MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: University of Granada
• Semester: 3
• Topics:

   

  Topic 1: Brief Introduction to Complex Systems. Concept of Complex Network.
  
  Topic 2: Complex Networks as an Example of Complex Systems:
  
  Concept of Graph, Adjacency Matrix, Random Graphs, Directed and Undirected Networks, Weighted Networks.Node Distribution. Scale-Invariant Networks. Small-World Networks.Node-Node Correlations: Pearson Coefficient, Assortative and Disassortative Networks.Modular Structure. Hierarchical Networks. Multiplex Networks.
  
  Topic 3: The Brain as a Paradigm of System and Complex Network:
  
  Structure and Function: Connectivity Matrices (DTI) and Activity (Multielectrodes, EEG, MEG, fMRI).
  
  Topic 4: Neural Networks:
  
  Concept of Neural Network, Neuronal Activity Models and Synaptic Transmission, Hodgkin-Huxley Model, Integration and Firing Models, Binary Neuron Models.Synaptic Models: Alpha Function, Excitation and Inhibition, Exponential Models, Dynamic Synapses, Tsodyks-Markram Model.Attracting Neural Networks: Amari-Hopfield Model, Hebbian Learning, Capacity of a Neural Network.Feed-Forward Networks: Perceptron. Firing Rate Models: Wilson-Cowan Model. Fokker-Planck Type Models.Balanced Neural Networks: Homeostatic Balance in Complex Neural Networks, UP/DOWN States in the Cortex.
  
  Topic 5: Concept of Connectome:
  
  Construction of Connectomes, Structural Properties of Brain Connectomes, Comparison of Connectomes, Computational Properties.
  
  Topic 6: Social Networks:
  
  Statistical Physics Methods in the Context of Social Models.Basic Concepts: Order and Disorder, Ising Model, Importance of Topology (Scale-Free and Bounded Networks), Glauber Dynamics.Social Phenomena as Cooperative/Emergent Phenomena.Social Dynamics Models: Opinion Dynamics and Cultural Dynamics: Axelrod Model.Social Networks and the Internet. Epidemic Models and Virus Propagation in Networks.
  
  Topic 7: Networks in Ecology:
  
  Trophic Networks. Stability and May's Paradox. Mutualistic Networks.Nesting Properties and Other Structural Properties.
  
  Topic 8: Networks in Systems Biology:
  
  Concept of Gene Regulatory Networks.Cancer and Systemic Diseases. Random Boolean Networks.Genotype vs. Phenotype. Attractors and Phenotypes.