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This book shows how mathematics, computer science and science can be usefully and seamlessly intertwined. It begins with a general model of cognitive processes in a network of computational nodes, such as neurons, using a variety of tools from mathematics, computational science and neurobiology. It then moves on to solve the diffusion model from a low-level random walk point of view. It also demonstrates how this idea can be used in a new approach to solving the cable equation, in order to better understand the neural computation approximations. It introduces specialized data for emotional content, which allows a brain model to be built using MatLab tools, and also highlights a simple model of cognitive dysfunction.
List of contents
BioInformation Processing.- The Di usion Equation.- Integral Transforms.- The Time Dependent Cable Solution.- Mammalian Neural Structure.- Abstracting Principles of Computation.- Abstracting Principles of Computation.- Second Messenger Di usion Pathways.- The Abstract Neuron Model.- Emotional Models.- Generation of Music Data: J. Peterson and L. Dzuris.- Generation of Painting Data: J. Peterson, L. Dzuris and Q. Peterson.- Modeling Compositional Design.- Networks Of Excitable Neurons.- Training The Model.- Matrix Feed Forward Networks.- Chained Feed Forward Architectures.- Graph Models.- Address Based Graphs.- Building Brain Models.- Models of Cognitive Dysfunction.- Conclusions.- Background Reading.
About the author
Dr. James Peterson is an Associate Professor in Mathematical Sciences and Biological Sciences at Clemson University, USA. His formal training is in mathematics but he has worked as an aerospace engineer and a software engineer also. He enjoys working on very hard problems that require multiple disciplines to make sense out of and he reads, studies and plays in cutting edge areas a lot as part of his interests.
Summary
This book shows how mathematics, computer science and science can be usefully and seamlessly intertwined. It begins with a general model of cognitive processes in a network of computational nodes, such as neurons, using a variety of tools from mathematics, computational science and neurobiology. It then moves on to solve the diffusion model from a low-level random walk point of view. It also demonstrates how this idea can be used in a new approach to solving the cable equation, in order to better understand the neural computation approximations. It introduces specialized data for emotional content, which allows a brain model to be built using MatLab tools, and also highlights a simple model of cognitive dysfunction.
