Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean Time-to-Fire for the Noisy LIF Neuron - A Detailed Derivation of
  the Siegert Formula   When stimulated by a very large number of Poisson-like presynaptic current
input spikes, the temporal dynamics of the soma membrane potential $V(t)$ of a
leaky integrate-and-fire (LIF) neuron is typically modeled in the diffusion
limit and treated as a Ornstein-Uhlenbeck process (OUP). When the potential
reaches a threshold value $\theta$, $V(t) = \theta$, the LIF neuron fires and
the membrane potential is reset to a resting value, $V_0 < \theta$, and clamped
to this value for a specified (non-stochastic) absolute refractory period $T_r
\ge 0$, after which the cycle is repeated. The time between firings is given by
the random variable $T_f = T_r+ T$ where $T$ is the random time which elapses
between the "unpinning" of the membrane potential clamp and the next,
subsequent firing of the neuron. The mean time-to-fire, $\widehat{T}_f =
\text{E}(T_f) = T_r + \text{E}(T) = T_r + \widehat{T}$, provides a measure
$\rho$ of the average firing rate of the neuron, \[ \rho = \widehat{T}_f^{-1} =
\frac{1}{T_r + \widehat{T}} . \] This note briefly discusses some aspects of
the OUP model and derives the Siegert formula giving the firing rate, $\rho =
\rho(I_0)$ as a function of an injected current, $I_0$. This is a well-known
classical result and no claim to originality is made. The derivation of the
firing rate given in this report, which closely follows the derivation outlined
in the textbook by Gardiner, minimizes the required mathematical background and
is done in some pedagogic detail to facilitate study by graduate students and
others who are new to the subject. Knowledge of the material presented in the
first five chapters of Gardiner should provide an adequate background for
following the derivation given in this note.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph