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El. knyga: Mathematics for Neuroscientists

3.64/5 (11 ratings by Goodreads)
(Computational and Applied Mathematics, Rice University, Houston, TX, USA), (Baylor College of Medicine, Houston, TX, USA)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 04-Feb-2017
  • Leidėjas: Academic Press Inc
  • Kalba: eng
  • ISBN-13: 9780128019061
Kitos knygos pagal šią temą:
Mathematics for NeuroscientistsDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 04-Feb-2017
  • Leidėjas: Academic Press Inc
  • Kalba: eng
  • ISBN-13: 9780128019061
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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

Recenzijos

"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

Daugiau informacijos

Comprehensive tutorial-reference that introduces the foundational mathematics necessary for contemporary neuroscience research
Preface to the 1st Edition ix
Preface to the 2nd Edition xi
1 Introduction
1.1 How to Use This Book
2(1)
1.2 Brain Facts Brief
3(1)
1.3 Mathematical Preliminaries
4(3)
1.4 Units
7(1)
1.5 Sources
8(1)
2 The Passive Isopotential Cell
2.1 Introduction
9(1)
2.2 The Nernst Potential
10(1)
2.3 Membrane Conductance
11(1)
2.4 Membrane Capacitance & Current Balance
12(2)
2.5 Synaptic Conductance
14(1)
2.6 Summary and Sources
15(1)
2.7 Exercises
16(5)
3 Differential Equations
3.1 Exact Solution
21(2)
3.2 Moment Methods*
23(1)
3.3 The Laplace Transform*
24(2)
3.4 Numerical Methods
26(2)
3.5 Synaptic Input
28(1)
3.6 Summary and Sources
28(1)
3.7 Exercises
29(5)
4 The Active Isopotential Cell
4.1 The Delayed Rectifier Potassium Channel
34(2)
4.2 The Sodium Channel
36(1)
4.3 The Hodgkin--Huxley Equations
36(3)
4.4 The Transient Potassium Channel*
39(3)
4.5 The Sodium--Potassium Pump*
42(5)
4.6 Summary and Sources
47(1)
4.7 Exercises
47(6)
5 The Quasi-Active Isopotential Cell
5.1 The Quasi-Active Model
53(2)
5.2 Numerical Methods
55(3)
5.3 Exact Solution via Eigenvector Expansion
58(4)
5.4 A Persistent Sodium Current*
62(1)
5.5 A Nonspecific Cation Current that is Activated by Hyperpolarization*
62(1)
5.6 Linearization of the Sodium--Potassium Pump*
63(3)
5.7 Summary and Sources
66(1)
5.8 Exercises
67(6)
6 The Passive Cable
6.1 The Discrete Passive Cable Equation
73(2)
6.2 Exact Solution via Eigenvector Expansion
75(2)
6.3 Numerical Methods
77(1)
6.4 The Passive Cable Equation
78(5)
6.5 Synaptic Input
83(3)
6.6 Summary and Sources
86(1)
6.7 Exercises
87(6)
7 Fourier Series and Transforms
7.1 Fourier Series
93(2)
7.2 The Discrete Fourier Transform
95(4)
7.3 The Fourier Transform
99(2)
7.4 Reconciling the Discrete and Continuous Fourier Transforms
101(2)
7.5 Summary and Sources
103(1)
7.6 Exercises
104(5)
8 The Passive Dendritic Tree
8.1 The Discrete Passive Tree
109(2)
8.2 Eigenvector Expansion
111(2)
8.3 Numerical Methods
113(1)
8.4 The Passive Dendrite Equation
114(2)
8.5 The Equivalent Cylinder*
116(2)
8.6 Branched Eigenfunctions*
118(2)
8.7 Summary and Sources
120(1)
8.8 Exercises
121(5)
9 The Active Dendritic Tree
9.1 The Active Uniform Cable
126(2)
9.2 On the Interaction of Active Uniform Cables*
128(3)
9.3 The Active Nonuniform Cable
131(4)
9.4 The Quasi-Active Cable*
135(4)
9.5 The Active Dendritic Tree
139(2)
9.6 Summary and Sources
141(1)
9.7 Exercises
142(6)
10 Extracellular Potential
10.1 Maxwell's Equations
148(3)
10.2 The Wave Equation
151(1)
10.3 From Maxwell to Laplace
152(1)
10.4 The Solution to Laplace's Equation
153(3)
10.5 Extracellular Potential Near a Passive Cable
156(5)
10.6 Extracellular Potential Near Active Cables
161(1)
10.7 Summary and Sources
162(1)
10.8 Exercises
163(6)
11 Reduced Single Neuron Models
11.1 The Leaky Integrate-and-Fire Neuron
169(3)
11.2 Bursting Neurons
172(1)
11.3 Simplified Models of Bursting Neurons
173(5)
11.4 Summary and Sources
178(1)
11.5 Exercises
178(3)
12 Probability and Random Variables
12.1 Events and Random Variables
181(1)
12.2 Binomial Random Variables
182(2)
12.3 Poisson Random Variables
184(1)
12.4 Gaussian Random Variables
185(1)
12.5 Cumulative Distribution Functions
186(1)
12.6 Conditional Probabilities*
187(1)
12.7 Sum of Independent Random Variables*
188(1)
12.8 Transformation of Random Variables*
188(2)
12.9 Random Vectors*
190(3)
12.10 Exponential and Gamma Distributed Random Variables
193(1)
12.11 The Homogeneous Poisson Process
194(2)
12.12 Summary and Sources
196(1)
12.13 Exercises
196(5)
13 Synaptic Transmission and Quantal Release
13.1 Basic Synaptic Structure and Physiology
201(2)
13.2 Discovery of Quantal Release
203(1)
13.3 Compound Poisson Model of Synaptic Release
204(2)
13.4 Comparison with Experimental Data
206(1)
13.5 Quantal Analysis at Central Synapses
207(2)
13.6 Facilitation, Potentiation and Depression of Synaptic Transmission
209(4)
13.7 Models of Short-Term Synaptic Plasticity
213(3)
13.8 Summary and Sources
216(1)
13.9 Exercises
216(3)
14 Neuronal Calcium Signaling*
14.1 Voltage Gated Calcium Channels
219(4)
14.2 Diffusion, Buffering and Extraction of Cytosolic Calcium
223(3)
14.3 Calcium Release from the Endoplasmic Reticulum
226(7)
14.4 Regulation of Calcium in Spines
233(5)
14.5 Spinal Calcium and Bidirectional Synaptic Plasticity
238(6)
14.6 Presynaptic Calcium and Transmitter Release
244(2)
14.7 Summary and Sources
246(1)
14.8 Exercises
247(9)
15 Neurovascular Coupling, the BOLD Signal and MRI
15.1 The Metabolic Cost of Neural Signaling
256(4)
15.2 Astrocytes
260(4)
15.3 Smooth Muscle
264(5)
15.4 Endothelium
269(2)
15.5 The Neurovascular Unit
271(1)
15.6 How Blood Distorts an Applied Magnetic Field
271(7)
15.7 Nuclear Magnetic Resonance and the BOLD Signal
278(8)
15.8 The Hemodynamic Response
286(9)
15.9 Magnetic Resonance Imaging
295(7)
15.10 Summary and Sources
302(1)
15.11 Exercises
303(4)
16 The Singular Value Decomposition and Applications*
16.1 The Singular Value Decomposition
307(3)
16.2 Principal Component Analysis and Spike Sorting
310(1)
16.3 Synaptic Plasticity and Principal Components
311(2)
16.4 Neuronal Model Reduction via Balanced Truncation
313(3)
16.5 Summary and Sources
316(1)
16.6 Exercises
317(4)
17 Quantification of Spike Train Variability
17.1 Interspike Interval Histograms and Coefficient of Variation
321(2)
17.2 Refractory Period
323(1)
17.3 Spike Count Distribution and Fano Factor
324(1)
17.4 Renewal Processes
324(3)
17.5 Return Maps and Serial Correlation Coefficients
327(2)
17.6 Summary and Sources
329(1)
17.7 Exercises
330(5)
18 Stochastic Processes
18.1 Definition and General Properties
335(1)
18.2 Gaussian Processes
336(2)
18.3 Point Processes
338(3)
18.4 The Inhomogeneous Poisson Process
341(1)
18.5 Spectral Analysis
342(4)
18.6 Summary and Sources
346(1)
18.7 Exercises
346(6)
19 Membrane Noise*
19.1 Two-State Channel Model
352(2)
19.2 Multi-State Channel Models
354(1)
19.3 The Ornstein--Uhlenbeck Process
355(1)
19.4 Synaptic Noise
356(2)
19.5 Summary and Sources
358(1)
19.6 Exercises
359(4)
20 Power and Cross-Spectra
20.1 Cross-Correlation and Coherence
363(1)
20.2 Estimator Bias and Variance
364(2)
20.3 Numerical Estimate of the Power Spectrum*
366(4)
20.4 Summary and Sources
370(1)
20.5 Exercises
370(5)
21 Natural Light Signals and Phototransduction
21.1 Wavelength and Intensity
375(2)
21.2 Spatial Properties of Natural Light Signals
377(1)
21.3 Temporal Properties of Natural Light Signals
