN&� Researcheje ��K� z,5Spmany, October 5–7, 2000, pa�59–68(E@rkhäuser Basel, <. Bishwal, J. P.c(2002N@ Bernstein-von Mi�a�e�CU`&�,�s�Bayes.�;�@bolic SPDEs. Jourd�3AusxTh2\Society, 72(2):287–298^��8). P"{g'0 n s&M&�d��i�Vqua$4s, volume 1923�Lec N� in�s. Sp?3er,!+0lin. Bouchaud!R8-P., Sagna, N.,Xd<t, R., El-Karoui �Po� A2�.���9�,PhenomenologA,6� curve. Ap ,2:Mo , 6(3):20A232. 8� Ci5).Aict �pz�e%�strong&� \s. A s|�k�d�open qu!s�o"Pr` 0. Surv., 2:10!�144�T �,Ax�Ji@���A)a�Tim��:!!10methods. 2nd Be!� etc.:5�-Verlag,&e�<ion. Cialenco, I ~�G�V-Holtz!�a �1�RMA�!�YR5!:@urbed Navier-Stoka Qa. SY�PrGe�their %��,0s, 121(4):701a�246�� , Go�rASBHuaY.��6a�ra�;!4fit�9!�ma���spdes dD�BK��v�Wise. S' ) al I�#$�N��, �4thc�Z�g6��J��o�A�e�w�#�m2 �a�kdiscrete��amp���H. arXiv:1710.01649.�Hef!E��M���i ermA��ui� dynamics:��i�"��anroach�� tern�$al.�� ti!!�%�ed u|�8a|35A�<380. Da Prato, G)Zabczyk�1e��}=[U:�}F����44��,Encyclopedia��s���McD. Cambridge Univer,_Press, . Doukhane�K4). M�p�485rB2UB�1u� New York.a a>�x!Iex%��s�#42Va4Filipović, D)�a��C�J)probl~AH@Heath-Jarrow-Mortr>!����9U 1760B��� ^։�. Fox%��Weisber!E�0). Non�rO\�s�A.�nle.+kE�r�Ap�nix(An R Compana2to2�RV" �� ��ih�(https://soc�0�.hci.mcmaster.ca/jfox/Books/ a/a |�/��-��-rD.pdf. Frankignoul,�m197��Large� e air-sea���a�`�s%cl���edicta�o. Else�_8 Oceanography S�, 25:3 55. Hair��V201�B Solv�he KPZub. Annal��}7, 178z�5Q 64. EHAs, IM�� IVx a'a��BWppriGan�@:�of �Q��� new ��forw ���'claim�lu��. Eco1�$a, 60(1):7�{10! übner� 0, Khasminskii�Rozov  B. L��!5Twou��b��$^ � Vk �U.�"�,� 14�160.h �0� .��%V Loto�R� ua�A"8]8�y�ta kernel�ior!]�� ؍’s }��-�ent2�_�.�]:�]ed���bM� , 10��(1246–1258J��1{ı̆,=~� On &c !*�*ofT0um likelihood���!�z .�PD�x��+A��R���elda03a143�63.&�"B �,��).B"5�. T���l,by� B. AP)Fͣ�}� . 9.U - Heidel�Z -�y*� � � p. X, 275 p. $ 27.30; DM 49.60a��7}TJac[�JI��OnX�t/ $ al g�f� *�v%9�s4Z�e,�2�law>́min�� de]#iés, � 232� 46.�!�Pr$ �201�\�D iz�!+=a� >I� Rosenbaum� a+�Qua>]n�o=&��vo��j: "�]QpW ACy� �� , 41 146�1484. &P�1w:D�6���O� V� e�N�8=� @ � � �m> , 5:204! 08. 2R�V%*�0����a�f��c66�mv"� �:.W�a�;] Pub�8�c6 $ Matemàt+��3��au045. Markussen�"����Ly��i2���a.: �o�\�d:����V�.aO�(li, 9(5):74�X(762. Mohapl���m-*� Llanar OJ Uhlenbeck1�<g mmunu��i�atu 3 "0  M� ���3AJ�4���4��MusielaI�199!8� � A]:u� �ees I �  �e&� \IGR-AFFI, La Baule. Mykli{�PɃ�Z�W�,�8�2I+63 *� semi.;5�at ]{n*u�y:� 77!�140A14A�P� ba] L.��O��� A. G��Adv400d Diffuy in Ra�x�M@ : Im� �[ijSea�$face Tempe:! Ano�Y�u Sci,& Busin}!W0. Prakasa RaoE��L"���Non���icB� clas�6kf��s� ed oi;�sG-m �(. SankhyāB . A, 64aut�1�!0�H%C�8�,Angewandte M�en j�h�scyT�*k. Teu} 0 Skripten zur��/�8 k. [1Tex�g�n-cal]�s].�:�Gcd, Stuttgart. Lineare, logl a_ule. [ +, *5)�cm+8]. Santa Clara,Q�Sornette �����2c��o forwarE~?'�sX�i st�o�� shocks. R� m��Studi�%�1)�T49 – 185. Schmidt, T �r��cd t risk� ��� �R� � 9A:% 68. Tu�&�,A<k�l.��v�aZ�� neurobi �:-�}&%��!` spiking 6��I�PMXc Biom.��T|t 73&t . Ut��S.�F�^��CN.�"' ")ari�$� .�L�2���s��<, Vol. II (Vilni�C�3�)% 51% L528. “Mokslas”, 0. Walshũ�Bi�U 6�'�Q.,M ARKUS B IB֢�, FACHBEREICH 12 M ATHEMATIK UND I NFOR l, P HILIPPS -U NIVERSIT ÄT9hRBURG , H ANS -M EERWEIN -S;�(SSE 6, 3503h /\ G ERMANY, E- MAIL : bib]r@uni��burg.de �THIAS T ��:��.��, >�� H AM ��B�ESSTR�55�146$R��!� ias.trabs�ham� �O��1 ݂AchievAN S�!Effā�c� Spa� ,�u� Q_�i�Dowl�k�`-Or2� MulB e Access R�05.06466v1 [] 18 May 2017 Xuesi Wam��� Memb[,IEEE, Jintao#enior6"� Longzh� He��JG�ZihanW�tN"����J4�S FeK��,� AbSct—I3is pap�a novel�!!.�@1.�a%. nono5$�  #�p�%$< (SM-NOMA) syste|*pr��rt�W6�e mutu! � (MI�Kcha�er�[��a5�� "U` cy (SE)�Dh� � �. Due �+�fq- -alphabet�ce-domai�(puts employ< y SM�2�eڊA5�co.TtMI lack�'kKd-�� -?�k a .V!z- �quantiRzMI%>��FurtherVY� F�yR;.�M��'�v� �g^inOL�JA1` $signal-ton��io (SNR)�� � SE���@��Wsis�ou�%poh 6�� !confirm)lsi1,�:0ults. 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O&�5�� T�����Fs :�� Ra`� ���9)�T &r\�vU�� e�to*��^��T�A��#���! main ���r?1�KF$1 ic��sh drawCs�p�N�>.���2/�F!�Ŗ"��;e~-s ��Uk��[" � �i�#�t� ��5� 2k�]��D!g�31l� �a� �_*�!"���M�e.ۃ.-�i=�!�f��J9!�llAjkg b�$� .�*Eqnd sto�k _>�& �!���T!�lH �uCr.�%Q�)!��fu�z �,���B8Appendix A. 1 U� iu\3�bl nd>�t�/"�m|!�!�n�N. z* dVC - ASN hx = JeK, ∅i �<�� e hϕ1 , D1  S1 6�P 7�, {pi }�x� � pi8��D2 8�2 8SEQ�%�$ ��+1 .Fx�h� .:R� CONDKte(JbK, �,�)���[ if b then� S1 else S2 Figure 2. Probabilistic verification condi genera �. Above, ite(a, b, c) , (a ⇒ b) ∧ (¬ �c). 3.2 Programs and volume computaX4 Following Ch��kov et al. [27], we reduce the problem of G:�ty that~t terminates in a state satisfyB0ϕ to weighteN��l (WVC) over formulas describAregion_ Rn . In w��f��s�begin byA aliz9�WVC�. V)% of a)Dula We will use LT�<denote first-ord.��in som!7$al arithme!�<theory T . Speci!�lly� consiF,two decidabl%s8ories: linear r:T�!��4strictly riche (Xclosed fields—Boolean!��b!�%2|of polynomial inequalities. Give!�-r!�∈!$, a model E ϕ,- d by m |=$is a point!,Rn , where n$the number!o free vari��sϕ. Thu)� view��aS)�Ti.e.,⊆f�.!�!�0Xϕ = {x1 , ., xn }=��R{�$ R The (unQ��)qB2ϕ�ϕ 1 dp � is short!A dx1 dx2� . dxA�$For exampla��fF�iA� R R2 ,��n [is area�ϕ. W:42��,We now definEMBc./�%6ass�$�wf gMpair (!� D), �ϕQ A��D!h�p.h�p!hEseti�<�a��tyA-�s funcI� such�: eachU  xig!ZM<ssociated with aBJ� pi (xi )sa2w��ia)bus its valuA�!�1�=�ϕ jrespectA:D, ��E�VOL1�)m�dA��}: R Q ���A$ ϕ EI 1. C�heA6�!j8�� x1 + x2 > 0,%tlet=x p2 }q_p1!p2A,%PDF�W Gaussian 2��m��0<0standard deviŅ�Then, R �$ = x +x >0v0(x1 )p2 (x2 )U�H= 0.5 1 2 Intuitive��ifQh<to randomly draw�)�!�Aex2 from2��� .���L���l0in+�.� =@ �.0.5. �0I�j�s RecallI�our go�;�s��])t.`�of�0predicate ϕ �'end a p� execE��,A��o�Pr[ϕ]e�a�show to encodriss�asB� �%�. 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P��  L�a�92(14�8102-��84, 2004. 62 �΋��D,�6������A��������The Control of the False Discovery Rate in Fixed arXiv:1611.03146v1 [stat.ME] 10 Nov 2016 Sequence Multiple Testing Gavin Lynch Catchpoint Systems, Inc., 228 Park Ave S ]28080 New York, NY 10003, U.S.A. Wenge Guo∗ Department of Mathematical Sciences New Jersey Institute of Technology Newark, NJ 07102, U.S.A. Sanat K. Sarkar† Department of Statistics, Temple University Philadelphia, PA 19122, U.�LHelmut Finner Instit��for Biometrics and Epidemiology German Diabetes Center at%� Heinrich- �e-University Auf’m Hennekamp 65, D-40225 Düsseldorf, dy !g† AEresearchAFWe-�4 was supportedAEtpart by NSF Grants DMS-1006021�309162.B[�,Sanat Sarkar�^�3442^�H273. 1 Abstract m ling%/�fe diq �rate (FDR) is a powerful approach to multA� tesA� . In many&$lications,a#�ed hypotheses have an inherent hier!W4ical structureUXthis paper, we focus onZfixed sq�9 wX#} ing order!�a�2��s been=0ictly specifi)�Tadvance. 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B ��"] d�Q�e�\qart2��X1�=C �i�( ��)4 V� &ߺ VIIN���A��[�SVT�:@G�racZI�7 #u��! ��!-R%I Sa e ScN\!�Ch�U(M�@1)L_� 4  User 3 θi ..��2 d• 0�n. ��' ��&og�x"!�iv�p�5�-�s( ;$Q��GEE��, !� :=retAp&%L�r�. C.��aBG��boldface) �l%�s (���7nR�by.cap�8>0��X��ca�(e�;�b��n-i>c�P8��set��r�i�6ic :1�X �!e i-th e{� � xL (i, j)B(��x XA�˻|[x] T[X]i,j .!1\/!�6C t�rc� nd jYcolumq �bo�X�E�a))l Xi,s)Y2�.j� ��:�H�:�t�:hA��u � ��(�^ J) X�5XH4XT UhIr(.�p J�per� � z��/Ra@inner product of @two matrices (or �vectors) X and Y by hX, Yi = tr(XH Y), and R = Re[ 8]. We use kxk fT@he l2 -norm of a b xE kXk =b�XbGXiR;$Frobenius A �x Xl\denote a k × k diagonal & with8elements s1 , ., sk '�(>��)g$ indicate �output��ny optimization problem such as arg minX∈X f (X) kHX∗ . The identity �W(order p is ��d!�\Ip . For an integer k, w)q�shorth!�not� [k]%M{1�k}�1;9big-O5mxO(.). II. BASIC S ETUP A. 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(20) ��6� 2bS∈T+ &G�.֜ Schur’ d�mo6�%N�\� ��2V��n �@(see [49] page 28A���e �e � ��9)�a��AM. �zB��G8%$.i�A3 7),�/MB%���%16u�i�:{i�8)PCBE�%xI��(5u�.�[D�k�� by 8�=��� .�2�����m��,.T�٠I��d ��� le� �p��.� �B^� 2 ���s�O��i;f�=�@(sD��W�s("~��)�7�h  ��,�'| f�� �W!pّ+1)�t��0)) Z^�h�E6�h^�,= h0 (s)ds 0 ! hq�7s)]�/W0�(�(a��� /�2@�O+ βk��s �W0 kkQ�kO�0 0 =L� Kv+ s,��k2 �βn5��F�t� �2�.�fB�}%�}*&sGe� �V.��m$�. ]�e�"ZIV-�m*<Co�g�:d�cse�i6j3@0�sl!&�Sɩ�x�3��2M� tr(�p�.<�0=r!�%��+> %OMB3�!�!biM���a*  !J@Cauchy-Schwarz in%q4O� �qLi֞U�Z!J qn�xR EFERENCES [1] T. L. Marzetta,�8NoncoM[�a�0���uk wire�K�w#'unl�ed Y!��b��� �a{(s,” IEEE R��.�^�W L� Commun., vol. 9, no. 11, pp. 3590–36TNov. 2010. [2] H. Huh,�;Caire,,Papadopoulos��HS. Ramprashad, “A�5 2�8S:�5 ��a]v -so- �I������9 �$226–32398B 12. [3] J<3ydis,�Ten Bn��,%�$M. Debbah,!�Ma&��AIAul/dlA5�9�:�N ma� do��@[?” %�J.!�Sel����n�0!� (JSAC)-�31)��2� 16!�17p�@013. [4] E. Larss�cO. Edfo*�F. Tufve A��T]�!�2���� T�EaU��7YiMV"W8Magazine �52.�� 18!�195%�,4. [5] C. Sh �dEYYu, Ni� and,�i,2���k Yang� L. Zhong%�Argos����@!��--�23��Procee�eW�18th Ann)��Io'��al�~�D�n Mob+8-6![�N ;ing. ACM�)� 53–6�6]�Rog ��,!�4Y. Bursalioglu% 6bG.q}4A. F. Molisch,(Michaloliaka�V. BalanI�K. PsounA�“�GW* synchron���<ln���G�b���o5 &Ued 6R�@nv!A�M 13, a��4E�$ 1815–18A�20E7]� Adhikary,a"Nam-Y. Ah �9 “J���O divb=���ngmT�]�-W1\j#�"_on In� ��eo��;�5�<�0 �644�X 6463%�a��8�\�k����� ��O!�!�tic b.w�!���up�w!�$ed��,link schedul�T��2���f�� Topic��SZ;a#��TSP���8i��5)87a�89�G%��9:��Eŏ Safadi,�Z�K��imie��Wa�9� T.��Rappa�2I�E�� U�>�� .�I�-���mm-��Y*��,��j����������6 � 1239A�25��10]�Hag��atsho��d���C�2�J�� � .H W�m["�{alh�-@�Yin 2� ZurrSe��r o߱�E�� . 10A�$11] ——�2�c ��� +!�( rom :��6 .��)t����^!~= ���_A�il�6Mb30�=318�7. [12�EKumaresai� D. 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So, KISOM AP = HAH�D;(I ~ T )D. � where D1 <squared geodesic9 �H. P • LE. Recall %`�LE minimizes ψ T Lψ = 12 ij (psii�(ψj )2 Wij )Qdo!Lthis involved comput,eigenvectorsA,4L or L, depend"�oI!.)a poinEn �< has close conneEE8s to diffusionsM8a graph—thinkuA�n term��am�tinuous time Markov chain: ∂ψ(t) =��L �.�tA2 soluE�e Green’s}@r heat kernel, reA �d�A�)�, exponential�L: Kt =�<(−Lt) = X ξ φξ φTξ e−λξ t , 146 M. W. MahoneyM3, +arey.��/ alue%�L%tn, �A��t 0)��general �)�,under assump!!�$e can show%�8 1 KL = L+ 2 is>aGommute%�aCu�of9�: +Cij ∼Oii + Lj� Le� Lji . Fo�6�e>ere�betweeQlq�'v�7 the FSM�Eq�,aIp!0pdumbbell example; we will getI e2@ more detail next%�.i�>�ef says%ZR!� approximairachm<�a��lineara� bina!�\ of neighbors. Let (Wn )e�i, !Q� [n] bI9�w-�t!��a Zxj!8�expana} xi ;n one 6 Kn 2���{�T. �� �� s PD1`$domain X :b, .,, xn . Also,p6w��λQ�largestmA�!�� �ŇM !�en� LLE = (λ� $ 1)I + W T�� �WA�a PSDm�ithu!��(. 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I� �=tj! n s��+-9�F�� %��S (G �������s�Xh�)�(���j$��\m, i.)c) �%Bb) *��"�1��jG ��d��A at)!K�22��0".0"�*"� ��n �������6��&�"� "Z��QP)f�����(1 (t′j :=ABb��X�Nm�.n��(�� ��C1� B�sX�X �� LI-�′A�&Q&O� �0�{�· >i�(��!e 1 wAX<#�p�rE�� ��9 Ac�M ledg�_�skhg`�%8k�d��O>"7��i���Hhe*[�al Sci�s Rese�� InstituteI�w hospitac �e� grat��.�Q�`8thanks go to Em��ily Witt who participated in the initial stages of this project. We would also like to thank David Eisenbud, Steven Sam, Anurag Singh and Uli Walther for helpful conversations. Experiments with the computer algebra software Macaulay2 [GS] have provided numerous valuable insights. The first author acknowledges the support of the National Science Foundation Grant No. 1303042. The second author acknowledges the support of the Alexander von Humboldt Foundation, and of%�$National SZ���X No. 0901185. 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Eagon, Cohen-Macaulayq�in�@ant�a!�54generic perfec��of6, loci, Amer.�Ka� . 93a871), 1020–105E�T0302643 (46 #1787) [GSA�niel R.A�ys-�<Michael E. Still�Z�2, a s��system research�aF , Availa�.8at http://www.m�2 uiuc.edu/h@2/. [Har77] RobinAtshorne,�<]lr� 1977�n��w�52. MR0463157 (57 #3116) [LSW13] Gennady Lyubeznik, A*1 �,%�Ul"2 d, Local cohomology modules�por� at6�� �@, arXiv 1308.4182aE$13). [PS73�rPeskinewTL. Szpiro, Dimension p ����e eA� � ie l� e. Applic��à l��́mon-E�de con_ uresM. Aus�L�}H. Bassc�A!o$othendieck��st. Hau��Études . 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Höfl!Z EQ!� .�on� � iP*�01�s2ep�^� =�Dicm.tu-bs.de/~bhoed�/� +s/�.pdf. �8�s!�a� [13A�F. Holt6�E!PO’Bri!�Handbook��A�&�EbAp�ory, Boca Raton (Chapman & Hall/CRC!S00�14] M.V{@roševskiı̆, O6œ)�dI&4USSR Sb. 22(4)�x�J584–59a 15A Lidɞ(H. Niederre� �,Q Fiel�=(Cambridge ( Uni�ity P�A�F997. � ��Ostafe�GHI.E. Shparlinski, P�Yra����s+hash ��s��� ���E%�!Xm:, C ��mmun. ���{�4e(�(7] C. Pomer� A Ta, Two S� s,�R�#Am2)`Soc. 43e~6), 147��148%��8!�O.c �,�Cba�� Yp��-�� SIAM�(II. 9 198��2e28e��9%`(Storjohann,�z<Ʌ�M�$�x��s#For�0PhD�]((ETH ZurichI�Z20�, von zur Gat���$D. Panario�v�:�MurveyN��1!�H01), 3–17. 20 ��Ʌ��F,$�6������B�����$}���arXiv:1609.02063v1 [] 6 Sep 2016 Zuse Institute Berlin I SABEL B ECKENBACH L EON E IFLER KONSTANTIN FACKELDEY A MBROS G LEIXNER A NDREAS G REVER M ARCUS W EBER JAKOB W ITZIG Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes A version of this paper is submitted to Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal. Date of submission: 25.08.2016. ZIB Report 16-39 (August 2016) Takustr. 7 14195 Berlin Germany Zuse B�HTakustr. 7 D-14195 -�XTelefon: +49 30-84185-0 ax:��125 e-mail: bibliothek@zib.de URL: http://www.z �ZIB-Report (Print) ISSN 1438-00642"�Interne%42192-7782 Mi��� 5� in NoJ� Proc%��I∗ Isabel Beckenbach1, Leon Eifler1, Konstantin Fackeldey2, Ambros Gleixn)l Andreas Grever2, Marcus WebA0<Jakob Witzig1 1 Vbh, Department Optimization, 9�, .�, M , {b�,e� ,gle�,wz�}1��2���PNumerical Mathematics2��� 2��� �fa-1,g%,w! 0 September 8,�sxAbstract In this paper, we pres!a new, o=�-based method to exhibit cyclic behavior in n6,stochastic pQ(. While our T� is general, it is strongly motivated by discrete simul%�ts of ordinary differential equ #re ߁��n6��biolog%��, in A%(icular mole �sy,. 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ACKNOWLEDG�C��:!�f*��ly=.D�A�7�i� I ce F�.(FWF) G_K\ No P23499- N23, FWF NFNxS11407-N23 (RiSE/SHiNE), ERC St�2�gJ(279307:;ph Games�Czech �_/IR :�GBP202/12/G061. REFERENCES Parosh A�3�,qvros Aro�Z,Bengt JonssoO�K�8�O,nos Sagonas.�4. �8^2z�4(POPL).zizf�� Moha�S,Faouzi Atig,>��,Carl Leonardz����.��t��MA�� �A*a�TSOePSO��2. J�j7,, Daniel Kro���0Michael Tauts?;�g%�33\�r� �ii_E���B!�ed>�� of C&!�S3�.�U$CAV. Tony �, Shazy, Sri�j\K. Rajamani, Jakob Rehof �Yic Xie�(04. Zing: A.���e��"�3�I(Aspvall,5 F. P�O nRobert Ec Tarjan.f!�9 7�-N ��%��:tru�Pcer�; quA���Uboolea�# @PLM`�3 (1979), 121 – 123. Jean-Marie C&�!�J�Tes "� 3. M /�7- ofs2 ut��$�l� �(In SWAT. E.L^G", O. Grr4(g, M. Minea)D.�o99bM�� *l����S�&00. STTT 2, 3 (�,), 279–287�u�E.�^ Emeru� A. P�< stla�$86. Automa�w6�5 of Fye-���e]" SLs U�� Te�6$al Logic S�5"�#CM Tra �P>m . LaH�.!��2!�86). Edm�e=T Jr., Orna=[��Doron�E�99aD6!q�L. MIT Press, Cambrid-]$MA, USA. B��*�Patrick�a6�1�M��:p�-�edvdSC��T�c�P�*�e� ��6� ! SIGPLAN I[�n��vonf ^ce5 �O�$-Or�edP����,%G ems,%Vuag�X!"Ap�?� s (OOPSLAw�<CM, New York, NY%$, 20–36."�H\doi.org/10.1145/2814270.$97 Azadeh *% Zach �K=%%F2.F^param� � *"j�b��u�UbF�oIi�� � ���o�7�6F���P�%�09| �8� DSred/P Atom[V�V?`���+�C-c 2a9I9�e&: j5.>�o_�RL�:�2 �N. �{R. Gar}`Dnd David S. Johnso�q$� �dAY?s�'���G_"�T�V,7NP-:�lsPP. W. H. Freeman & Co.J6 . P..�����-�p�M4H�� BlفQ� : AnA��r�r ��S3!�EFb $Problem. S� ger-Verlaaecauc�YNJE��a�2�!>5���abyX���!�E)�b�(�:6��:!wI�. FMSD 2��  1,5), 77–101J��$, Gerard J lzman� (Didier Piro*`�.��%@�ss"�C8: g Re�`5~7,�T�9}22~241�R ff �AܥO�"6��.�-J�s�jV)OLDI�1:36 ��e�e K"�K"7, Olli&.!�4Keijo Heljanko�2.-��U&�in�1 ed Tp of Multit�6��s..ACSD. V�Ct 2 , Chao� ~�A?  Gupta{�� Monotonic^ @e � Symboc�PJ,t� �f"�%f�* Shmu� ��R�O 2. D�W�w�C�r� al|h�Q� Collap �P��K. Sci1,��92), 33AU(359. Akash ?+Thomas F+1�� �"�A!�U*z a�$j  to S&�\-i\ 35, 1e\> 873–97. Leslie��a/78. TiY_�C�8� �����of Eve�#�i�EDis8-d ���Commun.��21, 7�@78), 558–565. 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Theorem 2 may seem a bit surprising; the key idea of its proof is that typechecking may require expanding recursive definitions, but their parameters only need to be instantiated with process names from a finite set. With a similar idea, we also obtain type inference. Theorem 3. There is an algorithm that, given any hD, Ci, outputs: – a set Γ such that Γ 9�, if s�a!�4exists; – NOno Γ �.5�4. The%p�s!�0arguments in % dure.cE�t4< freshly created 7$sses can b!o�ferred automatically. Remark 3 (I"Ding introductions)�AQs 3yD4 allow us to omit� annota5�4choreographies%.�� fun bUexpressr at�(are known (E⊢T �us,(grammAb�write:{� a�, our example)}, same reason�could!, adop!E to i! miss"24 (p : q <-> r)��a.y��y6j(, thus liftJ! pr� also � hav Ho think about conne-.\entirely. However, whileT type�)� for>��0do not affecte�beuour�e placeA�A�2��H does. 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Given a6��C,C$transforma�� 7P(C) repeatedly applie r)Ting procedure until it�`no longer possible, start3 fromu�inner-most subterms in C. For each �$ if p.!T0en C1 else C2:h, let r̃ ⊆ (pn(C1 ) ∪  ,2 )) be such)_,[[C1 ]]r ⊔ �2 is un%�<ed for all r ∈\�;�n � <= q :��!4replaced with:2��8p -> r1 [l]; · �; �n  C1 e�-�rZ-�C2 By�]ds of %� and EPPA4semantic#PCE�geAue 2�Pperties, where →∗�FE7$itive closAof$(. Theorem 96�Let C!�6�T. Then: (Completeness) �A�is �ed; (Prm�e�)5�σ, [[� (C), σ]]6:�4Correspondence:�G-%D: –!�G,aσ�(D G′ , C k�tA�G,�D) 0 �6 ! �� ;d " ��Nk�>e���!� exis!H′P!�� U�� f��6 � 4BB��_>���>>� . Proof (5�). :�bB�0are immediate6 AI%�>�%�~of!�$by analysiE�A��z� Q�onsEg�uinteres��(cases occurA�%fU�on�asumes a ��. I *?A �C)R��FK��n �A�also has�ס�ume�$label sele�ȡtrodu�F�ρ�� bran��ak��,n order to r�?%A(C%�4). 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DeepPa(:  Class�� *� ]olu�|al Autoencoders Eli (Omid) David� Nathan S.Ơanyahu1,2 1 arXiv:1711.08763v1 [] 23 Nov� 7 2�� � 9�u� Sci!0� -Ilan Uni�|ity, Ramat-Gan, Israel mail@elid�.com, n�8@cs.biu.ac.il C��r��)$ Research,e�|Maryland, College Park, MD, USA b8far.umd.edu AbctYis paper�describXproblemh!���c2��,ro�a novel�roach ba�on deepw =��a9� nId�nMd. 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(iii) I+ and g areDl, their c-superdifferentials*�Cdefined by (2.30) ∂f = {(x, y) ∈ X × Y : f (x) + f c (y) = c(x'},8�g^8� g c :�g67�. ��i.��on X ��n� 1) >z� ≤ |$ for all B���,%4equality holds!X!+ only 5�. We cO2.|lthe (generalized) Fenchel in[(or id![ty when:v�\). Theorem 2.19. Suppose!�< cost function c% ontinuous�bound!� elow��$re exist a%�L1 (µ) 18ν) such that c%:pa + b. Then, a coupling γ ofZ pairN, @olves�|Monge-Kantorovich problem (2.26)!S._there ��skU���f)��,supp(γ) ⊂!� c f=�!�G� Ga 2��ot!�Dal. Proof. See [6,�%�1.13]!��r!� is result%alledk(Fundamental: of Optim4ransport.  By#%�%\b��(or, ra!! , itaB�4) can be regarAas encod!�! soluE7to an o ��t�1��.�% the Jmnot6bT but satisfies suitablA� nvexA�`properties, we may modifyA��ni$ manner ofE�72�mu+ h��k�is� bA�EH.6",still applic��O. LOGARITHMIC DIVERGENCES AND RÉNYI GEOMETRY 13 2.4.2. c-divergence. Let f!m�aY`� U`��. 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[3]�1z� verm�@nd Elchanan Mosse~�.A��>resampl1�In�ycee#k 3%�tnineteenth annual ACM-SIAM symj% um on Dis�I����s, pa��268!U 76. Socie�;or Ind�����Aeed Maf�s, 200!�$4] Yuxin C�C*�ho Suh�_$Andrea J G3 mithY!Y�rO�Z !lwise ��T_�� EEE TransB�L�IFO@Py, 62(10):5881–5905�$16. [5] ViICh��0zhukov, Denis�t�;�(Kengo Kato.&_+2,��N� ipli�9ot�%�pe�e��aAlsumm"Fx,07�24 Annal/�S{�,s, 41(6):278e819��3��E[6] Oliv�Col��LArnak S Dalalyan. Mi.A�in *b�}7�im� for >���.!g Jour5-�4���Zar�n Re�X@, 17(1):162–192�!�7]A#,o Gao, Yu LuI' Harrc�H Zhoua�te-��g[��o.�� �)- of6-�3%-�6e�265 ~ 5. [8] JAltig!Bound�/%�a2*Bf5��e9f . arXiv p��in�0Xiv:1312.1207� 3. [9] Pe%b$D Hoff, Adf E Ra=bB��naS�r!�(Handcock. L.Z�Epach�o soca�f���..�� ameri� UB�a��?T, 97(460):1090– 1098��0��410] Johannes K[�0r, Uwe Schö!�)�0Jacobo Torá-�%� isB��: ���sY4�u�9�P$lexity. Sp� er S�yce & B�!Media��1�1] R Dun� Luce�Ndivid�����: A!�oF %�� sis. Couri-rpo��, 200A%12A�eng MA�(Jonathan We��!�,Philippe Rigz��02X%�e&���waW n.�>P� E_$:1710.1038%�,17. 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AcknowledgAs W�|��!�E��iS�N�%�8V author� � �r*�UC Berke�Ch�zor FeA� ship�MLse!.M��u"Ӣ* ��lorida &�s Depart�\. :��J. Amos,R9�T��apman,A� Hine�/,J. Paixao: SN#�o�Y � D6�Ch1�/��N�p� �, ԑ�g�o�7}� 7), A50. ��S.2z�P.K Jmo , D. Llen,�nd�Marh: E���a��SO�� �F.�r9%k�S���L�$, Canadiann�t\ll. 54��1�" 39–43. ��J�vzx�E. Dobb� B.�lins:��% &SDom��L No A�, Commu��7�2� 274�49), 5813–583;�4]!4J1EIJ.�p�:9� 5$s, DevelopA*q]E �, ��-Verlag,�� York�0��5]%�:��F. *��: Non-Uۯ6��:�ic%�b%��c�A��tic�y, Pu!nd Ap�#�d6���vF� 278,A�A� &�`l/CRC, Boca Raton, 2006. �kR' otti%�a|!� ic SN�A��QU�"ޘ�f�� Its �� s 16E<6). 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Key{ds:V�, ��)M�,5J.�)Ε�, R��,:I:N�$ݺ�,^�soI��,��ye��.D���io%�A"G-:�s���/V�� (RBF)V�n�Duse3MLSa�A~a�A@Jv�ed`� A@I* For �+ �a� =�/-BuhC�’.G~�ve�Iq�Z�tZ )��2e �1&:�E�z�pot@~al�ory�����mat"� 9�yE���7thA=7 Ef� "�� �S�Ni�on�B :6:G����i�� ce k| l >���I�g���yۂ%�e���a�"on�*te�in ���R��es%�J due �u"����I[��NS�d-�)(t��C�(��di��al�;��cosMBhuge >C�+�c+�er reR��s΃2]����iA~ availM  todayV���A mov!le '�� (MLS)*��[3]. ���� whol��m"� edur �!� glob�.o �q ill-���"R�Z-�p!!��Hğ�,few newa1>�9e!5�!�� typ-lle� �M ��R��+Q�m5K wa!�k��ofY�s and g<eometry. The sympicity guarantees the reliabilof�se methods with some conditions. In particular, we present Q0direct and in (RBF schemes\ their local spline vers_ T�st �|is paper is structured as follow� sec�X 2, a few boundary-type6���r�`ed. Firstly, we establish!� 560 Hermite BKM,��n�dBKM is introduced which us-fphysi�variable-stead�expan�0 coefficients%�� )�� has great potential to challenge�BEM!a typn� 6numer� technique. We also strongly recommen%�h nonsingular higher-order f!`8mental or gener!�olu%�as!�%z8for approximate�res�of]K� = . SeAq-�deriv �� pE��l5 $(BPM) by u�%multiple� iproE�princ%�RBF)f9�M�BP!�% proposA-ItA� noteAat unlik �Ea; does( requir"A erior nodAPo improve accuracy. SM��3iconcernAOa�]domainE�� }V. B�4Green integralA�� !oq��H modified Kansa’sMm (MKM)M��caf cates boti governing!EUe equa!�s a� same5� �a��ii4 significantly1��Q � 1U)9neighbor�Q0. Furthermore� develop%66dAv the MKM ca@�O!^(finite knot-  (FKM), i��pi� � pars.'!t rpol%4 matrix. FinalAʑ��5%�luA�s�\$remarks ona3se novelA��5e�Q��� R��A�!�E��tE���V� �bande���tF��$ Rapid cal��!�MwaveletsiQ scala= alysis of^A�Q*ion ar�W8 briefly discusiE$n appendix%��ga�a �eK2J� �:�elimin�Ddge eff�k of g��ica�on�)���,maging. fun�(ofda"U�L [6]. Since early 90a�,)���� �s �ܹX(PDEs have ba�mx�:Among!+m famous%#Ate~Qn [7],1 � }�t.a�[8]%�A� of2�qH< (MFS) [9]. Most!)�eaw�,=�0 author [5,6]qC���ey�2�B�+\as a competitive alterna !��MFS;fact,%a ier than %!k0 pioneer work) Nardini�8Brebbia [10] inEy 8-��$out��w�u8RBF terminologyF exis�C���s,��lie��7+dual re�?-dto I|ively]�)�Y\�i��ntext ] �� elez.��T� orig�3� %as ris%H curr%� pop��!���,(DRBEM). AllA! abov�3 �4s perform exceE���nI�wn Y�experi����eI�%� O [7,11]��nvery f[ r�iF%�( easy-to-us��0rit. However,S hloT � ��2/�y du%3� mixeݨ[� !��/�Xn-self-adjoint operator.�F� [8] �co� qun�4al drawbacks i��B=. LFy �, hJ0still suffers� ejly low �1inUn��aa� region �MFS ia� simp���d���[ma�� <shortcomaj�i���co � al � � alO outside& i5 impe� its pract� applicŎs [12]  BKM ��surpasM���t� it employ�� -s� F� �i&� �tFSE�1�f*� �T�refs��re! ,no longer ne�;�o U4 arbitrary fic�*�1g�.^ �f� �AK[ can {iZ)�te�� ����%,ed ��y6 blem� reU+few��  [13]. O� �oG  hand,!C�i� �!T�A7could� yield*W N�@ �l)( just "; E�Q�i�}�� t wh� volvAs���}�In ad��especi� �~ th p� l�U�all�Ha����� "�pglobalE&i�� �a�m.V�  ra%��F;;use"� basic"[d 2 rj = x − x j 2. Nn norm�ϕ!�!crade��a� > . ByAq�c!&� o re�e� (5)�,xac�^8satisfy Eq. (4)� !SE� A��u�3 �e��.1. Baary��� �s. t�re��Q �� �d, -ba%4  � -fre���J �`. S� R  demm �ai � �Xedi� well!. 2DE03D Helmholtz,&� % conv -diffu-pr.��c� }� y i�Gaim�=udy��to.Rթ��rand"  KM. To cl illust�$ our idea,����� e f3� exa�Y� los3 �~@ity L{u}= f (x ),E�8� Ω , (1) u = D"�� Su!2a) ∂ % = N .I'T , Xn (2b) α = Aϕ−1 {vLi )}, up = N +L j,(7) (8) wh��Φa�aA#�w"f!�� �@φ (rij). In mostZ��y:�e�� �]Nis ud b�j��� A��t�� valu�a�corresp�Tng ϕ through substitu��φ��o A]�eS a��H L. Ref. [14] favor�B thin plk�(TPS)A�|R���w.� TPS� only(���b�&�oN( 2D Laplace�� �A�vca�� @�� linkagc V�sZ� B�"}a1J{�. 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EmergG tech: ies (Wang�HBodivitz, 2011) hav� cently en��d us to collect proteomic data sets.~�resolu��.se+refGthe vari��YinV8ressions across��s� need. � ique�Kion of6ular s2�0s. Typically,>�� F�core-N��bas� a1�of�Ls,�Iignal!�ex� .M ant :���subsequ)�!�@ied. In Figures 6f(7 we displaH V%\!nA��iA0��on vM�%�%�Pof Sen et al. (2014). t 8 show� post-cl�ing>TI�� R4. AcknowledgeJ4 Radchenko’s�(earch was pY!� sup34�NSF Grant DMS-1209057. Computing A�$urces wereAivid)�!�$USC Center�$High PerfosceIE� R code �>y�uAforaduc!]!numerAo�4%Z�cA��F 4 can be downloaded from http://www-bcf.usc.edu/˜gourab/code-bmt. Re4ces Aitkin, M.ERubHD. B. (1985). Estimew$hypothe��tes!0�n8finite mixture F(ls. Journal��0Royal Statist�,Society. Ser�l B (Method��"P) 67–75. Bach, F. R ��H!�aoui, ZEq808). Diffrac: aA�$criminativ�=d flexir framework!�� Y�e) Adva! � Neural In%�%�Proces��T Systems, 49–56. Bel.S Niyogi, P �T1). Laplacian eigenmap��spectl�t�~��embeddAAD:��DNIPS, vol. 14, 585�91��ndall, S. C., Simonds, E. 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IvenA V.N. .�F.W. Jon�TS.Y. Jun}hKaitaniemi, N. KarakatsanisE;mitro 4elsey, A. Kimu!/T. Koi%� KurashigeE[�L� �S.B. LAXF. Longo[Maire,AFMancusiWMa��I�MendozaA� MorgAK. Mu��$T. Nikitin)��P�!�(P. PaprockieHPerl, I. Petrović�@G. Pia, W. Pokors /$M. Quesada% Ra%�E~Re!A. Rib  stQ FA? F. RomanI�Rusat G. Santine� Sasaj�D wkey�I. Sh!�I trakovsky%L@Taborda, S. Tanak)ToméSToshito!�N. Tr!+�Pa�TruscoapL. UrbV. Uzhin^�J�(Verbeke, M. deri!v�L �na��H zee� right!�M.  T. Yama��a� Yarba�7 H. Y�da. Rec) *�&� 4. NucZ  I��L5�M�in�]�(�eA: Accel��o��SS ro| , De� �Associaw Equir$, 835 (Sup�  C):186k 225,��<6. ISSN 0168-900F� nima��06.06.125. [3]� io L2� ��mpi�:� �p2�pr&; ��H-scale s��t'&� s. Ma�’0�sA�Univers��Oh �7. [4]�WChatrch��V.��cA.��SirunTumas W. Adam�dAguiloE�BergauerE_$DragicevicE#0Erö, C. FabjA�!�n��at a masB 125 GeV � �$CMS experiA>-n�30–61V�� r�(1. [5] Kyle&� $Juan PavezE� Gilles� . A� V� ��i���calibrA�5imina� class�B0arXiv preprin�4Xiv:1506.02169%�A46] Arnaud Douc!cnd%�L M Johansen. A tutor��o*�fil)�n�smoot~�: Fifteen years later. Handbook of Nonlinear Fi D8, 12(656-704):3�<09. 5 [7] Rita�a Dut�J ukka��and�Qamu" �a���LMichael U Gutmann. L" -free y\8by penalised lo� ic regres��.ZS 611.10242�<16. [8] Eirik En��, Chr�an Y Car� H, Reuben D Budiardjo ��WZ hlborz Bejnood, Ross J Toedt�N<nthony Mezzacapp�U!�Hn M Blondin. Turbul�\magne�field ac�f�from spA  SASI�s: ���c� collapseA ernovae%t,proto-neutroar v�z� �.� Astro� �H Journal, 751(1):26%L2. [9]�@@Gleisberg, Stefan eche,=Kraus�nherr Schu!�&Siegertiy J. W� r. E"�� �1.1" �A� High� u, 02:007�09� �X88/1126-6708/2009/02/00�R@10] Andrew D Gord68Thomas A Henzin� $ditya V No�}A�@Sriram K Rajamanib ��!.N  Proce���� of S Engineer4�p�p167–181. ACM, 2014. [11] Fl�n H�g, Jus�HM Calabrese, Björn nekWThors( Wieg��% as Ha �ta.�y��f�tochaW ��E�$ls–theor'�d�� . 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Vittal,.K�D�D�e�(oQof2���� #,/CIGRE joint�� forc!I) termmOks,|OC�ns.%#�.,� . 19, no.e0�pp. 1387–1401, Aug 2004. [2] H.-D. Chia�_Di�J M�8� !�o2��E�-^<2�#�:=Eore8��F�Ne�, BCU VgC�Ap,]$@s. John Wiley & S�LMar. 2011. [3] A.-A.!� Foua�+.��%em G$ ientJ�� UsA��N' Energy Fu�� ��.t@�nc_ HaA.(1992. [4] IAAsk�x��UP“ L�f L�s�B_\6m�� �Y�uz27���Baaar�RU �M)%Q�4I4,I525A533, NovA$@89. [5] Y. Xue, Q���a� S�$of �H Mo���g�"� an EV�2�). Nanj�aChina: JAn su S�o�c�� TechnA�y!rss,!j9,�6ese. [62Vo���C�m(ol. McGraw-a� EduIl, Jan!�9a 7] F�,shiesh, H. Ey stafa�(-R. Khatib,%�el���M.ansour,@���`]li�v� >����&�%Pa���A��5mit���ZE���%}��Q$Smart Grid��3I2, �64A�652, JuneUA�8]�)Liuw�dThorp��}�A�5niG& �.6�f�E��s"~͸_� ��TM] ��{on�mDisM2a*. 142 �M�35�360� 995. [9]!�Pavella��ErnL'!�,D. Ruiz-Vega v%_���� s: ah`""�'��s�&Y��X(rwell: Kluw�$cademic Pu���e��$2000. [10]�. Gur �1nd���ajapak��“Post-!����*m�S��&�=� ��6l)*�*�N� P�N�J�N31)x�5�O<3656–3664, SepEP�6� 1] T��o%J. 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This paper reports on a most recRg�@rehensive benchmarking activity which was independently performed��<the context of Hierarchical Task Network (HTN) Planning based�ASP. D�consider_stancesZ$several pl B problems, � are trans �to logic)\grams and solved by invo �n answer set engine. These experiments a,relevant, as��y%J! systems1<important domain�AI�on9z i�)xT(really used�!�1� p<. In particular,.O<DLV�XSmodels (version v2.27) ]d �behavior%zjSummarizA*0their finding�B��,%H authors state that�\was significantly faster"�n�inDir.�%�0y believe one!\�$reasons foG$is is grou�%�1 requires -�`predicates, creating many @=�oflprEY clauses=�ofta��rQ/. But=� ACM TA�an�Don Computational LA�4, Vol. TBD, No `TBD 20TBD. · 49 alsoa< clud-c!bet!Q5!not(only source%/$DLV’s suA�or�1}� } �:*)� tillR�rune��oa\-:ti�!7vide�T DLV. 8. CONCLUSION Af�an exte����d!wmai��f!�NalE�theoret�w rese��}0nonmonotonic ��databas!�durM�( last years�o�i����nDs became available)� caa� utilized�adv���d�0powerful toolI������ in a high��$eclarativeA�nerM�pr%<�)Y.back-end%�!��A�� Set PI��me8(ASP) paradigm,u�o4 soluA~�s�m�al�a�� enco!�I� �Hor�;( sets) of a2tXory. Ia��i͘ , we haveau sent��heEX�j��is a �7(-of-the-art:�Adisjun���e6�� unde��e�D semantics [Gelfon%�\ Lifschitz 1991], enrichE� further�V!�languag�struct�����first �a�s docuAW!R)�@a wide survey ove!U���G aspect:� is M d, c:!�techna , methodoe�al,E� appl��� W . St�Fng fromi� posi%�� core-�5�9�illustra!�@how knowledge repa��niI���o�p��eve%�a %3Y�!A8lexity, can be }(ly>���5�followlha Guess-Check-Optimize (GCOy. F)�mor�addres���-A1$vby�vi�!m�(lete picturյM �B2���U synt�5c fragAC� reof�$;��2loi!A� uby handl! D of l��� �� efficie�. Oa��e&�D� �Zana��o��� trib�Q thA�� M��iscus�<$a thorough�t �tB� �;(carried out��� �����"� !���s,6 E�various6A�%nwith &� !9�)�%q:& m� some e��nc鑡n%^arisone similarmRs,%�ma!��v��r rangE.m�bil�,and, due to !� built-in �ߍque �sophis�'a�process!�of���-(2 , i��Csui4to deal �(larger amou! of input:Bby�e�exAz ness (upW∆P 3 -)_a%�), it�Lcap�sof�N�E� 7�x� %�E ar6�Y/ �o)�a�iv �is lim�e � E��iA�,e Polynomial"� y. This _Hdissemin%d��cademia�xv umab|  lso&ind�:�+de���; texe�iofE) � emerg! I� of K�xManag�A/ In EIntegfon�psubjeceAtw� tern.{ ros f�QE - Europea� misY X, namely, INFOMIX (Boos%�Z���,Av_< IST-2002-33570) �CONS (� llig��Cvnt.���S� J� J132429)U�2" ��n9�pursu�umber!SB such� CFWF (A!��i� �1 ce Funds)� P14781����-� �d"� �in%TpLudwig Wittgenstein Laborator�&.G �s (�-�$ Z29-N04).e !��K�lN educ5� urpo��in cour �o�H�>4on AI, both in9��� Amer� uni^tie 2 has �@employed at CERN,�UJ���P�cle Phys� lo� 4d near Geneva,*�dvx �d�C ��!l�?�� lves�)lex*�manipul -on��-s� � �` �Polis�any RodAE�s S.A.q��sEk� �A>detec�of price2�)unH�� ,confi��"�iy�*@ �p&p 50 tby� �Secur%�E ExchŲCo�. W7�){�strength: DLV –�(�#��� id 6� � . make� attr �v��X�1!\�sB�U��inuousG x� A�im���� �&%�,"� �"� enhA�� ��. r develop� �w>�b.Min fu � � ��.>�aggreg�~ ot� ��f� LFX�,[Dell’Armi. 2003]Q(�ver� nven� U�� �^ofA�� acD�l�l�m � ��h�-;��sa�!=algYhmic l!z%!way&&.+ and :��� 2�ma�! �t� �tha���f re curWly &��gbEs [Greco9]�H�, refin �$  heurg ��my gene�p|  shoulE�ro\A@� Ascala� . F� �w>U�ach� < �b� ectGwe%d�*!� , as well��q0ASP� * A���us� �� �Umgbl� �)n�r5�r�]&@ ����" !on�Ρ����� %��y.�5!�gn��a-promi� "6%�ea� � $E�� � &�%�A�r l ie6�:��� rece% �� �˹ gra��f��a ���Wo�Group�q^��W�)��i��m� 2�k� �pE� �{HKNOWLEDGMENTS We wE� like� a5Tk Robert Bihlmeyer, FrA�4sco Buccafurri.� Cali\, Simona Citrigno, Tina ��L, Giuseppe Ielpa, Cha3(oph Koch, C$inel Matei�m Axel�ule�wh�hD�oem�  �Q�8Ilkka NiemeläE�Patrik �%M fruit���S:�mS< 0to Chitta BaraTLeo Bertossi, Jürgend, Esra Erdem, Michael Fink�%$$liana Sabb�<i, Terry Swift, �#��x �sha��h&5��sAT!e�/us�sugges�)�Ain�N!��anonymIreviewe � } valu�a���. REFERENCES A NGER , C., K ONCZAK , K., AND L INKE , T�,1. NoMoRe: A� eBNon-Mo� Re�ing�9$Proc. 6th : &� Conf.c$�)!�N*3OX (LPNMR’01), Vienna, � , T. Eita&W. Fab N�M. Truszczyński, Eds. LNCS / LNR 2173. Sp!�98406–410. A PT!� ! B OL , N.���4b��ion%(N. JN-�019/20, 9–71k R., B LAI!�H. A.)� WALK%��A�$88. Toward�w�� *�&N %��F"�s �"� �D�%3�.��,� Mink!hEd. 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R!],P, Abdel-ranhman Moham�$Geoffrey H\�nA>� �<z��%k�ek� ICASSP1n66�$6649. IEEE�!�>[5] Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, AntoS PChassang, Carlo Gattaex\ Yoshua Bengio. Fitnets:�� in �P. CoRR, abs/1412.6550�\4. URL http://arxiv.org/2*�. [6]9U�Eh1xnd Ruslan R Salakhutdinov. Redu"G$]0ity��� e�B6�S�%@ce, 313(5786):504A 07�(06. [7] Chr7dan Szegedy, Wei Liu, Yangq�3tJia, Pierre Sermanet, Scott ReA0�Dragomir Anguelov, Dumitru Erhan, Vin#Vanhouc� �$Andrew Rab�ich. GotAUU$)ol�e�6O�A8��2Compu��ViagpPa��n R.&i�1–9!015. [8] James�� tens�%�' via blJ��, 27th Int���al Co.�� MachA�Le�"q#73a�74e��1AL�9:���8Ilya Sutskever.Gy�>*I?f�� In:n ��8>��:|^��$1033–104i;1. �%0 Sepp Hochrei!�AVa Long�rt-D#�.��)�%^, 9(8):1)=( 1780, 1997t1]�K N��@raudolph. 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XI.�4LA�HW ORK�3Index���M��&�J)��i�'�o�jce as-M3���&��)"���,I��a� �"�1�E ��&B% �st����#j AE�o*[6�H�����,� � �d���/U��.| * �%���%� -to- � *�d�GC= [2�*13], n��GK-so��b6�107 35],"�.\@� [1��(A�per��l1�~�ran����C��*�y���a�5�-��� D Cv��Y�,�hA� �l�� ����vI�s,!"&��ն!��)��w GusfC�’�]�?�[D�"�i2� G:{., �"�]-��&g?tep�O�o� slightly �3o:�bMw>a�A��n�[�e*��6 %�.���ulm)Qal$� ��er%�moE��i��.&�_A >K?&e%&�_�&�0�� R)�?vA�H$�i��22/���?g hen JYq�thB-l��i llelb�!�:�����Ӂ�(I. C ONCLUSXo�I��i 8� �c��d� YXfo��n� � ��mp���.m Our �*QE0�6�*V&�&�c3�G���-fٷ"�M�iSJ!�Z4 enume��on he�A�+ fmV��( networks, �qand, as confirmed by our experimental results, the resulting algorithm works surprisingly well. Specifically, our 5�constructed cut trees for web and social graphs with more than one billion edges, some three orders of magnitude larger than can be handled by previous methods. We also discusse�4me applicationa�to �� data mining. Repeatability. As the imple%` I�70sets used in 6�Xs are available online,%�)� "co\tely rep�4ble. The propo] method isP\from http://git.io/ cut-!�?6$:��.A�lwww. cs.princeton.edu/∼kt/U�/�rhs://lemon.cs.elte.hu/trac/ �5 6.w�8snap.stanford. t6ih4aw.di.unimi.it !v@.php. Acknowledge!�yis A�( was supporA�Hby JSPS Grantin-AidE��Research Activity Startup (No. 15H06828) !�JST, PRESTO. R EFERENCES [1] T. Akiba, Y. Iwata PSameshima, N. Mizuno,�$Y. Yano. CmO� uda&%(massiveI�@s. In ICDM, 2016.A�$appear. [2V���jPoshida. Fast exact sh!$st-path di!�8ce queries on la� net!R�s!EPpruned landmark labela9�XSIGMOD, pages 349–360�3. [3���DLinear-time enumerev4 of maximal k-!�-conne��sube�s iN��random��A�!`(. In CIKM, �90�918�4]!:Asa!�XT. Nishizeki, M. Toyoda)�4M. Kitsuregawa!�M communit-N�I�-�u�u a�-flow !�,a site-orienA�frame!w4. IEICE transa�%��ia5�m)Alsystems, 89(10):2606– 2615�|06. [5] J. Bang-Jensen, A. Frank �HB. Jackson. Preserv�=�n�� crea� local��1�i<in mixedU� SIAMr�Discrete Math., 8(2):155–178, 1995. [6] P. 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A}� .� technolog� kes rapid~ de�2F��witnesq �� adop�$, quantify�h6��afX N an�ort�0problem, both%n analyAq,from a�al�y &Q ��*Tnat� r � % P �"F �� assum�� or tu1�pur~ !�Adis6~ . Our� �al �dem�� �e� � A is E�to!-�v@easonUj�� �a�]� DNN�facA.� . RelaxMe.��i!J"T 7ed ��rci� dir��  fu%r� %`o ��isticJ���[. R EFERENCES [1] [2] [3] [4] [5] [6] [7] F. Schroff, D. Kalenichenko, and J. Philbin, “� net: A uQed embed��L-&� a clusXng,”�TCVPR, 2015. M. A. Turk-<A. P. Pentland, v2�us! �e"� 6W�(1991. C. LuRX. TangKSur?$human-leve��"ha� �n lfwa�h g<�w AAAI�U. S. G��OU �ex!92��eC�O: FBI�uld bet�ensao priv�!Eac�u@2016. [Online]. A��P: http://www.gao.gov/�Pts/680/677098.pdf UID� “AadharY�7VY�� Y s://�}Tl.uidai. gov.in/uidweb D/dashboard.do T. M"��J% Thomas, Eex�I*�T^ @y. John Wiley & S� 2012%�(Whitelam, E!�borsky,AABlantB. Maze,vda��ill=�NE�ka4K. Jain + . Duncan,�AZ et al.%�XIARPA janus benchmark-bI��%NinE��WE<7. [8] [9] [10a��1a�13�1a��1a�16�7�8 4�2421] G.�HuE�$M. Ramesh,� Bergi�(E. 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I- 11,��^�z��Rapproxl��-A+�$16), which��ASM��j+�t��Eb:)��> 128� alsoN��| Martalò-Tripodi-Raheli (MTR) Z [34]��E�11B � sak<Pi%adapt@ @� C� [4-root raised-cq I�a�a6�lwr�he� � � il� out'8{Vm } as Vm = A X Ψ(mx)L+ℓm@6) ℓ=1 where E@, ., buΨk�defina } � "�"h is YGTXm ejΘm + Zm , m≥1v7)o�pro�� {Z��i.i.d.�rly-s�ic 2 !i,lex GaussianCemean 0�\E[|Zm |2 ] = σN Ts whili�y��}z, first-orderAkov'4 (not a Wiener�) t�a�-invariaQ - �i(probability5 a�kf �2��θk ,!�8 ∈ [−π, πa8e have pΘk |Θ '�(6|θ � pΘ2 �1>�6� !z� �1space��o ! �nAl.sta�A�a�R���i�re"V�ean;��i�98�t� us �!�ut' � S oneW.��HI�b>QAm� i���)�,�;*��5���aZɞMTRn�2W }��s !�uF�E�i�ing (1Řat�valid`"G�tgr�=X.+ sC observ.]11/"� : 1)g���ASM%�� satu� �  below?� �)��.�"� �� impl!��� .5 �results�.� loss0 � . 2 �Ro��)��i>!� �n���Y�SNR�n2���U=�%pR��incurs pKnoB��q��u[���M�� .���/A��giacc)�-, . 3)��i!7R%��t6��� .�� a��!�Eas �o justq� -/�!OY�ef�maH ignored�p�r:�MZ$� �ofR��s�_.o!�t aaue�.�entrop8<ource�� uld �� be surpri!��'impacq ��additiv> ![small�A���,�b �oft  nt  and/or=�c�nd (ily reduced>� consi�t^$memoryless"�Y = HX�Jf��xedsizM stelD (e.g. M f�)�� �6Wu� upper �L�("d$a genie-aidrgu��)& ≤ 3 Z) = H(X)�H(X|HX).��8) � term� "��s6x0 ambiguity du�� �randomn!� of H)+� al c� of%c� %, w �6���ΦX |+ Θ)�9) �A�furec�]v#it� of XE!�A7�A CM�>�� Θ. 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D ISCUSSION��author��[2Zreate: -off keyu�iEN��s� of W� &K�ɺ a double-��rec��� is���o� %�� Prmedi'�f� ency (IF)�*�,���e�� nvel� dete(  (k$-law devic�, a post ,!� ����y��wK AK$by optimiz�!�IF� band�b�� pery��Sle uX�(6A��)$F� � �� �viE�q����um��inc��Z� Ta�is.�k_Q}�we !��i of� es*8aw2v�WU [ � ai$�� logarithmM � z ��:;Dallal�@Shamai [35] deriv$6M�e erro� �b� ��(X� of!� I�ML!�Q�e� syst emploeKnoncoBnt demo���,e� as]�shiftq�(FSK), oe�� m�(OO��nL-poLY (PP��8Relevant analysa�0foub$[36], [37]%,re�ceE� reinA� @typ) invol� mo �OI�ed"�* . �26��rojeca�2* �to9� ��$kistic " SNRs 8 �8 X Karhunen-Loève expan��of U � �s Ag0,� ],� �Jxy �.pre-logZ1/4A�(44a��� ly 2N$ fA�Mresolu!$ 1/∆m���*_eIn ^words, �A does��!\�MA(og-to-digit> onver.(ADC)i�"� ev�"<Ts /L seconds. Ic adA�e & �u�wo ADCs e�A�e? <Es�G ng in�� offMby>r��laD#, j�� ��f�w� be 4 �o���x�X�nUADC: a �� �B�P ter#'nta�ate�an)t�r��, r , a��-�can6% �*W }��p.V2 P �|H% ly 1 �2q I0")�) !� o0�3 02|2�s 3/4.�αi!%��oI� to }�#pa. 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R R F���,"���" � >���o�?�4 xm�ax�6> � 1=E ���BA�oddY7:M I;����seL�.Mfw�z�0:�VA" (−\&���cz R1�a 1%��t =�z�t ��y t��1h�2�3��t2 ��atpM[� ���A.� �z� ����z) n ]�(1fY(1�XK�.0� ��+a+��I5%�r_�.J 4) T>` mpleD!�%��2E� >Ejas�z�-yq�X�|7 �# 2�%� ��t�Gs2 t +!� �a��%�%�� t� -��)eH�$1̙��to�6).�expon`�\�YA��;*G2  YM!U 2]!��!b� �iU{we obp�E�E��t���Bp� @R EFERENCES [1] A�( mir, Mehrotra�9@ J. Roychowdhury,�u�P*1<in oscillators: g,;f�tjS�y%�&�Omethod�d&�$�z� $,” IEEE ���.�,Circ.DSy�c: Fund|�o ](App., vol. ���no. 5, pp. 655–674, 2000. [2] E. Casini, R. D. Gaudenzi � A. Ginesi�DVB-S2%m algo�g s de�V�5iJ hf s�k lite�nnels� Int.!Won Sat.oz�m �Net�22,�3, � 281–318�,4. [3] G. Du�o%�Tar� �T. Koch��O=KiO���WM$MIMO micro5]$haul links'W.�y.%�in %��Conf.�zCo� (ICC�`4udapest, HungaA=LJun. 2013. [4] R. Tka�(A. ChraplyvFg!liu�}Lan InGaAsP DFB laser� J. L�� Tech1S�4)R11)S171!T17��1986. [5e �V�W�bI�E�L-locked loop dynamic�)A�� �4�!Onoise�nXFokker-Planck techniqueIProc.%>M�51 ��2�377|753, 196!.$6] M. 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Equ (3B2�lE��_���pt�`��L��W�N�r) �%! �3�  (N��$nt/!A c!b��2.qB�g�!�a .e.,�1= 0�/a|���LB����5 aQR� max_*4 ber H of�2���<$ex;F�cycliH efixw (%:ۑsyn�R�n� ).Q"�ws$ safa�8�>L  WF �&�!b&& �s)$�s6#� 26#or5#-L6#. )�L�)De �Eb�Go �e!��"�+���+HI]�u��.rz�2f�� <+k %#��"<�� ',6��I����&�x G� H ωi��n%�n,b� �0aH 0���1e �3&� �]ŝT�([�+�1 Es )^ ��% �NG{ E{!�!xUu�!� ��Z1gyAfzsymbol>? �Dj �A�]>��u�8�y.L� � A�$.�5�(ex�)�,B�n:Fѷ82BU 2� ?= ued Y �p��A�ɲ��r�!C'|>�$�t�q 16 k� 6q�7��a� �� 128 ���+!�d 8�%�X *%$C>�&Iin [9] c�Ionfirms this observation and shows that computing the Gram matrix dominate)De overall hardware9lexity S0power consumpi . InT\downlink, ZF precoding i X mostL$mon linear$@method [1], which*tputes xω = H∗ G−1 ω sω ) ere  chB -dimensional transmit sig�:Hthe data vector. IfGram -,Gω has been ��0d for equaliz)h�i �up� phase,P@n it can be re-us =ZF = =1; ?( to minimiz;,current opers s. Hence,|order22��-� com-� of6��!�, efficih waysQ<uteP!� =A`�ll active subcarriers ω ∈ Ω A>�required. III. I NTERPOLATION - BASED G RAM M ATRIX C OMPUT#P We now discuss exact�Lapproximate interpol%-ba!lIT�s%� low-�I�.��%"ut9. m�at� o.��2k� assumeA�at we have perfect CSI, so throughout ta�seca9�,1wi!GF� e�,σ = 0. In S (, IV, however4relax� o-CSI J�p^%$study%ormanceE �x�G5Awith im g$ CSI. As a�equA�T(3)E�=/cesA�A�FDE given by aa = Le�X �� 0 `=0 ` =0   j2πω(` − `0 ) Hb b H` H`0 exp W (4) 7 for w = 0, 1, . . . , W − 1. Given the FD channel matrices Hω for alQ� sR��, a straightforward “brute-force” E�$ach simplyqQ�s�] = HH���H u�e)iPv}O�hu�reduce%Z]�$of such a �i*achE= nextvN� A��-m�6�qTE�0take advantagE!� factm(i)ch:i(and hA8J1�)E( “smooth!I(o�r<rrelated) across='$s if L < WE� (ii) mass��@MU-MIMO causes an��a� knowa����en��ʼn0[2]. A. ExactE�-Ma�2�I.o T:PA�in (4)��a Lau�� polynomiaMs�x&!3variabl���=A��(I�,/W ); we ref���h��a�� [22]��,more details��^p�ce�9weś establish� follow!�result^�*b; afrt proof�i�\in Appendix A. Lemma 1. 6.�cm-0�]�X:w�=a�a��.e��Xfully�ermin�[rom 2L�'�1A�tin�*non-zero2���%$-points. ��n immedi�Q���] �l� , on)<y�e��o&F�*�%>ly �only ֣�ir�^�a� utedA- licitly. � �!��orm ��io�y,first define!�et�!� ) P ⊂��e�Hcontains |P| ≥ 2��9l9� ind!��Rden�Te k thd)z'ex as pk"� �k6�|P|�#, ~ a �A(�KrM P = {p0 ,U4�p F }. F� �m6���eu�U l�P��k�n=o1��-M|a,� �?A�.��,��W� er!�$ entry-wis:�e��g"� X� remai��B@.� \P . ��E�6a�cedurep%!�a��aF ��s)?a fixA}� (m, n)�]MOthe v^  gP �CA5� � isANstrucA�a4 Jxies [!< ]m,n�k�n (9��4P ,  T i.e.,r= [Gp0 <· [GUU���nɂ��!'� C|ΩA{�2�.��vA�9�F5� c�,!�* by y= F,L (F† HgP ). (5) Here, F represent� � × (�]��Ū�w$ we%B�+�r inde!� by PE�Ad� Llast Q�columns)�+W mz� rete Fou y A� (DFT��;6!8!�of   I DFT e/�x��ID�dAu[F%�= √1Wa}ec�, (m − 1)(n 0 . Similarly,9I9)* a (%�I |P|)�822�B>%�%1�%B� %A� �A9� wordsI�N�� �25) o� � �eI�Q TDE�� 1|�vthE�#!�9se elemET into% f� 4ency 8 10 i�41,1 9.5 9 88 300 �2 0th͛�7ion 1stR� 3i 320 *]I�H ω 330 340 Fig.X Illu� W��r�Zb���!�!�y�k1,1J\ ��ex�h��>�3�� y fifthF`ω�9i��6e� We[` a 128 BS antenna, 8 userB� system� W = 2048�@s, a delay spread!%L = 144,��� CSIFout BS- x c� ion. do�t via%<DFT. See [19]–"� addi3al� � otherj�(s developed�],small-scale,�-to��M� �$s. Althoug� :+is f to zlyB�!�)��xQ ���W6HDit is in many situEv s no ��c��u�A'hig��, %�xver�".a��F���, h� sa�a�)s unia�ly � tone�U�c2>��� "�a�d=ificand , Unfortunate�f "��ft�nfeasi� �i[%e =ɽ0ce of guard-ba�x X��in OFDM�$or SC-FDMA \standards [17], [18]. 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Youe@Effn2rchitec�0!�.�� �>�with �^-Seidel�-%�6��}T�CI_�!*Syst.a[CAS�2aya[U��889. [12U��-��E\de:=ab�h�!�de/�t.l�1or�KI�/3����94�897�03] H. Sampath%. “L>���LJ-t���B�%�^�faE�*�$*���un. Lett���6��-~ 239–241��02��,Scaglione, P�� oicaEfBarba#��a�A$B. Giannak�!��E���!�ig�or.��F7mR /Cde��r�_ V~50 ٱ�051!�064, Ir ��5.�2��u:��G�zeU0��/ � �%�Ś�s&w� �eed` cri]�onEq� �-�6 �47 , 2198!��2�/�)� �O[16ś0%�Fateh��D�dethal�“ASIC:�a>�in�� ��ٹ�Q�M_Qpaa�eh'~L�r�"�c���lY” ��_-S�c�(�M��7��175eF765A��֥7] ODraft S��; P�011:&% 0LAN Medium Ac��r�  (MAC�M Phys��,Layer (PHY) :#�A^ ; Amend�@ 4: E&A5Higr�Th��Dput, P802.11n/D3.0 ���0�8]�(eEvolved � ers� �r*��r?:Radio� (E-UTRA);�UkA�mod�OQX 3rd I�� !nership� �j�I�(�(), TS 36.21� an�16. [Oq� e]. AvailN�C: http://www.3gpp.org/ftp/Specs/html-info/36211.htm [19] D. Cescato,� Borgmann,�, Bölcskei�� Hans��A. Burg%)2 ]��B 6inE�:� �1EJ�Workshop>S Au�b%� q� (SPAWC" e 200�p�9� 94���6�MSE ��H..���R��&#��)&�6�2a��"� 6�� AsilomarA�#k� F��@d�[�2"x�0j194�4947 Vol.� 21.�V��"� i 2����%�� � � �A�a���5��71�� 1733, AprE��%��——E>B*ofnʫ sampled �unn�ircle���*B ��56, no���4�� 4761� �423] L. W. Chaiŏ�L �i� Y.A:Hu� “R5�.l��o���p�E al l��� }h��i2�� �238A>23i 24]4�L.� �.��a�>����9��*�G�A-� y3� �Ac1�"� e$ I1�6�112Ed�1) NIc�5�p�D�t,Björn$S. Kashyap..(C. Mollén,! �L!��Skowsky�Prabhu,!!$J. Vieira,*� Efripid| �F�8elach��!# D. V. PopeDis"�/centr�/�e��Lpr%C� &E4&> nd pla���(MAMMOET, Te�cRe]4CT-619086-D3.2�16. [26� ���esbert�:� Lcapac%of �M�`spa:S"vex�)�W-��un�O9 b �2�234"L8 ���P�But�kndV J. N!�l,"��"[#&���$ Academic�D New York, 1971. HUA JaeckVL. 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DM����R�bT (COVER IMAGE) 0.0093521026�0 11 �444 9�8 2�8 $47�4 9@ 98N�9-��5 ��L!5�d�<ces (�� }oa]�=��^�� �s� Qu�)v� �Hu{Nhe_mak�)�t��l�t�%��inf�2bl��tacke��oq>�fB;�)��: �d�!.�S (>F� &V.� STEGO2�7)��2)��2I�3)��9)�M 43I�0I'�5 @-�-��4 N89E�8 22< P ~y�f"�+!� AGA-��� �Lo-pa�e/Pi�6.m&VI.? � j � k THISTOGRAM FOR ORIGINAL�"%�-eS H��(�r�-�� ~� [pbGB � CB &�Cov�#��:-՛�&k �!+3al bal�&57BAifNR=u*/�juI�a^ play���c�'rol��*���l"K�iwr� !u� 4 CONCLU��#2,� "� 6�2*��UbeG�d+6ր�U�{2)ak in�Pnt6^�� &�SSS�1 crit�a"*a.��Lj�~"E�� ��G�S#&�H�’�.�t*� w� >}%�r�� kJ�.�$J�p&\%�M$ DRTal�� V1��i�-) E/� H{�� &��U��!�x� 1!LSB1 &��"*�\sC�l�]�d� >�"<"� E le m�;�b � `&y To � �%Nk�-sOT , j�()�^�$ ��$� d�S�#�$�/�4su& � �tE���x s"�U"� n "�8:6} �w Y�&?!SAu�"H  &� &�o-i !�) &u7��i�'.��Ri "�&�&bye��� �&)Y�J��4�8�4�.(:^�� combQ ~N��NI�,V+)�*m8R 03ll�(�mT�w8���C�l�76�&�(In fuC� �r�7of�F�s U�� II%  -III���C xplog �o�"Am��c�WTREFERENCES [1] [2] [34] [5 6] [7] [8 �910] [11 1�12145,T. Moerland. �  �*�!@. [Online]. Avail�X: www.liacs.nl/home/ tmS/priv�P.pdf. Mj�+XXP. R. Anurenjan, “A N�� g  H�f�M�)� uV Contourle*l(,” Rec�YAdv��� lligent C2�9�S��ts (RAICS), 2011. A. Cheddad, Jždell, K.�r�r� ��K�&�t��DY[��:� – surve�<*!#�f�l)r�( s”t�Sه PaC(4Vol. 90, No. 3�l0, pp.752–825. R. Gonzalez� R. Woods2��%I.�\!9�2ed., P�ice Ha�,PHI. 2001. W%1���ara�N� �,�o��&b��+! $amplitude,*}m!N ����PhD��sis, Nual!� ng Kung U�s ity, Taiw!�May�3. C.%�Qq L. M�ang%M`��in)�� �sG �*� J3�Q�Y!&Paa��nAgog�4d_�MWs 2004%�< 469-474. J. Xu,y�Yu�D. Wu�9�:_&ew�8L �����1�J. VisA� ��.-�R,I21I�1]h627–639. S. Lavania, P. S�LM��V�'anika=�v!G“Real-�<�l*;%� of: �iTZ�*E�#��R�!L IEEEe�rnX!�onferZ(n 6�y��c��� h�Re�, Coimb=}�e%-�1-5. G��,!/(D. B., & S,a!P.��M*.�S�2!��R /� rE� i=� ��.I���Z��8 Circuits, Powe�0 ���T���o�E} 2013IU 1188-1193EWM. BartA}“�#�Ape��u =r "� Auth�?� � .f��in ���|�U.S,M�O$5646997, 1sJ. TiU%�#�eJ ʩ��a�-� expa�aA�� `!. 1��A�deo1 ., v��! no. 8)<890-896, Aug. 20a�$G. Prabaka��R. 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However,ksu�roughput[xstill non-negligible. Hence, if�� IoT devi�8or sensors with �Tdata rate requirements��n}network%3,accommodate ��f-g. O .$other hand�!?]dem!�i �X (e.g. video streaming)/G� u�w �Lt be able to satisfy-0ir needs alth! ^1 relaA ly h%g$The second5��!�KA8EW9�9�scale-L�inten!Ơ, simply because more BSs means less load_!bigge i@s for each served�. I�is caseE�ASE�an ind-�Q�pe �!�U�aI%� benefit faC2�4 as long as it-EE:�(A��)MASINRs, � xamp!�I� low} codes��/A�pread e��rA�pechniques. 13 TABLE I: PatFss funca�Hs. lim E [E (λ)] F%�� λ→∞ L1 (r) = A min(c0 , r −η ) L2! + r) L3:� η �1 2 η (η−2)c0 ηπ ln(2) η 2 −3η+2 2� c2  0sin 2πD2 L4l20� 2 ) L5�e����2 β �v ��S c2 0 �2 βα .    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Single-slop��dels Wea�rtY^fam� power-law�� �-�$ attenu����pA�d by Lͪ�r�@ η , =�A�η  posi�!��� [42]a�u �)\ lear!_�n-\, since i→ ∞A�r 0 which:not physAly feas*c is%�ia.!�m�classA0��s!����idering.�fact,Jwas%�� [15]9�,SIR distribuE_(is independ�?� BSqH, a property referrAx�o�!�(SIR-invaria+ g (Rayleigh fa�l� ��s,%vextm d laa+1� Qa 5�!��3e^4]"s by checkm^� .�(in (5), (6) p(7)%A!�) �E �O etricsi�increasa�n)��theM 4 9. W1��aJ�� �A�tha��e one%�N *� by sl�ly�S�iљis}�Q�2��getJ��Gatb� desi!�-�ie!� D�� 1. Ej Ej suchl�sElR� mU), Z�  , �Yf� u�F η)��AsJ�a�ese6��� m�E]*� J��� � ionedA'�S�(on II. More���,!1.b� a�l.W�� �iF�H(Corollary 5a3ew�Tz�I�q�w���o� a�z� q �a Eg2 ·)�r0� ip veri� f��. �`bot� � �' trai�m�n�8V�decay�� e��t>r ccora�� ɮɀ�2�3. It:�4.R -cal�M�O����aA� per- �\� �aV���q%�F- a�A�1MA� %fc0 = 1���� :x�mit agrea��our�ult� !�fur�proZ1 a�ob�Ś hold�any��.�. 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N�  h i �−h̃I�dxɄ&� j} x Eh̃�  E ��2� 0 # !eʼnL " h̃eI�i�N"I A���e�x�] ��0A� 24�ݥ��tA� 0���BR (4���&R 61+t " # ��x� �@ fH̃ (h̃)dh̃ =�'�a� 5 �� Z1 E:@�21�*n o.��64� = Pe-�1B)�L {�(4�1 P, 2�+-(4�I� k* .]�"  (PDFWh̃. e�bsi�;� m�ndfG�!�v�;d } - by Markov inequaN2� �%�)�E[h̃�21 �  �)�O�O�1-I2 EQQ�.v�L#Q�9XQ��%b�'!'of��a�,��<&�-|2. R EFERENCES [1] M. S. Alouini�?$A. J. Gold�Mh, “A^�)of&�)mob�-dradio systems,” IEEE TraO9 on Veh. T#Q�ology, vol. 48, no. 4, pp. 1047–1066, Jul. 1999. [2] �J�S rasekhar,��C drew�)nd��G]5rer�FemtocedT:$: a survey�CommunwR,s Magazine, ��6 ��9 �p59–67, Sep. 2008. [3] ArrayJy,http://www.a#L.com/t5 /coo�UD-law/.” [4] Qual-F�1000x �Tch�Enge�c�s dA�6cinvOonm ies/I/small-!s. [5]>FDS. Buzzi, W. Choi,Han�G�A�8zano, SoongC. Zha “W$"(will 5G be?UJournm Selec'AeE�!;9�`, June 2014. [6] P. GuptaE� P. R. KumA�%(capacz wire�O1�%1:�Inf�*ory)�$388–404,�%�,0. [7] F. Xu�A>|� Scal� law�"r ad hocF���:d@or�7�.��9 X��F(� � Trend%#�NI��i!hE��1I��2 �$145–270,A�6. 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Fong University of Oxford Andrea Vedaldi University of%�ruthfong@robots.ox.ac.uk vedaldiF���flute: 0.9973 Abstract As machine learning algorithms are increasingly applied to high impact yet high risk tasks, such as medical diagnosis or autonomous driving, it is critical that researchers can explain how such algor��rived at their predictions. In recent years, a number!��<image saliency methods have been developed to summarize where��ly complex neural networks “look” in an n,for evidence �� 2��However,,se technique)�limitedAt <Pheuristic nature and !?itect�con!��ints. In this paper, we make two main-tribu%C: First'8 propose a gene�frame��UMLdifferent kinds of e!��nm>!any blaCboxY. Secondqspeciali!hento find! part!�5c0most responsia�ol classifier decision. UnlikeA4vious �s, ourM( is model-aA�!f!_testa\because E� grounded!�� icit0in.KIy�p�' s. u�X0007 Learned Mask Fig!� 1. 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Ie�� i�q,is taken to !��l��ke�$value αy u�1-3e�2A� not 2�b�� fi�� A_>���u|E � 5k4s α cannot be2C standardqW,, since some!A8are missing, soQ$�am$edOing%Ie`i� does!%adolvE M\8’s (Rotnitzkyu:01998; Dufouil2004; NaHal Research Councileq 0): ( X A�l i ) ri − 1 = 0. T h(αM�2��y��� aCsub!�o�+A/hen%�ed!�!�com.��Pst�F sed �Gs p̂q:xSi )/uK�a1-{.�y sam��cedurea!7SE��no>��(or xAi term%�bins ��400). VariancesA��u��b� sandw���v 'a���T, ignoring uncertaintya� α̂�N$9 5.3 E��nd)w �nd��nterest�)k4efficient βSzOB�. I5� !��m`V1�1��db&� N� . We��Llore bias, empirical��E9-basedAef errors��coverage� �dtes β̂Sz . 5.4 Results %�shown!(Table 3. CC!)always�ed, ofte'5:x poorly ing. Sm��, (at most 3%�!b true�E�(observed in��“��”��(i.e. N6ż�\set�4s: thiŠa s�-saaV( effect (Ne]�9)���a�_�� bove�k���.���rxlcU �� �eKwayi)large%��ples �i< vely. TakA�.\�s a gol9�, MS,-nd�g�m�� !kha�inimal:x�2)x5t0s). Precisionr MS�� �re% ilar, �$SM slightlapferiorA(� 2. 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Se�6�� nf-�on�po� E��!itera�!ly�n�o��lc<"by cor��,he error genC �:�.*Tmavwidp usedѽ�"#%�v+Q��� e fu� � �� wl wo a�ts: FU� %tryAwdef��NH<process explicit ��1�?I�ZJ�2�� �nEX,oit more adv�|v}frame�to��N[8ACKNOWLEDGMENTS��@�wA�uppor-�NaTal e�SciqFound��lChina under Grants 61771025 W�F61532005. REFERENCES [1] Juan C Caicedo and Svetlana Lazebnik. 2015. AcA� oba� localiz ��n�. In Ruter Vi�(ICCV),�5 IEEE IM"�nSal Conp$ce on."D, 2488–2496. [2]��jie Cao, Mingsheng Long, Jianmin Wa! ,Philip S. Yu�7.% Net:��"FtoadContinu��.��~���� 2��. [3] G�`hechik, Varun Sharma, Uri lit� (Samy Bengio�@0. Large scale on�[A�,�p rough�&. Jour!e of M�ne� Rese�� (JMLR) 11, Mar (2010), 1109–1135. [4!�ixiw Chen!uwen Lu anjFe1�Jie Zho5}�N �$ar Discret"�)�>]� *](TMM) �$�1��7�23��5] Tat-SA Chua�nhui Ta�Ric.�HE,HaoAHLi, Zhip�PLuo)�Yantao ZA[%�4."� D: a real-world web-���� u�Univers!�,of Singaporee$M ��y�c. YA���#*�h (CIVR). 48. [6] Li Fei-Fei/0Pietro Perona�405. 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CONCLUS w!��u� AV\Metho6p�5NBi&s|F�l@.A(Aa�^Xv� Xv�����u�o2!H�u�=z�n2 �)��k;>����K�7�a  &a3�T2� �a�x��*��o�� �.#�IL6�ts (OU�)&� �ib]a�an�;�V�d . D&�D*q8va�8� l"$Y�"���6�3� J�;�`Ax� same� um��^alJ84Řuc�K�H^>�Ib4�� e�o�w<x�a���d? �i�[wb�a&R6I+I��5�  RE�U@CES [1] H. J. Pes�q M. Plail, A�max�2PlQ?�� : A histo�9f ingen:5qG�sE I$ed opportu!�es,�Gy(& Cyberneti�uvol. 38d\. 4, pp. 973-995, 2009. �v J. T�ytts��S.�o���k)Zra�U�! X�J. Guid�G� �Dn;., �21 ��2 ��193-206, 1998. [3] Q. Lin, R. Loxton,�,K. L. Teo, "!Q-4&� � �ey�n"8y�&|�:�I�," JourAdof IndLmialt ManageeȅW c �10 ��1 �275- 309!X@14 [4] C. Hargrav�nd W.�d�; “D!za�NL��pr&�yL�c�`�cE��x10, nY338-342!x,87. [5] O. V�_ryk`(R. BulirschE �{/re*{��n Ann. Oper��sQ 372A357-373�92. [6yWng,A0Gao, Z. G. Wui� W. X. Zho# “S&Sy*2 ��b wo-p]R �B�iP>�� 2�35 �M�653-658%�� 7] A%N�R�“A InAdVR:�%�Lin Proc. AAS/AIAA As?JeP Spej5ista�Df., Pittsburgh, PA�A�AAS P�r 09-334.y D. 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By a theorem<LHerzog (cf. [LW12, T 6.3])| only need { R is a di! summandLĀpolynomial ring k[u, v], on which&4group Dn acts,!(have an one%}Tspondence between inde!jos!��,^���R�� �� ��s� � as an R- / . Leuschk�d Wieg@ poin!tE -',Remark 6.22]Jm2l��n-C!*���E�Af same�in non �arI;(mean!uE"dLalgebraic definition!�N , althoug)�)�sa]pmight not come from representE�!W� Z5�).AMreforee) formula i1EH,full descrip�6;6:fora>� . To� pute�HiNx>p = 2,A�tcan use Lemma 1.11. All in allA��e�s q5.4�Za�of Dn+2�$given by (e�r ≡ pe!U 2n�0 ≤�� 2n − 1)  2e  if e ≥ 1, �� 2· p   2 e 7−→ 1 r r+18<+ otherwise. p2e[4  2− 4n 2 No%.�Nexplicit�eledge�!�RM s ena� s usa�a�1~,F -signature���s! usA� [HL0�i11]. If�Y!�$ype D or E)�has FR (R,!E�)!� � HK�. THE HILBERT-KUNZ FUNCTIONS OF TWO-DIMENSIONAL RINGSDYPE ADE 25 Refer�v s [Art66]$77] [BD08(GS87] [BK05re [ 1 ri68!(i13] [dV34a �b Tc] [Eis80] [GS] [Han91�re!2M9C Kle8cKnö KSTm Kun7��] [Mon81Mon�Tri�L[Wit02] M. Artin. O�olated re�al !�ularitiea߸ surfaces. Amer. J. Math., 88:129–136, 1966. ^ Cove�EAT�RcDou�r�P�b�z�C2a8 p. In W. Baily��T T. Shioda, editors, C��x analys�Ynd���geometry, pages 11–22, Cambridge, 1977.l University Press. I. Burban� Y. Drozd!�xn��1:6S$. In Trend�6P!(orya���� d re)� topi�EMS S!�0Congr. Rep., ��0�L166, Zürich, 2008.7. R.-O�Tchweitz, G.-M. Greuel,��F#Schrey f�hNfon hyperM"6�� II!� vent!.U165A182, 1987E1Br��!�dS. Kumar. Frobenius splitt�Dmetho)71�66D��8ory. Number 231�� Prog!� A�ema� T. Birkhäuser, Boston%1(5. H. Brenn!,On a problem!�Miyaoka�0 B. Moonen, RA�oof)JG. GeXQ�� �fields�fun$ \- two parallel worlds, n��9�Z��Q��5A596��j��The�A����h:�multi�1�y�0graded dimens!�two. !\<. Ann., 334(1):9�110%V�66VyRmbb�a��m��,, 35(10):319�� 3213h 7. E!�ieskorn.�e Sin��äten k�J,er Flächen!�2�(4:336–358�� 8. D`nkmann.V����q rin���ADE. PhDa� sis,�}�, Osnabrück�013. P. du Val6�b�~ do� aff� !� cond � adjM� . I.AZc.�� ilos. Soc!�40(4):453–459a�34���������60�65����������8%191�\D. Eisenbud. Homological���Y�a^ �  interse�$, [ ���pa��S to � 6 s. Tra�i�)�260a��3��64�$80. Daniel��Grayso��HMichael E. Stillman���ct$2, a softw>system� ' arch Je�ic��. AvailO < at http://www.m�,$uiuc.edu/Mg/. C. H{f4of�ago�.�A�yk Brandeis ��!91�( Hartshorne�g�(, volume 52p,Graduate Tex�!g�^ Spa��New Yorki��� unekw�GY �. Twoa�orems; ut^�� es:z24(2):39�{404�C021C�w�P�� nskya�me��pri�MZ�!�4th. Z., 214:11�q135�$93. F. KleZ 8Vorlesungen ü�<das Ikosaeder un�9 e Auflö+� Gleich 9 vom 5ten !c! eubn!J188�F rr��Cң>�� � ���1m�7ů@Kajiura, K. Saito��,A. Takahashi%,rix factorizi��:� of qui . II: T��. AdvMc 211e�27�{62%���&� Noe� ian�b�cBR �&� 98���9�510�51976. 6��R. �}2 �R6u181ay al Survey� MonographW MS,�vvi� , RI�12�[�MM�b�-,s263:4�pei�7E Mason’sq\�(syzygy gapse��A��, 303:37N381���V�V<ivedi. Semistabi5 !�2�*2 M ��c!:g�284:6%� 64i��5� Witt�&�Gin Str ��y�eed"_,he ICM, 1:49���5�� 26 DANIEL BRINKMANN [WY00] K.-i. Watanabe� Yoshida:��� �a� equa%�� B'�coleng�M�J�c, 230:2�317%o$0. [Yos90]{ �noB�Mo�u : �R!Y�46A�Lon�/��c. 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[3] Bi����3m2�s, &�20`�$Claus Fiek��dd David Kohel, eds., 2002,� 1–8. [4] Owen Biesel and Alberto Gioia, A new discriminant algebra construction, 2015, arXiv:1503.05318v1. [5] Manjul Bhargava, Higher composition laws �applica�s, Proceedings of the ICM: Madrid, 2006, 27�d294. [6] Stanley N. Burris�DH.P. Sankappanavar�Hcourse in universal�@: millenenium edi��, http://www.math.uwaterloo.ca/~snbs�/htdocs/ualg.html. [7] Pierre Deligne, Letter to Rost��B5'L2 March 2005. [8] Ro!� Gilmer.�CRaymond C. Heitmann, On Pic(R[X]) for R seminormal, J. Pure. Appl. A)�4 16 (1980), 25%Q@57. [9] Alexander;8Hahn, Quadratic1.(s, Clifford%�rithme,�Witt groups, Springer–Verlag, New York, 199!�@10] Teruo Kanzaki�A�q� extension)�ded qgA>0a commutative$, Nagoya M!��49!H73), 127–141. [11AWdeven L. Kleiman, MisconcepAps about KX , L’Enseignment a25^�9!c03–206^2] Max-i Knus2b,nd Hermitian!�ms over�8s, Grundlehren !�l�ematischen Wissenschaften, vol. 2949��--� Berlin,!~�p3] Hendrik W. Lenstra, Galois!jory�� jmese��\�1�]dttmar Loos, Tensor product)�.Ye�unital=�fo�>�s, Mh.�. 122!Y(96), 45–9�5] 2��DiF�y(finite rankU�E�Yf(trace modul�!d4. Z. 257 (2007{�6A2523!�6] Ralph��lMcKenzie, George F. McNulty,hWalterTaylo��i� s, latticuvarieti !��1, Wadsworth & Brooks/Cole, Monterey, California, 198a�17Aq4rkus Rost, The2�1m7uby�Jxni-bielefeld.de/~rost/data/cub-!� .pdfE�2!<8] Charles Small ��r9ve�e��,a���� ��ie���gŋ%�72), 8aS�1�- 22 [19]�Stacks�M(ject Author�� pr, ���s��,columbia.edu��1��D20] John Voight, RѡlowIFTwith a standard involu�', Ill�lIDP55 (2011), no. 3, 113A�115�<21] Melanie Woodaussaposŕ�Tan arbitrary base, Advq#2262h�2, 1756��(771. 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A simple calcula7ustPro �Don 2.6 yields X R5xP= hh1 ((Ii1,n )θ ), �k`iL2 ([0,T +2δ];R2 ) i,k: 6!B, Ik2,n 2,n8× hh2 (Iθ− 2f��−θ , 6$�x$R�� �Xo�+R��2���\�z���%=W>��9W� �f��0n n =: R5,1 (1) +�2 �u. LEAD-LAG ESTIMATION BETWEEN TWO PROCESSES DRIVEN BY FBM 17 (1) The first term can be estimated as follows. Since%]!�((��f��( . rn2H2 , �Y , we have n |=�|]i�P5) on An (K(2 )). NiM at I 7→E�I)a�<linear so that XR5:�N� < ∞.J%a8a (2)%osecond t�p�W1�recall �!{�|N��2.[we�θ�n��|)]�Z Z du dv β(u, v) = |ρ|cH1 cH2 � I a�V�� e�u� a8|u − v|H1 +H2 2 uH1 H2 v H1 . By��, same reason��as�� 9), Q�!�9�.)  v �( n 3 rn |i�| if i!� k, and �9r�����h��>�>��T��4fore, it holdsI;i9�?i9 vn.�� X �Z�R�| 1!Q��E~2 I,i≤k ! + ..p�5(jMp-p�XJp�k>i 1A|.��rn vn�2�6J2PluggingA{15)!� 6) into �3I�$obtain ( )X 1�| |�� + rn�2n |p R4�~8 −2p E P sup ,1 . 2 + 1!��D,|2p%N ∈G1n D �  n ; 1Z, (#G n )vnp(H1 ) T ) 1 by (B3). 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[2] &�G0E., Kleshchev�Q 8G., Tiep P.H., :� �1�"�5� d natur��B% (, Int. Math� �sgt.,!��H6��4423. �6,Isaacs I.M.,2��lH� xH2��"=A &= �(multiplicit-in symme%$ groups, J� gebra 478%^\7), 271–282. [4] James%$ Kerb-�O represenm�D�y��A�n� n$, Encyclop�%%!ematic�� �%!ic�,�s, Vol. 16, Addison-Wesley Publishing Co.!��aa(x, Mass., 1981. [5] Macdonald I.!�� )�m�e irr� ible:��#:��s, BullA� ndon�0. Soc. 3 (197[G189–19!C6]6��CE� ator �Nu��?�e)<% rlesung �9(em Fachbere��5Mk MJ�Wät E�J , Heft 20! 94, avail�F8at http://www.mA� ku.dk/~ol�J\/manus/comb_ rep_all.pdf2&����Co�+,al Autoencod�?�Ad�qar�In�>%��!�zT Antonia Creswell Impe4 College L%o$ Anil A B`9thf(�Lac2211@ic.ac.uk a.b 4HBiswa Sengupta Noah��<Ark Lab, Huawei }�a�dp711.05175v1 [] 14 Nov 2017 bS.s S@hA.com AbQJ ct shapeah&fac�ork�9Bao e�. a�xF)B#@4nt space gener�$�e�@el�(r synthesiz��i�(�s� finegr��categoC"�,61��FV celebr�:6 ��s�-n-al^)a�idvF�tu�8y. 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These subclasses include symmetric unimodal linear mixture densiF� of the form n n X X p(x) = αi pi  for  > 0,4= 1, (10) i=1 l−βi |x−m|θi with any < θi or�w that is a���exponentially decreasing distributions, �∝ e  V��=m@ m − 21i , m + �� ���i� .�, n. Also, we establish variance bounds9tmore general (not necessarily 6�!5��)�)�de1�%��c0ed support [b�Lsl , b + sr ] having!Ҁ unique mode at x = b and satisfy(LLipschitz continuity n(constant cs)�8i.e., |p(x + y)|�| ≤&(|y| (11) !@!�x, y ∈R���.A�$re exist m0�uQ�2��Pidered in this paper E9 are !fHlog-concave, e.g., A��caAQ-�0ized Gaussian9i θ 1 eE�M� ,%�β%L (12) Z(θ, β) R∞5%�Horder 0 < θ < 1 wh��ZI�normaliz!r1X: K =!M ∞ 6�dx. Note ��te�u�<ome heavy-tailed63. UVKA���m� �sA6Pe been widely studied/us)xprobabilA#$theory, stAL<tics, signal proA��m@machine learning,0in particular)g$estimation"�t,ng [16], [17�8�920�1EH,us our extena$$entropy upA'e: ony�may �(road applic �4. 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[4%(Tsiligkarid^5� �C'�borY220���tr=�֑�{E!� Transf=�o<Ft, � 60, ��4)�(2233–2252�4. [5I��aA�@K. Yao, G. PottieI4 D. E�.�n%~�EANpy-��d sen6}@ heur�=r��in!jcee�7}��A���rnj8,al Symposiuml.���P&��)��Net�><s. Berkeley, Calg?\nia, USA: ACM, April 200-,36–45. [6]�Bak(�F. Ba/1E�Cattiaux)ʅ uill-�A�'plToofAS�$Poincaré*�%��&l6.�Bmea�{�> ��4=8�l&+��E�E�Aron�munUUbabM13)�60–6E�$08. [7] S.!�Bobkov }`Is��im�7e�analytic�qT.��N���XAnnal%�Pr��� �27ic)� 190A�81921, 1999. [8]�\Madiman,�� Melba�M�P. XuE�Forwar�d &yq��ppO�i���i���x o�y��i�Vvex� �� ConcGE�@�,ringer, 2017)d427AG�8AH�9%`-]@M.�“!O�ooaoordi.�A<�a:�;is#A[(=ra���cq��"U )wN,� .E�K1��5-��8 �94A2 4954�,1. [10e Hense\ “S�`ng{0vex bodies–���(r slice� �a!UW3Ea body�.&�<%}e�6Ameriy Mathe�.i�Socie�=��792�619A�25AF�8��11%� WebbE+�C!� ��� regu$��fex��Gx�ae Ded�\�aM�61I��1)8t28s�9��12]�+,MarsigliettiE$V. Kostina��A.B��!H2M)�.vBR<�:�B�Ie-�:or�=�FE� inI*2z� bzI5 (ISIT)E�7*Aq �P�5%s3]�fWal ��I"�a0X1 �.���rib1� �S�>st)�:?H��3%w�3�I200�114�2Bagnol)s�T�gstrom��L�P�p����>.E�Economic-M26I�2I44< 469!�0� 15E Saum��A Wellne)��r�ng= ity:�eview�5 s Surveys �a� . 45���16]� P. R��“Es �E�o�E��E( Sankhyā:� Ind�*9 �, Ser�R�A)�2��( 196%�7] E.�Weg��“Ma%!(likelihood E>a��R�� II��C�W6Q)��p. 216� 2174a��7E�8]!GroeneboM1�n�D�m�m�)Departm7���2�wx R 840��17 ~�8x ,19] L. BirgeE�y �:�!Wa��smoothn��`P�p!�I�6.��!97��98�V�7� 0]!� A. H���g?nd!�W dip ����Ca� 9�>w�v�8 �a21eEskenaz- P. NayR�~T. Tkocz{"�aNs:�6,&�v.��arXivM��t :1611.04Z201��22�)�H(GrootxUncerh��]*H� �����x"?�w6 b!�40K 419A�62!�3]~ Ge� �B.& “An � !?a&eH odel�track�: ,ellite image �N$ Pattern A� �s & nd Mӷne` llig��i18����U���24] W. �, A+B�DA��t�?f ͊�>t�.Z:�8 �%3�5m���h)�Zur U�ia�r e�(aren mittel%�5�<sche Zeitschrift ]�*a� ��9��9���6�>�2) ,S. Mitrinovi, �P+Vasic�J9 *=  1970 qb 27E�Raginsk)�ITso�&� a��M(  I:� N� �C.�sI�Co\ ]; w Pu�Ders Inc., 2014. ������H,,�6������C�l���,�%�Bank distress in the news: Describing events through deep learning Samuel Rönnqvist1,2 and Peter Sarlin3,4 arXiv:1603.05670v2 [cs.CL] 27 Dec 2016 1 Turku Centre for Computer Science – TUCS Department of Information Technologies, Åbo Akademi University, Turku, Finland sronnqvi@abo.fi? 2 Applied Computational Linguistics Lab Goethe University Frankfurt am Main, Germany 3 Department of Economics Hanken School of Economics, Helsinki, Finland 4 RiskLab Finland Arcada University of Applied Sciences, Helsinki, Finland peter@risklab.fi Abstract. While many models are purposed for detecting the occurrence of significant events in financial systems, the task of providing qualitative detail on the developments is not usually as well automated. We present a deep learning approach for detecting relevant discussion in text and extracting natural language descriptions of events. Supervised by only a small set of event information, comprising entity names and dates, the model is leveraged by unsupervised learning of semantic vector representations on extensive text data. We demonstrate applicability to the study!�Xfinancial risk based on�jH (6.6M articles), p ularly b2��X<government inter��%a (243��h), where indices can signal��level�_�-��4-related reporE�at.entity 5(, or aggreg- at n�(or European -x while being coupled with expla :�Rs. Thus, we exemplify how text, as timely, widely available and descriptive data, c�!<8a useful comple!9$ary source!�iYf for=�!osystemic)�Xanalytics. 1 Introduc!� Text" prese�90both major op!\unities`0challenges. 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Distress i��a for Hungary, Italy, Luxembourg, Latvia, Netherlands, Portugal, Sweden and Slovenia. Vertical lineiDicate bank-level d�events Adotted l5� out-of-sample predictions. 27 Bank ABN Amro ATE Bareal 8egon Agricultur X of Greece Allied Irish4s Alpha  Amager�en Anglo* Attic *\BBK BNP Paribas BPCE BPP� ca Civica Popolare:�$ di Milano4o Mare Nostrum 2;�,o de Valenci\�Cyprus0Ire!� &queH ulai��wag BayernLB CAM Caisse d’Epargnexa Gene!D�de Depositos Caja Castilla-La Mancha Espan @rnegie Investment)a(Catalunyaca! 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In Procee� s of!Zx DARPA Broadcast News Transcripap} Understan=� Workshop, 1998. 2. B. Back, T. Laitinen,;(K. Sere. Ne�� netw@Dgenetic algorithms�� ACruptcy2O` Expert Systems with Appl�qH, 11(4):407 – 413�6. 3. M�roni,%k inu,�TG. Kruszewski. Don’tIs�,�! a sx�a�$comparison!J�c�xt-E�!�vs. ng seman?vectors>�� -�852nd Annual MeeS Associ� !+ Comput�al Linguistics, volume 1, pages 238–247, 2014. 4.AVLBengio, A. Courville)LP. Vincent. Represen kH learning: A review!K$ new perspA�ve�EEEA�nsaE�(s on patterA[alysiI $machine in�ga2H, 35(8):1798–1828�`3. 5. F. Betz, S. OpricăA�A. PeltoU�,P. Sarlin. P��c%Q�d� (in europeanEzs. Jour!Pof��!�& �$ce, 45:225%L�1�84. 6. D. Bholat�Hansen, } ntos)TpC. Schonhardt-Bailey. Text mi!R%�!tG a !E�nY �e.d �Studiesrdbook5�33A�^ Eng^ � 5. 7��Björne�l Heim)3 F. G!��rE�A��a!X Pahikka�u�T!Wlak�' . Ex��%Za$lex biolog_ < e�lrich graph-based feature set �J�XBioNLP’09 Shared TaskAN�E� � ��0�pE�10E3�09. 8 �orsje,� Hogenboom)�,F. 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A newsi�<-driven approachřthe hisA�,cal value atipmethod�� , 42(10):4667!q675e|5. 17>��6�����de Jo�W!��Ek on�$survey of ���� �s from t�vdecisA�supN y��D�S � � , 85:12� 22�A2ɄHokka� T. Jacobs��AqslA��M. Tibb�The Riks�U0’s future i�L�ly�light�ig Datak Economic6 ���a��) 7. Sveri- k��5�09 19. O. Irsoi}�C%V<die. Deep recurs �n:� !GA���a�(in language� Adva( �/ V+ �309aT 2104a�� 20. Q. L��$T. Mikolov�ste�ed *� �$� ��� docu!+��->B 31s��.�6��M� �L3 , (ICML-14), �18� 196%o4. 21�� Lij nsky% time�@crisis: a corpus u�toe�con�A�; global &� F!m�al ,s. Cri2�l��coursef , 8(���5�l�6^ 011. 22. P. Ma�A. Sinha� KorhY J. Wa)�u P. TaR H. Good debt or bad  : De���= ori� ��eQ�a�63��*2 � A�.RSci!�em2x �5G782–7=�3.� Männasoo8�D�May Expla� a�& � EasA%�( tg�i%� �C* Ban�.{ 33:244{ 53A,� 24.]��,�Ch{ _orrad� �Ja�an. Effi�t esti� of worFin� spaci�:� ��� �r"� y  ony6N�s�� 25E� Miln�Rist�A�default%q!�>��..8*) tab��, 12:2�$�3yd�6 Mitchell\�M��p�0Z��!/��&S Q�s. Cogni�s!_,34��3i�429�0. 27.~NeA���A�}!� solvA�a�0nvex programmproble� �c �r- r�o (1/k2)�1,Soviet Mathe!�$cs Doklady"%27�E37A�376�83. 28� Nym��D� egoryEcKapado(P. Ormerod,$Tuckett>o mith�ws� narr,e�9�p s: exploiI�b� a� !icO&� ,. BoE, mimeo%]5. < T.* ilou% *�N���k7to�6�. ECBE�!�( , No. "�5. 30� RönnqvisI�oa�&"g�:i8�s,ity%7�rm���QuH�veM�e, 159 131z���[ & de�be�nep; �A��ƙ� the  E]:�Syma5 um SC � aI� al�ce�89� 897��2O,E. Rumelhart�E. Hint,  R.�Qillia* �`�r2�@s by back-propagaEZerr��NzH, 323(6088):533–5�'198:3..�On polic $ers’ los� �n�����e %�!Jearly w)[� I�s."� s Leu9(1):1�|%3. 34��Sc* r ���:t : An ��a��M�s, 61:8! �1 gA� 5. Hx ütz��men� wmea�N�� 1992 ACM/E ��ASuper �u!��,:� ’92��787��xLos Alam� , CA, USA��92.IrI^�� P3 . 362��%��J��en�&�retri!�&�� sens�V=�4�n�Y� on D4  A.�*x Rp�16!��1� 199!��7�|Soche�C^ �n)�6���nA�al P �&�cX (wTout magic). Keynote at%�� 2�Nor�<merican Chapter *W �)�E�6� : Human L� &i $ies (NAACL�4). http://nlp.�� ford.edu/� s/,</. 38. C.K. 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Our���is�mis�obring toge��� ledg��1���%��*AI� �qu�i nd i��con �cy in��� analys Avery nm�w,. Cross-stud/�nA��  domai�s highl���Study�uA�!�2D%, in fA^9�! eval�radpin!3}T, ��iѮ�V5�5�m����A��appro� ) betn market�in busi�IA���wntrol ��icat poli . Har4C�V!5�proba�(stic methodI&�ly E$rm exci��rm�I4�lt planA4��E�ac nuanc_>~f pseudo�$, scapegoan� ���,%$half-truth� add uheM� e A��earlie*��a)�p, [6, 11, 12, 14, 15, 26] cal��tMmodified:�&m(post-X �)�N igi�6X.6�re5� J inpuHspirit!eyA� similar�0AGM belief re$on [1]. Co� !Ao �IX��i_ ��hand,!�st�h��$r-investig< �A� was ADie� [3]ecoaAqonAVfitEXtye� form� s. Maclosely�1opo� �Y� [16]y� �reM|� �{:gso� �languageY7��removal .sT�#q �D�Ivh!�dͲ, *!! /arisons��their ��. 6O��� a3 mmodEwI�!�q7on��bd d ac�  s�al pa,� [7],:U{� � uga'�"��at�[�Q�lW feat judg� . Une���,�Y{� �a~ x � d-aly��>�-](‘executed��u�dhmin���!��c�+tly, >irr�a%�yi��yR"ndmproducQ $ops. In mo� &qi2)Fi �opic,.��or ot�#$��ialogue g�T[2, 8, 10, 18–20, 22 5]. WhileAA� assu�$ ny dGH )c: Culd�6vid��a#U ��� |B��" �A��%���n( [4, ��c�T� -� ��06E�!�$ ime-Q ent.:�!� � :q�, b}bserve � prog� through �� IF��of5�� ɰJ$�n!� for =4>gra��t$�(reA��t^ �#�aQ mula!Q.M��not�!J�)� ideax���A�JK%��us�-un է!� [Af�H' �wAom� .�/7y�� coupe�p �l1�d�'P!f�k$uri|� chang� �r�҅�rd ��5�E�81�� REFERENCES [1] Carlos E. Alchourró�& Gärde� David M�son. O �L�$!`�Tp$y C�<: Partial Meet CH �%S�R�WFu�!s. Jou�' of S3ic ]0, 50:510–53a�l985. [2] Leila Amgoud, Simonx�!� ,Nicolas MaudE�%s,�and ne�v��ECAI, pa!j33�^(342, 2000. ��Rf�''��F���S ͼ�C�(Elimi7+Se1 ��AAMAS|17�%� 0ear. [4] Juan1�AugH�0 Guillermo R.!ari. A Tq�b��S"�.T Commun.� (4):237�Q,7, 1999. [5]A�DBar� errLDov M. Gabbay. Modalt�Cson Net� ��T�& Verif�$ion1�1� . Sp n% !�86] Ringo BaumanIY Gerh�rewka.� A�s Vx: &��U��� Fr'%�IJ] 2734�`740, 2015. [7] Trevor J.! Bench-Capa5*� in Peal5 UO Value-bp:�.��y1i(��C&A(@, 13(3):429–448�03. [8f��8, Sylvie DoutreiG Paul�'Dun��A| in���& . Artific�Int�%�g6, 171(1�–71!� 07. �Pi� Bis�Ct, Cle�0te Cyrol, Flo�DDupin de Saint-Cyr �MarieChr�Hne Lagasquie-Schiex6jin5{ ��I0�K�of Up2 �SUMQ��3��43��1!MH10] Elizabeth Black%� Anthony H� . Re / OpA��sEffRan Opa@el�]1�D�I� TAFA��2a%39���1��9:�a�;�-J<1;���VN]�: A}�a9c. ]�Z R , 38:4A�84�a�12].�%m%�N��5�Bipolar; B�$Graphs: To��A�B%�U�s6ing��Sca'+Un�)ty�a� 1��1�9148�\1. [13] Noam Chomsky. Ho��v Pros/. Hay� Boo|+20 �4]q�(Coste-Marqu( nd Sébas�$ Konieczny��:�'-B�N A �%��<12�.gIn JELIUm39��4� 2014��5V���,R��8, Jean-Guy Mail��m� �. _f��ɶ$s: MinimalQ�*� s Statusm3KR%���6���And Herzig�MLau�2a�russel!V��u5+e��AR�E:.~� 7] P� M.�T�g"M �A��=��7Its2 da_al Ro�,0 Nonmonotonic�h ing, ��P� amm!kn-�Von Gam!y�� 6�77(2):3�_�`,8] Xiuyi FanS�F�.esca Tonlo ��Qy2`2�� 2T198�S�0�ae:9] ��xos Hadjinikolis, Yiannis SiantoAqanjay�? gil,>�%�� � $McBurney. �u�m8/�in"> on"+ �y.�� 1617|�20]B��MYR� de�Iasymmetr .2#��se� 4siDIn2��( 3055–306�L�21]� �h�  >�6�|� �!Kno�� COMM�20��2�008� 2] 6X@, Rogier van EijkR� .� a\��protocoleZag�purchase.(2<  Autonom��A3�Multi-�9, 7:23!:27Em 23] Henry� kken� )ia= Flex�2inU�iL�2V . J.a�G�1[ 5(6):100��104E<�0aX24B}�B �l�`a�qH�.9� EQee. � �>ew, 21a�163–18ŕ06!�45] Tjitze Rien�<, Matthias Thimme4 Nir Ore� 2��s�� � Stragegic: F��3 33�O %� ,ás Rotstein�rtín O\ Pguillansky, Alejandroo García �.  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Cyberne&�Norweg�{ '�Sq�cc �Tl��oc(Trondheim, 8Hay (emails: p.b.gar� 4rosa@ieee.org;�& ta.mq (@ntnu.no). >� A*�Centr�3r O �N�RC��ynooth&u��y, I��nd (e-�:john.�C (@nuim.ie). 27 2��%5 of E1O��P� %C�,:7!5� �5655: olav.f� =� 6��ADe�n1"$ – ��Y!*� "�Va�&T B^��-ngF� ���"m,4� &6�"T% �!f�.� �.�|� H��s��� �;tinuou( �az�~�+���� ���p��E�nq�8]��49 �et �um [2],i�In two��k've�}� ��]2on-Kdo��noA6� One!��b�. sli:q Ί FourR|"� ;'0:��$�s�5~5�@� low-� �o67�c&M ��erI/� � !�� �aS �e�: -up c�!�k��ct.�- �i1��c"�a�F!9�8~�"� � )n� tane�A5� F9�i&� �b ��Hi*� 9,� � �� .�)U*�� KA`ݽa WEC� �aE� -by-E' basi�x5 6Uhe _ emum-see�(&�;BY]}G�l�o��e� �pur�+�s|�, ԛ$ �"*>"�Q���CJan F�ly � (acc1��gA�� �iese�V�s�:��$:� ) Fu*��a*��*L �auaQBi.� �Y2`.&��m��N�o���t!D s [6!��[1; 14].�q�u�I�FsY�]}�{np��[7)�AW�p1B-X# veloG=� &�g�*1Ri~0&�BT�YAo�%�Q…-�c�ku�*I�%E �Y-] �U����il�2]�O�a96Fi9u �o�%�9m-�WEC5z EKF-�/&3 �oA�harmoR�.9�'vardc%�Th�!EKF�6ck�*Nx�i� ���eg%B�>FLL�au^5Lfi�wc �u(�!��3teg�R�oE*aOivg?- J@|";3� d2��s7 : ed [1��M2�1���y�,": �Cr�ve�B�C"=�,��:��w�*�if_ ��lVX� (o�x�;akd%� ���i�GIm [16]. 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FA�'d%��fF\�= �i: Sa�ω�hF� �# �t�B�5 .#Yf impedB [Rp + R�E] + jω[.`�� (S +�)/�)]�� Zt M�(t)v�+S%6� �+�#�,���C��c���C��)we�M = [� ∞) nuG:@#, _!E� "���V*��S�by R� �=��(*Qζ.t (5�4) �cancell� u${mp�Pz t��p� ��>������s��1aG� M̡�� omes�R�="�, (12)e5_�g�[�s,�� B3. 3ae�z� @fS�p"�uA�PC,A�Bp� �11)>�,  ��+=�l [21],{+�)!hP�C#d�rr5��� tg \ spa�or�aE�ma�3aGt)]�̂(t)��A�(1; υ[k�K�]A� (�]� $[k] !qi��N D���1A�N5  ���p0� �.25�K�!hK l?^�E8 excu)!tPTO��]�]ake6�. ���a*e ��. '� le�!A���sOdQ�.&�N�@V9��J�eP��S��ncq�� lso�� @ >�k� 2bA� ��Et��manipoņ�P ��c��!. J�%Z�a�&l Kb 1EA C D*�'nd� �2�m&+&.U*{^�osa �:��Ta1�,p"E(, Z T EMV ẋ2A^dt ��5) P̄ =���b T 0Fg����:de �l^I! has �"�>Ӊ� '�(Ú��Mat��k[ )���`-�� 6�(jA�� Sp )� ��!u� F |� )��,!aN`r 0Er-DP̄r =�a(t)��� -y6)%e�SA�� �ter��a�I]�(�b�a� � k&=Top��eE�G(1�43J� xU turn�!�q���E�/� cyclU,en!�� �%�*��Cimm)� 6�8)��fWlRC�7e��s� [�)��ad�A�> s)%��Z]AA�� "�� capt؋*F�y, CWR��(P̄ , 2rPζ^}> ��I|"���uD d P&�po�[!+Mu� unit u��!�s=��I>W ep w��d8, Z ρg ∞ Sζ�� k= ��n 8) 2 0 ω �'� \e�( ρ ede�A� nd g grav,alPQele%% n. I E STIMA�*4THE WAVE EXCIT @FORCE FREQUENCY 5�Fed�- FF�9",� I�&� by!�n!�-F�2M6,o ��< *r��� ��amplituds���o�!�Z� S��� aW�b� U '�#�H(t = kTs�Ts:� [k���Acos!�[k]"+ ϕ[��η� 9){�A1��2>B�� `�� � �z�Tw !=�sH" & F2s a�-� ��h&����  TMvυ∈R3� q "z as υ= ψ:T-�$��3%�η �Fzero-a��&��t��dom �s� cova�B�c�~�'�����d:�$ as E[$$T !��RwE[ηη �Qxl� s f ��A �h ,re,   9�Ts k)Ao-� 0 &� = � si6%�>E�0 � , 0 0 1!hR 5�= 1 0 0 &2oU��ea$� �l��yZ�z2�p�_��J��s0feA�IHr�-i� �vof��l6 ) ark]e �u wq�� ��a�.���tiY�T�F�IO}�IQf� tybDrixy �3, Jf%�JhEKA�i��*�mQ!of!�.)*$h(.), deno� Gyg1byOa�a0�f |υ̂[k|k];Jh "� X�h +1"$. TABLE I �"4ALGORITHM . 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(a,�)�S �:j,$frequency �^of the dominant IMF is adopted for tuning purposes [8]. Figure 2 illustrates the block diagram _�frequency estimation by this method. fe (t) EMD c1  c2 �.. . with amplitude ÂHHT , phase φ� @and instantaneous� ω6(respectivel�8ed as   q υd| 2 2 k(t) = c + " ,| !4arctan , (29) /y # φ̇ G�. (30) IV. S IMULATION RESULTS identify d-�� !�WH Hilbert transform .k� cns !+)j( Fig. 2. Fb�e 0(. The EMD �<ies local maxima%rmin of f%��,@ calculates upper< lower envelopesEf�such extrema using cubic splines. The mean valuesjA�G@are used to decomA�$,original sig intoY� +,nents in a sI�e fromAhighest4to�st one�� !&proceda,is summarizeA�$ Table II.!Sn,C$wave exciti(force can b pres�asm!X = (28) N X 1 i=1 ci!� + rAa�,"t5) A. 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C ONCLUSION This paper�����)&15 1f �s,�Q�/�r�2�rq��p[8�,��"�h"�EkI�WEm,}#:!�Mo��A durA�#Ƀ� !ces\42� :� �1S^.��� ��"7 employe�^� ���tiE&-�00!5Z�t�rel �o��in�� of a&�9�՛�,� e� schemD [7] !Q [13]i�a+��!��c%6�n�m�&e���[ 1F)�gm2�*� "�+anN�2z�'�B�/&&�i?ea��-F�� J� �����AB2DQ&����%�9 �i��K h:small. B�BT�5;)�2�=a�[Be�(A�HHT42�n�� .�*'-Iu]A/�� iis��� �NAA�0�s.���B ��p����a�|y 16%��J"���s����W���h��3Q��.V�� v Rm �a��� �as1QN��'�h.r is I[%6Yq s _' e ar�8�(�;0}�I^� �c%�I!_��e�\��lng��./ified�&�3i&"�6e*� �o��� ach)�9!l� E�is:< �c�k)H�N appl8technique*at deal���a]in��% �R� will b plo�3�u �\s. R EFERENCES [1] G. Dum4,, A. Babarit)bA. Clé�,, “Optimiz�!�ɈtakM�fA��9�;m�� F regardG=�Rcl8?$e,” Jour� of Offsh�Mechani�5,nd Arctic En�Ѐvol. 128, no. 1, pp. 56–64, 200`5l[2] H. Yavuz, T. J. Stallard�P. McCabMTG.�Aggidis�B2� n� I$-ba5"xZ!=�a��a"�<�)�@ve%in ir[2 seas%Proc.I<~: !�<gineers, Part A:=5 P�e���,)#2212#77–90%#7. [3] U��K�@R.  rtekin%�4 �-�m�b���l�7t7!� subm.�d=7�r��; �9� Oc� �E �A]A�;2�� ��3)� 255–272�15. [4]�J. Cargo%�J. )�l!�VA.�Plummer��S $r%�c -#"�;>��=aul}>%wa�-x<�mI�sm� Renew 6��94 �32–47�6. [5E�$Mendonça�S.! tinez��Af�i�7 ce e� to oi�1]��v����`7drz%point �@�rA� IEEE T�A�.� Sus�#F���72e3–11�6] E. A�&0lini, D. I. M�=ehand,! Bann�M. Abusa0 “Rl a@Ap!�^mhA ar���!neu;network)��I��..�Mar(6q�9)�20a622e7�1a7(7] F. Fusco%�4J. V. Ringwood-��5Ay� !e�� �4 ~;.��;�� ��4, �21–3 �3. �@DP. B. Garcia-Rosa,��Kulia,B����Ma lina��?j :�!�V��-����,�-�0&�CAh�IFAC-P� sOnLine��50M\ (220th 5 World#�gWB8), Toulouse, Fr;(E��7)�14 70�: 10. [9]� Hals% Faln� ��T��a��A aris��:ed� �C� �-�f��J��2��.|� ����.- 133) �031 10!� 13�1. [10]N�,F. Lizarrald��S.Estef�C��2X .��k!�� ing-�" 1��Dum se�M�g���in:��mAme�-�n!�e�4Conf. (ACC), M*0éal, Canada��2-�01!10�N11��Hierarchşrobust.��e9> �uncer�"5=�ѵ>� b>�52�958�66���12]���M��ntarella��DaC�m�30P. Rodrı́gu�,ve�)M�� .�vo IndudBal�6ctr�s, � �56�238��239���,13��TedeschiA���M�XTu�T �qSU+���@ -y�l�,"�$���r/J�� E&C �- 59)�10IP383!�384)��2a\�4%�(H. Sakr, Y. Anc�$. Metwalli� �S�*& 2 ��he�F�D�! ��R,��� i"on Adv���d llig 6�M� �( (AIM), Bus�� KoreiA5, A 136��137��5�G6VA. Luna,I ��uñoz-Aguilar, I. Etxeberria-Otadui, R. Teodorescu_ ,F. Blaabjerg%'�A�ion�FE, fr�Ggrid syn�ni���m� three-6K,-conn� Y�� h)adverse.�*� 6�\ .0I��26�99�� ��6]�pBoashash��E-L� �Kterpre�B�&2Y4a�(�g$ �-  1: F�G� als.�2#�M��8�F�4)�4520–538, 199%�7] N.� �, Z. Sh��S5 Long,a�C. Wu,A�a(hih, Q. Zhe N.C. Y6�CF Tu��He(Liu%}K empi��Ede&�A�*5��u)��n��a� non-o!M:�:� %�)0Royal Society��d�A��45� 90� 995%�8a� 8] W%Cummi�,��impuls�!�s!I"�� ship*� Schiffs-�k-� � o ��109�6%���3 � �*d O�8ng �ms: C ar� [*�o�"cluo@<�-�  Ex'!?L. USA: Cambridge Unia%9F�P\ �,�,�20�\Short- 2��forecasE�l " ����^p %;E�� �NN� i��1��i��0��� 21��$C. Harvey,\,�, Struct2 ��S�(�M )n� Kalman Fi�F�.2�.--( 1989. 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This implies that A ⊆F {�)2 J8��E W ) q%≤ it F#�ib� k)2 1 ≤i�%B1A)|Y15��+]�Z }>��i����A��+�A�M�c } + hQ%�F��!�� 2IA�eE� �η�E��nx}+ {FTU}a� �I�hYx�Uw /�ASaqM� �Fo�KJ��p }. By Lemma 6.12, Corollary1,�Qperty�{ofe�! @from Theorem 4.1,��0arbitrariness/K, �:m�Rs. 16 APPROXIMATE MLE OF DIFFUSION PARAMETERS Ergodic case 6.2 For all T > 0 �i(0 = t0 < · ,< tn = T , n�?N,��Xequidistant subdivision�0[0, T ] such e*δ�F$/n → 0 w�m�T +∞�  . We need�� �a��c5Uto 146.1. 2o3 �_�X�a diffu�� �i�(H1b-3b)�Ga�en�0all θ0 = (ϑ�AσAB� Ψ, πt-a.s. nonrandom initial condit!)��r��$, 1, 2, p IZ,��Θ | T1 DrA�!����| = OP��(-A�)!X!?!#%��� 0. (33) ProofA-6(. Similarly�ۡI�p2*� arllI�� J �  � c%%� sinceL statementz]9�kcases5�1%�?2 can be�veda���= same way.%���=!#6�%�m"�y)pA�µ0��µ(·�c0 ), νσb (P ≡��R�E �Ef pus recAexpresE8 (27)i��1;Is=;where f }) =�)/b�eBΘ ��fan�/b. 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H,>,���y�4.2I =�;%X��:� ( )=Z��=%� t%�b n ti)�@Pn�'.h?Q�2�^�=�<avME �?�TM "?, h� iNYY� &� zAh]qce�v):E:� Eeu; �7R���1����dew5�"�o:)1)J5�W"6�(but �+�o�*�a� $ ” n”)a��uJ.aTMZappears5� 2�';� 2�5 /T7/n� �b��esong lowAplargec Ag steal/ CLT. In taXt8��u.�@assum/at u%�7�n=�*dpro / 0 F�(-measur"�&�;�(��1y�.+$6��U �ъ � � Z���3eb5��2 sIG9�/$a�[ t�T<� B� �T n!�replac{� A �C��T Refer*.�<s [1] Aı̈t-Sahalia, Y., & Mykland, P. A. (2004). Estimators�"�;MS? Ppaced discrete observ� ,s: a generalA�ory��An�3 of S� �stics, 32(5), 2186-2222 [2] Bibby, B. M�HSørensen, M. (1995�!arg1ale es�aY��or�ly �ed �!�I xes. Bernoulli, 1(1/2), 17-39 [3�4shwal, J. P. N)048). Parameter -:� in Stocha� Dif%�ōEqu)& , Lecture/�eaU Mathe�&cs 1923,��Ilin: Springer-Verlag. [4] Borisovich, Yu., Bliznyakov, N., Izrailevich, Ya%J$Fomenko, T%H�8!HIntro$.! dTopology, Moscow: Mir Publ�'<s. [5] BrockwellEC4J. & Davis, R.ER 1991� (ime Series:�yA�p Methods, 2nd ed., New York: F���6qwn]Hewitt%��I��7��A&� likeliho?ory�WJ�D0 Appl. Prob.,g"|228-238. [7] Dacunha-Castelle, D)OloA�-ZmirouA�86)uJA�coeff�E�*&?� �"mOM�Q)YL0s, 19 263-284�@21� 8ENDIX [8] DohnA��G �7). Onu nga�=��.!�2T24 105-114. [9] Feigin%��D_�7�Ma�"=o.�or�" tinuous-tA�sypru�Adv:�88 712-736 [10] Zm9).�roximat݉�� l heme� �r� �w!�J. ��(: A Journal.8 ticalE�!(ied2�d20 547-557. [11] Friedman,mE�9�Z`�cQVol. 1-2.$$Academic P2?rH2] Genon-Catalot, Va�JacodA�A�93Iw=�M�9]e60multidimensio!+.�nn,st. H. Poinc-8aUab.1-0., 29 119-151�3] Huzak��A�Sel"p+n grow8I8%,�p���2Q.�, Ph.D.!�s��Univers�Tf Zagreb (in Croatian)��4>��6�y�o.��models.�� al Commun9�3 129-13af152i�200�D�A6Qem apY��%R� . Glasnik�a8̌ki, 36(56) 13!�h3. (hrcak.srce.hr/file/7900%$6] Kessler2����oCA E�;���uA-)��Dq��O*+, Scand�zq{A 4 211-229!z7] Kloed��(P. E., Plat Schurz, H��F)��On Effec�w �ize^z' ��o�Drift�ى<��PIz4�J�y�A�@. 33(4) 1061-1076� 8] Lanskae� (197���M/um� rast.Ain]�M�n٤6 65-75f$9] LeBreto�m �co�}e-�dsaWInge�RC.�� typ�0 �,E���ga�0udy, 5 124-14A� 20] LiptsA/ R. 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Fi�M��n� ��re-calib��Gar1 on�%6W+uwT taE=expert%�back. � H[13] Thomas G. Dietl$ch, Ri|$0d H. Lathrop,%dTomás Lozano-Pérez. 1997aZ�l � !eMultiple& � �4$ Axis20llel Rectangl!�Artif���t�0 89, 1-2 (Jan h�I), 31–71. https://doi.org/10.1016/S0004-3702(96)00034-3 [14] James Fould)�<Eibe Frank. 2010�$� ewAc���-"Dle��&�.I( Knowledge � �ee(RevI25,t*_,), 1âĂŞ25�� >���7/S026988890999035X [15] Xinze Guan, Raviv Ra%�A�Weng-K�,Wo�2016. E�u�iK-%��-� L�ay�A�'�2Recog�"�Time SeS4�D�San # dregressive Hidden Markov M�/!�!�ingA33rd Id$�al Co��onr��Ms$ne �p- Volume 48 (ICML’16). JMLRA0, 2330–2339)uA5l.acm /cit"<.cfm?id=3045390.|636 [16] M. Shahriar Hossain, Pas'k Butlh)PArnold P. Boedihardjoi;<Naren RamakrishnA�(2012. StoryA���in Ent!�Network�R�S�e!5 llig%)�A>sts�"Ng818th ACM SIGKDD=^rU� D"C3AU%��Md �(E!]2).X�, New York, NY, USA, 1375–1383. hJ� 145/!� 530.H742 [17] David L. I�ona�04AD�^Ac�S�cHe. Monitoah$:� � 2004r���n�i� 2Zh(IC-AI04). 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Intuitively, t!�$means thatnbehaves��otonically on both arguments, but requiring ?8the first one iEx( particular z impl%u| �!S y kw,�kw2K� at�8 (R → Type0 ) . We prov!�[�?-Qion%ny well-!�d1�@term e : C ! n gi! %� �e?��h)Q C? . T!Gresult �Dre general than it!� ears=�a-%$glance: no!1ly does,!�9t hWPs�Xdefined return and bindI��o �)�A� those=ac �r fun $are. Also,I�U�E�s a,other highermEcomputeW8s will preserveMR�ity. FurC more!�e rel<  i� e conclus-���theorem below is EMF? ’s validity judgment, i.e., we show%:A�sE pertAeare actuE�A4able within F? �oE�lyingA� meta �@reasoning. Implea'��T�y ions�F? A� devised aototypeE�<)ofAtwo�� E FAZUsers-�*ir)�0ic effects as�A�|Ddirect style, as de�n §2,E2th!EK�i n(get automatm�trewritten τ into DM. As explaE�Sinstead�@τ-arrows (H − a�DA), we ? use a dis!8uished F � τ�{ind��e wher�@ CPS should occuran�e6�i1��(be an alias�QQ4Tot 4(, which all�!�$programmer�)� extrins-abA the .8aAJ���Hhey satisfy various Q�Il!�, e.g.iek$ laws. 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If ye�ΠΩ(x� en y��zi� ��z) 'D!�\Πi�z)a�V�v!!�v�& f�  F (y)� Πf (Π�%(y)) � g�,� ,is LipschitzR�x8Ja3 By P5*v�1E� feasi�of ∂fH \& +�*�P�A���I%��� �0�%�PD&n�,!�M�) "� !�at eachQ�h λIu$�p&>*�k Sw�.��("� realA�t)�cma�� X�sp:$.H�= ?��"�#���G3λ) in soa �� �$�t| gap (�� x)�us�fheAbp�ofEXi_![@�yo O:=�%x∈X A��<�A� i:= inf &>�x=λ.N34 ���P�$P2 be��� (3)a�"�$%(27a)e� (27b� ake ? P1 +H, � , [ xT1 xT2 ]�nd� := [ T1. Not� P1EYe1 Ig�1A� p1 )� P2 �&(�2 ( )p2 ),� re n �n2z!�" �s�Ŕ�t�ma ldBQ�I.h�,�� ��� ��^� . Fu�m� by ()��)&� "" �vI#!l�a �%v�,%�>-be wri� ˙ a�1 �+  � P +>� aggr.�!�m4 T T T� �I)Jδy QGy Lδu u LuT Rδu�5� eεM�(�B).  == HO�v��exaw� �Yf�� +�� ��ds��h��+ Lδv+δv �+���|��sZ�p-B�!C. �#ed��.���&�m"�0�ge� ^�!��0M��las2;� � �1 �dconU- Q C. � �t���a���(1�yh R EFERENCES [1] D. Angelie�4E.D. Sontag. M#,Col-0s. IEEE Trans�/�o�n Autom&�CH/�Iol, 48(10):1684 – 1698, 2003. [2] A. Katok B. Hasselblatt. Handbook of d�&"F0s, vol�,41A. Elsevier S�%~� �e)$nt2. [3] S. Bonnabel, P. Martin,�$P. 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Luen!.era26� -���:-��,%�ls����1� Wiley, 1�I�i�(197��'�F� Mir�*-Vi�@ oro,p� �6� �A'Lur’e>z8�A{/cy�) ain.��mv�=d https://arxiv.org/abs/171�4645a��1EV�9i $ Mostajerao 6��&(.B  A�� ensuFXFAC-Pm,sOn�O,, 49(18):630�@63 �6. 10� �t  NOLCOS� �o30���2�� \<b+�!� �rank kA@ 2�Worlda�g��X 31� Moyl���D"� "C !- s����j c�Cbo��on ��D�ll,.(of Newcastle#ww.pm v org,L �p32�{ L. Testik�!.z of i2�8 s��� 24x 57� 575) e233`Newhouse��ne-�[ �,ic��&Vit� �� (or,e�rnqԅ� E>.���41 432!,��[3�$Pavlov, N.� Wouwi�$H. Nijmeij�Q�U�rm sRegul�!8&5 �2: AA0� �t�� C�Va�f ,35] Y.B. Pes�#�e��P1al Hy�m�� > le Erg�6!c Zurich lJ��advan5����uropean�\F!F�E��6�� F. 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Sh��Shu-Q�nHua�Ting-Zhu)�Ch��GHui�"����nݧɧ�m��i�iz�A]ha�� ��6��!#�of:� Ce�ed ���c���2��8�|����SFH AF�� Z���q(�GFu-N22(*���2�15��Bz��B�2���m�:�.+�. MIT4�ss, Caڻ, MA,��8.Fp��,�J�A!�L o(n)R���A� *;�l* %Cv��<.S�n9& �pro��!�syp�, a�16V 1616��09a���ez��2�R�>�FpfC@Wiewiora, Eric. F���-m ��s��f�v1��f6� 26th�� &p�v�T �9��1�ACM)Ob. NlaF�V��Benjam��A����5���^�f�Tr�8� 2: 6�690y 7. :�y��rg�3��"s�� zo�~�t�)�Say~Ali HeN����l`5*���� "�b"�5!�t���u�k!����,�� :�� , 60ж�2D127� ^ 6  ���F���E\. .�.?�c�5>� .v� �j��tems (NIPS) 29, pp. 1714–1722, 2016. Wasserman, Larry. All of Statistics: A Concise Course in Statistical Inference. Springer Science & Business Media, 2013. Stochastic Variance Reduction Methods for Policy Evaluation A Eigen-analysis of G A.2 In this section, we give a thorough analysis of the spectral properties of the matrix " # bT ρI −β 1/2 A G = 1/2 b , (20) b β A βC which is critical in analyzing the convergence of the PDBG, SAGA and SVRG algorithms for policy evaluation. Here β = σw /σθ is the ratio between the dual and primal step sizes in these algorithms. For convenience, we use the following notation: bT C b −1 A), b L , λmax (A bT C b −1 A). b µ , λmin (A Analysis of eigenvectors I)�hmatrix G is diagonalizable,!DXn it can be written as !�HQΛQ−1 , where ΛE�aG\whose(entries areb, eigenvaluesa0<G, and Q consistit '�ectors (each with unit norm) as columns. Our goal h�@is to bound κ(Q)�cdita&number��tU� Q GU��is inspired by Liesen & Parlett (2008). The core whe foll)��Rfundamental result from linear algebra. Theorem 4 (Theorem 5.1.1 of Gohberg et al. u,6)). SupposeN�. If H�pa symmetric positive definite1�!��HE-%0�!NLexist a complete set!;2��(, such that!X�y%�ortho!�al %�respect!�!}Hinner product induc)p<H: Under Assump%��1� Z well �ed�lwe have L ≥ µ > 0. A.1 D]�ility� First,:examinE�])of β �ensures�.;O�q`. We c!eYI� E(Shen e%��YAM( Lemma 1. Ca�A W�A�ts   A −B > A= , B C (21) m�$A  0, C !��BA�full rank. 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J�4Z��2!- �L."E��>i JA�s�\,,de- 100 C�A �b� Ŵ&���N�J�,2�� B1�s��� ��n�"�!�`f+%E2kof �&� .� a�4�o^��ż� �s%k9��7>� su&�C im�>���h6��2�� M,�,10−5 BER 10E: 9 5 �2� 020109 H49 ACKNOWLEDGEMENT149 C159�25n00_or�@suppoC JSPS<Pnt-in-Ai�"�P�t�$ R�G(A) ) N� 17H01280.��6<Y� 30 { 15 I��of6�s l ��E��3eK)e�j�-. �#sev�:�ar�sY`< 2F�a�a1��-�"( �.� 0 ͛*�9on��5 j"� (L�) 6� 6� 0.90R�8� �8 �7 �75V!WCh2D 6L�46� n��e<V[�%fu{�!��c2s�iL+-dash�J&� ��� &�$of��t.� Q* a�short a linal,� "|2�0j ] � � �_a�1�L���!.�� �'� In���0 �ɑ� T"�8d5[:pO23nmonoton�����A"�6),6��s0��5a?��3� P�����.�<4216Y�B�Ł� �c�9�j,&j�0.805�� B@_9,6��:_��q�ing!�% chie��0.647.k wh�O�.���j��2�M-re6J" 0.62�0.666��$�?�&� ci���1��s2���s"�$QF!�+& � �gu q5@��.��:@�e� �sX'a��"ŵ"ys bU5C+>��� e��i t aroun�7��r�R%�se fac�lugg" �>o�<cesK� �o.��su"QFwhe`wit�<�vMA2w�r%<���t�T left Dopen. IV. S UMMARY�.��$~S.B�Qnd �U �b2 �8�X��*#<4 R EFERENCES QT. M. C�'��LA. El Gamal, “Capa��A�m�  �g4,” IEEE Tran�X�Lory, vol. 25, no. 5,��P 572-584, Sep. 1979. �Q J. N. Lan�R, DC.T��;,G. W. Wornel ��o�$b,�d"jX.�R�;s: Eff�Wǘ$<�ou-1p�� �� b��50 �12 �83062-3080, Dec.<04. [3] B. Naz%6nd!mER)_F�.�:x.ne$/y�r4�n�o�H"�mP�f}57� 10 �46463-6486, Oct� 11. =HS. Katti, H. Rahul,!qHu%�Katabi,�MedardW0J. Crowcroft,�XOR�xE) air:\ =��Q1�A�ing!)t /ACM � N�Q EF16� 3 �497-5�Jun�08. [5]�ZhaV!u$S.-C. Liewf���[ y" ��inUY� �a��&"OR-lJOR^ �!�SZ=. A�NY�C�C�.q�7 �m788-796,�a 6] E�L�,R Zhu,a�PagNe,�H.Lim)�M.N\zVR� ne;D�c �Proc.i�I�< Symp�}�Aachen�17)�2935-293��7%��S�R�,a� Liva �S.(55��P�SR_: a|*�cR�R pers@9>�� I� WW,hop, KaohsiuA)NovAB 17. [8] Ka�rayananE��P�~ls2AT�A���t “J�G6oT"/nd:���:�Q E�4)}P45th Ann. Allerton Co�UMContr��3)., Mon�fllo, IL�`200)�D 5641-5654. [9] R.!�4Gallager, Low-�/�PPCheck�^P$MIT P�2,, 1963. [10]���. MacKay!}�GoodV�B*QN�v�$spars5T�e��~� b~�4�M�2Io399-431� r. 199Ax11]��Ric�3�s�-nd�Urbanke!+der!Qe��T�H0y, Cambridge *�^ ��2�bhLM. MézR�X�A��nta"U�,Anor�$, I��w��  Oxford h�s,h� 3] C���/a�(R. KulkarniiAH.V. Poo�P1�&�O R�L*�<+!���bp 51, ��� 4216-4236���5A 4]! J. 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R EFERENCES [1] Baillieul, J., Zhang, B.,%��WS.,b=�n -BraAwA,dox.�O|�i ��9�m1kmic�c ids.�=In DecI�!��C��p (CDC), 2015 IEEE 54th Annual%�yHon, pp. 6556-6563. ���U:��“F��henomenaa�DC\<�c������ 2016 �5th:��� �3286-329�03] Fisher, E.%i,ONeill, R. P-x,Ferris, M. C)}Optimal1 nsmiz�t)U!1Trans�u� on P2�C23.3 (2008): 1346-1355. [4] Ruiz, P.A., Foster, J.M., Rudkevich, A. !SCaraman � � Trac�D6��cA�|�?E.�5analysi-e>��� �$Systems 27 �12�D550-1559. [5] Full!TJ.D�amasra!TiCha�E��F"9 heur��cs�!7-W�-I�\V��P377-1386. [6] Soroush!� �6��(“Accuraci� �or�.��"�DCOPFE��A z� �9.2A�14): 924-932. [7] Hedman, K.W., O’NQ�A�Y�B.wOren, S.�.v��[�ingencBvn U���4I 09E !o�5%o08] Koglin, H.��A��MM�HI Overload �z�� corr��v]��onM�nt�Nnf.m]Sys}Cni� &��tr. Vol. 24. No. 26. 1980. [9] Van Amerongen, RMMed8!J�H%g“Secu��!/rol1 reA^e�re�!��Y���she% EProc. �P CTGRE Report 32-02 ($). [10] Ch��C%�!KChoA��Y)JEnergy 9Mby&J ���e-=>�5� De��y 8!� 1993!��2��25�:11] Flis��ak��<Stephane, et al.!.�T� infl�\�n>��� w ger� �a� & pru %1�I�KTe� 2007�� Lausan���1987-199!� 12] Liebc-Ai�Rizzi�� “C&�e�)+Discr�| Appl�Ma�s, 155Lepp.337-��$13] Hosoya!���00)�m�est$ �iI� J �C&�}���http://ir.lib.u-ryukyu.ac.jp:8080/handle/123456789/7748AB(4] Barrows,��Blumsack�+)Hin�@�U!m�ng~� ACL �)8Ina�tem Sci�^ s (HICSS)!<14 47th Hawaii IȄdnVb2374-237�g,15] Zhong, Q��a(Hornik, T.,i��o� i�invertՆ�i� new� � �g��d   I�� �=H97. John Wiley & So� �U2012. �y��IMAGE FORGERY LOCALIZATION BASED ON MULTI-SCALE CONVOLUTIONAL NEURAL NETWOE�l arXiv:1706.07842v4 [] 7 Febw\8 Yaqi Liu, Qingxiao Gu�'XianfengC �o)�0Yun Cao 1. St+>0Key Laborator�|Ino� �� , Institu��f2#�Engineer� ChA9e AcademO1�, BeijAD100093, - a 2. 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[21] Yaqi Liu, Xiaoyu Zhang \bin Zhu, Qingxiao Guan, �Xianfeng0�o�Listnet)V` object proposals ranking�, Neurocomput vol. 267-82–194��7��11] Davide Cozzolino, Diego Gragnaniello,%�8Luisa Verdoliva�Im-F,gery localiz)�lthrough the fusion of camera � , feature epixel $techniques�V<(Conference A>�@ Processing (ICIPQ, 2014)530! 5306! 22]%�Pshuo Xu, Han-Zhou Wu,� Yun-!�h Shi, “Structural design �onvoluA�al ne\networks for steganalysi ��IaSig1�Letters1�3, no. 5 � 708–712��T12] Miroslav Goljan, J!(ca Fridrich �8Rémi Cogranne�$Rich model�� .�� � lor e4 �-�� V�%�nfV�� V�=�185E��0%��L3] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua)DSabine SüsstrunkE�$Slic superE�s aM\ared to state-of-the-art) method)%�transa���s! pa!�n 1�ES mach�intelligA�-� 34, !�11)�$2274–228)��2!<13] Jan Kodovsky^�8Vojtěch Holub%�HEnsemble classifierE�B�digita�diaa�� ��T:��b��� ��7 ��2 �43a�444%�H2. 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For a given number C > 0?ddenote by Sub(Aut(T ))≤C |etu � subgroup� , actpHwith at most C orbi �\vertices. It is a clopenN _.{�0 (see Proposi��C 2.6 (3)). Theorem 1.1. Let T be a locally finite tree all of whose � have deg"≥ 2-ny1!F2�ure! �topologi usimple -in2��%Iis.>�f)�%D(out proper 1&2� �index%( conclusion = , may fail if~�t��T%�A#ed to)5of -1, !�LLemma 5.14 below. Fo=!�\Burger–Mozes [BM00], i%� customaryeMcthE�ersec%�of %� pen 2Z.��!QQ�1�compact)J@ H by H (∞) . W!�sov by Mon(H)�monolA�$of H, i.e.P(possibly trivial) inF�� non- !m normalA�%�eH. NoA� that H!uR4(if and only H = �. W�these�'�a!1�sa_hand,��.�cana$epitomized!! the �<equality: {H ∈B� |� } = v(�1,}. We remark �if C = 1��neE�N�!9,empty, while Ne�%9E�4semi-regular (%ӑ�,is edge-tran�Mve)!<at�contai%W least onm�, nameA�h T�+!n,type-preserva ,automorphism��hich is �$by [Tit70]�n generalq�ATan arbitrarily large CeQa��bAMe cas atB��EOxdiscrete, hence virtually free,i<�s�m [BT]), so)�A+�ꪥ�aar%�a�E��. 2 �� important��t'�a�m limiE��tj` need? be�zT. Indeed, explicit exa��e�a�-�B��H!�Q-� are>3 (�ped��2.P%�satisf���=u Jprovide�� �0/�2in�5, E � 1.2.1])�%R�RiI 5.13��). Thu�O ofV-co�$B��of boun�covolumea(� ,in2] . Ne�#helessq@itu�� changesa�a?consider ��u��� -dou�mq� ly o�of end%�a thickq*�(q\itat�� m�ed!W.O$≤2 ). Re�%�7 W��ll ����� �l�3�ky2.ny�!���b��l� � 2�Q�-&.i)!∂��2�,ed. Moreover!�!Е� rel)�� �i!d��has1�$classes. H�, Dset ST��iN *n� �!�inuouslyE��ly on TZ���,A�o���� quotie�@ y,A�Q� Hausdorff2���sA�al� sequ�s. 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B�f���Ŝ%9Ig�2 �5�*% �3��o! canaٵ�@ͪ�E�"aZ jus����%�a`�Rw��k is �R| Y �"��}. �eW�,i� ;�)��&!O"k�M G O#�B�t�� ��8P6S�� {�}kQ��' A.2.2A.1* w� MS20,&� 1]��� home� 2 p�05��e� N̂SA �e-�� co�&e�c�L���N*�r.o� G; 1, 2�13 , ���0\, lin06�h�A�+�I�V�sL�Bd186�j��%���.��{>�cdt����(ae���tq {0, 1}� ST��%l��=GuL ��&H d0 =��=G .��2 , thLen the classificatiotorem from [Rad15] applies, and5|refore yields a complete descripJlof ST . One should note thatE set%Xnatural numbers d such 'deach 2-transitive subgroup:HSym(d) contains Alt�is asymptotically dense in N (see ؀, Corollary B.2]). Remark A.4. ItJctuDa directosequence�)$ , Th%9, A (i), (ii)!/� �B�] �!x0space STAlt (!X�hR also!8�)}linfinite when d0 , d1 ≥ 4.q casre= 3 or# is!p explicit%alt with! �H], but one can show)� �is���iA#at z . Indeed,�de�AEof%�(s G+ (i) (Y�Y1 ) (wh� are <%� setsBN) E�Dloc. cit. makes se!�for all�5,3. For these}8to be boundary-.L�,�0however needs/require�<6= {0} (resp. Y1 �)5�!h -v). Under%�(latter hypo�is, iEU�t!�<possible to adapiideas �)�, §4]AK%�UA�!?0abstractly sia�1aD!(y represent5�Hly many isomorphism� es!�� spec�%�!�A�Xtrivalent 26 tree T3 IQ�nes%�ST3EXalternaa�ly!�Testablished using rank%� �$ algebraic1��o!�local f�zE�residue �or!�,2. An exhausw.�� M�suAn4�onsist� of (J of) B��ma��fAdH in [Stu16]. Refera�(s [AB08] PeA Abramenko%�pKenneth S. Brown, Buildings :a�ory)�A����4s, Grad. Textsv�Math., vol. 248, Springer-Verlag, New York, 2008.�10���AutU(!$ non-spher�d b�have unerTed displacement, InnovA_cid!� Geom. 10 (2010), 1–13. [BEW14] ChristoiX C. Banks, Murray Elderɖ4George A. Willak�Si�� of a.��Erees d!�mined byA�ir ac�� s on��/, J. Gł�� y 18�L4), no. 2, 235–261�<as93] Hyman Bass�vve!�l!ہ�graph%X �g Pure%�. Ai 89 (1993 m!. 2, 3–47nK90.m�E7XRavi Kulkarni, Uniform υ�ic��J. Amer.II S�v�3m!��4, 84k902lL01Bl�Alexa�(Lubotzky, T�"lat iProgr�inlematicsM�\176, Birkhäuser BostonA<c.,MA,A��1!�th�end�!�)h(L. Carbone,�0 G. Rosenberg%J. Tits��TB��Jacques" , Discret��criteria%�%M.a-��.!�� x to!� book> by HA��s)�A.��/2001, 18E��1%�dou63] N. Bourbaki, Éléa�a  math�@atique. Fascicule XXIX. Livre VI: Intégration. Chapitre 7: Mesu�e Haar( 8: Convolu5 etɘ́��� s, Ar it( Scientifi%�4et IndustriellA�TNo. 1306, Hermann, Par��1963 (F��h)!�<M00] Marc Burger%�$Shahar MozN�Ga��se�nga�!�s:��{Hto global structureA�$st. Hautes!T tude�. PublqU92�+�0aQ11aJ150. [CCe LPierre-Emmanuel Capr#  TCorina Ciobotaru, Gelf pairI6strong ", ityA� EuclV�n�� , Ergodic��@Dynam. Systems 35�15�f4, 1056��07�9CM11]r��@Nicolas Monod, De# �o��%Gly5 actm) into��pie����a�ca�4mbridge Philos��15�<1), 97��2�Dav�o4Michael W. DavAThe�,met�UTopology�"Cox� M, Londo�� o�gr. Ser�m32a�inceton�^ vers!}�P�����DMSS16] Tom De MedtA�!�. Silva��,Koen Struyve��Zal12�8$right-angl���, 2016!:�@eprint: http://arxiv.org/abs/1603.04754. [DdSMS99] John D. Dixon,e10us P. F. du S��,y, Avinoam MetA�`Dan Segal, Analytic pro-p �,, 2nd ed., C5� Stud. Advm$�61.%�Un�=UAT, 1999. [Gao09] Su Gaoa�variant&� >�ef ory,�^�W edEn͍8 (Boca Raton), U 93, CRC1�" , FL%��PR06] Yves Guivarc’hiBera�d R�c�y� oup-t:!.a%acts �A� Bruhat–��.� Ann.� �.�qc. Nora�$upér. 39a�06m�6, 87/92�sMar�tTim� ́e!�qua"Ar� ŬLie cor� on� Au��l�(Kac–Moody-��0 Gabber–Kaci���y!#15��p509.01976. 27 [MS20] Stefaa�$zurkiewiczoD Waclaw Sierpińs��Contrib�ià la ti�ieA� G<mbles dénombra, FundM� 1 �2�� �R�e27.Z&��Radu, AN 9�)��m%B x�2.�aZ�m�  Ańe�== (to�arI Invent ��)^�%Z49` ,Ser77] Jean-�{ S��, Arbr� Amalgam SL2, As�risquem�46a��72�  Th���ya�lemeij� 0Chabauty limi�BO a�}E6.�� Z�10.084��Tit70]:� Sur lI.p ’un a�, Essay M7� @related topics (Ma�oir@édi�Aq�G� V Rham)&� �,*� 01970, pp. 1886 11.[Tit86>��&andI) a)��7�u oceeDof $Ts—St. Andrews 1985, F�Le� NotE��12B�e�� ��A 86, �10–127a��8 48�TOTALLY REFLEXIVE MODULES OVER RINGS THAT ARE CLOSE TO GORENSTEIN arXiv:1705.05714v1 [] 16 May 2017 ANDREW R. KUSTIN AND ADELA VRACIU A BSTRACT. Let S be a deeply embedded,  cha\er�ca!Dtinian Gorenstein �� � . 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S��By~��� FRkK�M 6.2.�?.��W&��ch6���P� �W�n�[��dB�LeS�q"�;Iڝ�2�BI*p�]�sis"4D"�52WvTpac��ge#&d�!m�2%�L^)[ L� �_#��&���0sj]d�Vmt5t�s�2Jf^�*�)�YY�( � 1 )4!~�P!�}G2�J φ :��-��k"�J.o1�  m42LB{�I�V� 6�y�dif����!cwo�1��N"p ab�a��icX�z�Pbil$Z� M�eld (.P+\Gram-Schmidt orthogonali����5 ae $is x, y, zZ1(1 s�X j����� qf�}$(x ) φ(xy z)I9 2) T�}�yK$φ(yz) 6�z6�y �z~%� R7� s�� n-de� cy.^�(a�:�c��r oI��meD\�E,un*�ine^say u� �u��u3�e�,&U in:���婁����1or� btle �$�A5� fG�nf�s��exA6ory�^gritB[ by Kg9< Conrad [7, Exer��^ �]Be ke|:�!�( $I�VM�>!�&\ �z/��Y4,z1+U �� /�� . (O=�w'�ifNZiX�z!ZvX���T�P/lm?A8�1*)x�A= �yy1 )z1.�Q�a� @&[LZ��.E��a&�H3�y�8 ��}y2�� �!��u��&�X mayb�X[I� *ŏ� gha0yif �9�y�!{�:��z1 squa��tf�+A�+ �le��y�))k&2Q�!�e��1.� �1�:"�)��x$��(z21-�8z1 , y = (1 + 4φ(z21))x1 + y4z1 , and z = .��a for [P′ ]1 . Observe that the matrix (6.2.2) is a diagonal matrix. In this case also, we take D$entries on SinD of T to bu8e units u1 , u2�3"Hk . It is now clear�� �3) B�0= (xy, xz, yzAx2 −P�y Nz2 ). X alsoY�$row vector�tsigned maximal order Pfaffians"�(alternating-<d   0 u3 x −u1 u3 y�z 0  0 y  � ′*"3 x12 x%(4) b2 =  B_ �z E��W�� 0 0  0y N is T05) b′1 = [4�y)U9`5c�%f23=gu3!j ]. B]image!: eis equalA%�A�E�Xhas grade 3. It follows" �6) %' ��T D2 1 0 → P (−5)!E−A@3)5�� �26�!" a minE Thomogeneous resolution�A�/�; hence,.�eMxGorenstein ring with Hilbert see9a�5t + t 2a�,ne can checkIv sservmA�(u�()4 by hand A� = read<v��1216)1-D 5)24)V 4)15 of.��X2 from [11, page 36] inmO$to conclud���(socle degreE-h)V@2 is three; thus, �]1�⊆1. The i[�s!�-'"2)�qis obvious.  TOTALLY REFLEXIVE MODULES OVER RINGS THAT ARE CLOSE TO GORENSTEIN 27 Lemma 6.3. Let k be a fieldA(�arbitrary characteristic, P = k [X1 , X2, X3 ,Y��.L,Ys ] be a standard-e#,d polynomialEX over k!k<3 + s variables �8some nonnegativ!+teger s,),dn idealDP which!0A�ratedAf�f<tlinearly independent quadraticpmsE�0�2��uAP� y(Y6���)!=P, B be N '%��+CA�, �L�A1� ]1)5[�a2� >/ wa�8P/A an Artinian.�loc-Y$. Assume [E�(P/B)]�1�0Et��re!)$a presentaa� b ��B2�rB1 →0��3.1) aF�B%aa,P-modules, a �0morphism L : N �� B���Ldirect sum decomposi� s  �^� b2��� L 0�_ 3 2 )hL = ,��=���B!��B�������b!&b1, �� 0n2 , 0 L ^� Ilsatisfy)p�p� 5.3� cond � (a), (bc) �(dE)Lea�05.5. Proof. a��OMg>5�k6{]. View 3�a�sub��E5. NoticA�at P/B = */(d∩E� ); so w] y applyx E 6.2�Lpick a basis x, y, zA��so��eHm�or�>q�$ are givenax03)ea6�� ~�BV�by I�agQ�A�6k�6)eP�A����2:&��5 ��4),�Kpec��ly. A%'�0functor P ⊗z� to :6) obte / �e!%6�A� B : ��<�321 T 1 2h �0!� A��P6*"�= 2^VA�,�3&N!��P��. (Th Dstablishes HypotheA�B��)E�Y� ��-�-�\ rank��!p'�:2��P8!&!��<8 V h i Y1 · Ys �1)s!q7 ��N�_ �,n •ombKoszul �~$lex associ�> ��i� �J� VU '%�:q /BA�BE�|. I��,is language,�.�A9�eašd� I�-GA� V%��2 W�0�$ V h i ⊕ �1> ����=%}�# V 1 1 b 26VC5X���Da_��0,r 1�=� �� Vd>�0�( V2.E�B (B1 where e�ŗ��1 0�= .�� 1 1� T� mplet� ,e promised d.x!q(6)|le� 3.2)  A�� X���aQ�����29,  A"!<� <� b�MA= �, ��a��~ eE�. 28 A. R. KUSTIN AND A. VRACIU TheeU�s\s Qd B����B�oth(define*r� �gs.8 duality ensure e existi !\6�(element ∆�Pj (A :P B)<A,��∆B.  �,S denote �\¯���� S�X4x,y,z,Yi1 ,...� <�pset�mo�  �P� �i����>� X  h�)E([� guarantee 8at  {m | m ∈���}:�3C� �n [S]i 0 ≤ i�4 �A�%�:� �S%�let α1��an 1}of [P]d�=property��1:��b [S]dA0S. For each i� i, S.���d�� multiplic^map � 4) �×[ −i�\h� perf3 paiA� y�1% )3, sel#{α)c�L-t!� 9�U} M- }��� J� g ise�FN�lAY%Tens��,at if  m, m�,2&7%K n ( !�, if m = 1e� <α 0, !�6 "a>�h���4))�0V{�0 ^2��Q�A�� �i- i� M, A��3�U+ � = mb�� doe�(t divide m.����ra� �Bu !�� &�$, together �!�4"�s" A�2.3). U%��e>�1CM�i = 2a o*� [���BE.��[A 4+kk (u1 αx2 +oαy 3 α; h�L�,� ta��D%��3r be��33�=tbZ�. �O� �!!�5a��54a��T� 1)(C,in P. Recall7�Ŝ[�t2.4). A straightforward calcul�sh< =�Am ���2%�ŗcongru�to�I5 , ��o��� �^ =H≡0� .� half�:�p� . (H� �r #0is studied at)n 7).)>o�i todemon!��t�at "$*  (b) holds6�!D�3Na I1 (e<2 ) · S�� annS , L );\!�refore!$�.���c�%�se�*� asily�� �=A2$�!L%!�o�T�vZl��i ffic!�oE ��������FI�. uu1a�x3�2i�z +i�� 'y!x2 y ���u2 Ey3�u��z �z.*�x2 z 1���u22���C u xy2  lx3�3) 0 j���y ���yz2 8 �αxyzp G�y/ $ uu3vz2 l� TABLE 1= )QI4UP�pEK)�  29 �B�R��.z%�� ��2a/I1(E�mG�=1�O� �e�nd, 2  ·iT�~ 1�$ * �)ey%>�= >?� see�S�66����4i� −3 i��+ �S�� !7. J� of�.ust��e�res� 6���s, we 7xhibitf���>�!  with� E� mod AB1 .���8* E≡Ű· id C1 L�� next24�ie �m\ step��%�Z$ion. ClaimE=�9Il� �\�i� �� ��s � ) + A.�82X�ByJ , 2.6,N��� I2·Nn��)ET ' ����e��r�S��B �6�lef� � ��)m A�= c ′�.;pr���f���10) RO�A��Bm�pjVin.��� �, Write p = p��+ u 6� T-��s!H1*� j!�7k [� �]!��P28��i� Y%�AB,. Of course,WfIVR�~'E B;�seq�ly DFA�9">�)�E�\ Y . We5 tol��at !�%�.��E>�r 0nonzero9F of [X ;��k=, ]deg Y+2L 30 r�FX%�)[�A�con3�eyK )� :"j, so [.���2��� �0W "4. �M , 5� � 2 36�1�)Y%���;n b��� վ}8. 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Wh�(���v� ceduite*k tim�(i ��s��`. �lj�·Z�� Di+k��k��k��k� �!sA$�jk�]12�%�k+1 .6�.if n < k�$ � 6) m�=xb��e��,��mią� such�n duct�appea�C�n)��5��nde�7A�"� two j’s 9���,same, say ji��ji2��E{�i� i2��*1 <≤ ke��iVi1 + 1,b+�n"P �1)@�%��6"�IfS �,� :7��o b�V�l �closer"(�c32v�It 2L a M���<%7��m�&owords,���� �kU �h" _ Tor1�uis��� impl�2� %kk� 0��k, M<�'� { "N �   may �'�pe�d�n!��m u w *0 � I;Y-$�nnihil�' by (.�-)2� H(X1, XL,X3)k%�:�:��=&�.)4�&� � � V mostIit�&7��O�?�g �p�o} q �( a regular !j!8"�3�i�.�, I��M!n iQ!'� P ZD�1A`�RAP/J, G' J: an M-prim�/[1� $�s�0iently large. � = R/IR%*� ul� �BA�� It�no harmA>�.ize|t M�to infAY resi��f#%2M in "�� +c <�d:9��r� ; see, ��exa((8 [10, Ch. 0, 10(�]�P5�no9/��m�!4it less cumber��e�! new0, (P, M= A�U�E�1 �A+�0A&J  byj  A�A=0 quot!� M`0%�.�� )�� 9-Rees�2� >�'�-�t�1n0�M� I� Mn�) � IM�=U�,�insis�at=�<�C mn� ):� i (M�A� %�� i� ֡� RIfhe��j�(hav�3pth�P>�.��8HAuslander-Buchsbaum{ mula�ho�RhN)�-( !%9 M�I!,�j�.*��/�n�I��m M ��iMQZC�nd!�draw a�tradicH�.� F: d3 �*�.G� �F�+� �F"� F0 � P�l�'�A��-�$��m&2,0�f)�s)�!��(��F� P RA�.R-R0�-�4 vanishing� A4�+U42� at (p� �R� �T>���X�M�1�0�T"�0]�E!$�m�,H)rs!�on� I��Pl�G�0m έ� ��k%e/1�� NDEisenbud-Peeva [8]D��s ���y���� partic���'�i\I��G�)_a�e syzygy  im(d� �P � in_J)Hig�'�MkFaT1iz�ZM+[8,���t1]B��w� sui�0�e?� chosm2�F5�m$A[�pr� �ddi+qQd�}�2�I�.b�뙻BLevery BM���I&�3���#R.N�"-�eQG�x��'�A�a1�"We���r� �&6� 0-*N;��;�F�!:of.�.��8�833b�7�>�vx 62q �2�j� E� f"�A �B2e2-�^] *�.at l�\��/BQ�of�2�c� �c(q1��n*) sors�4�Bu�6�,  c 4B R B P ⊗ R 1�= P P�$B2 B BR�e47.5��a"���p�*�)$f R = S/: .4���r��S%Sn cS (R? Nlength\�J ��S���so, r&5*param� v(S)S"�6 �7�| S, n? A �n� ic2�:��*�<�/�j0 embedQ&��a� �a~wo�ZD ��1* � A� per u�IK�J�S.[%�ei� � /4B��10� 4, o -E= 5e��S!�FL;algebra� eld& 0. Ig5R� %R�*B� -��4G-�V� �8�1}3.1�J> k #$s 1.1, 1.2͡��Izo R�%7-A��smE�,) k ,Ma�”H��F]emdi<:�m�0of syzR2 (ωR j�7�k2!� prototype!�*� )�?!*how� D�� (��&�B�^/�4)�� �%��" �5"� �s.-�.x�q.�4��@ R EFERENCES [1]C"� }M. BridgL�S�:-;�t�,y Mem. Amer.᠘h. Soc. (1969), no. 94. [2] L. Avramov !��A18rtsinkovsky, Ab��e���-veihTat#, logy!� � /.�u��,!| c. London2���3) 85 (2002), 393–440. [3] H. Bass,�Nubiqu�of.h�a�s, WZ. 82�@3), 8–28. [4] W!Cuns%P@J. Herzog, Cohen-� N Camb%q SO.sAdvancedl(ematics 39,.Univers�Press\, 1993, [5] O. Celikbas,�Da��4. Takahashi, M�>7 ct b -��iU>5js, Kyoto�MaA54!^�1;295–31!^�62��%S. Sa�8-Wagstaff, Test�A�Ma���� !A6 AHr067 (2016), 55r56!�<7] K. Conrad, Ex� ory�� on bi"Hforms, http://www.mZ<uconn.edu/ ∼kcK(/blurbs/lin�4 alg/IH.pd�> D."T �I. [ , M�C�f� & �s��u�.� $s, Lecture�=es�!rM$, 2152, SpA�a�Cham, !. [9]�R. Grays@ 4M. E. StillmanA�"^#a softw�m�sY#!�@arPA�n�m ic geomet6Avail2at BKiuc%JQ�2/. [10]�Gr�@ndieck, Éléme�",de géomé�Gz0́brique III.0tud�)�d5B<aisceaux cohérS, PublQ<IHES 11e�1)��1�KuA�%�DB. Ulrich, A famil��)��xL 2 <@�l#�#gG�pc*� J �6�s�?� �B�t"� �^R`95��9���c461�2]i�jada�On � �-!�+y��,0�A2�� . 13u�Z$3, 1350107a�3�"E. Ross�5��TM. Şega, Poincaré Fof�� %0��ed.�� 8:�,��1�259�421���7g�4vg[14% Striul ��:raciu, S� .��V�of -��vaN�T ommu�o&-8����&�%�y20�215��ntemp ߅��,.>� �>ŷ�6�RIe�%�5]a���On&� )E.��O  36!G 08), 4472%H(91. A NDREWVK <�, D EPARTMENT OF M ATHEMATICS , U NIVERSITY�@S OUTH C AROLINA , C OLUMBIA , SC 29208, U.S.A. E-mail address: keb�@�i�s�( A DELA V R�<����{��vE 2{� OF J��| i5�arXiv:1411.6302v4 [] 6 Jun!�47 AlgorithmicA stru#� r�� �6�nck map�CTs M�(,Feighn∗ M� el H8,l† June 7Epbst�G Buil� <on [BH92, BFH00]7�#�[FH���l"?ψ) �l�o:' aut"| groupe�r�Aŷ �iPJa�en*lyYfulR�;G���c�M�ψVK? 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The first bouP�florem 4 now follows for all pm� [1, ∞] (which also implies the second U�in view of (2.2)). 2 Here k · kψα denot ?(Orlicz normCW paceHdrandom variables defined a�� :  kη _:= inf c%M�q: E exp n |η|α o cα  ≤2 . D. XIA AND V. KOLTCHINSKII/ESTIMATION OF DENSITY MATRICES 16 It turns out t!�%Dd slightly modified version�testimator ρ̌, minimax lower %Os are)r atta�(up toA{@arithmic factors)1;cas%:�Kullback-Leibler m . Clearly, Sδ!�` Sm . Let distance. For SAg +[0, 1],-�B= (Ijδ)S +*0Im Sm,δ := {f�:M }. D%� π %(Z)%�project-�Z~Hm onto $convex set^� .C�0:= argminS∈ Z�kE� Sk2!� Let !i �; ̂) aF%�0 =. We wia rove�i ing -��s!�theCs 4, 5%,�6%�A�5�y<. Suppose Assump��1�0, σξ ≥ T U8 9. 3 δ≤  <m 2 U m1/2 and�m�� ^��1.�� Theni�s (3.5�0(3.6)q���4δ . Moreover,!�A� 11� λ := r ��5�q � �n� V m .��n J�s2�e�, (3.15)�< sup Pρ K(ρk-��)�c r ρ!�r,m If).�<e�U ,-�p�1a+(1 + cλN���� �!W����e15stA�hol�f q(replaced byݥ?10.�OU . �J�$2 is satis� !�9�Um2v� (3.75��8��!�U ��)�6)%���3 �U;���%j� �q]11. 17 5�a��au�e�,�3I!� p mES2m��.m��n]�n!��95�10��!�A �i7) qc2M Remark 2.E��m&�-�V��X A)� If, underne010, we chooseA$δ=Y):��,a��t��!�lo>� �D!�16)u{�inequa2 �3]2#rm A), ��ta�ofqor�log m. U~��L9, this would requir�U choi�δ 3p��[]b! �so�c I& Lan unknown parameter��. R������in�E �iŁofSby  %(!\�-G U m−1/2 }resultO�a�:� .� %T!C?�Proof�dstart !��d2 ca�q�,8. Lemma 4. ��� Let� � � �.�� ��I��C !��etE0A�  �k&(G Skp ≤� � 23/p+1 r 1/p kZ−Sk∞ +2δ , 2(1−δ)J�   1� 18 ��-T�  !�formulaA� stra� forward:!�Q � ),2Q .� !e�δ� Z − �δ m a�+δ Im�4 ′ Indeed,*q () coincides)�JA (m , where S :� %���29�� δ 6  Z ��!�F���2� �=�� � �y!=A�claimAs�t.9M �& Uy�8)%m ^.���,B�� 2g�Qi.�  δ kp + k �Skp� = �)��Z m� �� !�2�% + 2δ.��Toi trol�0te&� �rAD haN side��us��i@�Ou�!�ich5���s +!e �� �have m�S ∞!� *� 4 9)�U  kZZ��)#e�"�S.5� S = _�1:I�� !_7{ F!{�F-� + 2δI. Us�V� 18),ŏ longi�Ah%>;e get2�����. � B�!'co)�O � ρkpe�.O. Th is end!� needC � kẐ>ρ��u�<matrix Bernstein�W exac�4as it was done�2$the ¯ suc�of�NJ �(5:� theIr~ s)S(note by ∆!�A �ppe;{ q qF�! An�L)�2OBN�Rcall A7� ¯ ≍��3/2�P�  �!� cond�2h �4ŧ ����n �4�5 (�W same*j Vf��6���� Me fromA)�ofYEhat!U ="). SettA�∆ =�=�1/p����SUs�: r�^ *B���82δ)$:5� ak�by%�.�5 2�b�R%�Iwe� �~ sinc��lef��FT�2;e[�reasonaQ can%�do drop$� �� 19�e,�exponential� ts”!�B�%��sA� vingm�: � only�$“GaussiaX Z[ +∆� get Ba�.& �( )∆��� ). E�� �p �J � is*w�a��X�5�W6)�~�7 �l�k�n �0r� � )"�$!�>? divergeA6 is� immediateaw sequ*� 1 %|Z:)�1EonexA�� at� �si�(Corollary 1!� [3]. �5� S1 , S2� Sm b!�nsEce�d let βP (λmin (S2 ).��Hsmallest eigenvalue!�S2 . ��β[�.���na�K(S1 kKakSi� S2 k'  2� . 2β�We apply�r�5�tS1���U obserE���a�q!� � �� δ/mW1:0�n.� ρk1�completi�.�9�2�.�conclud5��]a sX �e7 +erna�!�le�squares&�8��i�s= 3). It sh�%A�eM�s!��% !AclsmgdHilbert-Schmidt norm. As a �al �Ŝ_previou<�u c��b)��to�{,� as well (aA�ast�s ad��al.��)e�c 12VZ �0i.i.d. design*�Xa�. , Xn!� sa!��diJ�uni � � ribueΠ!#an ortho!8al basis E = {E.Z�Em2 },� &n i�*J�*�> 0��ZI6� l!.� iE(2m2 }A : s�h�"ρ̂k2eqCm &I .6�N U&$gradient (a*sub�)a�bfun�S 7→ k2� Zk22  8!�2( 4). By a necess��"wW��u� biz��lemA�1)+E�� m (�, ~ shM}D �t� �e<alce N9F�%� z�s� �m%point O<(see [2], Propos�  5, ChapI 4, Sm��1� botha��,F ��T:�� 20) h�%�Ẑ7 !��i%�I0Similar analyA~of� opti19E4-93)!�wa�<at   n m2 X (t�, Xj izYj )Xj :~�e0, n j=1�� 20 *�#(rewritten a*��� 21)��Xj�F* ��.�Subtrac� (3Pi� 0) yieldsm1}bo�F��=���a)�2)� �&� now ��eea�2 = �)%�:k�%�� �5�0-�- A&:8�� 53 }  )�%�VD� =J��E,iX-YM =m� ` 1X (���AP� E(X )i�����!��2��a. B��8��nf^e���o_ ��P Kyi�"[�16� .0�z�3) �~���.�$It remains��l�b oper��H�X�r6<� i+� gain �� RZ�y���29 Eit� V = -��9�. 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W�+number��qub��kAAq6 (�[��abQ�/ldima��o� is��y largeEw� �.`a��2< �mImor2 ��expV� ��for��jI�( everyQ��o�'�CK�e��6 !a high�alͣ). Refer:8�s. [1] P. Alquier, C. Butucea, M. Hebiri, K. Meziani,%4�T(!Limae. Rank penalized���of a � ,system. PhysEiReA--\88:032113, 2013. [2] J.-�ub�@nd I. Ekeland. ApNd Non�,�A�2> urier^ por W06. [3]� Audenaert� J. Eisert;ntinu�!<)� Aa��r!)ve�4opy - ii. Jour!c(of Mathemat� �(s, 52(11220�420H<[4] R. Bhatia. M��isis. Sp� !�1997. [5%$F. Cai, E.� Candès,�(Z. Shen. A n�2�MŨle!�. SIAM� n Op&4!J8(4):1956–1982�J[6]:���Y. Pla) �0oracle& �#a�low-rAJ9 rec$L�y�$� al i�A[noisy�O.�),. IEEE Trans\/�oB n In�7E�Wory, 57� 2342�% 2359�1. [7R��T. Tao��pGO��5A�x`: Near-�uz.d�� ���<6(5):2053–2080�0. [8]!\�C�aX. Ye )"�!2�. arXiv�wA[�t  :1101.608��I�9] S.�8Flammia, D. Grob Y.-K. LiuIr};�Q�4tomography via�6� : erro6As,�!�(� � �&� "�*s. NewY��fy_D14(9):095022, 2012��40] G. H. GolubW,C. F. Van LoA�mw}) Ds, volume 3. 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P %�� 6:"�=ed )���b�K� �%�1b� �u�I"y�)"�A2�A�V*�neY�Iu� %C ONCLU"�,ha�P7/�d1��,Q�_h<]� "lerE RN�A�ya�� �"� -Om/2 G � �~� � .�]�,a�>��*>w� �.a� ao��wB&ͺ6��> ��,B>�ht,�|uil���ng��P&z���3 u�tun� ��ѩ�#�P�,� JA�`'�(;# -L_P �' �ln>y -a2of ђ�� ��-f5�?�$̸�g� [ �`SI33�� *Aq!"Vk��rt&� 5?%f*(!6�sugges�atUE'#�s�z�_�'� )���r .(, �!(�� �H?)��P?�o23a�/B 3�'nje�Y����e�BQarq'� two�2� �s�/�Im�!�ybX#�T!@�0�m`w[\!��6&�J�hmOI; �/d1�;.Y� M,]�:#9UR%�bac.Z� ;C �0. ACKNOWLEDGM1�2��g RS,to Hugo Laro�i(le, Jan Cho�K�k�lst�vB t  e�f�i�jDÇağlar GülçehO�0 in MoczulIChiheb: bels Z.ne�q ham,��Z�I!�� � �@����!�th�u!��d,1op�JTheano ( �D �I Teb20�J Fuel� Bloc|S�v�f erriënbo"S�,25)uac�}leLi{���ue�resou�d-6 /\ uteCanada%�,CalculQuebec Sls���IBM$ SamsbE|Fsup�'1would 7� !�>��a�A9,Pranav Shyama�"��I";G�e��#�e was 1V� fun�6i0he�� ense_m�d�nRma�s A*� y (DARPA)�:Air 8�j �FT4hLab-ory (AFR�!aW view��pinA-w�,�H ings�`bede�/� �EApc��4� �e*�E"l>��ofkal ~� po�Aki�!0 partA�3FDe)>;'U.Sv vern"�. NHFERENCES Lei Jimmy  Ryan Kiro�Geoffrey�x�.�6I6\DRR, abs/1607.06450on6. URL  \�a�n.org/6+�. Phi11�BrZ(, Ouais Als�K�f��Doina�vcup. "�k���p6�g�/Q@`�Ne*�lAM�d!h&�op. 336�m 3373e� 4. J�V�,�nOsendorfh+D. KorLjN.�x , S. Urba�cP.� � ��4Smagt. On Fasta<out��� App={5)�o�tdf�N�F�%�xe-�xs, Nov���r�M3.6�j, P�P Simar�64Paolo Frasconi=L� �A"� Ah%cI  desc�7X>�iA� ult.1a��,R�w, 5�n�q�w%`B��4Nicholas Léon�ZkAo]k&Oo� �r�!�p� �RW�`�s&�$�E�Y�"����qAgU�308.34�3*JE��^:�*. Junyo�m�,, Sungjin AhM�Y.>l�.6 QA�H Q�*Q4b�609.017�)���bx +. Tim "��,!y%xm,, César Lau�h, Cag2< Gulc鐁�-�9�"?� Jv ^�{603.090�0�*othieu.�K�,64�,Jean-Pierre n. BinaryV* deep-F��*�b2�$s Ke��� NIPS, �& 123–313�y 5. Y;P Gal. A�0ore lyE|���dq�R�toP5獬qK. e� eu�Decu�5. Felix�pQD , Jürgen6OE!��F�$A. Cummins}��\�ol.�:�tin�I!8ionuu��Cy)0, 12(10):2451s47%�q%�@ Ha, Andrew M. Da� Quoc V�. 8a vQ6�910tI�Z|e+. KaiQHe��$angyu Zhana� haoq�"Rem��J��Sun. DA!"�P�lt"�'2�e�W^� 512.03385�>,5. Salah El @P!�n�&:��V��MF�vz��.�~6. ��� �� tish*~k, A�TKrizhevsky, Ilya Sutsk�Pi� RusloT� �0khutdinov. Im� ngB���bU�=co-ZMu!fe+A`ugors>v� $r�2x�5%�Esepp*. UOsucbPen zuy7scH�!l�$�ea:zen�� ster�/th], {s fur "L�ksr�ZK U u�Mun_"g. :��E J�. L��sh:=Iu~ %%(, 9(8): 173�17!� . Ga� E�YuA��+ǀ(Daniel SedrD~Kila $Weinbergerm�n| � �G~T>�� -���38~y6. DieÚk �%a } �.am: A�E�j�z�9>q�Q412.69!�20� � ou�S�,BXs Greff, Faustino GomezI�Ju�27��cl1Trnz p� �i&J�402.351��z�9΄ �,~7!Rol"�7Pgular;s rnnsa@�s�VOs2�%����p�1'511.084�x*o. �� Le, Nav�$Jaitl�yB!;Cf&^22��Y�o�B�tCg�ar8>� �$:1504.0094)P�5 � n(. Aň �!��k�12�mattm�(.net/dc/V).. Mit� PS7��M�RAn�) cink�O�cMBeF antori5 Bui�o� Z�5 anno�"�d�@�nglish:�}n tfr_ "l �/ ingu�bx�9' 31b�3cz93. Tae��Mo�HeeyoulU,i, Hoshik LeG<Inchul Song. Rnn�a^��� EFin asA�uto�B c Sp�^�R*�^A��U�fta�(ASRU)%}5. Raz�*)8, Tomas Mikolovie:�6N�!�]:N"� � �^2� 211.5063{̾be*. V~�� T. Bluche� Kermor�P ��J�~urado7="� ��es!"� �}"� �Y Hand�B��=;� f� Kamil  S-8�zYnu6g!x2�x. Sur�S-drߚzo�:AV&: 10.07675��+,. Stanislau "Ke��iaksei S���y8 0Erhardt Barth��1Q`9Ah,9F�.����q��. 5118%� 6. S�9ngh��Hoiem)��D�$syr�S�Z�:&?<se�wa����?ur>N May� 6. NF����H]?�n! ex� : MLa�6?�8R�*� �fi�q�.�G&s��|R��5;�192]|195)X� �>�\ano� Pyth rame��(�f�*y!_L|��4�, �{&� �5.02688,=uTijmen T�*A�:v# w6.5-rms� : DR�7�� a ruGh� �^�?�t{$. COURSERA��2��>B~ , 4:�2. A���M*�, DzmitrO hdanau, V��4nt Dumoulin, D#(iy Serdyuk,�8 Warde-Farley, �:0:=]!0fuel:�)� �E�� �� %� 506.00619ela� ida �iN.>�M�i�.�q��t1��e���s!j�� 30th�er�al Co"8~�1��u�T11��2� (3. Wojciech.;Vu Oriol!hyala)��6P� "$9 }J� 9."DŽ4. �3�Q,6 6�FLA PPENDIX S TATIC ID/TY CONN�^ONS E"QJ%Kis��@3�e�"AnonRC�er2�!w��r�6���goal .f�i���ng2"ZU<�J��5�o"�fUkA<(2)"�lN�I!��s0 +>,��6vs ��nt for ob�H�6�N�%w,&8*�, "�=&z,�al*d "�gi�QE�M�ɍ"4BӹR��m&pcz�$=�s� �c" f\Ts (?Ujvn$Y 6m ). v� ORz��&,sliF��5�� o�&�5�)K&13�,�?sea�$b� u-DGE4c]s,'C�h�+"aB7. :�28PC �9�%pj�6�76�1P�)"�'�(v(�S)�RA2<�r)�P�:�*1.�*0 0.8 1 �}:( 91 96 101 6�:�7*�a��.�4an),� r%��ar.6q �(!�� U<f"'<�6R�a�5��,��wi�ė%_&^d��i�ai�V&��Ab�b ���1 <���o0:1708.03751v1)�12 Aug� �7ا$ε-Admissib in H-��D�x��Non!4rics Keisuke Y��1"DFumiyasu Komaki 1,у D"��*&���a*�� Grad�x Scho�"M�o�ie�'�V.���"^kT,Tokyo, 7-3-1�,go, Bunkyo-k� ,kyo 113-8656� pan e-ma�8yano@mist.i.u-t- .ac.jp; k�R�aiRIKEN B�� S � e, 2�8irosawa, Wako C�X<Saitama 351-0198� Absth� : In���p\���Ej7of!��a.���  K�ɡ�hH��d1�al!M�@9�I�Y�� (#!cB��x�,nb^�g%��i�Qde�[�t�����c#��j �anin�����3�Yoften�b ks poorly�a c/Z�r�@�u" �In ���hW�3a[6+�, ε:Jproc s ay3*)ut^u! dem{i�us�!�~N�A>� Poisss�ode)�" �in��s�U�c���oa L �n� ��s. MSCa�0 sub :p. s: 62C15,20G05. Key�$�sE@phrases: Asymptote�Bayo%is� eci�$thC�� �>��2����( �'!� ��F6�M��da�p�oA6�'�XAy�a�(1��; , Θ is a&�O���P 2_)m${Pθ : θ �Θ}I.8-V �&, /�<��a�8�!dn X��� ׼�)� �� D�-; ��'ri{a8whg��5of \5DfunN  XapA. E��LDH�,ss'!×Rn�8�� R ∪ {+∞}� Ra6�o.*c!�>�d%]by R(θ,'� = L (x))d!(x)!*�  9+d� ��D. OuS)cus!D� a5�>{� εz��,B�!��as9Vs:!r�g9�is.;�le if��F���=ex� n.W� δ̃6 >���,5̃) <J�εA��'JKds!BR��O�\�'.��̃5#�i3~�to �at some=u�w�εgsu��ed9AZ%⁛��-_-��,�lmumD K.��a=�F�!�� /On B5�of���i!b�Kf��=A��=�!��s֒�o�If���): R(  :=�%� [Y�4{̃)]. !�,∈D θ∈Θ��#A�QJ�t%"F��R�i��>6%�n��!�A W�er ���is��fee�)pfurUn�d�g�)ee Bl^(�NDnd Girshick (1954)�rr(1968 ergu�.7), Har+1�n�8'znd Heat-nSudder�r 1978���l2;A���=��i���w�e�s�w���(qP�ia)B�� a��a���&top2Q�iI�+� abandoned��e!.�s���p"�&Ng�^��d*aO�R �st �zB(�J�s�v���*im.(�1�A,�ay� ���? �!��u��e'61�t�(�q���xN| h6eof�<�OBhA�n.� J��3�bgrea�6fu�! �CIn >\��)6\��a%�en��AO�)&hrO�P�f�a!*V ��s1�ie-�)!jB >94��w.��inv}"C � ȎBn�t�g�+� �K� ��.Ndα ,��re α�'Z�dC�A�0satisfies 0 <_~d→∞�δ��sup��{��/c< ∞. �bYwgax9Qach)&key}A� he���o�(�-�r�..� r)� 5��cZ�V� (��s09A> Wasserm'(200�C� �O� )\0� 5F I�H�h� ,���$. 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An�!�or �UJ�A� =�l  thu>��0ny�� �7J' ����.zVN� :^s. "K in p\�i�o��s9@�!� putQiNM�Θ�Jar������ �y�If }�;n �� � E�0. The estimat��ors discussed in Sections 3 and 4 do not depend on knowing the full structure of Θ. The rest of the paper is organized as follows. In v@ 2, we introduce d$properties`8�-admissibility� � its rela�$hip with a $ed concepta\d by Chatterjee (2014), �n as C6n�$. We also �� �4asymptotic not��.1K 5 xludes-�p! . An addi�(al demonstr< us1b0high-dimensio)\Gaussian sequence model �n L2 -c KHint parameter space!�provid)�Ap!�8ix B. K. Yano%T@F. Komaki/On ε-A.v� 4 2. Preliminaries 2.1. Bounds for62�0 In this subsIh%� �%0general lower�upper bWP R(Θ, δ) that are uM�la� \s. WhilXseB/,fundamental A�<have been widelyP!�literatM��s!� stic%�ci!�'oretic -(see,%example,Aj�p��5A�Lehmann �<Casella (1998)),RL proofs help clarifyENA�ofBb,. ThroughoutRk�use a fixed estimator δ ∈ D. 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FigS*�1��"�~� �)u<Rb��dћ:�A��oi�9auV�#a��A�a�Q��J` TABLE I AUXILIARY VERBv�TTHEIR NEIGHBORING WORD�SURROUND,UNIFORMITIES�G HEJ8�OF AN 6h� CONSIST� OTHER: �O{� MA9�0� HAS A SMALLV��8Y, ALTHOUGH ITSJ��|6��S .� "�� (a�`N = 4)XB uld ��� e? mus���n��IQ� e�� ; ( .e]$+B $an b illB ɮ� q  } .�  &� V*� } +  ?�����9066.�5352�3 21 179 ��� � 0 significant a:aoul��/5� � �“� �N(��9^�%�9�j7V=�  febr=7 n�- mpDdec�-� �$�.�P Rela�a��Ws:A� ���齩“ j�ϙ`BE a�Y: I�`�n��o :�s�kE!FC>! na�Aof"� ?��+�2"�* �倍�>� ��3��v! s. 6�a�p�m�j�f� ���u! as:\�/�e��Xj��� .� 2b+�EEL8 be an outlier �Ifor other auxiliary verbs. In addition, we should show the results of name Tmonths because these nwill havH same contexts when-< word is used as? of a ^. The )4“may” has �TasB��2:�august =i sens j� jective i�( dictionary6G�march F a D%G. O%])are�osemic��s _� 2_�able II%k�\ surrounding uniformity !� all !� cof�fth!��f!�applytest, on :Fpasse q). !jexampl!�at fail!!�{G5S, whose Z���is also smaller than every neighborE . Fo e ca)�Zn��mSXequal to 0.9808, and σ:� 0005%�`refore, m − 3σ becomes@$793, which?les�an802 (�� ). W�nnot sa)i!� .&�H poly%�, but� valuEt=�isA< y cl!Dto)lower bA6UeS a greaterH t�!2correspoI@2J�(In summary,+`proposed method can detec ��y| ��c �+ ,A�of2U!� !�e�i>$. AlthoughA�u$claim nothA��iI� statistic!�esM� , ev�@ negaa��s1 prac 0)ja2 thisI�Q`� z`it�be��.#B��> ��is9G from2y!� ceduA��wUW)�ta�!�R^mo�ZE�!8�k�se�urey��(d by a few,!Y any,�7B��s6��A2�!3�,�zcluster!��~��,be difficult��-��e.AQu%�<$meaningful��n%��a5�� �a�-� ��>to judge�]��furanalysi��~�is!Xthwhil�0is discussion��uldՅ�true IN.�Iϡ��<may1�!Ia��b�Wre�ɴinterest!B!��s�!�5 m�if]Gitɖ�s ��s\ “j�z ”,�� mark q|bill”%��x����T4 persons, such�]ohnP$“richard ober�\�,��iam� davi*7le�+ henr�� thoma�mc�e��edw u�.< �:��� !F�ssspellA�,regular noun)!~L19 does�� G�$a� sub)AnerrorU^�. TABLE II NAMES OF THE MONTHS , THEIR NEIGHBORING WORD,AND SURROUNDLUNIFORMITIES . O NLY� MA,�, WHICH HAScSMALLEST.E�� EY, PAS *dTATISTICAL TEST. 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IX. ��CL��+,��p?"��a�$-�c"<y bas�!��^"by"�Al��I�Z5�ana I  aBMU il�&ra�W �_pl��o)dQi~ expl-a�hZ% ling�wsemA��n*��wqn& �,feasibility ��(� R EFERENCES [1] Y. Bengio, R. Du��me, P. V�n�/ C. Janvin_%A neu�!�aiZ) languagD, del,�wNJournal!X�M�ne Lear� Res� �, vol. 3, pp. 1137–1155, 2003. [2] T. Mikolov, I. Sutsk� TK. Chen, G. S. Corrado)lJ. Dea ��DbLecaa��d phra�,�their� �V�a!Y� in Adv����N)�Iy� P"@( Systems 26��1 �\3111–3119. [3] O. Levy{(Y. Goldberg%y a�� �$�d�1�mzit�� � oriz�o!�֫�7, 2014%� 217!� 2185. [4]![Re�R.Mooney�8Multi-prototypemT-spacM'!y&meaA�%:�e�#!� 2010 Con�sE�e N� Ameri�� Chap� Associ% 7�C�al LinguE� s: H#�LQ�$Technologi� 2010)109E�D7. [5] E. H. HuangeFSocher,a4D. Man�%�A.!��N)��Ia�%��r2�,s via global���0C�m!RV/55Z�s!7A�J750th Ann�.Mee�UZ� f L%�P���sm��1E��2)8873–882. [6] ��e�Z. Liu �M. Sui��Aŧied m�-%��16 �disambig}�A�J��A�]& on EmpiAl M�.i��A1�L��M�(1025– 103A�7] L. W�0q , Al���SAS� s: A cise Cour^�n al�!�ce (Sp�er Te�2.)� s). �04, ch. 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J{gF^aN!a���#�%�E�Eor ��EBu!T�fis,���8�%�0�sMmсs"�7m� nume��g�.��I��a ��"�wheiG��k�sW���qHh:�%"�QR#�a�B��C���p8�Zch& i��. To RB! &O<p8Sr��mz�XN �[ �[�X[e� , (5�5ϔ[&�E�&&\b@��E����=� ��& begie���S`WJ F{�Rf[�Q �t��on�� �Ip�R��c* �W�Ind� ��M�_+���H� �8 �z��y6�"o ρ�! chan�*r(?� ��>#I�dΘ(K�:.4Z�(8Y)���&�Yt).�!�2)�IRm�0dE7�e>E�d9 in eac�h variable. The corresponding generalized distanc#3 �V 2 (X, Y ) can be expressed by (3.7), if the�@ectations on the right-hand side are finite. Note, however, that 4nice 2compu Q<ally feasible re�en  s of2��make � ntial use"[factoriz�4ρ which means��y�8no longer avail!F�R in this setting. 20 B. BÖTTCHER, M. KELLER-RESSEL, AND R. L. SCHILLING Let X��Y!\random5�s wit!� luesyRm,Rn , !�<ectively, such t!A4for some x ∈3�y 0n P(X = 0) = �x �Y �y) = 1 . 2 (5.3) A direct calcul5CMusARΘ(0,? x, k 0, gives .Q= γ · (y)i 4) �P γ = 2P(X1 6= X5 , Y Y6 )−�4�4�2 4)P(Y3 5< (5.5) where (Xi80i ), i = 1, . , 6,%� iid copieE_A=1��eADq0. Now supposeI@.��is homoaious!�/or roI�A� inipt, i.e. 5�α, β%�!U\2), all scalars a, b > 0UT orthogonal matrices A; Rn×A1�B Rm×m)�aX, ba� = aα bβ.�� $AX, B $� hold.�P� ity,!a06), yields ΘA�AJp |x|α |y|β Θ  y x |x| ,%�6)Aj7)  8) �%{515/ceq�� showm�u,/|x|, y/|y|)!�La constant. In partiA��r�})�ity�,degree r = sA%[R|� �%�.��iA��·� . Si�L�HLévy–Khintchinea�`mula furnishes a oneto-on�����eEbetwee��e cndf�its Z8 triplet, see (sHcomments following)!� orem 2.1,��ddetermines uniquely ρ: it�3��4to two Cauchy ϡ;suresAis�J– even��a lar�L claseTwe��s&�assump�?A 6)�0(5.7) imply a � (up to=�) cho�8ofX�,?�we have recovered Székely-and-Rizzo’s [ ness�]xult from [SR12]. Lemma 5.1. Let.� := kfX,Y − fX ⊗ fY k2L2 (ρ)���a.m d�m c�m�a��De�ion 2.3�%�\ the symmea�!k!z4 ρ satisfies #$integrabilA��c��S(5.1). I60:�(of order α�4�}e�2��y�l��!� each arguA�AhM�me� d�ng2N�iI1�$multiplica���e�E6of%4form ρ(ds, dt��c(�=`m)c(β, n)|s|−α−m |t D�−n ds dt. MoreA!�,2���"p*�靁p��.�α i�β . 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Ga��an &��us fi� � E��res ��Brown6<��� y [S y$Sec. 3] do� ( an analogu_ `z�|. As we will encounter similar (!�mor���)�ͼ���te�Fting,R onlyA%�t� �e7Qrefer�� proofs _ � ompan�� pape�~KRS17, ��.�rA{�a* 6�Ipe�"��c�}� negaN �ite func� Φ :�#→ R�GΦ� �5��f� ��x Rms E.I��0�RE(  ′i�I��+E� �p�7�� A%�ouslya��-R6 � GΨ q �a>� Z� v&P�d%��a�6L�� ����dw�Z G� G(Z �E( | G��7��*� �7�(1 ��,�be n-zeroV{� �dz�m��RA��d �yU structuA��ij by%�cndfs!�and Ψ60���2޹any � �  UC���)�d as G&t:= Cov2%;!ڭ9 E(X1�XY1Y2), (7.;��D>), (X2 ����2� _�. � now i��ifyN��%]~Y�+n7.2 (J���,v# �)�� sume�]  Y��/ e mog s EΦ(X��EΨ�< ∞� !/A!%areE���� .{�=. �.!Q 4) P����e����#to~8]. By���d�ingEځZaj ��c��.���w�Qe   E Z�$    (7g = E 6+�| XX)� Y2 · E2:N%�. � �� =: φ��?s :��J�� =;��tφ7^�A�+ E.1�T��D%�(:� Y+ N�Y=Es�, mx!�se}� &� s dueA-�c� �l/ s. A�����.bfor E(.��, X e�-�) turnsI i� 4). Fs�,� �5atW +it ��requi �6>.~�ePn 6 y d un5�����p�Vs, ; �[��m=of3 3.1�� R�s q ] Christ Bergi�unnar| st. PotEal��y�LocZ�CHXct Abelian Groups. Spri��,U(lin, 1975. ��] Björn Böttcher, Martin Keller-Ressel,�René�chill Detec 2� of�dGs II. D*F ���I &a nce. 2017�HL00] Yoav Banyamini8Joram L�X nstrF��o:Nonline!H�al d(ysis. Ameri�MathematSocie� Prov�0ce (RI), 2000�!0 17] FA�.6��: M� Mult"; �D�1� '�%4 R package ver� 1.0.%�LS11] Nail K. Bakirov%Gabor J���.Rs !~,central limi� ��� ��ry sequE���oA��f!#ba�J�Ap��oaP55(3):371–394, 2011!E SW13V�Jj��Ja"Wang. -Type��cA� s: C+ ion,� roxi!��o�yd S� Path7dperties, volume 2099 of Lem �� � Y!s, |A5ter2i 2013�X09] Pn$ J. Bickel% �YA Xue �c< �o��:9�* g e�AnnalsaZ%`�!�sti�L3(4):1266–1269, 12A�9. [Cop�(Leslie Cope��!j�79812�Dsö81a] Sándor rgő. LEtbehavi0� empia�$l characte�"c � E�=PrU�(, pages 130�44���8Auy81bZ��y|te����Us. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 55(2):203–229:��5] R7Tes�wa���"V �b �@ Jour�of6��� , 16a�29!G29AU98�uFeuAR4Andrey Feuerve��Y^Y82!��2�Y�FM77]J��ei<Roman A. MureikaI/�< its a�� <i�!..yIj88–97!�77- �23 [Gen!boph���noves��� j��9e�302.�HGFS09] Arthur Grett�]4Kenji Fukumizu���Ba�th��,SriperumbuduB� "�z�!oj��85E�9a� 2 20�� Jac0�`iels Jacob. Pseudo-DifferJ Operatodnd�kov�G�LKFourieru� Semigc Imper� Colleg��es�"ond!$200�wJKLS12] �, Vik�"hya Knopova, Sandra Landwehr)T�� *w A g� interpre��o�N� trans�  d��KUJpr�. Sci�� China:6�55:10I126 12. [KosA�DMichael R. Kosorok�^�7�� 1278.�DLyo13] Russell Lyo��P *�� � spac��CAi.C( 41(5):3284�305���0Mur01] Noboru�` ata.=NK �m2 �m� Z��  Third I!��nr(al Workshop �I&� onentU�� A�sig6SeparC (ICAA��)�;29aZ300�E�New�1� A. Newton�O��di"��p�by&� �Q.Vz�33e�35.�Rém�Bruno illard�A� .�^ %1292(Sas94] Zolt�$ Sasvári� a�ve�J6�zi&�F� 4kademie-Verlag"� h 1994. [Sat99] Keniti Sato.q��Pi�V"�nA.ly DiviM'a ribu <s. Cambridge UniU ty P�����9C ,Sch38] Isaac� 0Schoenberg. M�PiS%��p��ite"� �K���a�q*~� 44�52536�38!er��Robert�erf�Ap.� �T� emp�M2� �5C <. John Wiley & S� �QSR05] P .!mMariaM�HierarchK clus� ,ng via joint�#-within �s: Exte�) ward�"�mum.(�method�"� �Ck#if<!,on, 22(2):15s 183e�� H�́~����nU�3� �B���b���Re!: der:���� &� f930�R306�$ G�On��J%Q$of��>`+�.*1 E3�h4E, 82(1 27L 2282!��hSRB07] N���]�3:a��#A�A��`� ce b�&a�a�2&y4(, 35(6):2768 27� 2007a�cS10] �"��Alexa!� nurr� symbol% ocia�#a"%d solu���a stochaa� d.� &,. Electronic.� =x, 15:13�139e$�1�SSV12��L ��,� �m!DSon�Zoran Vo� ček.lnstein2����y? ��(s. de Gruyt{2nd e45�Ush��TNikolai G. Ushakov. Se�ed Topic� C &+�\VSP�7��0WMF95] Herman���%�(Ulrich Mü�Funk.�3�U��k�DTeubner, Stuttgarth�oZas�ViI+0P. Zastavnyi.a<B&qC�s�,�f�Z�,� , 73�!�|�2�4TU Dresden, Fa�chtung�$k, Institu� �Mh k, 01062 Q�G%=y E-m{add�;0: bjoern.boetQ @tu-pden.de URL: https://www.math.2$�/~ =�/B]��m�.k�qel�a��m BFa�rene.sQ�^[�f�� sto/?/ )�"2&e�EgExplor ��R�ized V�Y�P arXiv:1402.0635v3 [��.ML] 15 Feb 2016 Ian Osband Benjamin Van Roy Zheng Wen� nford*�t IOSBAND @ STANFORD . EDU BVRF�pZHENGWEN 207@ GMAIL . 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ACKNOWLEDG�,1� �.���o���z�lJ����L��:7 �0&8 �88 �.r�!�v �|:��.QctA��b �C�#"�"�#�can~`jlu�Sk�a�9�& iV�ѦF�is�-΢� �-�� CLUS��(AND OUTLOOK�~��ofa��Du play;!D�oS�6n�F* � alSi&�tk�o�"��!�6��A1B���6�=*G_�\-7E�e��V� � �B�-�Tpergro@&&0�V�y"4!�� � �GF�)/dfhe*/ ��!5"%x�#i��a.LM�*".�ofR\Zou, a�]A�&hM^�\e&A��t�(art2n�hU�O �A=gs&X ��r�vU��"��u�@�t"NY� � �c�hly quite9>:�Yr�v5iiS.�BQa�^ "~,� a �` Y�. Ta�[� � j ESN2zH$�2� �&�ia(ve�A!�not&\!(� �,�F���"qC�.L(Iwhy��J2�/v82�s�H2 @Y$&�XI p{ s%�.��,��rW�i#nh upone+�p�0"�c N�� �z FA5�f g��0s CDI-1028238��<CCF1318833. R EFERENCES [1] [2] [3] [4] [5] [6] [7] [8] W. M,t�c� d W..t�,���u&D�u� �4ideas immanent�{rv.�Yr/�Bullet��f2 J"{llogy, vol. 5, pp. 115– 133�43. C. K�I. Segev���d�og *stH-*�s�ce_��N�Z�N�zsci�) ��3�$71–1177,��0. J. C�gee}�D��i�S �g�WS+�e�eto�2�t{ ReviewsN���1 ��8�90��M~ rgula�nd C.-M�9ng�Te�s�a&�r)�1�m:s"n6&�cM.Hso"Eo� Jour��!0&ut-379��5�$2809–281%�X98. R. D. Caz, M. Humph)%� B. Gutkin�Pas��2f%t��$�&2�*;��&fs�I�s� PLoS��Ew � �T2, p. e1002867, 02 201I{L. Gil�# nd T!��x�:� Lear$�W)w �ge��li���/�hgq�-:��Appn�pt. �26)W�2M�(4972–4978�87��( Rosenblatt�a��: A���b����U� .storag��d organ�e��b�$� Psyc�v�#.ew � 65, no. 6I�386�08a�58.�<E. Rumelhart, G.�H�Dd* R. J�8 llia�5�5beeA�=�^�n�!Bby c/�pagY�in Par�X�l*Fe ed P"C`�,A�.��e J.!�McClellaL>Ed�@ambridge, MA: MIT�ss�86-1, ch. 8-18–36T, [9] �s[11] �q���1���1���1���1��18/420���ġ��22�22�2226G274 29] ���JnA�puEa�&��&e��K��s� emer:� coll�8�v�e"�7"� ieI�!Q�.�T�qcad. SciQǑ8, �� 2554�55E82. P"u�ArbibiE,J.-P. Joseph��AM�of �ticost3tg�l��� �lm� oculomot�� ssoc]-a��< Ǎ� �C" t!6:#�7i�m�31��336A95. X.A�auIM P. F�“Realr�pQ�*� of���m��%��,"F%�uo-�-�a�.� l� US�&} �^� a>iP,$ingi�LoS ONEM��8 �2, �52946���0aaA�T.!� schläge nd H�&rkram%��� � �wмstU@�sWR�:<ew 6�c�. <e�hv�U��&�p�!�al.# �14 ��1�`253!� 60, ��. H. Jae�� �Haa Har�c!=. �:�� ng��[0Bi_sa0\� �g�wi��sYIpy[r�� � 30 �56��a:�7�L�8�4�O*�`�,�G�SceHD’Haen��,D. 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In Appendix A,�$ technical�ail1#0 flawed proof ��]%L@given. As an addi!jal noteS0 stability of%FDN is!( even ensur!f all � �8of A lie within�@ unit circle. For%�4Λ 1.5 1 A = U!�$1 U = (12)!��24.5 2 The pole��)5Z�=!/�[IA6 )8 A]. (5) We c�2A�dgeneralized characteristic�Q� of A%@ delays m. Please!DA�atX [1,...,1]E��iIz standard f`� founE�lliterature [17]. Therefore, �-�Q@ ifwA�$) has only!�Q�ec, i.e.,%�E6<of magnitude 1. 1such a�9c:� we have"0= z 3 + 1.5z %� \− 0.25. Let us assumeQ� of dimens�$N = 2,)p�)t( m1 = 1, m2 � a�8feedback matrixE�(3 2 A= . (6Ex�4}�3Ity�$ decomposia-� ]�(Λ U yieldsP��(2 1 1 0 U= w,Λ = , 1 1 0^1 (7) %;�tA �U!�0an invertible �� ��,�,Mis a u�rdiagoa� �4e�E-�of.|�(1t<3)(z 1 + 3) + 8 )�!��3#�+�181 z1,2,3 = [1,!`,1] (8) C. L��Axe�FDN’sU�(ness shoulda � � o�(choice ��-� m, butI� (:� A�P other words, we wantA�yGzeE�%&ces AI�!�9�i���any �!X m ∈ NN 6 a V�xq�b��qt.1 Itembe��w!� [1�Bbeinga�tary, i|AAH = I,��a.con����AJp��b complete!q%��Ab(alternative���9) E�!B�> !�. . However1��3 ry, ��mh, ixB�>6ui�EXMa 1 =I�+ 4z + zA��):s�� √ 3, �+A�13)i�largestmDa�ƩqPn approximately 2.145fun�le.A�se exa!k$s illustra�� •!re�? non-�!0 triangu2A,%�which3� :��.:L��\>��(��sQ.notu�UA,A�th)�canA�i�� on m7o6�AM�A F�!l not j�!Wu. I� following�ex�i ng result���A�Ũ summar塡|�a� cis�Pfin���b main MX is stated. B. Motivatn�E-� are Ei� %f Λa��=��$mma 2 j=1 .�L3 (10)"1. An�xA�:�A!$un�95A��1F<��!p7 �2�!li  in9�)��S�( been named9T� �]�]< this manuscript^a>$erminology�avoided��reduce�#fu�� to emphas�� the �cyA\Ax�1����.j�2�8 Consequently, �� "� in:� �a�:� T!�� �[ SUBMITTED FOR PUBLICATION IN IEEE TRANSACTIONS ON SIGNAL PROCESSING, JUNE 2016 Proof: First��|� 0)| = |� (A 1, henc���ra} no��!Z5�m(is zero. Se�YT$if z 6= 0,� 3(z) = 05equival�to�be�s of vA√&�Av = D(z�� 1 )v. Wria`� ,= ρeıt , w�  ı =.��obta� Gρ)D(.)v . Usa�the fact�� D ��ywe Ib ıt kvk D(e )Av !� = kDc. �.<e|�x�b onents. 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Remark 2 The defined protocol has communic U�complexity O(n2 ) (mostly due to the necess$to @�e$matrix H).t�_of/�Pcan be easily reducedr�O(n) if we take at random not an arbitrary | but a' Toeplitz  z0same size. In� next sec��w!0scribe a� with��mR4 min(Q, CM<). (We show in S b 6 that no:^�public � ness%�smallerb|�, and�(conjecture `!�� holds forp�s �privater.) 9 A5Hlight upper bound. �her!�,at if k is a~ stan!��d{number!u-�bits is Med by!`8olynomial in n,!k-rp�E#proA a shared!�ret key)O0is longer (upA�Tlogarithmic precision)-%� mutuw formiM",inputs. More ;4ely, our claimm%dif a F���z! �d from T xA , xB� someF��Ehprobabilak�1�cǫ,!V4n C(z | t) ≤�A :P) + O(k �o^J�O(ǫ), w)��A) tranA�pt1q� . Si�P warm-up: determinist%[�UITout6�0. Let us firsnsideruXcase k = 0, i.e., AliceE�Bob doe�interactI�also,E�now, l ^assumA�ey useAGIwaH. Clear!�$this model� very weak [$in general:��can�tHgree on any nontrivA���onQ�!�out�!0ion. However,f%��s (a�� specSI�A/a�xB A� is me�Dbe possible. 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Our�of!�)7on-�IaGQ�s%) public-�ness. Is! sameI� true%�6=�8 private sourcee[IA��?)05!2 AllE^��are Aized. ItύX%$sk whether!_(can get rid!�external D �WeaRjectur�^at�((O(log n),  )-stocha��tu��!Q�W!y?�� made puree�termin��8(though it woula�$quire veryI�A`utElal�lIn , bua��i�Znot�]don�atgener4 ase.As!�of��t6fac>w��a�� ter under�Oing ofQ%b��non.ob!9�Is (such as Chaitin’s Omega number, [Cha75], see also [She83] and [SUV17]aJ08 Acknowledg��s �!�gratefu%�0Bruno Bauwens%��insight$AEen��In��ticulaE thank him8allow�usADrep�kQpr5:e “l_.�”��Sece?�3e��0�b�7�2toE�atten$Xthe improved Kolmogorov�-�A��-�(Slepian-Wol%��+ 2.1.A� � Tarik Kac�R or attrac�E>~��o [CABE+ 15]. References [AC93] RudiAhlswede�@Imre Csiszár. C��i�aK!F�<@cryptography - I:�sha!&(. IEEE Tran�`�3��Uy, 39(4):1121–1132, 1993. [ALPS10] Luis Antunes, Sophie Laplante, Alexandre Pinto,�8Liliana Salvado���curitya $individualAgta!3t. ICITS, pages 195–210, 2010�Bau18] 2� . OptimalA`Ʉ�V0polynomial ti\ mpresE ��a��sM wolf ŝem: tA�erU9.siAPc,ofs. arXiv pA�int $:1802.0075 ��8�BR8� Char� 8H. Bennett, Gil Brassard,iHJean-Marc Robert. P��cy  if�3by �P discu�$. SIAM Jou��onAZpuA�(, 17(2):210!V29!��8 �Z14>U�TMarius Zimand. Linear V �-ixi�a�short! grams (  p� E fewM�ų).�ME�29th Conm=��aa�alǩ�H, CCC 2014, Vancouv�TBC, Canada, June 11-13E:�4QQ24A�247i# . 28 y� Chung�~�nA�i Al-Bashabsheh, Javad B Ebrahimi, Ta�/)��Ta-Liu. Multivariate mutI�&� inspired!�` �-� "` !� ocee�A��A�!3D, 3(10):1883– 19 �5. �866] Gregory J.��L. O� e length!�pr-�!��(�iDfinite binary sequ���.Q]a��<ACM, 13:547–56EX66A��Cť���A<�of�� � %� id��� toJ N��\ (JACM), 22(3):329–340A�75�K7a�6E�János Körner. Broadcast channel� ��f �al mess��IR�u� Nu24��3 ��8�e~@CMR+ 02] Alexey V!�8ernov, Andrei AAIchnik8E. RomashchenkoA�exap ShenE�< Nikolai K. Vere-agin. Ux semi-lat of5��� !�rele� ”x% �  condim�to y”" ���o�xD. Sci., 271(1-2):6�95a{02A�N0�{J�4Prakash Naraya�� �c� pacitie��mab ple  al�� 50(12):30E� 3061�� [GK7��Pb  Gác� F!��.�$is far les� an F�e�bl. Co�l Inf-6 y, 2��14!&16��7��G�LVenkatesan GuruswamiE�$Adam SmithM�d-i�%�eT)�U� : Explici� nstruw M��o�U' �undJ��)�er!�� (FOCSa{<010 51st Annual ��D Symposium on, (72��732 1a�GS1�������� cod.�����N���@A�A�AC�@63! �3E�16� Hor0ADYasuichi Horibe. AM�e��V| ;�e!�(py. Applied�he�;cs le+ s, 16(7� %�130E�%�Kol65] �i�ev&vAE�r �e� �quanti! ve de���p �qM�emsA� orm.��mi[, 1(1):�B�7���6�QKR1!�� �.�A��/25nequaly�)0icK al,poi� "� �aM�on ��"� 59(11):7iV 7167!Y�1)YRV1!Y��b.���O-x�y:L�CV��� 2��Acom�Ntor�:�aA �bO 501.048 �%q LYC7a(�S� How Leung-Yan-Cheong�*lti-usYwiretapu� i�P feedback2 �ly 1976. Tech. Rep. No. 6603-2, StaA+d UnivaLMau92] Ueli M. 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Bio Ts 64 (4), 1215–1222.Jr�,D. Yekutieliu1)� ntro"� falseAco%.��, in multiple�g�%��9 nak&�, 116�188�@rnbaum, A. (1954)Ŝbi�.� f !� ific�. Jour���; Amer S al Associ�L 49 (267), 559–574J���5��^e7eġe$Q�x��fk)ara)�=�| 6�$to likelih��ri �)��A1C$ Mathemati��ls 26 (1), 21–36. Brown, L.!�A�,J. I. Marden!d89��et ȭ�jq)� �ng�1�s.��ei -a� �� , 20!k 235. Flut��T., X� n,� Prit�d,�M. Ste�sA�13)% �s=�framea~�, joint eqtl "�in-�A� issu��PLoS Genet 9 (5), e1003486. Friston, K. J.,A�P. Holm7C. �ce, Büchel �3 Worsley!f99). Ma%sub� fMRI ��co&j ��0Neuroimage 10i�38a239J���W%�Penny �,D. E. Glaser!;�0E�jrevisitSk�Ik$25 (3), 66AH667. ��, R.,V�., et al.^�1a��[͌ ��iILge�-wide a}�-:� A�ed]< 8I�48�,498. HigginsA7, S. GF omps!�A��D%�Spiegelh0 ��0A�A re-e ak�& random-�2� >` Royal� Dociety: Series A (}�in !) 172 e�137��$59. Iwasa,A� (199���A"G unbia a�)Wx mp��eu�ise� aa�triJ�� .��Institut��al �j s 43E� 65�0665. Lehmann,Ag�L���2�;�+ms��er�A�6 g!Eq�s 2 s 54!�552Bs�!�J.a�Romano%��6�.(.�Sp�er Sci,& B(<ess Media. 20 �,Aa�:Q�198��C�is��noncentchi squW� � �eRe�� 66–277.��� , T.�[�D.&TruaxA,67 �Ń��6&r�� �eD onen�familya?�e�^�38�# 6e�(697. Nichol�E�Brett%8�AJ e�T. Wager�� J.-B. Pol`����V a "z�i�!%��w�A�1 Z5��.���,��,53–660. Ow�] A. B����,Karl Pearson2�.6�]�,37 (6B), 386a03892. Perlman%�D� L. Wu!�� Pempero�Oe���ati�a M��1�  35��69. Pr�|�J a�uͷiA Cogn.a: Ar0approach to bt activ� experi��s-\��5� 2� 270. Ruff����Re� Giugliano� Braunwald �Gff% 4N. Deenadayalu-0$ Ezekowitz J. CammEJ�I%B.��Lewis&Parkh7ko>�� � aris��E?ef4 ^$nd safet���oa�0anticoagulant�L$ warfarin 0 atieatr-fibrill%?�:�29of �]is�2�� L� $t 383 (992a��9%�,962. Shenhav� � i@Y. "? a@�1a@Qu�fy��� �@in syst: � �� ews:%�r . arXiv p.#F H:1502.00088 . Stein%�� �k*�ժ HotellingeZT 2 -A�I�& ^a27�a 61�<623. Wang, W., ZE)�W� �n��0+ �it aneousc-wisee\!:� �eZ� ����0terface 3, 50ţ11. Zayk!#D. 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P ROOF A PPENDIX A OF THE P ROPOSITION 1 When ρ → ∞, we can attai�|e asymptotic closed-form express�for�Haverage sum-rate oflA3 -AS algorithm as follows:%!�Z ∞ (c2 ) 1 1 + log(1 + bρs x)fγ s 3 (x)dx = log A b b 0    NK NM X X µi,NM µj,NK iΩh +jΩg iΩh + jΩg e bρ Ei − ln 2 bρ i=1 j=1  Y ; iN −2B� − 2�bρ J(NM NK (c3 ) G� �1 XB��4ln ≈ log + bN���  L ��1�<��C )/��b6 53X R2� �,+ + ln (bρ)!) C�ln 2 i"h �!L16 �B��  %;�8  (c4 ) (ln ρ Y ) = .(47)A��n dbi� A R̄sum1(� mg( CR-NOMA-ES $RA PU-AS SMCG  12 10A�2��+��e� 300m2� Fig. 9: Am)q%UE1 vs.e-R�2 in ��, N = 4, Ps = 20dBm. less power can be allocated toa. Ia�dis case, R̄1c would decre��(when Rth in 0s. Again, all� prop�D AS schemes outper�� -RA, and )i` achieves a near-optimal 7ance i�de entire region. Moreover,~� .0�of %� is bette���aEat%� ��U!C�s�� r toL BS �itBopposite1�1��1� ��XBS. As discussed above,�!zprovide 6��� �%�.���<SU�-�d networks by taking advant�_�V instHneous channel condi�� s of9�(articipantsh0systems. 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F2.8� 6�2d . �@:=    ·4∂ ∂ ∂ F F ·  ∂xd Fd  1 d�[2 2 These matrices satisfy the polynomial identity under composition J(τ2 ◦ τ1 ; x) = J; (x))J( ; x), in_Lring Md×d (S[x1 , .H, xd ]). For s = (ss2"\sd ) ∈ S d , we defineZevalua�( map evs : c�x.F�h� → S, which assigns xi 7→ si , i.e., G(F )(>��) := F^��. (�(constants c �we have�(cW�.�$) = c.) Us!% this�:�� Jacobia� trix of a.��Hτ with its entries1 ed at%1point s �,d as:   A1� !� ; s�% x)�evs Fi F ,?8xj 1≤i,j≤d � @�s)�Q ). II|same vein, given an endomorphism�of1��.%9�]!Wobtain a%fτ : A'!�I*$d for each�, act!sHcoordinatewise, by I�(=τ�),�(x2 uq d %"(F1M�A� , F2R�%FdJ�$). We call�a� dynamical1�ioA�pA� ocia!�to�(. The imporA�H property it has ise� atibilityI<�cy�!v maps5�s:!�τ�A(f� �81 )(s). (2.2) !�(particular,%� iteri�of�A�!pona%�s �m� )m . AeRequence 7is �� is that i U2AisATaut]T�,}I�5T� :Nfσ�N�D��EPK bijec!y , because*�!$�−1 = fi��!��Q0map. A second2����e*e�%h�Ve��i�f-}�j�s�js∈S%y3)Vx).��>B!p�nalogousAHiXm)an af�zvariety AG�nAhLorem 1.6. In generalAiP$ nonlinear!, and�usually does not respect either additA�or:�$ multiplicMI�n%���EHmay�q��S�+�S ) 6=A�) + 2 )�,6=�) 2 ). Fur� moreJi��0b( 0, where 0�-(0, 0, ���0�AP)� abov���s are steƅ���sa� but �T emai�mIpaper� will!N���t!�A�case<.s aunless !}ified o� �.!�,the Appendix Mislpr��aoul�bat clarJa�e differa�s betwemvgeome�%}4algebraic view�m��s BM��o��Q� (Pro� 7.1���i A SKOLEM-MAHLER-LECH THEOREM FOR ITERATED AUTOMORPHISMS OF K-ALGEBRAS 9 2.2. p-adic approximate fixed p�W�s%�2b. Now!�%_alize)Ee %���!�intega6do!� Si< Zp --. � onsida�n2i� σ!) R = ��Z��.%d stud� -\FF���9follow� lemma�`erts �exist!�sapZ (mod p)�X(invertible 6�� for ^��E�*� 6^ L�02.1. Let p be (rime, let S =H)t(is finitely���; as a,module%6Eσ���F� 1WFd ) :,F� ZpN���n1�� .��%{ŕre�an E er m such ��very � �0�: �u�  � !�"Uw^wE �:����at s06 ies A,Nu���N�I�S���UJ(σ m0 ё� d >� sF��:A� x u�; �is,� 0 � v) ��I+. Proof%�� S/pSa�aM1 si�2�2JAqIF26�,���hasi� a+� � by$� I*�2�hepit�}M9. Take m�Z�b or�%of GLt /pS)�@let^ �:=!)� E2&�  denot Q5�@Z� ��Ik�� � &� . S%Kσ�e~q2� F A�Es2A�E�A� s1%�s2Uo ⇒E�A5)�I���9�It����* quotient� f¯ �(%K�de is well-m � milarly, I'A�!a%�� 5���s)@coeffic}A#AL� ^�� `s1 � .��, �A�a.akeh try-�� �n%[an�XbW%t�� EQe� ~ fσmE�(s� �; )) "@ 0s) � �;S � )>>��(!�^A�. Hi%�f��{ fix�a �zJ�-]AXl (j ≥ 1, soMX |j (s0-c�E�ma��� �2%�Ik 5.(. Substitu~�t�� formula yields._~X�m.Y�(By our choi) m, Ma�0)�B� ngruA��t�&{ �QS,� Trequired.  Remark 2.2�argum@of �� extend: ���F� �,� � � onl�weake� nclusion:!rep�.�s0|!�*� fun� � -����.��ev!��ɀ)��M7� M 2 = M0�dempot�in�+�_� 10 JASON P. BELL AND JEFFREY C. LAGARIAS 2.3. O redu�l �s��start�mbedd� then duJ XLech [20, §4–5]. 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(N',ade = �C :��W�*��)kV!&����(�;��NaȞ"(o%�y:&)16$b �a�8Nullstellensatz��L�iѠ�~$m:��"( = �r!�3�d�5�  Jage` H�����7�)�, fail�5>method�e��p��fe�2� s ariA"�7:� �ra !k:z�.Uu"K�� ]�*�Pa� cer�6��/ �2�ZjLR EFERENCES [1] J.-P�0��,2�, A�!�� U;�!Fory �Bs,�;�(mbridge Uni` !��P{, C$, 2003 [2]�;S.bf, A���sI"�� �6s,!r�c.(er. Math. ST7 (1956), 35–48. [3]̬ F. Atiyahe� I. G9(cdonald, InϞ=@v&-0H. Addison-Wesley Pu�|�Co., Reayg�, Mass.-London-Don Mills, Ont. 1969. ��J.ɵell�eQ�s�xkolem-×�-�)v�e92(��iq�J. o2 3 (200%,67–379. [5!�z$Corrigendu��:&�A���,�'J. J��8 �8), 2�272. [66��0D. Ghioca, T.�Tucker�D*�M�'ll-Lang� bl-étal;N�!E"J. I%132��1/m$no. 6, 165A+ 1675. [7]&0L. Benedetto,.��P. KurWf�gEH6���A��jZ��R�G�u� �$Annalen 35 �42), 1–26. [8!a� Béz�"<, Une généraliBLon du théorème de FD. Quart%T z(Oxford Ser.�$40aA89)�A8. 158, 133–13aL9]!h?"��J.-L.��eI0eger-Valued P"tq�survey�RTd Monographs Vol. 48, %�-�a��:a�vid+4, RI 1997. [10! W.�2��, Local�!2�e��alT�iY�Stu�P Texts, 3��� ��� F�198!�11]A#4Denis, Géomé� e1��i��ré�a� Bull��)zFra�122!q941q!o!��2] H.7�$F��'jM!V� ��a!� vent1n16i��7A{�7a224!j3]A�Eisenbud�f�m"42��, \�to�#s�Ky, SpzA8erlag: New York!�a~14]��Eve�*�,�va2�r PoorteR^. Shpc| nski�T. Ward��)t�c���ű!rQ� V�, 104�P�in.3�Q7�u]�ɼ!%�5%%R.  &. R � t be)vn�nw�se~-: 108!��8%w�2��ig16R���B� �P3��d3�+1s, , �t A^�pr�1���N��~y 129�#�0� 1392a�40��7�6��(M. E. ZieveA`_ �p� 2- ��a�� 2�co�(�II�%�. 171��H46a/48��8E>Hansel�' dém0��r�*4�,%bz8Comput. Sci. 43%��T�@ 1, 9���9�19�=$Hartshorne"� ic G��Z� m�7a�20]νecha�6�o6A�!��sY�, Ark%. �F53), 41AG421�j 1] K" � , Ei�?5�� E��shaft ?�@Taylor-KoeffizienC�)<�aM� Funk" a�Prq Kon�S�da�ndTAkad. v� tenschapp��E�(35) 50–60��22���O� �� *H]EA�"��" �CO  Philos�j�O  3�� 232s�Add"�� � �"����"��c.I6��E757), 54�Y242�� S�!th�Bfus��s�Q��ed.e�ٮF[  NeIX�,��E5] B.�K%� uorpo��į<, arXiv:1307.588E��6� J.F��S �fac�7���h�beter�; ���i|c�J�� 6���>o %Ri �d�%HMollin, (NATO–Adv�_u���In�,e, Banff 198�=Klu�%Academic� 4ers, Dordrecht%>$9, 497-528A��7bb"ijdeman� *on=)E�exp!|�t�5�$s, EnseignV+ �21�o75&�5a��6%�8]� Sierra,�aic izer�r, =Q�ށ". 363�I11), N� , 4`50A� ���9 [29]����0ige Sätze ü5�hgewisse Reihenentwicklungens<.<e Bezieh mit Anwa�%(uf Diophant��Gleic ,, SkrifA�Norske V_ sk.E. Oslo� t. NԻv. Kl� (193�a!) 30>��@ Verfahren zur BeD� �M�U�er.����d.��r 2��C. r. 8�Xgr. scand. à StockholmA*�3I �1�18A�31] V."�QE������&�a��1�fu��0ety% �hD4n. 289e�9A012& 13� 32��"N� , Ü!�0den Wertevorr�$on Potenzr%� im Gebie�~���Cn Z��n,�h(Reine AngewQ�15��2a��1�28; 6��6%�(3] Shouwu Z�G , Di�/bu���P�ic~�NL:bu�?�o��(fessor S.-S� er7�n: B  in D=(e���� �128�8430�"ter��al����6. D EPARTMENT OF M ATHEMATICS , U NIVERSITY CANADA E-mail �(P: jpbell@uwaterloo.ca�U�DMI 48109-1043, USABa�dlagarias@umich.edu BOR , pXtX(WATERLOO ,  �ON, N2L 3G1, M ICHIGAN , 530 C HURCH S TREET�<NN A R - �l��P��ct�drug-tar�Ų\(via��, lear'$ Ratha PecM�8Hao Dong1,2∗ A�Hryna Po3 , Zhou Tao �W��l706.01876v1 [cs.LG] 6 Jun 20��1� mpleX Labn �i� of EDqronic7 ���Techn2��6�China, Chengdu 611731, People’s Repd�cS.X 2 Big Data Research CeA\��� ���� 3 D~��t�0 �emad�y Biocřrge Man�x&�`, Virginia 22030, U.S.A DV� (DTI)�+�dAon plaM�*y $rtant roleA2 develop��.�  expe�,� vitro"to�Hntify~62u�!�v��G�n��(, laborious- time-�(uming6�rd��'silicoZ" roacR����oc a simu� � mach� Q�bee�jposM�s$��� �|*�-�,Ju/.��i atta_�9u�T�%�n�Ac|��.�;��aS�to�cO3�n%�N��,��A<�� ���66in"�Y)�l/� al&�Ms, (� "�, bin%^typC2 nd sQ�. Wm��s�3.b��i�8avail�/�" y may per� poor.���y5&!��i��ty-ba!� link.������:Z$ip�M$te network8�'�;Z6�P-�e DTI.^�-���u%�top�xE�.���1E!�op!�p���Msp2[ ��}��,�>�n�j�!�-Ss m!�be3 thanFL-<�;mpa�AF ��d !�'9� >}r�5 on neighb� $dex, Katz ���3JaccarImdex�sZx/t $four renow�?�bench�� datase*�i� �9��rkably-�M�8[6gg .alt��-)�5uti �8�l���e��it���m�s� �o���*�e�is #�BA#�p���� �P� D�%�[��s,*S"en :.�5!]��-�i�u�(. Keywords:.J��,�!��yM.�$, low-rank�* rix,q��Gq�� E/8 BACKGROUND DɃ�a new p�%A et5=cosTrg<[�(�oi�P [1, 2>.M  save )AiL , sc�$���� �)� ���-����%[�,M!as re�,��Mo�3<�T3�s����c�/�2T�-� iA�h9!� most32�v�z�/a�7A���@ they�4hel�@` dis)�� �4]-�*-ef]H� ���6�m32�� [a�1)��C�ĩ����c��n^����tei"V�r�ry limi�R[1��2u�r1Qbel7��ny�gle�|H������ �< �����%��y�"�f b� �7verifY��!)�t�7xtrem>N�!�E~&� [16–�%�!��=�tA��"C1�n���. F��> capa.��tE � ��-sc�u �A�pr%�� �f c�|ng, s��ng� proces�"�� ��d ��.��� ���#n IoA�� effie���l�"Q�m8.�:�j��>�s��eful e�!B@��zly novel%�J aRdidat��or"�8^/��00�a�1E!�� �yE risk�� edx.� � 4�Qwo maj�.�� � B���cl�4 &W \. DFb * ��%�i7 y, =I�B�e�[�s�M�r���-isC� �7re2w*� Efm�A�q��"� of(a�9� [2a23]s"� kin�I24��ut2  [24, 2��"F� �����N�-b� ��las�D, e� effoc.�p� ma��S�6Z8 �b_ � 9�] ��( 26, 27]. M�0��f@ [28� 0]NDTIծon��z'�n5E�� }m���w%�J<^�,��2���8a�;ch.GK)�:ru2�a��>0 ���Zas fe�STo�f�i����e&� &)I�"�����a e.g.Y@�?�sCO �rul�9�Z.� nega�� 4T3non(4ve pairs. NormA{a 6l�G"� I�!>`�tA�%�. A� b� �|�s�ߺ��i��;�At ӓ͢��n �&*� �ixNI =  lw .� �4"� �. .N lso|s u'*V  (wgP,�l��) �!��fJaylor�J�b�E redund.��[3 �woDS:2D� makes.��7���F �~�l�pa� [35, 36���o ��q�'!b��'^�:�{ �b[I� , na�Z�(SLM). O��M�eSLM��� &r J�f�or >��.�.&~�M�s ��� !�b� b�fR�0 vw lik� N�* � "d .8 2� O*�pr� a�ledge*� �H� � ���a�d,%5�A��c�E< ndj�)in�|� !�.ru �t����c��� "� �> F���wel�or* A���1�,DAX + E��ETHODS �!�&vo"S�i-�-2� /�w�,asb!�!�*B�:�q$MATADOR [30enzyme [26], ��channel exG-1 -coup� recep�w (GPCR),|manM��nI� K!t or�� ource ( �) (MayE�)Q��a fe� 7���s�HUq�& �!2��G 13� umAA� Q�,1< , we6��t�5 Z �C_ID� PW ID,��n�;fadjace�N��. E%y, .t� GPCR. ����r"�.k�  e�hum inP$�,�s� ���alE* ��< C�e� T�+XTABLE I:FG��2G�. -�MP2J� #%�s #-� "ons SO� � A 801 2901 15843 0.007 445 664 2926 0.010 210 204 147434 223 95 635:30 _*< �m��|all�J� :=�:�����=�2�� !�6 �$k&�l�:]��xA�E as ( 1-hi id6YM�<j Aij = . (1) 0,�? wiseU?���:+o�� Rm×n�k(nK��n�%of�� �2�u�| realEPE��n�  fa�.���e��mea�Y�vpor.J�? link5Ja would8" incorrect������D � ) �6X�Gmi�&�/k{for�F��+�R"�S�da��o�/��x!P�a���6�� A2M�s�F#!m,�'R0%� oisy%t AAo a�� r��I"� 5ata�-$���&�b�".H `�e![ out��h �� stra�� off�origi�n�ndBre�ed�o�a� ������_TL)@� i��U�k,�etest.w am5�-2!�� �!Tfu�>���6� scor���3 U�m�% iho"2� sg�.��=2) Obv�m�̀"�0?á� Eq.�#. H�e, we�j�X�V�b\�wA5Z f �a1X�9�umy�M~L~�n&Y��c�� (or row)^�u�)�i]�E �� K �,�l �e�c� nuc�� ED race on XE� ? on*.X+!3-��P�u�la`A,as min ||X||�T+ α||E||2,1 X,E s.t. K� �,�) ��!0||A :4= pi σi (i.e.=Zi -<�ular gE�A), Pn2 p = j=1  �(Ei#v @a�a�Eo�� a9teg α,�a�d�param��H� �a��? bala� a��w��(:�.a)� . MinimizO=9���U6h favor���l�L.i�,��*0�-��Z��lE�Dr) ��K. %�3)E=����.-��274��robC;(PCA [37, 38�U�;�i� �� �!��i�V� �r0K-9�e�N ��tf��,n : mode�6de ��t�?!I�-b. ��v�r*j����B�E���2as,M��JI�2�A�,JF� XL�. (4) )J4)�����a(_!r�x optA��}�a��1�dg�n@f-the-G�, s, *�W�� (IT) [39]�� cele Sh�� gradl$ (APG) [40}�u;�� [41>nd*�RLagra�E�ier (ALMB��I��9or� e �~ In�� ALM�ev� )�r�E�e o an��� %<'I mi?���iZ%�by �A�auyS��+}�  �g�|N�, + tr Y1T (A!DA�_Q,E) +  µ  !2T (X�J||6.�||2F +� $, 2 (5)[�µ����penalty�x(%�5EW��54and can be sol�ved by minimizing with respect to J, X and E,ively,8fix4Lthe other variables 3$then updat&�yLagrange multipliers Y1 , Y2 . The detailed explanation of how to solve Eq. (5) is shown in Table II. We denote the soluti EEq 8as X∗ ��E H. If Aij represents� interac�drug i4$protein j,&n Mh∈ Rn×n can be consideredq�a similarity matrix that describes !iesd,s. While if 6��� !x� s between; �� j (a�$ transposi�of� adjacenc�in)-2))B��m×m J���y�s8s. After obtainA%'O!��u�-� , we%;compute�score�R��$each pairs#chemicalI~-��sA�projecU�B�� onto!� lower-dimensional space as S = A�4. (6) 3 KnoE~U&$s Drug De�-f( Predicted2��$ Low-rankQ(X* Target I1 2 3 (4 m×n 5  .. . m �S%9MhS=AZAdjec6�8A∈ Sparse1E* 6K�n FIG. 1:a� illustra1�A�Tproposed method. First�-�k%,A-t�2 < are utilized toe>truct=� B� A. Second_A is d-s)eo a l>^a�a��a!�.��, whichE� be uIto depi � hidda_atternJ� nois�+ origiA9 data!nal�)I�-�isQ饄^�� /E��R�viacR��(. TABLE IIf�PInexact ALM algorithm9j:��S62��A=A+ Solva�(problem (5)a�m� 1�2 �a�!9:Y< Input: Given a%l0set A paramet�X$α, β Out,5�!�>B��nF A 1.1��5[Lcoefficient or weigh�\1�j�siTI �E͍�!using ��1�%�� t�G II 26���#���SMX6) 3. !!4 entr�Hof S cor��ond!�$to nonzero& of A(, i.e., ign�}Mi�.� 4. sore� rem��E��s�?�S�&�e uorder5�ThaOghest4�lTmost likely potential 2|� Ini0ize: X = 0, E Y16�@µ = 10−4 , max 10 , ρ.1,  &8 w�onot�� verged doA�f���I�4e J by J = argN $ µ1 ||J||�Y + 12 − (X +�/µ)||2F!�bX��XX�@(I + AT A)−1   P4AT E + J + (AT�fY2 )/µAb]��E]!6�(λ ||E||2,1��EP�( m��1�4.1%�"� � %��YFµ=�E) Y2 =��+�X J) 5Lu�!�by %�$min(ρµ, )� ) 6.��ck|co)�ncy �d� ||�|!�� < %�|| } end� le �� &��S�remov�F�set� ���iny��s�ray\� e\@ �`�s�a � �hRm� .mun:��ng B Z full��ces�0!�:���"�$ Fig. 1. T��I !� � "� procedu� 2^�SLM�*. 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O7 ur�EM#ext��a_e�o oun�"6W�%�� @is leftA��fut0� �. ∗ [1] [2] CONCLUSION AND DISCUS [3]D [= havei5 d a� ��-�, nam^� lear� � (SLM��o�"�he DTI1\AN � . It%��b�#,�at!2� �coG�}A>-�7chine~ and ^�. O� e handI2 does  r)� ad0�aA1����a�er�$of%z �Q�or negaT |@�� �9��  �t�>��&vIn!] B� �pU�a�� im�ant rol# mak�W�e��( homogenous*��-�� capA^� � �!or outl�&� i . By"�"� ��r* "E�D a clean (a linearc%oofB���sL"�"��)Y �(2���)��t��ay� � z�����.��$�bD&%���)�A�&� disadva"<a�� at we nei��e6"�e�f�"2s�F$Until now,��n�:e [4a��5�6�7�8$9] [10] E� Xronic address: haodong@(Hc.edu.cn; zhutou@us 0 Dimasi JA. N��developI UnimStates E 963�L1999. Clin Pharmacol!d. 2001;69(5):286– 296. C <X, Yan CC, Zhang 4Dai F, Yin J, Y. DruN`%1� ion:E"�s�wb sern)�|'E�Lal models. Brief Bio��8. 2016;17(4):69�8712. Hopkins AL �A&�c��y:�TDromiscuity. Nature%�>9;462(7270):167–168.. Wishart DS, Knox C, Guo AC, Shrivastava�\Hassanali M, Stothard P,4g Z, Woolsey J �Bank:a��o� hens:resource� in silicoe di �%0explo@Ln. Nucleic Acids Res�|6;34(suppl 1):D668–D672. Lounk�� E, e�� . LC-scale55�o� � ng�)a�� �*.� j*�-C m��s5]!�t2;486(7403):361–367. Pauwels�Sto�VAumanishiAQ�(xu� .i�profiles%B~)��ga�9�ach. BMCYD atic% 11;12(1!��9I��gA� Liu C, JiA�(J, Lu W, Li u Gaou W, Hu $�TY.��+�!.F$%�z�o��K'net �inw$ce. PLoS Ce%��l!� 12;8a�4e1002503. DudlAdhT, Deshpande T, Butte AJ. EA8�i5Va�diseast�shipsE�A��uu�F��F� 2)X :303!�H11. Swamidass SJ. M�+N<-molecule screen!repur qJd�32a�,335. Moriaud!�Rice�0SB, Adcock SAi�<as-Martin L, 6� �1��� [13 ���1���1���1���1��19���2��[2� ;�2� [2<�2<�2<�2<�2< Surg��8J-S, Jelloul MB!�lf� . Idx&fy�5 a cand`"�e�#�Pro�!� �� �X. >8� -�%3�3�8@340. Dobson CM. CqFx,nd �y.�804;432(7019):82�P828. Kanehisa M, Goto�ttoriXAoki-Kinoshita KF, Itoh�, Kawashima3<Katayama T, Arak=,Hirakawa M. � C �mD#u��:/ �&�s� KEGG�'35� D357��8CR, Sullivan DJ�usei%}#a2�$07;448(715��445–646. MacD�-$d ML, Lame� �hOwa��j(eon BH, Bil�.GK, S��Z�s0Z, Yu H, Dias=Minami!7et alYGA$off�������hU,henotype���z human cel�NatE!�zh06;2(6):329– 337. Xie L, Ki�8s SL, Bourne PE�ve��Y��� *%lyp�ogya mea�� ��*pon!�to�vidual �$. Annu Rev&��.a 2;52ц479. Whitebread!z�H�!OdBojanic D, Urban L. Keynotx$view:!$0vitro safety 2��ɠ ing:es�1ial��l�Zsuc�&fu �.� �.K  D�� Today�05;10(2��42�Gp1433. Haggarty SJ, Koeller KMpng JC���c$3$RA, Schrei�SL. M7).t0.N�e9$�ysi�dd$sity-or�,ed syn�is-deri�3deacetyl�P(inhibitors t,EN��/ ys�w Biol,03�5):38�=<96. Kuruvilla FGemji AFe ern��SM, H.+nro�  PJ, 6�� Diss� ng glucos��g!/N� n���:�microarr��N&L 42;416(6881):65��6�IHAshburn TT, Thor KB-�-": i���-ndQ�>�vexN!ngQ�a�A�� � I<E6 4;3(8):67��8$6H, Takig�X,I, MamitsukaZhu S. Skity� d m>�{�� [�C�� .�� �b� �(ewF@2 4;15A73��747A�lperin � BA�lf!�0H, Nussinov R� incipE%of docke�An6a�� search.{"!k$a guide to.�fun�5�sZ�f s: S2= F �,A� "� "d A� 40�)$443. Rarey�Kr���Lengauer��XKlebe G. 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EPL�tg17�&02k3] Güg �r� KuhnA�Dunkel Campillos Senger�PetsalCE, Ahmed� Urdia\EG, Gewiess A, Jensen LJ�"er;e� Matador: �E�� �a3=u r.JNxa� 8;36*�91"D92�4]-Dz R-Q� �R�L-L, WyB-H"�-C. Ac�te�� 0 p'endi�%�elimi�>�nj dund��c�7 �J Phys�89;11(12):123008!��5� Lü�*�mi� 0g links via l�����Eurn J BA09;71�62� 30t6]lJin C-H�At&� A�ex��o path%��.;%��xq*� hySv E �80� 0461)�7] 4�G!��n�anA�SuL�Ye��M�TRobusA��subr�$��lB<"@%�. IEEE TK? P<�� Mach���l�13;35a�17,84!7�8B���u�� ���eHr by�>->>���P95�e�2"<27t ��rAY�o�Co����q�L� (ICML-10)Aa10;66%��7%�09] Cai J-F, C�̀s, E� ��Z' �u\5value E$ 2A�"^.Ŝ`%�{SIAM J O�. ��2%�195(198a�40] W % J, Ganeshz Ra��P���YH =P�p� � mp���t"Q: ExacY I|rrupted9q�cee.�+ vex �"iz%�<. Adv Neural Inf)�jystM�20s 208a�41AE���Wua��M � F� �86}�9]iO�=�rM��� �Y��x." �al�#+in�,-Sensor Adap�0Em�B(CAMSAPE2009;61(6). 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Molisch, “Reverse link capacity of �-co�Tlled CDMA systems with5"arrays!b8a multipath fad!Y8environment,”&�OProc. Globecom, vol. 2, Dec 2003, pp. 839–843. [2] A. M. Hunter, J. G. Andrews ��SAG�b,“Transmiss!��D of ad hoc network �1�di! ity�IEEE IL. Wireless Commun., � 7, no. 12 �(5058–5071��.�08. [3] T. Bai%�8R. W. Heath Jr.%�Coverage!rat alysA hor millimeter wave cellularɆ��)g14 �<2, pp. 1100–11Oct�14. [4EM4Wildman, P. H.AM Nardelli,!� Latva-ahoJ�OnE�,joint impacta�atwidE> d orientae3error o7e�putA-dimT al w1�poisson���3, .�(7072–7085%� 2 �5]aDLiBi�F!��c!~i,!�D. Novl!#a��C%$mq“De��� �a1�of ini�cccATin=�� z�� ^�-��6)�10I�,6409–6425,!��7. [6]�HMaamari, N. Devroye)�,D. Tuninetti6��mWave !2��base s-�co-oper%�b�� qU ��5 ��4 �D2981–2994, April�6. [7E�Park,a�L. Kim �J. Za�J�`Tractable resource manage�� w��up�decoup��yr�-%�a�lay!�$ultra-densy�� �Rb���;6���6 �436A�( 4379, June�8])�ng AH M. Haengg)�4A fine-grained2f:��( device-to- f>6��6-�11� 494�44954,A��AS9]�$N. KulkarnF>�A. 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When sf 6= HT , the probability of observing s0f for α consecutive times, which may cause 27 the learning method to go back to the fir�0, is: Pr(ne |�\) = Pr({en0 −α+1 , · , } = {s0f6�} ∀;�� X�4) (29)   0 if&< α,� α q1 "�="= !"ne��(�Q� Pα `@q + (N − α)p q  Pr(i� b�>b:�1h i=0 (30) where q1 is (1� p1 ) and�$is number 5�Xations. Similarly, for !�case wM�=E� � after��oEB x:�e��J� X (3%�5�� ���2-z��!�.� �IM)�>��q%��2  2-��25��2!�1�X2 ). Here, we note thataA�}0AyF �< are cumulative .�distribuUnce p2 >AP�,K�+L) increases to 1 fas!� than- = HT�$owever, asA2<�infinityNe�R��dwill both approach 1. Thusz`�A�le6�Mgo Z�( regardlessaCsf jerefo!�R2Fens�8 func!J pb , �determin!2�h2g of go�c��P�� 1 o!���ismGed V�@must be designed %@priately to ensurM15%� only.� )� . 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Pro@,f Theorem 2 �I-����tE��m l maximum r!U� IoT devic%�at � correc��,s πrl2 , A�R Aa1� areaHPgeographical region o�6�i~ �e2i��deploy Pnd rl = min(trc , rd0�=a re�!A�i.N��J&�%J� . It assu�QE3rl�entir� W�network%,I .:W��rl�o�= A�scenario��our>� $. In a giv�n ime slot �  �t)�expected�c.���< periodic messag!�ransmitta[�i��Wd%��ed9#� nl = pf )�A 7 �e� ��b��� ���did�~�� .p n0Apfe� nl .� 9 Simqre%�.��outsid�rl �doa�%?m&�m%�)wre ez�b,ry!F�realloca!�RAPs βt!edifferY %�!j�ndEUe�a. may I���0��β� �a6+�(∈ [0, β]I.�of���VB��at any.c� : (-P β)! P (nA�B�) �0 %r C(β� t ),A�!S �4"S 4, k�Qk-permut�S�-�n%WC(#combin#�k2��in (34) �iders=^�sa(��.��tA�EJ2��asP ed!oa���βk�t�on-free%�ch=toA9�9"�iru�U�. FurR&z >�E[��]!�coF�� �Q�.�to 1based� β Z= 2� X b!�!��bB��b-�b).)�b=0!�`5) R EFERENCES [1] T. Pa�&0W. Saad, “L�2]+� Pmachine type communicE ,”aIProc.!!�LIEEE 50th Annual Conegce�UInform? ScieasSystems��*�ton, USA, Mar. 2016. [2] Z. Dawy,�TA. Ghosh, J. G. Andrewm�$E. Yaacoub�Toward mAYve:��ellular6���s�� ��W�y��C.�s, vol. 24, no.1, pp. 120–128, Feb.�07. [3] S. Kel&4N. Suryadevarab 8S. Mukhopadhyay�A\$e implemeni�!taK!�environ�lA�di1 monitor�t in h� �)�8Sensors Journal �13� 10 �<3846–3853, Oct%�03. [4] H. Far� �i ��ath�A$smart gridv�P�!�8Energy Magazine ��81J 8–!HJany0. [5]!�(J. Nielsen,!�(C. Madueno,!\�Kg @atas, R. B. Soren-0C. Stefanovic)y$P. Popovsk ��W��can w1�Q 0 technologies�� abou� upcom!j �Btraffic?a0EK6B>�!gno. 9),41–47, Sep%H5. [6] M. Mozaffari}M. Bennim M. Debbah%�Unman�R4aerial vehiclei� underlaid� -to-� :: Pere�q�tradeoff]\Transa��sa�v?15%� 6 � 3949As$963, Jun. ��7� Wein� M. Jorgov1��A��hai)��BA!kol!� “D�A��aA -latency,W-reli�9�.� s��eo��rol� �l� ��i��%�Inter�>al 66H, Sydney, Australia��e�,4. [8] L. Xu%�He � S. LI� jet��t\�s�indN0ies: A surveyy�>��I .al���c��� �A��4)� 2233a�243, NovE��9]asKhan,�U. R. Zahe!�a�� $“FutL�i%-et: �architec.$, possible2�\ key�llengeF��1��)0ŌB�Fronti�of9 on Tq�$y, Islamab�I Paki, Dec% �2� 30 [10�(Dhill�� H. 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E-mail addu�:�-s.w.c&� d@ttu.edu URL: http://www.m�  /~ l 4J��" *��*�-�lin�� �60BzZ�� djorM� @utaB���d#t�t. 4/~ dave 8?����00954�� DG] 22 De ��7�@ grow�v�bq(non-Eucl���nD�� �squa=�$ionic Heis(R@up Moritz Gruber *��jfi S�v C�eZ��� n-thv`�fw, up to*!.���q��on��W�space�RG�f�?- �C!�4 �� :��� � n+1*� stri���f*'�LJ_��(:n1)Kalr>�>��8 Keywords: isop�Ierimetric inequalities, filling functions, nilpotent Lie groups 1 Introdu'D In general, isopVa�� delimit the maximal volume needed to�X a boundary of a given ,. Differ�types#jv�<arise by specify�res!��t� to� ries and - $s. An inte4< clast suchny� is formed}� S�5g<. These describe-$difficulty�;@ Lipschitz cyclesX�hains. In [3] we proved an Euclidean behaviour for j��H in dimension m + 1!i2lnth quaternionic Heisenberg E# m+1 n b|m ∈ {1, ..., n − 1}, i.e. it1Xws like l m . The known!�ult%Fx!!�I9@( of HH n+2 �complexB��d HCn (see [7],[8]) suggestAbrowth��n!�nt�s�nu2&�n!&8. Our technique!H!�Dcould only confirm`super-5�� 9�$without tei�� exac)3th. 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J. �@Anal., 26(2):1596k616, )�� 23@ Fakultät fürE��e�k �8 Engler� e 2 76131&G8d Germany E-mail address: me.ge(@kit.edu �Ό���A,�6������A�*���]m��Stacked Structure Learning for Lifted Relational Neural Networks Gustav Šourek∗ Martin Svatoš† Filip Železný‡ Steven Schockaert§ Ondřej Kuželka¶ arXiv:1710.02221v1 [cs.LG] 5 Oct 2017 October 9, 2017 Abstract Lifted Relational Neural Networks (LRNNs) describe rel�$domains us!�weighted firstorder rules which act as templates for cons%gB8feed-forward ne%U�n ��. While previous work has shown that ���C can lead to state-of-the-art results in various ILP tasks, these re $Ldepended on hand-craE�. I}His paper, we extendG frame�of �with s�A\�lM\,, thus enabl! 4a fully automa!X*H process. Similarly�Tmany ILP methods, our Fi�$ algorithm Ieds!Tan iterative fashion bZp-d!b@searching through�<hypothesis space�hall possible Horn clauses, !� ider�th%� dicaA%�occur i!Se traiewexampAJas wellinven! softX cept!@tailed�he bestY�%�0 found so far-�!� periments%� demoA�ate�abilit!1�ica!�Dinduce useful hier%(cal:��A��o deep]$ a competi%~pr! \ower. 1 Introduction �� (i [15]) are9 sets!�e��-}��,q�re usee<!�E�r� from r� 4xures. A central characteristic uis)�(a different:#��eor each!V��M%(, but cruci!�, A���A��ebg��s%* shared. Ta�allows-�to!�:��AR�r�in. �%, despiMM�f� E�F�may vary�a,4ably in size aA�%�ure. InA.�� �g�, �havA��e�rn!1!�Z�such cae�on�Ohe 64F- dto be �e� dataQS��be acA�lished ���a� iantA�(back-propag�f!�e\F�� oA.s a nat�0wae�incorpoe�)�$ knowledge!�AFP,In some appl��hions, however, (sufficient) V� Vs lacka�!�bot�"�ttheir 1X%�J?!64. To this end, ��i�c�b�i� e ayj��� a$�. 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Spa%er}012) [3] Cohen!,!.,Tensorlog: A� enti�{de_veeI�U. arXiv��Y�t �[:1605.06523 (2016) [4] Davis, J., Burnside, E.S., de Castro Dutra, I., Page, D., Costa, V.S.�I�gr�V�(�'1� bqia�E$d of�)��P"�e�A�016th European!�$aan M�5�%V 8{+95!J�05) [5] Dinh, Q.T., Exbrayat, M., V5', C.: �4kU��A�markov*1�� !p�dA��of!v� �s �IJCAI.��-I��al Joint6�� Are� ial - lligaUD, vol. 22, p. 1249�p11) [6] Fahlman, S.E., Lebier�[.:�[cascade-�8�.� (1989) �DTHájek, P.: Metamathe�K�aI) ��4]бl& B� ess Mediab(98) [8] Kok�$, Domingos lu�A9��N�)l6C� ;22nd !E�r5rCo]H� VH44e��4�p5) 9 [9] Landwehr, N., KerQ (, K., Raedt�1D.:ua��se�� foilS JourAofB���Q,48�507!� 07) 46�� Pass^ i, A!Q�e�, Frasco!��k��:Y��'.Q  kernel-Y$AAAI’06::d%�21st 5_�c2_Y˅!Y�4pp. 389–394.b P�+ၞ(11] Mugglet�S.�ELin, �<Tamaddoni-Nezhad�I�Z: of3(�r�c dyadic�6�Z�p"Y=*�+ig�s��.B($ 100(1), 4�73��1�s 12] Opitz�(W., Shavlik�e��Heu�c�Gexpan��&�a�-�U:E�� �N��(1360–1365eP�3A,3] RalaivolaA�(, Swamidassaf��Saigo�Baldiip�Gw-����9� in+)atics. *�i,. 18(8), 109�> 1110!a/0[14] Rocktä�9l, �� Ried S.:y�"� p�eEI 1theore�g�_|: NAACL2�A� ed K"�b Basea��G!�(AKBC)��15] Šo�j, G., A�nbrenner��, Z&�j, Fa�uzka, O�ifw*�>�� �6�� NIPS2��Cogniō�C�/� 6R-��$Symbolic A�O���E��6������ ~�N��. :r �. 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AmDja-OghlaA�t���!�A\h adapvVdtr�5�%T�b��orics,�"H�&!��pA�a�(2):227Ey�4�����Yk�kel, O.��el-Gu�O Y.m�AcJ 2B �q�imTaɐ*�� ANALCOQB�6��7| 1. 3JcA.V Dempst N.�= LairW D. Bl !�xi�$likelihoodain6 te data%D�em�L2� � Royal2�Society�, Series B, 39(1):1–38, 1977. Yash Deshpande and Andrea Montanari. Finding hidden cliques of size \sqrt{N/e} in nearly linear time. CoRR, abs/1304.7047, 2013.����Improved sum-of-squares lower bounds for 2��� � �^submatrix problems. In COLT, pages 523–562, 2015. URL http://jmlr.org/proceedings/papers/v40/5B�15.html. Shaddin Dughmi. On the hardness %=<gnaling. In FOCS�354!�63,�4. JohKnagan׸Santosh Vempala. A simple polynomial-time rescaf( algorithm !+ solving l%�D programs. Math. P ., 114E8�0A:114�(08. U. Feig)g8R. Krauthgamer.U3!�Dcertifying a large1�clAJA6Pa semirandom graph. R  Struct. A�Ds, 16(2):195–208��0:��D. Ron�M t�su �!'%� AofA1�189\��1\ riel �. Relations between average case co!� xity%approxim3u`IEEE Conference on Comput.al�lM � 5�2. �hRobert6�The!�4bable value ofE�dLovász–Schrijver relaxzeQ� maximum independent set. SICOMP, 32(2):345A�70� 3. VA<ldman. Evolvabil!$from learnE5�% STOC � s 61!�62)��86S��A-F4te characteriz���s!=,stical queryr with!�lic/s to e�. Jour!yof%|8uter System Sci!�,s, 78(5):144a� 1459�,12. Vitaly F� Open%� lem:%�F��]0of�spars�4lfspace%%� .�128��128 ��4B��$ A generalR*ther��. ��608.0219%� 16. URL h�arxiv.�6+� . C��� :8, Will Perkins,E�B��/6�satisfiMR� ��)�plant�*olue�. �� �311.4821%�3. ExtA��d�tAG�A��x�5>MD, Cristobal GuzmanV�� SB��aU�}tochaA�0 convex optimM��.)9� /1512.091i[��Uٗ:{+8. Alan M. Friez�avi Kanna�A newaroachaA 1=�$Q�e�FSTTCS, �,187–Ma� C. Gao, Z�@)H.Zhou. SI�@CCA: Adaptive Est��'6�\Barriers. ArXiv e-prints�ptember!�04. A. E. GelfFA. 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Se�a$so [KW92],ٝoll� 5.33�a�7],2�� 3.5.���%[MA��l0��o.�mN-�Q��t1Q�.>n�f�~feU� �E2<E�=p@�4�!X R–*m hRa~� .gR&h@�/�<� 6A��� hR+f���R !��e*} < W has been defi�Ined above as the group of orthogonal transformations of h∗ generated by =0simple reflec,`. The isomorphism betweenB( and h give ~�a6@ of W on h, where�formulaJi�� is just wi (hj ) = hj − αj (hi )hi �is same Q<restricted to hRN�� W�<it also determin>��� �t by ��z ��z:���z �@ese operators are.t with� pect�!_�io!# bilinear!$m (·, ·)1hR !^to t, !J0fore W preser!v,each surface!��constant square length, (hR )r = {x ∈_| (x, x!jr} c!�t6 �$. Since we�0assuming that�< Cartan matrix A!�(hyperbolic,#!��@is Lorentzian on � on t!��e�ID��06 call!�,he nullcone,61�<.1� timelike)O291�>.1� spac2 �et!b all KP points has two conneE�8components, one�forward%n denoA� T L+��o!�. back/� /a . We have@�=a-L. EA�oEcse�!?Q<d m�M�u� W a�ich�sESistently!�$rays, RayxAO$rx | 0 < rEX R} sI)(rI[dw(x). A fundamental domain!�{ 10 e�%� �9o9V� defi�by C ±��x�tT L± | αi (x) ≥ 0, 1 ≤ i `}. ��union X> [ w(K,) w∈W is1�!�,positive (ree�$ively nega ) Ti)2�e%�0X = X + ∪ X!��]�.$. Clearly,ab%� 0%�C. For g2U�X�⊇ ��,-{itgpossibl�}at �E�� Ab�I@�,!�tains !�e�}[A��iA�ppens5�rank 3��� �(ces  �2!�2 0 −2 �  16��2and 0/ 1 2 .2 cor!�ond���o%��u� Kac–Moody algebra F [FF83] whose Weyl �4�i��@triangle�U0T (2, 3, ∞)%Kq(“ideal”.=�N}��Iv� �v�∞u),�H�WE{IA �ly��uat isa��0principal minմ0f finite type.aMZ . Su�n exa$ is E10 . ��A4follow!�descrip�� closu�%��Y�X (see [Kac90], 5.10.2) F; = {he�hR�� h, ha� � 0}�introducA�e notas LhRn<� , L0^"�< 0� ∂bG��=�Pro�Don 3.1. Let g be a��lexN , k �3$mpact realae�m�@gR spli \!�R ,� ����d�]�subM�� g,O, k>AThe�}4∼ = R`−1,1��signat!�(`av 1, 1)� t = i�� �=i2���1 = {i��� hR }�L�eUA G }1,A_ (1, u�)%�us!L���ven!߁�k adop�K fromE�theoryaM�dimensi Riemannwsymme> �� s [Hel01]� set (6) � �k �|k . Noa<�dinx af�� case"��k!��H>��%_al�ZccursE loop�xAizI�@ [PS86, Fre09]. W:g � p"� Y  t%��L&z �%�� .�(. Lemma 3.2)� inva��t=4V� �k)�6�  k��!�X11 Proof. As a vector)��,}=��N\�g�a bas�on���of��F ge� 0ors, hi , i =A��., `��cer�d multibrackets [ei1 , ei2 �  �n ]�� [f"�f>"��f")T"� ω!5�s�e6h�� � y ω(ru�) = (a�)nv|�E�ωS I�(hi so an R-)?fo� p 6��ka|![�T%Y$�v Aele� s z!U2ina�:0ob!medi�M� 6� i 1 v +v��� zD�Y r��)%,8n even, 2 2 1 i~���V�� z�����!�n odd.�4In particular, = 1!� se includ�K5��x!�12 (ei�fi )8�y2i�+. F��ou��g.���eQ%2� span!�� |�zR� has�I2� . Use�F~�%PAi character�R�#ad–i�� scalar pQ�t��"�Equ��0 2.2.1, appli�� E����s!'!��wea�5 ate:6?on � =�k!e sui2��p{ � ite. Fur� �mF��:`�!8%&� pr�tie� root!�ces6�  S  2.�� 2.2)��.5�gα�g−α&D�rA\terchangwω,� dual!3$es {ejα |� �j� dim(W)}Z{f  = ej c^-�6�� �W� (A, em βd<δj,m δα,β . 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F#2� .=N<�seB b �l�!�V�%D� �e͚r( Riemannian> $s [Dad85].�, obs�3!��s� �a/%��+< [HPTT95, Gro00]i�:RN�1�a%FA�E �H!�Q9 �3)o t. F/ ques � 3V2�y]�.E��s0% open��fu+, iffe� ial&�net5o d�Z]�:cs �%s elusiv�3hopetak�b%p elseE . Re�ces [A1  PS8 Abr ko�"<Kenneth Brown, BG !�$aduate Tex�+Ma/Datics, vol. 248, SU1ger> hlag, New York, 2008. [AR98]R��M!!Ronan, AracterizE6!�2�P4 "�%hs, Geom. Dedicata 73 (1998)�8�.<�1–9. MR 1651854 (99m:51016) [Ber85] Stephen B�n, RealA�me un. Kac-u$�D s, A �sA� ups �2 (1985�0–25�@803743 (87a:17021�� ( Richard E.&� �,!ctex�s, kac-m%� x�( m�>tProc. Nat. Acad. Sci. U.S.A. 8%/�86), 3068–3071. [BVBPBMR95] Valérie Back-�nte, Nicole Bardy-Panse, Hechmi Ben Messaoud,Ek0Guy Rousseau,� mes � <que-déployée��s� ̀br9u�:��if!�� et rac��iv< J.1� 171!��9=�43A�6%�,1314093 (96d%�`2) [Cap09] Pierre-Emmanue�,prace, “Ab�8@ct” homomorphisI.�Y*�10, Mem. 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Ddam=��uk�o9 �aWvt N\.�Yi�f*��lar�D5��f��s oHferences 1. 2. 3. 4D�$ M. Ausla�Tal8D. Buchsbaum, GV=s, Ih`�eHar�1�RmO1974.�=Baidya,� cell��hom�Fticq��,�O progO�. 3"YAXcaB, PhD�$�s�Il (, Georgia STcUnivers��IbEX(H. Bass, K-�6�y]st�"W Publ)pth. Ina%�Hautes Études Sci. 22 (1964), 5–60. T. Coquand, H. Lomb�� C. Qu{2́���: non-�����Z�;�p, Manus�<a M�115 (200��1�=520�y�A�E�68fani, T. Polstr4Y. Yao�liz~SerreeT&�F: !�!9�C=�� " via �&�-�Q8$s, 2016, P-inNJ։�at https://arxiv.org/pdf/1608.08591.pdf�CD. Dummi��R���o��Ab�ct9�Lthird ed., John Wile)�So�t!/ . 8.S0Eisenbud, Com��K} az�eM"8ic geometry, Sp�/er�04. 92[�%:E.�lEva�Jr.1y%�1�effic�)ly:�S<�s� wQ�, J. A { 27A��7@=4278–305. 10.!) Hartm� ne, 1Z��1977. 0\�BitmaneZ~��$, MichiganM�J. 31��8A�(167–180. �ZT.��, �I��>of>1�{Pac�=_i 25e68a��4e �4�(3. B. OlberNContribu�6��))qy:� memD�ofaFL.�wCo!�, ch. C&F�|�� fEm?{of h-� 0 s, pp. 38�)406, W? de GruytM@8. }X J.-P�A�rM�F�Efs et e7gpE,brés à f  veE=�i܋, Sé��zDubreibllgèb '�"éoriE��mbres 1%�57/195!Vno.Q�}8�1�5.!}�T�qafᎆ�F�� non.�� aY s, J8% ~ 69!� 81),�312A� 46. TR�Rek Swan�Tof �o�*�a-��,M@Z. 10��7), 31eH$22. E-mail� �� : rb��(1@gsu.edu Dߐ�t�gA��e3�E� ��Ļcs!!^�Atlanta#D 30303 |���Param\` ized� plexZDlaiAEm��o�� blems II.G�4Dušan Knop1,3�&<omáš Masařík_ ���Toufar2 arXiv:1803.06878v1 [cs.CC] 19 Mar 2018 1 :Applied. �,e5les2��@Prague, Czech Republic {knop, masarik}@kam.mff.cuni.cz 2 Computer���itu�a��i�(toufi@iuuk..`��3:��In�F�s,�!} Berg�'Norway і Vertex�.���t�:� a graph G%�^dW π� go� *���-of�K�t3��WK �t� G \"PR. Typ� �wan���KĂYWQhC.W }:��'�i��'OV����h��P o[� ive:ph"um}����ePBcD�n:n� ( ex. �uK�F expa�-MDn MSO�� mula�"�: M�0�4ay oB�[*]k.an FPT� orith�E the ~R�����b�e twi k0�Y��s`�pj4!�F�M��CC�(VC)��E. 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Mi�aG*�D�N�L/conc�|iS7: F;�0��xQctabi�u�");�c��mu�9ver"!jvo�{T. arXiv preprint, 2017 <:1709.02850. [4]�ganv:L, André NichterleinN mAC(ias Weller.j `I.>�s%�m��tO;aGi�a�th!�e�ory C�,,. Syst., 55(A�1–83��4)�I�h07/s00224-013-9499-3. [5] B�ur$T6s M. Mosbah�n*�V�-� *� �Aj�D:^NH. Sci., 109(1&2):49��2aE�9mEU�(304-3975(93A�@64-z. [6] Bruno C�% A�F���l��ofq! i.�Fogniz!H!`� �/�tyHInf�, 8%V12a� 5, MF<a>�0)\�(890-5401(90�043-h. [7] LenY�JT�wa�mO�C ADDouglas R. WoodallQ&�fp=�v�loA��Y 4surfaces: Part�Ts4sub 'of���-ency. �'�G�'%��y!��)$187– 195!�86�T02/jgt.3190100207. [8]!0ek Cygan, Fed�,�-�ma@Lukasz Kowalik, D" Pl Lokshtanov, DánielH�x)aPin Pilipczuk, Michal !4Sakr>aurabh.!� ���. Sa��g��2015. ��%�D07/978-3-319-21275e9]i��s�HnEva�> dos.�f�]!dsi�^,aneous dioph4�ne( roxi�;�o=.hbinatorU?�ō� Aca, 7a�e#�6)��7.�(7/BF0257920��10%�ku�ic ��MAn Grohm(�6�l"�]m�!S�mN�eF�  sit� Ann. PE�. 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R�b�+�s [1] E. Alibegović. London Math. [2]z"� A!��b~a���=��# 5B�@�s. Bull. Soc., 37(3):459–466, 2005.�[�n[� 52�4[3] M. Bestvinh4M. Feighn. Bou<o)fmplex�#�$>�� +tWVŮ�>vent.)j, 103%�4)(9, 1991. [4r��fnegZ#Z�2�d�/. J. D���a Geom!�05(1):85–101�2. [5r��� ��=’0Bk:6v(��8MakaninRazborov�#% ��eM!+co�Flog�� metho+)KEd0y, volume 358!r.�� AW Le49� Ser., pap 1–29�C,mbridge Univ�Xess, CE� 9. [6] B.�D�@. Cut�t�c"s3"�4�\>�Zs. Acta e_��0(2):14%u86%u8. [7] CrCas�%!B�NA,cura. Lk�p[6rn\ �f�@%s.� pr��4 arXiv:1006.21�@,2010. [8] F.g�ly�of�1w�c��.%��P`pol., 7:933–963 (electrr4�)%23. [96a��F�*�\."2 �%��th)� , 40a39!'404g!'106h��E�zXR al qU^% �(���).}�13 Israel J.5� 73:9A)12 oA11.o�%� D. G�^�s��teV8%�] �i2�|Yu�Tra� Amer2��, 360(12):630!p 6318��2n��8�iF�@��j�5 Publ� Inst. Hau}$,Études SciA�07:21!*290��3B��(V. GuirardeA�^��allN%�� Funct�(�aA�21a@22!30��1�514] G���a�E��!b_;�@&�? rank)�I3�:"�i etrg�Ta'$ogy, 9:183A�188�05. [1�T��unwood 7M.�mSageev.��-]D ��l�a�e� ��slSE�r (<6b���2��4C99E� 6] K!X�B�k,P. 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B�"�b�p"��E��~;?�2"��2 62 �P�,\ ** -*�paP f minimalPr_���w�C-�?� ��bL��g��� zero��� >�!1�s8�i��' Ua��)h�)��bE��6�� a��b� � 8$ F� �&�%��rJ 9@a+>����accor to&+ �1A��aJ��~n���� R�=+���� J�(i��~���Bq�:� ��aI( � �)�A8�5L# (m{�+10��1.26%A l� la�� lE$Ai e��A) =  1; 1 + 9�) ]�;V�)H�2&�&�RA)3&� )| ≤ 3l�I"��BWs 1.20E� 1.22 �5a�bF n = nY� ��g/�e&B&�.��D1�R�2A�Acen *2. tree�.5�~�+l ) I�� 3(3 ."<� EasyAp2AP��5:f��K� �5�Rdaugh= \.���{�1�l�>26�o�r��ځW6��e�MJE���E�0�i���1l�jBy�8��%��P*��1.18.  ��: J�of�F�V�+!�mNU�*�>�e�"jD!ItI 8��/UT6�'� �/3�F=GO ��U�8�(�S"�)%.7��=.�)qQ��aI��z�R&^KH{5�u0 the )G�KFW6 �-V. 26\K�.�.L����it of types TTµ generated by →µ and →α . =µ/α is the transitive, symmetric, reflexive closure of �L0/α . →∗�Ldenotes zero or more x,Tsteps. We will show A �hB ⇔ ⊢µ′ A = B. where`derives equations between �in�A$, as givenDefini3 1.12 !�Dover that this relX!�decidable. From now on α-quivalenc!assesc%qX �are-! [A]P[a]. =[µ] stands for� lityc!�se%� α-eJo�L ⊢[)0�] k)�%( � system of:5 w�c � [a] )la ∈�0. 2.2. Lemma.o na = b1��E = [b � both�<s can be done by�(”same” I E�tl#y have-*p length. Proof. Immediate 2.3�:U!.)q[B]J;�hCombining Remark 1.5, Propoa�oE4�8%�% s 2.IC�>2.3 we get WEAK µ-EQUALITY IS DECIDABLE 11 2.4. Corollary.>��>�Finally!.yxwe1at:2�6� In facA�aE$is a bijeca fA�Aj], treeE6��Q�Z*�Y�A]A�$B]. So we 5�Xfollowing 2.5. Theorem..�isyr via�(first order�s!�proced��6��A�6.-��e�part 2!7do not)>)P 1.22�4X. It only holds modulo 6�. Refera�<s [1] Felice CarEځ4Mario Coppo. D�H�ie�AUerties��(Recursive T��� C. BlundoJ�LC. Laneve, editors, ICTCS 2003 volume 2841 of LNCS, pages 242-255. Springer, 3�R. [2]Jörg Endrullis, Clemens Grabmayer, Jan Willem Klop, Vincent van Oostrom. On ���lA�4terms. 2011. FALunivers��HAmsterdam. [3] V. v.H��FD à la Melliès. February 1997. S�URS�� �l��arXiv:1711.03026v1 [] 8 Nov�7 Int_�g�0Fault Analysi���FElectrical Power Grids Biswarup Bhattacharya Abhishek Sinha Departmen��,Computer SciA-� ��of Southern California Los Angele!�XA 90089. USA. Email: bb �@@usc.edu Adobe S�� s Incorpo��$ Noida, UP�301A`diaM�a �$.sinha94@ge@.com Abstract—) �g! �ԡ�ghhe most important componentE�(infrastructa�hin today’s world. Every nɪ� pend!�on��sa"A?aWstamG of ie wn p%�� to�vide e-�;toKhousei�M$industries��malfun� of e7a small�A of a.l��� cause los�8productivity, rCue k some ca+ life�us, it�imperati��o design�%� whichu dete�� health -�9 � � take�.ULmeasures accordingly �beforel,erious anoma� akes plac�o achie�+ ob�J��ђ�(ut to creat� artifici���i}B���aa��z��� %�informIat any� tim\�d% rmin5-�A�Cthroughusage!. sophistic d�l��el� d novel m��nrar@techniques like rA��rA�Lneural networks. 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Acknowledg��j �5!a�,a/�onymo�x��(�=14wK�� sugg! )�@QB�.ub�?=:��7�A��p��. Ri�:� [1] Beatriz Alarcón, Raúl Gutiérrez,z4Salvador Lucas text-sencve��pai2z�I&^� �C&�CD, 208(8):922–968(10. [2] Thoc~�A�0�S8Jürgen Giesl.2�'a?Q�r"�eE .�� Ztical � er S|4e, 236(12):133�( 17��0�,3] Franz BaaFd Tob.VNipkow � R��XAll That. Cambridge Uni\"ty Pr��P1998. [4] Emilie Ball�,Paul Brauner!�`du Kopetz, Pierre-Etienne%�au Anto��Reill` om: PiggyA�� 9+on javaz,RTA ’07, v�(e 4533!`XLNCS, pages 36–47. Sp�% er-Verlag!�07. [5J������E"#�icu��] �� m��eAi(Software: P�/%��E9 A�, 44(!�29–162� 12. [6] PHdBorovanský, Claude Kirch% Hélèn.�j��@Christophe Ringeiˎ!Xov8hew!Z ELAN%}WRL%~985~15. ENT!{M$7] Ho��u CMIeaJ���R.(A�R���.A(�i�}��Ws&pX. Jour&F of S7�ic6�45(5):52i7550%\0.R/��+1�� m|� �3�<{[8J @Sergueı̈ Lengle��^�6��.�.` �:i�T�m>155�36PLIPIcsq>�74–88. Schloss Dagstuhl Leibniz-Zentrum fuer �A�k%T05. 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C) Comparison of muta! ` frequencies for patients o2j�4�s)�(numbers in !]TVenn diagram represent *w^�6average\2��of$cor!Y0onding groups%�(shown above) ~�s. 10 ACKNOWLEDGEMENTS This work was supported�part byHXIntramural Research Pro���NEI\al Institutes of Health,Library7�[Medicine REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 2H�i2. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. Kim, Y.A., et al., MEMCover: integrated analysis oE?ualU�ity%�fune�al net%i@reveals dysregulaKdpathways across multiple ce0�@ types. Bioinformatics, 2015. 31(12): p. i284-92. Ciriello, G., e�eE:�� �identifA� oncogenic�modul�GenomeA~ 2. 22(2):}X398-406. Leiserson, M.D�Si�aneousq�cE:A��5in- . PLoSe�ut!�l�3. 9(5 �Pe1003054. Thomas, R.K�,High-throughE �}rprofila[in huma~Nat!etw07. 39(3 x$347-51. Vaa�4, F., E. Upfal�rt B.J. Raphael, De novo discovei�Rednr�75-85j�$CoMEt: a s��Dstical approach to1�y combin%�a��>�al���5��I��.�Biol, I�16E! 160..^D.Y. Cho)XT.M. Przytycka, Underst%O�gVa-Phen  effect|�W via Nmh�A �A�]5� �a:P6(In Print). Babur, O])Systeej1]� �%�A)signaE3U���ɺ2u$of genomic.E1;�5.1;$45. HofreeaT�� ��- n straa�yStumor�)��.E�Methodi�3. 10(11I�1108-15=���>�Bridg���Gap�j|A�!�69�^� Fron}Q�O�3E*�2��0Vogelstein, B �0K.W. Kinzler,1�genesr�5�theA�ntrol��d!�04��8 �<789-99. Szczureke�@and N. Beerenwinka� Mode%�V�Me�� Z� }�5��$503. Kando�*�C=�Mu)�(al landscap)[Ap�iA�nce�4 12 major�!�)�ure�!�502(747-�4333-9. Wang, Xy$Widespread%^Htic epistasis amongf%})_Communj 4. 5%�48�o4Dwyer-Nield, L2�EWa2� �g�n chem��8ly-induced lungM�(susceptibil�q Kras5� site��murhXC57BL/6J-ChrA/J chromos��sub�ioneG�i� Int JMg�0. 126(-? 125->Lawrence��S=F=�heter�U�e���EiA�U q new-]-associ"9h=� 499(7457)!l0 214-8. Harri���HMolecular mechanismu clin!Z impact��DAPOBEC3B-catalyzed%Jz�i�gbreast �. B �}Re�R��H7: p. 8. Burns, M.B=i� AMn enzy�hsource�qF!+:v�Na64(743)H 366-70. AlexandrovAp.|��S��A�֥al��cesse�B�=u500(746m�0415-21. Shann��P�Cytosa��s oftw- environm !�A�S �m�c� biom5�"� H �.1x�E13��@2498-504. Su, Z.Z�$PEG-3, a n�ansS �ύ�( ressa !��,%� posi� � � �o� 4ag 3�v���� angiE�r �Proc Natl Acad Sci U S A, 1999. 96(26E� 151!V�0�nerji, A��e� �S� � � �o�%� {�t�lo�V 6I subtW ]R$2. 486(7401�05�#�S��X..$$The nucleoa^$ubiquitin-���!G4tease USP36 de$�a and� �� zes c-Myc oc�F'K  112(� 3734�^��D"[ lA�%$2� -�!�5)21�b�u"y ="��05(7484)�w$ 495-501. �me AtlasA�/, N]��I&E  chaA� eriz �\of endometrial carcinoma�l}�497(744�$6773. Cesca� D.W.<Haibe-K��m W. Mak,��ex�E�in:, refll cell�Nprolife)Q, whils dele�D$ polymorph�q����w��i�,�tiv��� !��9)tD2841-6. Periyasamy�d& �b�-d�@0Cytidine Deam�  I!�quired��Estť Re�Y or A�!2�. Cel �p"� �3�08�V�Y�a2rol��ina�$G and adap�aAID1!���(HLA-HIV/SIV �i��SH�n �� acaques. � On�2. 7(M� e344�Hec A*.`)= -med);�c��!;�d=;<links PIK3CA hel�Ldomainս�sR �K8papillomavirus-�n � develop�=Xa��4�6)eg1833-4a$ieira, V.C M.A. Soar�.d�c1� �!F�o!�%{M�9aaga �t �vir�!Wio Biomeda�a�%�3.�� H683095. 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N Engl J�?�,�-<58(2�=2059-7=4��46�4� ��4� \0s782498-504. 6 �����G,�6����߳C����K��arXiv:1803.02420v1 [] 6 Mar 2018 CLASSIFICATION OF GROUPS ACCORDING TO THE NUMBER OF END VERTICES IN THE COPRIME GRAPH TARIQ A. ALRAQAD Department of Mathematics, University of Hail Hail, Kingdom of Saudi Arabia t.alraqad@uoh.edu.sa MUHAMMAD S. SAEED Department of Matrs�KiVm�0ms.saeed@uoh. lHETAF S. ALSHAWARBEH�n� n0e.alshawarbeh.s�tAbstract. In this paper we cha�erize groups according to the number of end vertices in@associated coprimI(aphs. An upjbound o~$e order of>t0 that depends'v e2v�`s obtained. We also prove F 2−U s are only is whose:��$ have odd Vt�L. Classifications ofP ith small6�� v:'6�$given. OneQ!j0results shows �,Z4 and Z2 ×���D has exactly three!G�0. Keywords: C-��G%�$, Finite GE, End V �. Matq  Subject:X: Primary 20F65, Second05C25 1A�troduc!O( Throughout]�8, G denotes a f ��g�. T!�AF!8�a  G is 2 d by |G| !:!X-n elem�Kg ∈6 h 6g|. 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In [12, 3, 61] for instance,tconsiderkgraph M�ll nodes and links occurring within2data, %$abel each : ink. it�0esence times.�<86, 35, 48, 73],U1 duplicateW�i�,as many copi��s` number� �l\s (they assume discrete � steps);t�n�]eract!f(between two1 t a givim!�� )�d by a%'7he�ofbse% s at this�, !`%5 copy+�a' is!�nec!�to� #?e nextC��.)M8, 52]!{ others6Pbuild roability)�s:�xs are�ed togeG i�y can ? �d� M @stream. With such)ingA�ome keyE�ert!�) 8� w$equivalent�a6+�obtained �!�$d so studyA�%WI�4sheds light on!� originalE�. Howa�,!g cept.ke dens!$or clusterAl�k!0ttle sense on� objects �Q�$then resor�A E0 slic�approa( [61]. All$sexes have a clear advantage: once.�A%trans�edA�o one or�\%s, it.possible!`use  tooli��c`! �t-Wlinu s un�.)rnEx�,same spirit,��D powerful methods ���%�A%�$xtended toA��e�2V(dynamics. Ta2lea E��� algebraic.@j�temporal network analysis [3, 57], a� stochastic block models [90, 47, 14, 15]2 Markovian+\69, 70, 67, 68], signalsA-�� � s [2#4adjacency tens�$[72, 24], F4�A�!5�� walG$71, 59, 62�%dlet�3, 29��, motif count.��e0 6, 53]. CA{ly�Bse !As )�, higher-leve9�to !��set^H, whereas we focus %0he most basic �IZ�paT�Yhope th��y will!�m a unife�groun��e� �. Comple�aryA+th�q�es W �M�, ��2��va�m%X�R deal)�a��,�0a way similar$�w�we do �A~32, 5a�\In particular, path-rela��eea�$received m�XattenͤcaaǩK ir iA��t��!# sprea��$ phenomena� commun�[��Q�� 8u_[31, �W75, 54]a� terestingAalthough�s def��)�se pap�Ba�=th��w�"�n~� A�,I der�� mainş0-oriented. Fo�{�s �EF�� �!� centra�����"�co�b$components]�sa;of)s (apout%�� *� �)%�51, 6-'52, 75%' [16:�introduc�����Q�ts. Si��(�ma�8eatly change ov� E [44]��Qň)9�Jof��)�t G �. 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Corollary 14. Let �&,have s ≥ 1� a�s, influencing all other individuals (i.e. �set of s� nodes is�Dnected by walks toM� )of)J). Then� model (2) G�(nt. Indeed,6k��a%��er��sh, whi!-re 5�� aperiodic. In Section 6 it will be shownAt under�assump-b�C=p final -� x(∞�8 fully determin)#%K2p s’=Ps9 . Example 2. Consi�4French-DeGroot)@,, correspond!�tobweigh!�E�A<DFig. 5     <1 0 0 x1 (k + 1) ) x2( =  1  !. 3x33 ) 0 0 1 ��1R�� �( with n = 3i�s (5), R��6��@4. One can expect)�!s0“central”E� 2Ss -9 mostq tial �!AFezA��iA� confirm)��a�x�a!wforward��utaA84: solving > > KsystemA�equ$,s p> ∞ = pW and 01 = 1, 2 3 2 ��obtain��vectorJsoc�powerN( 7 , ). It%#6��teady Q�Ythis i�isQ�= (A1 0), /2 + !�0)/2, ,)> . 3.6. S6�1UN� Although�`�s�`(is a typicaa� havi �the �(2��re�0sit1[�w�v �0s do not reac.f�but spli!�to��clustersIb�Q reas��fo�(at�!Hpresence(:� (��(ed also rad�<s [97] or zealot8]!�<4. Abelson’s M�3�sE<Diversity Puzzle��E���E� work [34]E prop�$�aA�Xtinuous-time counterpar�16�� I(2). 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NewmaY\a��t8�3iT�h%tO�%r�jBjmod�, maw�I��,N0�a��s�O1+al in #A�&EW�-oIZI�io6%Hack���2�,'� act,��s�v�Wle �e��S.>5te�{4in [24] attempA�DL�A�b425l�c�z�eq%�y b.g �b��E�n*�Bfuzd�> �G [16�$�LccBs"$z�hax�A �(0�S�@woY��( solve i�$yst�� i��!}a�m.���t&_�c}c�"%H�3&?�existsnB��f� . Am wea�wo��e�E!���#+%}�u' [11] [20]eI%��� 1'�3��]�99i#�u�a(�Q�� ���{A��)"}!� �7%90]�) �fIfe�W�)�H!�!Y&�of.��&"W5&� �v:��&�.ir�j�88]. 6 CONCLUS��e�p�a-H�7�w97�%��1�ith� f~ A��G�r i&��A��)12!d5 �T6G�ie":��eQ�*�:�s"c<T �a���� 5���r�C�nng ����'� �e��~�o�oAenh ) ensFQ�u ;y�Z1^�d ��a���d*�Bal� !�ploa5�#.�.��(www.:��� .A�m�&:=%C�l".�ac'<! e%�D�eX�!�pA.e�6& .#-qB�=Z-�g'co�\dat�hFERENCES [1] R. Andersen, F� �u>�lK. LaG` 2006�C� ~~�+5jɂ"��VΎ�j: 47th Ann)| IEEE� posi�zn FaLE�_ _ r Scf�`e (FOCS’06). 475–486."�!doi�!10.1109//�.x$.44 [2] JaWl�P�q"^ Erik M�� llt.��5��Aň� �ny|�a0P Phys. Rev. E 72 (OctCD), 046108. Issue 4^��3/E RevE.72. 6� /I`Albert-László Barabási%�Réka $$. 1999. Em�Gc �zca C��ni-4s. 1R(286, 5439 (B$), 509–5Ht�"2W 26/s)�.286. =(.509 arXiv:4:/# +mag%��5ent/286/9/509.).pdf � � 0, O. ZaÃŕanM|ndA�Goebel%��91�&� �I�"� in S� %5U�9 I��G�C�Cy�,dv�}_6A�"�K%��M�M(. 237–242^�9/ASONAMA�@9.14 [5] Pierre Dw.Dt, J Callut, G Doo J N. Mon�;,Yves Deville!17A|�K&�*�e� �2 G0�/ . (12 201`p[6] Michalis Faloutsos, Petro2�!�Christ.�Q� On P�)-law RP�o8eс�)z et T���0 Proc�u):��p"�_s, Techn��(Archi� ur�Protocol�^�I ��88 (SIGCOMM ’99>KdCM, New York, NY, USA, 251!��6^�D45/ 316188.316229 -�Scott�0, Hanghang To�VNan Cao-�ing�L Xia5�apid "N!���C�)��(J>!� ACMA�6J�I*@>!+�K"�Manag (CIK%AHN 2463!46^�\45/3132847.3133170 [8] V Grolmusz� 5. A Note�A)�E of U&�:�ue�f. �ss. Let�]%6 (Jurn01��63�63Z�$016/j.ipl.0h.02.015 [9] T. H. Haveliwal%�03<: pic-&Zq�5���xtF �a"�We�f��.�Trans.l]on=�!��DL �E͘�eL � ��4�ly�n,3), 784–79^�09/TKDE�� 3.1208999�<6�[10] Chin-Chi Hsu, Yi-An Lai, Wen-Hao��,�g-Han FeA��Shou-DemK. A�4. Unsupervised��!, U%� S��t�:� ��E\L><TenhCM�oT�a�" on%��S%��!f� �� (WSD�� 77�779Z��018661. 8 `  JcuDLeskovec Jaewon ya!)Jul�BMcAuleye�3/���.����� thJ,CDM (2013). �p Ravi Kannan, Santosh Vempala��Ad : VettI�4.���C"�(s: Good, Ba���S�~�r��J�+$ 51, 3 (MaE�4), 49�#�5a�!E+2U!)990308.013 [13] Songs�Liu Laza���GN$�=porgiou Sophia Tsoka Laura Ben�6, AŨte��Kittas%Q�4.QUb& e�<3 lapp� �M��e0uM.mV��",�in teinIzi�*� PLOS ONE !�4)V9,371/journal.k .0112821 la4David Liben-No� nd J�7leinber�007 �=�-�Pr�[6�s.%�m.�Z�f* �.�p. 58, 75�7), 1011 1031. N�8002/asi.v58:7 [YMark Emp%�3.UK� z �2q� ���X��2� !�RRoE$/1307.7729}��.2����M. Girva�A���!�e�F�� &��i"9F�&hys%Re`m0 E 69, 026113�04e�7] M.>} �A`3� ���>�0*�j�b�� #W� 6� 27,i200� 39 – 5r socnet�($4. 11.009 } Pa� P��!Matthiea�tap���m !)� "LaΟ����� v��A�>��2�(8 R�� s�e�-.�� s (ISCI;�5�*�p�\er-Verlag, Berlin, Heidev g, 2�Q293V�4007/11569596_3a�(9] Daniel AA�ielJ!*�S� -Hua���gQ��A\�[� "�We� Mass�W� �� Its * �NeIJ�R5T12�. 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[1] Jacob Biamonte, Pe�#DWittek, Nicola PanABHi, Patrick RebentroLcNaA" Wie�0nd Seth Lloyd�F�549, 195–202 (2017) doi:10.1038/n"le23474 [2] Esma Aı̈meur, G*s Brassa� íb�)$en Gambs. �:�c�� un~g�v�"�lU#. M�t�n�8g#(, 90(2):261�087, 2013. [3]�X;�, Asha� Kapom+�8Krysta M. Svore�"+���,est-neighbor�� �TZ��� Info��ÁX., 15(3-4):316–356, M� �5. [4]1�� .�4Masoud Mohsenia1.��M���8#:big datA�� . Pha� Rev.&.�413:130503, Sep�4. [5] Y7<, Silvano Garnerb ! Paolo Zan;&�<:btop&Tpnd geomeA�� "�Jof ��.!�A�Commun�K8s, 7:10138, jan�L6. [6] Zhikuan Zhao,a<k K�tzs�k� Joseph F.���sb|aussias"� reg�(�20%�\7] Srinivasan Arunachala}K@d Ronald de Wolf.= urve���  .S�m2�y�(RR,�(/1701.06806E�$7. [8] Ric�S�&ttMSDnd Andrew G. Barto6$�Q����R2� �LmT. MIT P�, Cambri�c8 MA, USA, 1st eY�d, (1998). [9] Stuart Russev�nd�� NorvIcAr���fInt ce: A Modp'�A�D�.�nt�J�H� �Up�> Saddle Ri_� NJ, �3rd�82009. 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Q tr"���k�R:v@�nn59*J= &�A;Ax� �C\8"��B��6��enough.v������x ���;�|bq� z2� ��%i�� log-*@u 9Y�������e*�:��N"�5 circumwB!w���/2�no4� Û 2Ib!���� �6�-�h2[R� ]�!:] e.�F#�lpw +  ǫ: t R EFERENCES [1] J. Rissanen,�4 Mode���bH^or% d�ԡH/ ,” Auto1 ca, vol. 5��no. 5, pp. 465–471, 1978. [2] A. R. BarBp�� T. M�Bver �inR r�x�� �q�o �IEEE ��a��- *iY!{ ory,�? . 37� . 4 �,1034– 1054�P91. [3] P. Grünwald�(J. Langford�Sub�~�a&�FA<�b�{1mdl in�qif��O mis�Z%I�M�kne Lear� �66� 2-3 �D19–149, 2007. [4)Qényi�On� �oq!j=wTin Fourth Berkeley SymM!�n M.��S� stic ��PK���)�!F61� 547–56!U�5��B�yya�*�f*_&wo9BW�al popu��on-�ˎ.�*��s�Bullet�yalcutta 6�� ocie��3M��9%m09�43. [6]A�Van Er���dA/(Harremoës�-�.��!~(Kullback-Le.tr *PaNIn&�J�y,I��T�EY�Q�0E 7, al379!r 3820A14. [7%yun(, C. Huang,A�Q. LiI X. Luo� �s$Principle,���L"f��s 9Ual�E�k� Feschrift�� Jorma�b 200� 8] S. CA erjeN�d�e�.&�����B���� n���in 2014)@�I7]>~,G2�c�4)CE� 302%Z03A�9]..,��� � s: fBlgokri1&�UI�$Ph.D. diss0�X , Yale Unh .�09. [10:.% �A2w:��E{�aAnAnn6qng%myvm�E6�1J�S"6�.�h[gA=Ann*�of U�s)I 1080��100aS86�N�Nw%ngartn�=�I  pq��'cy�2��Y��sm7�2�Tѣ180�825��9A�suT. Zhe* “F�ǫ-�Lto�� : AnalyOof"��k.2Z�z�� 34, �W21%H221e��0%H�4��m�“]of Mixrx� ��]�J� .�199E�5] W. �b rind��Eive.z*5 Rad�Ba! �v}�� .}�201%��6��D.��<� *Dem � LT��. MIT �eO�5417] G. JamesoniL�^pls�]A:�< ��ulaA�� �0"�MUx2UGazet!���9� . 54�W . 68�15:�u�1 !y�fo6��lReú� $Sparse Sigaaaa Gene�2�#� D�p Kiryu/�e�WLnjun Li Student Memba[B , Kyo]�wan Jin, arXiv:1612.09565v2 [] 2 Aug!�7 ��J6,Chul Ye, Sen��.Z�, Abstract CI�ess�.�(ng�x �d7 ata-acqui%X��aradigm%�s �R�als. RZI�p8 �C�b�� show��aH��0����prq rob�u�r1\ nois�|>A �gs � red ��  � t8��HWUrreal-wor@ pp�#�s?; �a�#��K"� �%] cano�� �v�yer"h� %��,r�!avelewI��(�Dp�z�\Ecs :���|o 1�a�������2 �s�F limi3%to � M���Q�dnd Z�fQ4� �%b�papA��z � �La?�ori?>� 2M)J�i-J �cXR�xA< gramH� p"G��,q.re�]!�CTE>M��,g A���� �@�@I�LU�:� �pF�e��3n:Gs. 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It has been�� if T?(of full rowT�k�n �Vdev� of n!N$: m T SΩ T  I��INVsm� �w�!�z babiz2,:���O� e c� � assu��2��column�F��s (���*�"1neP!�aT IN ,z��� �of!X1��is obtai�%3�ofF� by�lac) IN)`. For ex��e%��  �y�di))��E)�� %��1)� m �_��yj/� u4�a�(x M P CN ˆ!!g4term θs pM q,"-{h$in�] (z� �#rpM��INk(r} r |J|ďsB��r@� ��2C�ClearlAW= ia2. How< �,��hypI�s!��f2�, TA� >� lmay� �r�!�^mod0z�a�8straightforwardE omitm�y"�prAt6[Y�m�Ap�,ix E]. 40 �x�B5I� W�seX�n�, (10)A��i�$)�(12E m�[,C1 δ ´2 KT� �2  N  m,.j fa��Ke�� @n by $˜ ¸ ,2 ¸Q ˜��\ ��&2��`ET›ΠJrp@ ��´-�E!�8�A�/!�˚J+�KTaD % rY�M����4 �Q }Π �JS� r},2$�� J��� 2�J y ´� ď~� � ��Ng��} B�"�C˚&� @ : Tr[3 FinE�verif!at�N2�ď 1 ,�Rupper� domina�B���%isV� lR EFERENCES [1] D. L. Donoho# �Com�&�(send#(,” IEEE T�r)�fc�, vol. 5�$�o. 4, pp. 1289–1306, 2006. [2] E. J. Candès, J. RombergpT. Ta ��Rk�"�r�"K)8inciples: Exact�\nstru��J�b�l?!;#%�  ��]����2 ��4�509� 3] A. Bec�o M. Teboul��“A fas��e�'Tve shrinkage-threshold�� algorithmtli$inJ�@blems� SIAM!I,Imaging Sci.-�-��1 � 183–202�d9. [4] S. Boyd, N. Parikh,!�8Chu, B. Peleato)�J. Ecks(EDi4'�b�*�&�fst�ticalO rn�via�y alterna�& dirJ" on method��$multiplier ��F� %��Trendb Mach� Le c �3, A��A~�2�11. [5E�Needell�J.!�Tropp� CoSaMP: I9�6&*IX�vFinaccufL�e �� `%Dmput. Harmon. Anal5��6 ��3)�30�3215� 6] W. Daih0O. Milenkovic�Subspa�ursui��re� ressEgi�V%EH^�� i��5 ��5 � 2230AM249, Maya�AR7]a�$Blumensath�M.ASDavies�9Vhar�!]��&�cVu2H� 6H �27 �-H265�745H�8E�Foucart��HB��-C : An:��=Q%;q��N�6�! A��6%8 254e�563�E��9> %5�� Deco�by� pr"J"�^����1)�1��20�t4215, 2005. [10] V. Chandrasek�"�Recht, Pe#Parril�A.�@Willsky%NB%�"geo�a�n�e��.a Mathq�9= 80!��8!S 2012�ɳ$Amelunxen,Al Lotz B. McCoy��A.}�Liv���oY , edge: Phase� * �c �-sT1 data)��F%�In�nce-���A�. 22429E�14�(2] Y. Bresl�$$M. Gastpar �<R. Venkataramani%j�� i�0on on-the-flyA)"w ���in!m�!�i�- syst�I0in Proc. 1999IR.��� y W�"hop!9Det��, Esti�E C$"� ���,�S�*, Fe, NM, Feb p, p. 48~ 1 [132BNear-�u4$N�� proj � s: U�! enmTD te�!�?�� ��A��(5406–5425a��14]!�Ru�$�%nd)�rshyni�;On�%��cB��Fx#;Gaussia�"'�W$Comm. Pure�� .;�6m��8�x 102a<104 ��8Aw�5JcY. Pla ��A!=�b����RIPlesA�  of�ed�" 7, a��1��723�725i�,16] H. Rauhu��� ����s� �ud(-�x"e�inI��e��q*M����M�s ���Sl1�e���o&/, ser�don Ser������M� nasia�Ed 4rlin: de Gruyt 2010�A�# –9���76��,!�C. Eld�D.�iW�P�ndall����9�b '�t%.redund�%di$ �a�!*e"�:b�K�3MX-��5� �7���1�aNam���E���lad ��R�,ibonva ��8�&K alyL�m7(�" �I�%�ut�� .R 34��i���1 2013A�9]�iry�S.��6��a���0“Greedy-lik� � �s��cV��%g�L� Algebra_L��i�-o44 �22–60�f�420� Mallat, A, tv'�2�4pro� ing:�-c4way. Academic�ss\� [21��N. Do��M��ttA�Eh)��nlle*�': an ek*� "� al � resolu�ł��A�en- �o&� � �� mageŖess"1��209a?21_�<22] J.-L. 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These brain networks were then analyzed using traditional graph theoretic measures as well as new measures that are based on spectral graph theory. Using data from populatioin groups that are expected to have significantly different structural patterns, we illustrated the increasing statistical power of the neworks as3nu!f� 5e�Rgrows. Moreover, we provided preliminary evidence on the robustness of using spectr� arametersAana!�>�and�Tir potential for discrw�t�between 9�p1d|n groups. We are currently persu? this line�,research try@o shed more light�us1��gYB�y�(characterizB�� �ffe�J��@ 5.3. ComputatioA�,Efficiency I!bis sec!� brief�)� an indic?�$the time eI our !�0llel implemen u!� connjvity bE��be�parcell cscheme%jcompare \ fast>X�toX8best multithreaAQ6��Ds we could achievem�MatlabE!Python s!�ta, packag�(After remov!�8isolated voxels�Tdata 7 http://www.math��L.com/help/stats/svmt�`.html 13 7. Acknowledg!< [17] WeA tefully a"e fund�-� d by�# Univers!eDof Maryland/Mpower1!� Stat��rough Cen�AT Health-re �(Informatics%+BioimagK(CHIB) mb NVIDIA RM� Ex!�e� _atm Uni[18] J��. ReE�Pces [19] [1] E. BullaB,, O. Sporns,E�lexMK���:!6�p�oretical�si%��,�fune|al systems, Nature Reviews NeuroExce 10 (3) (2009) 186–198. [2].���S�aaH�df!�A�F��H, Dialogues in clin��n2}��5}�13) 247. [3] Q. Wang, R. Chen, J. JaJa, Y Jin, L. Hong,�HE. Herzkovits, “C}�-Be��BA� P}� : A F)� AtlasE=0SchizophreniaU (”, submita:to)P�iY[ . [4%��H��s � L.��,P. Kochunov,( Sampath, �Edge-cE�ed dti6v�" sis: Appl��� ��.���,B��!�T15) 1–9. [5] M. Kais��A tutor�X!�)Gom!�al otopolog%�and spaɈ�eEfE��b%mQ��mage 575�1) 892��0!�46] A. Zalesky, (Fornito, I.!$Har�'%ICocchi,�PYücel, C. Pantelis,!j�T.hWhole- �anatom��: doese� choi��fE  mP�?6��u610) 970�83. [7%P,Ingalhalikar�Smith, D�rk!kT.�S]thwaite�TA. Elliott, K. RuparelE%$HakonarsoneE. 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Chuax�Pt�rewind: `U!��b�d6h6E�E�i�:,QI�b�,�$���e�'A�!O� ����ul�Mdia�d�fJce. ACM�!,pp. 78�790. ��G���Liu�� ���S��ChC�“Larg���� via� YC��tBf��Q�� 6���C"���C}�e�9�����227X�227��3]b��� , Y.��Z. Hu�9. Sh���R�9C“%1plu?ρp���-!P� �  �-dupl�zBd�jJ� 19th%�� �nE��aYP1�6�9�1,%��4r� 432.��f���T�?z���X. Xu�.��“���oh:b �BP�{�r5��D�{m��c�;�s�� �ɡF prin�z4Xiv:1701.07901%�7.�� Y. G�(S. Lazebnik��Gordo ��F�$ronnineS�I�<� .e���\ rustot��a��"AJmr���%����iK�F�E�������n#8�� ch. A�ll., v��35  . 12)�29�� 2929�3. [O���CBD: p�ldx.doi.org/10.1109/TPAMI.201�43 [6] W��.��R���,!L�J��)6��E� “S&�f� kernel)�in CVPR�AI�7��0W. Smeulders,��or� ���=��up��mG�J�����:b���M _%early��5���ns� a �p-�"J�v�m2���l��R%�22, n=�13��13�20����R. Dat��D��shi��Q�aJ.�;� “I6.: Ideas,g�l4��-trend���Qageܡ���� Surveh�sur), ��%�AP�.�#2008. [9�� �S. Kumar1�-F�5� emi-*l M� forihM�i��Y�=t�P-t ;%�M)tm2t34: $393–2406Uc10]t�'��ZA�E��M��>b�S&�?2a: a u�Uy�r�to8S�s +�p��!�in���in.��A�20��!� �, �H29���3%�11]���Y. Fu�-Ga�%��L. 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Yang, “Supervised recurrent hashing for large scale video retrieval,” in Proceedings of the� ACM�TMultimedia Conference.�,(�,�d272–276. [24] S. Hochrei!�4J. Schmidhuber��Long short-term memory,” Neural c%Cat%'0vol. 9, no. 8 w@1735–1780, 19975]m�W%$T. Zh (N. Sebe, H.(Shen et al.�A survey�learn!Bto !M�,IEEE Transac��s*-� Analysis�<Machine Intellig!1, 201�,6] W.-J. Li,!' �!"W.-C. K�$“Feature�ba!�deep s9���Lwith pairwise labels�4arXiv preprint (:1511.03855��5!847] Z. Cao, M. !��,9I�P.�Yu%1$Hashnet: D�>3( by continu)�!�V�� 702.00758EP%$48] V. Erin LioA�!0u, G.-0$P. Moulin,��J!��o ��1forEE act binar�des��V%�Y�� v�� >��5I�247A� 2483!e�9E��S� L. G!n�LA u, X��u �U�$“Quantiz%I�-EE�\ing: a general framework�� a�$able image%%J�� Q�2��ei�7 ��1�187%���30�I�yaa���A4ynE6}g� ]4%�%�V$ 606.00185��e31�RevaudE�Douze, C�h)HH. JégMEv�!�!��")collem��waP8circulant tempo!g enco�-�in 6?� �?:9�)j 2|�'�3Q9�5� 246��2�$Yue-Hei Ng�$Hausknecht�LxVijayanarasimhan, O. Vinyals, Ra4nga)(G. 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Bingham, C. M. Goldie,1�L="Re: (, volume 27a�Encyc@dia��M�maZ!nA��At%�c��,s. Cambridge.��P!U�,!"89. [4]aBol"́$�� rgs,!tChaye)�( O. Riordannreca�scale-fE@graphs. In Proceex�s��4Fourteenth Ann},ACM-SIAM SymCum�tDiscrete Algorithms (BaltimoreT403), pages 132!�,39, New York "�.^. [5]!�(Crovella, AA�stavro �0M.S. Taqqu. H.H*�6K���# world wid��b�M R. AdlaXR. Feldman, editor, A P��GuCto � a4 s: SI���Techniq& 6 �y��efed!:�e�sA�rkhäus�(Boston, 199!�6] G. Cs EH$T. Nepusz.��i%�� �5�w�packag��' �x" �&�6!0terJournal, C (@Systems, 1695(5):�T 06. [7]A�Das�L�o� V. FasenF �u� oremZ m �crisi�^ he I��� � �aLApprox�,e Reaso�$, 54(6):70�716AA13. [8�A. Mitra �S.I��. Liv�j�'\*X � $: >� isks��r>A9�v^Eje�edaS� $, 45(1):13���3��9�%�6���C� � an extrem�mpo�+�:�:� "$�7���u6&on&� 0Bernoulli, 17�226�6�5z.1. [10j��Detec� �aS�� �r�'�%�AN�4l!61, 20 j�1jj��� ^��:'y %F�*�| ocha��Y�5:195�38 (eleck ic)%�@5. http://www.i-ji|s.org/ssy/ viewarticle.php?id=14%32]�)de Ha�(ndA�Ferreira5  V*a�ory: AnA�e� . 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We show that if L is a nontrivial limit group then the nonlinear representation variety HompL, Homeo` pS 1 qq contains uncountably many semi-conjugacy classes of faithful actions on S 1 with pairwise disjoint rotation spectra (except for 0) such that each representation lifts to R. For the case of most Fuchsian1VHL, we prove further)L�[this flexibility phenomenon occurs even locally, thus complementing a result of K. Mann. We o<that each non-el7�ary free or surface group admits anM8 on S 1 Gtis never semi-conjugate to any2r�factors through a finite–dimensional connected Lie subg�in6 . It~exhibi/eA� mappaclass1p$of bounded�s have%6��b: . InbproceseA establishrthese r%|�s!�*veu�$combinatioHHorems for indiscret�^�PSL2 pRq which apply to most Fuchsian�and%xll limq|�s. We also show Topological Baumslag Lemma,B gene�\b���r2�(s into Bair!�\E=<s. The abundance!�Z–valu%��badditive defect–one quasimorphisms o%/se Ul would follow as a corollary��gVa !+ly selfA���,ed reconcili)�of!�( various no!�%�.cyA�AcPextant literature by !_Iat& y ar!z`l equivalent. Contents 1APtroduco 1.1. C]#ThM#!��IY#Sui�Q# 1.2. U� e Fami���Exotic GeL�Ap�sa��PCircle 1.3. An Axioma.ApproachAVN�� 1.4. F���8Rigidity 1.5. Mm��Ce��86. Note�W(d Reference 7. OutlinE-�,Paper 2. PreA�Dnary 2 4 6 9 9 11(6 17 Date:�n`ober 10, 2017. 2010 Mathe��s!E ject � ificE �. 57M05, 37E45 (Primary); 20F65 57S05 (Second$. Key word �,phrases. RotR$ spectrum,2��,��I�:V�,B�J�4. 1 2 S. KIK . KO.G. MJ 2AXV��2A4HyperbolA eometry 2A �s3.RO� �O 3x.oSet�� 3vPro!�e� nd D�� %$s 4. Split�`e ��MC�4]Very G�� Poin�v�A�mX�S ?In mA��4,ulling-Apart ��4�Al�24 Faithful Path��imultane�$a�rola]5� Numbers 5R���i.le��5� Stat�NA��C 5�roof 5�m�i�1� 5��Q�2-M�3�5a}�L�-26.y�s 6x0Tracial Struc�� 6r UV-s�3f��Smooth��7Z��7m,he Universal�!�(Nielsen’s J 7� �JB '(s 8. 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Recall our notation from the introduction: A˚C “ A ˚C pC ˆ xsyq. FLEXIBLITY OF GROUP ACTIONS ON THE CIRCLE 31 Let Fn denote a free group of rank n. Half a century ago, Baumslag used the following lemma to deduce the residual freeness of groups of�\form Fn ˚xwy Fn for w P. LU�3.1 ([6]). Suppose we have u, g1 , g2 , . , gk@, such that r( i s ‰ 1u0 each i. Then�@re exists M ą 0 >@ g1 ut1 g2 ut2 ¨ gk utk SL whenever |ti | ě M.g�P Sometimes called Bau)L�, this result plays a fundamental role in�< theory of limit-Sd; see [102] and references5rein.:v� geA�lizes�<multiple “twisA�D words” [64, 5],^ also4torsion-EG,X-hyperbolic groups [51]yXpresent a continuous veG�5�l%��is see )�ee$imply both7these��aaP0s. Throughout)dsub J�,AGlet T ba��set (of parameters) equipped with a decreasing sequ!_|U$ts T Ě T0�1�2U4. Defini�( 3.2. Let X ��t�Qspace%i�Dφ : T Ñ HomeopXq 2map. (1)�wsay( is attrac%� (to C) if�a2d a nonempty proper compact� C Ď XY�%�e+open U��C!jF/\atisfying φptq˘1 pXzUqR�UH��,t P T M . 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FLEXIBLITY OF GROUP ACTIONS ON THE CIRCLE 101 TAbroEonAB p isA�@lobal fixed pointTσ. Moreover, |ρpGqp|� |G{H (N. (2) Let ! bA�fin!�,orbit. Using%l nota!>s Y� roofp\(1), we observe rot ˝ρ1�βpgq{N%3 ρ̄ �B^,. While provxdir-�(ñ) inne� alreadyA��ni ˘ 1` ρE� p Y�q(Y�%��̃A�%�69� N asQ�8s.  Lemma A.6.-=0 , ρ1!@cirA��aEi�s!hL. Suppose either (i) ρ0 aa��1�%csa��4Euler class, o6N7�a common�`�z%� . IfdhaA&.��,k n so does�. P!�. I!CA�se (i), ��5!u��a�nclusion>7�8recall ���a:��!ρiA� if% only ρ �not)�a2��.  �J � 2.119hρ �n excepA�almset C;AI4particular, C eP Cant�#et �is caseA�, let h P S 1���b)� 7fun%�L which is continuous�is lo!y constaa��nJzC���T�ρ ěhE���ɷ-2� IaP. 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MJ e(2�3)iρQ��blow-up!!Z�]�, �����i 3:��oA�i .� �Paw)��I0 e� �1in �A.4d � A.6,1 ��two�>�s% .��.V-5� �� �T� Ji q�2.1)�= 2�02 A�� }7qqFv�! tis12���4e�? _�0m̄}�<monotone degree  X �h)}�m� B)�Bar�I�rte.)��3!�4), s6B7��%�:��2��6, �j bothN��or6>��apply� 1��5A|!�Zfirst%��byF0�4 a �iOsecond1G� .Q��q R Y`.  )E��6� J� map�%As�[74, Pro"� 7.6]��&4a path tht : t 0, 1qu Ď� q �P���hI�Id%$limtÑ1 htE��h�^n tρt  �h �0�} t u!���desir� athM6)ñ (5) �n�.�F!���<nteger–valued:� „ ˝� �´ab2��� ݉�2%se)� t τ7!��0 a� t eu �pmq˚ Bl�`�02�� n >��&V on L ˆ �I�n��E��'i L+` )� ˆ 2��)� �τ �� , as1��. A������ das elementarily (without u> coBlogy)� $en in [73,կ5.11]E Z�cͰ�7� )�clu�<19<<1.4]. Acknowledg��s�author�7ank�I�Bestvina, B. Bowditch, D. Calegari,'\Casals-Ruiz, K. Fujiwaraŝ0Ito, J. Kahn,.KapoviHDI. Kim, Y. Matsuda? Ohshika-H Sakuma, Z. Sela, A!��sT,M. Triestinoj@N. Venkataramana �9 H. Wilton� 8 helpful discus� �s)FB��Wolff4 shara'[104]T�everalRW ent:O���&6 ly grate� to K��n�< a number of ins4&Vw��A/ �, references,6n�[3!�O�TGthi 2��?4Tata Institute�Funda� al Resear� n Mumbaiɮ;��!ohB^�6Y�<Mathematical Sci�A�SingaporA here�� �t� �r��wac�uU 6�� ��rq �b��Ne#o F�� � r Gr_ HNo. DMS-1440140 at �V��5�4in Berkeley duE:(Fall 2016, վ�3 :��b� �-�%xa�2�Samsung1j!� Techn�f. <(SSTF-BA1301-06))Z2�^E� ally:h�imons.P�Collabor)h)bI� 429836,!�Dan Alfred P. Sloan.D�5eFe�hipI{by NSF V%�711488.�!4U��9in�A a De�A� of.#� =#J.C. B��a�nt. Ru�� V\. Alvarez, P. Barrientos�9Fil!%8ov, V. KleptsynLMalicet, C. Meniño �6�Markov��a�(�� rete�e;0real-analyticHdiffe"�s, In pr! %�. 2�!�(. Beardon (A`.)�L geometr�:u�, 1 ed.,!�du4 Texte�yHs 91, Spa#�er-Verlag New York, 1983. 3. Hyungryul Baik, Sang-hyun �>�w,Thomas Kober�FUnsmooth&�&c�n�V pactx -manif� J. Eur��8th. Soc. JEMS (a���o� ear. 4.x Barbot�,S. Fenley, F� 0seifert piece%�8pseudo-anosov ftM �e!�t. 5.�BarlevR$T. Gelanden�o�if��)�algebra!ԉ �ia~ofH itM�} Anal�112�p0), 261–287. MR2763002 6. GA�4umslag, On gen��ised f�pro�{s,%��.�L78 (1962), 423–438W�F56t 5 #3980) oladen*b�KrombergI�Koji &L�Cruc�� ��s� quasitree-ppl5,to_ �p�7  >!ub5��@. Hautes Études�. 122 AH !064�3415065 �6��%�a� Feig�{��$’s work:2� 6dkanin-Razborov diagrams, Gipic)"% �Cmethodea)�t�y, Lona�avM�Lecture �d Ser., vol. 358, Cambridge$v. PreO(, 2009, pp.% 29! 2605174  J :��B�x�"�  of�e,ma=�� ). Top��6A��0Am69–8|pR1914565 10. Francis Bonahon,x�t� � �@étés hyperbol dimen  3, Ann.�)A 124 (198�no. 1, 7A15A R847953 _�C4 natti,� Mont5 de� NavasI�C. RiRigid�c C 1.��� rval ari, \��c;I: solv��.�(t��). �$Raoul Botte��s�'�s w(characteris�BeA��fIn�-m�, D�U rential t!� ogy,l�i�VI�(Gelfand-Fuk*� (Pr�uSy ., P fı́ciaM�Catóa�<, Rio de Janeiro�2�7!�M�muin)�M�652�u�,� lin;�8I�X25–61. MR505649 13. 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Acknowledgem� The�F�e��leae�t!Bes@ults has received�!&��VEurop�Re I$Council un�!0$hUnion’s Seventh Framework"�Xe (FP7/2007-2013) / ERC8nt agre�( no. 306992E�hBeae#Hardness��$Preprocessa�grE�f�� 6 rgen�Found�. Refer�!xs 1 2 3 4 5 Ivona Bezáková�DVarsha Dani. Alloc �indivi2@goods. SIGecom Exm2,, 5(3):11–�(2005. Maw-Sa� C,, Li-Hsuan Ce<Ling-Ju Hung, PeP(Rossmanith,��P$/0 Su. Fixed-pa!w.U��se�mP cover p3. Discrete O�:4, 19:12– 22,� �. URL: http://dx.doi.org/10.1016/j.disopt.2015.11.003��i:"� F#�. Jianer �,Iyad A. Kanj �0Weijia Jia. V�+ �: Fur�] observ%щ�f  impEN s. J!��!Ds, 41(2):280–301�01v��$06/ jagm.2+ 1186�06/6���� Ge X��I � d upper bA�F�� or. �Dut. Sci.�01(40-42):3736�756�10A`Drek Cygan, Fedor V��Lmin, Lukasz Kowalik,E�el &, DánMarx,Tcin Pilipczuk, Michal �qSak�& aurabh. PQ�ized A5�$. Springer�5.z�86 7 8 9 10 11 F $13 14 15 \ X17 18 19 20 21 22 23�,3 Irit Dinu�8Samuel Safra. Oa �h�[(of approximi��um2C. Annals.mathe,cs, pa�& 439–485�a�0Rodney G. Dow !/%Eel R. Fe; s. F���� ]6DA(lexity. Tex�&�ua�Sci��:_X3. Pål Grønås Drange%� kus Sortl�Dregii|4Pim van ’t H�(-&�utes� �m �!�c�i� rity�1�' o���z$Y� � �a - 25th4rnHal Symposium, ISAAC��|4, Jeonju, Korea, December 15-17!�%�P�0�e��5�285–29 $�.r�\07/ 978-3-319-13075-0_23.7/N"�. >��S��, Gaspers, Di��Kratsch!�4thieu Liedloff)�:aIterativhmpr� � xact��.or.-`.E7-9):104! 1053%-�0F��<Fabrizio GrandonM+6��. A���&!� queriPach��analysie?F���� CM, 56(5)�09>��� �>{��E�ExIq� Y]. u0� tical�Tery<An EATCS!�ie>�40. D. Gross, MQini�(. Iswara, W��Xzmierczak, K. Luttrell,� T. Saccom���DC. Suffel. A surveeOn:�'�e�~�g�+!Uor� netv s. 12:89!�910, r �. Frantisek Kardos, Ján KatrenicIf<Ingo Schiermeyer�$��u� !��3pathq��c]�dissocie� nue��,�!�8 F� 2(50):700�= 70m�z��tcs�1.09.009}�� : �fanqp<. Recent develop��D�  : 1�Zlletin�!E4 , 11i@ 4. J_ar�Y�e��ivid�hmoys)nÉva T%�. A�za��3�  schedul� unre�,� (llel machinA�Mat�~\#+ 6:25!T271� 90. JohnA�Lew,Lnd Mihalis Yannakaki)� node-de�on� blem�� @ditary�p -s np-A/ lete ��. 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Brown ph�Aփ4A]Y{ e��g��$ �d2�X�*^D.� bn� 6�:� �56��8��"~ �^ly&�"�R��ѮKPH ��ν���� �� a A�e%M�:��AN�R!��& (!Ev��k]��&f (3.�Ilim2��':� yX$ |a|→∞0 Y]�F�!!�n a.e.s<�B� i.e.�26f�c52�`��sCu8rt�Q"}�W��?;δ πn N��Q��n� �CalT��x, �F @�>�� �*�i݆`&�N�!���@mea=ile�G�Z~%�oa�E$)� s��,"���ϡ�G=r?s, e>� �k-jr��ap� ce KR�K53or� -(n [−K, K]2,� . (W� _���i�"�A�s 8.2�\ �s�o� , SaI�[23]  � a'�A!3%�ls�VIe"$1��!]�*K0?�?�x�k�o ��&� � Kpd�O�ks� raia���1qu!yon:�B+�aj��x&e mBu�Y� S(”B�/2 ��?})ol=1� 3is��^L��F��"�ed>Rby�� �>�9!N�0adapted from �U[28]: D EFINITION 3.9. A decision procedure δ0 is a normal-form generalized Bayes pro 1�m with respect to a σ -finite measure π on Θ when δm minimizes r(π , δ ) = R r(θ , δ )π (dθ ), subjecbtheqtrict� thatF�m ) < ∞. If P admits densities ^��ν and%�m�lun) ized ( f� θ ∈Θ .��P R posterior risk ℓ�0 (x))>(x)!(dJ for|-a.e. x,s�n��i!� (ext�ve%�) B�=�.��!�@π . When a modelB, Stone A# showed)Pevery �z� ny�� lso 6��. (Sack!}finedFC� R in6! <m, but demanded X%�!y(·.<be Mjν-BThe noEof�%�6�� d��i)�s*Eؐ optimality were introduced by RaiffaM�>Schlaifer [21].) For exponential families, under suitable condiw, !{can%z �)xA� ssible es�tor!eB��.�first such NONSTANDARD BAYES 13 result wa!�(veloped by )�t[23] in his original paper: heAc�vM�,!�, statistical�F, problems wh!<a<2v�am��y!p�f�] exθ /ZθE� R xθ = e!�i'�,�]�%�AN�t��r) to1]�Fof� mean! one-dima{�o! N�� -�<quared error los)��s�� ultsIKfurther2��in similar ways by Brown [5, Sec. 3.1] ��BergerI|0rinivasan [3]Mollowing� oremE/ ivenab'We adapt"%�ement �is8Hfrom [17]. T HEOREM�x0 ([17, §5 Thm. 7.17]). Assume?-� m�.C� BCy,�e�A!;�3a)Jjointlya6 tinuous, �� vex in aALM#θ Y�sA��f��$(3.5) lim2`��=�(:all8L∈ Θ. |a|→∞ T�?�� OB����k�C$s have bee�,posed. Heath! L Sudderth [11] study%�>�Ri�in%P settAof-�ly ad�}vee�abi��spaceI�� RI$their mainm=�:2�1A1,I�2A0Fix a class D�Fk s. 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By�lequent, we have E[Q2N ] = E[ |W ] � which implies by Markov’s inequality that K1*. This�Tves (c). Regarding (d)�(e)� observeF\ h i > E [XN j |FN,j−1 �� %��h.� = w j E [2��0 by%,independence.betweenQ!:h1 , ., h wthe6C�68� wj . d �$guarantees�.�� hold. W� us obtain &SN jN /U(→ N (0, 11I0together with!P�Slutsky%�Theorem5�$that PN >A�%%hj qP 2�K j� �2x� Refer!3�s Anderson, T. W., editor (1984). An IntroducEu�@to Multivariate Statistical Analysis. Wiley. Athey, S., Imbens, G f!}8Wager, S. (2016mpproximY|residual balancing: De-biased in �@ of average treata_ effectA�| high dimensions. arXiv preprint �:1604.07125. Belloni, A., Chernozhukov, V tveriD., �ei, Y ʈ5). Uniformly valid postregularizata�confiI�reg�� �� many func!o,al parameter�z-est!!B�f work �� >�� 512.07619���@Fernández-Val, I � Hansen, C �@7). Program evalu �$and causal9� wA�!~�-5~�al data. Econometrica, 85(1):233–298.~�A=Kato, K �A�-r%j-sele%A�!]Hleast absolute devi �regresA"^�oa�6m,problems. Bi �ka, 102�p77–94. Bickel, P. J., RitovAI&TsybaE8 A. B�H09). Simultaneous amF�Classo�dantzig �or��e Annal*u�ls, pages 1705–1732. BonnetI�\Gassiat, E., Lévy-Leduc!�, et al�E�Heritabi� ]|�i>Z|al sparse linear mixed models. E!�$ronic JourA of2�� 9(2):2099A12A�0reslow, N. E.%Clayt��D.�K(1993:9��(generalizedR��� �� AmeA��n��� ssocI)$, 88(421):��.ühlmann%�A� Van De Ge�ޡ�9�� A�R : methodsoryR applicE� s. S��ger Sci�� & Busiw$Media. Cai��$T., Guo, Z6�a��C��intervAJR��-�y$: Minik rateA�,d adaptivityn�45!�61A�646. �`Demir!L M., DufloI���2��ILDouble machine learn���&!����f�L� >L<608.00060. 36 F��.��[Spindl �����V���.�"�-6#� U��:�ele�� ary,Q� a�2ach��n�.Reviewa\�d�i� 7:64A�<688. Crainiceanua� MiZRup� �,aZL(2004). Likelihood rA~ tes�VM.��� one � $component..�ahRoyaly (ociety: Ser� B (u1 al Me$ology), 66�v16AG(185. Fan, J �Li, R%r�0aw�V� ble �;�9Dvia nonconcave pen�#�!��i� racle p� iesB���4�s. .4,96(456):1348���3AF��Y>�� 12).N��in6t��` Ann.1P., 40(4�N�4�T, 2068. Ghosh��Thore���M%,e8 Non-:!��G2��-6�Q� U�ed=k of f� 2f_07.02883. Goem-��D�OHouwe � H. C�QFinos, L �!��T��,ng against aBh( alternativ�#A�N'��`: asymptotic type i error� trol6�y@ 381–390. Groll9s utz,ŷ20�J���N��%D�� l1-U�� ��m%�Uic%�$ Computing"A�8. Ha��PI Heyde� � 0). 6 ale Limit� Ŏe�Aْ �b#a7Mathe�a�u� s: Aq�of MonH ph �PTextbooks. Academic P� . He) ty�am�Kurland,F �F%�e�$Misspecifi{aximum ly�-*ͳ1h sed J�6���0):973. Hobert�p-ACasella)�199��TheM��im�BH priors on gibbs sa�nga�hierarch!9V��¯91(43�{46%��4�ui,!7K., Mülť�SmTWel�'A��Jo) �?in6�}g .�pql�[ \(just-accepted). Jankova!j�,�*W 2��Z�� inve� cov���Mion�� 1):12` �2� Javanmardu�MontanarH%K 4a).V��a5hypv sis �fA� & �d�al!fa�] �M� L� ReseAK , 15�286 2909!X����b���ڮ�6�� Kenw%W�M� !*Ro8J.� an� SmalliM��%C2� from]|ted1:&y�< 53(3):98�I 997. Lach�u�V�, �V�Pm>Ar� noGle�� �1�W*Q �b6��skewnormH��t2z���a S� a, 20!�30�8322. Lindstrom,!?�;�B� � ��81988). Newton?r���o,em algorithm� .$� ͔A�@repeated-measures�]��m"0 �Bd @3(404):1014– 10 �tière3, Alonsoao\$Molenberghf� A�T�A9�����r random��Ao ���'�.5�A/63y 103� 044. 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R EFER'0S [1] L. E. C�N$n, A Cellu���C�e�Imp��W$Kalman Fil�A%. PhD!�@sis, Bozeman, MT, USA, 1969. AAI7010025. [2] J. Choi, D. W. Walkectnd J.XDongarra, “Pumma: Parq��l���K0�N�&�%��}�^��Rur���pers,”�$ cy: P�c[ExpervN(vol. 6, no.a�,pp. 543–57Tr994. [3]FoA.�o De Geijo(J. Wat@ “S ����-un���������9 �4, � 255–274!�97. [4]ASoflik�FJ. Demm� “C.G��-e�al)� 2.5d B0#!�lu*�i�(9��in��#�s��A�17th I���a}j�n��P?�nY�P$��sB- V=��e0t II, Euro-Pa��`11, (Berlin, Heidelberg),%Ȉ90–109, Springer-Verlag, 2011. [5E�DeG<ndaJ$A. BarrosoE�N��t� !��e�2=� ACM,IO�5MP�2 �74–80v03. [6] M. Zah"�,s Konwinski$D. Joseph,AvH. Katzpҳ toiciL�IÝ� MapReduce>� �h��ogeO .��)� OSDI � 8, pe4Dec. 2008. [7]^ Lee,�Lam�Pedarsani�0Papailiopoulo2nd5 Ramc� �r�Ca�p���uJ+*�-g"�eN�r4��� %n)1inF�Xiv:1512.02673, 2015. [8] S. Dutta, V� dambe)2 P. G�{�r%�ƙ -dot��<B*�transk�s.mly��d$$�r��t��� ��~�%(In Neural I*3L]�K)�sI# 2092a�10I'6. [9�u�T\Dn, Q. LeI G. Dic-m�NA"$rampatziak “GUTZ�8 %K�a!C� a5R�6!R330At�0{10]qYu%�$Maddah-Ali)S S. A��meh)W*A*%��:G�U_��_�-dime/��a0�u>i�,>.Rin )R� vR 30)Ud4406–4416, Curran AssociE, Inc.,� �311e�BläsA-Fast MɓMuO�"v5No. 5�!d`�Surveys,� U+�C�~a�Libraryk��12���+.s!! �a��al.�u] �/ deadA�1P$2017 IEEE 6�Sym�Wum on2b� y (ISIT�Z240�#$2407, JuneV. [13�1C. SuhI3K.BHig� ���$. �� 6��18ak422:���4�-H. Hua%!�A. Abrah��“"- �-� >!�M��o�"I%|%t�T�_��I&��; C-33I��5�528 � 198�15��-Y�$�uE�J.>���F��-��n"�I�a�v etic7siga�HgA3one����L�sO<Y�a����e���, R ��73��,741, May 198��16!k�IKedlay�&C. UmaL“e�*+)~2"pnd�� A��Z�T�,SIAM Journal�)cing-c40> �6)h 1767(802�R�4 �u��D��"7,wavelets –�: E��e�,�%^conG}!. W. C�d�S�vsearch L�&�o�0P. O. 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AbP�.�!-9�%\&/9��K�;2�!n>M�>���Ps<�o OPTH.r^�� �H���9%��e$1�:�uF� �>m75Al�uaa>�.�"�Y艘�iT=�/&�<= max` u,cu�: )B-cu /$u∈V (G) . ��7*�Gbe rewri06:��2 �| �r=S).l���%�it%ˁ(}5�e]��n� 6 �u6�= + E2�=TG �562�:KA<E���s-��=95����fI.^p��T��is.n$Ns�H�7^�)j�>� i�Z%C��* l1�i�)~}�ofɤ��n� ���iY=*:��pś degre�!��  �e�X��e�DSchild, Fox-Epsteia6 Kl [20���) twAX0O(n(logn)tw ) isAp tw2u�� �Katsika� 0s et al. [31]7m�+ depe�5~V<Z ���FPAo(� �l� ��,/�n� last�"� #�n� �!��N�k = �eN&!&he�7�al�r� : � Aute���s35]lE^ly���am�g=�g7�6���� �>(� �� can � &,BA1 IsW��Mj(again� z>�!b rI" contrib!9]�iBYU�lzD� traX!forward:�)20vIA��9y!�6M�>%"v�i�:<)$19, replacq���by%�  �2�v�#�K�o c&o]�r�m�pr$ k-Ca �r��k-Ma2�n 0+ | �kq a�#��!�an � e#nc*�  { '�F�)A&L � "F ,F< s �!D Acknowl�7 Thank�&And�! Feldman�d Vinq( Cohen-Adda�helpful�cus�$� comX. Re�;dces [1] I. Abraham, D. Del_, A at (V. GoldbergaEd R. F�(rneck. Vc-d"K%!�k� �" @n I^(O. al C�quium�Q@Automata, LanguagwRiEming, p4 690–699. Sp�'0er, 2011. [2]�����HB)&��L ably e"3B�\.��|J. 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T�gap,52bilityBsimilar��which exists between Maximum Acylic Agremeent�!�(MAAF)%�+5��F)�(MAF) -'roo!�%. [21] �is!|L so surprising given �h%(essentially9Jt to !�Az bothE kun M"EFMAF ( �are>Z�%�Y rSPR F@TBR respectively)8firmly!e0APX. Alongsid)�complex!s9��s-�,it’s tempt�to ask-�of�problemA Es i!]�a1(in somea/hmal sense) be “reduced”a eachi.!y�e�$-hardness +aT0 already showa�atAxlbe 'edOa��a highlyYiG-preserv� way. Can 36F�HN?c6��UJ5� 7 Aca! ledg�Uds Leo van Iersel was parta�Dunded by a Vidi gr�0� �G�N��0lands Organis�!Y SciA{Dfic Research (NWO)EcbyB4TU Appl�Mathe��,cs Institute)w work!�E�,Olivier BoesEiDGeorgios Stamoulis�suppora?� NWO TOP 2 ƀ. 23 References [1] B.L. Allen�0M. Steel. Suba�4 transfer oper�s A�their inE> metr�on evolu!� ary Cs. AnnaleV Combinato/P, 5:1–15, 2001. [2]��Baroni, S. Grünewald, V. Moulton,�C. SeaC. BoundAJ!� numb�f hybrid-� events%� a consist�j.�� history.=�@al Biology, 51:17�82�5. [3 �ordewich�Linz, K!R. JohF���Ai,!-$ algorithm���ui�he ��z%��Y�E=v�inforI](, 3:86–98�7. [4>��!JLcornavacca, N. Tokac�,M. Weller. O�ae fixeda8ameterA'ct�? of�� -bas*(hylogenetic��taA�!urnalA�y.opages %p�9�16. [56��> Com9>QR>2��E���-pa:��4le. IEEE/ACM Ta��sA� t%���Bi6�44(3):458–466�%��6���min�yB� �.�� ��DiscreteN�,, 155(8):914AD�2YE�7v���R!�ul%,-visible net�݁dvE� �F, 78:1t141!&%�H8] J. Chen, J-H. FamX�SSze. P1� ized%�"�6k� �m�� By 4in multifurcat�\� Theor�al-��e��$ce, 562:49aq51�"�1�"�9�F. Shii[J. Wang.!|� ng�yH�S �o � ple �J�e�B�ia�y823%>�810] R. G. DowneI�M.Fellow� unda�+��u%N���, �s4me 4. Springeri3. [1�[( T. Drew, BdRuhfel� A. Smith,�J��ore( G. Briggs0A. Gitzendanna,P. S. Soltis)BD. E.  . An� look at�� �b�an�;�p, reve�a famili� ale. Syst�a���63a�36a��3��14��2%�FelX (tein. Infer! P���i�|Sinauer Associates, Incorporated!?�0T3]�Gambette��Berry ��CA�(ul. Quartet�"� 2�yq�J�k��6�e#R�8, 10(4):1250004�12��4�Gramm,!� Nick% �,T. Tantau. F�)�L��e�.���s�� �er��r(1):79*�0� 08�5]{D.ACGunaw� (B. DasGupta �L. 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MaVena Janos � Lucy Knight, Mrs Muriel Beaugoni�<0r. Pierre Guyz+0Dr. Michael SGklA=�Davidѝrett.!�%�20] [2%��2!�(REFERENCES `4 [�[%�4] [5!�6]@��3=$4] C.T.C.%^u$B. Gabrys,�*�+:�M�� A�*��;X !e�ofy39�r&N�,�Ical.�a�Zf8, 35, 1116-1132Aa 3. C����a��6xgd"�,�Zd "�cb2eafe$s. 463-464J~X85-1290, 2012. R. Huisk�J E.Y.�cChao,�J urve�#:C��*�n.�N�s2�N�2�f�1decadexh B�N�.Jg$83, 385409 . P.JuF�%gast, 2OYf)��J�]&�Z!�.��m�de�, �]2��@2, No. 6, 343-366�97. M. qJJ���� �AAbof2��dev�i: W�"�w��w� w*#!��xrtu�Idi*�h-=�a*>i448(5), 767-778Ej�5!HS. Walk�c�Aa(h�RY9APq:�ar�G�Jy,&�^���a���Re� �dUe 2i227–2E�`991. L.D.Dorr, R.A. Boiar�d"]10q!�#6��� 2��%�4���<05, 5–11, 1986�|�2�H�2�I27�D�q�2���7�M�K�&tzp�8ck, M� aldw�� C.W. �ry�gWr�)E Laz,E� Rullkoett!r�I�U�Ialign����afd-�d{#�fGVY��,.|h=�5�@, 30(7):1167-1175E 2. C���� �J.� PJ .�� Cha�)�z���+ �� � ��(A@6��Bone & J-1�SKA0, 94, 156-156f��.�PJ�� .��I�-b�d�����hloaI��ipa�JG�Z��R� 30(12)�52024 �2a�1l�S%�l�#P. Hal< �nAo�etrR�,It.���]��� :���a���6F`"�A:����h,39, 2303-231R006N���AaDelNm�Az��� fg�@��"or5~H5�2�2�`m?��:B�3��y!Y)�.Res., %�212-2221!���D!}Nicol)oB.Hzac�H$H. Katoozi!� D.T. Davy:� risk�#�2� � ed h���mlH, ASME�� engi�b�Div� $ 50, 427-4h001��Browne�R�Sa���!nGregs� �RF�^@ A� beafC*K�l �s,��O s 20&-�2� 9. F!Dar!M�Rw{�k�R.M��pden, S�C�1@ thod��I�� ��B�..�.v 35(9-155-116)� 2. J. Shi��� 1M.*� , G.Flivi����Se"@4�Y6�/2��Xto1&�A� * mant�ick��/!th.����.2 98Eng.17:1671-168i��4!��E8Dlis, E.V. Zaretsky!� Augu �P2�%1:EY8ircraft gas turЬ� k �*�=2HPropul8��P�W 15L658-6 �9# E. K�%, KAyWooa�6���d�� tol��almp�fatigue&���%K!"3$SME, Aeros�Cu � a 8997E� 2. Y�mgnQ. Liu���>�W� %&utomobB+� n�9cee��%Ly �I �$ �n�a&(�[ art D.� A`.�j4216(6), 455-47U�P. Jacob:o G�~iAn1 icitm,"� �pc�Tr, Glasgow, NAFEMS Ltd�� 2. A GodeA0M..� �E�N�u%r:� �1�C�fe���� *� 6G gait�H�u�V�>|Q�2weJ=v+, 267-27���SA`(Isukapalli,�$Balakrishn�wDP.G. Georgopoulos,�lF �2�euERert��ro"�qA��  �A�s"�Q�* E�s�;�(, 43rd IEEE� f. 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(1990�447�.� u&S.�1$Gagola IIIh=1��’�K�d�ni>�aV4Pr�"8Camb. Phil. SocC=�5�< 2 (�=k93�;06. [3]nP#��mI@.j��sn�n]��=�N(� 1978A`�7�;�3�3[4]�' ,rishkov�8, avarnitsi�6�G�*B*�J��, Appl., 5, N~[8$), 441–4���A.�j�Sylow%=���eQJ:��y, 3�7N 7!;09!;81!<1825. [6�chb��}1U��+N' >|��`�/. J. � >1 . 265�14470�<�7�7]A2: Jr�0�v"k�Iĉ; Macm�.Ln Co., New York, N.YE��5�434E��I�4��A�emáP� e E*) ı́�)0a, São PaulU� razil E-mV~;�$: shuragri*F�Sobolev k� A�"o�s�?$vosibirsk,<%BY� zav@�wD.nsc.ru %O��COFIK� NESS�.LOaDCOHOMOLOGY MODULESi IDEAL' DIMEN%a ONE"�.308.6040�.28|7� �t KAMAL BAHMANPOUR, REZA NAGHI∗/< MONIREH SEDGHI &/B�R��a2�No�0&�(�necessar�local) �9�, �a@ R-mod�and I�D%�l��R"�"���N:�D$ExtiR (R/Ih�)# �9�!"d-�(q�.>< kly Laske�& ( i ≤ cd( G +e�mI n�\S�$ cohomolog]�� HIi [%is I-co �w I-weyx�M��+�on IM�a19-'!6) e2��-Y&��k5,�� �5 a��) �&����� 9.���23��ny���x� ��K!�HIt%/� �s Hom1�#/K�# Ext1J���F q*E;Pn-n�,XNger�u�$E$lizmaiz}�)�,<Bahmanpour-Naghi � � !� Brod�3 4Lashgari [7]. 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In the case S is B(�=dall finitely generated modl�,G�following lemmas were proved by Dibaei and Yassemi. The"�@ofs given in [11, 12] can be easily carried over to an arbitrary F���S���R- ��. COFINITENESS OF LOCAL COHOMOLOGY 3 Lemma 2.1. (cf. �LTheorem 2.1].) Let R�4a Noetherian r! �$I an ideal�. 0�s 0Lnon-negative integer5let M$�n�� such that ExtsR (R/I, M ) ∈ S. If ExtjHIi (M ) for%�i < sg!�j ≥ 0%�n Hom?�s.?��) 2.1 2,5 �A� !;� � - +1 �6(j 1 i s Ext!HI.���b>�9�3� I-�5�F�R%yM a%� zero5��,9�, dim M ≤ 11 Supp �� V (I).!yi�yy statementm�<quivalent: (i) Ma� I-coi�4 (resp. I-weakac ). (ii)b��s.!eA� Ext11XreN' h f Laske#�). Proof. See [4, Proposition 2.6] :[5>�87]).  Now we��(prepared to) ���� � first mai%7e�(of this secu. BeforeR%L� 8y�4,e�us reca<<important concepDhomological dimens�of� �� N with !�ect��)�a, R. Fa��N e� cfb� V� fV�, deno��0by cd(a, N ),A(defined as  := sup{i�ePN0 | Hai (N ) 6= 0}. =!iV��.��AB::R/I = 1R� condE*V� Exti.�is��� Y��a� cd(I�) + 1m�]Z�TSAi)����P�vO�N �����!�� �;nyNDQ�Mz��N �� (���z��![ somR}Z��= �G (v9��<A�>*� &/ Z��2*]����2���5���W� ���5����y6I !by us� sam>of���y�l.��~ ���s� orde� ����=⇒ œ(we use indu�� on i. Wh<  ="��dexact sequence 0 −→ Γ�M �/>�0, k�e ^R�*5 B^�# �.�v) .XBQ�.�M ). A6�O!%�: �,%��j, 1��>� , it1�� s .�� )W���>O�. It nowS from LP  2.3 bC��B�� x4 KAMAL BAHMANPOUR, REZA NAGHIx∗ AND MONIREH SEDGHI Assume,Q9 velyA�at i > )&�A9 result ha� enI��f� ���ђ HI0M , HI1 �. i− %B���,%Esoa/% �sR 2.2�e R� .�zF��� ��. Now2�ag 9�� 5�JV� � lica8 i��=m��i��  s immedia7g[206� 3.9]) !zB lu- (iI T�Lobviously true. 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This^ �A"� on� B }�readyA fA�G�\�h���ɘ�K���paper.��.r�ahmanpou["Naghi[2]�q 2.9.� �j- �� �e1q}�Ł� B�"�t��5R�&B Jll�����6T B�>��YO%��ny  ���K!�ٵ..�N�� L���� � zB��y#�L9�4/K f�6F�V-� By virtu�6[!�8AY�6x"p % 9^�thyD^���.��tA�5 ��'�Ka�� � JN��*�BK4.3],  9��.�&Z  1]8e��aM%v�J�9 . NexM�^*"����H �/$0 � �d�.� 6^�, t+1 1�XA �`YC�r�K�$L, K) :fM� �.1���2�6P��2�K)��s�&�^M�,�itA&�tKwien�Q�r]#�#�atA0B��u&B$�Z"��.� a4.� E�Y4� , Acknowledge%t authL$would like�thankau@fessor Hossein Za�$EP�4�� �$ �$ drafem< valuable discus�s�� Ns�Schooo(PMathematics, InstitutAgr Resear n Funda� al S!��(IPM),ite$ancial sup�$. ReferJ s [1] K. �l�,j.�)>7 � �l�s,� . Sc�0to appear. [2:a�%�R.��r� nes�lo�%"4%�ym(Proc. Amer.y�oc., 136, no. 7(2008), 2359-2363. [3]6��J���C���E .(�sAsm�p"2&, J!�$gebra, 321�@9), 1997-2011. [4:�,2��Mc' dghi9#,u1/1&0Abelian�c. B(2��5���M���� �'rint. [6�v�+Q(Bass number%�^/� �c>auston JM@67] M.P.6T F.A.*Y�A.����y ssoc; im�^���,��J� 128 A500). 2851-2853L!��,7 [8N��0R.Y. Sharp, L:[�;1�aI�F ntro�#�$ geometrica�@ xs, Cambridge University Press, d,1998. [9] G. Chiriacescu,�q4, Bull. London}� 32)), 1-7. [ $D. DelfinoeH�T!� rleypu5�>��,APur[ Applu� 121(a�), 45-52r�1!of*,/S. //�,�:vq1A�a�>����\$nuscripta � . 11���5�99-205��2z���F�pezt�*funYofj�� Comm5 , 34!x,6), 3097-310���1�e,Divaani-Aaza���A!��fR rv�V� 133!655-660!�T�}�}���"�#5�� 2� 9681-69�5]�,GrothendieckFz, Notes�0R. HartshornePctA� �iM�, 862 (S�I�gTNew York�^66)!�6Jx��C"{,�c�,es� sceaux�g ts e� ́oré��,de lefschetzE ux%4globaux (SGA2)�rth-H��0Amsterdam,196a�17]>��Af�, dual�8>� ventA;$th. 9(1970A�45-164��8�I(-I. Kawasak�,�.�5B] 124a�E�275-3279� 9] H� sumu��A�N2 �|2,�.F' UK!�867 L0] L. Melkersson, Mo�3�9��J2.���A���,�@u+ 49-6%�$21] W. Vas�%elos,a8�i� ��eM� { (N^� 1974A��2� $I. Yoshida�v�{^��B&W di"�/aNagoya��J. 147!��7A79-19��23%�Zöschii$�M"� .� 102 (198!�1-32. D�0�tX ��r"� hArdabil branch Islamic Azad�X, P.O. Box 5614633167, =D, Iran. E-mail add�0: b"�4@tabrizu.ac.irn���v of T7�,h���dZ[ � 2[ � �[ �D. 19395-5746, Tehru uF���n� @ipm�>��!���$AzarbaijanB0rbiat Moallem6F���se �@��Huniv.edu w���1 S�3 Esti� �o�Indivi����bPopul���,ean Field CoR l L Q�)to Dem���CDispatch arXiv:1504.00088v3 [] 30 May 2016 Yue Chen, Ana Bušićp�Sx@Meyn Abstract—��p��&cerns��e�problems�a mI�f��c �- ing.� p�model$goal is� bK$e jointtribu�$HH"a� !k �3 typ�3�i5~ e ob�)|equ c28 a noisy measurh5KXqQ�l�Tult?� �o d)��d-��� reg1��0wer grid, bas�8,n randomized��I(algorithms.!T$prior work��{a*at H� 1�v9desig 4~$ Cggr�8R load!-�*s as a D�l�resource<th�)uracy mA��r excee tra�3`87 fr)y 9 -�per%�al costA"nearly U7 in m�) ases)�inform}0exchange betw�-!h� a@��l, but-5'ed\!Roveral%�� Nitn �� 95�p%�consumpQ�o�sp avai):�t�%�e�� �orB/�6ho1��0Kalman filter1�b<tructed to reduce3�s:6 mmun�6!^�iI�s,��(id1� %�(ac!�teu�%��e�!Cva;ce+�q� of?ice (QoS$.� }�% L. I. 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Magnitudek�e6z�obNv� for TCL �4 The structurF\ectors is also similar. z,4 shows four w 1�o�| matrix A, corresponding to the 8� :�� maximum m�(ignor7�Lduplication from complex conjugate pairs). v1 0.2 Real part 0.1 v2 v3 v4%e−&< Value τ : tim! �ep (secs) [Θmin , Θmax ]: tempera%,ldeadband (o C) θ0 : ambient2)� R:�8rmal resistance/kW) Ccapaci kWh/ `�:)�! nois =d) %etr : energy transfer r!�([�ai = exp{−τ /(CR)} 2 [20, 21] 32 ∼ N (l.5 × 10−7 ) 14 Imaginary5W,2 Parameter2VA�M*. An$is on 21 ffoCA�rstEBQ�AE��aY�@. A finer analys^Iy$continuous)��/.�state e�STCLs (as$�sidered in [11], [18]) may give greater insight on A�E�}@eted_these)�\s. 12 V. C ONCLUSIONSeco BionaA8a Kalman filterL, joint popule H/individual dynamice�$possible, A�performEn0is remarkable�� test case. . In%�$icular, it>,very surprisA�4to obtain accuEstrackof bothdmean � vari�of QoS�an ��,%o,n extremely A� y estimat�U=8. An open topicTfue�researchA���sA� L�NHtechniques that tak!to�@ount opt-out, whi I(used to ens�4 good�<to loads [3]. ItE=�b�)�!).< a reduced order��=�%i��U�� I��-!?1�. AA+natively%�A�~ to� loit- ��!distribu!1�U�,in numericalGTeriments. When subject�)0A�trol,\$ histogramYis�T4�a.diz$al Gaussiaaa�aEvi!ain%xQT interval specified by1�A���!$ nonlinearqQ- WuctWk!�A�1 i] �. R EFERENCES [1] M. Huang, P. E. Cainesi{R.DMalhame, “Large-yÐ costcoupled LQG problems with nonunia� ag!o: Iu�0-mass behavio� �>d decentralized ε-Nash equilibria,” IEEE Trans. Automat. Con%�� vol. 52, no. 9, pp. 1560–1571, 2007. [2] J�8thieu, S. Koch,�s�D!llaway��S:v%��8rol of electricm?8to manage real-��e��imbal�@�,:��< Power Systems, �28 ��1 �43�44��t013. [3] Y. Chen, A. Bušić �S. Meyn�9w risk�<�� fieldA��)�ap"��au%c�e!��m� �s �in 53rd !� Confereon Decis�5�C-� 2014 �<6425–6432. [4].{8$I. Hiskens�Achiev��-lab� B�!b Procee� �s"�'�-`992` 184 A' jan.�1. [5]aBarooah~iSpA ���e��os�}�d%?� flexi �� reli��ancill�� ices!b,a smart gridׁ��$. 48th Ann�CHawaii I�Z�I�o��6�I_ Sci!�@s (HICSS), Kauai, Ca$15)�270Au 2709. [6]YUP.^U�!�J. EhrA� “A>����!�� u員ll t deferr%Ś�!�>�A{A�-�60-�m:<2847–2862, Nov!�45. [7] H. Hao,�LiiGKowli�5��.OB���P�through M�!�fan%�8commercial builA� HVAC sm� ” .�� on S%� Grid ��5 �mD 2066� 074, July�4. [8]�rooks,��Lu,aaLReicher, C. Spirakis�2B. Weihlel�DE� dispatch�)|��!�E��Magazine ����3MBE@9, Ma�0. [9� KizilkaleL�R���j A cl� of col�a� �t���t"� � �oin�c-I: Coo� 8versus��-c�� �� 1� solu��Ilin �6GR�� ��H3493–3498. [10] K���r5 ko%�l-C. Tomozei, J.-Y. Le Boudec)�`M. Paolone, “GECN: prim� volt�a��Eac�2 0networks via َ���-2��u2, �S622��31, M� ��1] L.AZ TotuEH4 sc!� y�C!�thermo �i�AEjPh.D.A} sert/ , Faculty6Enginee^A���0, Aalborg Uni!�ity%�a�12��*��LW Stochas��"ls. New York: John Wiley & So��198%�<3] N. V. Krylov,A�S. 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Q�):H�� �`�tW2w.��:Q ��;y"�@E�woR�en��eF-� ~�<�=e)<�h96���s� �23[�ee- [Au!�I we3��: ���O]0�tradic-!�.k��a�  c���F�a��2M2!�&V99-s��Z t"T5��:��h M1 .&(D(M1 ), F,C2�� *]��ofO2:O; � 3/A�2����� KR��1"�UT ⊇ FC, ��1 |CrAc�| �� 9) s?����(]��6��;2��3e �2�"�2_</3)rd"*�0�I�a�A�5�IJ��� ��)ߵc���uul>�� get |F�@� (2/3) · |M1 |.�i In the latter case, from equation 49 we get |F| ≥ |C| = 2 · |D(M1 )| > (2/3) · |M1 |. Thus, in either\Jhave K(265��Since each node v ∈ F ⊆ T has degv (M r ) = 1, and si7 edge e7M r3�weight wr (e) = δ , it follows that Wv (wrU$δ for all��s:��. Hence,�0get ∑v∈T C!%δ% �F)3(2δ 6�� NextD note ���in�$contribute�Xe same amount δ toward  �s of both its endpoints – one t% !3!��o%�small-��!�: �� = ��F�� !�S T )�B ∪ S%��V{$� S = 0, /sget>r�c∑ M�V B∪S 2h(4>Z0 22 This inA�<lity, along with]�(8, gives us �X (u,v)∈M1 (Wu (w) +s )) +�5�V �(1 −!�� )E�M1| +F�� =1�+//3B2�R !�4K |. Te�st�U�:�P1. Corollary 3.16. WeB�′′ )%s(1:u�s!� V Proof.m�|M� |M1 �|M2 |,EU�crq`�adding"5�$ies statedA�Claims�4 A� 3.15i�not <at noe��-I� under � is caed twiceWA�left hUhside. 3.3 Extensions We g��Ta randomized algorithm�Xmaximum bipartite match�4maintains a be�OHthan 2 approxi√ m�THin O( n log n) upda� ime.��full ver�a��papere�de� tA� scheme us �e )} ideaWsteadKapplyTH�d �al�=�[2]- � ing CsetWresidual���s���1!]# frac�^.n��4 deterministic�� ��5] (see Theorem 2.1). To carry out �-v-rDguarantee analysis��� to chang!Ke pA� of LemmaA�81 (specificallyI�'�E�'5). To��, arbitrarily�_( polynomial.��= IZ�vof%���-!`Linto multiple levels���p �.sis���!��G�s)6Definid 3.2)� next >aM7Hsubgraph induced by non-S. E�ѳI� ;a�a kerneIZ��LIntuitively, we spli)���% is� again)two%7�s��d�ngy���i�?%8� �̓a�� iteri� form�`%$)hin ourv)Iof V %Jkeep do�JH�K 7$s, where K)@sufficiently larg��tegerJ show�At (a) M8structure can b��i��@O(n2/K �O� �O�@(b)!combia�%�J��s��ll"se�! s an αK}^e �JR�!,G, �1 ≤>< 2. Byu�1.3aVis�b�-6�to�lize!pA�x�i!7�r.Kin G. Sei�bK%�Jddetails. 4 Open Problems  is�{presen�c�o:��dynam.��sc��1(. Our first�ޕ�A(2�� )=!�ɃH�a gene�e�O(�n�(�] , 1/H2e8 exponent hiddeaO% <lo�� ic factor1tݫ, howev��is raM hug��t willA�!�res�� o bradow mO bis= to O ��2 )eϡ�increa��6+ ��is �%1�.q�in �Ma�����aN��.#also a�ed���mm�^��to~N���Kon*\%�� >�� i��!|�yjH K!�e}��Z��)2aches�(s K becomes�� 9� oapre� ��is�desig�B���X � R -inQm�ag ic.��AX�e��s �even N( and if� �a� ���0. 23 Refer� @s [1] Amir AbboudG� Virginia Vassilevska Williams. Popular�/je��s imp��trb (lower bounde�� 1 -D�s� 55th Ann0 4IEEE Symposium��F>�� Compu��S�0{�FFOCS 2010, October 18-21, 2014, Philadelphia, PA, USA, pages 434–443,.�.F2 � SureQ LBaswana, Manoj Gupta�L Sand��$Sen. FullyU��:�m�) }y . SIAM J. �@., 44(1):88–113�5.! ounat���1 �$D, 23 [3] Aaron Ber� in%�$Cliff SteiJ��� �iFs�.� ICALP1/$167– 179t�!g [4�x�as!���.( ��th! 6�e�� SODAy6.aw$appear. 1 ��@Sayan Bhattachary!�onika� zing��� XGiuseppe F. Italiano. D2j 6��data "tE�� tex coverW��!�@RR, abs/1412.1318�M`$, 3, 4, 17!�l, 27, 115 [6] Michael CrouchX8Daniel S. Stubb! mproved eam��� �� )a, via unB�%��Klaus Jansen, José D. P. Rolim, Nikhil R. DevanurilCristopher Moore, editors, A� ��, RMe� =� ator Optimi . A�!�`Techniques, APPROX/RANDOMa 4, Septema�4-6)l , Barceloa�@Spain, volume 28 � IPIcsQ�96E��04. Schloss Dagstuhl - Leibniz-Zentrum fuer Infor��k r�.�;7].)��R!�rd Peng>)eF�)�!�n 54th���54�K55Am013�3Ax�8Ax4 [8] F*4Sebastian Krina@@Danupon Nanongkai)�Th�aphol S_$urak. Unif_� strengtheL hardnesI�>A�&onlin� trix-ve� � icEL�. STOC1�21–3����9��$os Israeli%�Y. Shil . An��i_parallel*� m>�aC �ces� �L�s, 22:5�:X60, 1986. 2, 48 [10] ChaE%ihonrad, Frédéric Magniez)hb0re Mathieu. MJ semi-!m�4with few passeIRiC�-iCu740i�� Nomin͜er�uI[23!c 242. Sp� A# 2012e H11] Tsvi Kopelowitza�th Petti� 4Ely Porat. Hig�J67o� 3SUM2��If�,a�412] Ofer Neima� ,Shay Solomon�mplbdI�6 N� 4�CM6���y�i�ingQ� 745–754�8a�L [13] Krzysztof OnakE�<Ronitt Rubinfeld!����� �{3�a�Gve١A� 42nd ����4E�46 ��0�j14��,hai Patrascuq}0 �6�orB�� Leon��J�uulman�B�,2�603–6�ACM%7�0Id5] Davi�^le)6��D��j��BH�j: A d ty-siv0 ach�^An< 24 [16] Piotr kowski. ���(�s%�5�$nnectivitym18 CM-! "  Discrete�%QZ11��12�07)�7] V.Vi . Oa � ��mmTe chro��c clasn a p- �.u kret�!(aliz., 3:25N�dL1964. 38, 39, 42 [18>w��Re��� h(Kibernetikac�9���9�765�7 38, �X42 25 Part II DYNAMIC ALGORITHM FOR GENERAL GRAPHS: FULL DETAILS 26 5 Preliminarie.��r��writeupI�J���� 6���r��. Not�js. 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Now, tak�s�scalar multiplication of Eq. (2.16)�%P�subtractAres<ng equ >� @p20), we arrive at ρi dǫi =1��L)� div(!��)2�!��,!�%�1) Us}!� = ψ%�θη !�)�, 1�HHelmholtz potential �1�entropy�!!X.=�,.$with θ be�(Dcommon temperatureB.z4 at a point in9 mix.�,5+1) along e-A14)-d�s in  i  1 i ∂ i i 1 q 1 1 i i i i ρ��+!P� v !l · Le div a�2E�$· grad(θByd t θ2��v o0 dθ ρ dψ .%�2) + η:��6dti Iy�u%�!6 fact that�i =�∂ψ E00can establish 2ollow!vIs�:�θ  ��A i diI  di θ  �> *�id&+ v5 ψ )� +η =!4 11� ���O dt θ �!�!)�b3) = dtALfixed I�!8subscript “θ ” mean� �a!; e derivataX�# o bea�en keep!*=T. We shall define X 1X%�4q= qi, r = ρr)��4��� !ik�reli�M�23)A�2) �mmyover i,J�24�< get ! ! q r�A� ��1�,I ��= T .F�>�� I�E�MA� iA�I��  1f Q+ E%�ρM� 5) � >AV=��5)%| he balance��J�-rat2�produc�kζ�L �R��!� i T�)�a�2��.��ζ=�:��e�6) We Iassum��M[tot�ǩ�a�be addiAyly spli��to�0dueͩrmR ffec�� .e.,�!1(ζc )�d1?FG��a wor��AtmixAs(ζm )A�� lso requi�at each��0se quantities�non-negeO, 6 s�`-v�is2?��!�$second law v(rmodynamics5satisf��Tautomatically. This im��i� q.�( ≥ 0, θ2I7J�]5L ] ;. !-�:U(e :%!��:��I07a)E87b.9 choo!L�� k(ρ, θ)� , k r, 1Oq:7b)6��5(s. Also, if;��%Q1�dissip��ξm�θ��,'n X q�� ɭiC.�@����8�� θ f��ayi Aa�X Ei +  i X &= �=!�%&9)�EF 28)q:0re-written as> Ga�e�7�Xm ·v�� %ρ  շdt  =��.{ 30) a� ��xPw i J=�∂���t�+ @ k�!�L��! X ��=ρ )B(� v� i P��ψ!�ρ1 i� qaa6averageR� of#; . 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OzertpF�UI Erdogmus< E��Lo�:y def�VV cipalq���s 2�� b` 1�24]$1286. QiaoeP:� E)et� �a A76G"�a���Z��4I�26 �97. Ray� a�� " �bd�-b�mBb�g2b� ���e|R! 45�� $2536. Schu{�r���  Fs: Basic)y, Camb� Uni���P� . S�����^��u&pro�� �ser����Sca�9avian *V*� �19� 12kn�� F���*X�B<data,  oulli 22� �420! ou��J.-�ZhaC.��E��e _ squa"MH�o� a��Ay�a+modal� f-��,R� pp. 64�$665. Szabo� B.,��cZ�a :�A�* �F���c*��6� 5�credib�/�h���.��3�1�3� 14� 3W�V^V��A&� Weak�� verg��� Empi��l� cess�=��, "�, MR1385671. FL A2Topolog�A��,� ps://arxiv.org/pdf/1609.08227.� Yo�yV%c�S��#*�. �2\E�6�2:Y�f%� ���0�� 102.z����5�E��|umQ�Taccele��d*=A��NCabs!C88.03913. 34 ������B,&�6������B����&"R��arXiv:1711.00303v1 [] 1 Nov 2017 ASSESSING THE RELIABILITY POLYNOMIAL BASED ON PERCOLATION THEORY SAJADI, FARKHONDEH A. Department of Statistics, University of Isfahan, Isfahan 81744,Iran; f.sajadi@sci.ui.ac.ir Abstract. In this paper, we study the robustness of network topologies. We use the concept of percolation as measuring tool to assess the reliability polynomial of those systems which can be modeled as a general inhomogeneous random graph as well as scalefree random graph. 1. Introduction The robustness is one of the structural properties of a complex system which measures its ability of continuing perform well, subject to failures or attacks. It is needed to quantify the measure of robustness in order to decide whether or not, a given system is roA`. The most common measure6c� a networkg�r)cfailure pcomponents is all-terminal reN (, the proba-8 thatre C(n operating^|munications link between any two$�n ]system �.�� of a  interaciag�(, can be de �,ed by analyz�^:R�underly"graph. A � pairq�Xsets G = (V, E) where V%=(Lnodes/vertices and E2!�edges/!�s)> connE_wo elem�JV %� .�a real1]�5 !hpatterns5lDthem are represent)�D� in a � , respect-�@. 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M��oreno-Noguer. 3d Human Pose Estimation from a Single Image via Distance Matrix Regression. arXiv preprint arXiv:1611.09010, 2016. [12] M. Oberweger, P. Wohlhart, and V. Lepetit. Hands deep in deep learning for hand p��e�^�� 502.06807�5. [13] ���TrainzHa feedback loop forZ��TIn Proc. of the Intern%g\al Conf. on Computer Vis!�p(ICCV), pages 3316–3324, 20 �l4] I. Oikonomidis, N. Kyriaz and A.prgyros. Efficient model-basedAtrack�of �articul� s usdKinect. In British Machine��ereA"D(BMVC), volume 1, � 3%{�1!{h5] G. Pavlakos, X. Zhou, K.Derpan� K. Daniil�0. Coarse-to-Fe,tric Predict!D!��SE��-I�3d Y�>%� .� 7828�L6. [16] A.-I. Popa,A2ZanfirI��C. Sminchisescu. Deep Multitask Architecture �A grated 2d%�u�Sen!l � pmO� 701.08985��7!G7]!�Sarafian!I(B. Boteanu, Ion� �I.A,Kakadiaris. {�p6E$: A reviewAA�literat�,and analysis(covariates.B�A�)�Under�B<ding, 152:1–20��6��X8] T. Sharp, Y. Wei, D. Freedman, P. Kohli, E. Krupka, A. Fitzgibbon, S. Izadi, C. KeskinFXRobertson, J. Taylor, JqottD. 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S��>"b�i�-6���C�a�Tɮ��!"A�� "n `2:�-%�R��e��3�Z�C�^N)�Q�o�A�2P a�x�!�I�Emp!�by �2��� "�< �"�E/:� Eh�6���.��� �� abov�cA A Y��"�+�,mV�{�U5!�Ter�@ e [1N6] 8 ��A�ti>&�,.0�ssqXA� �:�!fI,. 8 CONCLU�rCpa�wDC!J ��s�J� "�-)"xO=�2��A��aPN����P� s�yd7ai u�v`WNL�]1s Irc��Ra$�2��s�`�B�e� S K�!�.2 3�wم��ljeoj)<�dx ��2���N��g�>�K ��|)@-�g��if6�K6�s aligm)V9 �sNA��i!�"�n.��b�<mm�y A��ugg�)��%!�s_�5&)t�V�fE��!wbelie�'wc� %� 0�S9�Aal!��~fu�Tb&EQ � �Tto�B��S� @^k>da��� JT<# ��x�0Za�ct�xU'�s� a�U�io��m�� ��� �OGdynam�!&teamworIb��R�U�bXE`. REFERENCES [1] [n. d.])�St�C�YS�F�of+1. Tre?6 in C".�SHces 10,��( Z), 464��470. �X�C/LEarl Bartlett. 2015.h]mu"�a�b4_�T�Q�H�U*�X�RescuI����(J0). [3] J.A. C�I n-BoRH�,Z] Sala�� nd St�n�e.9 Sha����M �a!�rt%m"�$,ing. Cu�[iss.:<hnd�lFA"7%�m D5). [4] T.:�S. *vS,, M. ScheutzR  Y. ZR6%B7. AI@�l��e��H% -Ro�i9�!S �DoRR abs/1707.04775%C�7�5] �5TYu � �N4T��P� �E� qhas N�h: Mov�yBeyond.4�3 Soliloquye�8IJCAI. [6] N. J!� oke, . Gp0n, C. W. MyerM$J.L. Duran��Jm�� !(� -7� veQ�%-�3!-7] Na�>J C zamie C|hristop�W2��asmine L � 20>��a��6���siz 37, 2 �`, 255–285. [8] David Guv�6.)Oin? Art �S!�llim(XAI). h�V8goo.gl/ geab6t.o�IDARPAfgram. [9sW. Ahar 7. Worksha�k�~�� :~�B2iby2 }�?!��B@7. [10] Anca Drag!�Ken9LeHSiddhartha Srinivas �3. Legib�e�PrediK of iHMo�OEvHRAtX11] Maria Fox, Derek LoZma�<Daniele Magazzenu e-a W� �XAI53�-j�i[12] BA�odwS. FlaxmM�!�$uropean Un�Treg+=�`on& Uic���-��P�a�)Y(m�8”. ArXiv e-pr1DQ a4:1606.08813 [1��}�N.y�he�WiNA906. Me�M� e "��:y �iY �rX�kb8S� ol. W�6rgj�K49� 06), 1312<332a=(14] Richardu[�yF�5��,4. VAL: Auto� �c � ion,� tinu7== �mix��iK#�i|�o� �N PDDLA ICT��@15] John Frank We �al^� Owes You 64oBfa55LK9yf�Srbaa6]Z�1990. A1(`�o���mod�cZBtegies �o(&4 -�ire�� AAAIo SAog SymCUum �C�F�B�9Rear��7�4agha Kulkarni,^�Yantian��"[Ttya Gautam Vadlamudi, ��axk�i�Bq� as gf�,Dis�'�V}�B�q��� 611.05497A��� [18],h LanglA�Bena:dows, MoZDSri���!f(Dongkyu ChoR��A��y� Int��tE�Pm S8E�!�/IAI��9=,nia LombrozoE��2�w���ab�D�v� =. Oxfor�OndbooY think 5"K��2��60��76e �0� � Mathieu,Y <S. Heffner, G. F�.win> J. >9 �00( influ���sJ, Aͅ�s��j�a,N Jou�<of Appli $Psychology�00T021] Hugo Merc�0%��cperbei� 0. Why Do� �sM�? Argue4!��k�a�^Theor`FM^�a�&�BI��� ��2� Mill y�76�in^t8>�s�*�sI� �S�jl 8 R@���@�7�@07269 [23] Tim � , Pi+T�{ ,Liz Sonenber���jAI: B�9!� InB^s R �AsylumE��b��I" [24�� anna D Mo�L!�\William R Swartout. 1988B=a�rtqQ: ABEvey. >��.��� it�=Sou\ n Califoravɕ�Duy I�N1s Ibv�(5] Vittorio�0er��i P S_\$raj, Steph� Ro�P�h�R�0Manuela Velosi� 6. D��� -�r NA�A�^ verbᷥ�%xRO-MAN��6L Smith�F�B���IlE��P nɹ�2eF7] ShirK1$ohrabi, Jo4pA. Bai��SheilaMcIlran?W�eT]�ˍ�s:mD>�G���Y�͡�8]�'<de Sørmo, Jörg��sel4�,Agnar Aamodt�05B*���-��� �� –P&� !d GR`aZV� Re$ (200229]�$. b>��6��aaZ&i�=4�&�Aw�B' F��СK�A�� م�c� L�U0, (AI-for-HRIA30����a1� R2�s( - A Mutli-�4�taDa#jl=AJ��% 2�GfQ�s�!udi��A&�d!xCh��1]*rJ�c�A�� Hankz ui Zhuo�Eb�6.%�%�i"&�U)��T�+2�RSS2@5)�F�: �F nomic Coll��v���b+%�2���7NE�:<:^! 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J� ���f��� c 2�|B�a�&� R��%,µi (p,P2�9)�.cq�-V7�!��|at F�kS!�-�>�µ (m,%� �=�� �(��e"�) T "o-! �W� Z�%<Ĥ� isM  �i:�!%�گm b s�m ObserK5�aX��yi��q����"mKpde�� %4m��T �RuaU �}^�T�� � {��n� ��9.1.4]�>k�Rh ",b�t� ���TD-�I>ix�RaB �C�F�Qů.�0!%�   +A�"�5�F�U2_��l0 b S>4� X7�� if v�OR/m (SocM�Tob�=*H�t�B��N=�m�vI�R/L;�a��,�b2 ,�=("Z 6j�! j:2  T!U R b���n* p�B�N�o OC!�e�(`E� ���b b�B|'�7. I`bp!(so"C2��e俩�R �K�u��{Au2�k� C%�� C)v!`I3������"� �$M�5��"^ � � �G��:E;A�  ��h*�, &�%,�C6�6�1-6)?�� ty [*v11.2.8]�+ge"�L s Hn�-a�-2���T, z5 � %`��3� �Y� mnM��i��!.�x Gr%+<ndieck’s third�� quadrant spectral sequence [15, theorem 10.47] p p+q q Ep,q 2 = Ext R (R/m, Hm (R)) =⇒ Ext R (R/m, R). p Since R is Cohen-Macaulay, we have Hqm (R) = 0 for all q 6= n by [2, Corollary 6.2.9], and he��E �,collapses on� n-thumn, wh�� ��n�$ ∼ = Hom��)�R/m. R m It follows, from [5, Theorem 9.2.27]!9�a!his Gorenstein.  By using�Dsame argument as i �proof of%above c�,5-the �ing cor�ry whichzDa characterizationRCohen-1|8 local rings. CEH3.21. Let (R, m) bePomplete6, with dim (R!�n.! �L are equivalent: (i)N. (ii)�Tre exists an n-perfectA�sidualiz!>(R-module. P!, . (i)=⇒F(. By assump�$, R has a ? =<, say D. Now, by�!e0 3.19 and [13!�],Q& D, EA�))%l���� � ). Suppos!� at T�E���n�.�� 3.�th.> sem=2 � CeZI%T U��C�- we ha�ida0C) ≤ pd (T %�qK C�9Z!6�R6iI� Ques!�A`2. CanA� omit� condi 4’1-dimension��ocle’q"qrX3.20? More precisely, ie:�J%��n��R}�,? Acknowledga�%� authorsA�, grateful to�refereaHr his/her invaluabl��mH s. R)8nces 1. W. BrunA�0d J. Herzog ,:Hi�h, Cambridge University Pres.�4, 1993. 2. M.Paodmann)�0.Y. Sharp , L�(cohomology:a}Dalgebraic introduc%�e�<geometric applic�`.|����p8. 3. L.W. Christensen, Semi-YP�txe)�Ltheir Auslander categories, Trans. Amer. Math. Soc. 5 (2001), 1839–1883. 4.B}�%DH.-B. Foxby, Hyper-�i�*�A))�A�!�0Commutative R�S, Avail%��-phttp://www.math.ttu.edu/∼lc)�/download/918-final.pdf. 5. E. Enochs�0O. Jenda, Rel v�H)�.��D, de Gruyter Exposec�l!&Lematics 30, 2000. 6.6�ÍE)��rued�,N|. Scand. 31 (1973), 267–284. 7:[�LIsomorphisms between=�Ek.a!f��.���y�܉�s, ��40�07), 5–19. 8%K(S. Golod, G�l%Zgener�ked сidealEgudy�<. Inst. Steklov.Qicq�y�D�i��.*165�t84), 62–66. 9. R. HartshorneF�, A��nar giv�<A. Grothendieck,B vard}P, Fall, vol. 1961, Sp��@er-Verlag, Berlin�067. 10!�8 Holm, P. JørgV�-s%6Q]0.���s,��Pure aB59A��5(2006) 423–445. 16 M. RAHMANI AND A.-E8TAHERIZADEH 11� D. White,i�� "�ce over!ocii7! �I:Kyoto%C(. 47 no.4, �T7), 781–808. 12. O.Mm���� A�A�grade �a-(, Arch���5e#88a#�9a#P302. 13. B. Kubik, Qu2�-o%A�n5>. 6��1AV20��229. 14.! Re�#he��nI� or X, Proc.�] Phil�G�3A�57) 28!��D5. J.J. Rotman, An6+to2�Q���� ed.Y�$, New YorkA09.. 16e TakahashiEfD.-�.��a� �s!lN�>�10),0) �0. 17�XV. Vasconcelos, Divisor!�ory~)�2z North-Hol��MC Stud. 14,6� Publish� 4Co., Amsterdam!^(74). 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(4-By���w!J!-� li��e-s5�)%~�� �516]��K �:�rB������8xB�P���Zas�- 2w��L. R EFERENCES [1] [o �e] www.!.,rnet.org. [2:�hgoogle.com/loon. [3] S. Jeo�O. Simeo6�A. Hai�Jch�1J. Ka'“j$ clou��a uav-m�Q<#let: �3Fp;4!6�a����u� ,”!nf$�aŧIET�l�m"�<s, Jan. 2017. [4�W. Loke,��#1 of�1�-Ttgs�po&��� hallenges��(airborne fo��+��*!� �s�arXiv pA�j�<:1507.04492, Jul�,5. [5] Y. Ze!gR. Zh%qfT.!�Lim� Wire�-!(=%� un�H�d���P vehi��::rW�� IEEE%[ . Ma7�,vol. 54, no.:+<pp. 36–42, May�6. [6] Mݦ�adpour, D. Giustiniano, K. Hummel, S. Heimlicher,�8S. Egli, “Now�AJ:r?: dela�{)��feE time-crit�yae�2K�,in Proc. ACM�z&�on Emerg�Z�N�� �E&�B��Technoloa8, New York, Dec�3,%0127–132. [7: 8B. V. den Bergh~Pollink� B. P��ner%�Micro�-�� ^��:��e��Ralysi 9�%s2~ %)9�� .��2)�7, !�141�49Y�4. [8��Th� 5��!�)�uav��Ӻ �]%�H+����p m., E��6M�12 � 4983A�9969�A�9]�Zhao,E�mmaM��Ea} gura%m$A message �#�� �E�deliv��in sparsF*�ad hoc5��.� I�*�n�Wal Sy1�ics5CAd Hoc.�a��qK20 Tokyo, Japane� 2004M��8E�98. 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We have theorem yield E(φk (Zt∧τj )) → E j R t H+ Rt + Zs ds 6 0 Zs ds, h�� taking the expectation of (A.4) � lett%�L, we obtain 0 E + Z u` j  6 |b| Z t 0 30+ E� ds.,h By Gronwall’s inequalityeconclude? g=0>′ frF�H�P(Y 86 j ) = 1r��,�then jlHj I�-�ZX� . Since YU�Y ′ have càdlàg trajectories,y se a.s. .�� are bounded almost surely on [0, T ]��TQ^1�A7−Q�as�I�. This Ek�s)6���^.�A@setA84non-negative rEOdal numbers Q+ is countable%�IJ6p�1U�t�Q+ � . UsA�$again thatnP ✷::..|getny��Ry< B Likelihood-�8 process Based!Jacod%�XShiryaev [23], see also"lMémin [21], Sørensen [45]ChLuschgy [38], we recall cera|( sufficienta)dia��s%;!�absolut��tinuity!�probabiac meaA:aw<duced by semimara�pales together with a represen�*m$correspond!�PRadon–Nikodym derivE (lZE). E~$appendix (6z�8proofs) already(ar�@ Barczy et al. [2)- decia#�t!�� it hereA� well%+better U1��be�self-con!oded. Let D(R+ , Rd ) denote%space!a$Rd -valued.� func)�definI.R+ . T0(ηt )t∈R+ U canonical�Ak� )@(ω) := ω(t), ωe%��,m8`Put Ftη2 �(ηs , s3�-t]), ig�xand ! [ η \ η d d Ft . Ft+ε [, s� �� Dt -� � ε�+ %B`Ψ ⊂ Rk be an arbitrary�= emptA��t���la�ψ , ψ�Ψ,�R��o�e 98)��(� d ),.* ). Suppos!�atE each.m��jr �E�1�� ��2� is a:F� e<6Z| characteristics (B (ψ) , C, ν 0) associated F0a fixed Borelm¡K trunc�pUm h :A���Rd!�ee��.�, DA��D II.2.6A  Remark 48]. Namely, CtAP h(η�|t )�it2! weo�(J'�M�mB�s� (predict�) quad�gc vari �5q% ef� Rd×a�of)��o�� ous �� part (6��of η2�1zis K mpensator-A�integerq�random-�8e µη on R+ ×!v9�ICjumpsP2}�<given by X 1{∆a�a�$6=0} ε(s,,) (dt, dx), t(ω,  := J se� )�ε(t,x�� �Dirac�at�,point (t, x)e��i��E��−�. + , '�0A8�0 8M�-k=�j� hav��finite] overe�� !� rval���aVppearHI� �jdecomposi A�D ηet = η0 + Mt + Bt , �@ M�special>�(e !$Q�und�\5�l�:m��� X %�[0,t] A��� � h(%Ps )), 316��� � )�(M�c!r a lo�Y}!eUM0 = 0.� mA�atten��t 8, by our assump�,'q�C =F, does not de�⡫,ψ, although�E.K migh,0 on ψ. In ad��,aXum�����(q� ({t}m|� �0� every.�!b��A�E�� G��!x0=�1) some� Rd�&6L�. N at � !;6�� 6>  Z tZ)����� h(x) (e�aC�)(� dx) )� AE�=�A� +!> Rdn + X0 (xHW�)��JF�2�� V� , Th�� 34]. Morea��,) :F��us �E�choose a��decrea� �,Ein�� , adaptedUZ(FY�E��F!��0Ū�a.A cQ�(c:7��:)�� 4all symmetric �ve%�� �o�dAY d ma$es such �  Z�cs� dF Ct =%�AZ�-* )#ECU�. Due� �y\�� �� X*/ c�,� choi��=Rand2+ipossib� 2<� 6<Pro)0onI�9MCoroll� II.1.19].� �P���.�$σ-algebra�C�eep� � �4ist a P ⊗ B(� �-� 3"�"� d )�f �A��� !�=���ψ e e Va��,� �:.& !���M �+�2t� *� QzβRHsatisfying e (B.2)i��03) q��� = ��>#��,a� Z q 26�� (s��� 1�K�� <��,1)����m@ =��Q�e Q�βA�%-M�mM4)/�0��4���e �(���)��B���, 3n)⊤ mj�ՖsFurA]6O~B��.8uniqueness holdn� �G� lem��a�"/ � 6+to% trip�"Z �� the &�\��� �as its ��  ion.���n�*Pψ,T/lyŌ�� Y�ect�/ e � �Pψ|DT� axm�U res�0��t�to d 1� /$(similarly�Z e� and,&* �,q6K^Z�b ,form Z T Z d b1 Tq�e<�Bn�d&7 A� ��� ) =-� v� logqa�0 0�5)<i_ Z T�+T a8� i.��^2r( :logB>��� B�+ 1:"e|e 32 a�$Q>2:Q&"I.5#A detail��ofA(B.5) u��� Vm�]aD b�5und� >�, A7A]. C�mi� oreme�*ZB� s In w� follows� p�s� �l�P��.A �uWese >�)� stud�a�4 asymptotic be� ou"pMLE!(b. Firs_ �Pa strong law of large"l!�W mˉ���s.  C.11�$. (Liptseraq=�<36, Lemma 17.4])��Ω, F,2� , P!��ltered� "m���usual�� s.].� # square-� �g��>��� �B��� filtNon2��� P(� �r�1 �ξ&8 ��gressivo*{��PL  Z t 2 ξu dhM iuɛx.r Pa�w(C��l0 � ξu2@&� as� ��L�,��(h�J��nOof M �% Rts dMu �(C� z�02w��.m0 2 0 � If2�4tandard Wiener10��pr5V5T�� .�ca�$relaxed to:0�� 4 ��^Z��e nex�(�boub�]|multi��eFb, � van Zant��6&: 4.1]i��2}�n.��{!Uq{� �{� Y@A�( d-dimensio�n�� >c�� � m�.��C hW Q��+�  u� Q(t)%�n invert�  (���)� �x�2all*��� t→∞ kI�kAh P ir � m(ηη ⊤Z�η� d× d"AT�xi�*CRk :j�v$ v.J�(��P)*� D (�!�, v���1 (ηZ2��,&�Z �6�q�(normally di� bu�)E�in��e���l . We�� atQ�, C.2 remains�e i�=�is��%��t� t0 ,� �)�t0 �d++ . 33 Acknowledgements�would6 �(ank�+referenr his/�com8�,helped u improv�cper. RCxnces [1] Alfonsi, A., (2005). ON�e!Jcretiz�scheme���CIR (��Besselm�d)a���HMonte Carlo MethodsA� liTs 11(4) 355–384. [2]H 8, M., Ben Alaya Kebaier�MPap, G.�16). AB��maximum%W, estimA ��a�`-type Heston model. Avail��on ArXiv: http://arxiv.org/abs/1509.08869 [3]2��HDöring, L., Li, ZF���3)parame� �6 ritv af�=l Elect ic Jour� of S�87 647–696. [46dZ��A@Yamada–Watanabe6 ult)5stochab difA��n� .!��s�kX. Ia�nal6��G,Analysis VolHt2015 Article ID 460472, 23 pagAg[5����Sh.��� ��%q�GE�\ stat �d.�4time branching9� Rimmig� H. ALEA. Latin Ameri>=��P* abMathema%�=�T. 12(1) 129–169. [6]6/@.2 (2012). P^ca��L ro iffu�d$s: ergodicUnoncaa�.\�Ma8 s 28a�60�63a��7���aZ��F�� m'or%��!<� ��-:��2��U|;Ap�� 3���552–573. [8] Billingsley, P. (1999). Co��_%a�x�� G#�2nd ed. John Wiley & Sons, Inc., New York. [9] Bhatta�� R. Np82�3!ѝ� entral 2�)�  iter� logarithm%CMarkov���X Zeitschrift für Wahr�inlichk �t|ie\ Verwandte Gebiete 60 18��L201. [10] Cox, J. C.�gersoll�EI�$Ross, S. A �A�or6"� termquctur%r� �� � s. Econom@ a 53(2) 3�407�,1] Dawson, DkA����X Skewa��v�"��Bgroup�խ�B:$ The AnnalY.�$34(3) 1103a�142�2] DudES R. M �AV Real6�Lx. Wadsworth & Brooks/Cole AdvanD#�BEd8ftware, Pacific�&4ve, California��3� ffie%!(Gârleanu,E~(2001). Risk valu��A��caA]8lized debt obli�%$ons. Finan�ivts�57��41al(9. 34 [14.��0, Filipović�(Schachermay"�W�0�P:1��a.�in�!+�.=��ed.k 13 984!�05� 15] Fells195! 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N"RSQPq%�8G �a{Wly�}ia��"�%2O in&Ib"�s,*�,�L�gR�!"RA0�c&���&5/:o&�/��!@�in�he�JE l9�>I�5A3[9] of�_b-�Bx4r ��a�$�a� �-�i&�wUp# ob�� � ����� Y9�i��m �� Ʉ� � >M.�p�m&�  d�[���I��go ��Ei|�/EL*�/�aMari�we �C�l� except M� �E��&ommon P�(!C of ��� ��� �I%R���52��5c � �i�#, }��K = 3U �i"�/�6W�w�%�M$ !\%"�1( 100�6A%�4�Nz�seM�A �:�Zd��MLDy���!TM�%�L�o]0. VI. S IMULAQ�S IA�%��~a&�ux�d��OF��i�RA2���b�"!���m!�som"C2�e9 tech���-��i�$�� a� ar a�s (ULA)!� omni"_��K��s W0 wave�!���T��sIv�fig��$ (if unspe�M� few <'),%� repe'Z�o��Zqsï] }%�5� curv��>� ��Ai00��� ���'H:4/ o arg���1@ ��'h-to2k��io (SIR)M2at 0dBE�!q�� 6D�s:� "L1B��� ��b� �q�as7�.�5� �1 + �]�a���� a��&�F4ۡINR pe��x��s���h"���%l1�"$� ( 0dB'O 30dB��by�3�e#&B�� ��l��>x� C�Q?)�Q�!�-4. 2�m���&� �?is��� �Cƣ�L���S"�� All}�m��i�}��� &��9(-in~7n�f�nF��$, the stee�qring vector of the desired signal is modeled as a1 = p + 4 X ejϕk b(θk ), (106) k=1 where p corresponds to c<irect path whileC<(k = 1, 2, 3, 4)N=�scatte�@4s. The angles �D� .D���are randomly and independently drawn in each simulation run from a uniform generator with mean 10◦ and standard deviation 2◦ .�� !1N��� 6����u vly taken �!@Dinterval [0, 2π] V��. Both !P{change Krials)�� remaining constant over snapshots. We firs!5 comp!XTour proposed methods w!Dsome classical RAB (i.e., e�d%/ iagoAl load� IH a fixedfaE�equalAP10 times%<noise variance, !-RCz in [4]�$ch estimat :{ _4 iteratively, !<J �dthat solves an online quad3 c optimizI,programming, yrefers�USQP Y [6])I� numb$ of sensorju�4sources (inclu%2 the 6��)E�setiM =!)�K =a\a�ec �8. For this case�y, we >he INRm8terferences-to-%m� �o)e 20dBc$illustrate� S?perform!� versus UZ%�in 100Yo!�Fig. 5)twoI��rs A~arrA��d~be2��^ ions!@θ2� 0◦�θ3 = 5, 2e��other user-defined parameters, if unspecified, (e.g. w,step size µjforgettA�IZ λ)�manuallyQ/ �giv)54best algorithm.?QG8is also appliedks ���scenarioi� then5�Ih!'QgtoI-2,* !� A��Q|�a>:8�)Ii� AsNI=�)!2E. $ input SNR.�!�E�64 �7:� 12 15 0 5 ^ (dB)2 �5 0 Oa�um�� �t>�� �L [4] a�$[6] OKSPME −SG CC MCG −5�−�00 20 40 60��56��HLOCSME [32] LCWC [9��}�8%0 y�w ��5�1 �2'�2 �3 u� %z5. Co��nt lo������%o)�9��,Ib0,I#, � �=�? T 6. �U��2 U� TABLE VI C HANGES OF I NTERFERERS 0 − ��N�qa �I��rs (K ") EN�1%AK�8 DoAs ◦ 30 �w ,�r . �2�} ��4 = 4  θ5�� θ6 = 6. 25I6�:��� � }a|26O In ei�%� 6 or �7�'ca�R��ate�"i ��has aA�y��Hilar or slightly be� 2�g d toYm �ofe��b�� m have���b�I�~. Fur� more��:��CCGP �-M��s �tchiev��y close c�E = . 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A� , a2g�.� is observ� ��U� ied �Ais1bec!(2�n�of.O94 �A��   dynamic�0environmentalQ �3M a�25e�a�a���m� �]m�2\ �d6d�G&L � �1� � &� &�2��ɖ ~� �B�A�1�\ �−20) .�Q�< 8.�!D!LF� � 10b�5�N �E�4� � ���=i)��o^o�IZ�b�>��9�d;�j=%un* ti��e�system� �  T�eB��mHD. VII. C ONCLUSIONv� &��I�*� ��oz exploit��4of cross-corre� � pione�Horthog� ( Krylov sub5 � addi0, low��lex� RAB��"� 6 f �Y �been d� open�)�y :� we+�sbe upda recurs��t0out matrix in�� . Ay ed st2 .,MSE analysis"6 �g��fgn" rel!�!E p���m� ngu��s_Das prior knowledge� �provided���e%T�u)�al-b͐"� �Ph exist!)�&� 9b�c��d7discusssSi� �5� �AP>�]( robustn�against ��R��W�a�F4: 11. *� D ���,� ��B�dif�nt choioof^%R21�=b d excellUout��*s e�� (medium-high*S(values. R E�XNCES [1] H. L. Van Treea��0Array Process��New York: Wiley, 2002. [2] S. A. Vorobyov, A. B. Gershman�,Z. Luo, “R%� AdapM� � q��ul Worst-CY�P*�&: A Sol�� S� �l&a XProblem,” IEEE Transa#�saz 1�| Vol. 51, No. 4, pp 313-324, Feb�3. [3]�<Khabbazibasmenj,: �,A. 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Maggioni, Estim�ZF$intrinsic *r; of^ �sS  noisy�2�1�e#�G�sɁ*SVD��X: IEEE/SP 15th WorkshopA��S� st�( Signal Pro� ��C2009, pp. 85–88. [2] D. Dı́az Martı́nez, F. Mémoli, W. Mio, &� .R�f��,2L)�eF trans 9 ,: F. NielsengLBarbaresco (Eds.), G% ic S� !R�I&U (, Vol. 8085LecezNo} in C� er ? , Sp�Her, 2013)794! P01. [3] C. Villani, T��%� Optimal T��p���� �58Gradu, Stud�in Math�s, Ameri� 4al Society, PrE�n-,RI, 2003. [46��B��, OldeNNew6��@09. [5] N. Fourni�0A. Guillin, O�G��converg�� Wasserste�'��em���� ��A�Theor<�R� ed FE . 43 [6� GarcEv -Trillos,A�u�r��of�� �%� ∞-El5�Ŭ�a%YCanad� �J!alG9��s, doi:10.4153/CJM-2014-044-6. [7] W. Allard, G. ChA�2e�-�K�ic� � for � sets II:]�e�-resol4analysiA;pplM�( Harmonic A�,32 (2012) 43a�<462. [8] J. BerkC,, T. Caelli, FE��surfac�)��s2 %�c2; chni� �,��i P?rn �`Mach Intell 16 (1994) 111al111!N09] R. Rusu, S�103D object map@ veryday�*�p+$in human l� environŧ, Ph.D.A�%?�T�tsche Universität München (�). [10]!� Medi��HM.-S. Lee, C.-H. 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C2�=�c�E�ra��q  +�DV>G �A6�� ����� �������� 8,�c� I����Y�R ����+��i0+�*��� ���R ����L �� S��L� ��, I-�I/ � S B ,ih 2�A, ( A2, j��q�"�A��a�%���/0x]Mum, n ?"�JAP~0�%�8� i —� ount+�%l"O�q�".�wE'de6 (�c�!���?2�@Q�ies �b$�!�d �B;"rK�@"�c�5n empi��Hba� M�"�-%G!;"4'�O�y��E b�.� ed��, mq1cho&4G)�a�) iety��/i� [+� :�+0 �io*�/-1 �—��ai�zA bal��h1r/�. �,~�4\-%�%�fo5�-� lapp�9D�,�*�8����sD�U�� j�C 1389! �* A100�P�yB, s�+:� solve by�a gene@B"�* . 5"'%$s 5.1. Det��(�S� �e�"a M�9 EY% SO, dat8~#�Cof 300| $�s�5�&�Resslw �7]*�uQ!=���,)J � x3iJ"*��]J�0.2%, '��6�� *� 2.6E/.� bserved"Mx3.5(tt|7"P,5)D  ha5�R.8#align�`&��5� : 14�5ť labe'I� 10238w$�l*ths}X� ed 1375�D�e{1$s did not m.1�&s%inf&�:i~�5��50 9 evA�Fk��s�wa� i"ed 60-the� +�dMH �)�% 528q�*�a<�cV$ie�wask +!�djacency�u�"�#06). Been carr1�o�T#M�so�H�s& B9 (popM�� �0200)w�s�a&&�F rY ��0.3� ��F0.��l�/�E%�& steps-- s: 5�$ el�N2��q&�w��,��typ�Opa�,- 8hoice—outbree�U�,�quf'dividAR� �)  s&he win�T55M��EI��M��ss*�: 3 . 27�.. T/41l g!�\1 s: 4 9369 �����dA��iy0� 533 ite)a e Tr�er: *�5�o�&UG 0.3917,-� 197 �� yP�*�%7. 0M"G2�I�w�-e��r�c�, arts Odotted���2��k�t�!" ���t'Exper�S!�Data OxUm%N��26���"w%tra ( network. S�FA�a���Gied� � , }��)� �+�e"� &u �)92� :) 18153�) 2633IA�6s �) 1�*�3��1��*� F*�*�A�*a�I� 8. Wa*A��A�"7< Jyp#(�� ��A3es�V�e���82���S90"�( 5. AQ_�.�7��5�-���ZW ��L*�( � Y��(�o�()E 6h� Q� -m�B�%kf� oΆ�^���W��pa��/a� stage: 12�O43�O� ���6 9119�,oN� 8%o> 652>����)���� 6���+0.576��25 �>��9���1�c�a�pk pB&� 3�k�<-P� (3)��5 b/7A � &Emetho]Ylea�=quares,�,1e & ��:n M� 8. L- � y�H1 (a)u710��E s. b% �Aeno7D)�t��� .�]%_ ncluL�4;6�r��� &����3!Ys ��sP full� �/�oNS�}!�)�mW� velo� s!ͦF-�G1�al �:��s� chaoS 1&�C�Cgeomef  analy�CAc�e��ly� fC� �.rai"/IGX. REFERENCES [1] N. HAHckard, J. P. CrutchWQD. Farm�<nd S. Shaw, PhyscReviewFZJM�, Vol. 45, 1980, pp. 712716. http://dx.doi.org/10.1103/N4RevLett.45.712UP�9!o6��ay�s� e (aT !U� (b.[2] F@�ng, Le�FNo�in MafA atic�898, �366-381,S�� 0.941�0.1805w 164d0.0295�)* 54# 8226*(622 0.1056 �*, A"�%� 0.001M105 E445E47y&w* ! 0062<34��0.886�F�0.5404 .*[3] X!�em�4!�А. Hub2VerlagKN Zeitschr�7Hfür Naturforschung1��2%��7-�497-802. [4] AL.Ko<B. S. McNamara, �(x S�2s, E<�1.W�417-45W�5I�<В. Janson, A. NA� vlovb�VbdAnisliclienko, “Global R2� �:.�D��Bi�I� !#Sec���CaT�n���,�_8In: G. Gouesbet0S. Meunier-Gu�-D-Cluzel, Ed., Chao Its:��, Nova�U�Publishec New York,f �3)o287317!n6] L.! Aguirre�8E. M. Mendes, IX�n��al Jourof Bifur{O��-��6!�96 p79-294. Z�\42/S0218127496000059 [7R���S�Bil��s�L D z85a�95 {39-258^{�l016/0167-2789(95)00116-L [8 ~CaoFd�110�M�43-50nc��Sd�7d$8-8 [9] > X. MaquetFw�58v2, �202-215nx�w$2)90109-Z ��W�� 0399�u0.0463 �.���( t001�. �4(O���/�� 4848 9�g�_ 1851�CE��P� 1�[ �� 2.1037���l12�^u��% , 0.120o%302^&n 10 p <;�c2>�t�"�yWMs �"! ��E�(��edN. ���in"� � 2&_) m�@� �90=�i(a '�eB��� �(for flows. *gB�ew�M4 ��urb@�� �N�E�uz.�{�l�Hto"=N.P�� o7� �r�ck �E�t �" � �j.� 1392 z�` [10]�hT. Ro!: tein6�J� a���C.De Lucau� q�73e�4i� 82-9��84)90226-7 [14]B�С.� ellih.��E�r49�r � 4955-4972�`11]�SauNA�Le.��7� G 3811;f6�06�72.4� 5] L� Shilnikov��L..��DrbTurae��$L. O. Chu,�7�M. e5Qud�a� �T�Z�ya �N"�M�Dma�Mrt��2��Worldɕ�t� � ͘L Singapr�Cnd19!�0 [12] R. Braw�� . F. Rulk��E.TracyU �view =�P-�3784-380b�=JE.49.1�6]u�H)Ilbxg�+A. Katok%&A FrhCours�1 —Wit3Panoramaa�Re� D ��s%+,Cambridge UnR�s� �PB�,��EW3]a�L!( eede�6�A&� >��AQ��2E�[ 5817-5826^D=A.42.1!7]!��d4ikulchev, Tech��l }�s:�33��7ͽ�t69by�434/S1063785007��48r�)�y(���1 Hard�� x$�W�6 Leaf  E3}Tr>�S"H�, arXiv:1711~ $43v1 [] 28u 0 2017 Absorb�BTof LDPC Codes Ali DehgY\ Amir< TBanihashemi, Senior Me@ , IEEE De�A&R� C� TG�EOee}#A*rleton]E@, Ottawa, Ontario& nada��tU� 1�!�t14I(LETSs)�knU9�t#E�c�pLa ��Ŕerr�� or r"�Tlow-denE��!$ty-check (!7) c!8V,Ead�?ve�Dte Gaussian (AWGN)�Fnnel un�rkPUeco]&q�Ohi� ��;vol1)���catego�- � ! � sub.&�elb;J;%:�,.,�h9ANP-ha?m� x�s� %uWK�av�JW� vail�^o=�'pap�swe!���at,Wa ��!m%l�,�R)+vAo�a_�aominkF&un��)��n!� b �A-�a1J�x�O�,$ny guarant1ipr�PQ also��Ap �� ��U � W �j��. i�)G�I�9� au�-�g�r!�.�%��W,dex Terms: L���,>k TS),�6�� AO�)z��b)�i�), 6�� (AB�:!� (E "H c��(�-֡` . I(NTRODUCTION�b�ei� fla�of�����G��Kto cerY!��b�ior-S� ���T�$r -U M�PS, refer�Ttoe,q�%�. 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Definition 4.6. We say that a lcsc +T G is cohomologically <pe dimensional if Hn (G, E) isN#��Devery n ∈ N when Ef�aN5�\continuous G-module. Not�at an�Lly generated discret � w%@classifying space^u�( CW complex#n exa of a�%<. So are�nec� Lie Ts (e.g. by the van Est �orem [8, III, Corollaire 7.2]), and, as+ follow�proposi!� shows, s } Mal’cev � s. P, 4.7.B#� �~�J4of. Let G be a>K�� l̃!� csc,N� in whichEt co!�,act. First n5�F��y!�`G stops after degree d :=A�4(G̃); indeed,A� a Fréch�MV E,Y0Shapiro lemma9�65 1] gives U� ≃i<̃, Ind(E)), andq n > d`right hsid%�ishes (a instance~� >)��V!eA�q5�,NT� ; weA:�vaM4e statement by!.ucAO on d 9I . In�cas!d = 1,Hhave G% R or �ZE both!�these i�^ For2��v�ep,IP �:� with d-.� ambi2��takA�(central sube�� Z 6 G, isomorphic to either Z or R, such�*G/Z�! gainJ��w�A�le%UhasA��?4 d − 1. Thene�0we just saw, eU��ib�AT8thus Hq (Z, V )���� 2�E\in particular, HausdorffV� 3.1]�Ua~PHochschild-Serre spec)J equeA�existsL no 5a8��\E2 -term E2pq = Hp (G/Z,�x). 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By0above remark,$multiplica0hmap m : G×G → G dualizes�La degree preserving 3�a |llevel of polynomial algebrasI�heA�!8following defin �4makes sense. D7.6 (co-.���vity). Let G, H be Mal’cev groups. We sayia linear�, Ψ : Pol(G)� H) is >g� e if>��@iagram commutes: ?G) El /OTG2 ) . (7.4) Ψ⊗Ψ  3�H3� 5H 2 ) R%�H 7.7. By Lemma 7.2 Aa�5v� × 1� on a> :��(B��)!+i�B-!8�� ��)� it!?,now straightA� wardA;check)�)--�a-C(ative Hopf-M0��co.�on �AK$tipode inv��!co� ev1 . N�� also!"\at in this terminology a�ongly :al,:p�veQ�P homomorphism betweenN�� nothA�but a 6�$e categorya' w�js. 1��8M��R�0let Ψ1 , Ψ2F�H)astB��6Me,�2���s �(gi,j J.Fbasis!�� �$(hk,l ) beZ'��H� supp�ŗ(for all ℓ�Q, . , rk�!� i, j��ŕ�(�ζ � (h1,=���(!B�i��5) 30 DAVID KYED AND HENRIK DENSING PETERSEN Then%Z�=%Z. Proof�Thow ��(ξ}| by induc�Ron d :=�9 ξ. TEse d ���q�l�� and ��c�1�#8s directly from��0hypotheses usAl(Theorem 6.1M7d > 1!�given. S.u,(ΨP 1 ξ)(h�)8 !r)a �)(k2�k)%� some h, kiH. Wri����!�Ű�� �6�5ɶ� �� asaŨa�a�1;�is�s: 1n(h����1%x)(� ) = ���)( (��#X =Li %·, c ��+"k) i =��26G 2G�G �H��2 ��2N��I�A\�. U%�����u�@0on repeatedly)JassumpE�((7.5) impli�ʡ5�>� q� word%�mb�x�dAމ�6.21 i�����syξm3ξ.  Ob+� if ϕ : H�v�Ga�6rA��nWeCes���0J�ͻ�-&��)R� ϕ�/B�H)i�(next resultIsŢnverse��!s�,A�a�spiri�at�� actsA�a “tot����g space�� G. As men!�(ed already,!Yi�]id!�f� ofc� "�)4of regular fun�u�s�J �can� � deduced�I classical *%�Z�t�Mš dicQ @ [5, Chapter 1]. �x7.9�*� Ů@csc nilpotent LieE�b2:�  IѺ=���%���ere J@unique continuous �2�6� suchQ�DI�e,ϕ. Further,5�i� is&&if� only ��Bbijec��Ns. Fix*� ba���{���}C{hi,j }�|-`�,!��p Ka�!S F baie free J~A/�c!� cl(F�5max{c �,H)}Id�4generators f1,f�f1, #E1jOque9�2b s ϕH : F�H �ϕG�G ~4closed images,$ ed�NA��by Q(f:=��� W.� Y <B! !n0 (i,j)∈Brk� �S3�H!� red,i�topF e?m e��(�*�)� � H ha!m�� ��,���s�- ually surM4IfAP� .PF/ ker(�) ≃�y�A2��� (��$H ◦ Ψ)(�j )(f1l%�G :���t;���� 7.8, f5T = G ���f�F in�m��Zevery ζ)Pol0 L p�,�e.��edF����(ζ)��$ !! (f )�F��)�2�f% ζ(I1l )), POLYNOMIAL COHOMOLOGY2 pMAPS ON NILPOTENT GROUPS 31 w�4separates poin�tG (�H� �)! concluda�ate! ��1!KusE�U*� ϕ̄eH2)�!��wL4erefore obtain:{� B G ���:v ��→ G ` !�1�!;>�e�sam�� trueE��:By� struŰ��  ϕ(hI��M���aJ�s mhoM�I�!��gE� K� E%� "V z �l2��>�∗Eh!�a�lso provS Gqueness�f,ϕ, because �� w���aer2OgcΨ!7�n%+i+�he*�* ξH� m; ξ(ψ(hE�ψ �3 A�!� m�.��(!yA�!kU�a��sR�weBG � . If�,is moreover q��� n Ψ−1+%N&�᯦���U�i%��aL����6zψ&� . Agaby!� 51��w.���f.� !t��  = id�6�H  "�10%* *�H�;�M2 *�w�n�.!%;gap5 �GF �R&��GfF .ZveC A�� in*C ݇A��u %�JI !���Vo��w�7.9%j�i� � �b�j� �� R]-� >�9ecomple� �s�h�a6xexa}whE�"U�H. References [1] Ar��< Babakhanian, CoA8lo-MethoW �G� �ly, 1972. ↑16 [2] Uri Bader��<Christian RosendZ,nd Roman Sau� �O�  cp� Lweakly almost period�  re2 �nAs, J. T��ywAnaly�H6 (2014), 153–165�,9 [3] Gilber�8umslag, Lecture��s� �N" ��s��1Dt5, 6 [4] Philippe Blanc, Sur l$1A��n� e de� es localeS %�� @, Ann. Sci. Écol�@rm. Sup. 12 (1979�37��8� 9 [5!��m!]Borel, L6> T, Second, Graduate Tex�҈Mathematics, vol. 126, Springer-Ver!& New Yo�199) 427, 30 [6] LawE[!� Corw�lnd Frederick P. Greenleaf, R6���J X �dahir ap"�<s, Part I: Basic"orIexaa'%�90%(!�P, 7, 8, 21, 27 [7] Pa��0k Delorme, 1-Y�)�AsésUt�gtaires2��d@ semi-s�es et ;<olubles. Produit�nsoriel�E MBk�,, Bull. Soc.%�. Fra�105E07), 281–336�9 [8] Al�$Guichardet.� ׅ�i>fet�algèb � A��8)F$2, 3, 4, 51L9, 10, 1` 2, 1!_$6 [9] Step��,A. Jennings,�< z� AY!��a� of inX�e]� s, Canad.AXA�. 7�55), 169a87�6 [10� exan��S. Kec��, CG ical� crip� s��o��zv�`19Aa [1�]�Kirillova� IntA J to!d�d��y�A"�4Cambridge Stud!�in AdvAd !:�13!/5Uni 4ity Press, 200�;L5 [12] Michel Lazard�Ý�u�E�anneauxM��naScique� �8É.N.S. 71 (195���0A��1m��=13.�Leibm��Po"� mappABA'Q4Israel Journal= 129�02a"A#P60. Erratum availableE516A�,, 22, 23, 24� aY [14]�T toly���,��]���p��s7�� MS Transl�39E�1)sA�5]J%, Auto��� �;!�of �k��s� etin!$Symbolic L� 15%�9), no. e�4–214��20 [16] Yehuda Shalom, Harmonic a�J���Qlarge-s�� geomet}men!U �!ct~th. 192�E�1!�18i1�9��2���[17] Hsien-Chung Wang, discrete subI"! solv�aU , IM�".464%��6�f�U`9. ↑7 [18] George Willi��-lyxonnectku.�,���l8�m��~���e-�� Au~�l* �al��iety 5��97��4��4��$7 David Kyz�D� �tSofJ�TCompue�ce,.of Sou� n Denl\Campusvej 55, DK-5230 Od� M, )( E-mail add�_|: dkyed@imada.sdu.dk /���Origia�<Article Proceedq��J` Con�  on Mec� �c�4Design Enginee�@ &�  Manufa� �iA Toulouse,�2(, June 18tha0th� 14 C/� of G-c�pro1,�m!��ng into STEP-NC Shixin XÚ 1,2, Nabil ANWER 1, Sylv�,LAVERNHE 1 � Labo�ire9�N�O,Recherche en!�d�$� sée, ENS-Ca!, 94235 �p {anwer; lavernhe; sxu}@ens-c8.fr AbA{ct:�, (ISO 14649)8 ecom��a!mi� standa%repla'�r!�l� A��c!W3al-V� 5V3d on o6983 du� fea� %8machine indepenf� �acterb M�:cen� rolN�� effiŜ, CAD/CAM/CNC!�eroper!�ity)� -us�6 � mportanBr both m.v� capiz��of �!F,knowledge, n thel} the %0�rE�� tedi�P task� carri!7utx�s)#2a�DB hidd�l low�"I� . 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T��A�i�of���byAc3) AA�YCA�2�� P K jA�  %8 ;�\, 5�%���A1αj,k ,N hP i   # = P K K �� β · α�N4; µ , Σ r k,T, j,r t r r=1�h(10) with initialized valueg1 ω �� ��1J�� )�V�=��(j=1 ωj · .9��j��j�A D. I���ƹN�+�D� !�propo�\Hmethod must be ableA�pr�s!�H future trajectory ���b@historical inform)��7�:)�isPion isU_ by i�ly applyMC driverEc�l�@ d ine0Aq� agat.0� �<It �z�=is�a kine�,c point mass x!;A�(ego vehicle}(some assump[Hs as follows: • O�4a short periodA��{�,J\-speed changes are smallbcan!�tre��`�a�� stani�0the lanedepar%�behavior%"� k%| D dur!/%-�on!U cess�99)I4emergent brakems, such�collisG$avoidance,�< not considered.%!Road cu�A^ �tinuous.$differenti!A�� 11slowly ���< To reduce calcu��onE�$lexity, we%g�E�0ing scenariosA�a r�e�a )��4(ρ < 10−4 m�t�)%@refore, =0J�%+%� �=�� 2� abov2��,%�0*0 is shown���1,which�{�t!�A discretizi�A� of .�a�se���>0.1 s. A.�a? 7: Upd�%I�99�ف�� v  =* ρ6���H�4Q ssign��b� "�⇐.��� ; ; end!,le 11: ReturU "x &�  f4 � "z � �q"� �@. 8: 9: 10: IV. 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C ONCLU� �e�@>newv (6���)% 2� �fT�-�h�!���-&�Z�-?:a� xrst��KH-i"$ �.�f� "�U�,� luG)qw�, �ve&5a�I�N+�6v�(�Y)bdi.�The��pe*{AI� �6"� by�J�bdS!�Gaussian�_�t[)!�lTMarkov �  . �2��{ le"�om~W���e^ata c6X&Y�.,=�eB<�b��A=��k�>&q0EB9 "?1_1�&� �&� nd�� �Se=', ���\=�( �e1�:��rI~�=&�M�� �� tegy!ÅR5�� isc8Y"f�s��&� *B *�^[ �h"�.��ato�c�'advantaAm�.��sA�i*��-q�-�.tIa&k *� �9&?�-�%B�=��o2%D�nQbnY8�stZ]�3Pith�n!��0. A PPENDIX A��Appendix� * ^^ %G rans� matrix, T8I�nA^^ III, C. H�Wi��MALA��Gtg# 6�L ��n.4"@Vt : ST �N = {ξ S#��B�g�f6�g� n }�1�6�, S�,& � �2� ANa� mk |f M = {1, 22\�K} if m7e!!, k∈{1,2,· ,K} �b�; �e�,�g�)�:f�Tp_>���� m� N���,� we�B 0"kd%Ma8�s�5�"��!I�]��%(s {mt }nt=1 ^ ⇒ 6q �Zf�Gon (22e$*�0} M-�p*(e8�� ie\%e�j��αi,j.(Fi,j , i, j8!:u ni�e�w!?� 1!�� coun�XQ�t &kmi%�j )9ni9P >�%N% at H i. Ku>�p, , i=1Q = n > 5 ���5�in�Eo�� �mQ\ T as  α1,1  α2 T =.  .�*�1,2 !2 .. . Au· &�Kua*     .. ����K�eαK,2b L !��4) K×K R EFERENCES [1] J. F. May%� C. L�1ldwin,LP�  Oim�]^of id� �f e caus�<acFE�f9� �b�E��e�Z��� EermeasEtechn� es,”_Rnsv3�R�P$ t F: $ffic Psych9d!�Bs ur, vol. �xno. 3, pp. 218–224, 2009. [2]!�S!rickman,!SmithO R. Jones%Lan �d�y�y�_� t��#Ur��Ce68 Inc.,(07-0495)�7. [3%�Wan��d�Knipl= $“Single-� way &� �1$es: Proble:F�zk���& h N_�e/�p!{�.mR�R!� �hech. Rep., 1994. [4] N. Aks1@ag�(S. Hack B. Lest �JhXwswJ�J4M. Rizzo, “B�@M�hv=-up� �-x�Q�s��( real-world� SAE ��n�P�"� � 2016�R12 [5]a Guo,�@Meguro, Y. KojimaIT. NaitoEDA multimodal ADAS M�unmar�[urban"�*�g!�� $text under�. � IEEEA�nsNz(lli�f !�i,�SE��sq6,e4, a$1690–170e15. [6E_Lee�,Choi, K. Yi,!�Sh�!��B!�a�-�Oa����c�^ trol*��u0)&[ �@n8>Aa_ un��U� � U�� Co W�E1� P�ic�ha��2m��1��3a:�1A��7E� M. Enache�Net!� C ammaFnd�Lusetti�w9�%�%��]�Da� !���e��p�� �17)��6�� 642–651���L8] P. Angkititrakul,a�TeS5.�Wakita��O� us4 stocha;IW ��7k>��mX�Bw�+!�Qw�3YwI�Uw�2 ��1 �174!��8)�81. [9] V. Gaikwd�d!�Lokhande�Ae=d�w�%�[ �c�b�]�V��# �9�2 �91a8918!�e710]��S�M. Ito�4�T|agaki�MM]D)- a d�d�cM� scheme: E�� ��f1�x ��d&��UpreOa]>�cc%@iPB�!,HumanMachine:D�4�D�5) 66! 67E��9�s%�efèvHjA. CaR"�h�<8Gao, H. E. TsenY:nd�{�Br/ll.)� �lJF"�s-��9I%����"�mk53M�-� 1705A�7209��2>(�M.�3��ȶ(�-�Ι(��eJN hybridvTomatadr�ppF$e lyapunov"�R����1-)��2 39% 0. [13]!�,A. Albousefi%�Yi!��D lev,!�Sy�= K. O7GakahAs[=�H.-H. YaA “AP-s�-"� suh v�o mM��.�.�Dng�1�al"�6�%+ Jour#of�!T DOI:10.1080/15472450.119614��14E��=S. Glas�A Y.“$��laTB>����Y: A� oreOA stud� j1p_�aoP�ta���#͌�2"226$ �4e�06A 5] Ge�io,A Casavola,Franz�Z Lupi Brasia�!I.�SpA� U/Dime-to-! �-5�* 1*�ͣ ���N�al High� Tr 0lAd�S�V�p  0903� 16���- �em C.-L. Che �V�O3��"� �� � �t �sceJ � in"(Aue��(Robotics & j (ICARCV 10 11thE�rn�Co�P�e�#�o�EEEi�e� 187��880!�7]��Dahman� Chad!�A. Rabhi� ,A. El Hajjaj���"�� :�~ ^ a robust�Lagi– sugeno fuzzy yer%$^�� . !�ɖ 58� 59���3� 8] ——�N2�| ��|�� �6��s:2�*� ���Ͳ�8%� 113%�149, 2| 9] T�VCh�WC.-m su�+)�L.-� $ “Oulx"� �wzmodul� irregular5�? �Ag TZΖ �9Ƀ�  50%�� (. 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CONCLUS*Y�g, l!?�ס0 �X� ��b~hv&�, cust�)6c%j"5. NR`-:�o�>�*�v03ck ad 9�ilU/;�P"�,�� �ies�Pf�<���$ GSS ���%�\. Fur"4 9W�dA@)V�G*sG*�8��-�7�n�U ard "�_"t wj��9��"�\�o� 2��rea>�� � �8Uins�T�Q�f�p1H"�@D� .�9d"- �steadfasSX, &� 5(�a�^cy �� �U\2�."e <�3�*��a�� ��b#4�o-{&�B�J� �sIfe�0effor�> Nume���w=+�m��eg5�.th "���DE.+J��!2� �tVt � l�4�!25*er� ��4� � � resource6�9� "r!"0� �U�LS � 5xUk"Uz�dlb�: V� , !� �!� �@!{v�.� 3. S�(*a II!fb D [5] I Rechenbergg �Cybern�9h4�h!r�2�xq~�G�<. royal aircraft&� $, libr 7�4� , 1122, 1965.K ��'"Q1:�HE0�f,lA�r8, db fogel, ed.�BLChap. 8, pp. 297-309f(98. [6] D F0ERTZ Michalewicz, Handboo97^��a�ylor & FQ8is]7. [7] A-D elbrecht,G ��alq�� . Wiley,}7. J6R X: an [8] MM Ali, C Kh�traporn�)$Z Zabinsky%�A �h�!*-!���H�s& ;���\� 3�e�Ain�.N7$2g,” *�h�Gvm��2<, vol. 31, no. 4%�( 635– 672�05. [9] KV Pri�4RM St�JArA,pinen (2005)2�M&�2�:�X4/ ap& 2J�� . Sp8per, Berlin [10] F Kang, J Li,Aa, H Li{11).�-&?��R���9���N�J Softw 6(3):490–497 [11] R Hooke, TA Jee'(1961)lFDi�g cA�u�of]�2�s#�&y�xs. J ACM (JACM) 8(2):212–229 :� �^�v5`� + � �3�JR kF�83). "J2A".B,Bendall, DS &L(+molecu{I(to man. Cam_pge P-�=. C + �G2��76�he�R�fdp�C�.�GJ&L. ISBN 0-19-929115-2^�5�� ��7 f8 �9 � �1)�T�>&��+4 '<7. REFERENCES [1��e��I, ��.~*�Fet56�Q".ET: B1e}��6�*�sm�1, p.�<. [2] JF KennedyA� AC,RC Eberhart,�i2��:gan KaufW Pube�,1. [3] J Hol<7, A%�Q +k�2nd.�4=S9���MichilE , An&1bor���7�G(4] JR Koza,%��@lZam�': A� digma��8\ly breeP� &�0�-~�tgra�of ��(s. Stanford� , De�<��a�)�er Sc�K�90.A� 4] PSI�,eC�9aCOny!, �.�,6`�,�"x�s%��M 6al��s: ToNIs Mem-&�s"ac�lk@ Con1�Mq� � (re�I826). 6E4 XS Chen, YS O�9�M�.$m, KC Tan,�8. "A Mz=8Facet Survey on�.��$EEE T�L"kP= :�, 15 (5): 591�U�N�[�Eb��(2010��R�>$ Frontier:"<D)�I�- Past,Evj> & Fu�E�,al �o�`( Magazine 5� : 24–36!@`7] T Ichimura, Y KuriyamaE�9|2 "Lea�Oof �=� �;� f llel�8 GA � a� mG"� ���ro2jp�i%��n|svNn N> N>�s0New York, NY.\ 113!s11 ��8a�Agu!, A�4menares�ReݭT �p re"Y>uT��h�9Gtic dom ) =&=R�� ". P�>Analys$ nd A'P�is 1 (#�5��`61. doi:10.1007/BF0123802%�$9] M Ridao�"�R�Elme, E��(acho, M Tori�)��A_�o�MA���2����uG?two man"8;h?". LecAz Not�*I|er �Uj#��x (�<Verlag) 1416: 10� 1146<3-540-645748_396�.�-Y �?@O Haas, K Burnham!+ Mill.. �>$@� radi�apyMd@ar ge�D ry". Physs<�i�H�dIUW�BhRy 43 (8at179�193. 5�88/0031-9155/43/8/013. PMID 97255� 46 ��s~�s�@S HarrK E If���(1QI"�@*.of & /sa�sng filtCGby:5Yi� ���y�>jSig��P�,X,46 (12): 330���3.%(109/78.7353� �A$A Augugliaa(L Dusoncheta1Riva-San� iny2 "Serv:�A!�+ens�8�d*Jd���6-�". ElcB P�A S=n�sJ"earch!�  5A.66],h16/S0378-7796(98)00025-X. [tBR WehrenmN@ Lucasius, L BuydG Katem�,1993). 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VI.�NNCLUS��We�*sen!��].�&,t��R� V]3wR�!�9.�rrobotic�Z�sa�seoV�l<����za$ &J�%n��m3�>� ,�;� �^�n "�7� � .�7&n�a�Y��� �j�G� hIp3A��oL �s 0�C.h .� �8s !�� )Oh1"�Bɪk1l\5� lex��i"�~%���%%s�&�� pz� #&.�MRa#exe'!�Iil�jrnl!��:������C"�v6PPO�S�b)bS�a[s�7��Ś�s%!f�s�,i �� �{p4�Ya�Rl. q*q�2k �%A�erK�weWy"� Q�.(� A��A��  ����n�-A�atsF�"���aDіɄ�Q�enM��7l�� m ��7w% ��G�C�Z;�%� <4b. ACKNOWLEDGXxS R�� reh2qi��p���>po .� Army.E�e�Lab� C��^�>�Wmp5�ed�k Co?F���AA�� m}DW911NF-17-2-0196 1K� VK�� nK�� >K���inA�th Toyota �%:iCyPhy c�edr. R EFERENCES [1] S. Sast��8M. Bodson, Adap�m� : St�5�C22�F��R"��. P=�ice-Hall, Inc., 1989. [2] R. F. Stengel, St"“Ral^��C1xApp��@. John Wiley & So��f06. [3] G. Kah�p. Villaflor, V. Pong, P. Abbe�!�4S. Levine, “*�2awZp�A�"}&&d1�,W]�CoRR, vol. abs/1702.01182, 2017. [4] Y. Niv, D. Joe!-. Meilij%�� E. Ruppin��E.�(Z��in&�2��:�d�T�aԉƅ�� fora�?"�3� 2002. [5]!8Pou�G�N. Vlass� “M� N>�bCF2��"�e�G�i�X�oi�e�|' x�i�( Int. Symp.&Ar��ialelligA���M�z�Bcs,!j,08, pp. 1–�6]!R<M. 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H)��w�A����xargWJɢ�i��C� shorteneǃ�o��ake�������o�itha{�4�A�� �>p8����n�iv�kn\t)diUA�.nՆ �td)summar�� "-meP �S=on����t29.organ|=�a���:a�> � ZR ect k-}�%��'#�iJ� nd fg ��;.L��3M A ve�y2C�� used"�,@_`�!��%].V�s 4, �ch"��e"��m�&U���1q�ane unmi�6��.�.gn�� �*[se��̭���� ��� 6��p-��s'j�7�h��nX�!ii� �� .,!� 3, 4��5�C1 9�uK�2L�\ZL�4 or ��$A�)Mxi�ͤnt&-�25��i&�͝��a 6� E�po2��"�n�!M�.}!"6"�,r��Mt.����A�����!�!�A�� �]7:h 5��4�!XIt ��e kippm'q� a8\ngY�Q�J!mSE���i G\n��f�epX��n��te�. 2W�ckg�ta�Nm{u)isY  ��n�q�)��w��"��.pisa�uscript^1uz�-OA<�_.I�>�� J>�s��1� igEbv.�~Q�f�$�e��8�!�&(+��-A�] �s�Otiv�I�1 (%C some�P.vcY�;�e l��X������K!V�r��%G $�jA���.��!ё�$&�  � �6"� 11.u �*f Ja>J�S� ,n X e(S/J) = 4p)λ(Sp /Jp ).E�0H⊇J ht(p)=ht(J) HN(R2�F����A�< R:λ(M 8" �� S-mo�� M . Re��IT��J*��9ձ_iff�pf �h!U�a�B Ass�. Also%�9��J,�d J uG8.x�kA6!�� ? �um ����9J ⊆WA�����aRf�i��> �1� �>]�  i���Y�q��:!"Q 55de�Ba�ayv��f� e he` �em ; λ.�λm i2��J��m�9oq��p.6��pô�-'� t7eiQ�� !&λzE��iA��!�i.� �>&�mT!eiA� )!�t9e� � !�R��:-%�2�eriN��8ak+)��S��* .�H�IE�S�(�a���*��J��H3eu%AF �J�k��J = I. +�� �fEi�e.��}:�26E�.q 2 � ��H ��NA���i se>�3 (%$Pr��119+�2%Pa :� SV�nn, ebra�B�l��fl . SuI�-1= 2!5�ځ�6�J)��3����4 �"�M�7�i��i2��(�wE�.<2�2ms #61�!�7�or� �2�y, , ax + b@x� 4ht(x, y, a, b)�� = 4. In [17] it was shown that such a complete characterization is very special and cannot be extended to higher heights or multiplicities. In fact, for any multiplicity e ≥ 2 and any height h ≥ 2 with (e, h) 6= (2, 2) there are infinitely m?�nonisomorphic primary ideals of m�y e and �0 h. Moreover,a�Cy can be chosen to have arbitrarily large projective dimension. HoweL0in Sections 4r5 we g0a c>{of�� to a�,three linear!�e . or�:(�2��two 2� E8is sufficient f@ he bounds�Xwant. 2.2. Linkage. Two os J��K�\a regular ring R are saiE �b�\ked, denoted J ∼ K, if!i re existsIPsequence α = α1 , ., αgE� �$K = (α) : ��J K. NoticeI��defini!��ces JE��K!>(be unmixed,�X⊆���O- T has been studied sinc!Y�Ce nineteenth century, although its first modern treatment appeared ia� e gr!�-break!W8paper by PeskinI�PSzpiro [24]. We refer�8interested read(1]�[18 their 7!p�s. We will need a few results regardingA�E8 Theorem 2.4. ( ��- ��,�) Let J!]an1`IFA�S of m�g.,Z�beN! in J)�set2�n, on%� (1)2a�at is,%�H� K via α; (2) S/Ja$4Cohen-MacaulayA��4onl S/KF%�4; (3) e(S/J) + K) = AS ). Ix eas�FcheckedI�if!��iR ��Haximal length in an-M�J�enI�a}un ��u��lia�A��4AE� %�usa6His fact several timA$$The followA�"�se�xwell-known. Lemma 2.5 (cf. [9, ,6]). Supposem��L@m~ �s both �a�sa��. T�pd)h�= L)z�6 z10,,E��7{.�almost � e8�s��� �8!wS. If��s �f ��J!Q!aenUo�≤ ��KA �1�S3. He��ϡ��eşsmall2�+re��rec somea4%tructur!��.�V �\mkA�.. F�! �o���){� qfield kA3a�lgebrai�y closedev redu��*�tN(case occursa�Mproofo�E(10.1. Also, ��0a homogeneous �� e�yed de ratea?HJ contains at least!�AI�50form, otherwiE��ٮ non-Q�C. A TIGHT BOUND ON THE PROJECTIVE DIMENSION OF FOUR QUADRICS 5 T2-�Ltq�-t%�tic vers of lass!\4$of Samuel !�Nagata%oE�2.7 ( ![25] , $ [22y40i�y� =^�,6��I���= 1M�%�1x(d by ht(J) �!g�s� next��wed%�� �$simple low����AE&.��6�2�. Propos��<2.8 ([14, Coroll 18.12��pE�2\e4>��p �fy�-!#(p) ≥ ht(pm�6,=�A�"�of :��. � 2.9.%�^��mof�Qq�_ . If�= 2 �a�y 2� x, yEa(a quadric qp Š p�W$ , q)=�^ �� )�ficQ I��m��varie ���degree } aNY�|��; n equ^-or� ed}A� �s���� best f� our pur���H� � ��.7���s from2�V��E�2��2�@3. (See [27].) By>�� ��� E�)J.��*,2.10 (Anonym�\[3], Swinnerton-Dyer [27y��3U�� ��F�nB��M�= 3MBa� ��ne-9-/$ing types:t ]2c) wh���xEb�y��.1�cipcubic!R�m� HaVI2 (M ), M�M 002 × 3 matrix�BY�x ��.�I is necess� �aa�4zerodivisor ons]�I�<��>��f 4Iz:W�(��d!Xbyr� 1];a[]$AQ9rived E� work!PBrodmann-Schenzel [6,.X�] ��T11�x�3�3A/� U/�4]/��ih�/�r5�qV-�r)�quartic.*$, q, q ′Y+�x .]Er�q ,����s� Ayjs�4^sor a 3E� symmet�MV�; (4) ei��eZ2[� 2��,�� ��i/s, or a�j@�5�7 1� 4. Rela�AI�$s. Finally�y .�-�$authors’# ed H main M�:.^�2��5��.5��} &Y �I`� v"f by n5�H 0a polynomial �S"� w �I�,� 2n − 2. "�� � n is t� � �RCRAIG HUNEKE, PAOLO MANTERO, JASON MCCULLOUGH, AND ALEXANDRA SECELEANU 6 In partic��e�a�4 indepRnt��o��(wo satisfie6���6��ɦing��a ^�l�M )� Enghe69 13!��6.) 2.8], [119����I8 �n; � R; j-�g > 1 �Acby��n�[)� 2g%�g + 1=�� �R�IH.$��]S/I�6�. �j � ��pFouni�1�A� grad�6� .�:j�nesɻa more ��lM\�R�n i�6]..E�-���sɘ" 2�3 ^� by 45M�2p�ag st 6A{�d�b %N�IB/� exactly/�i��6O�7henceuY8= 3. 3. 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Namely, w� take|$= (x2 , y $ax + by, c dy)p I3:'��z.-� + cz) in�� polynomial ring S = k[a, b, c, d, x, y, z]. CRAIG 28 HUNEKE, PAOLO MANTERO, JASON MCCULLOUGH, AND ALEXANDRA SECELEANU These correspond to the9sI2,2,1mL,1,2 from [19]. More-�\lly, we previously posed�follow�(question: Q 0 10.2 ( [15, @6.2]). Let S be aB#!�let I �nIA"�S ��tIn U3hav�hht I = h. Is it true that pEX) ≤ h(n − h + 1)? TU�U�in%  achie[Dthis bound for all! <sible integers h� n. T.@paper now answers E1-$ affirmatiA� if n�,4, while our5y M([15] gave a2@� bE�hE2. Not � if theyhas%{si| <�,!1would gia ��oM�rojie$ dimension!�m��g.�=�!} is)� atic![Dn – much smaller( hknown {��Ananyan-Hochster. Appendix A. Resolutions�$Primary Id�O IS is s�one�ollectE�detailf!,many unmixed%��p N� �lisA}m�structur!ceorems�S js 4B�5A 4e technique is%� sameEG each��uO: one r�veA5�e%�q �g!k�Bly A�us %DBuchsbaum-EisenbudA�\ctness criteria to checktcondia�gat ens � �%[!�4exact. If F•�� $of S/I�$∂i denot �0ith different�map, PC-�amounts�a�A;8 ht(Irj (∂j )a�� j%;a� j. H�Yrj = pi=)D�1)p−i rank(Fi )2��expec!���jth�%�Irp29�E1<r × r minors ofB0matrix associ���t�t[.���` over%�%�)~Z��+ 1� j > !�)Z5��aI� �isU�4(cf. [17, Prope�on 2.4��e���sA�at X = 3,��=�sh��%�( j if !o1, 2, 3N�� . j�+$≥ 4 We d!is!�licitly�$Lemmas A.1%~A.2i6$reader may)%e:remainAones wA[!� help!� a compute���gebra system, such as Macaulay2 [13]. We have��A,a supplement�L6/� file a!��tp://www.math.unl.edu/~aseceleanu2/research/fourQua�0.m2 Throughou!��� rep<nt inde�� linear!5 ms s!N����,H�)Aa "  three5���eI'. %s!ra� LB���z�xyz, Cx�0Bxz + Ayz), w�-ht( s , A, B, Ci��5AA en L�$)-~ary, ��L� �" e(S 6.A� of. Consi!�!�!�@lex So ∂1 S5 2 S9 3 S6 4 S1 �F0, A TIGHT BOUND ON THE PROJECTIVE DIMENSION OF FOUR QUADRICS 29  � = x2%'!%:!3$  −Cyc Bz 0y 2 �z0  Cx1 Az x+6�x- n/�2 �0�B� Ay �xmxy�(∂2 = f x +− ]D �AB 0 C '$��6� x � u j���C !� ��y P2=�C 0! r� ∂~ ��B�−A �4�z2I� s 0 ��0� !� 3�AlB 0�% ��A�x�!%4  #9� −x vV����4=y�C& w�−BeA &� x2 ∈ I1�|1 ), x6� �6 �42 �  x5z 5 "�5"�  J�4� � q�y� . Its�~�� √ ��actGfo�m�a:�L, :�i�? . As �W�pD λ(Sp /Lp� 6j �f=  at <��.<.!���2. If J����2 + (� � , da�ef ��,   a b c��� x + I2 =���Jn�(J) = d e f ���{ B ���,R\) : J =2ma��,�A, (aeAP bd)�~(afcd)��(b e)yz)r =��G�8�#�  S 14 �I�U�I�2�I� 2�.i6hAʍ�xz yz�� �30���q��xi��Aa��Le�a�e�z+��e� a d@SV^�>1��be�e 9���g��  6!u���0 b e �}#x�1�� c f " 0 k�#�y �*2��%6 hj�y�,��QU+ �,1n��%[>�2��x��0>2$�J X �7�%�+)�a"!@ "i"!��z%T6� (��2^��8Q-� 0y)� .'R%�!zEU!�2J�%�#� #�� �)m )�x�EW��:�������%�1����A6 `yFw�A+ � i)�� y7A���-8 5iP\�x 3af &� b e���I= easy� , � ɭ�i�" �.� s FO x7�3�7�-�7�-�2�h, z6��LB ��, ��, ��c I2c4 Rl���x�^��Rves J&(�� �� � ���n�}ū.}2^� ��J��2.� XH�� <2� The incluL ⊆B����I�clear�^�by��01. 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Tigran� e�Melvin H� , S! suba)#� :@$�s;0 stillman’s�j�! ure,+"dprint: arXiv:1610.09268. ,!= �a!�by*�!j s, M�[!�.�#�t. 19 (2012), no. 1, 2. 233–244. 3. Anonymous, Cow$4ence, Amer. J. X�79 (1957), 951–952. 4. M. F. Atiyah� I. G6@cdonald, Introduc� ][-8�, AddisonWesley Publishing Co., Reading�Dss.-London-Don Mil�xOnt., 1969. 5. Jesse Beder, Jas)�cCullough, Luis Núñez Betancourt, Alexandra"0, Bart Snapp,�0Branden Stone5��larger &x#� &x#�Dregularity, J. Sym;mp. 46%�D1), 1105–1113. 6!M,rkus BrodmanI�PeA�LSchenzel, On varieti�'almost� imal degW in sA� co��q� 305�06M682, 789–801. 7)Hessandro De Stefani�jVF-� shol$graded_' s, p8.L507.05459. 8. David #�,� geometr��Xsyzygies, Graduate Text�#a��4s, vol. 229, Saspger-Verlag, New York, 2005, A~$�'A�s,&��M�� ic�`. 9. 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E 5$�Z:�� �& � (2@5=<, LB����z��" ��dC,�s �k��n enuk7+3Ų�n�  [ 1 � = Pn ��P�V$ . n n p .p 1∈N Rv_Y��a{E� �'-�C%�fA�� Bcb ga :��.a�PrüfdyO`�R49-at�+��2�*�1Pin72i�U�: �f�t"� .0��.N>C�b9��F-J<�d>��*�  �Z��F�/� �.�R���6m��a�U�Ơ���$>�i�:�HL��bk�=�nre��*��u�mk4+I!^ ei��ћ.�pō!�  @'3 illu���yJ �5)R : >�n�H�i�?:)��9_ tw��DD . ���� �6� ���.� ,�>0��0A��a�it@,a��M��u!�gun= � (1@O >> n%p���� Ɏ&t$ 5.1 �IE�Z �����"B�r&al"gsuc�7�h�%� �hq2������ �.∪�� hq� � �9�X B�U�! a*=&q7qj���jc N. B� �a%\ :* @ �"l0�B�v]Sces��a.4�j��C6�hai�5� �I��� ���o� 9�M\�s[#<Swe�u����.�d�p"=%%YJ�=>���.�a�;�x &^FI'%�V�Rtan�Yly9��(PM[�B�Uys�3p��'^��� the �F:/�1%^"� 2v�0%�B5�,�d�9R>�z�`.zQ��sM��G�f��K 1�p�� paraNbmr��a3"��}E��sڨak��"\�q�  /!m?�y*� o �%is,6|z?��0~��m e��3qm < qn�so&I� e KoY����.�5.4�t�eW:�n!"ti�G�B�6���4e antimatter. �uThe following example, on the other hand, exhibits an antimatter Puiseux monoid that fails to be integrally closed. Exf 5.5. � D m D�M =: 1/2n , 1/3n | n ∈ N is clearly��. Suppose, by way of contradiction, that M is iB�� By� orem 5.1,�re exist �scend!!<sequence {hrn i}j yclic sub ��sM suchw [ M= 08. n∈N Take k �*� hrk i. It�(easy to seePd n(rk ) = 1, which implies n(rn  for each!@(�� k. Let d@2a 3b% some a, bN0 . Si��rgL/2a+1 +1/3b+1 satisfoN�#  , itMT � rVM \�Now t!ℓ�N9� .hr�iE!�n( > k E�A�efore,! '�,1. Because r!7 an i!�(er multiple!�0, we hav-Qd(F2c 3d !Xere c !7a + 1{ d�b. HA 8 1 1 = 2c−13d c(���8 ⊆ M. 6 23 So �� E^ s, t-xand nonnegative coefficients α!X�.αt-β0, βs with ei! � &6= 0 or )��yA�a�P t (5.1) s 1 X αi�i = + �i 3i i=1 Afa��sEq IDif necessary, we c�! ssum-^A���Z�3 ��jEx�iA_�,�. ! and j6�s. If t�e��n1���a�02t one obtainMz�tKA�mil�6, if s.K��s "�� fact%9�{0, 1}�ces 1/6%��{!�/2!u1 /3,!� /2 +%�/3}, m�s a6�,. Remark 5.6E�u^M in E���$ couldI�als�VDen achieved by ver-� firs �4   n q(M) = �@�Z!_ r, s�(N0 , 2r 3s !�then usIJ�nes��, alongIo�'fa19�5-"0M, to concludM�<. We are ready n� �o!(4struct a famil��@semigroup algebraI�Lout irreducible elema)\. 10 F. GOTTI Defini� 5.7. A�,ral domain R�/called�V providedI R has no w� w�A� V�s)��b!�studi%�H Coykendall, Dobbs,%� MullA�(in [6]. As !Y next�pos �reveals,��.W:E�se�be us�=_ a��y5\ over�i!�( fields. Pr� 5.8.�R�Fja�)�J:� �le� be a��trivial ��j��e)�&� cond%4s hold. (1) Ifa>!��#�t��5(F [M] ∼ = X]. (24920�a��n BezA~)�%of��^�nNz�644 ensur�� 7$isomorphica8�(a� +) �.?�,3.4 guaranteBB��)m5"� !): s. O)J.� *2)� restateU�6[2,�## 1].  ���9�� B��0A�.��5.8e�6�_.��1)�%� T�is,$sider�uQ�u 5  h1��: "3 i. 2 3 K 6� a���3�!�<tom. However, (XI ) (Z �· �i�?� &$ ch�Uof ida� )��s doeI� stabilizemile%X] happe���� a Noe��ianUsJ�we won!wh0%#n��s9�� ' :�nB�to)� Ques�P10. I�k- e��-Bt���y]>�� � %��A! M])�qƍ�ny (or� �)/Jp F ? g ��o�Z����y�dJ�� �s. ThI�5.11.��e�r���i p ly m�non}�j{� �F �cCo]�see�dprimes P := P \ {char(F )}!w�,eZ �p��P , d�e Mp e1�p*_ i.� !0ug��qq1 Fv�{A�p ] |d }. C� �, }Mp)�.��i�. In ad��, b� 1/pn+1 di�a��p!��F] ]A=unionaoa�F� N� $Q, namely,L= ∪� �Ox!�us2��F��b2Cr nce F�J�,>_�y>�%� >e!gŐ.�:�Final��lus  �|!% P�s���F� pairwiseA��-Y�. S&V� jV���e� s p, qMk� �pl �qe� �Q/��Mq ]. � φ : �� q ]1�n��,sm) ��proof!�q�4.6� � ATOMIC AND ANTIMATTER SEMIGROUP ALGEBRAS 11 j h&eg(φ� p ))��0iVvery j�N. �f *� n > vp (G))). Z%�cm�,  1 vp deg {�vp pn  X pn� 2) = n + - �.M�n gd(Mq )i��onY powerŝ�q�+A 1/p �Mq•Fp� �  n�� �+p +�0a-�e��(X)9�& "Hof� 2)3 rise $&�l� iO ntabl$lle�IZ�.->��|ch co�te��IK�uM6F�f���perfect ? of �!�(acteristic, } cer����s� ��4s.Ň�Me� . ForU�� �xE��Ma  sa� �x�Gn-divi bif x/I�� nd�/� � :/�>C�E�� r. �e,.A�-� �K=I6y �nE;�22�2. Giv6a FAZb��x��� ��.�� ��|F����p!���6��F . F�%�introduc.wcla[ o-s parameA%�z?f�� numba�� ��Dp}:   1 Mq := i,�� . pi q j��Mq:s!��p=�5��qE? bb of�1+!�M�E� F d�min� �Q��, �  F � ��|6�� . O�again%_yuse��rgu��� e "�gE;�i N7 to sh�6¢6: �x��Mq �šH��A"an G.�%k�d�nct q�?��.v�0�P�q�P 1ŗ�)� �[��� �iEeat2U�a D�2,(X p = vq q .aqn�\�q *�\qn��n, f� A��result�5� ����c���� Z��,� $desired. I�ly re�g.��� j!��42{ �( To do so, %\�M%u�Fe f ���=� X q1 +� · + αn�0� ] \ a�As p6�a:�p) Frobeniou��msm x 7A<�x9 surj���vA��d9�b�,� �:I�� gs βi �� ��=�pE�s�#. Alsoh� � ilit�M 2� qi /] MM1 ≤ i�nMR :e�{ p� 5k��-k/p:n��-n�/%�.�in)�&%;��z� 12.3"�13�� 5.12�5An�si .5(2)]j�s=Matr�D:2� GCD-I�( whose quot��.isUDofZ�$$n D[Q≥0 0lso�&8j,. Acknowledg�s Dur�pre�p�of th�ap �(uthor was s rt��HNSF-AGEP fellowship��ferences [1] M. Amini: Module amenaMX�pF� , Se��Forum 69 (2004) 243–254. [2] D.�A�s�J.2kL. Hille�,M. Zafrullah� noid�E��ion� . )�s, Comz lg. 35�D7) 3236–3241. [3F��D. F.��s6��Factoriz%��&h|,J. Pure Appla�%�1990) 1–19. [4] E. Briales, A. Campillo, C. Marijuán,�(P. Pisón:� bina��c�$d syzygies6���%0ll. Math. 49 �8) 239%�6. [5] W�un S0J. Gubeladze:=譻 %<discrete geometr�n G E�,oric varieti�((L. Bonavera �d!dBirAeds.)AT́minA!$ngr. 6 Soc�(France, Parr2002, Ek127. [6]�2��.!i*�B.�: O�te�1ĩ�no atom%;UN27 !:9) 581A�583AN�7:u�%�gammenga:�embed��t��,��AM"32E�11) 177A%85. [8]AGerol;er[dF. Halter-Koch: Non-unique:��:`� ComQ7�a� Analytic�y,E�bA�A2 ematAiHVol. 278, Chapman &�Tl/CRC, Boca Raton, 200AS�9>��AHtsAlengthA�mer1�(Monthly 123a�P16) 960–988. [10] RY @lmer: A two-dimen��al *���oa`� �C�,��c��qEX44a74) 25�!�0k�12k��Qut��� RingA (hicago Lect6in.7� Univers�� 3(Press, Londa�198�.12}%�T.A��k��D��properaX!T���s, Mich1\J. 21��6��8!�13jl� Nilpotent"Hgcom5 �s��2a175) 9E��0%�4]A�0Gotti: Increa�Fve"n of ordere�FF-M`s. [arXiv:1610.08781] [15.`��OG a�"�=urk :� 2�a . 16E� 7) 20pp. o$07.01731v2q�6q%�M.�Atomic!��Oboundedy��t� B��Ue� �W�9��7�@�7�08.04044��7��,�{ 4 H. Polo: Thre]�1of dens& ��i.[ 701.00058b8]��$A. GrilletōU�a�dv���'FFl, Kluwer Academic Publishers�L�s�H�ޡ_19] G! gman��eK�I|M�Pra�iOu�.m��6A�40���248�80] S. K. Sehgal�J "dsm! �i�!l(. I, Canad.a[�qa69) 41��413. D� �t�of)�P4, UC Berkeley, 8CA 94720 E-mail�(: felixga7<@berkeley.edu ������I,,�6������F����,����Learning Objectives for Treatment Effect Estimation arXiv:1712.04912v1 [stat.ML] 13 Dec 2017 Xinkun Nie xinkun@stanford.edu Stefan Wager swager@sta"TDraft version December _�Abstract We develop a general class of two-step algorithm �hetero/ous t� effect es�( in observa!Pal studies. We first .e margi$ Gs and]< propensities to!mm a`-� funcg, that isolat,he^��� k�, l0hen optimize 7�l!� ed odX. This approach has sev%7Padvantages over existA"@methods. 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Let γ1,n &Xγn,n be a real numbersv γ� ě 0�x6Ilim max ( 0, n�1ďiď�8Ñ8 n ÿ i“�Z2γ P r1� 6 let.���r �r�r6�� such that�all nk |r�| ă c&�� �M6��and @�H Di�x N Dn , ď  , @ip@n �i! :w<� ε. Then, lim %R�! 0. Proof� Le,1. Define an �Htriangular array η:���!-(of row-wise��4t random vecto-�&� X :�Rm ˆ rR bcpξ onα �q]Ky&H m Ăn pf q; f P Wn pW pξ��,A q. Regarde�process 1n pxq; x q a&Ă Vq, w8 m V etf v@: X Ñ R, f pw, u  uIpw!��x� P X , b�uA�� Q ?1 W1 ˆÿM���!0ÿ ` ˘ f pηArq ´ Et� P V.827 It�possi} to follow%argument�in 4.2 [40]A�/check.condi�s 5ioned Lin or��o�Wi)=CWn�asymptot��ly equicontinuous. By Dudley [12], tt== ; wj ´ xa0u-��uW8 Vapnik-Čherv>,kis class, jE�}�m. For dA���detail�jO�Hes, see [35]. UsingmG 2.6.17 (i� m (ii)!+, i�=!~�@ at C)�>��E7�� n��� �Ltoo. Consequently, H \ h; h]��h-OaIp P C>��C�u' m vE� �>A�iIn�� graph �. 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Brin, HigY8dimen�al:.,�s, Geometriae Dedicata (2004) 108-163. �&] J. C�,n, W. Floyd,E8W. Parry, Intro$"ory� n Richard~ ’s3�$$’Enseign �Mathematique, 42 (1996), 215–256. [Dix92]�D. Dix�Randoma��s`F%�sym��c �, Discr>,}. 105 v�2v5-39. a9 G. Elek�$N Monod, OɵZ�9���@Cantor Z2 -system{( c. Amer. XSoc., 141(10):35493552,!�013) [Gel15] T�:�lP�(�A �)2!�R %��. ��R6�Not. 2015, no. 19, 9806–9814. [GM16>u�. Meiri. �5gru��S!W)erty uW� I1�e �;on, InF���,m Xappear arXiv:1505.06881�,hS87] E. Ghy/�do6�S� escu, Sur�1u5e $*qu�3 déQ́"Z5,es du cercle!U�m� 1�dHelv., 62(2):185-239, 1987��S!�G. GolanE!M. SapirE"5f �O R’J� �a=00 AMS,�*) , arx) 8.00493�"�T+�*] 9 f���stabiliz�5� H=*."�1�R�P�o*8�8 St. PetersburgEu Journal=���6!�53)V�oAu�&�-�r"D<:F�-!�6!!(2572 [HNN49e�$Higman, B.� Neuman)�H., Embed�� �SELs,�~London�. a� 24��49�;47��a>�� Kato�@|Clblatte��=�b moder�_�Rof dynam��@s, En�1op�:of��@�ci_ Appl��io8dvol. 54, Cambridge Univers�RPressA�95. W�a suppl��(ary chaptert �PLeonardo Mendoza. 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As future work, we would like to obtain semantic characterizations of the degreel,sharing, in ��Fform of, e.g., preorders on typed processes that distinguish when one p $� “is more parallel” than another. We pl@lso to extend our�al rel � hips#cover��ing disciplines with infinite behavio dnotice ��approach![8] w_$recursive B [7] and ?aL (yet non divergent)3�has been incorporated into logic-based sessio)^<s [18]. Finally,!�%% plore whe!8�rewrit!E'dure givt § 5 coA!be adap�Da deadlock resolut�DH. Acknowledgements.!��a^�ful�pLuı́s Caires, Simon J. Gay,-.�e!�0nymous reviewAMforAn$ir valuabla��mj8sugges�s. ThisE� wasAHti! suppor�by%$EU COST Ac:$ IC1201 (BI$ural Types Reliy@Large-Scale Softw�HSystems). Dardha isBp� UK EPSRC!9lject EP/K034413/1 (From Data vto Se)��: A Basi �(Concurrency! Distrib%�$). Pérez�e(affiliER(to NOVA LabAdory�8Computer Scienc!� d Ina� atics, UnA�$sidade NovAT Lisboa, Portugal. O5& J.A�$ 15 Refe�es [1]: (2014): �� LA��,>��d Non-Determinism. In Essay) �Cthe Luca Cardelli Fest - Microsoft Research Technical Report MSR-TR-�(-104. Avail%�,at http://re ?.mR�.com/apps/pubs/default.aspx?id=226237. [2B��0& Frank Pfenna�!0):6 as IntuiA�is��0Linear Proposs. In:|c. of CONCUR 2010, LNCS 6269, Sp���er, pp. 222–236, doi:10.1007/978-3-642-15375-4 16. [3>���,>��D& Bernardo Toninho�!� �%����2�. MSCS�x17/S0960129514000218. [4] Marco!�,bone, Ornelaq�,& Fabrizio M�7si�Progres|a-E al Lock-F�v%S0 COORDINATION-K845BK49–64�9I<62-43376-8 4. [5:��8 & Søren DeboiiAA GraphE��Aщto� for Struc���d�munic�8 in Web Service:! ICEM<Amsterdam, The N�9$lands, 10t�� June/(., EPTCS 38EC 13AB�7�4204/# .38.�6] GeraAHCosta & Colin StirlE�(1987): Weake�,Strong Fairn!�in CCS!�f.�$put. 73(3)� 207� 44, U�`16/0890-5401(87)90013-7. �6*awA��R��2�$ Revisited�ieeedings�w(rd Workshop� �B�I� ��, BEAT!>,4, Rome, Ita�01st September!5_162 ���3YX=`162%a8]6���, Elena Giachino & Davide Sangiorgi��2�j� �s�|:���N8 PPDP’12, ACM �13A�1505�01145/2370776.�9A��9:���orge �#�<5): Full versions �t��paper.B�. N�www.j_5(ez.net. 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Parry,!��r5or�*C7 n Riw �d2��� )!�.�J�Enseign��A� emat��, 4 �6), 21�$256. [7] S�6�UXy, Murray Elder, Andrew�'hnitzHJennifer Taback, Ra�9$Z$�G>�4s Geom. Dyn. 4Am109)�9!�12�8] Gili 0%J2�AJ}JI-aF4 preprint, 201N�9.N��H^��U�10.V�, Mm� Sapir, OnJ�#ofR���,"� in Advan� StudV inI�5��cVUMSJ-SI�mmO, "Hyperbolic%wetnd !�- y"���0 1501.00724. �!.�.���?#�=�y:� ^B���Vi�-.W. (�)�s. Memoi�#!� Amer2�130, ��620e��Ee17�3]^l�%Òo!Q�o 5O� (Russian)!�. Sb. 19 �� 8, 3�`0;�1ˇin.!�. >4�<7-8, 1077–1130��4j��65�F[ es:� ��#� ��. Journa�JJn20�4�\!j1,%a�4%`5] 2@p�,T&���a����ii�ofJ=�s!�Ta)E� 1412.774�H6] A.Yu. Olshanskii��� "��$k2�pr�[�o.U�"Pzv. Akad. Nauk SSSR SMP . 44A@�8��H-�0�321!��7�rkq�Combin�"8�a�f: synta� sem9�c!��ger Mono�_in !���$201e� 8] Dmytro�-R 7�r���e�Z�:��nd &I ))�{<y, 279—296, Tr ��8., Birkhäuser/�$Basel AG,  �z%��9J��2�(�a� R���A9 i� -ez? Can� set.��. Ded a 17E��1�35��� L[20] Vladimir Shpilr*1UAlexa�TUshakovZ�om����*�.c kx� rypt)��X�&N��s!u(p. Sc. 3531���0�15��64� 3 �h John�1"�Q, F�of G-t�f. Arbore"��)�4 (Berkeley, CA) 8), �68�O� ci�A�nst. PubX , 1�$, New YorkG�9A�<22] Yan Wu, Xiao�0$Chen, Dist�ureath ��N�(. Chin. Ann��aqB 3)��45, 80!,�8�� 2�]�U����PARAMETRIC INFERENCE OF HIDDEN DISCRETE-TIME DIFFUSION PROCESSES BY DECONVOLUTION � T1512.08193v2 [] 19 Deca��6 SALIMA EL KOLEI AND FLORIAN PELGRIN A�.�8 stud� ara�ic�froachthidde�screte-h`DO�mod����p'��trQ}�mx�iz�-E��d�/vo��k�p jleaҫ estim n�=�2��!�(stochastic unnonK driftkif ��AO�g�i T" �c� �iFc����nr��te spac�A�. A�_���isFSŤ asymptH/�"_%� �or,�?�t�i2v\`�c��$On�dz�O,�o�� nume�)�Hgar6��%F�methods� p�w8(Monte Carlo ExX�)��M�$1�$Likelihood�!, BayeQ�s'� �~\1� voL%)�E��� ourH�!�Gut \�s�S �um ��EI?�o�>�d!s! �u�VA�?%��5-��o' 1�#-<� ��tA�/I�%G/� Ist���;�'MN\tun!�mk�e�% 1 I*;o�#�i(]mot���e"W <a�-Z%�i�y&-[��:  YPE�X3| εi (1) X�B = bθ0 (X�` + ση �,3(U݆es Y1 ,"�,Y�x�+u�r� vari!�st�P���Y�X�Yun R��o!Fy � i≥Eq�a�-�i�!f��aergodicA:�cA�%�d)�s�wo+sur~*�������io\��sa��#! aW be"soΘ GRp ��Bc��, akG4�O#upe�i dimes*al1��o�!O ��W���e��)�i"" r%��rJz�o=9P� 6�� .�3� inno��s (!�-�!)F�e���ip�n��t)J.p@Hk�buA�(i.i.d.)B ~�#�r+M�r.��A�%=hg gfi�2mȅQ�.gnisD/�~�p6��e!um9�l�e9mu*A6�"�s>3�d�?E:G�ynamic9m�Y�]�IN cipl�� ��R�g)*�a"@, . 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By �O�*� uni!��'6���q�b�Z7r�����(��6�� � N���"1:-*���5iK3%n�u. he U "Law`�Ln4�N=���l 2� 2)."bi�%rD� 12�s�a��� (A8)� !� 34>MI�t" }[�M�ldetai���e2�2.2. %"�T����dq�h �.d3<0s ��t%�&�b�+. B>z|�lx&in*R���. � �3��`� `nce-co A�LCLTE@����ٔ�,�� r� �h P� to [V]e���mY]� F*�eE[��e�t�,�\u��1���!�at: A1$*��Xi!rα- hE ��7Q k��e�7IW2��&� E4A8-��h�}�(F��a n.; esti�mator of θ0 which satisfies: √ L n(θbn − &8) → N (0, Σ($) . SketchL��proof. The asymptotic normality follows essentially from Central Limit Theorem for mixing processes (see [Jones, 2004]). Thanks to the consistency, the proof is based on a moment condition of the Jacobian vect)#Xthe function mθ (y) an ILlocal dominance condR�@ its Hessian matrix. For further details, see Appendix 5.2.3.  Tz%5hing corollary gives an expr_on!�� vari�-co z5�+1d2 for9practi�$implementa�: CxH1. Under our assump#s,Bpn{�is�|n by:   +∞ X 0 Ω0 (E] + 2 Qj4 = Vθ−1 Ω !2��j ;/, 0$j=2 with Be =.>��n h 0 i  4 E ϕ(Y2 )u∗∇θ lA Y1 )j�     0 o aK E b2�(X<+ σθ20 [�-� �  ���i�+j !w�.��j N��������. aiA�gradient�Tis taken at point θ =���;qc moreI�6�A�0BaLI� [V!��]j,k   1≤j,k≤r = 2 ∂!�  ,θkθj  F��. jS�P�!�S>�4 a��f64. 4  Applici�% CIR�kcess W�rsia�!'�/stochas��volati��Pmodel  Yi = Xi + εi�� Xi+1�(µ A�Xi )∆E�\ ∆Xi ηi+1 (7) whereC yls a log chi-squared distribu�+�8 ηi a gau�. ��>4is can be also�n aY0discrete vers�� so called!��t���� a� independA:0noise between%.4log-returns YiEl��=0Xi . HeAE�w����a��e thatH��1�7��reate�`@an zero. To ensur=��.�,_mak�e-M��j�f|: PARAMETRIC INFERENCE 7 2κθ ≥ 1%g<c := 2 > 0, 2 σ��(is known as�Fellerݻ(s�f@Cox et al., 1985]��� ie:Z�� Xicergodic�ρ-��. F)Dy��s�i��.  fθe�t!)prE�XA�gamma 2/�γ(a, c) �0Genon-Catalot�h99]). F 4.1 a := Minimum!$trast esti#  IA*!�as�I ,s b· , σ·��lre�S�eZ�O (x�� σ x ,�΁��w� � b�d8(1e� κ)xa� �θ,��,�x ∈ R∗+I�W(κ, µ�). 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Lu Chen,2���6��� 5. Hyperp��e�!Vgaussian!�]R���statist�)�2��6��iga:$. Yun-Nung ��Dilek Hakkani-Tür, Gokhan Tur, Jianfeng Gao)sLi DeA�i3�EY4memA��%%Y��� rry���Xmultiturn spoken langua�L nder�:�2���INTERSPEECH. Nils Dahlbäck, Arne Jönsson,%�`Lars Ahrenberg. 1993. Wiz�Dof oz studies: why4howv, of Intellig[ &� facF�Lucie Daubigney, Matthieu Geist, Senthilkumar C< ramoha �<Olivier PietquinE( 4. A�� prehensiv�N�*:^��oEbl. volume 6. Layla El Asri, R�XLaroche)�B���0��ask�le transfer��$reward inf\ce5T!xDMLIS. Yaakov Engel�05. A"� %�re� ��s� V. PhD�Hsis. Mehdi Fatemi, :��<Hannes Schulz, J He, a�$Kaheer Sul6���P�6� two-stA�' F�u���s.��� u�6� Ca� �� resl�AM Hee4on, Dongho KimAi$rtin Szumm`(Blaise Thom,@Pirros Tsiakoulis)�StYoum� 3. Pomdpb0�� r adap)|3 ext��d� �Sig7. Re-�s J��8Filip Jurcicek, � � Kai Yu)�>�� 1. O� T2�a��G��1~��laC*� w�human� ject ̐IEEE ASRU. Shun-Ichi Amari. 1998. Na� grado "5} % %��N> ��u)M,. MIT Press,q�10, p$251–276.FHe> 4. 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X{>UMMARY B�i"�|�s�?��V;ch�`�4����a��T �ler�)y �lV#>a>�sbVIN����f� cris���� �pry�i-}�J&  �a P& ���aVe�� � gniz:��a��c!of��5H�sa������ ��s:g<�-$ oadb��W4!C.�*�\ �:op�f�o:�6J�E�mmo��X��0 �Uas^pD2�� WU�� U�ies�C�-ƃ�.�B�s;*��� !"@f�c�uat i�s 0[�C .&��T*�Q�e�_H��d�b }�t�>utU�!h�1�6�L �*�3%lb <Na��i �W_e9�]/׈l}5� j!��,�I|ɫ�>r>Ż%C�� �(>�!���soɨ�a$(�� �pla��d�loyme�N %�BS at�s d�Iq.i&�o�X��$us��E�a�am~&��v]�9�dX6w1 uAEn e&��]7a�*!$���>i�p�ua;�� 9!% �Mr�"�n&Jr����Awa�� ƺ�t�f��i���:��e���)g�ia�M� matca|�I �"n@�&;�d!��0�,�  C�on�invite> qG�cw�*%�0a��B2ԯ [62Tx��'A��5e��,^�H��&/1�>x.�,*�Rg�e"�K�"т���d�HE��'er(s)EHbep�ck�p��&"P��o� [6V�64��?9,an be accoun�Fted for by circumscribing our unfaded interference model to the rest of �i&d, separately incorporating+\terms that correspond toD,rs whose fad6tis known. ACKNOWLEDGMENT Motiv Z�discussions with Prof. Jeffrey G. Andrews are g�fully ac\�ledged. The efficient editorial handl�Tby Dr. Bruno Clerckx a�:xcell:@feedback provided9$the review�are alsob��� A PPENDIX A C OMPUTATION OF Cexact For given {rk }k∈N0� H0 ,r� )` mutual information under#non-Ga!?�an z in (2) is   q −η I s0 ; P r0 H0 + z q% &  =h (64) P2-� − h>�s0 E:N5�T(z) (65) where we haveA3roduced�difE��t!�4entropy h(x) =|@E [log fx0 (x0 )]I*x0 = [<'(x)]T . Expect%,�s%�evaluaa7Dvia Monte-Carlo ov-JLrandom variables {sk2�{H , 31 A>averaged J8multiple realiz �of!� to obtainM%�5)I�(large-scaleatribu!� of/�,Eitst C̄I$�,� ^ed�b���{]o. War MIMOIsforegoa/compu)Dd involves channel matrices�8signal vectors,)�a2R� of a ,, x ∈ Cn besN�%�.�1�T ) =(%�yrB D ERIVuq (27) � SINRmuXby (3),   E log2 1 + #�|%$$∞ k=0 Z   *= Pn,�, > ν dν Z06Xe c = F A�dx g�xi h 0 (66a'7) cm*@(67) follows from!TU�%�ge y = ��(W�)%���CCDF F�H|{r (·) can k} be-�ed ase�e�( |H0 |2 > xI&� =P P%# 2+N r P�X|H | k 0 k=1 k " # η P6 -$ = E e−x�O( )Prk |Hk | +N0 /P ) {r k c �x)�  k !�VIη =e @ "q# Y}xE vp2� (68)9) �\� WbZ Y 1-�((r0 /rk )η4 (70) 5��8J�expone��diy�a)o5����9����y�!>(. In turn, }� B!fact �84��IID. }&�C.&�S��(43), (4!AND (5�Plugga�AU PDF �fby.�&(2�~4nto (42), s? Zm@�?a 0(1−sinc δ)!s0es /θ s? δ L C̄ ≈ C(θ) dθ + 8 δ+1 dθ. 2 θ0 1!