Upcrossing-rate dynamics for a minimal neuron model receiving spatially distributed synaptic drive

Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise.

The synaptic coupling between neurons in neocortical networks is sufficiently strong so that relatively few synchronous synaptic pulses are required to bring a neuron from rest to the spiking threshold. However, such finite-amplitude effects of fluctuating synaptic drive are missed in the standard diffusion approximation. Here exact solutions for the firing-rate response to modulated presynapti...

Using neuron dynamics for realistic synaptic learning

Computational tasks such as object and pattern recognition rely on deterministic learning in the brain carried out mostly at the synapses, which link the brain’s neurons and shape the overall computational function of a group of neurons.1 Modelers build mathematical abstractions of synaptic learning by approximating the behavior of biological synapses as they try to copy relevant processing fun...

A spatially distributed model for foreground segmentation

Foreground segmentation is a fundamental first processing stage for vision systems which monitor real-world activity. In this paper we consider the problem of achieving robust segmentation in scenes where the appearance of the background varies unpredictably over time. Variations may be caused by processes such as moving water, or foliage moved by wind, and typically degrade the performance of ...

Supplementary Materials: The Bogdanov-Takens Normal Form: A Minimal Model For Single Neuron Dynamics

The Bogdanov-Takens Normal Form: A Minimal Model for Single Neuron Dynamics

Conductance-based (CB) models are a class of high dimensional dynamical systems derived from biophysical principles to describe in detail the electrical dynamics of single neurons. Despite the high dimensionality of these models, the dynamics observed for realistic parameter values is generically planar and can be minimally described by two equations. In this work, we derive the conditions to h...