Densities of Excitation and ISI for Cortical Neurons via Laplace Transforms – Toby Berger (University of Virginia)
For a canonical primary cortical neuron which we call N. we introduce a mathematically tractable and neuroscientifically meaningful model of how N stochastically converts the excitation intensities it receives from the union of all the neurons in its afferent cohort into the durations of the intervals between its efferent spikes. We assume that N operates to maximize the ratio of the information that its interspike interval (ISI) durations convey about the history of its afferent excitation intensity per joule of energy N expends to produce and propagate its spikes. We use calculus of variations and Laplace transforms to determine the probability density functions (pdf’s) of said excitation intensities and of said ISI durations. The mathematically derived pdf of the ISI durations is in good agreement with experimental observations. Moreover, the derived pdf of the afferent excitation intensity vanishes below a strictly positive level, which also accords with experimental observations. It is felt that our results argue persuasively that primary cortical neurons employ interspike interval codes (i.e., timing codes as opposed to rate oodes).
Toby Berger was born in New York, NY on September 4, 1940. He received the B.E. degree in electrical engineering from Yale University, New Haven, CT in 1962, and the M.S. and Ph.D. degrees in applied mathematics from Harvard University, Cambridge, MA in 1964 and 1966.From 1962 to 1968 he was a Senior Scientist at Raytheon Company, Wayland, MA, specializing in communication theory, information theory, and coherent signal processing. From 1968 through 2005 he was a faculty member at Cornell University, Ithaca, NY where he held the position of Irwin and Joan Jacobs Professor of Engineering. In 2006 he became a professor in the ECE Deportment of the University of Virginia, Charlottesville, VA.Professor Berger’s research interests include information theory, random fields, communication networks, wireless communications, video compression, voice and signature compression and verification, neuroinformation theory, quantum information theory, and coherent signal processing. He is the author of Rate Distortion Theory: A Mathematical Basis for Data Compression and a co-author of Digital Compression for Multimedia: Principles and Standards, and Information Measures for Discrete Random Fields.Berger has served as editor-in-chief of the IEEE Transactions on Information Theory and as president of the IEEE Information Theory Group. He has been a Fellow of the Guggenheim Foundation, the Japan Society for Promotion of Science, the Ministry of Education of the People’s Republic of China and the Fulbright Foundation. He received the 1982 Frederick E. Terman Award of the American Society for Engineering Education, the 2002 Shannon Award from the IEEE Information Theory Society and the IEEE 2006 Leon K. Kirchmayer Graduate Teaching Award. Professor Berger is a Fellow and Life Member of the IEEE, a life member of Tau Beta Pi, a member of the National Academy of Engineering, and an avid amateur blues harmonica player.