On the phase reduction and response dynamics of neural oscillator populations
We undertake a probabilistic analysis of the response of repetitively firing neural populations
to simple pulselike stimuli. Recalling and extending results from the literature, we compute …
to simple pulselike stimuli. Recalling and extending results from the literature, we compute …
Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools
The extreme complexity of the brain naturally requires mathematical modeling approaches
on a large variety of scales; the spectrum ranges from single neuron dynamics over the …
on a large variety of scales; the spectrum ranges from single neuron dynamics over the …
Waves in neural media
PC Bressloff - Lecture notes on mathematical modelling in the life …, 2014 - Springer
This is a book on mathematical neuroscience, in which the unifying theme is wavelike
phenomena at multiple spatial and temporal scales. There are already several excellent …
phenomena at multiple spatial and temporal scales. There are already several excellent …
Oscillations in large-scale cortical networks: map-based model
We develop a new computationally efficient approach for the analysis of complex large-
scale neurobiological networks. Its key element is the use of a new phenomenological …
scale neurobiological networks. Its key element is the use of a new phenomenological …
Second-order information bottleneck based spiking neural networks for sEMG recognition
The pattern recognition of surface electromyography (sEMG) signal is an important
application in the realization of human-machine interface. However, due to the disturbance …
application in the realization of human-machine interface. However, due to the disturbance …
An effective kinetic representation of fluctuation-driven neuronal networks with application to simple and complex cells in visual cortex
D Cai, L Tao, M Shelley… - Proceedings of the …, 2004 - National Acad Sciences
A coarse-grained representation of neuronal network dynamics is developed in terms of
kinetic equations, which are derived by a moment closure, directly from the original large …
kinetic equations, which are derived by a moment closure, directly from the original large …
Population dynamics under the Laplace assumption
In this paper, we describe a generic approach to modelling dynamics in neuronal
populations. This approach models a full density on the states of neuronal populations but …
populations. This approach models a full density on the states of neuronal populations but …
Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling
Computational techniques within the population density function (PDF) framework have
provided time-saving alternatives to classical Monte Carlo simulations of neural network …
provided time-saving alternatives to classical Monte Carlo simulations of neural network …
Kinetic theory for neuronal network dynamics
D Cai, L Tao, AV Rangan, DW McLaughlin - 2006 - projecteuclid.org
We present a detailed theoretical framework for statistical descriptions of neuronal networks
and derive (1+1)-dimensional kinetic equations, without introducing any new parameters …
and derive (1+1)-dimensional kinetic equations, without introducing any new parameters …
Neural field model of binocular rivalry waves
PC Bressloff, PC Bressloff - Waves in Neural Media: From Single Neurons …, 2014 - Springer
In this chapter, neural field theory is used to model binocular rivalry waves. During binocular
rivalry, visual perception switches back and forth between different images presented to the …
rivalry, visual perception switches back and forth between different images presented to the …