論文 - 田中 剛平
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Epidemic spread on interconnected metapopulation networks 査読あり 国際誌
Bing Wang, Gouhei Tanaka, Hideyuki Suzuki, Kazuyuki Aihara
PHYSICAL REVIEW E 90 ( 3 ) 032806 - 032806 2014年09月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
Numerous real-world networks have been observed to interact with each other, resulting in interconnected networks that exhibit diverse, nontrivial behavior with dynamical processes. Here we investigate epidemic spreading on interconnected networks at the level of metapopulation. Through a mean-field approximation for a metapopulation model, we find that both the interaction network topology and the mobility probabilities between subnetworks jointly influence the epidemic spread. Depending on the interaction between subnetworks, proper controls of mobility can efficiently mitigate epidemics, whereas an extremely biased mobility to one subnetwork will typically cause a severe outbreak and promote the epidemic spreading. Our analysis provides a basic framework for better understanding of epidemic behavior in related transportation systems as well as for better control of epidemics by guiding human mobility patterns.
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Finite-size scaling in globally coupled phase oscillators with a general coupling scheme 査読あり
Isao Nishikawa, Koji Iwayama, Gouhei Tanaka, Takehiko Horita, Kazuyuki Aihara
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS 2014 ( 2 ) 2014年02月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：OXFORD UNIV PRESS INC
We investigate the critical exponent of correlation size, related to synchronization transition, in globally coupled nonidentical phase oscillators. The critical exponent has so far been identified for sinusoidal coupling, but has not been 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 nu(+), in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of nu(+) 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 nu(+) increases with an increase in the strength of the second harmonic term. Our result means that the universality of a critical exponent can break down in the globally coupled phase oscillators.
DOI： 10.1093/ptep/ptu015
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Analysis of Supply Stability of the Power Grid in Eastern Japan Using a Phase Model 査読あり
Motoki Nagata, Naoya Fujiwara, Isao Nishikawa, Gouhei Tanaka, Hideyuki Suzuki, Kazuyuki Aihara
International Symposium on Nonlinear Theory and its Applications (NOLTA2013) 69 - 72 2013年09月
記述言語：英語 掲載種別：研究論文（国際会議プロシーディングス）
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Efficient recovery of dynamic behavior in coupled oscillator networks. 査読あり 国際誌
Kai Morino, Gouhei Tanaka, Kazuyuki Aihara
Physical review. E, Statistical, nonlinear, and soft matter physics 88 ( 3 ) 032909 - 032909 2013年09月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
We study an effective method to recover dynamic activity in coupled oscillator networks that have been damaged and lost oscillatory dynamics owing to some inactivated or deteriorated oscillator elements. Recovery of the dynamic behavior can be achieved by newly connecting intact oscillators to the network. We analytically and numerically examine the proportion of the oscillators that are needed to be supported by intact oscillators for recovery of oscillation dynamics. Our results show that it can be more effective to preferentially support active oscillators in the damaged network than to preferentially support inactivated ones. The conditions for this counterintuitive result are discussed. Our framework could be a theoretical foundation for understanding regeneration of oscillatory dynamics in physical and biological systems.
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Nonstandard scaling law of fluctuations in finite-size systems of globally coupled oscillators. 査読あり 国際誌
Isao Nishikawa, Gouhei Tanaka, Kazuyuki Aihara
Physical review. E, Statistical, nonlinear, and soft matter physics 88 ( 2 ) 024102 - 024102 2013年08月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.
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Effects of seasonal variation patterns on recurrent outbreaks in epidemic models. 査読あり 国際誌
Gouhei Tanaka, Kazuyuki Aihara
Journal of theoretical biology 317 87 - 95 2013年01月
担当区分：筆頭著者, 責任著者 記述言語：英語 掲載種別：研究論文（学術雑誌）
Transmission of infectious diseases often depends on seasonal variability. Mathematical epidemic models driven by seasonal forcing have been widely explored to understand recurrent outbreaks of infectious diseases. Here we present an effective method to examine the impact of seasonal variation patterns on epidemic dynamics. The idea is to represent the seasonal variability as a piecewise constant function and analyze the seasonally forced epidemic model by means of a numerical shooting method for switched dynamical systems. Several illustrative examples demonstrate that our method is useful to elucidate the effects of various types of seasonality in outbreak behavior. First, we clarify an effect of the shape of seasonal forcing by comparing sinusoidal and square wave forcing functions. Second, we demonstrate that not only the intensity of seasonality but also its temporal variation pattern significantly influences the outbreak pattern. Finally, we reveal the mechanisms of transitions between different outbreak patterns in an epidemic model driven by realistic term-time seasonal forcing and one driven by seasonal forcing estimated from real data. Our results suggest that accurately estimated seasonal variability is necessary for better understanding the dynamics of infectious diseases.
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Long-term fluctuations in globally coupled phase oscillators with general coupling: finite size effects. 査読あり 国際誌
Isao Nishikawa, Gouhei Tanaka, Takehiko Horita, Kazuyuki Aihara
Chaos (Woodbury, N.Y.) 22 ( 1 ) 013133 - 013133 2012年03月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER INST PHYSICS
We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean value on the sample average. In other words, this coefficient characterizes long-term fluctuations of the order parameter. For a system of N coupled oscillators, we introduce a statistical quantity D, which denotes the product of N and the diffusion coefficient. We study the scaling law of D with respect to the system size N. In other well-known models such as the Ising model, the scaling property of D is D∼O(1) for both coherent and incoherent regimes except for the transition point. In contrast, in the globally coupled phase oscillators, the scaling law of D is different for the coherent and incoherent regimes: D∼O(1/N(a)) with a certain constant a>0 in the coherent regime and D∼O(1) in the incoherent regime. We demonstrate that these scaling laws hold for several representative coupling schemes.
DOI： 10.1063/1.3692966
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Mathematically modelling and controlling prostate cancer under intermittent hormone therapy. 査読あり 国際誌
Yoshito Hirata, Gouhei Tanaka, Nicholas Bruchovsky, Kazuyuki Aihara
Asian journal of andrology 14 ( 2 ) 270 - 7 2012年03月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：ACTA PHARMACOLOGICA SINICA
In this review, we summarize our recently developed mathematical models that predict the effects of intermittent androgen suppression therapy on prostate cancer (PCa). Although hormone therapy for PCa shows remarkable results at the beginning of treatment, cancer cells frequently acquire the ability to grow without androgens during long-term therapy, resulting in an eventual relapse. To circumvent hormone resistance, intermittent androgen suppression was investigated as an alternative treatment option. However, at the present time, it is not possible to select an optimal schedule of on- and off-treatment cycles for any given patient. In addition, clinical trials have revealed that intermittent androgen suppression is effective for some patients but not for others. To resolve these two problems, we have developed mathematical models for PCa under intermittent androgen suppression. The mathematical models not only explain the mechanisms of intermittent androgen suppression but also provide an optimal treatment schedule for the on- and off-treatment periods.
DOI： 10.1038/aja.2011.155
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Robustness of multilayer oscillator networks. 査読あり 国際誌
Kai Morino, Gouhei Tanaka, Kazuyuki Aihara
Physical review. E, Statistical, nonlinear, and soft matter physics 83 ( 5 Pt 2 ) 056208 - 056208 2011年05月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
We consider the robustness of multilayer networks composed of active and inactive oscillators from the viewpoint of interlayer coupling effects through the aging transition [H. Daido and K. Nakanishi, Phys. Rev. Lett. 93, 104101 (2004)]. We show in detail that two-layer networks increase or decrease their robustness depending on interlayer coupling schemes compared with single-layer networks. In addition, we find that an increase of mismatches of oscillator types (active or inactive) among interlayer-connected oscillators reduces the robustness of the networks with mean-field, chain, and diffusive interlayer couplings in two-layer networks. Moreover, we discuss the robustness of networks with more than two layers.
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Mathematical modelling of prostate cancer growth and its application to hormone therapy. 査読あり 国際誌
Gouhei Tanaka, Yoshito Hirata, S Larry Goldenberg, Nicholas Bruchovsky, Kazuyuki Aihara
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 368 ( 1930 ) 5029 - 44 2010年11月
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：ROYAL SOC
Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.
