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Complex Networks

Complex web-like systems are found in nature from physical and biological systems to social systems, which consist of a large number of interacting units. The behavior of such systems can typically not be fully described by the properties of the individual units alone - instead the key lies in the interaction between the agents. The study on the physical systems itself whose elements interact along the links in complex networks is interesting. Also, the interplay between the dynamics of systems and the underlying topology have drawn much attention.

Bioinformatics

Developed the next generation sequencing technics, cost of experiments is dramatically dropped down. As a result, tons of biological data are produced and stored somewhere. Everybody expects important biological principles are uncovered beneath the data. However, because of lack of proper tools, much of data are forgotten without proper analysis. This is the point of attracting interests in bioinformatics. Based on knowledge of both computer science and biology, new bioinformatics tools are actively developed to take care of precious data like undiscovered gold.

Systems Biology

Understanding the world surrounding us almost always implies breaking it down to comprehensible pieces before collecting information about how these small parts interact. In particular, interactions between the constituents of biological systems take many disguises, from food webs in ecology to various biochemical interactions in molecular biology. Focusing on the cell, the variety of interactions between genes, proteins and metabolites are best represented by networks, offering a new way to uniformly categorize these dramatically different systems and their associated features. Intriguingly, this approach has uncovered unexpected similarities between eg. the world-wide-web and the protein-interaction network, suggesting that generic principles and mechanisms give rise to their structure. Our main research interests and approaches are well characterized as "systems biology," where we focus on developing both general and specific methods to understand the principles behind the design and organization of biological systems. Most of the work is theoretical and computational in nature, but we are also involved in smaller experimental efforts. Interest topics include gene-regulatory networks, protein interaction networks, microbial communities, biofilms, robustness of biological systems, and general complex network theory with emphasis on dynamics.

Diffusive System and Information Spreading

The diffusion-controlled reactions, in which diffusing particles are immediately converted to a product if a pair of them meets together, are related to various physical phenomena. Examples include electron trapping and recombination, exciton fusion, wetting, melting, and commensurate-incommensurate transitions. Among these examples, dynamical properties of wetting, melting, and commensurate-incommensurate transition are known to be related to the diffusive capture process. The diffusive capture process consists of a diffusing prey and diffusing predators. The prey is absorbed, or dies, whenever it meets any of the predators. The effect of the underlying topology on the diffusive capture process is interesting. As an application, I introduced effective algorithm for information search based on diffusive capture process. In general, the dynamical properties of diffusive capture process are closely related to the first-passage phenomena of random walks, because the reaction occurs when diffusing particles first meet a trap or an absorbing boundary. Random walks on complex networks have been studied to show that the dynamical properties of random walks are closely related to the topology of underlying networks. Therefore, I studied on the interplay between the topology networks and dynamical properties of random walk.

Modeling Social Systems

In society, there are often also large numbers of entities that makes up a whole whose appearance can be hard to predict from the entities' behavior. Modeling of such behavior has a long tradition in statistical physics. This is not to say that statistical physics can be immediately applied to sociology -- the different traits of the entities may be more significant than their similarity.

Network Biology and Epidemiology

Complex systems studies applied to areas such as genetics, medicine and cellular biology is interesting. The interactions between units (genes, proteins, metabolites, cells, etc.) build the functionality of organisms in a way that cannot be understood by a reductionist methodology of understanding systems by studying their subsystems, and the subsystems by studying their subsubsystems. Complex network theories, and simulation techniques, are valuable tools for understanding the emergent features that give biological systems their functionality. It is interesting to find candidate genes (genes that, if expressed differently, would affect the disease) for allergic rhinitis and other complex diseases. This is a very complex problem where one, typically, knows some of candidate genes (involved in the signaling pathway from the active receptors) but have to find the others by integrating various information, ranging from expression studies to text mining techniques. Traditional epidemiology has focused on situations where the probability of disease spreading is the same between all pairs of individuals in a population. However, social systems can be described as complex networks, and in such systems, the dynamics on the network (in this case disease spreading) can be affected by the spreading of the disease.

Self-organized Criticality

Gould proposed that biological evolution shows intermittent bursts of activ- ity interrupting periods of quiescence. This is known as a punctuated equilibrium. The idea of punctuated equilibrium is that biological evolution occurs episodically rather than as a steady, gradual process. That is most of the major changes in life forms occur in relatively short periods of time. Such behavior of species has evolved to self-organized a critical state.

Nonequilibrium Phase Transition

Nonequilibrium phase transitions occur in various systems including hetero- geneous catalysis, chemical reaction, polynuclear growth, fungal growth, and branching annihilating random walks. An interesting example of nonequilibrium phase transition is condensation phase transition. The condensation phase transition involves the irreversible joining of diffusing particles whenever they meet. One important class of condensation transitions emerges when the diffusion of the whole particles of a single site is involved in addition to the chipping and aggregation.

Financial Marcket

Financial market is an interesting example of complex systems, which are continuously monitored. The recorded economic data is greatly increasing and becoming accessible. Through the analysis of empirical data, it is found that many different markets share some universal properties. For example, long-term volatility correlation, the fat-tailed distribution, and herd behavior were observed in many different financial systems. In particular, herd behavior have drawn much attention because such a collective behavior is occasionally occurred in case of financial crashes like Black Monday.