Koji Iwayama

Characterizing global evolutions of complex systems via intermediate network representations

Recent developments in measurement techniques have enabled us to observe the time series of many components simultaneously. Thus, it is important to understand not only the dynamics of individual time series but also their interactions. Although there are many methods for analysing the interaction between two or more time series, there are very few methods that describe global changes of the interactions over time. Here, we propose an approach to visualise time evolution for the global changes of the interactions in complex systems. This approach consists of two steps. In the first step, we construct a meta-time series of networks. In the second step, we analyse and visualise this meta-time series by using distance and recurrence plots. Our two-step approach involving intermediate network representations elucidates the half-a-day periodicity of foreign exchange markets and a singular functional network in the brain related to perceptual alternations.

Finite-size scaling in globally coupled phase oscillators with a general coupling scheme

We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize fluctuations in coupled oscillator systems of large but finite size and understand a universal property of synchronization. These exponents have been identified for the sinusoidal coupling but not fully studied for other coupling schemes. Herein, for a general coupling function including a negative second harmonic term in addition to the sinusoidal term, we numerically estimate the critical exponent of the correlation size, denoted by

Self-organization of orientation-selective and ocular-dominance maps through spike-timing-dependent plasticity

\nu_+

Definition of distance for nonlinear time series analysis of marked point process data

, in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of

Intra-day response of foreign exchange markets after the Tohoku-Oki earthquake

\nu_+

Possibility of short-term probabilistic forecasts for large earthquakes making good use of the limitations of existing catalogs

is approximately 5/2 for the sinusoidal coupling case, which is consistent with the well-known theoretical result. Second, we show that the value of

Contribution of hidden modes to nonlinear epidemic dynamics in urban human proximity networks

\nu_+

Change-point detection with recurrence networks

increases with an increase in the strength of the second harmonic term. Our result implies that the critical exponent characterizing synchronization transition largely depends on the coupling function.

Decision-making ability of Physarum polycephalum enhanced by its coordinated spatiotemporal oscillatory dynamics

In the primary visual cortex, there are orientation-selective and ocular-dominance maps. These maps correlate with each other. Although many models have been proposed which explain the formation of the orientation-selective map and the ocular-dominance map, these models contain a physiologically implausible process. It is indicated that spike-timing-dependent plasticity (STDP) can yield a “topographic map” without any constraints. We show that large STDP time constants yield the orientation-selective map, and small STDP time constants yield the ocular-dominance map. This result suggests that the relationship between the orientation-selective and the ocular-dominance maps can be explained by the modulation of STDP time constants.