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- Wulfram Gerstner, Werner M Kistler, Richard Naud, Liam Paninski, Werner Kistler, Dane Corneil +17 others
- 2013

Preface This textbook for advanced undergraduate and beginning graduate students provides a systematic introduction into the fields of Neuron Modeling, Neuronal Dynamics, Neural Coding and Neural Networks. It can be used as a text for introductory courses to Computational and Theoretical Neuroscience or as main text for a more focused course on Neural… (More)

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial… (More)

Spike-timing variability has a large effect on neural information processing. However, for many systems little is known about the noise sources causing the spike-response variability. Here we investigate potential sources of spike-response variability in auditory receptor neurons of locusts, a classic insect model system. At low-spike frequencies, our data… (More)

We analytically investigate the interspike interval (ISI) density, the Fano factor, and the coefficient of variation of a leaky integrate-and-fire neuron model driven by exponentially correlated Gaussian noise with a large correlation time tau . We find a burstinglike behavior of the spike train, which is revealed by a dominant peak of the ISI density at… (More)

Signals from different sensory modalities may converge on a single neuron. We study theoretically a setup in which one signal is transmitted via facilitating synapses (F signal) and another via depressing synapses (D signal). When both signals are present, the postsynaptic cell preferentially encodes information about slow components of the F signal and… (More)

- Moritz Deger, Tilo Schwalger, Richard Naud, Wulfram Gerstner
- Physical review. E, Statistical, nonlinear, and…
- 2014

Finite-sized populations of spiking elements are fundamental to brain function but also are used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasirenewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic… (More)

Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of noisy neural oscillators with spike-triggered adaptation of arbitrary strength and time scale. Our weak-noise theory… (More)

Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this… (More)

Exact expressions for first- and higher-order residence time statistics, count statistics, and spectral properties of a bistable system driven by dichotomous colored noise are put forward and discussed. The employed method is based on a discrete kinetic scheme and is valid for a wide range of parameter values of the colored noise. This permits a detailed… (More)

Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of… (More)