A powerful tool for the study of neuronal networks: Multiplicative point processes prove ideal to describe the dynamics of populations of neurons in fundamental brain research and engineering applications.
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In an article published in Frontiers in Computational Neuroscience, Stefano Cardanobile and Stefan Rotter present multiplicative point processes (MPPs) as such a tool that enables them to accurately describe interactions between multiple neuronal populations.
The scientists were able to show the suitability of MPPs for a range of biological functions that a network of spiking neurons can assume. For example, competing populations of nerve cells describing decision processes in the brain, as well as the interplay between excitation and inhibition or the basis of “central pattern generators” (which are considered to play a crucial role in the coordination of certain types of movement) could be described by these comparatively simple mathematical equations. The scientists hope that this new theoretical tool will help both to increase our understanding of the dynamical properties of interacting neuronal populations, and to improve the interaction of future neurotechnological devices with the diseased brain.
Cascade models treat the generation of action potentials in a neuron as a stochastic point process with an internal state variable. This makes the statistical analysis of such neurons more accessible.
Cardanobile S and Rotter S (2011) Emergent properties of interacting populations of spiking neurons. Front. Comput. Neurosci. 5:59. doi: 10.3389/fncom.2011.00059