Research Interest

• Hierarchical community structure in Supplier-customer network

We studied the overall structure and the hierarchical communities embedded in the production network of one million firms and five million links for trade relationship in Japan for the year 2016. The visualization of IN, OUT and GSCC (Giant Strongly Connected Component) decomposition of the production network shows a very different structure from usual “bow-tie" structure, which we name a “walnut” structure. Schematically this structure is illustrated in Fig 1 (left). By using the Infomap method, we uncovered a 5 layers of hierarchy of communities [Fig. 1 (right)] that reflects extremely complex nature of the network with multi-scale inhomogeneity. Level-by-level study of communities and “irreducible" communities (communities that are not decomposed into sub-communities at the lower level) are identified. We also showed the overexpression of some of the major communities to identify both the industrial sector and the regional decomposition. We reported how mixed are the IN, OUT, and GSCC components of the walnut structure in each of large communities. We further provided a comparison between the study of communities and input-output analysis.

Figure 1: (left) The Walnut structure. The production network forms a walnut structure. Areas of each component are approximately proportional to their sizes. (right) Hierarchical structure of the communities. Five Levels of hierarchical community decomposition are illustrated. The width of the triangle originating from each community at the n-th level is proportional to the number of its subcomunities at the (n+1)-th level.

• Exponential random graph models for economic networks

We used the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms [4]. One of the well-known and simple models of the exponential random graph is the Bernoulli model which shows that the links in the bank–firm network are not independent from each other. Another popular exponential random graph model, the two-star model, indicates that the bank–firms are in a state where the macroscopic variables of the system can show large fluctuations. Moreover, the presence of high fluctuations reflects a fragile nature of the bank-firm network.

Figure 2: The phase diagram for the two-star model. The red circle indicates the position for the Japanese bipartite network of banks and firms for the year 2005

• Collective motion

Flocking is one of the finest and well-known examples of a non-equilibrium dynamical system with many degrees of freedom. We investigated a model of flocking in which neighborhoods and forces are defined through topology based rules. The rules allow the flock to remain as a single cohesive unit even under open boundary conditions. The fluctuations in velocity and speed appear spontaneously without any external noise, which is in stark contrast with other existing models in the literature. Fluctuations are characterized by scale-free correlations, as is observed in real flocks [Fig. 3]. Furthermore, the dynamical behavior of the model is investigated by computing the Lyapunov exponents.

Figure 3: (a) Plot of the correlation functions C_v(r) for velocity fluctuations for flocks with different N (indicated in the legend). (b) Plot of correlation length ξ_υ versus the flock size L.

• International currency market

We analyzed daily foreign exchange rate data of 75 currencies from a period of over one and a half decades (Oct 23, 1995 - April 30, 2012) to observe whether the fluctuation behavior in this market exhibits any universal properties. We observed that the normalized returns r quantifying the fluctuations in the exchange rate of currencies can appear extremely different even though they have been adjusted to have the same long-term volatility. The distributions of the exchange rate fluctuations for the currencies are typically heavy-tailed, with different currencies distinguished by how much leptokurtic the corresponding distributions are. The cumulative fluctuation distribution possesses heavy tails, characterized by exponents varying around a median value of 2. This suggests an “inverse square law” governing the nature of fluctuations in the currency market, analogous to the “inverse cubic law” that has been proposed as governing the price and index fluctuations in several financial markets. It is seen that systematic deviation of the fluctuation behavior of different currencies from a universal signature depend on two key macroeconomic indicators related to the economic performance and the diversity of exports of the corresponding countries.

• Modeling the self-organized critical evolution of the wealth distribution in a society

Using the framework of the Pianegonda et. al. model, we studied a conservative self-organized extremal model with a stochastic bipartite trading rule. More precisely, in a bipartite trade one agent must be the poorest one and the other one is selected randomly from the neighbors of the first agent. The two agents then randomly reshuffle their entire amount of wealth without saving. This model is one of the few examples of non-dissipative self-organized critical systems where the entire wealth of the society is strictly conserved. We estimated a number of critical exponents which indicate this model is likely to be in a new universality class, different from the well-established models of self-organized criticality.

• SIS and SIR type disease spreading models with partial isolation on networks

we studied the effect of partial isolation in disease spreading processes using the well-known models of susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models where individuals are located at the nodes of several graphs representing the contact networks in a society. In this model, we imposed a restriction: each infected individual can probabilistically infect only up to a maximum number n of his susceptible neighbors. Numerical study of this model shows that the critical values of the spreading rates for endemic states are non-zero in both models and decreases as 1/n with n, on all graphs including scale-free graphs. In particular, the SIR model on square lattice with n=2 found to be special case, characterized by a new bond percolation threshold.