記述言語：日本語   掲載種別：論文集(書籍)内論文  

© 2019 Elsevier Inc. All rights reserved. We present here a new extended model of the gambler’s ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is difficult. 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.

DOI： 10.1016/B978-0-12-814928-7.00016-0

Scopus

記述言語：日本語   掲載種別：研究論文（学術雑誌）  

© 2018 The Author(s). It is well known that when a pair of random variables is statistically independent, it has nocorrelation (zero covariance, E[XY]-E[X[E[Y] = 0), and that the converse is not true. However, if both of these random variables take only two values, no-correlation entails statistical independence.We provide here a general proof.We subsequently examine whether this equivalence property carries over to quantum mechanical systems.A counter-example is explicitly constructed to show that it does not. This observation provides yet another simple theorem separating classical and quantum theories.

DOI： 10.1093/ptep/pty086

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.14923/transinfj.2017JDP7027

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/j.ifacol.2018.07.224

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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：Springer Verlag  

We present here a new model and algorithm which performs an efficient Natural gradient descent for multilayer perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the “Whitened Neural Networks” model. We make the whitening process not only in the feed-forward direction as in the original model, but also in the back-propagation phase. Its efficacy is shown by an application of this “Bidirectional Whitened Neural Networks” model to a handwritten character recognition data (MNIST data).

DOI： 10.1007/978-3-319-91253-0_5

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/j.physa.2015.12.023

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10015-015-0220-2

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Special Issue: The 4th Young Scientist Meeting on Statistical Physics and Information Processing in Sendai

DOI： 10.4036/iis.2013.61

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人 電子情報通信学会  

The process of pursuit and escape underlies many biological phenomena ranging from predator-prey interactions, combat and sporting activities. Time delays, τ, arise as a consequence of the time taken to identify the opponent, formulate a strategy, and then act upon it. Here we consider virtual stick balancing (VSB) as a delayed pursuit-escape task. The movements of the target in VSB are programmed to resemble those of balancing a stick at the fingertip. A model of delayed pursuit-escape is developed by assuming that the target movements are governed by a simple random walk and the movements of the pursuer by a delayed random walk biased towards the target when τ=0. When τ > 0 the movements can become transiently biased away from the target. The model reproduces the oscillatory dynamics and statistical properties of VSB. For both model and VSB, transients occur in which the pursuer moves inappropriately causing increases in tracking error. The presence of a signature, or trigger, for impending escape suggests the possibility that escapes can be predicted before they occur.

DOI： 10.1587/nolta.4.129

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/j.physa.2011.08.010

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

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：ALIFE ROBOTICS CO, LTD  

We discuss a new take on an old mathematical problem of chase and escape. We consider one group chases another, called "group chase and escape", by presenting simple models. We have found that even a simple model can exhibit rich and complex behavior. The model has been extended to investigate the effects of (1) fluctuations in chasing and escaping movements, (2) reaction delays when chasing, and (3) the conversion of caught escapees to new chasers. We show that these effects can add further complexity and result in unexpected behaviors.

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1063/1.3664409

Web of Science

PubMed

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

CiNii Books

記述言語：英語   掲載種別：研究論文（学術雑誌）  

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in-house laboratory component ensures that students have the opportunity to directly compare prediction to observation and motivates the development of projects that push the boundaries of the subject. The projects, by their nature, readily lend themselves to the formation of inter-disciplinary student research teams. Thus students have the opportunity to learn skills essential for success in today's workplace including productive team work, critical thinking, problem solving, project management, and effective communication. © EDP Sciences, 2011.

DOI： 10.1051/mmnp/20116614

Scopus

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  

We describe a simple model developed under the new idea of one group chasing another called, "group chase and escape". We will demonstrate that even a simple model can exhibit rather rich and complex behavior. In particular, we show that the appropriate level of fluctuation in each step of the process for chase and escape can minimize the time taken for the entire catch.