�1)�� 2 Fa)�CE�asm��14i (29)��aboɈ,egrals yield%%�! �,* �Kively. RA�Ad�t�g�s��>���ifacilit�k�bD vok!=E1 a���i (a), ���D�et dt, in conjunca�X idAQtie�[65�$appropriatB.0s. Similarly,�TJ+�4!" �g� on�parts%I71) us�A�4[66, 2.325.6],� �7728.1]%a0 3.194.2���%�~ �ea)re2  claim� � A�!�<EFERENCES [1] J.*B , F. Bac� �i�OXR. K. Ganti, “A tract)Jach��ca�age�� ! H�uular networks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Nov. 2011. [2] B. Błaszczyszyn, M. K. Karray �,H. P. Keeler�Wireless��(ear Poisson& due�<strong shadowing�� �� L6��14,�8,�@4379–4390, Aug.�5. [3]:��N. Ross �A. Xia �hen do w:��X>���?!cP2014. [Online]. Avail!��: http://arxiv.org/abs/1411.3757 [4BDS. Buzzi, W. Choi,Hana%$A. Lozano, �CE.Soong �J.Zha “W $will 5G be�E<J. Select. Areas:V32)V�6)V<1065–1082, Jul%V4. [5]E�occardi,A�,W. Heath Jr.��(T. Marzetta �$P. PopovskI�Fivm rup��$ technolog��re�v�s  5GA� �M Mag.Q� ��2 �,74–80, Feb�46] M. Haenggi,!9&� :� O. Dousse �4M. Franceschetm�HStochastic geometrym�� graph�� ��analysi� de� �>s}�J. n�27)��7 �102aH1046, May 2009. [7]!u C. P�0 M. Za]�nE�)Mic�C�S�aq� fŐof��$rferers–�� I: I*�6Zf,error probab���y!�I�v��� �(2176–2186Y�00. [8] ——����- �I: ChP capacit)��i.���rum>��� Z�>��87�956���96�]N�GQNae�N��D. Cambridge, UK:  Univers��P���,��2. [10]��De�&W. ZhouU�u“�0Ginibre point��c��as a ��B�repulK5/� v���͑10!/121, Jane���11�5S. Gomez�fVasseur ergne,A�\Martins, L. Decreusefond �a�eI�HA case study on reg�L!?in�[� �[( deployment�9�iG. Lett���4i�421��24,2�12]��Guoe0.� “J%|spa�aQpropagi�%��]��q�in�c.iqGlobal T�� Conf.,!!)d ��6. [13%o. 2�.�� N. Jindal)aS. WebA primer!^��� յ�i^ ;1q �^��4��15� 163&��14��$S. DhillonŪ&i B� :� “ModeF��0of K-tier dow��<k heterogeneous j� z�30���3)�550–56�pr%��2!�5]� Mukherjee���D:� �!]2��Z5%kb�� vol.B���7&585, 2���6�Singh,� .�!�FnOfflo��n:��m�s: 1�Al�Q �d�R insight]:z}7M�2489 2497�E13.� �3�D�7ES<ElSawy, E. Hossa�H�.�R�8Q��F��A_8IcXcogni YZB| : A surve�f���Ss Tuts��152j99eDL019, Third Quarter 2% [18]D�H��� :��2 �out� ��� �5υ�Eu^�It11 ��P139� 1401:v�9F� �6� !��X>� q2�el6c ���sm antenna�� ^��� e@!zpp. 58�l593��y20nAsymptos ٍ gainEim�~�a4haLerize�2��$in generalY`qpB�MT ̡t�96!�97z ���21]!zD. Renz��P. Gua�*�"A q%�,system-level�*of upli>x���?)�iN-� b���F���Mp 2453� �4�Ju�%��2F��W. 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Cambridge, MA� : MIT Pre�02001, pp. 849�56. [2]!lSoltanolkotabi, E. Elhamifar)% E. Jcndè)+Rob�V�pace 9/%Ann. StaA�8., vol. 42, no.� �66�l699, 04 2014. [3] U. Luxburg%� A tuR1�oR�p kic� Compu�, {17 {�4)8395–416, Dec.!7. [4E+J. Smol�,I. R. Kondor��K" f:@�o~ .”�JAnn61Y 6 �E82 4 ory,�3. [5�D. SzlamE�Mage#�i)��R�CoifmA� “R6��o�! aphs���F-adap8 �sm�es%]J. Mach.�4�.�%�.-Y�9)Q<1711–1739, Jun%S8. [6]�hu�S. Nara�" P. F�� ard,a�Ortega � P. VAl0rgheynst, “+ emerg�ofield���M �5�: E)a� highd�57 al d�5$to netk)�l�r-� dom�$!  IEEE�5)�i�MagazineM�30Ip�3)83–98,A�!�7]�Buhlmanni��.�  de GeA]ѡ�High-D�/'�:�,s,�oryJ Appl%. �$er Publish!# Co., Inc.�1. [8E\ SandryhaiM�J.��F�(uraE�Discre�(�6y$ s: &�6�a-d!<� %<Tr?� �6=LMZ�6�.12)D(3042–3054Ec�e!M�3�9%MMilan�� 4ouS8jrn image&��:U%ins#nd�s,�* pr��theor�wal�B��Y�tQ�x106a"28, Jan�A 10] H.�aEgilmezqA.u “S���+(anomaly detE7� �Q�E6 wire�*sensorU���i��4)�2�� 6�Acous�[, Speech�F�4(ICASSP), May ��)�108�o 1089. [11:���,�H. Chao2 �B�q�*�S�I�$GBST: Sepae tAQ�D�s& .|2%\predic�� (�o�$p'�� 2016J:��IEE��i�(ICIP),��tD �237�237�2]�K.��%=6�Per./Md�ue�:-chan�!wavelet�" bank ��&3�d��� �Vn� ō��6���78A�27�Juim�2!��3�* Anis%� Gadd-�6��Effic�& �p�}selI� bandl| �e�&�W�s.�&� "-͔�L� V��=���4���1M�37%�378ů�lE�H6. [14] T. Hastie,�STibshira�f�J��ied��ŕ�lC,� �8��a,al�7�r��:%�� �/���i E Q�$on, 2nd ed�� , 20�E15]a$4S. Abu-Mostafa$don-Ismail�=$H.-T. Lin,鯡��F=�2 . AMLBook��%�6]��I��4J. D. Lafferty���f�"��i3�4�;�0> �nEu6% Nineteen>+ :�~N6 , �  ICML � 2.��D Francisco, CA, US organ Kau �n�ers��0�b�1a�32%�7B�E. Pavez)g6��=�ed under&[ %+�s�e e� aint)&A� Jour� of Se/ed Top� @=�y%M��M�11I�m�82�841, Se��� 18] X. DoA�$D. Thanou,�&� ��B� ��1�� ",� in��� �"�� 侺�2J (6160–6173� �w��89] V. Kalofolia� How� �lR "�)6y�0�i� 6�19>�:ArtqK�Ellige,y*� (AISTATS���.92�92�,20�,Segarq A. G| rqu" teo�$A. Ribeiro%��N� topology�j �G�X �Es:�� MeA Z�| s�sM��3I�)� 467e 836�21]��$Pasdeloup,!� Grip�� erci �Dapsto��M% Rabba Cha� �e"�'��^�N� %� ; I�/�� onar==f!� 9!� �!PP)"�V4 ��a�22]�zMeP9J~ vV� Causa�=�� of u`@�u���b�ѝW� :65 ��8I�207!�(2092, AprilA��3]�F�M_hnston��}LuE�On��3�!�2%ity� 0principal comn�_� in� �6н0y Amer�?y~al As�%�i�1048m�68a 693!��0e�4]� Ravikum4M. Wainwright,A�Yu�(G. Raskutti�� ��a. 8*�!imiz!�l1-pens log-� $rminant dince��EJ ronic..sEJ�o��5)�93�980\� 25EuFr"�&�!�R.2 � �&�,rsF.<�wdE!��J lasso�Bi�ic�<�9Ig�< 43!� 4��Jul"O26� ,Bıyıkoglu,a(Leydold)�Z|dl�G“ٮ�e��na���Le�'CV��he�� 1915EE��7%9% %-�G� ban�� “DN4 �f# manifold�� a�Bg)�M�12316��%�5��8f��.��K��n!!�!"u!�Ax��)%��R�-SV�� � 484�� .�29]aeeN����I4 ��.�e ���:�Ez�� guste&� 2017 ��N� on ��rch^en 653�653A130��M. 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Iź easy1�Y =� grid:��pro@\s a good enough accuracyI�Z� ��. adepend.Q�i66b�de!��dlor1��21�Pec�number!�.5 . 17%B� Sherwood: a". 18.�� 7: I.Pe: left�Zb, righ #Z�a 8: Effect�x �`� `)�!� restM�analyzA+" evM��!�local� cknB �� [ a�lm%� ubes)a2� - f'thCm�ub� rface��� ��� he2/�m �angle θU�i1��9 �value θ�U� y�"� leaECed� � �, �as] = π.=�� �$�r� : l:�� ��s �1third (�A�,let) 26 θ9� 9: L%p�20VM =�9a � 3-rd��NL� 2m , ��!+Fb20a�VK 9 hobserve a higher growth rat5)%Nm�2��i� �̉�A#=�Next,��q Zi�� maximum �1�|(takes place �� .���zb�:a�is � �&midpoine�+%MM/ . At%ʼn�-� �)-� =-� �endE��b�@stant. 27 4.3.�O{ bolic"F IiX��r� ase, both� PF8� ("� > 0)Š!:�n� �o���u�fUn��s�X �problem-f new�� �{� A, ��)%Don� ar. ToK \ve it, Newton’s method-�ied. 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Ad metric( is donevindic% l:��!�:��s&� �� lete�R�m��sf�"( � 2� phenYon�invX�g numer��ly�emphasii�Jm7�U�.���t .9 . Acknowl��<�s� work>Pfourth author was sup�Ĺ��P"�,Russian Fedeo  Ge�_0 (# 14.Y26.31{ 3). ReE�tces [1] W. M. Kays, A. L. Lond9�C�xct Heat Exchangers, McGraw-Hill� D York, 1964. [2] THBergmanW8S. Lavine, F. P�$cropera, D DeWitt, F� �als!j~A0�M �T�Ӏfer, John Wiley & Sons, 2011. [3]�$Žukauska�dva�A�QH�I 8 (1972) 93–160. [4] C. Iwaki, K. H. Cheong, H. Monji, G. Matsui, Exper�y��xFluids 37 (2004) 350–363. [5]! S. Paul,!{$F. Tachie, J. Ormist!�Interne�al Jourof � and l F^28 p7) 44� 45p�6pB. Beale%mB. SpalU!GUL�sW Structq�3!"99) 72!#75!�(7] Y. Q. Wa_!L.!s Penn!�S.6���Nqb �1|,: Part A: Ap���s 3 �<0) 819–845. [8%�M.!/(El-ShabouryF4Zm��,m A: 2m��4 m 5) 9l�19 [9%4JayavelbTiwari,f�v�M��Ak &)Y)�19%��9Ap!�949. [10%O,T. K. Gowda,%�. VePatnaik,a9�A%kNarayanaE�N. Seet mu, �6>��1998) 4!�5!l11]!g(Zdravistch,a A. Fletch!��MAQ hnia�� 2�5Ea,5) 717–733��A [12]k(N. Dhaubhad!�J.ReddyE�(P. Telionis^��� F��i��7�87) 1325� 342!��LS.�jN�M%�$Bassiouny,��m�> Engineer����P�! ing: E@ nsif�"!&�3I0) A �1aZ14��A. Kh�=,J. R. Culham�0(M. Yovanovi!�^�� A}�29 4 s6) 48E� 4838�5]A~�Lf�Yeg Lin,a� Zou,Liu^_��I]� ��31A�$10) 32–4�6]!�BenarjiEZ Bala �$. Venkates�^���4Y08) 44!�46��17�%HorvateBMavko,}�P���6�49�� 6) 6�71e�8e����P�� JackE��$Thermophys� A 2v� 2�!53�54��19�8�A�hseen%�Ishak M. Rah�PRenew ]Sus� @Energy Reviews 43!'15) 36��38��20]!��D�ndau, E�$fshitz,)� Me��hics, Pergamon Press, Oxford��87��1]��Li,!� G. D��J��a/uip7ChJ*Sci�60%u5) 183�184^2]��JA��u�kHigh Tem<�� OY%%Corro A�(Metals, Els!$r, AmsterdA� 2016�3]�l�E�al�Grove2�7 ed P-�36�3�6!\77��77aH 24] Z. Xu��!� osso�F�5ruemm�8 ]55 ` 135%� 1) 024108��– %�5�Geuza] (J.-F. Remac��Vfor}ͱ in2��7�(�9��0�`1331. doi:10.1002/nme.257��26]a$M. Gresho,��L. San�7� A>��a^ �F� e EM� �, Volume� IsotaRal���A�,���e�� iche!� �0E��7%Tayloa�. 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REFERENCES [1] G.Victo Sudha|4Pe And Dr. V.Cyril Raj��RqXw On F/A�Sk��T"�"?X Imp�/Of Svm �>�1�U�.��-a��7aցI19] */�*nJYL, VXOfF.�H &2XSur�6(Ijcses)�W$.2, No.3,2ma"�3, D�����"y-4M� ��uI(�M"bi� Ap* `,Vol. 37, pp.`31�$99. Djn7N8“�0��!���� *V7���F � ”,�U9. K.�\Yeung*� ( W.L. Ruzzo� Principal�f;6j�]wE�:xk�OQ[ U�E e~Y. 17 � 763-774�1. ^�9��A�9=!��m+%�,�a&DN.�9e��BMC Bio"� \2007. "�9,; Kun Huang;"5�I�Fr�ft Co-��N}8to Id�9fy%���3�Bg�A�}9 �2��6� J�'Con�d� QcJCBS.)Y�2IV 428 �"43)[9. M9�S�MBing-B���ach%FDe/9�� �q��R29�ca� , 10th mb6�2���Dlligent Systems De%&12( ISDA)E533-538A 10. 9�#��S�Eht%���kY !X Pa��n�oghHonm��9e�481$ 1491v06.� 9�a��S�h�+�Ph^�a�)6�&% "�C�� } �L ISCCC-2009, vol.1, ��>�6�A��A�� 9�:�5\����.)'59%�$1425_1432 �-0.�-�-� �.P.K�8b=�&(�-5J��JrsO ��i1� � 58960�0[B�BSa9]*�!�2!���%!a New Mate(4I� 1_12E^�8��8�nu�on �� Ś�8i�Nu�i��:h%�X]�ACSECS 2a(rt II, CCIS%�180%� 57�b589� 7 . Xiaox�;c Arun4<na)(Ad�m Mond�f “A�_q% �g�V�a���m&Qd!.8��N�H6:76/1471-2105/6/76�85. Abdul Nazeer�d<A, Sebastian.M.P%q�I�H�� "q �aReXFn&M �2e�e4��SWorld 6(en&iei�&�1%�1-3�49. http://www./ �i. 0.org/cgi-bin/��/!'aH.cgi/. Ferenc Ková��(Csaba Legá�e4Attila Babos ,*e�V*! Me� �p� &� �2003. MpRlkidi\eBat�)�k�7(nd M. Vazir7p�f“On�!pjR!:`�*Ub�n�R� .�3�^, !9 17�  2!<,pp. 107-145,��1. �G��arXiv:1609.03251v1 [] 12 Sep 2016 Postp&#Di �ve2_ly Priv�$��0 Jaewoo Lee Kj St"& �, �ii A 16 � JLEE @ CSE . PSU . EDU Daniel Kifer�W�DKIFERNY�&_�s>Y �s�dif}�t�a�p�cy runA fixed* 0�i"�5�# -Irns s��"� �o�?A�ay�mH^ �med��(. How�51$*D� rel'Ye} 1��a��l�I�MB from �Phe�.�5= judg�D��p�&[%d�Xos.>5Lz seek�-*� � �q�b�.corpoG]ng�&��o�M� 6 � �1h�I�w W��d� ]an1.�b� , fuA� util�G�e2�E�EJC�!Y �is crucACԀ�s H. Spse_�0�a-pl.��A)>)�&+ K(D, θt�� ) T�A a loopAL re�Zb��T�!�fi8IQ�D �X NF%�iB9A� ��θt =>u���2�� YyHtth1k=U�A�>��Ae�m!Ine)7%�u� , inAvcl�(^<�1I�reg��,g�b�M�L��1; )#Dmiz'a�=*A5h�9G t+1 M;} �osiAcorem (D & Ro 201 �i�UK s�1�f�K T -Nje�}G A be�Bs 20�lyQ� . 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M�E'�O"*F4 Research 32 (t 413–424:��$Vieille, N ��2u play }a bias+in?!��<0nd Economic B��41 o4206–226. Han� S a�3��"�3-sS$rum methodYR�%w�5�@-x� -Verlag Berlin Heidelberg. Hubáček, P., Naor�� Ullm�M 6. W�#;9li>���u�in 6W5�?�@q�B�|Systems 59 (4), 722–746. KapurE�!iBaciua�, Kesav� H. Ke��9�j�Qin' .  meas-f�I.�� ����SM� 26 (��)(2. Kocaoglu)Dimakisa�8 G., VishwanathaL, H*&bi,�M20!/i3��ausal���^� 611.04035�*z7 Kovacevic �Stanoj ��Senk, VE.a�� harde[&Q��� A�����: IYp1�4Workshop (ITW)�i2 IEEE.,  �,�e 51!�51!�ovaevi:���.��5.��1of�pl��2�n CEB�~24��69�182. Nara]�(�4.e���Me^1ism De�H��4.�ldI tificPshE��FEmaS EquilibrikBin;$n n-personO�Py76�"]academ�0�sIys 3Mz48�y�9��ye{��Okada, D�00*O�o��boIh�d1E ���z� �z30�z�2p247. Nie,A�M�Y02. A�atrղ to myA)�!Qa2,~9W��to�8 m)lcs�mONot:/De�_�!�physics,6 8 Queensland, Au�F�l�)b9�,ūf9��u=X-9':� AJ*� .�Q`9� .�06 (0� X7. URL http://www.world%�I-�com/doi/abs/10.1142/S0219749908003256 Shor, P. W.A�04�U�`� �i7queS ���.��Z�y# mmun-�.�� al P)_ 246 (d45�� 72. Slepi�SA_ WolfA� 73. No�9�co� !�D<͈D՜�+a�$EEE Transa��s� .��M �1��47�o(480. Srikan�PH ��, Roeɞ20�. MinMax����, pp. 23�%0251. Watanabe��198��atA recogn /s a)��:� . 4�R413 (5� <81–387. 70 ��̃��C,�6������A��������1 Mixed Strategy May Outperform Pure�: An Initial Study Jun He, Wei Hou, Hongbin Dong, Feidu"� arXiv:1303.3154v3 [] 22 Apr 2014 Abstract A pure s��metaheuristic is one that applies the same search2`hod at each generation of-4algorithm. A m%�s o� fo�$selects a 6h�probabil� ally from'�tr [�F��h. For example, a classical ����,6��mut � with�Lty 0.9 and crossoverN#�,1, belong to:� 5p<s. A (1+1) evolu!Fary� using�but noz�i!1j�. The! pose!/Xthis paper is to compar!�e M�,ance between>���jp��s q,main results v e current }�are summarised as follows. (1) We construct two novel>��V5Kr solv!<<the 0-1 knapsack%�@lem. 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S\E�i)a�ex�A^ut�al9Xis usuAV4 more challengE�e|whe R.Y<�n! �n1# �Ter(s) (see [1, 4, 34])A=�%�+ly evidA�B��� ��ics} reby2���ak�place9Tgiven geometric domainE group!�(autonomous a�}�ngm�4e ultimate goa�]to de�!!�u� so asac!i lishE4require��sa�AH)% (1xlo�#a targe%�1Y0a priori posi�.�)A�le at Mame�� obey�theA�=�A�geograph�~ onstraint �input �A4 figummua��l�6��task in��minimum�sib�mou���f � [10]Q� ha�',long history%kre!�extens�a�varA�re-3�s�al��(s have beenA�posed &inv�O�ge�M[mathemat%%theore !��u���s�ue liter��Y�( emphasis ovbabil4 �[34], g%�d appl� ons [!cop�NHrobbers [11], class�`pursuit and evasion [32],ipr�Y as r�stoM��t! ng [U �aaph [3!mani� . A surve�tQ ;*������f�h!p [14]��2�- 2�, ers wan] cap�m evad!who try�avoid!,. 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Wh�rpromi%��e#Z�I"|'ha��en �Y �6�, $^O�m:4�������qA:��ann�assum�����O)eL ')1��0 a�1ed�u*�+!�^�a�pI���fE� ��5� ��vI��i"\+�4���A"u^"�A�D�A�T�!Zour�R�I�[apE+we aima�].������W3an�k�iH�opeN��6E��+qui�n/��.��� B�� � its 1,2,3��"i��!g�D��t~ �@��Q�I*[O�S�ce,,H�G&^\Pennsylvania Philadelphi�KA 191TUSA {s� ,x� z,k� D}@seas.upenn.edu SV�u��mxs ARL MAST-CTA W911NF-08-2-0004�ARL R1016!�+UWA�&Kn�d��. 1O8:ah�oTA���tI>}� . n�;�bѪ�R|)a�du�����6H�.��{�E .(�-�� . 1)V {  a nove�lAus-lik�q?;thVI. >q. 2:Q�*� &��!!�}�\t te-of-artJ,�  �< 3\Z� 2� 6(�a� m;ge,�-�qA��l�i� �,��C��-fxA�guapee-jS�q. 4�� >� Q1M�-O�d �a�Tu ��F&Aw*� !�iG synt's��R%u%#)L�%A��?!o�a� !�’ȿ�,L+]# brief'iewJ�� 23�I it��:��aP�to� ���p�ifzV$ es�u toY/ %�� * �p���6rigor�$�!�D�U%�0 topiA���z,wo5�" ��@2en����s V�VI�� �:. "�v=��l*) �NQ�T VII. II. RELATED WORK�&FQQ = extM�@�agOet�@��8��pp"�Ti1E<, Zach"4 37] s6an-I!�` �-%��r� �s�P��)��$6�#tify un!�P.geo�@^�\)wnK_��?�;jHv�m.�� .� �iA�� � &�%. s. Nguyen��[adJE� \��}ng�$�-�C�"Y � �o�� �AY u�A��s� �.�5� � �cr�of k�njpl�m!y�yl �%�� V � �c���Y���y. �V, fV�����(�u ���ph�pe�'z�im!�� %T G��peni!8V���� &\� opt~Be�Z5��U�h �'�c�^� UO"d ��l7CtF���t"���4���`�pJ� ��a� an i4�9�. �OeadBA5z><mi�" match�L[15!h218] �l%:�MYN~���s�) noisyc2!�� y���!/�@ quadc#�c7\gerA��S!�a[�x�=�gXU!�ed Rayl4"60�G.=%^�e�\���oA� �<� �4% , Hua�lnd Guiba'E�4�B�C�)Q�6]W W�l��v1*%�QA��*� "� 󹁀ve���)8�'�#.t��E�P���x)E�.�����by 8G�Fitq![�m���\��W. %IE�L�T=!Mx.�more ef� &`-� se�k�� d� x * j.A�P�lY^2/�B&t�!�M� ed j��o�Z �e"JI� ?k�n2[�y�a�[�eF�rY�ng�����lseݥ 5?��e�f�,�lޱE��!*���X ultaM� L* u And"D0(SLAM)j�2� ��/�e4,�� not �/A�o Nea% �Na bor (NN)� M�"8Likelihood (ML).��S�, [Y, Itea��vE[os�7�P!L (ICP)Cs8, RANSAC [8], J� atiQvu��nd�X,nd (JCBB) [2�v��]Sub�^0 (MCS) [3], Rt��F� e S!t(RF�3�HaOm�!U�iA�.��F��j1�UǡJ� 6�XI��m�3>�  ��ei�)inϰL fash�y�sly��AX>T� t&�a���lM��'[7!��9�^oradem�2�m �B2gv [16]. C!�DM�4q��& � Arag�0�1] $#Y�o ʭ����P.m�/"J1�@ion&�~ud.@��y� olu09�a��eF}�&.5Dor "� 8�� HPRELIMINARIES, NOTA( AND DEFINIS �Uy�Zry�W|Hub4�Ow-$�e0 fact�/I� �y� ���n� th"' M��!��r�  t���� text���0A 24]. A'In�eA!�s� y a zis`����A�( G = (V, E)� �,V = {1, 2, . , n}?�%�Ip>a�$E ⊆ [V]2 &� &edgtbE de�/6 � un�E�ejvirhs-A�|� 2�� Nim�� ex iL<T!�W�Vv� TNi = {j ∈ V | {i, j}E}. A�lE��s\�(ce i0 , i1 9�iY �H|%�� {ik−4ik `e a�k = 1N�'9�co��ed&H�re�th"�+i=��1~ . Gi�-�� .�#KadjaceDB4A�7by  1,�., [A(G)]ij = X0,F�f � � �d�^"�4∆(G�@!"�4 p9�[ )]i!�|Ni |Qo |·|2 cardz}k�aAtfF�di~�� 6�I�V ×V��w�3a4I5A , w)?1-Z6�EH0 w :S�� R+ h�e9s� -[]Fi�>�w(j, i)%� I�2�2) 0, ^>%� Intu�tly95�> 0!�ID�W�m: S �f� AC ex j� �i ��j6j.���}a� NA . X���61din�;(= j∈Ni AY�1!QA)�ּ (.�-r�M5A'LB�r� Z*)��a:���b4any�!��i�U�l���out-bran��t��ha-�?ex!�镁mE&Y8 %(�h��� "�F\3�b��,�!]bal�L�� in. P1�1�� ��-��dX5�=(= (i,j)∈EM�ji��./��O�����Fx�0i \�X%%"s u$o��/I�! � be9{unOBstuyGE� S La��j�L��N �� �=�� − �+ (4) By�e�,A1 P=� on n5�� !u�ud-!-9��i��U(�e� �o��s �8��4бy�c� �l, ��<%96<��by . F �= (I + ��)���) (5) �V�t" !�M�] Per�s� s %�%�kpr�kU*d\w"��5�>�{�r�ed dynam�>� s [4 17], [�nA2�i|��b"�T(! A�A�ex.0Dj in�>vX�s n�of��kov�)�H[2o� Tdneg�y�s�� ��x!�*J"!�ll ���su ]rei� �1I��9"�r��ρ(A)��a.N�%Sx A�iFto (��San.ofPM���AA� l ex&�O!5K. i(k→∞ Ak ne4� ����1�2{�ano:"�!� irre��C���;T"� �[{z ���l�m .C�=s-%>�r�P�b� ��%*>��x�modulu�m^�Z4$�x� �:��>6%��V�$EO3�qc߉"9 EU��0 )�J U > �cu�nd^��e����9�c�ve8��t�is�a rsfW`,q��y���t�3́�ure0�McoW�8 �mt1Ab�# Y�te�� ���%��cr &6D !\AB(. . Let [n] B� �� some X] � }B��n) V π :D� L= �v�RAG!� A@�i�'�v�s% �8%�9a�s a��),!%O, ter��� ym��3 Sn �W�� �S�"�� ed 1a n × n.��q�Π.%5 0π(j) = i [Π0 �6� {� or���i��(ly Πej = e < ej!=�jtv3non��&isp�����!�\ �sFUon � g �� d(π� π2 �d(e, π1���@hΠ*(Π2 i (7) .���� A, B� $tr(AT B), � �*tyo�rE�#E��II�A =��s�Eπ2%!&�~��� &� �K=�!"�y��&dFasB&�;5[�9�yB��+!5b� slI[ ab5of������eA%I_ m.XΠ��a�>_-�.s��C�)� "�^s R�.u0� ��ro��*� ���%0ARan, a; u�:�protocoF"u *�aFr $de4Y�aA�?��#� , gg�t�H-�;T�Ǎ�uA�ɞL�i>'ig�V,�r� �r��P�et xi (t� �RQ�� !�� i"$im$� �O�'5Yen%���s�by X l4 + 1) = aij xj} (8)� ∪i P mE%≥ 0A� j�=��A popu��v��t%_!��(-onverg>]G�8�� ���.!�iw~� G!�� �, 0)�b! x(�� � �� )x(t� 9)�x = [x�(xn ]T�( 0 <  < 1/�� *�X. IV. PROBLEM FORMALIZAc&R� eUA�P%�2�!$� t >J>,�a�%6$^re ۈ�.+��m�N�s�iin�Aӫ�&�%�&R '>meras �&�a scen!w�]t.U" ?m �*� x! �Y��%lyI��a�W < a�� .Bq�o�?e(A(�[ +  encoA� i��Q.�A�t��*L��VR/6 �(Niy�E\ }C%�A &{v�i��j ���2!�"�* πij�U������"�:5�E�0(l���ky �lth-��` ��f-�- k.,�� �� ,. Obs7- gWN����ij�� �D*�a �=� ◦ πj�}a�A�π�,� �^d �/��� E )<�s� �g0 "�, ��“unm'��M��sc)7=� s [6� 39|Q)-! alog"�k�bt �~�][Fspa��in 1 A&^ )�� �G��R� ��p ρ : GE GL(n) �osf k ρ(g1 g� �)H2 ). S1 S2 S3 12 V�� j�Fig. 2"Hhi{n =u@i��S��S2 , S3�*a��m%�t#\�Jop:��� F�Bottom:.�F'�)  π12M)�2�A��3�πi2. 6��#�s�fa� π eyF the,� �gy wO�, |I�B��Q~ e ijN}G% >� �.P �j�*�b � �U�o�e�Π] ρ(a �)^�2� v�����a"A� D�VD , EwD &��� :� �m����dgS���kA����*�if ��!]kl��ٙg! [u�o�y# al [Π)W@�. �F�3��\���i�ofY}cy. D� 4.1 (H �3cy)�z�YZ��{A� ij }&��X&�!if QU�� ej��k�� 0) {!�}ni=1 �'� >)�I�� �2, k ���Im� ���e0��o�� R�� J�� �J� ∀!�1���d�B.�Nbt�,e m��$�B���g�+S_�+�s:��2=�F3): R N��,�1n� π Ŋ�,*�%��!�)���%72!882) Remark 1: U���� �cŎ$���ghtR  b�4��&h�I� YQ� �!(12) e$eo�r���"�1# loo<v3nU����)��m�1�s�/֞*6k�?cr{&�, V. DISTRIBU * AVERAGING� �O�y�n���u*_ ��a  Supdn�� U��a�S2�(veG&ntu� �a� �xP biF7!xG����(%I(t h���"$e �Zwa�%llI ��; z�rS�� y1� �,_Z�  �*lu.\�t��u1���b�f���sta4�ncQVQR,4or�,eVe  q� �2 lax%u�a�3nd �Z���s�(s*����T!o�i��p�hi��4%x hul�T!��m × mRZ���x&Q�62�f���.�!"c6�"�3;4&w�wE]*��fy ��I�� ;g: X  1ɾΠ ��� + Π (13) 4�| /� �Π_ΠTx ��ΠTc%�.y�� X� k) cuF �r�y[iΠ&�F (D)�14"��D!�!zB�W�� <(��� ��5�Y�cMށ�*�M�=, �Aw(�on.`��ks Π(0 a�s)�Les _��Q� &�.( V-B. After�.��of�sY!;X!�ret�n� � Q ��ol� !=�3m'�,�L5byA ,� i �+Z!� (15) ݰ� A%6�m8m�00B��)��XΠu�I !W�*S_��H"ʇ"I� ��!�O(m3 ) y Ŷ2:oB�` 7�+-<�e>��4�sd߁L�$`�U!! i.e.!� Y�! e2"wFV� ( U=Π}N (16��7) uZ�$3: (Intrin#�ambigL�) �{W� %�(Sm )n<��a�]���t�A%��nE8Π0<Sm , P T�A�aN�l��qF�����t6��A!��X=e|f��ro}�l*m* [30�zmo�:��V�,�fcan fi�)m���o8��ap-ɢby-�i� �AG s��F.:�� � outgoing & A�X�kinUA�= �0A � ���t\!���+aRneces�;�6*� E��w��l�97�oBas60I�q�i�G�~!u=4: (Eq��c��!��eN�)�8e � � a�[ Πi0 Π�=&�` &v ���a3 �w(���ab j0 n�%��sE�0 }i=.� .w��nA>�bles a��0�8Π−1 i0 Πi ,t we obtain X  1 Π0j (t) (18)�i + 0 + 1) = |Ni | � j∈Ni which is a component-wise Vicsek model [17], [32]. B. Properties First of all, as the sets of stochastic and doubly stochastic matrices are convex and thus, closed under convex combinations, we naturally have the following lemma. e ij and Πi (0) are stochastic then, Π%84 Lemma 5.1: If� Π e ij�(Πi (0) is � for*Pt ≥ 0. Similarly, iEareF6~�!�dou6(_� _ Next,A ,show that inJ8 noiseless case!��tocol (13) with a distinguished vertex %rges toE�nsistent solution under mild conidis o zLsensor graph. To pro%�(is, we need�:��:5r2: Given�H G �conA�A�`rooted-out branching tree%hasatj�matrix F (G) as defined in (5) satisfies: (a) ρ(*,) = 1, (b) 1!�,an algebraicAjT simple √ eigenvaluea?� %f$correspond� '$ector 1/ nEK(c)�limit <exists is g%by lim !�k�HcT , k→∞ (19)a�ere cI�A cT 1/. A!�of��lM�42 can be foundA>8Appendix IX-A. Ec!� presAthe oremIQ0nc�PrMi13EA cYAlabel!`from arbitrary initializaAI. � th i5.3! ��eB���B�(heavily rel��on�. TKe��.� G�6_ out Y^anI� pair�associ��s��uv�,�i!ensus!}i�E�N�!2�v}�set-hq�%H s up%b4 global permut��,i.isE1���tA�(Πi0 Π0 tU520U5�{ }ni=I��q� � {�(�A�ect��)%Π0!�a+5��0. Furthermore� to�W�|w^�enb= ΠT1��1��$. However,A�@general���,Z� will!l!�)�. Ta=�f�we�Uuld!�ve! %�A��AassumA�perfectU . We�izeY�� �&���4of interest. Ca-�]�����Dn n !$ices A�m < nJ?!)��Tonly outgoing edges. A�a�at�R!:y non-N��re��@a (directed) pathm�(t least oneJ��exe{E�e succee� ���ides us �!� of F (D).�4:!����D.�!�6� (���D.�W has 1�an����!�� ��E�tgeometric multiplicities equala�� number ofJ!��,���iA&ymptot�GUZ�r a�T0form   Im 0e����e (21)��F21 0N��4a�b94C. An immediatE� sequE�of-��5 E������%� 5.5�Y6�m�`^.a*� a ex afM a"�ide���s��$}(i,j)∈E%��͌� I �o)���of iQ�n�+!J�A�DRemark 5: Although�� !�(not guarant �o���bQP true�� )��l�n�,ARis�C<ified experiment� (see Sec�[ VIIlm�8moderate levels�S%�:~�� �ill recovered. VI. DISTRIBUTED ORTHOGONAL ITERATION I!{> ��,�X ��t!�ecentr���� mple��aIA�s�d��metho���posed by Pachauri et al. [28]. First,�briefvie! �=inAfcep�X 3BaRI( discussion!v1<IVE���-��or data.�� N �c��a��Z llow�'optim���(blem: X min�<e d(e πij , πi ◦ πj−1 ) (22) π1 ,π2 ,...,πn ∈Sm U� � @equivalent to max f Π1 ,Π EΠnEX i0Πj ) tr(ΠTi� (23)2e��I!� e ab���ul%�, eachkA��a����omak��he1 |�E��iA ctable. 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Wi/t lzof"5tyi'su�2�'A1E�*mm}K9A6�2on��E� z�t"m,s� R1 0a#�G!�m (29) D1F22 �)a.��,u� by&= induK �: Xm 0 k[ 21,k X(3n5�k��� w�,,k+  ,k +3F21� �>��(j�3is �3-co�to some:-!^exAb5�aE�1�k�  l� enough�r�� �yj 4 k  4"� ��E!W6& �0 �%,ctly k insid� �eB? i�.� 22�*A�� R EFERENCES [1] Rosario Aragues, Eduardo Montijano, � Carlos S&� n7� >G�d4�-� system��&munD�.� �R�ics: Sci� x�S >�6t;�97–104, 2011. [2] Søren Asmussen. Applied �Lque��v�-� Rringer t& B�� �M�3i@08. [3] Tim Baile O�E-*0Nebot. Locali�i1E�-�- enviroks.��(autonomous -*<, 37(4):261–28a`00� 4] D;,ri P Bertsekc\nd John N Tsitsiklis. Pa(elg�9(� ( H0�:O^. s,1 23����cp ll E)0�wood Cliffs, NJ, 1989. [5] Paul J Bes u8Neil D McKay. M�2�reg�(" 3-d shape6  -DL [=�ay%Q$586–606.�.�)�oSociet�  OpAK� Photonics�892. [6] Yuxin C�� Le�=as Guib!PQix�Huang�,ar-"&� ol0 *vi:}?�r1��:��Con�ce�;Ma�e Lear�Ao014. [7] Alexa��CunLham, Kai M Wurm, Wol  Burgardi��F� DellaertR:�l!!p9*A�� smoot�� mapp��wq�#� .�>��q�B Auto�' (ICRA)�2 IEEEb on1� 1093a�100. 5 @$. [8] Mart(, Fischlers$Robert C B�2a] ando� mp�2= �0aradigmE��5�)1��&��� �e+ and a�mav cart��y�.���@the ACM, 24(6):38a�395, 198a��9a��e� �>Fox, Jonathan Ko, Kurt Konolige, Benson Limketkai, Dirk Schulz,�#(jamin Stewa!��D=�%Ʃ� expl�)���-�a��ing�)�$94(7):1325!�339!�L06. [10] Chris Godsii�,Gordon F Roy�4�A@5��y�e 207����N�13s81] Gene H Golub�, Charles F VPoan. Mi ��s, ��,3. JHU Press��1Ab# �Har�a Mike!S phenW$P�bA� C#%�$f�@�.��Alvey/�o�-m�� 15I�( 50. Citese�198�j13� ger A Hor3)��R��so�A�T. 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This is only possible if both the second and�third row of J H̃ are zero. So M has size 2,6$claims (c)�(d) follow. Lemma 4.5. Let n = 4,  x1 x3 + cx2 x4   3 − x1{8=   1 x231D x24 2 2 1 2 c 2 208+ 2 x2   ��� x3 b−x4 �Z40 x1 and cx4,0 cLx1 x2 XC1 bDcx4  0 as in l�P3.7 (with c 6= 0).  !PM ∈ Mat4,4 (K), suc!�$at deg det-t�+, �� 2!�en!�`re exists a translation GF  %9 G(x)�%�M�x{K 4#4In particular,:x��=:�Lx = 0. Proof. Since� quDKA/ det(%^+M ) isE6 , we dedu5� &0) = 0. By way@$completing_�s`esA0can choose a 2��9C� A�linear� F :=!((G−1 (x))%�ofp formE�AEa1IW�bAyAxM��dE�AN�aMy�bAz"2 E�d2 EA�A� � a3 P�3A�A5c4 0�4A� Noti9#Q F M Look!at�,coefficients� x31 , x323 ,e�x34 of!� J F %Jse!�at b3 =�= d4 = c0.zi� x2% �,�a� , x2� r! �4�I�Bu����d�a�c0. ~��u�4l!� u�u�3bu� b2��a�d0. So F��trivial.< ΁����Fq= . HeA�H̃(GibF ��a^ ,� �ede� last �s from!!i.�)i`e_�4theorem 4.1. F+[dB4, T 3.2], itO�t!�(1E�8satisfied if rk�OQCSo assumM� = 3��na�ag��� caseA_aZ�$3.1. • Ha8��yiB#��!== SH(S!D 1 x) hŌa�(first 3 rowf�0̃ may be non�u Ii� leada\principal minor matrix N��s��E ���@similar over K to�@ iang�� >�,� n so2 ; tsel��65�N"$not 21 .^�� ^^�-��4.2F��N�NL� �)_6�0 f 0�b  �S(4.3) 0!pb 0 wh�5�f� �b��(independentQ��żK[ic5 , .P, xn ]. Consequently�EA(���S�M%��:6��,5�� V�c-�izAz�of -�isQ�!� . IfA�negatA���a2�columnJ: {,replace b by��3�f !�t�we get�(  0 x5 )�x4 %x5%��0��0 WaKn eve���SٸT���E�� 6�as above� (2)M)e�4.1!�%��Ta�A 1 . aZwe� H̃2��0mallBm determina�wi,become e�$ On accoun[Dru,  �1��.3�s permut�m� V�mFproposi� 4.6 belowE�infer� x + HaTtam� chaa��>�673.1 or!Zin>S�2�����T)IH(T��A�����aT...,xn!aE�y���4in pairs. Supp�i&��R �2�Z�%� TM�}��T]n�ř� J�� may .�݋.�>�v�� ���2A�I is nilpot��as wellBK.� ���M8%N~� E4Corollary 1.4]E>.� ��Z� So wi�.oMlowA��|�n�>isy�4. 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[dB1] Michiel de Bondt.<ieu�space! co�* ?s= Mat�9@. arXiv:1310.7843j3. A��2Rk��R%o�s4�HJ�K(tH)b$�E�c�S�cnY�g��2�t 501.06046u�F�#Ru��C�5z�kelleH?�4ver�<T5� ��6_975 ��6 ��4R_��Q"�)=���3@jacobian rank two�d 0579�dlDru] Ludwik M. Drużkowski�u JO�2ectur�qbe o5o=��t%. J. P3Appl. 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Tarditi, G. Morrisett, P. Cheng, C. Stone, R. Harper, and P. Lee. TIL: a type-directed optimizing compiler for ML. In Proceedings - . 1996� on2�@ language design � implement%<0, PLDI ’96,)8181–192, New :r�.�\. T. Terauchi. Dependent�$s from cou!�exau�s^��37!�nnualZ1�D-SIGACT Symposium �incipleEPr��L �s, POPL�10�19�30�� :�� 2010 �DS. Thatte. Quasi-s!(�c�ing^���1�Y� � sf��]�5�s, ��9�367A�81�J��8The Coq develop!� team�e coqs8of assistant req4ma!|!�tchnical report, 2012. N. VazouE� M. RondonI�@R. Jhala. AbstracYinEd!8R�� a�022nd European]�)�J�E�PSystems, ESOP’13, pA�20!�\228, Berlin, Heidelberg,!�p3. Springer-Verlag. P. Wadler] R. B. Fin,. Well-typed!>aXHs can’t be blamed>� m� 18th�:�M mingY�� �L: Held as 276 Part� JointY�C���s!9TheoryL�P!�ice9DSoftware, ETAPS 20�!Ca) %De��6^A09JA G. WinskeAADhe formal semantice�R� : an�� rodu��d. MIT Press, Cambridge, MA��81993. R. Wolff,!�(Garcia, É���oI�<J. Aldrich. Grad�]!�a��e^�25.��c5Z!Y0Object-orientY!�, ECOI��1�r 45A�483^L11JL,A. K. Wright%�R. 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H��* bqva�{�*8W"� 6̑"��.� 3 � M strongly 6#1 �k �yI��si��)��1� �!P�G. N�4theles�A�i� �2pF good�+*�4th� �h in�Z�c|�H}fia�iC "A ! � 41!����obo�@� intu�. G. De�p<5of (48�[,tanta���a� M:~PA�a�B�^�PY~IZ�Hh mit�� @be 2 γ̄ P |hP |Xry γi,Ԉ&0+i ξ̄ |hS |�+��hohS"9 tw44�cp'�xo)X� X$"2Ax:���th`=�| value�W�d!��e&����jW� mean� is�E!(�� )^;I�#no9.�r�, 2 2�e&F " �e!`�Y��hSai�u��Tcdf!�Y = X�5�X9(Qxα1 ), X��82 ): y α1 P (Y �yh ��( y>0 (86) e�p α 1+� �24H�e  �i1����e�IdQE�!� BS�x�r(4g� (8\� combus6�- ("��eWa�tuy.e��)%:*|!a!6L+� ��7� 79?U any ����"� #8=98$41). F. MoZ��"� � e SU &< , "QEfL�� i��A/m���szu!A!9,=&��^6� 6#���A�. %��i�L .�` ��w.~F�e5W0.�!�a��57� �l���I@ Wi )2� for 16a�>��o�Ů%� D�RQs 3�  3`�N�:"�6�tZT quen�M5[|\�P u��&���nd!�n switer�o&�>�R��&E��r�anQ� �l!� �$oizi,"�:P. R EFERENCES [1] A.C , S� A~]�scK<1st ed. John Wil�[\nd Sons, 1947. [2] H. Chrff,�NL9of��]s,0�,Ann. Math. S��Ist., vol. 30, no. 3, pp. 755–770, 09 1959. [3] K. J. Arrow, D. BlackwellICM.�Girshick� Baye��ax ʂio�2����U�A�lem �Econom��a, �17� 3/4 �� 213–244%%9. [4]� Wood�+�e��Fč�t�\0� of b�uu��� Bi ��k�63�w ~101–1)e 1976. [5]! Siegmuk=��a-� : b�# confxe`terva%y�s�<Sp��e��r )�ic�a ew York: )-Verlag! 885. [6] V. Veer'pli, T.�war)�H. Poor%"Dec�Aal E= "��� �I;�u8/er jRa��9!FE~*��Yy, IEEE �j/;�%�39)c�2)�43!�t442, Mar 1993. [7] R. Ganesan,A~Rao �T. Das��A�`sc�1�b1��P��ach��Fpr�|monito!}� Semi���u�;ManufTO � �� V��21 �m\X399–412, Aug 2008. [8�K. SahuE S. K!�“Di�sbuY � 9����g��$ shift-in-, "/$P 0T��>y� �9�T�%�64 ��1)��8�4103, Jan 2016.>6 [9]�Bessler,-��App�@&.De�f$Exp�� K-Q�In} ly!�y.+�8: Part I-Theoryk parti3aߍ� ics, �� d Un�sity.a,60. [10]9M Lai,yY. Xi�-8nd G. GeorgiadiI^Quick� �ehc�f� "9ci ce�I�or�e �I;>��� 57, ���8)y537�� 5386Q=11��1%w,Nitinawarat,��K��iaiV.��{Ttr���d��' ��hf5�9 Auto��cUR�W58M9�0 �245�)24AROctA=a�12]��Naghshva� T. Javidii��c� )O�1V��� ��-��.-H�4m��6 �70�M2738, 12��3������Aadaptiv� in�?veZ��i{ JourO of S�Ned�hic�m�N6��7)O�5 �768�82,2L�4�Co�#�Q. 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Recall that a/ ! µ on a <able space pV, BE+ �eM8 countably addiE<mapDB t �E!E�,the compactiab�r0, 8sA��set 6 ANNE VAN DELFT AND MICHAEL EICHLER R` :AiCq. A�Fa�is neaeapfor σ- �Tity to hold (although $�fI�-�s� �)��tvµpV qsdHsufficient). We not�7Dat ` is an example�!z,inted convexe,)�is, itS�aA�nonempty � %�,is closed un�3nonu�I$ multiplic)oKcontain �Dzero of element. I|moreov��nsA| ` 8=o s. T)�E��a�,��sMi� H gener�Q:�ED� ZD�?ofvBM. For%�purpos%w�papere�araZlely @res!�in=� �z�ofe�` !�e p �� =�#!{ sista��ll!��-5�-��sP�-@ theorya^ cone>��oreferA�(Neeb (2000)%�Glockner3). To�De such�8meaningful from!\�ra�cal ��)�I�importanM�we%�describaem���aa�<��preserv! mapA�at ( its dual (�) intoen�8a.e., viA78ntinuous linear��al N!�A�-* . Tha�llows!%relate�E* *!��%a family�V_� M� s, w�VEwlatter�� s us��51 informi���Eq�itsel�y�i�l howea��8trivial task. B���wa�troduc�� ���?E�shA} heurA���yլ������]� which we Ede�� by L!m���th��wh�is yieldm]g�can ��`1�*!� . R� 1. 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This map is clearly monotonic. Moreover,<ity implies thatT ∨ yZ���)j(y) and�% ′ )�φ( ,. So it rema!to show lφ�(surjective `�� NLI� f��X� �f ) for)�, 0%$!5. For%m8first claim, we6��`◦ j = IdL . Indeed, _ _�!i) = {y X%|%"��%"�}6��y)�x �every !Y��!��M5�we ��� +��$we have j(1�)!�� �P. (†) To see this4compute�2;� = j(R��w�} \�{!� :���,E ��} _ ≥GA�$ 1H�� join-irreducible5�U� =p Here� used)�j: onto%�>U� elemente[$. Now † .�� �YM�%Ee%V!�.g��2"�e thusA:W�)φ(SS:B�N&��Q��)El�2�� ).  Theorem 3.2. Let J ( I ⊂ S be twoe�tmial ideals. Then sdepthS (I/J��<� n − dim LI/J TWO LOWER BOUNDS FOR THE STANLEY DEPTH 9 ! RFP�( + 1. Proof ��d��l$ . Considei�%�(semilattice)��Nd�$�18preceding lemma�2(e correspon.SU(preserving �:cI/�Let mm�zA�}EX!Uhe N���6{�,to LJ , i.e.��:2� generated��W�i�I� J in�@. By construction� maps��a L�,We interpretPBHas exponent vectors��.atT and ]are lcm -���I�� /J- �,���tFs E��#E� $= K[x1 , .P, xd ] in d variablesi��i�8llows from [10,A�E� 4.9]�1I�>�� dE�{�(2��A�� d�e�+B. ��by%e same argu��B��[a]V�.��1� hence�"u�iId Remark 3.3. It also hold�� ~�and$2a�e� fE��provenR�� , usaM:�$11] insteae�.�� !� . Wea��sA�A1exampl{.inm"�l!hre�$no inequal�betweenE�number�$�I!L or�Xdimensa? of LI . Et3.4. (1)6��. I = (x2A��y��2)� �SI�, y, z]%�is easy ��|at l(I.3, soU�2.5 giv�he boundU S/I �M�3E/3 = 0. O�, other hand,��= 2 (FB�a an embed� into N2 )2��3.2,A8�e!Oterr��2 =��(2)�)� e�F�5 ]�-)K2�4all squarefreeդ deg 3. Again,�i�TuB1T�55T2.�* �a�S(ally verifi{m = 4%0in N case5�6= wors^� |�4)<�4� no�� with sm!�mMǡ[:� IA is s* �o)e�)A @Stanley–Reisner-� of a�tex de�os�c s# �c$$lex satisf N�sa!� ure (A�4.2). U� %'@result, CorollaryE��33.2%��i�!� ~�y2|�co| if (i)I � 3 or (ii)1�� 10 L. KATTHÄN AND S. A. 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As3immed %���!*�  2.]�4.�#�=4.5 we�%.I���$6 �6Qs�J��rAxZ�MY�I�`yF^� i�$inm2��2��$G6�$�^J3��3f�$� �l2#doubl�J6�� �JM�B�x!*u#} 2��x�"���!&�)�a"�9��c"Z&.P �! S/ I�^���abf� �#�(z �8is large enough6O�7]O��^�Z��*^Q ������{"d 1#�42j"a>i��6{BW−i~ Q� −3~ �S���ru~O.j � the .N�L��^ E�� aFI#ie2l�.S14� 4.2]�+ �15 2.1I�I�R�� AH��^M*;"2�aV�5��Z>E �2\5�l"�/� 2� Ac� ledg/�"� wishHthank Christian Bey�Bpoint|ou�0refer� [17];us� s [1]�)$M. Ajdani,�)8oleyman Jahan, Bm�i1. of 2–CM�'��yTco��83, Bull. Malaysth. Sci�6c.,�(appear. [2]�(Cimpoeaş,qdI��R� � � � �f*�<, Central Europe�ournaE5�FMathematics, 7 (2009), 629–634. [3] V. Gasharov, I. Peeva, V. Welker,E lcm-�1��resoluXs,q. R�1,Lett. 6 (199u�no. 5-6, 521–532. [4] G. Grätzer, Latt*rory: F /^�, Birkhäuser-Verlag, 2011. [5] J. Herzog,# urve�!6b� ”Mm-�I5�7iXd Applic (”, A. Big��, P. Giménez, E. Sáenz-de-Cabezón (Eds.),�ce�4]MONICA � Lec<-�s!X!� . 2083, S:H$(2013). #� T. Hibi, B��::' 14��[76SA�6P S. Y�mi.��(i)J part�Y.RU�,��A�, ic C�,. 2I�@8), 113–125. [82��`M. Vladoiu, X. Zheng, Howay��up�e6aj�aY�"�� � 322!ve/A�9, 315A�H3169. [9] B. Ichim,�9 KattA��nG�DMoyano–FernándA,�\behavi�f:��!-.� ��eAt. [10�u� u��� � I6��e.�6��X1] K. Kimura, Lyubeznik.a�� arithmeti $�r��^q�%|s,e&. Amer. iSoc. 1375�$3627–363A812] F. Mohammada� oweredw���c�(fx8a chordal graphe�m.Q~ 39n11), 375Au376�(��SnHrey, R. H. Villarre�- Edge fs:Nic%6�/�p��Drties, Francisco, �op�3(ed.) e�5�.% gres�coB�/�i2�/�c)xPHomology. Berlin: Wal�3$de GruyterV> %~��in���985e|�6%@2) [14] U. Nagel,��Röm�)Glicci}�� plex� J. Pl-�[9r21ija�(2250–2258A��5�/ R. P���k�h�.��(eyed Fakhar���us ���W�is�#�.6� ? No�gs Ep�� c. 5�.� 1106!10�6]� Rauf^�e*tty��/ltr�IE�r�<�0� � o regular" 0&TL�QiTRoumanie (N.S.) 50(98)!� 07),��4, 34e+�5E�7]�� Rein!���A hI)e��la@�5� �&�of"�9, OD7�1��x2, 16E.70!��8� �;6�6w of weakly��ymatroia�e�)4Je (s, IllinoisA`%"6t 19]ECU8, Linear Diophaj �e�)�,lo��co- y, InventQ*(68 (1982), ���7�93� 0] W.aTro>7�e�3m��+%fedw s: D"� \y, Johns Hopkins Univers�8�<s, 199K 21� Woodu"e, Vert:�5��)Tob"@<�;hella �v��)V� E�.��t;323�3246.Y5� �� < Osnabrück, FBX�fk/Infor� k, 490692-�H Germany E-mail add� : lkl$en@uos.de R SchoolAhA r Instit A�Resear�4n Funda� alazz s (IPM� @.O. 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O�  hand,N_ `H� (arbitrarily D���Ce� hold"�E 15!�!\��j�6�ifV���w(F)� 1u�I�� "l%UJ��K.� >4q yield�.�e Oum�Kwe �pid%�.�)�. C��!e���,2ρ−1 ρ ( ��I �ρ > 1/2E��g; m� �� �� (4\ �=% & ρ ~ 2%!� 1A� �ε $�2 �R�)���kρ a�%�A���R���2�4�2� �4�O�4�O45�Eu�i�� m�We�rk%()�Hgh!�canA�ex� �eM�6:r� , i� ems h�toq struUny meaa�ful:I�"^���t��E.ASC�V�F�sI term������expliciPaG � Au�DludA�e��'��B��con=E by.� x�ı��- &n�M�!��MU a"� Jye�"G ősen���δU �iiKbest on� �d �"�K– �. 7. Co���sA�V�E dynamic gram�B�D)�ache]�U�wQ�l� ag�5� ic f� work origaK!eI&j ��� Ewfturns�A]beXy "�G�!W�>�F%� �%Q upA 1000.Nfavor�F��a)QO:RWer>�Pan -U��G4e literature. �R�a� oret��N�& viewanE��Y�!J� �b�3H X(same pseudo*���K O(nc) asE���2O>�� v�g� fur�!7� "�)�ure� !��N)V�byvi��ajPracter*T |linea axm Oan=�"�N!t!� ute upper �-�� stud]OA�E&Bi� !Zedt$her surpri�:b�a��rp no =X%PW6UEI �a*�p2,, w�5A��mo���4A!Uallb �lfu!��earchօ�.oextene�K5V�s!Wp KP 28 g2� s.�wo�E�baPte��I��*�ny�,on new bench�P�  ch�N�R�u�<. Acknowledgment�����e authore[1]�j/Itus)�Aco��e��i��1El �%�ɻ!&�LRosario Scatamacchia8supQ�� fe%�hipɪTIM J�R� Open Lab SWARM (Turin, Italy). UlrPferschyF\��Uni3�te Graz�� ”C� -Sel�-Dh”. Re�[ ces !/$A. Ceselli%�4G. Righini. An��q��a12%d�a� izedJ>OpeE�ns ReI� LjV�s, 34:394–404, 2006. [2] R. S. Dembo A8P. L. Hammer. A*�6��>�s. Metho��fN���, 36:49–60, 1980. [3] H. Kellerer, U.5�, � D. P���K)�!Ts. Springer, 2004. [4]!_Lodi,� MartA NLM. Monaci. Two–dimi�l!�a!��s: ��Hrvey. European Jour-.��al5p8, 141:241–252%i2. [5]6��� �0P. Toth. New T�dYV��Q"V��"N����,23:325– 33 �!��62��%���A�C�E�aV�� . Mac�@ Sci�E�633A44E8. [7ju�B�: A9A%Co�Wer Implo�Rs. Wileyf�9�8].yA�minimal���]�� qe4, 45:758–767n7. 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Onl3��g� �f( 1�(X ha �z�f�{shape)��c� ituta�)�toughy�I�� i1 Lproject LOCOMORPH [1�O�C�� new,��� edoR algorith� {!�!�-� �za&]k ZB& a�lo� � �e c un E>�!e�b��velopa�!��t��gr�� "uI! spi ne� nete [30]Aa ste��C t ion). Aca ledg/ s M.H.�supa d�Swiss N�� al S� ce FD Fe?Dhip PBZHP2147259. U%�dthanks Juan Pablo Carbajal, fruitful!1�'�i�!G �liter4e. Both9��n�! EUCogIII!�E4(FP7-ICT 26998�ma!7 us talk!� eachi� . 7 Re� ces [1] P>S. Y`-231688. [2] A. Albu-Scha��F, O. Eiberger, M. Grebenstein, S. Haddadin, C. Ott, T. Wimbock, S. Wolf��G. HirA~ er. "! ics.&J Auto�hon Magazine, IEEE, 15(3):20�@30, september 200�3] K.J��tröm !��R!�4 Murray. Feedb��S�: An IA��!u� E# tista �E�!,rinceton Uni��A�PreB �p4] Eric Brown, Nicholas Roden!J$, John Ame�4Annan Mozeika,;8k Steltz, Mitch�R Z!�(, Hod Lipso:4Heinrich M Jae%Y�#A�cover:�al1n gripper&e . jamm�(of granular"F �.A@�caCl Acad!!� U.S.A., 107(44):18809–18814, Nov 2010. [5] K. CaluwaertsEID’Hae!�D. Ver�ete �8B. Schrauwen. L&.��� �:� �eservoimpu��J��s. Artificial Life, 19(1):35–66, 2013. [6] J. P�i�A��r�!-No�-ari ! : Be� GeneraIQ��Na� al D�$. PhD!x sis,1�ALof Zu!��2. [7e�0Emami-Naeini,aK F. Frankla�A�J.!IPo�,U�tY3� �9 ice Hallq�0q8] R.M.&��,�,Dzyakanchuk,i Flum��H!us� e}Hunt, R�� Luch!(er, B. R�r�7Scheideg� R. W�$�.�o�!%�)K��� a�l:�*� � ��eor�6� Z�9–34! %�9].���A�\Ijspeer�6%�R"> �W. Maas���t��ew� فu>��A� A� �l��. B"� CybernX�sa� 5:35A�370�1. [10��� ��ol�f�N�i.�#a�.����� .�� 106:59�613�A�11]���,2 , P!��ma�@aamb�k�R�e� � of%q� �a LOS ONE, �e8669��4!E2]lA�hFua=0D. KoditschekI0J. Guckenheim��!<m���lad l���:0� nd� ,s. SIAM Revi 48(2��7A��0E�06�3] G.�ornbyes Takamura,�Yokono��PHanagata, T. Yamamoto �A�ujita. E�ro�! ga th AIBO� "�-v�i�� 2000�Dee� 6%CRA ’���)1al'*�� A,volume 3, pa� 30445 .3, e 8 *F. Iida�-Gómez �y�. Exp\��� 9�a��c�\� r�quadru� \��P� ڡh�O 12th�,f.� �A�)h1($ (ICAR05).�22��$235, Seatt��h 2005!�5]El irk. Opti�� �z ory:��i��. D  Pub/� aZ�0E�6]� Laschi�Ci��eh(Mazzolai, L���r+' )Follado��P. 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First, observe that G H can be produced by taking the union of Ω with corooks on the bipartition classes of�\ two connected component Ω, � is, �= c4∪ 4R(n, n) =' D(Kn ⊗ Kn ) underc�appropriate vertex labelling. Recall from O��a! 5 zPG ∼ = H if and only (there is a �4-biclique join1n- s i) co-r)f aN�� of�. -�suppose�Pwith σ 0 : V (G) → lH) an isomorphism. Then by O �- 20 �d, at line 7 in Algorithm 1�B��B encod�~inA�s�E the ��in��ls 8-1!^0en write down%\M�]asK bijeI�σ. Now= H. Ei!� we haE�e situ)��a�$Figure 2 w%�0e are no>��0Ad!�the a5 �s not%c�p!c�c5B4. Mor�mmE$ gexist^f�, but) y doYsatisfy$ necessary�( sufficientA5�deMe&-�)� for�U�IAwis case,2� �� �3�17)��% is_-��_I� check!�atyp chosenBk , a set SA�a�ic9oQKa [in i,1G H. Thea{statem! $is equivalto �A�Dpairwise adjacencyF!�{�Se$G H, whichM$polynomial|S| = n 9!B�sYD. used �runtimenY@8is O(β(Ω)en2��a[0) factor arisɅ�enumerat�maximal �sU��u4 mbeah� Q�O(r\TH� F�1�. 6 Co� ng M q�B��qBi��<e Graphs We nowA�si��gE�)dwe �L directly ��le number!; �� �4. For example,b!cl�S�b�{z)`� `.A�s:�21�U6�.aQ such�jnstance,�know �2 �find �\JJq��n.q�A4�,��Propose� 7. WaParacterA�L�VV�certain)s ��91!��f��� JextreAIE�!�.1 ECases !z,n ≥ 2, def�1>)c Bn ,m�}even n,�i��e 'K n2 ,E�8a perfect match�removed)�oddNF�Bn−1 C n ad� al%�exed}�m��t�!�of��in onu�Q?io2� v!� give M����B�!�d�3%clarific��E2��,���K)(E*llDa crown %Uj�t�"��follow)(sult.� U* 8 Le� be a�1{on )��4���hn, β(G) ≤   2b!�c bn c 2�2 −A�n��; 1, n!�@. (35) Moreover� is bour �s��ura� :K d Bn �� Wen ceem �%��Qowe sh!?assum�C hypothesi�vA� n�en show� A�*�onsequen��: %�n + 1�E 2. A����p2 AO.�4, any�VA^�G��be un ,ly described�be!���e]  a sub�(�o�u S ⊆ V0� �,7�assoc� �dq willmQ+Q� 21 S0 NG (S). 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How���n O( n)-��/�E!7 dual!� blem��1E��hA�f,�u �n?( alisA'�+�8� mD �$s [CPRS10]��� �yV�ofJ\on� es ab!1b so a���(�e6! co�)�� �r�I� 26 AcA�l5@5 s WemZ�"�Dank Sandi KlavžarE<com3!�!6 texta��)Qat ɉ�� �4��}�n���an?6Po Antonios Varvitsiot�/!�m� �uiQ>��style) e paper�^9�rh4A%,T0of of��. References [Bab15] L. Babai.  I&S9a��Q; ���T. �C(2015). arXiv: 1512.03547. [BJP+ 09] E. J. Baker et al. Ontological �c*5viron!t$: A system%m� ng as-phlype a0�W . Ge� (cs, 94, 377��09). [CEL86] K. Cameron, J. Edmond�L.��&�on:�p. Period. Math. Hungarica, 173 (1986)!HCFSV04] D. Conte, P��ggia, C.AusoE(nd M. VentoaOirty Yea�,�G  M54in Pa�Hn RecogM�+�t%j>�. Artif!Hell., 18, 265 (2004%L07] E@CheslMUM.�Langston�"Ral!n$etic Regulg8y Network Analy�2 Tool��P High Throughput Tran2(ptomic Data�0 Syst. Biol. Z.� 150–165%��7)fMRc%�B�urcelle%�(A. Makowskye"@U. Rotics. LinearI� SolvS  Optimiz�jPr�:e�%�A �B�3 ed C�> -WidA� y Comput. �, 33, 12 ��0%f�0P V. T. Chakaravarthy,�P�� t, S� ��YA$bharwa7�Ff ng I�� t Se�  Unaa��P� �H. 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In summary, we address visual execution monitoring as an hybrid deterministic/nondeterministic state machine streaming perceptual information, for both monpthe exe �Xand suitably directing �tperception. The VExM refocuses= rede!MPfrom a failure accordKdto learned policies. Assum!�� r �!�vidcp fully observable environment:�$ relies onm� m$ [15] for �uon9limportant objects involved i "task 5-�,�likewise�ass!��Ldiscrepancy between  inferred )�!p%Z�ik$one. Hencevcase of 1H,�@can always resort� recovery �y !P ensur!=(n optimized5aearch=)� into a � wher.v�be retrieved. II. R ELATED W ORK Aear!�t definiA3 s of]jmonQ�in non2�.�(s have been�roduc)�4[24], [25]. Si!30then an extraErary amou!��f!, � has Rdon)�ddr1�B��respon%�c� 2t$o robot ac� . Severalb��� ��ureAy�D6]. For high level `A~$s a review!N��efforA�s giv%% [27]i�rolABIbe� i! q��(was alreadya!es)rg4 work of [28],Y�Upe�errorsEu8 could occur at=� time6k��a!�|by [29]. 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ACKNOWLEDG� v � "f [û_�F �V πst ]" "+ ~ 6� } Oobj argu�"%Mx# S�, ('�& s"� � � πu ��2:�y�SS  �� V TQ"lr�i l�p�EU H2020X ond�C s 643950.�pFERENCES [1] A. Krizhevsky, I�tsk? �&G. E. H�Mn, “�net��m]%-�$.DolJual neu��_ ,”*NIPS 20%\ Hpp. 1097–1105. 1 �_�S?(n, K. He, R�rshick ��J� ��F�Er-cnn: TB v alti�i��W ��ZQ[`R���,�X5, pp. 91–99. 1, 3 � I O� �qu\$s ott e ch�� cup �x4�se� )�*� helf"�|TV"�� d�Av er�^� 07?% 69% 57% 8�v�^�1 �7 �91�f�85% �0�a�yp 61% � 0.6 i,l 53% ,a? 0�g�6� 4 �� a: 06|0 w - [22]  �3 4] I ��� 6G (���):5] [26] $�6"�;= � &�a�E���y�sio`i��"" [27g�809] [3] C. LuE0Krishna, M. B�r teinI�$L. Fei-Feie*�}re� ship6?�cY~�lqjpr>Wm ECCVEu6,a$ 852–869Ew2 [4]aAntol,a�Agrawal,a�pM. Mitchell, D. Batra, Z. Law%�=,nd D. Parikh �qa���q�%a&answer�* �((CVPR),2015�m(2425–2433e�5]� Al-Omari,�F\Chinellato, Y. Gatsoulis�C. Hog>+A.�y(Cohn, “Un*WbA�i.ext;8�Y7m��fFI"in %h�.��K ��6�-s50�508�6])��(nd B. Bhanu%6�SI{p0!�p�.Q pattA'�f� a1!�6�g4I�al%b$IEEE PAMI,�S(. 38, no. 4I 78� 799 �� 7] P!��~kiE� Pasc�8F. Viola, H. Sora�AAllardE> Banino, M�cnilAGoroshA�L. Sif�>@K. Kavukcuoglu, eC��.%�L|.!�to 0�8�.��<arXiv:1611.03673�8]AZhiqMottaghIC�K��E�J. Lim�Gupta,�uA� A. Farhadi��T�y�t�A�. �A��i="�TJ�� ��"b,�l �%�j ICRA�$7).%���7)�335�� 3364i�, 5 [9�LeC���Y�K ngio�H�G2q�D�@2s��N�{I 521I! 7553 s 436–444��K�{T.�6Fergus��A bzRanaly0uM7�n_"me'X� )�$Ann. Stat. r209a��38897�, 2�! [11]�� McDermott�8GhA~�b%�Howe,a�Knoblo��A. RamE�Veloso�!Wel�BndPWilki�;(“Pddl-theuE��?� *�;�i%�199i�12��HelmertE�Con�3�Ae- J� "Z)e�e� pddls� �^Artif�(teavol. 173)�5-�`3–53�D�0�� [13�Cashmoap�M�'�x�LoZ00D. Magazzeni,��Ridder%I$Carrera, N��lomeras,�FHurtósI^M.+�s�Ros�: P��a�.�h�j 8�. system�6 ICAP ť33�341��(14] V. Mnih� 28�D�Rlv �!�usue�VenessI%1%�l ! �rav�;(M. Riedmill B�K�Pdjeland,a?�O'V�v� � ���H�j�&�� �� f�� .t 51�� 7540 �52a53��at�,�15= A. 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In: Extremes 19.3 (2016), pp. 371–403. [28] E. Mariucci.}DAsymptotic equivaly pure jump�Tprocesses with unknown � �\and Gaussian white noise�, In: Stochass�P R0. Appl. 126.22��(503– 541.�@9] M. H. NeumannnM. Reiß%N(Nonparametr��s1.��L)L�`from lowfrequency observa!a�s�4Bernoulli 15.1�09-c22�248�030] R. NicklF��@A Donsker theorem.��measureuTJ. Funct. Anal. 263.10}12 }(3306–3332�1�,5�,KSöhl,�Trabs%1High-9�:��.�� B�� Probab. T�Xy Related Fields 164.1-6��6A�10).�2 �XC. Noven, A. E. Veraart �A. Gandy��A-�T-driven rainfall modelI�applic)� to fut!W pricing5�TAStA Advances in StatiA�al%r ysis 99.4%s 5), aS�4E��4-qL3] L. Rüschendorf%c�JE�$C. Woerner�8Expansion of tr Ah distribu �sI�� Y�in sm�timyJY��8M�Q�8!g96E84] K.-i. Sato. ]}a�Linfinitely divisible6��d. Vol. 68. Cambridge Studi)?-Kd Mathe��cs.AhnsIel�the 1990 Japanese original, Revised by 'authorn�:yUnivers�Press,V9, !�xii+48 ��5�2Y� Quantile VB�n�5.9 (20Ay 3484a�52���i38 \K��A NOTE ON HILBERT-KUNZ MULTIPLICITY MOHSEN ASGHARZADEH arXiv:1603.04297v1 [] 14 Mar 2016 Abstra�$�In this note we first give a new bound on eHK (∼)%�DHilbert-Kunz multia?!XTof invariant rings, by5 help !�(Noether’s d�n,�@simplify, extend Akpresent6�ahe reciA��,formulae duea�,L. Smith. HeA�ved�� (< over polynomial �E�!8result is tightaRqDfollowing sense: OF@complete interseca� Q��isoI�singular�,we show that]N�� ”e!�R/I) +)�R/J) = f )”����t wTp. dim(I) < ∞ when I*xan m-primary unmixed ideal link!+ o J along L a re� s��e f . 1�trodu�$ Throughou�QaE are!�w(e character�D8 p > 0. Let F nAq�) be%,PeskineSzpir��ncta� The j�!�∗-lo��(A, m) �n ��� %defin�Qℓ (�@A/I)) . n→∞ p��m A T��i �6� a. Mᵥ1As\such a limit exists [7].f��� %�I, A) :=: encodes%.DinVOP[14], et cetera. Some��sE�uting ie� is difficA�av findA�s may!�Aasona��(task. 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In this paper we will use a simple notion�co~l domain, motivated by three +idera�ps: firstly, to focus on decla#ve 5 0, rather than!^@oftheoretic or op V@al issues; second _Lprovide a purely rel�Tal framework; and thir7�if�He interplay between � -specificedgramming resources such as%� c values iprimit�(predicates,(general-purAG.Y�� Y� Y data%\tructor ^defined\X. 2.1.1 Preliminary no%� Beforjesent�B��sA��aA�4mal way, let u0troduce some !� ly syntac!� e!�(t will be ua Tall along the paper. D��i�d 2.1 (Signatures) We assum!� universal.! s.@ Γ = hDC, DP i we7$DC = S S n%�$DP = n∈N n ar!�finite%�Tmutually disjoint setsA��fA� ;C e�Hion symbols (calledJ�in�sequel)fB�� G�,AJpecA(A� rankiY(arities. We)TuseM�� 2E�5 s S Σ9 , P !extend!�Γ �h�a2��'1"3�n�U�� U��, alsoN���TaEdea iM F]� come I�F�, whileF4�s%� ��} userQs. Each � mayb!�$y countabl�p�t�n-aB��. I�|E� e, P!@ s ex!�ed��Q� M<(set. 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HJ(�!CoMEEe,N�!!�i� Lt�\"*��QW��b�(*���L�Pz 1987"� �s�� s a ���-t%���3 �Y�Bskmf� �NXt T"�aUsp�N� (Gab��llaJ LeviO1; �� 1995�� MW�5H���&�D�T*� Si (�! , 3).N� �G.�&����g$�, "open J ���cQ answl`?�MCLP>�In�{  Si*��B=�9���9�e���;!��uPA!�"ly_��.��B�"V�Pt-,"�|� (Apt!� 0; Lloyd E� �!Fb:��,�'�_�n�C-&�(Cl�81979; Falaschi Y#�3|�nA�D8,YO89; B�� 94);a/��p=�'�;�a//��%�:E�2�32V\J�+�'���L( selve%�d�a S2 -B��n�c_`���* ��lidE�:�e�I�!F6�.;�Iw� ��5qou�jQ�w�*�qc�HAKA A]d�� Π, .R���(�:-����Xe�����Π� ���U�d���"� U� "3 <D,C&xto capB��s�io" ^&�<�T� � �d�� ��^�o�/6:&�: 9�of"�"�LC]�6ma��K���s� 6%� *$��, observ��ables and (D, C)-entailment) 1. Qualified constrained atoms (or simply qc-atoms) are statements of the form A]d ⇐ Π, where A ∈ At(Σ, B, Var) is an atom, d ∈ D is a qualification value, and Π ⊆ ConC is a finite set of constraints. 2. A � A]�4 is called def��, primitive or equational according to the syntactic form�A. 3. A ri�observ!� iff d �\ {b}%����satisfi(|. 28 M. Rodrı́guez-Artalejo6 C. A mero-D$8az 4. Given two�s ϕ :.Aϕ00 ]d0 �!�80 , we say that7I.I-H40 (in symbols," <D,CM�)�th!�Dis some C-substitu!T θ �Pying A0 = Aθ, d0 P d��Π0 |=C Πθ. We will focus our attention on.[-� s because�Dy can be interpretA��s7��s!�4valid open sol��sA�ePic goals in SQCLP(S, eE as!0�sef SubsecYl 3.2. The example below illuaates�l main technical ideas from DA��i L 1. E H3.2 (OYU�!�)�2�Considero4admissible tri�underl!�� b�1Mthe set%$R-c��ts: Π = {cp> (X, 1.0), op+ (A, A, X)× (2.0Y )} !�7≥+�3 9.*� <K9Then,�followa�are1��1 : ϕ1 = q�,c0 (Y ))]0.9M�( ϕ2 = p0 ( , c(X$�8$ ϕ3 = r6#�, ZJ&ϕ0R&�c(Z 0 v�7 R0 !�!R(U, R.�� m<U ,RaI�3a>I�thanks�θ!8Z 7→_�}�_ ich �:esF���V��a|�0��� 0.8%�!�|=Rm�A�a= nded mean!yofi��a�R� ��J releU$ not depen�?on�� ?EN�} predice motiv !%$first itemaxnexUfii. 2  2 (Iq��s) Let hm��i�any g�Be�n:� �Aт:!�E`�qc-6���a5 I!(���Q� closedi�F�. In o�O, words, a se WD�wA�UA!)y"� cond�E(s: (a) Each��∈ IAkanj��. (b) If2A��<��n ��� � suchA� t ϕI5<e�n also�(. 2. Assume=�Bb I. 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SB6��!; a�'gi�f�uAs�!�Lbrai���i_n!� p (���q�K�kE��k)R�&�#� �nO3chkT<���Gy��w � ��au �mpzA�?@.��F"�>%��%Za � �l{�B�lBVλE*>λ*J� 3aA�!=:�$ λ�}ǩz� V�8��n� U2�8"j@"� vL. �3P�� Vµ� �= µ� �,�6= µ��i� !�!> <M�U-"µ�� ��%�LFY-��3�i��9we ^��=:�'�]`9 �y%��,&!%b&�^�ha?�mb^at�4�Ed� Y( U (or |h| JaOi��� �n!��h(��8= F��s�� �G~fO A�A x, B& / T5�Uo�p��E���%)��M����@M)�hasBs��r2 ^^T&'%C �e��= ��7��b3(e�)�a�<in"�ZR� %�s, yet`6Fin ��l)"H)%xM�, ��>��.��Dca� "(%�proper,|")�Y"H�`*(>�e�ν-�}�e�, µ, ν���5Yj�a�&@% �A�A alread�8en}��$���m y M�f�5�EB 8 �0Y �� not  ����n7)�ET��%���OXAD�9��ν�.1�%��? c���a�%6�)a%�]����2�N &>�hFm1� � �`1� , κN�.Gl%o �=ut�'r�N� >\ �����l 1��ۡ�h6�*!Q.�we-��r�� ��In��2H��2��/A1& �L�b�eR�?�G�r�ne�9B=�Hn0REFERENCES R�Rls [1] J. N. Bray, D. F. Holto<C. M. Roney-Doug1Ae ���STM�s1� LowD�@ al F�e C�U�GU�,. (Cambridgeu� versHPress, 2013). [2] T�euer �~,l. Hamiltoni��ycl�?!F �graph���d2�s�^Tll. Lond. Math. Soc. 4y=�2010), pp. 621–633. [3] L. E. Dicks��L7A�$. (BG Teub?0Leipzig, 1901� 4] W%EKan�(A. Lubotzky�Rproba4�t�x��a�>%Cw(. Geom. Ded�F<a 36.1 (Oct. 199�7–87. �20P. B. Kleidma@;!�$W. Liebeck ��� 7��b5)�:��(s. Vol. 129z�� . [6%�,Y. Lam. Intr�2�C to Q"~?,Forms Over F�. (Ameri�!��e�:�0Society, 2005c7]6��1wShalev� �m�oI��,�3)��s�?