Stochastic Methods in NeuroscienceCarlo Laing, Gabriel J Lord Great interest is now being shown in computational and mathematical neuroscience, fuelled in part by the rise in computing power, the ability to record large amounts of neurophysiological data, and advances in stochastic analysis. These techniques are leading to biophysically more realistic models. It has also become clear that both neuroscientists and mathematicians profit from collaborations in this exciting research area.Graduates and researchers in computational neuroscience and stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, will benefit from this comprehensive overview. The series of self-contained chapters, each written by experts in their field, covers key topics such as: Markov chain models for ion channel release; stochastically forced single neurons and populations of neurons; statistical methods for parameterestimation; and the numerical approximation of these stochastic models.Each chapter gives an overview of a particular topic, including its history, important results in the area, and future challenges, and the text comes complete with a jargon-busting index of acronyms to allow readers to familiarize themselves with the language used. |
Contents
1 A brief introduction to some simple stochastic processes | 1 |
2 Markov chain models of ion channels and calcium release sites | 29 |
3 Stochastic dynamic bifurcations and excitability | 65 |
4 Neural coherence and stochastic resonance | 94 |
5 Noisy oscillators | 124 |
6 The role of variability in populations of spiking neurons | 153 |
7 Population density methods in largescale neural network modelling | 181 |
8 A population density model of the driven LGNPGN | 217 |
Experiments computational consequences and methods to analyse experimental data | 242 |
10 Statistical models of spike trains | 272 |
11 Stochastic simulation of neurons axons and action potentials | 297 |
12 Numerical simulations of SDEs and SPDEs from neural systems using SDELab | 344 |
| 367 | |
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Common terms and phrases
action potential activity algorithm allosteric approximation average axon behaviour Brunel Ca2+ calcium cells channel noise compartment Computational Neuroscience constant correlation corresponding cortex coupling Destexhe deterministic differential equation distribution dynamics equilibrium branch Ermentrout excitable excitatory experimental Faisal fluctuations Fokker-Planck Fokker-Planck equation frequency gating Gaussian inactivation inhibitory instantaneous integrate-and-fire integration interactions interval invariant curve ion channels Itô Journal limit cycle linear Longtin Markov chain membrane potential method Na+ channels Neural Computation neuron model noise intensity Omurtag oscillators Paninski parameters perturbation phase Physical Review Poisson population density population firing rate postsynaptic probability density reset response reversal potential Rudolph saddle-node bifurcation sample paths signal simulation solution spatial spike train statistics stimulus stochastic differential equations stochastic process stochastic resonance subthreshold synaptic conductances synaptic input synaptic noise synchronization threshold transition two-state values variable variance voltage white noise zero