M. Y. Choi

Synchronization on small-world networks.

We investigate collective synchronization in a system of coupled oscillators on small-world networks. The order parameters that measure synchronization of phases and frequencies are introduced and analyzed by means of dynamic simulations and finite-size scaling. Phase synchronization is observed to emerge in the presence of even a tiny fraction P of shortcuts and to display saturated behavior for P > or similar to 0.5. This indicates that the same synchronizability as the random network (P=1) can be achieved with relatively small number of shortcuts. The transient behavior of the synchronization, obtained from the measurement of the relaxation time, is also discussed.

Factors that predict better synchronizability on complex networks

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network, the suppressing tendency of the heterogeneity of the degree distribution, even for shorter characteristic path length, has also been reported. To see this, we investigate the effects of various factors such as the degree, characteristic path length, heterogeneity, and betweenness centrality on synchronization, and find a consistent trend between the synchronization and the betweenness centrality. The betweenness centrality is thus proposed as a good indicator for synchronizability.

Solvation in molecular ionic liquids

Solvation in 1-ethyl-3-methylimidazolium chloride and 1-ethyl-3-methylimidazolium hexafluorophosphate is studied via molecular dynamics simulations by employing a diatomic solute as a probe. It is found that solvent fluctuations are chacterized by at least two distinct dynamics occurring on vastly different time scales—rapid subpicosecond dynamics arising mainly from anion translations and slow relaxation ascribed to anion and cation diffusions. Fast subpicosecond dynamics are responsible for more than 50% of the entire relaxation of solvent fluctuations in the temperature range 350 K⩽T⩽500 K. It is also found that solvent spectral shifts and reorganization free energies in these liquids are comparable to those in ambient water.

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows

The Metropolitan Seoul Subway system, consisting of 380 stations, provides the major transportation mode in the metropolitan Seoul area. Focusing on the network structure, we analyze statistical properties and topological consequences of the subway system. We further study the passenger flows on the system, and find that the flow weight distribution exhibits a power-law behavior. In addition, the degree distribution of the spanning tree of the flows also follows a power law.

Synchronization in a system of globally coupled oscillators with time delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results.

XY model in small-world networks

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally coupled XY model.

Comment on: Ising model on a small world network

In the recent study of the Ising model on a small world network by Pekalski [Phys. Rev. E 64, 057104 (2001)], a surprisingly small value of the critical exponent beta approximately 0.0001 has been obtained for the temperature dependence of the magnetization. We perform extensive Monte Carlo simulations of the same model and conclude, via the standard finite-size scaling of various quantities, that the phase transition in the model is of the mean-field nature, in contrast to the work by Pekalski, but in accordance with other existing studies.

Synaptotagmin-1 binds to PIP 2 -containing membrane but not to SNAREs at physiological ionic strength

The Ca2+ sensor synaptotagmin-1 is thought to trigger membrane fusion by binding to acidic membrane lipids and SNARE proteins. Previous work has shown that binding is mediated by electrostatic interactions that are sensitive to the ionic environment. However, the influence of divalent or polyvalent ions, at physiological concentrations, on synaptotagmins binding to membranes or SNAREs has not been explored. Here we show that binding of rat synaptotagmin-1 to membranes containing phosphatidylinositol 4,5-bisphosphate (PIP2) is regulated by charge shielding caused by the presence of divalent cations. Surprisingly, polyvalent ions such as ATP and Mg2+ completely abrogate synaptotagmin-1 binding to SNAREs regardless of the presence of Ca2+. Altogether, our data indicate that at physiological ion concentrations Ca2+-dependent synaptotagmin-1 binding is confined to PIP2-containing membrane patches in the plasma membrane, suggesting that membrane interaction of synaptotagmin-1 rather than SNARE binding triggers exocytosis of vesicles.

How Noise and Coupling Induce Bursting Action Potentials in Pancreatic β-Cells

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as well as that by channel-gating stochasticity and examine its effects on the action potential behavior of the beta-cell model. It is observed numerically that such noise in general helps single cells to produce a variety of electrical activities. In addition, we also probe coupling via gap junctions between neighboring cells, with heterogeneity induced by noise, to find that it enhances regular bursts.

Network marketing on a small-world network

We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts–Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturers selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability α is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price p of the product and the referral fee r are used as free parameters to maximize the profit of the manufacturer. It is observed that at α=0 the maximized profit is constant independent of the network size N while at α≠0, it increases linearly with N. This is in parallel to the small-world transition. It is also revealed that while the optimal value of p stays at an almost constant level in a broad range of α, that of r is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.