Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley
  Dynamics   Fox and Lu introduced a Langevin framework for discrete-time stochastic
models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system.
They derived a Fokker-Planck equation with state-dependent diffusion tensor $D$
and suggested a Langevin formulation with noise coefficient matrix $S$ such
that $SS^\intercal=D$. Subsequently, several authors introduced a variety of
Langevin equations for the HH system. In this paper, we present a natural
14-dimensional dynamics for the HH system in which each \emph{directed} edge in
the ion channel state transition graph acts as an independent noise source,
leading to a $14\times 28$ noise coefficient matrix $S$. We show that (i) the
corresponding 14D system of ordinary differential \rev{equations} is consistent
with the classical 4D representation of the HH system; (ii) the 14D
representation leads to a noise coefficient matrix $S$ that can be obtained
cheaply on each timestep, without requiring a matrix decomposition; (iii)
sample trajectories of the 14D representation are pathwise equivalent to
trajectories of Fox and Lu's system, as well as trajectories of several
existing Langevin models; (iv) our 14D representation (and those equivalent to
it) give the most accurate interspike-interval distribution, not only with
respect to moments but under both the $L_1$ and $L_\infty$ metric-space norms;
and (v) the 14D representation gives an approximation to exact Markov chain
simulations that are as fast and as efficient as all equivalent models. Our
approach goes beyond existing models, in that it supports a stochastic
shielding decomposition that dramatically simplifies $S$ with minimal loss of
accuracy under both voltage- and current-clamp conditions.

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The categories of this paper are: stat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat