神経科学のための数学 Mathematics for Neuroscientists

Gabbiani, Fabrizo/ Cox, Steven J.

Academic Pr（2010/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 486 p.
• 言語 ENG
• 商品コード 9780123748829
• DDC分類 511

基本説明

An integrated introduction to the use of mathematics in neuroscience that guides the reader from the elementary to the advanced stage through a sequence of concrete MATLAB computational models.

Full Description

Virtually all scientific problems in neuroscience require mathematical analysis, and all neuroscientists are increasingly required to have a significant understanding of mathematical methods. There is currently no comprehensive, integrated introductory book on the use of mathematics in neuroscience; existing books either concentrate solely on theoretical modeling or discuss mathematical concepts for the treatment of very specific problems. This book fills this need by systematically introducing mathematical and computational tools in precisely the contexts that first established their importance for neuroscience. All mathematical concepts will be introduced from the simple to complex using the most widely used computing environment, Matlab. This book will provide a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students.

Contents

1 Introduction 2 The Passive Isopotential Cell 3 Differential Equations 4 The Active Isopotential Cell 5 The Quasi-Active Isopotential Cell 6 The Passive Cable 7 Fourier Series and Transforms 8 The Passive Dendritic Tree 9 The Active Dendritic Tree 10 Reduced Single Neuron Models 11 Probability and Random Variables 12 Synaptic Transmission and Quantal Release 13 Neuronal Calcium Signaling 14 The Singular Value Decomposition and Applications 15 Quantification of Spike Train Variability 16 Stochastic Processes 17 Membrane Noise 18 Power and Cross Spectra 19 Natural Light Signals and Phototransduction 20 Firing Rate Codes and Early Vision 21 Models of Simple and Complex Cells 22 Stochastic Estimation Theory 23 Reverse-Correlation and Spike Train Decoding 24 Signal Detection Theory 25 Relating Neuronal Responses and Psychophysics 26 Population Codes 27 Neuronal Networks 28 Solutions to Selected Exercises