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Phase transitions in mixed populations composed of two types of self-oscillatory elements with different periods. 査読あり 国際誌
Gouhei Tanaka, Yusuke Okada, Kazuyuki Aihara
Physical review. E, Statistical, nonlinear, and soft matter physics 82 ( 3 Pt 2 ) 035202 - 035202 2010年09月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
In globally coupled networks composed of oscillatory and nonoscillatory elements, the balance between the subpopulations plays an important role in network dynamics and phase transitions. To extend this framework, we investigate mixed populations consisting of two types of self-oscillatory elements with different periods, particularly given by limit cycle oscillators and period-doubled ones. Phase transitions in the mixed populations are elucidated by numerical bifurcation analyses of a reduced system. We numerically confirm a formula determining the critical balance between the subpopulations for a phase transition at sufficiently large coupling strength.
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Grazing-induced crises in hybrid dynamical systems 査読あり
Gouhei Tanaka, Shigeki Tsuji, Kazuyuki Aihara
PHYSICS LETTERS A 373 ( 35 ) 3134 - 3139 2009年08月
担当区分：筆頭著者, 責任著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：ELSEVIER SCIENCE BV
In hybrid dynamical systems including both continuous and discrete components, an interplay between a continuous trajectory and a discontinuity boundary can trigger a sudden qualitative change in the system dynamics. Grazing phenomena, which occur when a continuous trajectory hits a boundary tangentially, are well known as a representative of such phenomena. We demonstrate that a grazing phenomenon of a chaotic attractor can result in its sudden disappearance and initiate chaotic transients. The mechanism of this grazing-induced crisis is revealed in an illustrative example. Furthermore, we derive a formula to obtain the critical exponent of the power law on the mean duration of chaotic transients. (C) 2009 Elsevier B.V. All rights reserved.
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A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer 査読あり
Aiko Miyamura Ideta, Gouhei Tanaka, Takumi Takeuchi, Kazuyuki Aihara
JOURNAL OF NONLINEAR SCIENCE 18 ( 6 ) 593 - 614 2008年12月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：SPRINGER
For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.
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Complex-Valued Multistate Associative Memory with Nonlinear Multilevel Functions for Gray-Level Image Reconstruction 査読あり
Gouhei Tanaka, Kazuyuki Aihara
2008 IEEE INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, VOLS 1-8 3086 - 3092 2008年
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（国際会議プロシーディングス） 出版者・発行元：IEEE
The complex-signum function has been widely used as an activation function in complex-valued recurrent neural networks for multistate associative memory. This paper presents two alternative activation functions with circularity. One is the complex-sigmoid function based on a multilevel sigmoid function defined on a circle. The other is a characteristic of a bifurcating neuron represented by a circle map. The performance of the complex-valued neural networks with the two kinds of activation functions is investigated in multistate associative memory tests. In both networks, the connection weights to store the memory patterns are determined by the generalized projection rule. We also demonstrate gray-level image reconstruction as a possible application of the proposed methods.
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Sensitivity versus resonance in two-dimensional spiking-bursting neuron models. 査読あり 国際誌
Borja Ibarz, Gouhei Tanaka, Miguel A F Sanjuán, Kazuyuki Aihara
Physical review. E, Statistical, nonlinear, and soft matter physics 75 ( 4 Pt 1 ) 041902 - 041902 2007年04月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMERICAN PHYSICAL SOC
Through phase plane analysis of a class of two-dimensional spiking and bursting neuron models, covering some of the most popular map-based neuron models, we show that there exists a trade-off between the sensitivity of the neuron to steady external stimulation and its resonance properties, and how this trade-off may be tuned by the neutral or asymptotic character of the slow variable. Implications of the results for the suprathreshold behavior of the neurons, both by themselves and as part of networks, are presented in different regimes of interest, such as the excitable, regular spiking, and bursting regimes. These results establish a consistent link between single-neuron parameters and resulting network dynamics, and will hopefully be useful as a guide for modeling.
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Collective skipping: Aperiodic phase locking in ensembles of bursting oscillators 査読あり
G. Tanaka, K. Aihara
EPL 78 ( 1 ) 2007年
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY
Aperiodic phase-locked firing found in biological neurons, called skipping, has been mainly modeled by a forced nonlinear system with noise so far. In contrast, we present another mechanism of skipping as a deterministic collective behavior in a population of coupled bursting oscillators. This collective skipping emerges when the highly irregular repetitive bursts in isolated oscillators are incompletely synchronized by coherent feedback inputs due to mutual connections. We show that the phenomenon is dependent on the coupling strength and the number of connections but almost independent of the network topology. Copyright (c) EPLA, 2007.
