|
PART I Conceptual Background |
|
|
1 | (48) |
|
Why Study Brain Dynamics? |
|
|
3 | (11) |
|
Why Dynamics? An Active Perspective |
|
|
3 | (3) |
|
Quantifying Dynamics: Shared Theoretical Instruments |
|
|
6 | (1) |
|
``Newtonian and Bergsonian Time'' |
|
|
7 | (7) |
|
Reversible and Irreversible Dynamics: Entropy |
|
|
9 | (3) |
|
Deterministic Versus Random Motion |
|
|
12 | (1) |
|
Biological Arrows of Time? |
|
|
12 | (2) |
|
Theoretical Accounts of the Nervous System |
|
|
14 | (13) |
|
Three Axes in the Space of Theories |
|
|
15 | (12) |
|
|
17 | (5) |
|
Direction of Causal Explanations |
|
|
22 | (2) |
|
|
24 | (1) |
|
|
25 | (2) |
|
Engineering Theories and Nervous System Function |
|
|
27 | (13) |
|
|
27 | (2) |
|
|
29 | (11) |
|
|
31 | (1) |
|
|
32 | (4) |
|
|
36 | (4) |
|
Methodological Considerations |
|
|
40 | (9) |
|
Conceptual Clarity and Valid Reasoning |
|
|
41 | (1) |
|
Syntax: Well-Formed Statements |
|
|
41 | (1) |
|
|
42 | (1) |
|
Nature of Scientific Method |
|
|
42 | (7) |
|
Empirical and Controlled Experimental Methods |
|
|
43 | (1) |
|
Deductive and Inductive Methods |
|
|
44 | (2) |
|
Causation and Correlation |
|
|
46 | (3) |
|
|
49 | (168) |
|
Mathematical Preliminaries |
|
|
51 | (97) |
|
Scalars: Real and Complex Variables: Elementary Functions |
|
|
52 | (4) |
|
|
54 | (2) |
|
|
56 | (1) |
|
Vectors and Matrices: Linear Algebra |
|
|
56 | (16) |
|
Vectors as Points in a High-Dimensional Space |
|
|
57 | (1) |
|
Angles, Distances, and Volumes |
|
|
58 | (3) |
|
Linear Independence and Basis Sets |
|
|
61 | (1) |
|
Subspaces and Projections |
|
|
62 | (1) |
|
Matrices: Linear Transformations of Vectors |
|
|
63 | (1) |
|
|
64 | (2) |
|
Functions of Matrices: Determinants, Traces, and Exponentials |
|
|
66 | (1) |
|
Classical Matrix Factorization Techniques |
|
|
67 | (3) |
|
|
70 | (2) |
|
|
72 | (17) |
|
Function Spaces and Basis Expansions |
|
|
74 | (3) |
|
|
77 | (4) |
|
Convergence of Fourier Expansions on the Interval |
|
|
81 | (2) |
|
|
83 | (1) |
|
Bandlimited Functions, the Sampling Theorem, and Aliasing |
|
|
84 | (2) |
|
Discrete Fourier Transforms and Fast Fourier Transforms |
|
|
86 | (3) |
|
|
89 | (9) |
|
Broadband Bias and Narrowband Bias |
|
|
90 | (4) |
|
The Spectral Concentration Problem |
|
|
94 | (4) |
|
|
98 | (15) |
|
Sample Space, Events, and Probability Axioms |
|
|
100 | (2) |
|
Random Variables and Characteristic Function |
|
|
102 | (3) |
|
Some Common Probability Measures |
|
|
105 | (6) |
|
|
111 | (1) |
|
|
112 | (1) |
|
|
113 | (35) |
|
Defining Stochastic Processes |
|
|
114 | (2) |
|
Time Translational Invariance |
|
|
116 | (1) |
|
|
117 | (1) |
|
Time Translation Invariance and Spectral Analysis |
|
|
118 | (1) |
|
|
118 | (5) |
|
|
123 | (1) |
|
|
124 | (24) |
|
|
148 | (36) |
|
|
149 | (1) |
|
An Example of a Protocol: Method of Least Squares |
|
|
150 | (1) |
|
Classical and Modern Approaches |
|
|
151 | (2) |
|
|
152 | (1) |
|
Classical Approaches: Estimation and Inference |
|
|
153 | (31) |
|
|
154 | (7) |
|
Method of Least Squares: The Linear Model |
|
|
161 | (6) |
|
Generalized Linear Models |
|
|
167 | (4) |
|
|
171 | (1) |
|
|
172 | (6) |
|
|
178 | (3) |
|
Bayesian Estimation and Inference |
|
|
181 | (3) |
|
|
184 | (33) |
|
|
185 | (2) |
|
Evoked Potentials and Peristimulus Time Histogram |
|
|
187 | (2) |
|
Univariate Spectral Analysis |
|
|
189 | (18) |
|
Periodogram Estimate: Problems of Bias and Variance |
|
|
190 | (1) |
|
Nonparametric Quadratic Estimates |
|
|
191 | (6) |
|
Autoregressive Parametric Estimates |
|
|
197 | (3) |
|
Harmonic Analysis and Mixed Spectral Estimation |
|
|
200 | (2) |
|
|
202 | (5) |
|
Bivariate Spectral Analysis |
|
|
207 | (2) |
|
|
208 | (1) |
|
Multivariate Spectral Analysis |
|
|
209 | (2) |
|
Singular Value Decomposition of Cross-Spectral Matrix |
|
|
209 | (2) |
|
|
211 | (2) |
|
Linear Prediction Using Autoregressive Models |
|
|
212 | (1) |
|
Point Process Spectral Estimation |
|
|
213 | (2) |
|
|
214 | (1) |
|
Hybrid Multivariate Processes |
|
|
214 | (1) |
|
Higher Order Correlations |
|
|
215 | (2) |
|
Correlations Between Spectral Power at Different Frequencies |
|
|
216 | (1) |
|
|
217 | (104) |
|
Electrophysiology: Microelectrode Recordings |
|
|
219 | (38) |
|
|
219 | (1) |
|
|
220 | (1) |
|
|
221 | (3) |
|
Transmembrane Resting Potential |
|
|
221 | (1) |
|
Action Potentials and Synaptic Potentials |
|
|
221 | (2) |
|
|
223 | (1) |
|
|
224 | (1) |
|
Intracellular Measurements |
|
|
224 | (1) |
|
Extracellular Measurements |
|
|
224 | (1) |
|
|
225 | (1) |
|
|
225 | (23) |
|
|
225 | (3) |
|
|
228 | (11) |
|
|
239 | (3) |
|
|
242 | (4) |
|
|
246 | (2) |
|
|
248 | (3) |
|
|
250 | (1) |
|
|
250 | (1) |
|
Predicting Behavior From Neural Activity |
|
|
251 | (6) |
|
Selecting Feature Vectors |
|
|
253 | (1) |
|
|
254 | (1) |
|
|
255 | (2) |
|
|
257 | (14) |
|
|
257 | (1) |
|
|
258 | (1) |
|
|
258 | (1) |
|
|
259 | (3) |
|
|
259 | (1) |
|
|
259 | (1) |
|
|
260 | (2) |
|
|
262 | (4) |
|
|
263 | (2) |
|
|
265 | (1) |
|
|
265 | (1) |
|
|
266 | (2) |
|
|
268 | (3) |
|
|
268 | (3) |
|
Electro- and Magnetoencephalography |
|
|
271 | (23) |
|
|
271 | (1) |
|
Analysis of Electroencephalographic Signals: Early Work |
|
|
271 | (2) |
|
Physics of Encephalographic Signals |
|
|
273 | (1) |
|
|
273 | (2) |
|
|
275 | (1) |
|
|
275 | (19) |
|
Denoising and Dimensionality Reduction |
|
|
275 | (8) |
|
|
283 | (11) |
|
|
294 | (19) |
|
|
294 | (1) |
|
Biophysics of PET and fMRI |
|
|
295 | (2) |
|
|
295 | (1) |
|
|
295 | (1) |
|
|
296 | (1) |
|
|
297 | (2) |
|
|
298 | (1) |
|
|
299 | (14) |
|
|
299 | (6) |
|
|
305 | (1) |
|
Statistical Parametric Mapping |
|
|
306 | (4) |
|
Multiple Hypothesis Tests |
|
|
310 | (1) |
|
Anatomical Considerations |
|
|
311 | (2) |
|
|
313 | (8) |
|
|
313 | (1) |
|
Biophysical Considerations |
|
|
313 | (1) |
|
|
314 | (1) |
|
|
314 | (7) |
|
Difference and Ratio Maps |
|
|
315 | (1) |
|
|
315 | (6) |
|
|
321 | (22) |
|
Local Regression and Likelihood |
|
|
323 | (10) |
|
|
323 | (3) |
|
|
326 | (2) |
|
Local Logistic Regression |
|
|
327 | (1) |
|
|
327 | (1) |
|
|
328 | (1) |
|
Model Assessment and Selection |
|
|
328 | (5) |
|
|
328 | (1) |
|
Selection of the Bandwidth and Polynomial Degree |
|
|
329 | (2) |
|
|
331 | (1) |
|
|
332 | (1) |
|
Entropy and Mutual Information |
|
|
333 | (10) |
|
Entropy and Mutual Information for Discrete Random Variables |
|
|
334 | (2) |
|
Continuous Random Variables |
|
|
336 | (1) |
|
Discrete-Valued Discrete-Time Stochastic Processes |
|
|
337 | (1) |
|
Continuous-Valued Discrete-Time Stochastic Processes |
|
|
338 | (1) |
|
|
339 | (1) |
|
|
340 | (3) |
Appendix A: The Bandwagon |
|
343 | (2) |
|
Appendix B: Two Famous Papers |
|
345 | (2) |
|
Photograph Credits |
|
347 | (2) |
Bibliography |
|
349 | (14) |
Index |
|
363 | |