17ADBNEIA - Nonlinear and Information Analysis in Biomedicine

Summary of practical applications of the fractal and multifractal analysis, applied to biological time-series. Introduction to deterministic chaos, dicrete and continuos systems with chaotic behavior. Takens theorem, practical computation of selected invariant parameters from experimental data (correlation dimension, Lyapunov exponents etc.). Tests for determinism and nonlinearity. Fractal analysis of biological time series. High-dimensional chaos. Multifractal formalism, estimators of Hurst exponents, self-similarity of time series.Relationship between information, entropy, systems, signals. Information entropy, applications. An 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.Temporal Logic and Timed Automata Examples of advanced applications of nonlinear and information analysis in biology and medicine.

Teaching takes place in the form of self-study with regular consultations. In addition to the examination, a written study is required by the student on the subject.

1. Summary of practical applications of the fractal and multifractal analysis, applied to biological time-series.

2. Introduction to deterministic chaos, dicrete and continuos systems with chaotic behavior.

3. Takens theorem, practical computation of selected invariant parameters from experimental data (correlation dimension, Lyapunov exponents etc.).

4. Tests for determinism and nonlinearity.

5. Fractal analysis of biological time series.

6. High-dimensional chaos. Multifractal formalism, estimators of Hurst exponents, self-similarity of time series.

7. Relationship between information, entropy, systems, signals.

8. Information entropy, applications. An average mutual information.

9. Continuous and discrete communication channel.

10. Relationship of information and thermodynamic entropy.

11. Principle of maximal entropy. Biosystem organization, models and system identification.

12. Introduction of statistical decision making, testing of statistical hypothesis, Bayessian approach.

13. Temporal Logic and Timed Automata

14. Examples of advanced applications of nonlinear and information analysis in biology and medicine.

Required:

[1] Christos H. Skiadas: Handbook of Applications of Chaos Theory, Chapman and Hall, 2016

[2] David J. Lubliner: Biomedical informatics: an introduction to information systems and software in medicine and health, Boca Raton : CRC Press, Taylor & Francis Group, 2016

Recommended:

[3] Andreas Holzinger, Igor Jurisica: Interactive Knowledge Discovery and Data Mining in Biomedical Informatics, Springer Verlag 2014

[4] David J. Lubliner: Biomedical informatics: an introduction to information systems and software in medicine and health, Boca Raton : CRC Press, Taylor & Francis Group, 2016

[5] Raymond W. Yeung. Information Theory and Network Coding Springer 2008, 2002. ISBN 978-0-387-79233-0

[6] M. Cover, Joy A. Thomas. Elements of information theory, 2nd Edition. New York: Wiley-Interscience, 2006. ISBN 0-471-24195-4

[7] Leon Brillouin, Science and Information Theory, Mineola, N.Y.: Dover, 3rd edition 2004. ISBN 0-486-43918-6