Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Single Differential Equation Description of Membrane Properties
  Underlying the Action Potential and the Axon Electric Field   In a succession of articles published over 65 years ago, Sir Alan Lloyd
Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical
understanding of excitation in nerve, and how the axon conducts the action
potential. They uniquely quantified the movement of ions in the nerve cell
during the action potential, and demonstrated that the action potential is the
result of a depolarizing event across the cell membrane. They confirmed that a
complete depolarization event is followed by an abrupt increase in voltage that
propagates longitudinally along the axon, accompanied by considerable increases
in membrane conductance. In an elegant theoretical framework, they rigorously
described fundamental properties of the Na+ and K+ conductances intrinsic to
the action potential. Notwithstanding the elegance of Hodgkin and Huxley's
incisive and explicative series of discoveries, their model is mathematically
complex, relies on no small number of stochastic factors, and has no analytical
solution. Solving for the membrane action potential and the ionic currents
requires integrations approximated using numerical methods. In this article I
present an analytical formalism of the nerve action potential, Vm and that of
the accompanying cell membrane electric field, Em. To conclude, I present a
novel description of Vm in terms of a single, nonlinear differential equation.
This is an original stand-alone article: the major contribution is the latter,
and how this description coincides with the cell membrane electric field. This
work has necessitated unifying information from two preceding papers, each
being concerned with the development of closed-form descriptions of the nerve
action potential.

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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat