Aerial view of Pescara

6th Ph.D. School/Conference on
Mathematical Modeling of Complex Systems
Università “G. d’Annunzio”, Pescara (IT), July 3 – 11, 2019


This is the latest in a series of events that started at the University of Patras, Greece, in July 2011. The previous editions were:

This year’s event is dedicated to the memory of Professor Gregoire Nicolis, of the Université Libre de Bruxelles, who recently passed away. Professor Nicolis, one of the founding fathers and most influential advocates of Complexity Science, was an invited speaker in the Conference on Nonlinear Science and Complexity at Pescara, July 2009 (see his presentation).

The focus of the 6th Ph.D. School/Conference this year is on the connections between Information Theory and Complexity through the fundamental role of Entropy. It is primarily intended for postgraduate (and advanced undergraduate) students primarily from European countries (but students from other countries are also invited to apply) and offers four coherent lecture modules, taught by experts in each field, on:

  1. Fundamental Concepts of Complexity in Physical Systems
    A. Bountis (Astana), M. Robnik (Maribor), Ch. Skokos (Cape Town), M. G. Velarde (Madrid), J. P. van der Weele (Patras)
  2. Complexity in Biomedical Sciences
    A. Athanassiadou (Patras), V. Basios (Brussels), A. Bezerianos (Singapore/Patras), A. S. Fokas (Cambridge), A. Piattelli (Chieti-Pescara), A. Provata (Athens)
  3. Complex Networks and Information Theory
    G. Pistone (Torino), S. Puechmorel (Toulouse), J. J. P. Veerman (Portland)
  4. Entropy and Complexity
    D. P. K. Ghikas (Patras), R. Hanel (Vienna), S. Thurner (Vienna), C. Tsallis (Rio de Janeiro)

Scientific Organizing Committee

  • G. Amato (Università “G. d’Annunzio”, Pescara)
  • A. Bountis (Nazarbayev University, Astana)
  • A. De Sanctis (Università “G. d’Annunzio”, Pescara)
  • S. A. Gattone (Università “G. d’Annunzio”, Pescara)
  • C. Mari (Università “G. d’Annunzio”, Pescara)
  • M. Parton (Università “G. d’Annunzio”, Pescara)
  • A. Piattelli (Università “G. d’Annunzio”, Pescara)
  • J. J. P. Veerman (Portland State University)
  • M. G. Velarde (Complutense University of Madrid)
  • J. P. van der Weele (University of Patras)

To be announced.

To be announced.

How to apply

Postgraduate or advanced undergraduate students aiming to obtain a Master’s or Ph.D. degree in any scientific area involving Complex Systems are invited to apply to Prof. Angela De Sanctis, at Each applicant is asked to submit a CV, including a transcript of grades obtained in his/her undergraduate studies, as well as a personal statement explaining why the School will be useful to his/her current studies, including names and contact information of two senior scientists recommending the applicant.

Based on the above information, the Scientific Organizing Committee will select 35 - 40 applicants to attend the School. To obtain a Certificate of Participation the selected students should attend all lectures and exercise sessions of the School. The total number of instruction hours is nearly 28, which corresponds to 3 ECTS credits, as stated on the Certificate that each student receives.

All interested students are invited to submit their application at the latest by May 31, 2019. They will then be informed about the decision of the Scientific Organizing Committee regarding their acceptance. The selected students will be asked to download and read preparatory material provided by the instructors and placed on the School’s website. In this way, the students will be better prepared to follow the lectures and exercise sessions of the School.

Attendance fee, living expenses and financial support

The attendance fee for each student participating in the Ph.D. School is € 150. Limited financial support can be provided to deserving students after sufficient justification. The attendance fee includes:

  • Participation in all lectures and exercise sessions
  • All printed material related to the Ph.D. School
  • Participation in all the School’s social activities
  • Coffee breaks during the School

Comfortable, low-cost double rooms will be provided to the students at a seaside hotel in Pescara.



The School/Conference will be held here:
University of Chieti–Pescara
viale Pindaro 42, Pescara

Reaching Pescara

Pescara has a small airport, Abruzzo Airport, very close to downtown. If traveling directly to Abruzzo Airport is not an option (very likely!), consider going through Rome Fiumicino Airport From there, there are many bus connections (~3h 20m travel time), with either Prontobus or Di Carlo Bus.

Another option is landing in Rome Ciampino Airport: from there you can find bus connections to Pescara with Prontobus (~2h 30m). If you are in Rome but not at the airport, in addition to Prontobus and Di Carlo Bus, you may consider Flixbus and Arpa-Di Febo-Capuani-Di Fonzo buses.

Technically you could reach Pescara by train, with trains departing from Rome Tiburtina station. However, trains on the line Rome–Pescara are quite slow. On the bright side, the trip by train is interesting since trains pass trough many small rural villages in the innermost part of Italy. If you have time to spare (and no work to do... probably no Internet connection there) it could be an alternative.

If you are in Italy everywhere else, you can reach Pescara by bus with Flixbus or by train.


This is a list of hotels in downtown Pescara or near the place of the school.

4-stars hotel
Location: center of Pescara, at the seafront (the school place can be reached by bus in 15 minutes)
4-stars hotel
Location: center of Pescara (the school place can be reached by bus in 15 minutes)
3-stars hotel
Location: center of Pescara (the school place can be reached by bus in 15 minutes)
3-stars hotel
Location: close to the university, at the seafront (the school place can be reached on foot in 15 minutes)
Location: close to the university (the school place can be reached on foot in 5 minutes)
3-stars hotel
Location: at the seafront (the school place can be reached on foot in 15 minutes)
A tutorial on Information Flow in Directed Graphs
Università “G. d’Annunzio”, Pescara, Italy 1 – 2 July, 2019
J. J. P. Veerman — M. Eboli — L. Moscardelli

The goal of this tutorial is familiarizing the student with the notions of information flow in graphs. In particular, it will be considered the processes of consensus and diffusion on directed graphs.

  • Different graph types: directed, undirected, multigraph, (spanning) trees, k-partite graphs.
  • Elementary notions of graph theory: subgraph, induced graph, cycles, paths, walks, in- and out-degree, neighborhood. Euler and Hamilton cycles. Notions of connectedness for digraphs.
  • Equivalence classes and partition into strong components. Condensation and “topological” ordering. Different types of adjacency matrices and of Laplacians for directed and undirected graphs.
  • Basic Linear Algebra: Statements of Perron-Frobenius theorem and Jordan normal form. Relations between eigenvalues and eigenvectors of the Laplacian. Relation between spectrum and graph structure.
  • Discussion of direction of arrows in digraphs. Definitions of consensus and diffusion. Linear differential equations and exponential of matrix. Relation between discrete and continuous processes.
  • Characterization of the right and left kernel of the Laplacian. Asymptotics of consensus and diffusion in terms of these kernels. Consensus and diffusion are duals.
  • The pagerank algorithm as a diffusion type algorithm. Pagerank as a consensus type algorithm.
  • Related topics in the social sciences.

Prof. J. J. P. Veerman (Portland State University) will be the main speaker of the tutorial, covering most of the topics outlined above. Prof. Mario Eboli (Università “G. d’Annunzio”) will discuss the applications of graph theory and flow network theory to the modelling of direct contagion phenomena in financial markets. Prof. Luca Moscardelli (Università “G. d’Annunzio”) will present an overview of the studies on the coevolutionary and aggregation-based opinion formation processes in social networks.

Participation is free, but we will appreciate to receive an e-mail ( confirming your presence, for organizing purposes.


Angela De Sanctis (chair)

Gianluca Amato

Stefano Antonio Gattone

Fabrizio Maturo

Maurizio Parton

Adriano Piattelli