Web of Science

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）  

Virtual stick balancing (VSB) is a manual visuomotor tracking task that involves interplay between a human and a computer in which the movements are programmed to resemble those of balancing a stick at the fingertip. Since time delays and random perturbations ("noise") are intrinsic properties of this task, we modeled VSB as a delayed pursuit-escape process: the target movements are described by a simple random walk and those movements controlled by the computer mouse by a delayed random walk biased towards the target. As subjects become more skilled, a stereotyped and recurring pursuit-escape pattern develops in which the mouse pursues the target until it overtakes it, causing the target to move in a different direction, followed, after a lag, by the pursing mouse. The delayed pursuit-escape random walk model captured the qualitative nature of this tracking task and provided insights into why this tracking task always fails at some point in time, even for the most expert subjects. Copyright © 2011 by ASME.

DOI： 10.1115/DETC2011-47312

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

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）  

DOI： 10.1063/1.3569508

Web of Science

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：EDP SCIENCES S A  

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in-house laboratory component ensures that students have the opportunity to directly compare prediction to observation and motivates the development of projects that push the boundaries of the subject. The projects, by their nature, readily lend themselves to the formation of inter-disciplinary student research teams. Thus students have the opportunity to learn skills essential for success in today's workplace including productive team work, critical thinking, problem solving, project management, and effective communication.

DOI： 10.1051/mmmp/20116614

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/1367-2630/12/5/053013

Web of Science

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）  

DOI： 10.1063/1.3460193

Web of Science

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）  

DOI： 10.1007/978-3-642-15979-4_62

Web of Science

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）  

A rather peculiar phenomenon has been observed while a human was balancing a stick on a fingertip. The balancing time improved when the subject moved another object with the other hand. This was particularly so for many subjects with medium stick balancing skills. On the basis of this example, I consider how this seemingly simple task is composed of intricate mixtures of feedback delay, fluctuations, and predictions. I present some simple models of dynamics in which these factors lead to complex behaviors. From these examples, I infer that the concept of "nonlocality" could play an important role in characterizing biological and physiological systems. © 2010 International Symposium on Artificial Life and Robotics (ISAROB).

DOI： 10.1007/s10015-010-0837-0

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1371/journal.pone.0007427

Web of Science

PubMed

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1063/1.3141429

Web of Science

PubMed

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1098/rsta.2008.0257

Web of Science

PubMed

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/1742-5468/2009/01/P01032

Web of Science

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）  

Web of Science

J-GLOBAL

記述言語：英語   掲載種別：論文集(書籍)内論文  

A model for a 1-dimensional delayed random walk is developed by generalizing the Ehrenfest model of a discrete random walk evolving on a quadratic, or harmonic, potential to the case of non-zero delay. The Fokker-Planck equation derived from this delayed random walk (DRW) is identical to that obtained starting from the delayed Langevin equation, i.e. a first-order stochastic delay differential equation (SDDE). Thus this DRW and SDDE provide alternate, but complimentary ways for describing the interplay between noise and delay in the vicinity of a fixed point. The DRW representation lends itself to determinations of the joint probability function and, in particular, to the auto-correlation function for both the stationary and the transient states. Thus the effects of delay are manisfested through experimentally measurable quantities such as the variance, the correlation time, and the power spectrum. Our findings are illustrated through applications to the analysis of the fluctuations in the center of pressure that occur during quiet standing. © 2009 Springer-Verlag US.

DOI： 10.1007/978-0-387-85595-0_11

Scopus

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）  

Web of Science

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）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Escape from an unstable fixed point in a time-delayed dynamical system in the presence of additive white noise depends on both the magnitude of the time delay, τ, and the initial function. In particular, the longer the delay the smaller the variance and hence the slower the rate of escape. Numerical simulations demonstrate that the distribution of first passage times is bimodal, the longest first passage times are associated with those initial functions that cause the greatest number of delayed zero crossings, i.e. instances where the deviations of the controlled variable from the fixed point at times t and t- τ have opposite signs. These observations support the utility of control strategies using pulsatile stimuli triggered only when variables exceed certain thresholds. © 2008 Europhysics Letters Association.

DOI： 10.1209/0295-5075/83/48001

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/j.physa.2007.01.015

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

CiNii Books

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  

We presenta simple dynamical model to addres the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the "space" variable, which is opposite to the normal description of stochastic dynamics. The notable feature is that these models can induce a "resonance" with varying noise strength in the time variable. Thus, they provide a different mechanism for stochastic resonance, which has been discussed within the normal context of stochastic dynamics.

Web of Science

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  

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how far ahead in time to make them. We also report that noise can induce oscillatory behavior, which we call "predictive stochastic resonance".

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

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）  

DOI： 10.1109/FOCI.2007.372153

Web of Science

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）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Motivated by recent studies in human balance control, we study a delayed random walk with an unstable fixed point. It is observed that the random walker moves away from the unstable fixed point more slowly than is observed in the absence of delay. It is shown that, for given a noise level, there exists an optimal delay to achieve the longest first passage time. Our observations support recent demonstrations that noise has a beneficial role for balance control and emphasize that predicitive strategies are not necessary to transiently control balance.

Web of Science

J-GLOBAL

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Motivated by recent studies in human balance control, we study a delayed random walk with an unstable fixed point. It is observed that the random walker moves away from the unstable fixed point more slowly than is observed in the absence of delay. It is shown that, for given a noise level, there exists an optimal delay to achieve the longest first passage time. Our observations support recent demonstrations that noise has a beneficial role for balance control and emphasize that predicitive strategies are not necessary to transiently control balance.

DOI： 10.1143/PTPS.161.314

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We studied a random walk with delayed feedback around an unstable fixed point. It was found that the random walker can be kept around the fixed point with longer delays. This is in contrast to the normal role of delay, which is generally thought to be a source of instability. We discuss the connection of our model to stick-balancing experiments, and propose new type of control paradigm called "delayed stochastic control." © ISAROB 2005.

DOI： 10.1007/s10015-004-0337-1

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Web of Science

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 SOC MECHANICAL ENGINEERS  

This article discusses issues of controlling in situations where fluctuations and delay are present. A new paradigm for control schemes, termed "delayed stochastic controls", is proposed for use in such situations.

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

遅れを含むランダムウォークについて概説します。とくに拡散の速度や確率分布の振動がおきるような点に着目します。

記述言語：英語   掲載種別：研究論文（学術雑誌）  

The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.

DOI： 10.1142/S0219477504001719

Web of Science

Scopus

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：WIT PRESS  

High frequency market data has become available with recent developments in computer technology. These data have some unique characteristics that do not appear in low frequency data. They are important in understanding financial markets. We present evidence of a unique property of high frequency data by proposing a new model. In this paper, we analyze tick-by-tick data, the most high frequency data available, of yen-dollar currency exchange rates. Focusing on the direction of up or down price movement, we show that a non-trivial structure exists in conditional probabilities of binarized data, which is apparently invisible from the price change itself. The probabilistic structure has a strong bias not only in the first order conditional probabilities but also in the higher order ones. Logit models are often applied to the analysis of the direction of price change. However, we found that a conventional logit model was not sufficient for our data due to its non-linear behavior. This motivated us to develop a new extended non-linear logit model to reproduce the binary probabilistic structure. This new model has overcome some of the shortcomings of the conventional analysis such as AR models and logit models. It can successfully show that the structure is such that it refers up to the previous few minutes by a model selection based on Akaike Information Criterion. The empirical result is consistent with dealers' perceptions that their strategies change slowly in the time scale of a few minutes. Our analysis here opens a possibility that this new non-linear logit model can be applied to a wide range of binary time series to extract their non-trivial probabilistic structures. Finally, in order to investigate the generality of our model, we are now analyzing the tick-by-tick GE data on NYSE, which is also one of the most active stocks.

Web of Science

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）  

We study here a random walk with delayed feedback around an unstable fixed point. It is found that the random walker can be kept longer around the fixed point with larer delay. This is in contrast to the normal role of delay, which is generally thought to be a source of instability. We discuss a possibility of our model to stick balancing experiments.

