Summary of practical applications of fractal an multifractal analysis, applied to biological time-series. Introduction to deterministic chaos. Takens theorem, practical computation of selected invariant parameters from experimental data (correlation dimension, Lyapunov exponents etc.). Tests for determinism and nonlinearity. High-dimensional chaos. Multifractal formalism, estimators of Hurst exponents, self-similarity of time series. Information entropy, applications. Average mutual information. Continuous and discrete communication channel. Relationship of information and thermodynamic entropy. Principle of maximal entropy. Biosystem organization, models and system identification. Introduction of statistical decision making, testing of statistical hypothesis, Bayessian approach.
Contents:
Summary of practical applications of fractal an multifractal analysis, applied to biological time-series. Introduction to deterministic chaos. Takens theorem, practical computation of selected invariant parameters from experimental data (correlation dimension, Lyapunov exponents etc.). Tests for determinism and nonlinearity. High-dimensional chaos. Multifractal formalism, estimators of Hurst exponents, self-similarity of time series. Information entropy, applications. Average mutual information. Continuous and discrete communication channel. Relationship of information and thermodynamic entropy. Principle of maximal entropy. Biosystem organization, models and system identification. Introduction of statistical decision making, testing of statistical hypothesis, Bayessian approach.
Recommended literature:
Leon Brillouin, Science and Information Theory, Mineola, N.Y.: Dover, 3rd edition 2004. ISBN 0-486-43918-6
Stanford Goldman. Information Theory. New York: Prentice Hall, 4th edition 2005 ISBN
0-486-44271-3
Raymond W. Yeung. Information Theory and Network Coding Springer 2008, 2002. ISBN 978-0-387-79233-0 Thomas
M. Cover, Joy A. Thomas. Elements of information theory, 2nd Edition. New York: Wiley-Interscience, 2006. ISBN 0-471-24195-4