Introduction to Computational Neurobiology and Clustering

The following sections are included:

• Preface

• Contents

The following sections are included:

• Introduction

• Electric properties of a neuron

• Lapicque or I& F model

The following sections are included:

• Introduction

• Case of constant input current

• Constant input current for a finite time

• Constant input current with a periodic pattern

• Periodic instantaneous inputs

• Exercises

The following sections are included:

• Introduction

• The Fitzhugh-Nagumo model and the general properties of differential equations

• The generation of spikes and the Hopf bifurcation

• A more realistic model: the Hodgkin-Huxley model (HH model)

The following sections are included:

• Introduction

• General definitions

• Uniformly distributed random variable

• Exponentially distributed random variables

• Gaussian random variables

• Poisson random variables

The following sections are included:

• Introduction

• Definition of a Poisson process

• The integrate and fire model with Poissonian inputs

• Computation of interspike intervals with Poissonian inputs

• Numeric computation of interspike intervals with Poissonian inputs

• Neural computation with Brownian inputs

The following sections are included:

• A brief overview of clustering technique

• Distance metric

• Clustering algorithms

• Hierarchical methods

• Non-hierarchical methods

• Graph-theoretic clustering

• CAST

• The Kohonen network

• Numerical investigations and applications of Kohonen algorithm

• Conclusion

• Comments and comparison with other algorithms

The following sections are included:

• Working with proteins information

• Protein sequence similarity

• Protein structure similarity

• Protein-protein interaction

• Experimental methods to identify protein ligands

• Computational methods to characterize protein ligands

• The neural network approach

The following sections are included:

• Appendix A Tutorial of elementary calculus
  • Derivation of the results of Chapter 1

• Appendix B Complements to Chapter 2
  • Solution of the Exercises of Chapter 2
  • Matlab programs

• Appendix C Complements to Chapter 3
  • Main definitions of matrix calculus
  • Matlab programs for integrating the FN and HH models

• Appendix D Complements to Chapter 4
  • A simple introduction to probability
  • Program for simulating the U(0,1) random variables
  • Program for simulating the exponentially distributed r.v.
  • Program for simulating the Gaussian N(0,1) r.v
  • Program for simulating the Poisson random variables

• Appendix E Complements to Chapter 5
  • Matlab program for simulating the process of Lemma 5.2
  • Matlab program for simulating the case of two input Poisson processes
  • Matlab program for solving the system (5.22)

• Appendix F Microarrays
  • Measuring gene expression
  • Applications of microarray

• Appendix G Complements to Chapter 6
  • Kohonen algorithm in Matlab source

• Appendix H Mathematical description of Kohonen algorithms
  • Convergence of Kohonen algorithm

• Bibliography

• Subject Index

• Author Index