Naoki Masuda

Global and local synchrony of coupled neurons in small-world networks

Abstract.Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated so far using model neurons with simple connection topology, real neural networks have more complex structures. Here we examine the behavior of pulse-coupled leaky integrate-and-fire neurons with various network structures. We first show that the dispersion of the number of connections for neurons influences dynamical behavior even if other major topological statistics are kept fixed. The rewiring probability parameter representing the randomness of networks bridges two spatially opposite frameworks: precise local synchrony and rough global synchrony. Finally, cooperation of the global connections and the local clustering property, which is prominent in small-world networks, inforces synchrony of distant neuronal groups receiving coherent inputs.

Chaotic block ciphers: from theory to practical algorithms

Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto components from both dynamical-system and cryptographical points of view, thus to explore connection between these two fields. In the due course, we also apply dynamical system theory to create cryptographically secure transformations and evaluate cryptographical security measures

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.

Transmission of severe acute respiratory syndrome in dynamical small-world networks

The outbreak of severe acute respiratory syndrome (SARS) is still threatening the world because of a possible resurgence. In the current situation that effective medical treatments such as antiviral drugs are not discovered yet, dynamical features of the epidemics should be clarified for establishing strategies for tracing, quarantine, isolation, and regulating social behavior of the public at appropriate costs. Here we propose a network model for SARS epidemics and discuss why superspreaders emerged and why SARS spread especially in hospitals, which were key factors of the recent outbreak. We suggest that superspreaders are biologically contagious patients, and they may amplify the spreads by going to potentially contagious places such as hospitals. To avoid mass transmission in hospitals, it may be a good measure to treat suspected cases without hospitalizing them. Finally, we indicate that SARS probably propagates in small-world networks associated with human contacts and that the biological nature of individuals and social group properties are factors more important than the heterogeneous rates of social contacts among individuals. This is in marked contrast with epidemics of sexually transmitted diseases or computer viruses to which scale-free network models often apply.

VIP-Club Phenomenon : Emergence of Elites and Masterminds in Social Networks

Abstract Hubs, or vertices with large degrees, play massive roles in, for example, epidemic dynamics, innovation diffusion, and synchronization on networks. However, costs of owning edges can motivate agents to decrease their degrees and avoid becoming hubs, whereas they would somehow like to keep access to a major part of the network. By analyzing a model and tennis players’ partnership networks, we show that combination of vertex fitness and homophily yields a VIP-club made of elite vertices that are influential but not easily accessed from the majority. Intentionally formed VIP members can even serve as masterminds, which manipulate hubs to control the entire network without exposing themselves to a large mass. If based on network topology only, elites are not distinguished from many other vertices. Understanding network data is far from sufficient; individualistic factors greatly affect network structure and functions per se.

Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Phys. Rev. Lett. 89, 258702 (2002)]. Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.

A computational study of synaptic mechanisms of partial memory transfer in cerebellar vestibulo-ocular-reflex learning.

There is a debate regarding whether motor memory is stored in the cerebellar cortex, or the cerebellar nuclei, or both. Memory may be acquired in the cortex and then be transferred to the cerebellar nuclei. Based on a dynamical system modeling with a minimal set of variables, we theoretically investigated possible mechanisms of memory transfer and consolidation in the context of vestibulo-ocular reflex learning. We tested different plasticity rules for synapses in the cerebellar nuclei and took robustness of behavior against parameter variation as the criterion of plausibility of a model variant. In the most plausible scenarios, mossy-fiber nucleus-neuron synapses or Purkinje-cell nucleus-neuron synapses are plastic on a slow time scale and store permanent memory, whose content is passed from the cerebellar cortex storing transient memory. In these scenarios, synaptic strengths are potentiated when the mossy-fiber afferents to the nuclei are active during a pause in Purkinje-cell activities. Furthermore, assuming that mossy fibers create a limited variety of signals compared to parallel fibers, our model shows partial memory transfer from the cortex to the nuclei.

Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics

Abstract.Cellular automata are widely used to model real-world dynamics. We show using the Domany-Kinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out. The analysis of the original and reduced models reveals generality of this paradoxical behavior, which suggests that autonomous or man-made periodic or random environmental changes can cause extinction in otherwise safe population dynamics. Our model also realizes another scenario for the Parrondo’s paradox to occur, namely, spatial extensions.

Networks with dispersed degrees save stable coexistence of species in cyclic competition.

The nature realizes stable biodiversity, even though it escapes naive theoretical predictions. Coexistence of competing species is known to be facilitated by, for example, structured populations, heterogeneous individuals, and heterogeneous environments, which in one way or another allow different species to survive in a segregated manner. In reality, individuals disperse and interact with each other often on networks of habitats connected in complex ways. We examine how heterogeneous degree distributions of networks, namely, heterogeneous contact rates for different habitats, influence stability of biodiversity. We show that heterogeneous networks induce stable coexistence of many species in cyclic competition, whereas well-mixed populations do not sustain coexistence. Coexistence based on networks does not require heterogeneity in environments or phenotypes, or spatially structured populations. Together with other mechanisms, the effect of heterogeneous networks may underly stable biodiversity in the real world. Key index words: ecological stability, population dynamics, cyclic competition, complex networks, scale-free networks

Extremal dynamics on complex networks: analytic solutions.

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(k)) in the quenched (annealed) updating case, where kn is the nth moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent gamma<3 (gamma>3) for the quenched case in the thermodynamic limit. The theoretical value xc fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, Pa(s) approximately s(-3/2).