Bosiljka Tadic  Jelena Zivkovic  Milovan Suvakov  Zoran Levnajic  Marija Mitrovic  Jelena Grujic 
Physics of Complex Networks 
Robust emergent structures with scalefree properties are often found in nature and in artificial evolving networks. They also can be found (as parameterdependent) structures at dynamic phase transitions in fluctuating (static) graphs. Over a decade of the
intensive research of scalefree and other networks,
science now begins to reveal
that certain structural charactersitics beyond the connectivity might play a role in diverse (dynamic) phenomena on these networks.
Often such higher structural properties requires specific algorithms to be detected. In our research we focus on:
Structural properties of scalefree and other networks beyond connectivity distribution;
With emphasis on objectlinking and search for hidden structures on networks; And their graphic visualization.
Complex Dynamical Systems  driven, selforganized,
far from equilibrium ... systems
are in the focus of the modern statistical physics research. Study of such stochastic processes on networks
involves additional complexity in that the networks' sparse connectivity provides a topologically complex
environment, that may affect the process in various ways. We study various types of processes (random and adaptive walks, diffusion, transport, spin dynamics, conduction, ... ) on fixed or adjustable network topologies.
Particular focus is on revealing the structuredynamics interdependence and to
developing tools for detecting new dynamical phenomena induced by the topology.
Theoretical models of complex networks may potentially explain the basic
principles of the networks evolution and their emergent structures, and predict future developments in realworld networks. Recently we developed a model
of cyclic, correlated scalefree network with the statistical features of the WWW (Simulation_sizes_up_Web_structure_011701.
Main application of the statistical physics is found in the understanding of the dynamic processes on networks, or modeling and optomization of the networks function. In this respect, our research is focused on
models of information transport in communication and social networks.
Furthermore, we consider the networks (graphs with complex topology) as
the appropriate structures in modeling new functional materials and properties of the soft matter and biological systems.

SelfAssembly Processes in Nanoscience 
Selfassembly of nanoparticles and/or biomolecules into largescale structures often involves nonlinear processes with driving, constraints, and selforganization.
Numerical modeling of selfassembly processes and emergent structures are indispensable in reversed engineering of new functional materials with desired physical properties.
We introduce network models of nanoparticle assemblies on a 2dimensional substrate and
study their conduction properties via singleelectron tunneling processes. Two types of
models are considered, models based on aggregation of cells of nanoparticles and models of (correlated) deposition of nanoparticles on substrate. Another class of network that we study emerge in
the
assembly processes with biomolecular recognition.

Genetic Networks 
In the postgenome era the large amount of bioinformatics data, especially of the genomewide expression measurements, contributed to understanding that gene functions, which support the living cell processes, are not isolated but mutually coupled complex patterns. These patterns of gene interactions may vary in the nature and intensity during the cell cycle. Recently, approach to modeling gene interaction via network models has opened new prospectives in analyzing the bioinformatics data and, through the formal theory of graphs and physics of complex systems, traced a way to understanding the nature of gene imteractions. In one approach, the attempts are made to reconstruct the underlying gene networks from the expression data (inverse problem) and, in the other, network models with in advance fixed dynamical and topological characteristics are studied. Compared to other complex dynamical systems, additional complexity of the gene networks comes from the fact that the nodes on these networks are genes with (partly or fully) known biological functions. This appear in the mathematical models as constraints to be satisfied in a combinatorial problem. In our research we study both dynamic expression data and network models with focused on discovering dynamically stable structures and check them against known biological functions.
An alternative approach is to introduce models of genetic networks based on
the collected experience.

Coupled Chaotic Maps 
/Networks of coupled maps (discretetime dynamical systems) provide a
simple way to model complex systems due to their computational and
conceptual simplicity. Depending on the network architecture and the
coupling pattern, the system's asymptotic dynamics reaches a particular
emergent behavior whose properties are usually robust to maps' initial
values. By choosing the connectivity and coupling properties in
accordance with the known data, many selforganizational phenomena
observed in the Nature can be understood and/or applied. Moreover, the
network prototypes behind the known realistic collective phenomena can
be designed by controlling the emergent behavior in relation to the
network topology, and in particular the ...
stability of complex structures.
