Contents -- Preface -- Neurobiological models -- 1. RC circuit, spiking times and interspike interval -- 1.1 Introduction -- 1.2 Electric properties of a neuron -- 1.3 Lapicque or I& F model -- 2. Calculation of interspike intervals for deterministic inputs -- 2.1 Introduction -- 2.2 Case of constant input current -- 2.3 Constant input current for a finite time -- 2.4 Constant input current with a periodic pattern -- 2.5 Periodic instantaneous inputs -- 2.6 Exercises -- 3. The Fitzhugh-Nagumo and Hodgkin-Huxley models -- 3.1 Introduction -- 3.2 The Fitzhugh-Nagumo model and the general properties of di.erential equations -- 3.3 The generation of spikes and the Hopf bifurcation -- 3.4 A more realistic model: the Hodgkin-Huxley model (HH model) -- 4. Definition and simulation of the main random variables -- 4.1 Introduction -- 4.2 General definitions -- 4.3 Uniformly distributed random variable -- 4.4 Exponentially distributed random variables -- 4.5 Gaussian random variables -- 4.6 Poisson random variables -- 5. Simulation of the neuron dynamics in interaction with a complex network -- 5.1 Introduction -- 5.2 Definition of a Poisson process -- 5.3 The integrate and fire model with Poissonian inputs -- 5.4 Computation of interspike intervals with Poissonian inputs -- 5.5 Numeric computation of interspike intervals with Poissonian inputs -- 5.6 Neural computation with Brownian inputs -- Clustering -- 6. An introduction to clustering techniques and selforganizing algorithms -- 6.1 A brief overview of clustering technique -- 6.2 Distance metric -- 6.3 Clustering algorithms -- 6.4 Hierarchical methods -- 6.5 Non-hierarchical methods -- 6.6 Graph-theoretic clustering -- 6.7 CAST -- 6.8 The Kohonen network -- 6.9 Numerical investigations and applications of Kohonen algorithm -- 6.10 Conclusion -- 6.11 Comments and comparison with other algorithms.

7. Clustering and classi.cation algorithms applied to protein sequences, structures and functions -- 7.1 Working with proteins information -- 7.2 Protein sequence similarity -- 7.3 Protein structure similarity -- 7.4 Protein-protein interaction. -- 7.5 Experimental methods to identify protein ligands -- 7.6 Computational methods to characterize protein ligands -- 7.7 The neural network approach -- Appendices -- Appendix A Tutorial of elementary calculus -- A.1 Derivation of the results of Chapter 1 -- Appendix B Complements to Chapter 2 -- B.1 Solution of the Exercises of Chapter 2 -- B.2 Matlab programs -- Appendix C Complements to Chapter 3 -- C.1 Main definitions of matrix calculus -- C.2 Matlab programs for integrating the FN and HH models -- Appendix D Complements to Chapter 4 -- D.1 A simple introduction to probability -- D.2 Program for simulating the U(0, 1) random variables -- D.3 Program for simulating the exponentially distributed r.v. -- D.4 Program for simulating the Gaussian N(0, 1) r.v. -- D.5 Program for simulating the Poisson random variables -- Appendix E Complements to Chapter 5 -- E.1 Matlab program for simulating the process of Lemma 5.2 -- E.2 Matlab program for simulating the case of two input Poisson processes -- E.3 Matlab program for solving the system (5.22) -- Appendix F Microarrays -- F.1 Measuring gene expression -- F.2 Applications of microarray -- Appendix G Complements to Chapter 6 -- G.1 Kohonen algorithm in Matlab source -- Appendix H Mathematical description of Kohonen algorithms -- H.1 Convergence of Kohonen algorithm -- Bibliography -- Subject Index -- Author Index.