�M\Wia Con�) � =�9��J�% gebra 184!� 1996ML31 –5!��8z���T;I �f �M�. E � U �5E June!q�5 �103–11A�9]I�cchin)"4A. Maróti. O�e $*� Nea�U�M�PraT!�Vue,137.10 (2009 �320A�321!10z���SR �Y d qu�Ws�rel�IAAZ��� :�� Ischia �5ory 20082���4. [112���,.2I)N+-J}Ѕ�)5)�� )5ECust6203AL2017), 9�� �ER. Wils��A7�j�S.�(. (Springer��on�\2).FD�hl�6��arXiv:1606.05240v2 [] 18A ���7 A LINEAR TIME ALGORITHM FOR A VARIANT OF� �FMAX CUT PROBLEM IN SERIES PARALLEL GRAPHS BRAHIM CHAOURAR Abstract. 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(2) For (1), we first determine a bound on f (r) = (1 + η) · r ��bn�. By taking its derivative in r (i.e., 1 + η�ηD02r+1 / log2 e ��observe that f is maximized at r0 = 0� 1/η! B�e_@1, and therefore � ≤  0 >���(=rT�" _t2η!jU9�% �= a!mX5 Consequently, apply!0�b� 0 as well%�0obtain 2q + 2!� + r6�@=  2q  2q a + M�� η)(9�)b0A� '!�p r =.+ . a aM�2), from the definition of bi it holds %�(b0 + b!�)/2 =  �(%�A21)!�ηEO@, which implies !�K���= �B �0− a 2 ! q 2n89#Q�/%p�ED = a We now show to proE�4e key lemma usA �L �3A�Y" �5:8Opt(`0 ). Proof!� D2. The whole phasea;!�block)trank `, with no buffered old rA�stsz hence, byA6� T, T��,K�0aGT(()eε%��`$is a lower�J��� cost�� in a !le �. U ��5 �E4ε.#b|�≥ 2`Ak(`!�-� �:��) ε2 = 05 . I�)6��)f� On��o�w hand,2���)%t m!2` by ��3��)|7I8follows.  3 C6separae�!R arbitrary-� sizes F��%,E{e�M,X may be “scaled up”Arropriate��nd��n�extenda�toQ, Theorem 1. W(6. Fix posi��tegers `EUβ �xa constant ε ∈ (0, 1). Assum�atx line-�iA�of��least!�$+ 1 equidi Lsitesere ex3 an input �xce�̅l`%D betwee)�!��sjhtwo optimal algorithms, oneI��a1m� βAp �^*�%� ):��,M� Ω(`q�!Zrs)�fix�:�� whos �a�LssertedYd 2. I�is ?@, we replace each�3a packet1���of��-)� same%�_any5< soluA��vout los%b generalit� llTbelongmAjuch�are�<(cessed togeaj�.A����Ja\attAyis�r�m� �s canA� kept�w��� �both .��at-��`4�c�^of<5 2E��a�:�>;�secondA). H!��,a�� ae �d �$ capacitie�ha�sA��p��h�· ε2�� −1log  2  1/εt �|�sMr� aAfed ε. S���resul��i��2|4still valid whmJ,total number!,e�e�3nota�4al but greater���n�+ 1e�YarrL �t^ only!c!�)~2`3 ^�� remainAGones canu0help nor hinds$e performa� �fE�5�. �j�� Let m�� �n�b 1)c,I1 m��largesAk� � Eѥ�2m�� n. We ��i�woEd�s�1ini�Ir�m���U-b� f��:��\k)!�  Q����hk). 1. 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In both:  }ph��!��=f�(too �Qtoq �)E�� Q�A�6 na��0R�64 512 0�!� 0.4I�!: �0��8!�1�1A�0.A�!�%vA�VI3�0!��0%��n��0�5! rYe90.3��4 �5|1�6: �&�C�c)�(solid�!�Q�5�Z1�I �p"A ateD64e5qO��lap� e dot��s y ���u2�[6� I E(I/n �E(W from�v1. ��2���2>��y� ��� � �horizoy � indic� � �cɠ���a� permu �h:�Y��f�!3�HA��7�-J� I�����28�E3�=A��3�= 26 25��(223 22`9 ���Wp���|�1 q>�E�27l�3�l�Q�7: DeY �5A#��a��pI W (b���) %�Mw� &1�p (B‡ runs)M���E is� dire]A �E��-k 6�4 (ignor�/ a multiplAU� factor� " on p�GB Refer�ops [1] Y. Akimoto, S. A. MoralH Td O. Teytaud. Analysis�run  optimizc &O �s)DC &�E�Ddiscrete codomains%< Com� r Sci�\, 605:42–50, 2015. [2]� ssafe\E. Upfal. Fault tolerant"� hnetworks. SIAM Journal on D�Mathem $s, 4(4):47w0480, 1991. [3 xtete-5,@M. Cauwet, J. Liu� 6?Simple�cuD !�regret%-continu.)8.ZV#� 9# 17:1�27%#6. [4~����.�EvJst� gies� addi�� e: A��O� ,I�� �vdJ. He, T. Jansen, G. Ochoa) C. Z�Ds, editors, ProceeA�Efa!� ACM��M� on FD�a� *Gen� A6 \s XIII, Aberystwyth, Uni�50Kingdom, Janu 17 - 2M\<, pages 76–84.}%SAv�5�S.5dif�$t types of1�in!Pn�In!JTFriedrich, F. Neumann,�na�. Sutton�R�6�14A5�!i�%]=v , De!�D, CO, USA, July 20!=�4%#6, )= 205–2129?A�6]� Auge� d B. Doerxeor��r�j Q , heuristics:2��4recent develop~, A� me 1��SerA��O$� ��euA. World�s0tific Publish�A0Co., Inc., RiEdge, NJ-201�D7] I. Benjamini, Nrge!4. HoffmaJ nd E�i ssel. Mixe�PE�,the biased c|shuffh�aasymmem exc�5ces�Lransa�IEd2Ameri_��tal Society, 357(8):3013–3029!��0A�8] H.-G� yer.6*"��� y environ%��:] %u issues guide � pr�ce.5� methodX appl� mechanicsE�enginee�,, 186(2):239Aw�6�00. [9] J�,B. Rozière��.�E� Ffolios ����y:� Anna��f=[ �ArEI(ial Intelli�,, 76(1-2):14!n172!me (10] D. Dang.:%�<P. K. Lehre. Pop� ions6be �ntnin�ckAVdynamic �a.�ica, 78!6660–6�� 2017. [11 �sgupta��ZA� chalewiczr =�)��c�M�{�p!�Der-Verlag New Yorkq_Secaucus}] 1st �!�i��199�2]!TDiaconis. Group Repres�.E< Prob�ax�S�؅L�' 1. 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UN ptq :“ ? σ N i“1 s“1 Using Lindeberg-Lévy CLT A�a �ce� -dimen�Bal iid6Ys ř1%Z.� řT tr q ε�, .�,2�@sJ uiPN , we have��H0 D r�1q;T qsJ Ý � rX1^XTU(, N Ñ8 ř�J sA� Var r 1�ř 1,s>(s “ Λ. I[AG(e t-th diag� elem�of%&�, t matrix ΛaUy.]�[�r!��i�CuppE�f-F]�n posi��8pt, vq is ˜ ¸ t v tÿ2�Cov ���,�uyVar s ` B"�� � u�E.  �` R ��, *Dt`1 t ă v. More��, l.���r�~se�� ogue��!�tq,�h T NE� ÿ V2�6��;�´ tq.>���H�5, N s[e%sq6L? t= 1��? # r)�N��s!i` ff+ i���vTe��r ´ t v B« A Yi $(Ysi,t ˘ i� lF. - T ´s%!� �t�n���N����T p�s!� T ´��1J��!��p� �%p¯�ri,t ..��h�U��E(Cramér-Wol�� vice�end up ˇ:� D A�max ˇA�t!rET qˇ.2 %Xt!�DXT ˇˇ t“1,...,��1!��8 >�T T ? rmaxe9�t z%� st}tq *ˇ- m�24m�2G�t 1 ˇA� K�T&s V ptq?N ´t U;��X� st X�# ˇ. �.�Ñ� �.��pXAX qV��pX� Xs %a ��E:�t���� of���26 � b �C3 %��.� �H�W�a�ˇ ¸!I��� τ� � τˇ��˘%�!<!��@ ` 1<� ? ˇ pa� ` σ���v �δi�Y��´e�A�.4�!a Q ��^ˇi�%� Tm��T�7:� �  � N � ÿI�.�� � P(� � Ý p�� εsi,�� � , � 8,��6� ��OP p1q `R �ˇ σT 6*�� ř� o�τ1 T����v . I1 A � �t 1 `� Then��:�, it holG 2 ˇ s!��%�` `QQ  12!�!ڥ�Ysi,τ `!a ě %.�A�!���:��'W��!�%�e�8I &���akτ $�� A�%�!�ÿ.e�N�-�!� �!�%RMx �1 �Q��� NQ~ ~E�Jz$�P.za]M|�I weM �%�Uj�I�E� σp0 1q )0%"6��$yFˇ !�E� 1 řG�1.�| � 6��S � � nolafter3 1� τ ď ���3� �n "� � obtain!%FN TI�´ ¯ˇ!U �1� s ���Za� ?AjY��r]���$�Z�I4�. Hˇe��8E� E����´AwQ�: �2q�$Acknowledg�  Instituy al suppor� Barbora��was��7,RVO:67985807� �e�earch�Michal "< ] = Czech Sci�  FoundXprojec�K�@DYME – Dynamic Models in Economics” No. P402/12/G097. Refere�l Andrews, D. W. K. (1991). H osked�� autoB�Zst & � � � q�m�. ��e�la, 59(3), 817–858. Bai, J.3<0). Common break���@��. Jour!�of.p�ds, 157(1), 78–92. Chanr8, Horváth, L.,bHušk!�, M ��3��h��-�*��J��2/al Plann��In-�0, 143(5), 955�,70. Csörgő}/.��%� 7). Limitq�%" ��P;�A;$. Wiley, Cd�r. 2Q�bB���2���!uTime Ser��D, 33(4), 631–6486��.��Z^�09). RAK�)�2+5��4 N. Balakrishn!�(E. A. Peña)�M.AnSilvapul4Leditors, Beyond ParaI�%^LInterdisciplinary Rei�0: FestschriftAHo�Hof Professor Pranabaa@Sen, volume 1, pa��293–304, Beachwood, Ohio. IMS ColleEos.��n�A.�(2)En�o�4ty, mixing, diI�b����%�mo���4 GARCH(p,q)-pr�!L0 T. G. Anders��R%KDavisa@-P. KreiPAK(T. Mikosch,5S Handbook!+ncialE/� I/1 48A%496!�rlin. Sp8 A�Madurkayi��Bi���Myp5�I$UzI1%�Q . Acta Un/9 Caro!�e: Mathe��(ca et Physi���2�L�4�������!�ae�. T� ng"�al.���A� t�� �\ boot� p. M�Oka��(6ab�6�D 689.���86). Erratum to:���� e�-f��9(2), 23!3238�� /?��tor�g B��)�<Source BroadcastaJ�s Lei Yu�5$uqiang Li,aTior MeB, IEEEi� Weip!v%Fellow  Ab!E�ct arXiv:1601.05661v5 [] 18 Mar 2018 h�p�.HDe j�o�s��-Ab/I=?of seqa memory� 6�2��b�� Ra� inner b!'%k�sOj�u� �s�Dadmis�-creg.���dDch��p�� vely*�� unifynexng q�� also& �>��an ���degrad >�. W9 ��i5B9"Q or b��)�9K� B��.��,not only rec�� Zbest  F�.<�  liteaU!but)�g�te�new!nults.�%3ext� the >4oB� Wyner-ZivB��Q}ZF ��w��9e�@available at deco��. 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Yu, H. LiQ �W “Dis40�0�s�<LJ&� �0degradE0�0”� `Proc. IEEE Int. Symp. Inf� �aory (ISIT), Barcelona, Spain, Jul. 2016, pp. 1834–1838. [2] C. E. Shannon, “A mathematical thebof�munic`1�Bell Sys(ech. J., vor�7 pH623–656, Oct. 194y 3] T. Goblick,!+Th�0 vlimitis �K�1ssion�data 9ana�9)U�s�%-�T�E2) �(IT-11, no. A�,p. 558–567 �| 1965. [4] M. Gastpar, B. Rimold-�(M. Vetterli ��olE , or:@�t : Lossy ��--�6P$ revisited��� 49, ��5)e 1147!�D158, May 2003. [5]J�Co=�A^� pres(Bof���PIxRE-737)4�1 w 0-21, Jan%�@9. [6] S. Shamai, VerduiR. Zamir%*A5Ic l=�/9�L�v�44 ��3 �564!�79! �r��9ApD7] V. Prabhakaran,�Pur-�K. Ram}�d“Hybri�Agital-Md code.�5�}��f�oM�iߵ�hnelE�� v���5-siO44573-4588, Auge�@1. [8] Z. Reznic,A�FederJvV���Ru & expanar��52)��8%� 377aT37�06. [9E�Ti!� S. Diggav-�]>��pproxim�C(characteriz�� A�5X)n6��� �5regiov��� ��1uQ�24-136M�20%t10v�ag�Ion ‘���F��’r� ��6-�10%�( 5966-5969,�D6. [Online]. Avail�5�: https://arxiv.org/abs/1607.08292. [11] K. Kheze��W J. Cb/!�-�usepar%�!�z6Ej��R�.!�>� pgr���v �� �� 1764-1781 � [12r��QE���wadm�tble�IHEu;A�e� �correl�R �e�v� 6Mp04616-4629, Sel 01��13] P.Bergmans�J�R�E6S�emr��&gomponA��\19i��2IJ,197-207, 197�l14���M�?n9M�A�omas, Ele6�d�I*�9��Xy, Wiley, New York, 199��15�Minero�Ui �m��Y.�KExunifi�@�;�agSo h��)#���!��_QG509-1523EG�5AG6]�El Gamal�Y.-H. �NetworkJ��. Cam�Xge UnzA�s�&Press^�7]aL<Nayak, E. Tuncel �(D. Gündüz%�&� ��kF��:�h�� schem��� � 9@ 1782–1799, Aprŀ�0!8]!�Gao% �‪��6r�/�r����7I��9E� 5660 672eI�t�%a 9] O�yevitz)ZM. Wigg�9 “O��2�9��discrete*�BFm�feedback�q�� � :���20` AhLee%l S.-Y�wungE�AF�'�nM�2!=o �y�bF401.602a�� �MeYassaee|R. Aref)T�A� �G �Q<�iZ-�Dvia Fput�<istic�#5bin$�v+ �6��67%� 6786, Nov%>84. [22] P Gács%<J. Körn-���o &D>is far �D=8�nNl��ntr l=�.��ɕ탱8491���723]%2hlswed)�:���OQ?>���`�c& 5>݁.�.�in�c. 7th guesK�f1 x�o��41974. 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F#M2�o�Zk"9 � T� �<1 a�:�'neu� �I%��s2by 22%�3 ՕB %�J�[. Tak�-oge!�� =ȡ�v�"��0�cc� !��%� in.� �>�AYguide fu�"��e�E�H&� ��u�&vi{ & D. ACKNOWLEDGMENTS�would>�8ank Laura Sesma%�e.� �q:�  A�A� ���a�. nded~ ���,!�! �! Ex�,�6n �,mo�#)g Inte� on (MMCI)�2 Saara�8 University, Ge�6y,YTAlexander von HumboldtW%tdo�/al Fe�� 2<�<d a JST CREST Re-w�UGrant (JPMJCR14E1), Japan. R EFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [1.�1/�10163(18] P. MajX0ta%A. Bul!�, “Ey2)ck18eyq[human–�E';+� on,”A�AdvW�� Physiolog�5��, 2014, pp. 39–65. Y. Sugano, X. Zhang,N��AggreA�: C� ��st2!�of audiEat/�n public�p� �8Proc. ACM Symp.�r E-� Soft"Techn��y�6, �,821–831. H(5httar, S. Müller, M. FritzAS�d>s Pred*�f I& t� I2fixe%V M�6��(IEEE Conf. )t er Vi�ap�P!$rn Recogni!5��5 �98�990. K.� Funes MorI0,J.-M. OdobezE2c8� *� 3d��*I�rem� rgb-d� N�� Int. ���:!�es7 ��3 �P2787–2791. T. 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Persi Diacon@nd Bernd SturmfelEZ',ic algorithm� �s1_� �a9@ al di�. Bnn. Stat��6��6� 397, 1998��@3 [EKS14] Alexa� Eng�.̈mlomas KahXR�$Seth Sulli�I$. Multigra!�co&.ZV(� �"l��s!�� ) <. Comb., 39(2):3%�3721�P[ES96] David Eisenbud�Bq�B�Oi��sI4)�E484!C1–45%@`6. [HC71] J.M. Hammersley`(P. CliffordA ��f��on2#�e H Tpublished, http://www.O�slab.cam.ac.uk/˜grg/books/hammfest -c| .pdf�71�u'LChristopher J. Hilla�I>��F�2�0esa]"�Odimensio�4�l� � Յ�IBA�2�1%L25%�2. [KRAM�T]6%IJoh�s Rauh�'�'er��'�s�sus S�h. Abh!| th. Semin!\iv%�A484A4187a��0%:�0�x[Lau98] Steffen L. Lauritzen. Gw&t s, v�G�e* of Ox!�ew�%3Sci�) Se��. # U�Press., !�a�[M2<�#�nA�cLagan�+ tich�Zof"!M���I)c. Am-� Soc��<29(6):1609– 16�.200A Oos16] FlT?�n@Xosterhof�G��|6:�(�.�Q�6{Ah:��JEindho�I!���t�U�T6Nology, M�re�?Pory.tue.nl/855107. [R�xQ� A��h �aN&� �<"P k3,N . \protect\vrulA=dth0pthref{ �xarxiv.org/abs/1406.5936}{arXiv:���4 �6]�E�E�>eLif�8�M�!baac�+higa�coudr!jer�=E��� Symb� 8p, 74:276–307eZ��Sam17aE�!z(V. Sam. 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(1994)�O���A�s6G� om�=?:�s� LWchaK^�%$�inu�{Eco2Da, 62(1):43–72. ��8Belloni, A., ChaJ�D 0rnozhukov, V.)w Hans!�C;X01��Sp.�� 2 ��e !�fc :��*minido��.:���80:2369–2429. arXiv:1010.4345, 2010. [3] ���2�� (2011)�apenG�ed Q��l�."N���= dim}��.��. Ann�2 of S�$!�s, 39!k82–130��0�<293�B009. [4�����L2QafL�E*�9in�>2��:���B!4ulli, 19(2):52�c547� 1001�=�8!Y��52���!0)-V.�g6�� f�rE�a):Mh��s�12.1297�%��6΋�!?�IN: 5�.&� -&Fd. Adv`(lsiR�i�nd e�@s. 10th World ConEFA 3% SocieJAug�=A� , III:245A�95��2!�220�1. [7�����n, C. (2014). Inference on treatment effects after selection amongst high-dimensional controls. Review of Economic Studies, 81:608–650. arXiv:1201.0224, 2011. [8] Belloni, A., Chernozhukov, V., and Kato, K. �@3). Valid Post-Se��(in High-Dim��Approximately Sparse Quantile Regress�$Models. ar�d312.7186, 2013. [9] Bellon���@5). Uniform post 9f�i5� for LAD r��m�%(other Z-est�tors. Biometrika, (102):77–94�04.0282�d 34 BELLONI CHERNOZHUKOV TVERI WEI [10���Wang, LIh�1). Square-root-lasso: Pivotal recoveryA3�s)�psignals via conic programming6��898(4):791–806�009.5689�0. [11���LFernández-Val, I.,%iHansey9An�P � evaluatA% withFdata. U91.2645�A912���and6Pa�-=� -�!-�s%g!f� %fA�nonparaE�c]J. The An%jDof Statistics, 42(A:�5A;7885V105.147��3] Chamberlain, G. (1992). Efficiency bounds A� semiZ���1A� ca, 60:56�596!��4jern2 4Chetverikov, D-�Ka:$Gaussian au�ions ![Lmultiplier bootstrapexma�! sums�h�@.�$random vece}� jQ<1(6):2786–2819U212.690�L�2��5���A0Anti-concentrI�Land honest, adaptiveaUfid��bandsz 5):178!�181Y303.715�J[16���C�8l limit theorem��� 9�in%�� 5��s!H0xiv:1412.3661e[�4!H�7��V1AsupremE empirical��cesse~H44):1564–1597uVE88iVE�8ֻ��T$Comparison!�� ��6�by�Y��gq":���bability�0orye6PRelated Fields, 162:4A!�7��301.4807%����9����E5m6�Y�_r�!�Pincreasing complexity���r �� 5couplingEg��502.003M�5. [20N��bLMelly, B��K&�onrLnterfactual distribu���.:"81:2205�R268a �09��95e 09��1N���� �(Spindler, M �ANO &�!|� regulariz�d&� in linear���� many�y( Jinstruq s. 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Hence, Condition WL(i) holds for some ϕn satisfying ϕn . δn . To verify 6D�Xi), note that by Assumpd 3.4(!�we have 2 ] & 1 and EP [Sũk 2 ] 6 EP [|Zuj Xkj |2 ].�|4 + |4 ] . 1@� uniformly over ũ = (u, j) ∈ Uer k [p̄]N��v)j���we us�$e decompos%L� � −  ′ k = (fu2 fu2�)��+ X j (γuj' H�� )Xkj e By (H.2)�(H.1)�%L!�2��and?�%8in U. p (I.7) |:��| . |u~3�|H�k ����,k1 . p + p̃21�F��, K%{O���!z8�]. Therefore, j�� n��e suchIs2�� 6 ǫn ,5&  p |!�>��!�|k!�k∞ + �2 � ·6e�  p !P8) . D�26<�·?�l. 30 BELLONI CHERNOZHUKOV TVERI $WEI SinceE�< max j 2 2 supli |e�n1/q Mn,1 16i6n,j∈[p̃] u∈U !B.F�:&� 2 kXij �a�S2 F�v,vqA�aBPMarkov’s inequality)�,with probabi�1Eco(1),�0 dUe (ũ,u�E�)6ǫ n� |En�7!�A�k ]!���(n−1/2 . k � �] In ad��N]�,q E��e � dUe ��)MEA�E��],  s  2 a �e���6���(;.)2 ] |E��·.,��+I �*j  g. (%��+!� 2 )(M��)� ǫn ��P Further, let U ǫ de�� a minimal0 -net��$U . Using ��(I.8)aA obtain��I�Ez� U��,=�2 |(En%�$EP )[Sujk %�sup2?�ǫ�B��+El. To bound the first term o� e right-h!�(side of thi.��@ apply Lemma P.1 E�Xui%$p replaceda!� @̄, respectively,/�1, 2 Z��g�)!�B�E� e4i = w�$ _= EP1i , .�,���i Q�n$fui ui i 1)(n. With  ELK =!max!w!��i��:R~# " 6 EP-�%��R 4���4 4U� , |Z���p. n2/qM� which�f{!��l%�yieldsAt�5�%r{aGq? log an J� .P�Y� iymalogar an =��N%�imEviii)��us>v �i"x EZy  ∆n%�s �s"� �  n �S�POST-REGULARIZATION CONFIDENCE REGIONS 31 Next,��v� *� L.1�e func� θ 7→ Ma(Y, X \θ) is convex almost surE�)�is%�i�(requirementar>x��� t"a 6#�(a.b 4   [∂θ Mu��, θu � � V�, au )]a}δi/8 fbu2 r̄uj + (��! � · a�δ, so��b��<e Cauchy-Schwarz%�triangle� ies, s�� wu = p�c� �A� ��V������,√  6 kfbu �kPn ,�J���/( " · k� � .JsupiYy�Ji�. ^6 1��so �IJ.1 showAatI�nm�v F��6 ��>�� k)�� (sn i� /n�8. Also,!��2,v��(I.9) tJs�zkZ��� B�� �*�" �"CnZ!� Vi�To!pve>j�b), a�, Appendix L,wa��=6G Y b0 = Ψ �j 4diag({lũ0k ,.8 }) �� = luj0���[S 2 ]%�, Ψ ; v . 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ZE�M 65 E8��Aqm4M/�$$   p k�J 6ҽ �� a8k 0 Z M�2 Aǫ−2 ɫ�U�n�"&!�A�+\�Z?; dA�g√ Z x�M: p3�3� uN�6Fb�I�  �+ A2�M�  �n"� ��)fxP@�x� B3E�/� �M� �) ~ k)0~e��7 �(�=k�2i�*U i�p) j m��+3.� (we used the� fact that integrating by parts gives √� Z M/ k log1/2 (1 + 2M/ǫ)dǫ 6 M (+ 2!�@ k)). k 0 Collecf\the terms, we obtain  l I1 . kM RJ |U |X(p + (log k)u�n  �p) . Therefore, since K > (E[M 2 ])', set�r K k K$ δn = √�v{�I.z� n )7�L I2 = E " sup max En kθk0 6k,kθk=1 u∈U   (θ ′ Xu )2 − E[(θ ] # ��R]�6 (�/K)2��(E[R2 /n �6 $2� K %t1/2�En Fp��.8I2 + . .B���, �` 66 BELLONI CHERNOZHUKOV TVERI LWEI Thus, because a�a + b)!Rimplies2 +��bE/have pV��I2 � 6�:t��up to an absolute constant. This completes A���proof.  REFERENCES [1] Belloni, A. and Chernozhukov, V. (2011). ℓ1 -penalized quantile regression for high dimensional sparse models. Annals of Statistics, 39(1):82–130. ArXiv, 2009. [2] B���83). Least squar!� fter | see�0on in high-dib��lBernoulli, 19(2):521–547. 6���32E�,BB�,%XKato, K)P�Robus�� ferea�in%<.��<approximately sp%INy mode%]4rXiv, 2013. [4���Wang, L �!��S%<p-root-lasso: Pivotal recovery!� �(signals viaA�icAmtgramming. Biometrika, 98(4):79!I806!I0xiv, 2010. [5���DFernández-Val, I-^ Hansen, C �!`Pr� evaluat!� with%d2� data�.:�6�Drlemann, M., Enkel �S u8Kuhlenkasper, T {(4). Unravel��a}rel�`ship between presidential)��v nd3<economy: a multi.semipara%W�c <,ach. Journal!�Ap��d EH!�lcs. [7] Bickel, P., Ritov, Y �Tsybae��A�09). Si�8aneous analysisc�LAA� Dantzigm`or. AV��7!�(1705–1732=v08. [8]J=Chetveri��D �2N!s,Anti-concent on�8honest, adaptiv�&�f!wce bands�.�eZ��$42(5):1787�818�A�a`�9��Gaussi��u�4ion of suprema!c empiricalaScesse~��4):1564�59���2. [10ֱ�5). E�A�A�iAc,r bootstraps��v���increasaɥ xity�%e* ed g1 coupaH�s1{���5�1] Ji��B.-A� Shao, Q.-a�����QIʁ$Self-norma���CaC@r-type large devii��indepena�8 random variabl!� Ann.�ebab., 31!|216A,22 � 2] Ledoux�C�TalagL (199�qPrFility�TBanach Spaces (Isoperia�y �prM !��>rgebnisse der Mathematik undihrer Grenzgebiete, Springer-Verlag!K,3] Negahban,�� Ravikumar�'$Wainwright �Yu, B%\<12). A unified f!V work%CBf.Bm-est��ors��deAos!c< regularizers. S-al Sci�2, 2�R538��5U�A%�Q14] Ru�on%q�,Vershynin, R�08). On����nstruct�F,from fourier%~U�Tmeasurements. CommunicM@on Purer��5�$cs, 61:102� 04E�5] van%�Vaart"� Welln�cJ.E3<6). Weak Converg! iy��PQ#. S-� Ser� in 5L4s. Fuqua Schoo�:pBusiness Duke University 100 -�@Drive Durham, NC 27708, USA. 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Kruse R, Borgelt C, Klawonn F, Moewes C, Steinbrec�$ M, Held Pv����uh13. Du K-L, Swamy M N S. Ne��N�� �Sa�st�  Le�$�.W�Londo ^|4. Jang J-S, Sun C-T, Mizutani E ho-F�doft-eing: A �$l ApproachA��9Machine 6��PN"(ce Hall, UpA�Sa &River,vd Rezaei A, Noori L, Taghip��M�� U)�tRBF�Mod���w@Inhibitory Concen�� VaV&�D$&mi� (by MTT Assa C$r Cell LinAD�rn1 Jourof Iny ZEuology�I� er Sa�$ce(IJITCS)%�h6, 8(4): 28-34. Nelles O. N�ic :59�.I<01. Kasabov N. E�R%ځ��QN – "��ppl�i?bi�Ejmotiv��oc. “ik$�or ] %h�p! , De%%O" ^!26c ”,�gaporeE 8:271-274����:!�!�A�2���Con-� adap� �u , deI�m�B� Nrol. Au)lian J.�A �s�t2��P�(y)��s �4, 5(3):154-160V�� Conn9!onist?9�J�,03. Lughofera�5�i� �%�2�, AdvA��du�)�=�y.a411. Bifet A. A1H2) : Pa��n:� ��D�! >�OSa�sse�0, Amsterdam. Belikov J, Vassiljeva K, PetlenE, Nõmm�90A novel Taylo�� � �a��A-�.��NN h �e </of AN ��sq27th C�se!`ACU'ce, KunmQ"%@a, 2008:474-478. j��5�.�e-spacc! dN�� ilL* �a6 � � �S � �<WCCI 2010 IEEE Wt Cong&f��al}�<Barcelona, Spain�@10:3816-3823. Cyb!� G.A�roximK��superpos5*�"$a sigmoida&�. Math�w)�S�"�sq�a�(89, 2:303-3�0Yamakawa T, U���oA> Miki$Kusanagi H eo �@�o��� 2`to 5q�c ��$*2b I3 behaviorU;nd!@�f.!\i� Logig >,“IIZUKA-92�EpIizuka, Japan, 1992:477-483. �9�.����u��M꡸ "��,�tor��fil�+ngA�:��Hybrid1�: ��,>�� Mr%tic As&%�,97:331-349. 1�.��Analog i�  �!f"*E�=�on-board"% �2�2�!�A�Ѿ �9:144-1��W] L-X, Men��J� �6T$s, un� sal ��Q�)orthogo!y0least-squares�.�.i� Trans. onFK!�,, 3(5):807-8A�TakA��T� geno��M�*��$N��� !�2��A��z , Ma �a�rn!�%?@85, 15:116-132. S �, K!MG A��|F��i��. )jSe��}! $8, 28:15-3�+ jung? ":R �:�"<��Us:� Inc.^� (87. Polikar> Alippi C.� �ik$�n*O!E"environA���m)�!S>�:{ ��8(4, 25(1):9-�8Jin Y, Hammer B�[^< �Big�-�2}�(ce Magazineu�9�2-� �F�)man��H$�eA}Tibshirt �R� Ele���V� "<�,j er� �� io. � � � ,Bodyanskiy Y�zol@zhniy V. Cascaded!(re" /�s� (�)J> �� Int. Symp!�� "�. Ins, Leice� , UK� 10:26-29.F��(kshenev I, >���AH1� "�"� E��aB��3r.b8 of European Un �S� aiV�z*� d(EUSFLAT’03), Zittau, GeP%�y� 03:375-37F��0Otto P, Pliss�Popov� �n�3��� comb@ 3 vari./�f)*$�h�r�Z�s�! e No,in Art"�09��D2003, 2774:967-973B�(Viktorov YeI��cI:=h.@ ucubic # a-ɟ"D"�{t.T *AO�o� a�.� %Y9, 16al245-25F` TeslR (N, Grimm P.�l6� ��&V���P� �1� )� E���W?I,$ColloquiumQ/Goetz2� 9-46:f$ V, Tyshch��O� Kopw i DE!I��d,.�&"45�urP+I�,�on pool 6�a�4A�e� AR�.�!��er �!��qX6(8):11-17. 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A PPENDIX A TABLE OF NOTA� S� C C*�U>aa"� Cރ <)  !}qxs1 �5��!*��r1rb�x:x  k Shlb/"�!�!u�2S��al���s E V1e/Rangb�m{ nÑ8 R��! ,? k�(�', k�"� su Ď n B�3` =!�9P ���nR) �8", kqu2(� P.V%i$ 41 E1 &S��oc8E.D;��<���be����uV=!]�laIiA�oxdf4Ns fal2|7�9��P�9fRr�a���./a���u2�Y��L���v�awa �"�Y B%<]  CB�e�F� N"9(OGS2mL��f��B Q Me��he w����o���Ju"; S*}2�"�z�$i�8� A2R�d.��.XnN4)�/*��el�� s Am�\�&:� O:�jEo:�� !�A�]] x ? �H�b�x �P R R! Rate���G��� *o Er pg k ` 2�hq6Q q�� m6�� N n �D �"7*!k%xxq �� ����` RLP Gilbert–Varshamovf�a6f cap�^acity of quadratically constrained omniscient adversarial channels Key rate List-decoding capac�] aN]8Linear programmY8bound, an upper  on�r �Vr` RLD,myop N/A RRankin  o> 6 �N. c1N�n´1 Radius region ? Cap ?pxpmq ` ?!�l.lD n sQ , nrq “ B , `N ` nδS q for m P Orclpz5\xq Optimal solution to oizaXI.27 ? � nrstr�,a strip ? An 2A over!�Lof?B n p0, nP q withAhntX0error at most� SQ`James’ attack vector Qu=4of s r ropt � ?!B �,iq s sQ E 1%4E Y Er See Equ�9B13 Item XI-C.315 F 1 g „ N�dγ 2 In q k P t0, 1unkey `�r|M!G�$|{2n s ? %5)�X s, ? nN q X C pkq ? n j�'m�,U pr2nR sq p�0R m zQ P Z, i4´{δ ` 1, ¨ , ,u N P Rą0 n2 key�nRϢK$, j P r`s .Jιq5 Pwlog |� | n �$�0 Rcode´A� R ` �¯M 1 2 7 0P 4N pP ´N q |CI,1tP ě2N u ? `Mn˘� {n 1 P 2 N pα α ´ β ? βqE$ , ? P `2Aq2whereHm? ,β 4.72 Dˆ ˙ ? pP `σ 2 q N q´2P 6  1�02 N σ2 `P ˘!� 2N �B�26F�28 Ga\� R PP`σ 2 p1 ˘ q w.h.p. |S| S�4tsQ piq ui“1� ? s P E��/!�sA�$S 42 szE�iY%eYxPC ? ? 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WArgu at thisJ}i;e%amm\ing�yM recanto1mY�I_8enjoys a vanish��prJ)��asympto����%! �! limnÑn��a�X�-�( “ ě 1 q� m�H ) ÿE�F3Bi Ppm m� �B!�1u| |N:pm |pe\ qc |� Ppm R)Bq�< $3 Define e� 1tmP9u %�A� � �y Hpmq�,Hpeq ` Hpm|e.Pp Mq3 1*006:��# `2�Y�,. It follows��-�5� /P Z � !W!�p�´ �´jjq�� jN �� ´ 1Q0 qA5+ I q� 1N�6Cq\�^B1�V ÑA�Q�.�g*��C Q UADRATICALLY CONSTRAINED LIST- DE�DCAPACITY A. Achiev� . nRA�PWe use a random spher ���awK���E�{quE� Pchosen independently?e�� ly at n from] Euclidean �$e centered�y0�,r8 nP ? . Since ?��ha�NB�of����$ received N .5�! uaranteed��li��in�shell&� XYqe` will��v�@eMā�stronger�Dult: Lemma C.1. T.� a� ant c �.?�%A4, but possibl�EN �d R*M M�?E�1 ěI�82´Ωpnq . P @rSh z�, |B py�( X C|9c&H   Proof. Let L b � desi!�� (. At first,��increa� h4 1�by1 m�$amount. As2%[ see later!�is $be helpfulG n-�\Afo� �1/e y�. �-4δ – N 2 {8!� ?�y�  fixed yw2�  ? �8 show nN ` nδ E�yALsuffic4ly �. 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Wi�DNew York, 1991. ܙ���C,$6�@�@$��Porting HTM Models to the Heidelberg Neuromorphic Compu4��Platform Sebastian Billaudelle 1,∗, Subutai Ahmad 2,† 1 Kirchhoff-Institute arXiv:1505.02142v2 [q-bio.NC] 9 Feb 2016 2 Numenta, for Physics, Heidelberg, Germany Inc., Redwood City, CA ABSTRACT Hierarchical Temporal Memory (HTM) is a computational!%�ory of machine intelligence based on a detailed study of !a4neocortex. The^p CBpH, developed as partTHum!��Irain Project (HBP), is a mixed-signal (analog and digital) large-scale pla%� !cmAA+networks� spik 0urons. In thi�4per we present!.D first effort in p]}VIBM^P. We describe a frame� �simulaE�keyE�0operations us��� �s. 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Hu&��1�jr�N�niB�h��AISTATS,B� @ ��21��ra.mHMatej Vecerik, Thomގothörl,>�Raz�+P�Xn�$ Raia Hads�Sim��� ���  �˅�:�_s�� RR, !� 4282b ^L+!a2]��4eshteh Sadeghi%d:2 ,(cad)$ˆ2$rl�>��i[;+ lighca �' ��L 42}*z� 1,�H3] Ahmad El Sallab,��Abd6 Etienneȷ�,Senthil YogaJ . E&?jfHlA}kee3P�st� �@�6�F43��%b4�@h�ulmerg"� B� (Michael I J��e�d4 ipp�tz. Tr����JI/V#E�ICV�� 188�189��?R13ι5]:i,lev-Shwartz,kedmmYa� Amno�6 ashuxaf�ulti-��Z�ʼn"��aJ�}.�A�329i���b� 29�\�Josh � Rachel Fo���R4Jonas Schneide�r, Wojciech Zaremba, and Pieter Abbeel. Domain randomization for transferring deep neural networks from simulation to the real world. arXiv preprint a�L:1703.06907, 2017. [27] Eric Tzeng, Coline Devin, Judy Hoffman, Chelsea Finn, � A�l, Sergey Levine, Kate Saenko �PTrevor Darrell. Adapt�Lvisuomotor represent%�s with weak pairwise constraints. In Workshop on ! @Algorithmic Found K�of Robotics (WAFR), 2016. [28] Xiaolong Wang !��Abhinav Gupta. 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H��assump! 2�A�"I.œ�second>t�fL= x4/51!�at�>,lmost surely � πz /2. ��Tn�.�5� �(ame scheme 0F#�w"� e �t�L&� �jL&��L͒2� ,)��e���1 4.905 26 E"M�d 9^ 27��5��25 .� 03� 37��35<360362�)�!�� sponi���P�c� ' tablW*  1/4� T �N�a�� �1&d 2_ .w� 6�.\ Z�V 5��.� 1.36U 30�705�7F�!�11!�09% 8!�08t>�!�10�07 7066 Th� �� ests�t� E��5�� a, ,�&3 E ��Xade�A $n observe,� e0�:��x .,high (≥ 8%�r mode��l:� (upA3�4�� 300)he �H $m less goouan ����"� of course( surprisingZr(����%}]y26��:� 596 1.448A�3�31�42� Af32 $0.4AS54.R /Ae249�DA�38 442� � � � 5���ۆ 44. Ac� ledg0s�am0k Herold DehlB �helpful�.� a� liIry versT �$paper. Re��ces [1] R. C. Bradley (1986), Basic6per�of �ng ��di� s, Dc�*� A�pstics. A^veyPre� �V|s. Oberwolfach, 1985. E. Eberlei�tM. S. Taquu editors, Birkäus�,165-192. [2],\Dédé, Théorèmes !&mfo� nels e"<!8@de la densité sk ral ur des s4s �,onnaires. Ph�d�, Uni%�B Pier�4t Marie Curie,1�9. https://tel.archives-ouvertes.frX-00440850 [3] J. 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R EFERENCES /�4Vajjhala, S.P.z8Fischbeck, P.S.t�7. Qu1x!>ng��icultyE�F��YUS6D �t 8�. Energy Policy, 35(1), pp.650-67��$2] GlavitsA�H. 93, Sept.��n secu� enh� g[!�t�encN��!dre״du�i�!Athens YTez199�HPT PܪeuY s. J٦��n:�i�Con�(VoY�� 16-21�h EEE.��hMazi, A.A., Wollenberg, B.F)�H}s , M.)86A��Wah�\z-� b��b>4�.�Trans҆on2�s, 1(3)�258-264/�0Granelli, G., agna�, Z ��F., B�stiAM,��a�,��Innort :2006. OM�m��v�����c2_� manag� �t�\cb \�a�y��?b.4� i�, 76(6-7 �549-556k�Bakirtzi6�.G)�$Meliopouloa2 1987AQcorpoC�CWA~ope K2��Ar:��=cm+.� onM�C s, 21�669-675P�Rolim, J�ac�), L.J.Bic9b�X�eƁ�a ����AA$?IN��"i� 14q�336-34a�7]�� her,Z��ONeillE2PƠnd Ferr!�M.�(2008A�M96�1sV�:�< 23(3):13461355 � RuizA� a� Fost�4J. M., Rudkevi�(�C�an2�1a�O�qst6�t:� &p!Dn 2011i�)<9�= Society G�?p�eK�i8 � . [9] Fulw��D�amasra!S�(Cha��!J12). F�h�� .V-�ͺ[7)[w�386X�,edman, K.W.,=�!�F|fEBii Oren��ab 2009�,.�]���D���a��si!\>EJ�24qF15�58���:��!� O’U��!� , Ju��A ��ewaRZ�AF��U *��ZY�M bID(pp. 1-7قͬ Wang!Wy"��A.��AJPa�#gɠ oxa�B�of �G]l. a�� prin&"�522� 3] Kammer!� R., Frmel�,E�maiss �Milbredta��31\Co?V !G�9ou���an-automot���� �Pb��nd� ՛�i�\In IndQ�� I7$cs (INDIN) � 11th)v6!*�%�16ڭ=�4]a�rA!d, G. (B�) Cut-�z?� brid�F��to �FP�.��York: D�I�! 4549!~5]U� 2�6).&!M-Braess*�Kin DC�c�SM�acn�Ƙ!KCo� (CDC)&6)! 55th3  on � 3286-3293��_� Dorf��! Bullo,l2013.>�`@t�MSL� � al.�J Ci�j��� I: R�Gr Ps, 60��150-163���) Blumsa] S�S 2006)��iq�iPn:j[Dsՙ�>5u-iI�C �$ia�Ph.D.�s��,ܙ. Public� (., Carnegie�lo��@., Pittsburgh, PAA-8] Zia���R.�MHMurillo-Snchez, C.Ei�Tho�lR.Ji�1."� : Steady-KDKe ,"y�I��� toolɉ� q�^ � !.�E�I1 .% an;q� , 265�2-1e9]6 , Zh��c�-(2015).LJ�1ox22�Uu�(smart micro@f. y.5m.4th�0A2Mi56556-656y5R��2���7� Novela�o�G�!�q�ofa�2�� Model�=H� ogene��"�sm� pT��0709.07569, ac�I�{ Ame�n��(AC�G8aa(��REFINEM��|r�LEVENSHTEIN BOUNDS IN q-ARY HAMMING SPA pPETER BOYVALENKOV † , DANYO0EV †† ,ȟ@MAYA STOYANOVA∗*��@1.01982v1 [] 6 Ja� 8 D��{�{�mem���9Hrofessor Vladimir L\�sht1�,(1935-2017) 2��?developGGin t].@o'��q-u'Ha�s �s; t,�Io!��q�6rypOe� �JcHrܳl u!�be&��amA"�u��iL\)relev��U���ig!> iD�tafnd � *"��) �|�{Ur��A�r�"�0�� )�sog%D(a MacEliece `%q��ee�1�EC/�:s ���$aUl!F; arE"���!fhd�Lfae �Vc��.2GV � a����=e� �w2��*�D, {�e E� Keyw�� . 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Acad. Sci. Paris, Ser. I 350 (2012), 867-870. [12] P.K. Rai, A note on the order ofx S:v of��, Available at arXiv:1606.01493v1�3�K. i@On classificationOg �hav!NqTmaximum order, Arch. M�H107 (2016), 455-460vP4] A.R. Salemkar, M.RhMoghaddam and M. DavarpanahF4@eedi, A remark on! N�p-�D, Comm. Algebra 35�007), 1215-122%(5] X. Zhou,! �o:>k\22 (1994) 1-8. (Pradeep )t,) Department!m!6�Cematics, Bar-Ilan University Ramat Gan, Israel E-mail address: raiprdiitb@gD.com ��1 InteA�Pive Medical Image Seg�)�us!�$Deep Learn with ,-specA) Fine-tu Qf�U710.04043v1 [] 11 Oct 2017 Guotai Wang, Wenqi Li, Maria A. Zuluaga, Rosalind Pratt, P!�l A. Patel, Michael Aertsen, Tom DoDAnna L. David, Jan!jhrest, Sébastien Ourselin,E_@@Vercauteren Abst!+$—Convoluaal neur0tworks (CNNs)a&�e achieved state-of-the-art performance for autom!� m)� i%�s=�. HowevaZ theyc$ not demon�tkLufficiently accurate�4robust resultsw clin%�,use. 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SQ( Cal!$gh undesir��du���usE�0extra RAM, ma�$beneficiala�+� u!e block!nsynchron-,��h�}delete()�X��. �!\�<dispe��-�e �h�I��lthread!\ eratv����h$frequently � each1�which�x!��ym� spe!�q��4. 8 S�� IA�is papA !,author propo�� -&newaE  i��ax5�K(dynamic set�w bas�ze>u scheme ~<%!opreli� ry testaXnducted %� a�,totype Java- mR� �  seemAconfirm)�(it maintain)́ perform%�-]con1o)�onsQ * exten��Dof great practical�or� A^ank� them,=Ck �-d��adaptj sizu>��)a�U3or dea�f � ang7 indicD @ �re $ �# some�r�5 Asy=� w " �$strategy. eI vari����n ,�no !�t Q;�-�1 in com �^�P%7N�=�applic4s,�7make taY"useful a wide 5$profe� ala� volvI�faRar�l1 gram��0. Acknowledg!:%m�wo�5lik-�\ank Prof. Jacek KitowskiKhPiotr Matyasik, Ph.D. (AGH)�!�i� ��' environws)c0Paweł Salata  help��6 � in launchmulti� %�nts%�a�. ReferD (s 1. R. Bay�h0“Symmetric !�0ry B-Trees: D� 9zA�e�e� Talgorithms,” Acta Ine�aG , 1972. 2pC4M. Schkolnick,�Cq�cy�Ou��� �Vct 1977. 3. N. G. Bronson, J. Ca� $, H. Chafi)Y(K. Olukotun|A}�]&- *� � in Procee!�%al15th ACM SIGPLAN, 2010. 4. T�w�d�Helgau Non-��K-!uSe6 %z kAc.k�oInterne)al-�!/PrincA�Dis* ed Sys � 1. 5�!Hormen, C. E. Leiser%D,R. L. Rivest%=$ C. Stein,�Ue� to AY  3rd � MIT Press009. 6. F. Ello,P. Fatourou,yRupper i'(van BreugelF4F�J5AL!4299�4ACT-SIGOPS sym� um%0. 7.!S�isuU�t-�E�Ie�in 2-3=�Bl vol. 14, no. 1, pp. 63–86a"80. 8.A� Frasm�PՊ -freedomEUnio ita+� Cambridge, Tech. Rep. UCAM-CL-TR-579�04. 9.� Hank. . Ottmann%�!�dSoisalon-Soininen, “Rela� al�jdd-black�)w9�!  Co� xitya�97. 10.a�$Herlihy, YAiv, V. Lu� gco �N. Shav“A s2 0istic skiplis�g��%4th i2>i�a>S� ��oe� commun͠��pl�h. Springer-Verlag, Jun. 200�1.�!� "L Ar�M���]��gћ"A� seviA 2008. 12.aAM%SZJl WingE�L!Pizability: a correctn@ cond� Ŗ��object-�CM Trans on��Pr� Languag�n�cI�2%�0. 13E| V. H�a�Jon�%�t �-�lJT-��>2!��u�!�P��isma�ٶ%4�v itec�a+(12. 14. D�Knuth,� -�A�u� = @, Volume I: Funda��al}, 2nd E)s8. Addison-Weslee(73. 15� KułakS%�A.�0van Emde Boas'as a �!�m4=��  set al�>v)L��c)� ��^aE!�ce�ExperiF��26��2��360–3�s14. [On�]. AvailX �: http://dx.doi.org/10.1002/cpe. 2995 16.��T. Ku!ndA�L. Lehma�� nipu�ofbE�.A Dat.� 1��17.A� Lanie�AShash�A�2* 9[ b-�UWZ� 1986A�( Fall joint�EEI��a286. 18E� Lea,9�t.rA�Y . Sea� M[ : De�. %@�nM�ed. Bost, MA, USA: 6�8 Longman Publisd Co.��c.�99. 19��5�k S. B� YaoE�Ef�ent�� ing �9D*� !�B%R��6� "� 1981�de/Mehlhor}NäN “Bv�rd� di� arie" ( o(loglogn)+� o(n) spaci Inf.!yKA�tt.M�35I�4I�18��,189, Aug. 19��,21. O. Nurmi�FhvD. Wood%1�u AVL   Main-MZ� O, u cyE}HKUST.%�46. 22. W. Pughg9aB�s� of�d �e)�College�Kk, MDE0Bb80. 23. B. 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I�" nai885e�%�oU)�gEs,�Tpre�rA:Y���T�a&�)�5"t !>v#p4` E XPERIMENTAL A NALYSES.%� in:!�mu�Ō��B'Z&Z��, MHR�Rual N" j5s) [9�Rquipped#9$�0���)�����H69�����e�1/, nam� �Ag��!J"@g[18z9* 70R� ��! 5Ѡ5T��']�:h/10. 1 AnalysiŰ0�Pe*�}n B"m\�mA��e�\l<6H%� �&HSGDa�9E�-j\h եy0Y�"-8:�W, Sp, �@�G�i�Y *�}Y M!�d =$@ 2�E� mv�kK)6�R4u`�*K :� �A��+f�E� [12]�T depicB]�$FU�]]]�� �%�>�by� W^e.�t�� txa���8 �a(� � m )"p  )p � � **� " tQ] � W5<"�h!�6� 6 ��� ��� 2� 6b2:�4ult2b18JFe^U�I�net!�5Bgrop.% e{f(%)"�Top-1��R�z!�����������:�30)@30.31 29.13/28.9714 28.71 80207$00695/27.91N05/29.818$H64*49 27.63045N0 7.86�58<5B9f2 �H17B 051BZ72T83B1�25r53$1466T 7.11 072�v��H�44k� ers �`-4N�nd 18�B18)���A �" aug"� (DA qba�T�� 1�� 2,�Z:� � show� N�.'tbe~!� V2B� (](�;C " $ =�rV� ��&��Ŋ� 20cN�QD\.�:� n�*6�E�Sp/����i�$erF��<�)PE:C� v� b�u2Q��2��6.z���51]� *�-�=S=A�64%, a�2%Ea%3%�_�����PE� , Ob%�S]B2H.6Howf0� Q6�$ SJxJs�1 ��A�28.02%:\�# � Y 0.28 �.06% E�!�4.�byU�S�+thI@(6.77 J8.25%) � % �+St6��k& "jDe�1t ua�� ^;!n� :� q�a�}�&�1%��?z$"� Vof*�)�Ob1� Px�PIEdQ~POEA &�/>h�PEI WrE�s 6.81%E+Ad5%��le PMRS!:23%yA�81%:��:mty2�N t�!���%]�_ %#~ �5�lto���C"�U�G!MA��I2^ex�pP|r high1b�[1"n u2< Spɉ�%.OA�59%!P0b)I 5�I96Y�64^W�G 1�x�DtI.L . 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O�ll����:��~q��e�)�-P�#N;.� RCD�RSD� " T � +&: mh c��'m�[ medium T�#l��M\160���)�Q; Qer� � Cifa���p*�TIqlan� ��Z �KA�&PW>dev<�!d!�new5h� O ��V t�h as mR,NQ�z��o.ogt8o�.��A� Recuu� N �* ��&��,Q�q)�2�V�* Q.4U��Fas Adam� trus~kg�M� belie��.9K"�<*K���D"��� tudy"��Q�F!y"�9Z ��2���to�R��e�under^S�S?ep >ae�. R EFERENCES [1] [2] P. A. AbsiE� K(Gallivan. JZ�diagon*->��," �� 6Epennme0t ? si'�.4c. 31st IEEE I��Co�Acousteech Sig�L&�����|me 5, pages 945–948, Toulouse,��]AMay�6. P.-�(, R. Mahony)XR� pulchre. 2�?"�(� Matrix M&~2PUP, P#�et��NJˊ�� 7�3:>��(%�d�K 110-� 6(��an�Opth (RCD� 2N]�d (SD)V�R� ) ,C eFL M�.�B [11]- .): ()Z�.� a>  � ^�.�-��-RSD �{�n�)����( [3] [4] [5a� 6] [7] [8 9] a� %x~ [1.1/156(1218320] �1$ w. 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Clearly, 2�"�7��q#���e� e_����)lex^of 3�vy/ stud� �;�V rian�.re�(�1pic� futN"?<R. AQop)�E)%�seemsA-th�o%��e ~�1[at��� >�hyper%�s-��=�sti1X. �m6�0��ed]�4+�l� eat� i�?�+� ject�� aimsJ�ia F`$0g2�$π-calculu5����)  servIsol4%$$conflicts &%��!@Aet?/a"�nelxi�]8sU A?� ded-."_6 ands�)L7. ACKNOWLEDGEMENTSq uthod_+%�t�*(ank Dale Mi��z�anonym�8je PODC 2001��helpful��>.� 8REFERENCES [1]c. Dijk�5. H.���R:�\B$�Acta In�a��, 1(2):115–138, Oct. 1971. ReprinO O�3 ng S�%s T�9,s, C.A.R. HoaR�pR.H. Perrot, Eds., Academic P�9,e02, pp. 72–9S��in�%r� synchron 5��� of DV5P&z7,s. [2] N. Fr� z�M. Rodeh42bb!Uct �4 typeY�Aeb�%�un�(m�DProc. 21st Ann. IE�( ymp. on F�e��C�= er S�F|e, pages 373–379, 1980. [3] O.��5scu�8C. Palamidessi.|� a11A�2� In J�ury�ditor,� ing�FOSSACSA�0 (Pa�/8ETAPS 2000), Le�5S*�Z� 146Ag60. SA[(ger-Verlag,` . [4%�L!� , I. Saia�� R. Segala� ime ���.U2��Y�n !�osiumPr�?pli�Di?b* ��(Pa�’94)5�14!�$23, New YoL40USA, Aug. 199�*CMI�. [5]�Milner,!yP(=�Z D. WalkerA��( of mobil�i�, I%�II& m�#Bnd )wEW 80(1):1–40 & 4 77aw892. [6] U. Nest9. Wr ik8‘good’ encoA a]�0 �0?A>6y�JA�rrow, IQ3 r2REXPRESz�97: E�4ive�%in� currPH(Santa Margherita L�1, ItaaSepteG@ 8A\2�7), vol�87�Elect�4cI� in �l-�y�. Elsevi Publ�1 1997ll � !�� ppea' �a)� _%�. [7]:9.!a=�5�5ive p�of= .��d,n�!I�7ce Reco�Df POPLE�7�\24th ACM SIGPLAN-SIGACT f&�#gramm�Langu��q25a� 265,A� is, �{)�. [8] B.%ier�ndaN. Turna Pict1 h l h&��pi*Vof �r" 2$ 250–273%��z��'.J�UR�{44, LNCS 836: 2� 24< X�A Shrinkage��) pHeavy-Tailed Data: High-Dimen��!3(obust Low-R� Matrix��0very∗ Jianq�� Fan, WeicWaI�Ziwei Zhu arXiv:1603.08315v2 [] 4 May 2017 6#! �DRes<%�Finan{J]: weton Uni�Ety. A� �)pa�* "Zp�%r ��*-d= 5&� al i� �Fnp3r�7 s5r�7 data� iden� scnKqgh.it* reduc!_���D� 1s�'$ sub-expon�+al�(subGaussian&� %Nto mer�� ed�o6I� g . As�"�)ion�'i� � ,���-;es��$eJ-rABmIBΘ∗ ��trace re�37m�� Y = Tr(-T X) + )J mpas%Lf�H popu�0pr��0s: sparse linGPs�m�s�nsa���le���m�-task � . 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Develop!O4 17, 525–532s73) 3:sNo5j�%of�l�*Y5r} .}\44(1), 270–278 (2000) �aballero)X$Martı́n- P, E., Riesco, A., Tam�0, S.: A decla'5��er.[&s1�s (� ed %]o!� Tech�7�Fp. SIC-15/13, UCM (2013), http://maude.sip.ucm.es/∼adrian/files/conc !�24ONCUR 2004. Sp0er LNCS 3170,%H 292–307 � 8fTrans�!in RCCS 9�s 2005s s653 s 398–412s(5) 9. Field�, VarelaAA.:t ors:�*�9�[modeli mainw! ly ��!2�� in unreli%�environ�%:D POPL�� 19�> 208.Qu��%Frank� P.: I')duR=�$ing: motivET,i�ess !ch�ng>2nd�hf.��C�� Frontiers� 38�39y�(1. Giachino�O�A,, I., Mezzin5vCausal-=C�" !� 5� FASEa�Bm84q�37��384!� 14) �0Kua�_P.,fF� N�9Q[a.5lo��4 �Y�AGERE!�)=8�W935��3.!-dauer�T : Ir1ɒ� heatX,�bAc�5� �sAaBM Z�235, 183A91�� 61) !_b�,."mi�>�$StefaniaW��A�llA16�in 2wpi=$u�A@6E 6901)5297�E11%��5%2e�&B_,6���)J�.2�.� Theor��<,. Sci. 625, ��M[<6) 16. Lienhardta��r��A5!le absC-t me<e�0�'sp�=overhead=3TJu FMOODSAa2E& FORTe' 2 Int’le�s �4��727�4A�1���12) 17. Matsuda, K., Hu, Z., Nakano aX= �Takeichi: Bidir� alizE� trans[E�&�Lic der���vie��3�8"]-A�� ICFP�A7I*4A)5�?,7) 18. Nishi�$N., Palaci�A�Vidal, G6�% rew�ne�: Kesna�D., P�?0ka, B. (eds.)y�a�Fi�2InF@�a.��`Formal S"�P �v2%�De��L(FSCD’16). Leibniz:a�,eeB � In-pcse9 6) 19. PhY ps�� Ulidowski",ng algebraic�Y� . J.: �#l �6(. 73(1-2), ��96w!�20. Sve H��redluo#L.!� Earl� Bp un�)d&�,��EI�i!t9th�7SIGPLAN�shH1n 4I%2��3K � 0) 21�,oms�$M.A� AxelH�%�pre=�.� m���le �Aal&� RFUN6�IF�ѕ�(2016),��|0 ar 22. Ti�D, F., YoU�5��M�-i^pi-��>�Meth.�^�(. 84(5), 68Q7� H15) 23. Yokoyama, T6o�|Y��2�NClec� ic inoB oret� I�er�xeN 253(! 7��8�0)�� 8)Wor5��le M �(RC�'9) 246�,6� , Glück�$Principles!�2�=�"�6�A�5th��a� �ac:Y 4A�54.A� 08) 25��Funda�/al�=�flowchE9�){>�N 8�H115M� �#O +(power graph!��!��"�C� arXiv:1606.07258v1 [math.CO] 23 Jun 2016 A. K. 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Complut. 12 (1999), 117–132. 3.11 [17] D. Eisenbud, Commutative Algebra, Graduate Texts inb�hematics, Vol. 150, Springer NY 19955h [18:gThe Geom�p of Syzygies: A Second Course�A �ic3a!mmuΫ229��2005. 2.6, 3.1 24 A. DIMCA, D. IBADULA, AND <. MĂCINIC [19ݠFaenzi, J. Vallès, Logarithmic bundles ���H9�,��-Verlag, Berlin Heidelberg New York, 1992. o%�7% Papadima,a�I� ciu,�(Milnor fibr � of a]^.�$: from mod!� resonA] to}?0monodromy, Pr�(�9 A~. �:TDOI: 10.1112/plms.1202!+ [28]!K!d henck, El��ary| ific�i�%�configu �e�P2 , Com��. |Helv. 78!�403), 447–462%���[29S|9�. s: comp� o �conjece.>� }�$–Sapporo� 09, 323–358,a�,. Stud. Pure ���, )?dJapan, Tokyo, 2012. 4 [30]e:0ernesi, Defor�2�of�3ic�ma�Q\ Gru�+(hren b. 334ٰMy 2006!%3 [316k�]8local cohomolog��Jacobiaa�ng, DAI 19�@ , 541-565q�32]A�S�/8S.O. Tohănean�co8geneous divisor��srael�� k20ѭ, 449-48�2�!<3e)>iPro!�ive dual�/.F quadA}c l� vecte\0elds, Discret-� 339A�16%��1E�a� [34ż Ye, ClassU�!�e�i��2� of n��p�a%�yacH5 265�a 24A�(256. 1 [35]6;Ňn��ofZ i�(related top� Annales d��L Faculté des Scien��\de Toulouse, vol. 23 no.� d, 483-5A��6%� Yuzvinsky ���E� ly fB6� 4a given inters�on�/��Amer.�.mq118(199!&74�7"d,37] G. Ziegl��(Combinatorien"E !8. different)a�s�I�76�(9), 116-154a�Universi!Bl Côte d’Azur, CNRS, LJAD!��( E-mail add�`: dimca@unice.fr Ovidius X!K%�e���%]In�� d124 Mamaia Blvd., 900527 C�8anţa, RomaniaF�enis.iba�M�v-o � .ro a�Lon Stoilow Institute!E�, P�|Box 1-764, RO-014700 Bucharest, ^�@Anca.Macinic@imar{( sAn EM��o !� absolute tinu�sxbivariate Pareto distribution ��C608.02199v4 [stat.CO] 18 Mar 2018 Arabin Kumar Dey∗ , Biplab Paul%�DDebasis Kundu Abstf H: Recently [3] used6�to estim�s� |(shall-Olkinv�0. We describe5 ��1 E�oA� thi��9>study� *� paramea� by2� both� pres�(%a�outof a�T� scaleW. 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REFERENCES}^(M.Marzinzik%-$B.Kollmeirj�3DPvADe��A� N%;S�trum.��By-ck!�P�CE�<c5$s”, IEEE*nsa�sLT r And AudiohXce@A(, Barcelona �H10, No.2, Feb.2002,�Q 109-113Y�$7 Screenshp|G�UE�U��p=M (� �<M.�\MoattawMU, Homayounpou) A� Y4y��9��1A�v0!5C&�0! ( 17th Europ\Si�:G� ��N<#L(EUSIPCO), Aug. 2009� 2549��5�$Dr.F�N+�+lZ@%�as `isLLt Professor Dept. ofv�N *�N, Pv�N. S� as t� 12�8ft�A6��r#��')Rsej aL���#�4es QoS�rov���} gene�� wire�r sA@n-invas=���*on< gno " engu@�� !1�m_Cs������&�vO �A23 . �&0 Namgook Cho ��Eun-KAjg Kime�Enh�.dIS JSs�A�4EvYraSC��@A{a�� m� On�s�r E5ro�Pis 57!4��iuzgEd 3 rd:dCoՖOn2�� a��=(ICECT) ��v�; �;441-44�^8] Wo9Gevaert,z�$rgi Tsenov%�$Valeri Mla�v,D%�9��d� ^2-� Of&�/��Q,*���BelPE?20,{�0%�1-�[9] %�.Revad�$.K.Rambatl� $K.V.N.Ande%�A N�Ap��ToJ�H �� �#�.�%:�%�IJCSI V>]} M} I��)�8,  w�rche� 484-4892^40] Abderrahman\hr:Sm J�0Michel Rouvae�����݉Z� � � R&�(6��WorldZy� �,2�{Y� � 1, N�{�� 2712�a �X!�Bey;Tem�El Poo:aDA c �!�5 volu����Ges_.u$in Video L��0l Pigou, Aä�!va)Un Oord� �Sa� DielIE Miek�\n.= k."5P�*�q X �'�4� l � [%� �/�vplJe��**I �.�5�!� �Zw�>-toKQ5R>�.ep o�I!��� u�A^bizY7�Q�IEOu Li�<n�.A�<wofold;�> , we�uD!NkT%� �0; �>+��)��BLQ�����'� ���O! -v��;dif�t ")ach�/n$MontalbanoR�$setQ,wZK�`5(e-of-the-arpD�1 ��&�; �Z]~! 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Newton-Raphson with SuperLU Direct Linear Solver We leverage the-0[16] sparse d 9s2� library to investigate parallelizability of R$power flowB�over multiple threads. There are two stagesE |8: factorization5 into lptand upper triangular matrices,T ing �rres�3-\xs. Care must be taken to permut�e ^xreduc amount�(fillin that ks durp2�|, which can dramatically increas XnumberX$non-zeros ^e1� �(. We utiliz 9approxim!�Pminimum degree reorde �rom!D COLAMD [19] packaA(o limit!�-in. Sin�is is aQ6method,,reno iter)�Dnecessary. However* total==comput 4 may still!�(high due toc inAFnt cos%w!�) 6gEpH main benefit of us!�4sIHM� ��%�it more robA,for illcondiA�ed vcEn llowY}to�A�0ed in cases w��m�Krylov�fails;(converge. Bu� +with I)fve 6�ForJ^�r, we Q/an1�ve -to *Buy��Q� each � 5�. SpecifI�h@tested a bi-conju�I,gradient sta�J zed � � [20]a&AQlcY al routinA� quir!Zs��ed�� F�Each 2K��!�assig!�a blockazpro�8or caches. 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U��%� ��2Zi �� we c� <�up �%�ٯA��ng�!2:�s� Tabl�HSolIj1� զ�(in Matlab $ Bus NO. .X Win i7/16GB Mac i5/8 l Oo  1.121744113 0.319107 047195@8K 3.9944 5.439 *89616*59578$H6K 17.6397 38.928!799942 092241 9K I�(1E�() 7.2K × �324,21841�4.4"2.3182X 4501X28�D4.997�$954925 57�!$11.8052 2�031 115.dP6.0988 4.346155 230!@55.291 9.980889 �E9thr��, v�� ���isE�da�� 906 LV�5��>upq 6_b6Mi]aft}h"rs�O�is�ex � subs���5 � wh A�meters�� adju=�revY a voltagoopc�cint viol3� carri�ut a ��}is� vary�� of580 val" ��er.��� � 2�temq� ex on aabdo�5Mac� uter� $ ua�% � �D 3 .u�.2 es� ghly lily)!�5�<%˅�eP!*�!(4 benchmark er (�H)!h onenc lyP ould]aus!iy manyo�a� u Y�N� Y�%{*�9>�to le� an 1utL : ** �Bin �b. Time ���k( miscellaneTope��ns,�lud|� initiE�,S0termedi{ }s, etc., �rec�EN�“��$” column.�0 [2] [3] [456] [7 89] [101]�{3� q]�� %�M� H���� (' Mm)!�>a I bcan�� u0 memoryA�r� . ×T-�� �� l� 5�F�n ���ion@�rast,.LX s�y } Q�enabl lus� ,��bfrequ��& �Mion&��ae trenE/app�'inwrte� L &alysis. 5HACKNOWLEDGEMENT Th� � �l�! A6]��paperI $been suppo� $by LDRD fu �t C2Re e Divi_((CRD), Lawr�$Berkeley NE�al Laboq yaM�S��!�@ject. REFERENCES O [14A�E�,16] CONCLUS�fut�E w@to fur���lv��:te� �ao�� �s, es���N7s w�� fideO��1b��!�=haȁFsharedM�� ��%cur��Lv��U���ed-FJ g IA�.�s:�� AVI�=1�>1�?$M. Bazrafs�@��$N. Gatsis,��Arehens�Mo! ng_ T��P|D.|S�s via�BAdmit�� rix,���T�. P<.,p. PP, no. 99, pp. 1–1, 2017�7A9��1��2��2���nv�nc�����M�!] � 2�Load-FE#ZIPs��V. Rob�4, M. Tarbouchi�F. Okou%�P� )3�on Graph�P�!�Un�A�ConMv E�J $of Many Ne�B� Sm��-�8)�4-�639!�$648, Jul. )�dH. Nazaripouya, B. Wang, Y DP. Chu, H. R. Pota �DR. Gadh, “Univar�<�series�dic�soti a hybO C. Qiu,C-x. Pr �$ve Schedul!�Frame�!� Elec� Vehi�, With UncertU !? of U��BW=�I�,net Things Jq�4)�1, a�052–63, Feb.�7� et al.I��s�V�consi� u�y�lo��b2���ʻz��4E� -�d�)�v)�. ��f�5 �-)���al.�on}���mun; q (e�a�Comm)�D5I� 313–3185�e�HI�E�q�.��V char� algo�&!��%%�p�"a�m>q|InnovaK� Techn�.�(ISGT �e��8Energy Society,�� �m�Y. Xio����Nk�u�$ed OptimalqR !E%�gr �Sg{ 2Z qon�ArXiv pr.  170304552%�7.��+ W. S���-^��"�  ofK!��$!�mob� batt�Fin6�"� Appl.-Q$, vol. 190I/128��301, Marq�W.��KerF,62� ����a� ,�i PBoca Raton, Fla.: CRC!-ss%2.�VSaadat,-� YL.��Hed States: PSA Pub.A0.�T!� LAB-D Sim�Lion Software.” [OnO]. Avail 0: http://www.!)0labd.org/. [A�(ed: 29-Sep-�].mOpenDSS!�$ SourceFor�"[^ds://s*f*net/pr< s/e��dssny(R. D. Zimme��VDE. Murillo-Sanchez�o J. Thomas�t@MATPOWER: Steady-%L OpeI�s, Pla� BA-� Tools ���� ems"J !�Edu"!i� 5.Mu26�v� 2j9�v$1. J. DemmB$J. Gilbert �X. Lie�,An Asynchron�"@ S�nodal A��ŠSC(Gauss�(ElimineP� SIAMqM�'x%.i7�0 �' 915–9a�JanaO99.A!^  al -2��$nersc.gov/�]s/c.� -iR&M�P. z)n rcia,�L� ereira, S@(Hneiro, V. M. da Cos� N. MartiA“3 �!� � "#��� � �  in� *� ��J �� 2IT508–514, May 2000. T�Dav� J�U(S. I. LarimE�. G. NgI2 Cs A*x(Mx(Dx(Ov(U;EACM �Ah�Z �3M3 �35�z76, Sep�I04��vD)er Vor�L“Bi-CGSTAB: A Fast�Smoothly�� ing V0 nD(5E�!oSolH(of Nonsymme+ g'� � Q� Sci.�L.Qpu"� 13I�-�63�d644� 1992� Jalili-M$ di, Z. Zh� !r V. Dinava��$“Large-S�)B�$ SP'ty ���� al�:�oony�GPU �2P? ��.��� 2 �7)�125a�1266,"� �2. #�SYMMETRIC INTERPOLATION, EXCHANGE LEMMA � @SYLVESTER SUMS a D:1503.00607v3 [] 6A S t6 TERESA KRICK, AGNES SZANTO,2!PMARCELO VALDETTARO Abct���] 5�V LagrangR terpp`(a beautifull$�$her unknowp$oh(��.�. H[we � ve �iA� Excht Lemm!a2 l2�xpl�*�&m E-$natural wa4e full descrip�=o�dou;sumre" tro�,�Sylv$er in 1853o�7sub�a�$n�ir Bézco"�',s. Keywords:W�� $0 MSC: 13P�� 65D0�� ��: Chen�J. 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In: LeA`NoQDiq�er� , 136q�� 135j��h�d chapter�g$BFb0026595�6] Swakkhar Shatabda, M a Hakim Newton, Mahmo�e Rg=xd, Duc Nghia Pham & Abdul Sattah 1�/��\\�! : reT? e di��56Aa�E5D�6v.N^(14 Suppl 2( �SI\�BMp-Eq14-S2-S1j� �u3549842It �uD7] Alena Shmygelsk� HolH Hoos�N� AB.b:9�sI�U~%E�_2D%l3D:=_*� ]�GRU6e�N�)B63j��<555464�;88] Thomas Stü�|&5;.9<0):p76o7"� e�a�y�Ls 16(8AD$p. 889–9�^QK�PS0167-739X(00)00043-1f�$inghub.els� r aieve/pii QP043 D19] Chris Thachuk,�5A���"'V2x69>�^W8 R!8I!42Z�8-342f;�# 207192m`~_H20] Abu Dayem UllahO athl�% Stei.V1A*A h�-q+V�e2ng�ng~�:�`�.�RF11��1%OS3&N`6#11-S1-S3Z� �'3009511ix�S41] V Černý�x&dgK:�=t�ftrave?alesma�8 lem:��e�=�� U�2���zi�tn�v-cs 45(lm�4� 5j�. 2>aP�=00940812*� 07/B 7\ D� X�Y Z�Y��12 b ie.Z[f��as�\�'inuou�[,#f�\�j-ed �ml�--�(force fieldv A�s:&b,"][�Bi2� 80(N2ber 2k� 715–173*O ��1.24065V�+ &0,6 7�� ��BRAID GROUPS OF TYPE ADE, GARSIDE MONOIDS, AND THE CATEGORIFIED ROOT LATTICE arXiv:1703.06011v1 [math.QA] 17 Mar 2017 ANTHONY M. 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A�n-;�Z%2believ�J �:A.��#� ف�exact �toMK)*�IPSMT solvers. Symbolic:%���9�ZsA>�Y� �0esa\�� ice%�a �F oret!T �ioJSOmplaML�mun�3�oh�[ ied QC��h�-�e�sIFln��$of MAXPROB:uM 7, 2& 8,aig]2:el�![)��4� sen�[#>����4�> 'jgnAte c!i �'nno:of��m�:K or quantiA�v�j� v� 1`iAc�ilQ&ABs��esearchxSP �'s2"se,!6[�ERC St�!ngaDlnt 279499: inVEST. Guillermo�cPérezP 8n F.R.S.-FNRS AF/�L4FWA postdoc fefVs��kT@hanaël Fijalkow% t'�ouTr� ^A+T]"��A][Feavali��number�(a�� E�k Sha�r0Almagor, Mich �dCadilhac, Filip Mazowiecki�PJean-François Raski�=l�Ye�R� ,earlier draf�E is p��. Refer� (s [1] C. Ba/�$J.-P. Kato�PrwRp�iof�Mel ch��E@MIT Press, 2008. �~0S. Bharadwaj,(Le Roux, G.=� �UHpcu� du% techniq�1A�m�tu���?���A IJCAI, paV,4273– 4279�l17. [3] T. Brázdil, K. Cha� jDQMmelik, V�Xejt, J. Kretı́nský,*XZ. Kwiatkowska, D. Park�Nnd"Ujma. V."$�BaKtde�o�y9 �n"ܹB�@ATVA, volume 8837M LNCS � 98–114�4. [4]6�%;M�S�mer. Fas��dynamicw)~�mall:�#on�Cdqq�?e7"-h� �� �%i.1%� SODA � 131� 336. SIAM�1. [5] F2lesinsaQ�%�Größ1|!�leiQdZU :U:��)�� QEST�45–5%eE�6e?$Courcoubet�)� Yannakaki 0a� plex��o*�fJ�J. ACM, 42(4):857–907, 1995. [7] P. R. D’Argenio, B. �% net, H. E nseniiK.a Larsa�YQ%�$ty analysiš!��systemsK4 �rA�l% PAPM� MIV,Q� 2165�]� 39!;!�p�5!�200!�88] L. De Alfaroe{Au.-NR�. PhD��sis, Sta� d Uni�ity%8�9%�Dehnert�� Jung�mJ��)0M. Vol@/ stor�&c g: AE?rE'=.]Ta\In CAVE�}10�~0Eilam-Tzoreff�e &�"ks�p.N&. Dis�s Ap� d Ma�`8atics, 85(2):11��13�K99��11] N!��EGi��t,aMHor �0Y. Oualhadj. �grecur!�l�*s�E*(!�lA�� Y+automataE8E. Csuhaj-Varju�2(Dietzfelbin%�a(Z. És�r(editors, MF�Ց�634!�]I 26a278. .K��12]�tFo� e��E_4pcroft)� J. Wyllie1�r�L subg�H4 homeomorphism�lem-or�=� . Sci.g& :111�{21Aj80. 1.i [13]kF:3��P{ly* !i1T ��nd �rolF! empo�I��Tinti�RSSEr�14]a��Yuepqonflu��I  s: ArnY �f9BhAl�*s � erm rem8/ ��@^ @ B@.!"��27��79!�89K[15��elbling�� L. LittmaM�nGPoreMi�c��5NT: A survey. JAIR, 4:23q285!�96. [16]�. KawaguchiZ� d� explor�E�AA"� 175��76�+1Y7]�8Kolobov, Mausam:S. WeldI�H. 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Refer��s [1] J. Abuhlail, Zariski topologiesE�cNm/ �"c ,s, Algebra C�Pq., 22, 47-72 (2015).� 2 [2];% AltmPnd S. Kleiman, A Term�Commu.ve\, MITN 2). 4 [3]= Anni; ssoc�dE$A-� P�%VNo�XR!�4, Ph.D. Disserron, Uni �$California�!Berkeley�0�5 [4]�Atiya�#PI. Macdonald, Introdu�$�{R�(Addison-Wes^Publish�Co., Reading, Mass.-London-Don Mills, O�$(1969!m06 [5] Y. Baba%dM. Harada, On Almost M-ProM$BdIQerous A�i!� (etal outcom�.;%�he� pl c. I�m warn  abY high�Gsum�(E��� Q@4of fossil fuel�2 glob��rm� get��stuck at���Dages!>s [Xiang=�08]�ri�ga�&ices a�few 0mp!�I�a� rɮ-�mFs. qala�� 2a!n enA�s.3k8travel expenses�@c!ulda8a� ��)!mot�Jion. It(, 1notA��.�is dif�ticonvenBal��!�vans�0s ded� \oI5 oE�eg�< ba� [Levofsk7 Greenberge'1] �%b^ limiR�SE'ect%i$ing. Taxi ice�vid���/nef�5�A�advantagEL>�wel�<s� mpana��.l�l\ofH�s:� � fleet siz J�>�� r_steametD>litan�as����lyq-xa�%���=on)w:i\A5*� means P., %� J. Y. Yu,z C!#C� rdia&� *4 InforV on S)� EngineeA�,�/c9*� Montz L, Canada. 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