Mathematics for Neuroscientists

ISBN-13: 9780128018958 / Angielski / Twarda / 2017 / 628 str.

Fabrizio Gabbiani; Steven James Cox

Opis

Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory.

• Fully revised material and corrected text
• Additional chapters on extracellular potentials, motion detection and neurovascular coupling
• Revised selection of exercises with solutions
• More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Recenzje

"This is a big book in more than one sense. It has a large page format measuring about 20cm x 27cm making it easy to open up and take in large swathes of text, equations, and figures. More importantly, it covers a very wide range of mathematical methodologies relevant to neuroscience. ...I would highly recommend this book to those with an interest in computational neuroscience who wish to delve more deeply into the biophysics underlying cell-based dynamics and computations, especially if they are interested in flexing their mathematical muscles." --MathSciNet

Amazon Editorial Reviews for First Edition: "I really think this book is very, very important. This is precisely what has been missing from the field and is badly needed. " --Dr. Kevin Franks, research fellow, Richard Axel's laboratory Columbia University, NYC

"The idea of presenting sufficient maths to understand the theoretical neuroscience, alongside the neuroscience itself, is appealing. The inclusion of Matlab code for all examples and computational figures is an excellent idea. " --David Corney, research fellow, Institute of Ophthalmology, University College London

Spis treści

1. Introduction2. The Passive Isopotential Cell3. Differential Equations4. The Active Isopotential Cell5. The Quasi-Active Isopotential Cell6. The Passive Cable7. Fourier Series and Transforms8. The Passive Dendritic Tree9. The Active Dendritic Tree10. Extracellular Potential11. Reduced Single Neuron Models12. Probability and Random Variables13. Synaptic Transmission and Quantal Release14. Neuronal Calcium SignalingNeuronal Calcium Signaling15. Neurovascular Coupling, the BOLD Signal and MRI16. The Singular Value Decomposition and ApplicationsThe Singular Value Decomposition and Applications17. Quantification of Spike Train Variability18. Stochastic Processes19. Membrane NoiseMembrane Noise20. Power and Cross-Spectra21. Natural Light Signals and Phototransduction22. Firing Rate Codes and Early Vision23. Models of Simple and Complex Cells24. Models of Motion Detection25. Stochastic Estimation Theory26. Reverse-Correlation and Spike Train Decoding27. Signal Detection Theory28. Relating Neuronal Responses and Psychophysics29. Population CodesPopulation Codes30. Neuronal Networks31. Solutions to Exercises

O autorze

Dr. Gabbiani is Professor in the Department of Neuroscience at the Baylor College of Medicine. Having received the prestigious Alexander von Humboldt Foundation research prize in 2012, he just completed a one-year cross appointment at the Max Planck Institute of Neurobiology in Martinsried and has international experience in the computational neuroscience field. Together with Dr. Cox, Dr. Gabbiani co-authored the first edition of this bestselling book in 2010. Dr. Cox is Professor of Computational and Applied Mathematics at Rice University. Affiliated with the Center for Neuroscience, Cognitive Sciences Program, and the Ken Kennedy Institute for Information Technology, he is also Adjunct Professor of Neuroscience at the Baylor College of Medicine. In addition, Dr. Cox has served as Associate Editor for a number of mathematics journals, including the Mathematical Medicine and Biology and Inverse Problems. He previously authored the first edition of this title with Dr. Gabbiani.