B Information Theory () | Mathematical Institute Course ManagementInformation theory is a relatively young subject. Every time you make a phone call, store a file on your computer, query an internet search engine, watch a DVD, stream a movie, listen to a CD or mp3 file, etc. However, independent of such applications, the underlying mathematical objects arise naturally as soon as one starts to think about "information" in a mathematically rigorous way. In fact, a large part of the course deals with two fundamental questions:. The student will have learned about entropy, mutual information and divergence, their basic properties, how they relate to information transmission. Understand the theoretical limits of transmitting information due to noise. Conditional entropy, mutual information, divergence and their basic properties and inequalities Fano, Gibbs'.
Information and coding theory
My research interests are mainly in Group Theory and its applications to areas such as Combinatorics, Galois Theory, Geometry and Topology. Current research projects involve dessins d'enfants and Beauville surfaces. I am currently working on textbooks on dessins d'enfants and the theory of algorithms. I have supervised about a dozen PhD students. I retired in , and since then I have continued my research as an Emeritus Professor. Mathematical Sciences.
A major stumbling block to cracking the real-time neural code is neuronal variability - neurons discharge spikes with enormous variability not only across trials within the same experiments but also in resting states. Such variability is widely regarded as a noise which is often deliberately averaged out during data analyses. In contrast to such a dogma, we put forth the Neural Self-Information Theory that neural coding is operated based on the self-information principle under which variability in the time durations of inter-spike-intervals ISI , or neuronal silence durations, is self-tagged with discrete information. As the self-information processor, each ISI carries a certain amount of information based on its variability-probability distribution; higher-probability ISIs which reflect the balanced excitation-inhibition ground state convey minimal information, whereas lower-probability ISIs which signify rare-occurrence surprisals in the form of extremely transient or prolonged silence carry most information. These variable silence durations are naturally coupled with intracellular biochemical cascades, energy equilibrium and dynamic regulation of protein and gene expression levels. As such, this silence variability-based self-information code is completely intrinsic to the neurons themselves, with no need for outside observers to set any reference point as typically used in the rate code, population code and temporal code models. Moreover, temporally coordinated ISI surprisals across cell population can inherently give rise to robust real-time cell-assembly codes which can be readily sensed by the downstream neural clique assemblies.
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