Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal invariant sets of the diffusion tensor and the development of
  a curvilinear set suitable for low-anisotropy tissues   We develop a curvilinear invariant set of the diffusion tensor which may be
applied to Diffusion Tensor Imaging measurements on tissues and porous media.
This new set is an alternative to the more common invariants such as fractional
anisotropy and the diffusion mode. The alternative invariant set possesses a
different structure to the other known invariant sets; the second and third
members of the curvilinear set measure the degree of orthotropy and
oblateness/prolateness, respectively. The proposed advantage of these
invariants is that they may work well in situations of low diffusion anisotropy
and isotropy, as is often observed in tissues such as cartilage.
  We also explore the other orthogonal invariant sets in terms of their
geometry in relation to eigenvalue space; a cylindrical set, a spherical set
(including fractional anisotropy and the mode), and a log-Euclidean set. These
three sets have a common structure. The first invariant measures the magnitude
of the diffusion, the second and third invariants capture aspects of the
anisotropy; the magnitude of the anisotropy and the shape of the diffusion
ellipsoid (the manner in which the anisotropy is realised). We also show a
simple method to prove the orthogonality of the invariants within a set.

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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin