B. Tadic: Network Research Highlights

Physics of Complex Networks

Structure & Algorithms

Robust emergent structures with scale-free properties are often found in nature and in artificial evolving networks. They also can be found (as parameter-dependent) structures at dynamic phase transitions in fluctuating (static) graphs. Over a decade of the intensive research of scale-free 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 scale-free and other networks beyond connectivity distribution; ---With emphasis on object-linking and search for hidden structures on networks; ---And their graphic visualization.

Dynamic Processes on Networks

Complex Dynamical Systems - driven, self-organized, 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 structure-dynamics interdependence and to developing tools for detecting new dynamical phenomena induced by the topology.

Applied Network Theory

Theoretical models of complex networks may potentially explain the basic principles of the networks evolution and their emergent structures, and predict future developments in real-world networks. Recently we developed a model of cyclic, correlated scale-free 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.

Self-Assembly Processes in Nanoscience

Models of nanoparticle films

Self-assembly of nano-particles and/or bio-molecules into large-scale structures often involves non-linear processes with driving, constraints, and self-organization. Numerical modeling of self-assembly 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 2-dimensional substrate and study their conduction properties via single-electron 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 bio-molecular recognition.

Genetic Networks

Reconstruction of gene interactions from the expression data

In the post-genome era the large amount of bioinformatics data, especially of the genome-wide 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 re-construct 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

Chaotic maps on networks

/Networks of coupled maps (discrete-time 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 self-organizational 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.

Physics of Complex Networks	Structure & Algorithms Robust emergent structures with scale-free properties are often found in nature and in artificial evolving networks. They also can be found (as parameter-dependent) structures at dynamic phase transitions in fluctuating (static) graphs. Over a decade of the intensive research of scale-free 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 scale-free and other networks beyond connectivity distribution; ---With emphasis on object-linking and search for hidden structures on networks; ---And their graphic visualization. Dynamic Processes on Networks Complex Dynamical Systems - driven, self-organized, 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 structure-dynamics interdependence and to developing tools for detecting new dynamical phenomena induced by the topology. Applied Network Theory Theoretical models of complex networks may potentially explain the basic principles of the networks evolution and their emergent structures, and predict future developments in real-world networks. Recently we developed a model of cyclic, correlated scale-free 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.
Self-Assembly Processes in Nanoscience	Models of nanoparticle films Self-assembly of nano-particles and/or bio-molecules into large-scale structures often involves non-linear processes with driving, constraints, and self-organization. Numerical modeling of self-assembly 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 2-dimensional substrate and study their conduction properties via single-electron 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 bio-molecular recognition.
Genetic Networks	Reconstruction of gene interactions from the expression data In the post-genome era the large amount of bioinformatics data, especially of the genome-wide 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 re-construct 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	Chaotic maps on networks /Networks of coupled maps (discrete-time 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 self-organizational 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.

Bosiljka Tadic: Network Research Highlights