Introduction to computational neurobiology and clustering

Contents......Page 10
Preface......Page 8
Neurobiological models......Page 14
1.2 Electric properties of a neuron......Page 16
1.3 Lapicque or I& F model......Page 19
2.2 Case of constant input current......Page 26
2.3 Constant input current for a finite time......Page 30
2.4 Constant input current with a periodic pattern......Page 33
2.5 Periodic instantaneous inputs......Page 36
2.6 Exercises......Page 39
3.1 Introduction......Page 44
3.2 The Fitzhugh-Nagumo model and the general properties of di.erential equations......Page 45
3.3 The generation of spikes and the Hopf bifurcation......Page 50
3.4 A more realistic model: the Hodgkin-Huxley model (HH model)......Page 62
4.1 Introduction......Page 68
4.2 General definitions......Page 69
4.3 Uniformly distributed random variable......Page 73
4.4 Exponentially distributed random variables......Page 77
4.5 Gaussian random variables......Page 81
4.6 Poisson random variables......Page 85
5.1 Introduction......Page 92
5.2 Definition of a Poisson process......Page 94
5.3 The integrate and fire model with Poissonian inputs......Page 95
5.4 Computation of interspike intervals with Poissonian inputs......Page 98
5.5 Numeric computation of interspike intervals with Poissonian inputs......Page 102
5.6 Neural computation with Brownian inputs......Page 107
Clustering......Page 112
6.1 A brief overview of clustering technique......Page 114
6.2 Distance metric......Page 115
6.4 Hierarchical methods......Page 117
6.5 Non-hierarchical methods......Page 119
6.6 Graph-theoretic clustering......Page 120
6.7 CAST......Page 122
6.8 The Kohonen network......Page 123
6.9 Numerical investigations and applications of Kohonen algorithm......Page 129
6.10 Conclusion......Page 142
6.11 Comments and comparison with other algorithms......Page 144
7.1 Working with proteins information......Page 152
7.2 Protein sequence similarity......Page 153
7.3 Protein structure similarity......Page 159
7.4 Protein-protein interaction.......Page 161
7.5 Experimental methods to identify protein ligands......Page 162
7.6 Computational methods to characterize protein ligands......Page 165
7.7 The neural network approach......Page 169
Appendices......Page 174
A.1 Derivation of the results of Chapter 1......Page 176
B.1 Solution of the Exercises of Chapter 2......Page 178
B.2 Matlab programs......Page 183
C.1 Main definitions of matrix calculus......Page 190
C.2 Matlab programs for integrating the FN and HH models......Page 191
D.1 A simple introduction to probability......Page 194
D.2 Program for simulating the U(0, 1) random variables......Page 201
D.3 Program for simulating the exponentially distributed r.v.......Page 202
D.4 Program for simulating the Gaussian N(0, 1) r.v.......Page 204
D.5 Program for simulating the Poisson random variables......Page 205
E.1 Matlab program for simulating the process of Lemma 5.2......Page 210
E.2 Matlab program for simulating the case of two input Poisson processes......Page 212
E.3 Matlab program for solving the system (5.22)......Page 214
F.1 Measuring gene expression......Page 218
F.2 Applications of microarray......Page 221
G.1 Kohonen algorithm in Matlab source......Page 224
H.1 Convergence of Kohonen algorithm......Page 228
Bibliography......Page 232
Subject Index......Page 238
Author Index......Page 242