https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.

/pdf/spiking-neuron-models-single-neurons-populations-plasticity-58gzrd6ih6.pdf

Spiking Neuron Models: Single Neurons, Populations, Plasticity

http://people.physik.hu-berlin.de/~lindner/PDF/physreport.pdf

Effects of noise in excitable systems

We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (±2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.

/pdf/adaptive-exponential-integrate-and-fire-model-as-an-2sker0s7pf.pdf

Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity

http://www.buzsakilab.com/content/PDFs/Buzsaki2010Neuron.pdf

Neural Syntax: Cell Assemblies, Synapsembles, and Readers

Spiking Neuron Models: An Introduction

It is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion, the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel that describes the shape of the spike and the typical after-potential is included. Our model neuron fires if the membrane voltage, given by the truncated response kernel expansion, crosses a threshold. The threshold model is tested on a spike train generated by the Hodgkin-Huxley model with a stochastic input current. We find that the threshold model predicts 90 percent of the spikes correctly. Our results show that, to good approximation, the description of a neuron as a threshold element can indeed be justified.

/pdf/reduction-of-the-hodgkin-huxley-equations-to-a-single-cs2uyrj58w.pdf

Reduction of the hodgkin-huxley equations to a single-variable threshold model

We present a spiking neuron model that allows for an analytic calculation of the correlations between pre- and postsynaptic spikes. The neuron model is a generalization of the integrate-and-fire model and equipped with a probabilistic spike-triggering mechanism. We show that under certain biologically plausible conditions, pre- and postsynaptic spike trains can be described simultaneously as an inhomogeneous Poisson process.Inspired by experimental findings, we develop a model for synaptic long-term plasticity that relies on the relative timing of pre- and postsynaptic action potentials. Being given an input statistics, we compute the stationary synaptic weights that result from the temporal correlations between the pre- and postsynaptic spikes. By means of both analytic calculations and computer simulations, we show that such a mechanism of synaptic plasticity is able to strengthen those input synapses that convey precisely timed spikes at the expense of synapses that deliver spikes with a broad temporal distribution. This may be of vital importance for any kind of information processing based on spiking neurons and temporal coding.

http://www.t35.physik.tu-muenchen.de/addons/publications/Kistler_vH_NC.pdf

Modeling Synaptic Plasticity in Conjunction with the Timing of Pre- and Postsynaptic Action Potentials

We investigate the propagation of pulses of spike activity in a neuronal network with feedforward couplings. The neurons are of the spike-response type with a firing probability that depends linearly on the membrane potential. After firing, neurons enter a phase of refractoriness. Spike packets are described in terms of the moments of the firing-time distribution so as to allow for an analytical treatment of the evolution of the spike packet as it propagates from one layer to the next. Analytical results and simulations show that depending on the synaptic coupling strength, a stable propagation of the packet with constant waveform is possible. Crucial for this observation is neither the existence of a firing threshold nor a sigmoidal gain function--both are absent in our model-but the refractory behavior of the neurons.

/pdf/stable-propagation-of-activity-pulses-in-populations-of-572ryciaza.pdf

Werner M. Kistler

Papers

Spiking Neuron Models: An Introduction

Reduction of the hodgkin-huxley equations to a single-variable threshold model

Modeling Synaptic Plasticity in Conjunction with the Timing of Pre- and Postsynaptic Action Potentials

Stable propagation of activity pulses in populations of spiking neurons

Modeling collective excitations in cortical tissue