Complex networks, word frequencies, game theory, research


My overall research interest is focused on investigating collective behavior of systems that in many cases, in principle, can be described by simple local interactions that in all sums up to a network.
In the case of non-trivial network structures, they are often described as complex networks, and consist of both randomness and structure. Different structures might arise as a direct consequence of rationales used by the entities forming a network, or from more indirect reasons by suppressing non successful structures in terms of functionality of the system described by the network.
The structure of a network can be analyzed and described by using various measures. Different structures might produce different dynamics for systems "living" on top of a network, like the spread of a disease in a social network. The network in its turn might alter the structure directly or indirectly as a consequence of the disease and one can study the interplay between structure and dynamics.
Networks can also be used as tools for solving specific tasks, like finding communities of correlated stocks in the stock-market, properties of the configuration space of complex systems, etc...

Another interest is quantitative linguistics and word frequencies. This field is quite similar to that of networks due to the similarities in the mathematical approach and modeling. Instead of a node we have a word, and instead of the number of connections we have the frequency of which it is used in a text. I have been mainly interested in how certain statistical properties depend on the length of the text (size of the system).

I have also been working on problems related to game theory which addresses questions like what are the equilibrium strategies for a specific game where no one can enhance their payoff by individually changing their strategy. The problems I have been working on concerns traffic flow and reversed auction.

Complex networks & Physics

In recent years complex networks have drawn a great deal of attention from the physics community.The recent progress and attention is to a large extent because of all kinds of data of real-world networks found in economy, ecology, biology, etc...
The nature of the networks, showing non-trivial structures - like scale free distributions, and its applications, makes them interesting for people with a background in statistical physics. Many methods used in statistical physics, such as the concept of entropy and Monte-Carlo simulations, are used to analyze the networks.