Speaker: Takashi Shimada

Title: The effect of laziness in group chase and escape

How to chase a target or how to escape from a target is a classical problem in mathematical science. In real systems, such as hunting by animals, it often appears as a many-body problem. Recently Kamimura and Ohira introduced a simple model of such group chase and escape and reported an interesting collective behavior (2010). In this talk I will introduce our recent work about the effect of laziness in this group chase and escape model. We find that a division-oflabor way of introduction of lazy chasers improves the chasers’ ability to catch all the target, while uniform laziness always does not show positive effect.

Reference: https://arxiv.org/abs/1612.04556

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Speaker: Nobuyasu Ito

Title: Car traffic modelings and simulations

Car traffic flow of Kobe city was simulated and a origin and a destination of each car is assigned randomly obeying macroscopic traffic data, Ensemble of simulation results are analyzed with a standard multivariable statistical analysis. Correlations between car flow of road segments captured about 128 road factors from more than 20,000 road segments of the city. Top 11 factors statistically explain 37.3% of the simulated traffic, and top 33, 69.0%. These factors will work as skeleton of Kobe car traffic.

Reference: Takeshi Uchitane and Nobuyasu Ito, "Applying Factor Analysis to Describe Urban Scale Vehicfle Traffic, Simulation Results," (in Japanese) Journal of the Society of Instrument and Control Engineers vol.52 (2016) No.10 p.545-554.

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Speaker: Hang-Hyun Jo

Title: Spreading dynamics with bursty patterns

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence. 

Reference: H.-H. Jo, J.I. Perotti, K. Kaski, and J. Kertesz, Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes, Physical Review X 4, 011041 (2014).

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Speaker: Yohsuke Murase

Title: Effects of demographic stochasticity on biological community assembly on evolutionary time scales

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/f^2 fluctuations are found for the model without demographic noise.

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Speaker: Takayuki Hiraoka

Title: Agent-based approach to simulate predation and escape behavior

The predator-prey interaction is one of the most important interspecific relationships in ecological systems. Studying the population dynamics by Lotka-Volterra equations, both at a mean-field level[1] and for spationally heterogenetic cases[2], has a long tradition in populational ecology, and microscopic description of the predation and avoidance strategies has been recent interest for behavioral ecologists[3]. Starting from the self-propelled particle models, I address the issue of how we can simulate the pursuit and escape behavior in simple agent-based systems.

References:

[1]A. J. Lotka, J. Am. Chem. Soc. 42, 1595 (1920); V. Volterra, Mem. Acad. Sci. Lincei. 2, 31 (1926)

[2]J. H. Steele, Nature 248, 83 (1974)

[3]D. Weihs, P. W. Webb, J. Theor. Biol. 106, 189(1984)

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Speaker: Naoki Yoshioka

Title: Kinetic Monte Carlo algorithm for thermally induced breakdown of fiber bundles

In the framework of the fiber bundle model we introduce a kinetic Monte Carlo algorithm to investigate the thermally induced creep rupture of materials occurring under a constant external load. We demonstrate that the method overcomes several limitations of previous techniques and provides an efficient numerical framework at any load and temperature values. We show for both equal and localized load sharing that the computational time does not depend on the temperature, it is solely determined by the external load and the system size. In the limit of low load where the lifetime of the system diverges, the computational time saturates to a constant value. Using this method we check the Arrhenius law of lifetime for equal load sharing in the presence of any types of quenched disorder distributions. For localized load sharing, we show the modified form of the Arrhenius law does hold even in the presence of quenched disorder. Moreover, we investigate statistics of jumps of epicenters in successive breaking events. We show the epicenter jump distribution shows power-law with exponent -1.5.

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Speaker: Fumiko Ogushi

Title: Bidirectionality of interactions enhances the robustness of evolving open system

An important feature of complex systems like living organisms, ecosystems, and social systems is that they are open. Our question is when can such complex an dynamical systems exist with inclusion of new elements. We investigated the effects of bidirectionality of interactions on the robustness of evolving open systems using a simple graph dynamics model [1]. We found that the system with purely bidirectional interactions can grow with two-fold average degree, in comparison with the purely unidirectional system. This shift of the transition point comes from the reinforcement of each element, not from a change in structure of the emergent system.

