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Courses

An Introduction to Synchronization in Complex Systems
M. Biey, M. Bonnin, F. Corinto and M. Righero
Torino, May – June 2016

Course program

PART I (M. Biey)

  • Introduction and examples (1h)
  • Complex systems (2h)
  • Discrete time systems: The logistic map. Fixed points, periodic points, stability, bifurcation diagrams, sensitive dependence on initial conditions, Lyapunov exponents and chaos. (3h)
  • Continuous time systems: Generalities (state equations, existence and uniqueness, phase plane and phase portraits). Fixed points and stability; examples. Introduction to limit cycles, Lyapunov exponents and chaos. (3h)

PART II (F. Corinto, M. Bonnin)

  • F. Corinto:
  • Limit cycles: Poincaré maps and examples. (2h)
  • Limit cycle stability: variational equation and Floquet’s theory.(2h)
  • Harmonic balance (HB) and describing function (DF) techniques. Examples. (2h)
  • M. Bonnin:
  • Phase oscillator model, Kuramoto model.
    Floquet theory and state space decomposition. (3h)
  • Phase model reduction.
    Synchronization of nonlinear oscillations using phase reduced model.(3h)

PART III (M. Righero, M. Biey)

  • The Master Stability Function for synchronized coupled systems (2h)
  • General synchronization properties for complex networks (2h)
  • Synchronization in networks of bio-inspired oscillators. (2h)

Remarks

 

An Introduction to Engineering Quantum Electrodynamics (QED)
Árpád I. Csurgay
Faculty of Information Technology, Pázmány Péter Catholic University
Budapest, Hungary
Torino, April 14 – 16, 2014

Course program

The interaction of electromagnetic radiation and matter is the fundamental physical phenomenon that moves natural and artificial electrical, electronic and photonic ‘machines’. In most cases either classical theory (Maxwell’s equations for fields and phenomenological constitutive parameter characterization of matter), or semi-classical theory (Maxwell’s equations for fields and Quantum Mechanics for matter) adequately describe physics.
In many recently emerging applications, however, only few photons are participating in very fast interactions, thus the interaction can be understood only by studying the atom-photon or molecule-photon interaction. Nano-photonics and nano-bio-photonics are emerging engineering disciplines. The modeling, simulation and design of sensors, microscopes, e.g. photomultipliers, fluorescent microscopes, devices exploiting FRET (fluorescent resonant energy transfer, are based on QED.
An introduction to quantized electromagnetic field theory will be followed by a review of cavity QED and its applications to atom-photon, molecule-photon interactions, together with applications in microscopy, and sensors.

Remarks

  • Course schedule:

    Day
    Hour
    Room
    14/04/2014 10:00-13:00 Room C
    15/04/2014 10:00-13:00 Room C
    16/03/2014 14:00-17:00 Room C

 

All the material related to this course may be found here:

 

References:

  1. Cooper Pair – 1991
  2. Devoret – 2003
  3. Ishizaki – 2009
  4. Coherent Delocalization Theroy – 2014

 

Computer-Assisted Proofs for Chaos
B. Garay
Faculty of Information Technology
Budapest Catholic University
Torino, April 16 – 19, 2012

Course program

  • Two introductory examples;
  • Fundamentals of combinatorial chaos theory in 1D and 2D;
  • Practical criteria for L–R chaos in 1D and 2D;
  • A piecewise affine G-horseshoe;
  • On chaos in a nutshell. The horseshoe is chaotic;
  • Chaos in Vallis’ model for El Niño;
  • Structural stability, also from the numerical viewpoint;

Barnabás Garay’s Technical Biography:

Barnabás Garay (garay@digitus.itk.ppke.hu) has a PhD and a DSc in mathematics. Between 1976 and 2009, he worked in various positions in the Mathematical Institute of the Budapest University of Technology, Department of Differential Equations. He moved to the Faculty of Information Technology of the Budapest Catholic University in 2009. In the last decade, his research interest has shifted from pure mathematics like qualitative aspects of ordinary differential equations in infinite dimension to more applied topics including the geometric theory of discretization methods, computer-assisted proofs for chaos, applications to dynamical models in biology and electrical engineering. .

Venue:
Classrooms: C
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino
ITALY

Schedule:

Lecture Day Room Time
1 16/4/2012 C 13:30 – 16:00
2 17/4/2012 C 10:30 – 13:00
3 18/4/2012 C 10:30 – 13:00
4 19/4/2012 C 12:45 – 14:30

 

All the material related to this course may be found here:
Toward computer-assisted proofs for chaos

 

An Introduction to Synchronization in Complex Systems
A. Ascoli, M. Biey, F. Corinto and M. Righero
Torino, March – April 2012

Course program

PART I

  • Introduction and examples (1h)
  • Complex systems (1h)
  • Discrete time systems: The logistic map. Fixed points, periodic points, stability, bifurcation diagrams, sensitive dependence on initial conditions, Lyapunov exponents and chaos. (2h)
  • Continuous time systems: Generalities (state equations, existence and uniqueness, phase plane and phase portraits). Fixed points and stability; examples. (2h).
  • Introduction to limit cycles, Lyapunov exponents and chaos. (2h)

PART II

  • Limit cycles: Poincaré maps and examples. (2h)
  • Limit cycle stability: variational equation and Floquet’s theory.(2h)
  • Harmonic balance (HB) and describing function (DF) techniques. Examples. (2h)
  • Introduction to memristor circuits (4h)

PART III

  • The Master Stability Function for synchronized coupled systems (2h)
  • General synchronization properties for complex networks (2h)
  • Synchronization in networks of bio-inspired oscillators. (2h)

Remarks

  • Seminars on specific topics related to synchronization in complex systems can be scheduled during the course.
  • Temporary course schedule (schedule of future lectures to be defined):

    Day Hour Room
    28/03/2012 16:00-18:00 21A
    30/03/2012 14:30-17:30 6D
    02/04/2012 14:30-17:30 13A
    04/04/2012 14:30-17:30 6D
    16/04/2012 13:30-16:00 C
    17/04/2012 10:30-13:00 C
    18/04/2012 10:30-13:00 C
    19/04/2012 10:30-13:00 C

  • All the material related to the course may be found here:
    Part I (right click to download)

 

Dynamical processes on networks
Ljupco Kocarev
Macedonian Academy of Sciences and Arts
University of California San Diego
e-mail: lkocarev@ucsd.edu
Torino, October 25-28, 2011

Course program

  • Preliminaries: networks and graphs (1 hour);
  • Network models (2 hours);
  • Introduction to dynamical processes (2 hours);
  • Linear processes on networks: random walks and consensus (2 hours);
  • Searching strategies in networks (2 hours);
  • Synchronization phenomena in networks (2 hours);
  • Epidemic spreading in population networks (2 hours);
  • Social networks and collective behavior (2 hours)

Literature:

  1. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks, Cambridge University Press, 2008
  2. D. Trpevski, W. K. S. Tang, and L. Kocarev, Model for rumor spreading over networks, Physical Review 81, 056102 (2010)
  3. L. Kocarev and V. In, “Network science: A new paradigm shift“, IEEE Network, vol. 24, Issue 6, Pages: 6-9, 2010
  4. D. Smilkov and L. Kocarev, “Analytically solvable processes on networks“, submitted for publication, 2011
  5. I. Tomovski and L. Kocarev, “Topology independent spreading processes“, submitted for publication, 2011
  6. D. Trpevski, D. Smilkov, and L. Kocarev, “On the number of infective nodes in epidemic models“, submitted for publication, 2011

Ljupco Kocarev’s Technical Biography:

LJUPCO KOCAREV [Fellow IEEE] (lkocarev@ucsd.edu) is a professor of computer science and engineering at the Faculty of Electrical Engineering and Information Technologies in Skopje, Macedonia, and a research scientist at the Bio Circuits Institute, University of California at San Diego. He has coauthored more than 100 journal papers in 20 different international peer reviewed journals, ranging from mathematics to physics and from electrical engineering to computer sciences. According to Science Citation Index his work has been cited more than 4500 times. His scientific interests include complex systems and networks, nonlinear systems and circuits, coding, information theory, cryptography, and computational biology.

Venue:
Classrooms: 10I, 5P, C, and 5N
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino
ITALY

Schedule:

Lecture Day Room Time
1 25/10/2011 11T 11:30 – 16:00
(including lunch break)
2 26/10/2011 C 10:00 – 13:00
3 27/10/2011 C 14:00 – 18:00
4 28/10/2011 10I
5P		 11:30 – 14:30
14:30 – 16:00
(including lunch break)

 

Practical information:
All participants are welcome. If interested in attending, please write an e-mail to mario.biey@polito.it with your name and position to help us organizing the course. More information about practical issues (as, for example, available material) will be sent to registered people only.

For PhD Students:
An exam will take place at the end of the course, so you can obtain the corresponding 3 CFU credits. Insert the title in your course load to be able to print the “statino”.

All the material related to this course may be found here: