Construction & Analysis of Complex Networks [Data- driven & Computer- generated Complex Networks]:

• Networks from Data [gene interactins; on-line social communications, human connectome, EEG mapping,...]
• Models of growing networks [Scale-free, Clustered, Correlated, Modular, Self-assembled simplexes];
• Algorithms to explore higher-order network properties [Centralities; Modularity; (weighted)Partitioning; EV.Spectra; SpanningTrees, Clusters, ...]
• ALGEBRAIC TOPOLOGY of GRAPHS --- Quest for higher order combinatorial spaces in complex networks

Dynamic Processes on Networks [Simulations & Advanced Data Analysis]:

• Traffic of Information Packets with Search & Queuing;
• Random-Walks true & advised.RW on Networks;
• Spin-Reversal Dynamics under field ramping on complex geometries;
• Single-Electron-Tunnelings under applied voltage on networked structures
• Coupled-Chaotic-Maps, SYNCHRONIZATION and emergent collective dynamics on networks;

Emergence of Structures & Properties in Nano-particle Assemblies [Nano-particle Films; inhomogeneous 3D Nano-structures]:

• Simulations of SELF-ASSEMBLY processes of colloids and prefformatted Nano-groups;
• Exploring emergent structures of NANO-NETWORKS by Graph theory and Algebraic topology methods;
• Simulating physical processes on Nano-networks;
• Exploring the nature of FLUCTUATIONS at nanoscale;
• SINGLE-MOLECULE Force Spectroscopy --- Theoretical background and Data analysis

Nose Signals in Complex Dynamical Systems [Send-Pile Automata; Barkhausen Noise; Conduction Noise in Nano-Assemblies; Traffic Noise in Communication & Transportation Networks]:

• Simulations of Dynamic Processes & Analysis of recorded signals;
• Signal Correlations & Emergence of Spatio-Temporal Patterns;
• TIME-SERIES mapping onto Networks;
• MULTI-FRACTAL analysis of structured time series;
• Finding and analysis of CYCLICAL TRENDS in time series data;

Quantitative Study of Complexity [Network representation & Methods of network theory applied to different dynamical systems]:

• On-Line Social Interactions==>(un)directed networks & bi-partite graphs;
• Functional Nano-Materials modeling by graphs and simplicial complexes;
• Finding Spatio-Temporal Organization (in physical, biological, social, geographical ... systems);
• Graph-theory framework for EXPLORING COMPLEXITY at nanoscale;
• Algebraic Topology of Graphs: Search for Hidden Structure of BRAIN NETWORKS mapped from empirical data;