This course will provide the students with a number of general tools and theoretical background to approach the problem of disease under a network perspective, the levels of complexity that need to be considered while studying a given pathology and different ways of approaching it, from the clinics to imaging and theoretical/computational modelling. Topics include complex networks theory, neural diseases, cancer dynamical systems and bifurcations, as well as microbiome organization and dynamics.

The course should provide also a number of case studies and open problems that facilitate students to see the potential problems that remain open. When possible, students should have the opportunity of collaborating in some ongoing research projects.  


1. Complex diseases: definitions, open problems and need for multidisciplinary approaches (including case studies).
    Historical perspective on disease: from cybernetics to networks.
    Levels of complexity in the study of disease.
    The importance of evolution. 
2. Complex networks and the diseasome. Introduction to networks and network measures.
    Robustness and fragility. Hubs, connectors and paths.
    The brain connectome and its architecture.
    The breaking of modularity. 
3. Cancer dynamical systems:
    Cancer as a complex adaptive system. Biological and clinical views of cancer.
    The hallmarks of cancer. The steps behind tumor progression.
    The evolutionary ecology of cancer. Cancer as an ecological dynamical system. Growth laws for tumors.
    Cancer-free attractors. Bifurcations theory. Bifurcations in cancer models.
    Genetic heterogeneity, instability, and thresholds in cancer. 
    Standard and non-standard cancer therapies. Immuno-therapy. Differentiation therapy.
    Cancer spatial dynamics. Solid tumors. Cellular automata models.
4. Order, chaos and criticality. Deterministic chaos. Dimensionality of strange attractors.
    Variability in EEG and ECG data.
    Criticality as a dynamical attractor in brain function. Implications for disease and treatment.
    The microbiome as the third brain: tipping points and engineering.
5. Neural networks as models of brain funcion. Network damage in Alzheimer disease. Network of psychopathologies.
    Associative neural networks, attractors and disease. Catastrophes and break points.
    Immune system as a fluid neural network: memory, adaptation and response. Diversity thresholds.
    Beyond disease: NNs and consciousness. diseases.