377(1)
21.4 A Model of Phototransduction
378(3)
21.5 Summary and Sources
381(1)
21.6 Exercises
382(1)
22 Firing Rate Codes and Early Vision
22.1 Definition of Mean Instantaneous Firing Rate
383(1)
22.2 Visual System and Visual Stimuli
384(2)
22.3 Spatial Receptive Field of Retinal Ganglion Cells
386(1)
22.4 Characterization of Receptive Field Structure
387(3)
22.5 Spatio-Temporal Receptive Fields
390(2)
22.6 Static Non-Linearities*
392(1)
22.7 Summary and Sources
392(1)
22.8 Exercises
393(2)
23 Models of Simple and Complex Cells
23.1 Simple Cell Models
395(6)
23.2 Non-Separable Receptive Fields
401(3)
23.3 Receptive Fields of Complex Cells
404(1)
23.4 Motion-Energy Model
405(1)
23.5 Hubel--Wiesel Model
406(1)
23.6 Multiscale Representation of Visual Information
406(1)
23.7 Summary and Sources
406(2)
23.8 Exercises
408(3)
24 Models of Motion Detection
24.1 HRC Model of Motion Detection
411(2)
24.2 Responses to Moving Stimuli
413(5)
24.3 Properties of the Correlation Model
418(4)
24.4 Equivalence with the Motion-Energy Model
422(1)
24.5 Beyond Correlation in Motion Detection
423(4)
24.6 Summary and Sources
427(1)
24.7 Exercises
428(7)
25 Stochastic Estimation Theory
25.1 Minimum Mean-Square Error Estimation
435(1)
25.2 Estimation of Gaussian Signals*
436(2)
25.3 Linear Non-Linear (LN) Models*
438(2)
25.4 Summary and Sources
440(1)
25.5 Exercises
440(3)
26 Reverse-Correlation and Spike Train Decoding
26.1 Reverse-Correlation
443(3)
26.2 Stimulus Reconstruction
446(2)
26.3 Summary and Sources
448(1)
26.4 Exercises
448(3)
27 Signal Detection Theory
27.1 Testing Hypotheses
451(3)
27.2 Ideal Decision Rules
454(1)
27.3 ROC Curves*
455(1)
27.4 Multi-Dimensional Gaussian Signals*
456(3)
27.5 Fisher Linear Discriminant*
459(2)
27.6 Summary and Sources
461(1)
27.7 Exercises
461(2)
28 Relating Neuronal Responses and Psychophysics
28.1 Single Photon Detection
463(4)
28.2 Signal Detection Theory and Psychophysics
467(2)
28.3 Motion Detection
469(3)
28.4 Summary and Sources
472(1)
28.5 Exercises
472(3)
29 Population Codes*
29.1 Cartesian Coordinate Systems
475(2)
29.2 Overcomplete Representations
477(1)
29.3 Frames
478(2)
29.4 Maximum Likelihood
480(2)
29.5 Estimation Error and Cramer--Rao Bound*
482(1)
29.6 Population Coding in the Superior Colliculus
483(1)
29.7 Summary and Sources
483(1)
29.8 Exercises
484(6)
30 Neuronal Networks
30.1 Perceptrons
490(4)
30.2 Hopfield Networks
494(4)
30.3 Integrate and Fire Networks
498(5)
30.4 Integrate and Fire Networks with Plastic Synapses
503(3)
30.5 Formation of the Grid Cell Network via STDP
506(4)
30.6 Hodgkin--Huxley Based Networks
510(6)
30.7 Hodgkin--Huxley Based Networks with Plastic Synapses
516(1)
30.8 Rate Based Networks
516(3)
30.9 Brain Maps and Self-Organizing Maps
519(2)
30.10 Summary and Sources
521(2)
30.11 Exercises
523(6)
31 Solutions to Exercises
31.1
Chapter 2
529(2)
31.2
Chapter 3
531(2)
31.3
Chapter 4
533(2)
31.4
Chapter 5
535(2)
31.5
Chapter 6
537(3)
31.6
Chapter 7
540(2)
31.7
Chapter 8
542(1)
31.8
Chapter 9
543(1)
31.9
Chapter 10
543(4)
31.10
Chapter 11
547(1)
31.11
Chapter 12
547(6)
31.12
Chapter 13
553(2)
31.13
Chapter 14
555(1)
31.14
Chapter 15
555(2)
31.15
Chapter 16
557(2)
31.16
Chapter 17
559(3)
31.17
Chapter 18
562(5)
31.18
Chapter 19
567(3)
31.19
Chapter 20
570(6)
31.20
Chapter 21
576(1)
31.21
Chapter 22
576(1)
31.22
Chapter 23
577(1)
31.23
Chapter 24
578(10)
31.24
Chapter 25
588(3)
31.25
Chapter 26
591(1)
31.26
Chapter 27
592(4)
31.27
Chapter 28
596(2)
31.28
Chapter 29
598(4)
31.29
Chapter 30
602(3)
Bibliography 605(8)
Index 613
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.
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