Population Density Approach to Neural Network Modeling: Dimension Reduction Analysis, Techniques, and Firing Rate Dynamics - Softcover
Synopsis
Population Density Methods (PDM) have gained prominence in recent years in Theoretical Neuroscience as an analytical and time-saving computational tool. The method involves solving a density equation (aka, Fokker-Planck) instead of simulating many individual neurons. Simplifying assumptions of the underlying neuron model are often made so that the resulting PDM equations have low dimension for tractability. Thus, dimension reduction techniques are vital for physiological modeling. An introduction to PDM and the relevant issues are discussed in Chapter 2. A 'moment closure' dimension reduction technique is analyzed in Chapter 3. We show the equations are ill-posed in the fluctuation-driven regime with realistic parameters despite several contrary reports in the literature. The dimension reduction method is even worse for the more physiological 'theta' model (Chapter 4). A robust and accurate alternative reduction technique using a moving eigenvector basis is developed and implemented in Chapter 5. The stochastic firing rate dynamics of various neural models are analyzed in Chapter 6 with the tools we have developed.
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About the Author
Cheng Ly received his Ph.D. in Mathematics from The Courant Institute (NYU) in 2007 with Daniel Tranchina. Currently, he is an NSF postdoc (MSPRF) in the mathematics department at the University of Pittsburgh with mentor Bard Ermentrout. Cheng Ly's research involves analyzing stochastic neural networks in Theoretical Neuroscience.
"About this title" may belong to another edition of this title.
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Population Density Approach to Neural Network Modeling
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ISBN 10: 3639157532
ISBN 13: 9783639157536
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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Ly ChengCheng Ly received his Ph.D. in Mathematics from The CourantnInstitute (NYU) in 2007 nwith Daniel Tranchina. Currently, he is an NSF npostdoc (MSPRF) in the mathematics department at the Universitynof Pittsburgh with nmentor B. Seller Inventory # 4962615
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Population Density Approach to Neural Network Modeling
Published by
VDM Verlag Dr. Mueller Aktiengesellschaft & Co. KG, 2009
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Population Density Approach to Neural Network Modeling
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VDM Verlag Dr. Mueller Aktiengesellschaft & Co. KG, 2009
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Population Density Approach to Neural Network Modeling
Published by
VDM Verlag Dr. Mueller Aktiengesellschaft & Co. KG, 2009
ISBN 10: 3639157532
ISBN 13: 9783639157536
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Population Density Approach to Neural Network Modeling | Dimension Reduction Analysis, Techniques, and Firing Rate Dynamics
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Taschenbuch. Condition: Neu. Population Density Approach to Neural Network Modeling | Dimension Reduction Analysis, Techniques, and Firing Rate Dynamics | Cheng Ly | Taschenbuch | Englisch | VDM Verlag Dr. Müller | EAN 9783639157536 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu. Seller Inventory # 101563337
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Population Density Approach to Neural Network Modeling : Dimension Reduction Analysis, Techniques, and Firing Rate Dynamics
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Population Density Methods (PDM) have gainedprominence in recent years in Theoretical Neuroscience as an analyticaland time-saving computational tool. The method involves solving adensity equation (aka, Fokker-Planck) instead of simulating manyindividual neurons. Simplifying assumptions of the underlying neuronmodel are often made so that the resulting PDM equations have lowdimension for tractability. Thus, dimension reduction techniquesare vital for physiological modeling. An introduction to PDM and the relevant issues are discussed in Chapter 2. A''moment closure'' dimension reduction technique is analyzed in Chapter3. We show the equations are ill-posed in the fluctuation-driven regime withrealistic parameters despite several contrary reports in the literature. The dimension reduction method is even worse for the more physiological''theta'' model (Chapter 4). A robust and accurate alternativereduction technique using a moving eigenvector basis is developed andimplemented in Chapter 5. The stochastic firing rate dynamics ofvarious neural models are analyzed in Chapter 6 with the tools wehave developed. Seller Inventory # 9783639157536