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A hybrid systems approach to hormonal therapy of prostate cancer and its Nonlinear dynamics 査読あり
Kazuyuki Aihara, Gouhei Tanaka, Taiji Suzuki, Yoshito Hirata
NOISE AND FLUCTUATIONS 922 479 - + 2007年
記述言語：英語 掲載種別：研究論文（国際会議プロシーディングス） 出版者・発行元：AMER INST PHYSICS
This talk is to review our recent work on mathematical modeling of prostate cancer and its application to hormonal therapy of intermittent androgen suppression. First, we model the tumor growth of prostate cancer composed of a mixed dynamical assembly of androgen-dependent and androgen-independent cancer cells. Then, we introduce the intermittent androgen suppression to the model as feedback control with monitoring the serum prostate-specific antigen, where the controlled model is described as a hybrid system with continuous and discrete variables. Next, we analyze nonlinear dynamics and bifurcations of the hybrid system. Finally, we discuss a possibility to improve the hormonal therapy.
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Synchronization and propagation of bursts in networks of coupled map neurons. 査読あり 国際誌
Gouhei Tanaka, Borja Ibarz, Miguel A F Sanjuan, Kazuyuki Aihara
Chaos (Woodbury, N.Y.) 16 ( 1 ) 013113 - 013113 2006年03月
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER INST PHYSICS
The present paper studies regular and complex spatiotemporal behaviors in networks of coupled map-based bursting oscillators. In-phase and antiphase synchronization of bursts are studied, explaining their underlying mechanisms in order to determine how network parameters separate them. Conditions for emergent bursting in the coupled system are derived from our analysis. In the region of emergence, patterns of chaotic transitions between synchronization and propagation of bursts are found. We show that they consist of transient standing and rotating waves induced by symmetry-breaking bifurcations, and can be viewed as a manifestation of the phenomenon of chaotic itinerancy.
DOI： 10.1063/1.2148387
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Crisis-induced intermittency in two coupled chaotic maps: Towards understanding chaotic itinerancy 査読あり
G. Tanaka, M. A.F. Sanjuán, K. Aihara
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 71 ( 1 ) 016219 2005年01月
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：AMER PHYSICAL SOC
The present paper considers crisis-induced intermittency in a system composed of two coupled logistic maps. Its purpose is to clarify a bifurcation scenario generating such intermittent behaviors that can be regarded as a simple example of chaotic itinerancy. The intermittent dynamics appears immediately after an attractor-merging crisis of two off-diagonal chaotic attractors in a symmetrically coupled system. The scenario for the crisis is investigated through analyses of sequential bifurcations leading to the two chaotic attractors and successive changes in basin structures with variation of a system parameter. The successive changes of the basins are also characterized by variation of a dimension of a fractal basin boundary. A numerical analysis shows that simultaneous contacts between the attractors and the fractal basin boundary bring about the crisis and a snap-back repeller generated at the crisis produces the intermittent transitions. Furthermore, a modified scenario for intermittent behaviors in an asymmetrically coupled system is also discussed. © 2005 The American Physical Society.
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Multistate associative memory with parametrically coupled map networks 査読あり
Gouhei Tanaka, Kazuyuki Aihara
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 15 ( 4 ) 1395 - 1410 2005年
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：World Scientific Publishing Co. Pte Ltd
The present paper proposes two types of parametrically coupled circle map networks for multistate associative memory. One of the networks uses a circle map exhibiting an attractor-merging crisis of multiple chaotic attractors to represent a multistate element. The other uses another circle map whose bifurcation diagram serves as a substitute for a multilevel activation function. The configuration of each network is suitably selected according to the dynamics of the individual circle map so that the network can bring about self-organizing chaotic dynamics with an association of a memory. Namely, the coupling term is determined by the generalized partial error function in the first network, and by the weighted sum of inputs in the second network. These multistate networks can be considered as extensions of two kinds of interesting binary networks called the parametrically coupled sine map networks [Lee &
Farhat, 2001a], respectively. We illustrate that the proposed networks can exhibit desirable associative dynamics that is missing in the conventional multistate networks © World Scientific Publishing Company.
