Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivatives of Entropy Rate in Special Families of Hidden Markov Chains   Consider a hidden Markov chain obtained as the observation process of an
ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how,
in principle, one can explicitly compute the derivatives of the entropy rate of
at extreme values of the noise. Namely, they showed that the derivatives of
standard upper approximations to the entropy rate actually stabilize at an
explicit finite time. We generalize this result to a natural class of hidden
Markov chains called ``Black Holes.'' We also discuss in depth special cases of
binary Markov chains observed in binary symmetric noise, and give an abstract
formula for the first derivative in terms of a measure on the simplex due to
Blackwell.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con