Projekt badawczy - prof. Jurij Kozicki

Title of the project: "Structure and Evolution of Complex Systems with Applications in Physics and Life Sciences" (STREVCOMS) / PIRSES-GA-2013-612669 

Coordinator of the project: prof. dr hab. Jurij Kozicki (ZZM IM UMCS)

Participants:
UNIWERSYTET MARII CURIE-SKLODOWSKIEJ, Poland
UNIVERSITETET I BERGEN, Norway
UNIVERSITAET BIELEFELD, Germany
HELSINGIN YLIOPISTO, Finland
ORT BRAUDE COLLEGE, Israel
NATIONAL PEDAGOGICAL DRAGOMANOV UNIVERSITY, Ukraine
INSTITUTE FOR CONDENSED MATTER PHYSICS OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE, Ukraine
UNIVERSIDADE FEDERAL DE PERNAMBUCO, Brazil
HOLON INSTITUTE OF TECHNOLOGY, Israel
IVAN FRANKO NATIONAL UNIVERSITY OF LVIV, Ukraine
UNIVERSIDAD DE FRONTERA, TEMUCO, Chile 

Estimated budget: 366 900 EUR 

Duration of the project: 1.01.2014 - 31.12.2017 (48 months) 

The aim of the project is to make a major step-change in developing novel effective tools for studying complex systems based on stochastic geometry and stochastic evolution methods, on appropriate methods of analysis and combinatorics, as well as on numerical methods and computer simulations. The network we are going to create will unite efforts of leading specialists in this area towards scientific excellence, will establish new and strengthen existing long-term collaboration links between them, and will train a new generation of young researchers in this multidisciplinary area.

The proposed research is assumed to employ existing and to elaborate new models of real-world object, and hence to have direct applications. The systems we are going to study consist of large number of interacting entities and may evolve in continuous space and time. Both their structure and evolution are of our interest. Such systems appear in broadly understood statistical physics, including its industrial applications, in spatial ecology, evolutionary and population biology, epidemiology, etc. In view of this, along with mathematicians the network includes physicists and biologists working with the corresponding experimental data and experienced in modeling real world objects of the mentioned areas. In this direction, we plan to study structure and properties of complex networks, such as polymers, irregular and random graphs, random fields on graphs, and their applications in the mentioned areas. The microscopic evolution of complex systems of this type will be studied in Markovian and time-delayed frameworks. Their meso- and macroscopic dynamics will be deduced from the microscopic theory by various types of scaling procedures. Along with systems of interacting entities we will study objects which can be characterized as evolving complex shapes, where methods of stochastic geometry ought to be especially effective. Such models have various applications, e.g., in neurogeometry and visual recognition. Recent progress in this direction has been based on several ideas of Laplacian growth, stochastic Loewner evolution, conformal welding and potential-theoretical skeletons evoking a revolutionary development at the crossroad of statistical physics, stochastic geometry, complex analysis and dynamical system theory. The problems to be attacked include the Riemannian and sub-Riemannian geometries of the infinite-dimensional space of shapes, shape comparison and modeling by making use of infinite random configurations, deterministic and stochastic shape tuning and its geodesic equations, infinite-dimensional geometric control.

General progress of the project

Project achievements

Publishable summary

List of publications 


In the framework of the project, two PhD dissertations were completed and defended:

1. Alexey Tochin "General Slit Stochastic Evolution and Conformal Field Theory", University of Bergen, 6 May 2016
2. Mariana Krasnytska "Phase Transitions on Complex Networks", Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 7 September 2016 

The results obtained are periodically reported on conferences, seminars, workshops, etc. The corresponding information is available at:
http://www.icmp.lviv.ua/en/content/interdisciplinary-seminar-structure-and-evolution-complex-systems-applications-physics-and 

The list of publications created within the project is available at:
http://folk.uib.no/ima083/strevcoms.html