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Advanced Topics in Nonlinear Dynamics (Phys-465-0) – Complex networks and disordered systems

This focuses on understanding the main concepts and algorithms related to the structure and dynamics of and on complex networks.  Consequences, applications and limitations as well as related analytic and numerical techniques are discussed through real life examples and projects.

Topics covered:

  • Introduction, Graph theory (Ch. 1)
  • Key algorithms (Ch. 2)
  • Random Networks (Ch. 3)
  • The Scale-Free Property (Ch. 4)
  • The Barabasi-Albert model (Ch. 5)
  • Evolving Networks (Ch. 6)
  • Degree Correlations (Ch. 7)
  • Network Robustness, Percolation (Ch. 8)
  • Stochastic Block Model
  • Communities (Ch.9)
  • Spreading Phenomena, Contact Process (Ch. 10)
  • Network Visualization, Cytoscape, Gephi
  • Network Controllability
  • Maximum Entropy Models
  • Link prediction and inference in complex networks
  • Network Neuroscience
  • Disordered Systems: Harris criteria, Sinai walk, SDRG, Griffiths effects, Magnetic models
  • Hypergraphs and Simplicial complexes
  • Dynamical and Multiplex/Multilayer Networks
  • Quantum Networks

The online textbook:

http://networksciencebook.com/

Highlights of Student Projects:

Parth Bhatnagar: Quantum communication networks

Jose Miguel Cordova Sanchez: Learning in Networks

Elizabeth Duvall: Chicago transportation network

Seoul Lee: Open-source software network

Elisheva Siegfried: Partisanship in the Senate

Tingyu “Mark” Zhao: Tokyo Subway Network Failure Analysis

Cong Shen: Author network of top-cited HEP-th papers

Ahmed Alrabiah: Interdisciplinarity and success in science

Diya Basrai: Functional connectivity between premotor and motor cortex

Danyang Chen: Leviathan: An Agent-based Model of Primitive Society

Saanika Choudhary: Network analysis of a galaxy distributions

Samira Khan: Analysis of fracture networks in hydrogels

Eliseu Antonio Kloster Filho: A Network Science Approach to the World of Painters

Yiying (Grace) Liu: Networks of superconducting transmon qubit system

Shankhadeep Man: Networks in micro-roller motion

Highlights of Student Assignments:

 

Parth Bhatnagar: Network Properties of the Quantum Internet

Jose Miguel Cordova Sanchez: Measures for Complex Contagions

Elizabeth Duvall: From networks to the adjacency matrix and back

Seoul Lee: Small-world networks

Elisheva Siegfried: The Knight’s Tour — Warnsdorff’s Rule

Tingyu “Mark” Zhao: Speed of Epidemics Spreading in Networks

Cong Shen: Network Concepts in Feynman Diagrams

Ahmed Alrabiah: Quantum random circuits

Diya Basrai: Neural population geometry

Danyang Chen: Diagrammatic representation of the perturbation theory for multi-mode systems

Saanika Choudhary: Sinai walk: random walk in random environment

Samira Khan: Topological Chaos in Complex Network

Eliseu Antonio Kloster Filho: Network motifs

Yiying (Grace) Liu: Quantum Walks: Quantum mechanics in Networks

Shankhadeep Man: Graphlets