Stochastic Neuron Models by Priscilla E. Greenwood, Lawrence M. Ward (auth.)

By Priscilla E. Greenwood, Lawrence M. Ward (auth.)

This booklet describes various open difficulties within the idea of stochastic neural structures, with the purpose of engaging probabilists to paintings on them. This comprises difficulties coming up from stochastic versions of person neurons in addition to these bobbing up from stochastic versions of the actions of small and big networks of interconnected neurons. the required neuroscience historical past to those difficulties is printed in the textual content, so readers can clutch the context within which they arise.
This e-book could be invaluable for graduate scholars and teachers offering fabric and references for using chance to stochastic neuron modeling. tools and effects are offered, however the emphasis is on questions the place extra stochastic research may perhaps give a contribution neuroscience perception. an intensive bibliography is incorporated.

Dr. Priscilla E. Greenwood is a Professor Emerita within the division of arithmetic on the collage of British Columbia. Dr. Lawrence M. Ward is a Professor within the division of Psychology and the mind study Centre on the college of British Columbia.

Show description

Read or Download Stochastic Neuron Models PDF

Best biostatistics books

Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS and R Examples

This e-book offers equipment for interpreting info utilizing parametric nonlinear regression types. utilizing examples from experiments in agronomy and biochemistry, it exhibits tips on how to follow the tools. aimed toward scientists who're no longer acquainted with statistical conception, it concentrates on providing the equipment in an intuitive approach instead of constructing the theoretical grounds.

Social Inequalities and Cancer

There's transparent proof from industrialized and less-developed societies that melanoma prevalence and survival are regarding socioeconomic components. This attention-grabbing quantity, the 1st to check the significance of those socioeconomic variations relating to melanoma, offers important info for all these attracted to the connection among public well-being and oncology.

Analyzing Microarray Gene Expression Data (Wiley Series in Probability and Statistics)

A multi-discipline, hands-on consultant to microarray research of organic processesAnalyzing Microarray Gene Expression facts offers a finished evaluate of obtainable methodologies for the research of information derived from the newest DNA microarray applied sciences. Designed for biostatisticians getting into the sphere of microarray research in addition to biologists looking to extra successfully examine their very own experimental facts, the textual content contains a distinctive interdisciplinary process and a mixed educational and sensible point of view that gives readers the main whole and utilized insurance of the subject material to this point.

Some Mathematical Models from Population Genetics: École d'Été de Probabilités de Saint-Flour XXXIX-2009

This paintings displays 16 hours of lectures added by way of the writer on the 2009 St Flour summer time tuition in chance. It offers a swift advent to quite a number mathematical types that experience their origins in theoretical inhabitants genetics. The types fall into periods: forwards in time types for the evolution of frequencies of alternative genetic kinds in a inhabitants; and backwards in time (coalescent) versions that hint out the genealogical relationships among contributors in a pattern from the inhabitants.

Extra resources for Stochastic Neuron Models

Sample text

McKane et al. [43] indicate how such a structure can be described in a notation that leads to familiar stochastic objects. , 2-) dimensional function such as (VEt ; VIt ) the voltages at time t of an excitatory neuron paired with an inhibitory neuron. If we have a 2-dimensional spatial array of neuron pairs, where the pairs interact with neighboring or nearby pairs, the interaction may be modelled as a discrete Laplacian. E. M. 1) 49 50 4 Spatially Structured Neural Systems This is a pair of reaction–diffusion equations where the diffusion term is the first term on the right and the reaction term is the second term.

T/ ! 4, bottom row. 4, and a bit positive in the last part. 4, and that of a noisy limit cycle in the last part. A consequence of the sigmoidal response function in this delay model is that a positive real part of the dominant eigenvalue gives us a noisy limit cycle rather than divergence. The fact that the histogram appears to change continuously and slowly across this bifurcation of the deterministic model suggests that the effect of smoothing by noise is present. 4:4 It is an inviting problem to show this analytically.

This is another example of smoothing by stochasticity that has not been investigated by stochastic analysis. 2. In [44] the individual neurons in the system are binary. They could have been modelled in any of the ways we saw in Chapter 2. Would that make a difference to the resulting population model? We think that the answer is ‘no’; in other words, we suppose that the stochastic Wilson-Cowan population dynamics are dominant over the details of the individual neuron dynamics. But that question has not been examined carefully.

Download PDF sample

Rated 4.52 of 5 – based on 15 votes