Mathematical models, Dynamical systems, Markov Chains, Complex networks. Inference: Dependency measures, Measures of multivariate dependence, topology inference of networks.
Modeling. Mathematical models: stochastic x deterministic, discrete x continuous, static x dynamic, linear x non-linear. Dynamical
systems: topology, stability, robustness. Markov Chains: Homogeneous and Ergodic, Probabilistic Boolean Networks (PBNs),
Probabilistic Genetic Networks (PGNs). Some examples of mathematical models for biological systems (cell cycle, epidemiology,
signaling pathways, metabolic pathways). Complex networks: de nition of free networks of scale and small world. Measurements:
diameter, centrality, clustering coe cient. Modularity. Clustering algorithms in graphs. Inference. Dependency measures (Pearson,
Spearman, Kendall, mutual information). Partial correlation. Local correlation. Variant correlation in time. Measures of multivariate
dependence: Coe cient of Determination and Mutual Conditional Entropy. Applications of dependency measures for the
construction of gene regulation networks. Biological case studies: topology inference of gene networks of a malaria parasite from
time series of gene expression measured by microarray; stochastic modeling of cell cycle control dynamics; inference of cell cycle
signaling pathways from the kinetic model of known pathways and dynamic measures of concentration of chemical species
belonging to the system.