References:

[1] T. Shimada, “A universal transition in the robustness of evolving open system”, Scientific Reports 4, 4082 (2014)

[2] F. Ogushi, J. Kertesz, K. Kaski, and T. Shimada, “Enhanced robustness of evolving open systems by the bidirectionality of interactions between elements”, arXiv: 1703.04383v1 (2017)

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Speaker: Toru Ohira

Title: Effects of Delays on Stochastic Systems

I will present a simple models in connection with random walks. The first model is a classic model of the gambler's ruin problem. By incorporating delays in receiving of rewards and paying of penalties, we extend the problem. We derive an approximate scheme to find an effective shift in the initial assets of the gambler. Through comparison against computer simulations, this approximation is shown to work for small differences between the two delays. The second model is a relay of a message by collection of random walks. We investigate by simulations the behavior of message transmission in the presence of transaction delay. With sufficiently long delay, we observe an optimal number of random walkers in a relay.

References:

Delayed Gambler's Ruin, Tomohisa Imai and Toru Ohira, arXiv 1606.0342, 2016 http://arxiv.org/abs/1606.04342

Delayed Random Relays, Koki Sugishita and Toru Ohira, arXiv 1609.06574, 2016 http://arxiv.org/abs/1609.06574

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Speaker: Beom Jun Kim

Title: Role of generosity for cooperating society 

One’s reputation in human society depends on what and how one did in the past. If the reputation of a counterpart is too bad, we often avoid interacting with the individual. We introduce a selective cooperator called the goodie, who participates in the prisoner’s dilemma game dependent on the opponent’s reputation, and study its role in forming a cooperative society. We observe enhanced cooperation when goodies have a small but nonzero probability of playing the game with an individual who defected in previous rounds. Our finding implies that even this small generosity of goodies can provide defectors chances of encountering the better world of cooperation, encouraging them to escape from their isolated world of selfishness.

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Speaker: Seung Ki Baek

Title: Symmetry and Chaos in Evolutionary Dynamics

The prisoner's dilemma describes a conflict between a pair of players, in which defection is a dominant strategy whereas cooperation is collectively optimal. The strength of the dilemma can be parametrized by the cost-benefit ratio of cooperation, denoted as $c$. The iterated version of the dilemma has been extensively studied to understand the emergence of cooperation. In the evolutionary context, the iterated prisoner's dilemma is often combined with population dynamics, in which a more successful strategy replicates itself with a higher growth rate. Here, we investigate the replicator dynamics of three representative strategies, i.e., unconditional cooperation, unconditional defection, and tit-for-tat, which prescribes reciprocal cooperation by mimicking the opponent’s previous move. Our first finding is that the dynamics is self-dual in the sense that it remains invariant when we apply time reversal and exchange the fractions of unconditional cooperators and defectors in the population. The duality implies that the fractions can be equalized by tit-for-tat players, although unconditional cooperation is still dominated by defection. Mutation among the strategies breaks the exact duality in such a way that cooperation is more favored than defection, as long as $c$ is small. Furthermore, if we additionally include win-stay-lose-shift, we find that the resulting three-dimensional continuous-time dynamics exhibits chaos through a bifurcation sequence similar to that of a logistic map as $c$ varies. If mutation occurs with rate $\mu \ll 1$, the position of the bifurcation sequence on the $c$ axis is found to scale as $\mu^{0.1}$ numerically, and such sensitivity to $\mu$ suggests that mutation may have non-perturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics, establishing the arrow of time on an ecological scale based on information loss.

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Speaker: Seung-Woo Son

Title: Network structures of a model of open evolving system in a microscopic level

We consider a growing and evolving network model which consists of signed, directed, and weighted links. At each time step, a new node comes in the system and attaches $m$ random directed links having weight $w_ij$ from the normal distribution $N(0, 1)$. The fitness of each node is given the sum of the incoming weight. When the fitness is negative, the node is removed from the system. Depending on the number of interactions $m$ in this network, the system size sometimes immediately drops to zero, sometimes grows to the infinity. In this study, we tried to figure out properties of network structures on a microscopic scale and find certain conditions that allow this open system to grow.