


Politecnico di Torino  
Academic Year 2015/16  
01QFXNZ, 01QFXJM, 01QFXLI, 01QFXLJ, 01QFXLL, 01QFXLM, 01QFXLN, 01QFXLS, 01QFXLU, 01QFXLX, 01QFXLZ, 01QFXMA, 01QFXMB, 01QFXMC, 01QFXMH, 01QFXMK, 01QFXMN, 01QFXMO, 01QFXMQ, 01QFXNX, 01QFXOA, 01QFXOD, 01QFXPC, 01QFXPI, 01QFXPL, 01QFXPM, 01QFXPW Complex systems and networks: physical phenomena and social interaction 

1st degree and Bachelorlevel of the Bologna process in Telecommunications Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Mechanical Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Automotive Engineering  Torino Espandi... 





Subject fundamentals
This elective course provides a general introduction to complex networks and systems with the aim of understanding their key features and behavior. Basic mathematics and tools, with emphasis on the geometric intuition, will be used to explain the possibly complex and sometimes unexpected behavior of systems occurring in many real life examples, from electronics to biology to social science and even the telecommunication networks. The complexity of a system is discussed in terms of its structure and of its dynamical behavior (the socalled "chaos" lies in the latter). The course also provides an introduction to bioinspired neuromorphic systems that mimic neurobiological architectures occurring in the nervous system of the human brain. The synchronization among interacting systems and the physical mechanisms responsible for this phenomenon will be briefly discussed as well and concludes the course.
All the basic concepts are illustrated by some application to science or engineering and simple tools or Matlab routines. Two practice (lab) sessions will be organized, with focus on a real example (the Chua’s circuit) that demonstrates the chaotic behavior of dynamical systems. A selection of real applications will be thoroughly discussed in the class. The students will be guided to discover the analogies among different networks and the possible effects of their structure to the system behavior. Some of the questions that will be answered follow: why and at what rate innovations (new ideas and technology) spread through a group of people? how we can predict the spreading of an epidemic in a social network? Can we devise a clever immunization strategy? What is the best placementscheme of a limited number of sensors for the detection of a contaminationevent in a water distribution network? How we can describe the dynamics of biological systems in which two species interact? What are the causes of the possible instability of analog electronic circuits due to their unexpected chaotic behavior? The following paper is suggested (it focuses on the first part of the course): http://www.nature.com/nature/journal/v410/n6825/pdf/410268a0.pdf (Steven H. Strogatz, "Exploring complex networks", Nature, Vol. 410, Mar. 8, 2001) 
Expected learning outcomes
Knowledge of the key mathematical tools for the analysis of complex networks and systems
Basic knowledge of the principles underlying the neuromorphic systems Ability to select the most suitable model allowed to describe a real complex network Ability to carry out a qualitative and quantitative analysis of the dynamical behavior of a complex system 
Prerequisites / Assumed knowledge
Basic knowledge of mathematics and physics..

Contents
PART I – NETWORKS (~2 cr)
* Introduction to networks: the origin of complexity, examples (airplane routes, social networks,...). * Basic concepts of graph theory and network models (regular structures, ErdösRényi random graphs, smallworld and scalefree features); Characteristics of real networks. * Interaction within a network. Diffusion of innovations and epidemic spreading. * Discussion of practical applications (e.g., design of a sensorplacement scheme capable of detecting all possible contamination events for a water distribution system, error and attack tolerance of complex networks, epidemic spreading in social networks...) PART II  NONLINEAR DYNAMICS (~3 cr) * Discretetime systems: one dimensional maps (logistic, tent). Fixed points, periodic points, stability, bifurcation diagrams, sensitive dependence on initial conditions, chaos. * Extension to the analysis of continuoustime systems. Examples: the Lotka–Volterra equations, i.e., the socalled predator–prey equations; The Van der Pol oscillator, The Lorenz equations (i.e. a simplified mathematical model for atmospheric convection), the Chua's circuit,.... PART III  SYNCRONIZATION AND NEUROMORPHIC SYSTEMS (~1 cr) * Coupled systems: properties and synchronization mechanism (the discussion is based on simple examples). * Bioinspired networks and neuromorphic systems 
Delivery modes
Standard lectures and practice sessions in the class, where simple exercises are proposed and solved. In addition, two practice lab sessions are organized, with emphasis on the practical realization of a simple circuit exhibiting chaotic behavior of dynamical systems. Numerical (Matlab) routines or tools that are useful to stress the key aspects discussed during the lectures are provided as well.

Texts, readings, handouts and other learning resources
Supporting material provided by the professor (papers, lecture notes,....). Videolectures (streaming) of all classes.
Reference textbooks: [1] D. Easley, J. Kleinberg, "Networks, Crowds, and Markets: Reasoning about a Highly Connected World", Cambridge University Press, 2010. [2] S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford University Press, USA, March 27, 2003. [3] S.H. Strogatz, Nonlinear dynamics and chaos, Perseus books, 1994. 
Assessment and grading criteria
The verification consists of a written exam that can be possibly complemented/replaced by a small project work. The written test has duration of one hour and consists of questions with multiple answers and/or open questions and simple exercise problems.