DOI： 10.1117/12.548492

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We analyze tick-by-tick data, the most high frequency data available, of yen-dollar currency exchange rates. We show that a dynamical structure can be observed in binarized data indicating the direction of up and down movement of prices, which is not apparently seen from the price change itself. This result is consistent with our previous study that there exists a conditional probabilistic structure in binarized data. The dynamical and probabilistic structure which we found could indicate that dealers' decision making is based on a binary strategy, even if they are unconscious of this fact. © 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0378-4371(02)01958-1

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

The purpose of this paper is to reconsider the Busy Beaver problem, which is a modification of the Turing machine's halting problem, in the light of a dynamical systems approach. Numerical experiments show that the spatio-temporal patterns of machines can be roughly classified into four types. In particular, well-regulated and self-similar patterns are found in most longer-lived machines, which include known best Busy Beaver machines. A relation to the Collatz system is briefly discussed. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0010-4655(02)00356-9

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：サイエンス社  

CiNii Books

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We analyze tick data of yen-dollar exchange with a focus on its up and down movement. We show that there exists a rather particular conditional probability structure with such high frequency data. This result provides us with evidence to question one of the basic assumptions of the traditional market theory, where such bias in high frequency price movements is regarded as not present. We also construct systematically a random walk model reflecting this probability structure. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0378-4371(02)00561-7

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We investigate here a stochastic three-state element whose transition probability depends on its state at a fixed interval in the past. A rich dynamical behavior which does not appear in a binary model is observed in this model. A resonant phenomenon due to the delay appears as well. Furthermore, an analytical expression of this resonant characteristic can be derived in general for an N-state model. We also discuss its application to the dynamical time series of yen-dollar currency exchange. © 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0010-4655(02)00357-0

Scopus

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）  

A one-dimensional ring composed of stochastic binary elements with delayed interaction was studied. The interspike interval histograms and resonance or rhythmic behaviors arise with noise and delay were also studied. It was suggested that the noise and delay accounts for the rhythmic behaviors of network systems.

DOI： 10.1016/S0378-4371(02)01068-3

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We study here a model of globally coupled units with adaptive interaction weights that has a delay in the updating rule. Simulations show that the model with such delayed synaptic change exhibits dynamical self organization of network structure. With suitably chosen parameters, “dominant” unit emerges spontaneously, in the sense that the connections from such a unit to almost all of the other units are especially strengthened. Such weight structure facilitates the coherent activity among units. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevE.64.066205

Scopus

記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人日本物理学会  

「ノイズ」と通信や相互作用の「遅れ」は多くのシステムに存在し,複雑な挙動を引き起こす.ここではそのような複雑な挙動の理解への一つの方向として,ノイズと遅れを用いた共鳴現象を示す単純なモデルを紹介する.その性質を調べることにより,情報処理系において通常障害と考えられている「ノイズ」と「遅れ」を活用する方向を模索する.

DOI： 10.11316/butsuri1946.55.360

CiNii Books

その他リンク： https://jlc.jst.go.jp/DN/JALC/00066089421?from=CiNii

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We study here a simple stochastic single neuron model with delayed self-feedback capable of generating spike trains. Simulations show that its spike trains exhibit resonant behavior between "noise" and "delay". In order to gain insight into this resonance, we simplify the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this simplified model we can analytically compute interspike interval histograms, and show how the resonance between noise and delay arises. The resonance is also observed when such elements are coupled through delayed interaction.

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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  

We first study here a simple stochastic dynamical equation with delayed self-feedback. The model is investigated numerically and we find that its dynamics show an emergent regular "spiking" behavior, by "tuning" its "noise" and "delay". rn order to gain insight into this "resonance", we abstract the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this abstracted model we can analytically capture the time interval histograms between spikes, and discover how the resonance between noise and delay arises. The resonance is also observed when such stochastic binary elements are coupled through delayed interaction.

Web of Science

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：M I T PRESS  

We study here a simple stochastic single neuron model with delayed self-feedback capable of generating spike trains. Simulations show that its spike trains exhibit resonant behavior between "noise" and "delay". In order to gain insight into this resonance, we simplify the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this simplified model we can analytically compute interspike interval histograms, and show how the resonance between noise and delay arises. The resonance is also observed when such elements are coupled through delayed interaction.

Web of Science

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：M I T PRESS  

We study here a simple stochastic single neuron model with delayed self-feedback capable of generating spike trains. Simulations show that its spike trains exhibit resonant behavior between "noise" and "delay". In order to gain insight into this resonance, we simplify the model and study a stochastic binary element whose transition probability depends on its state at a fixed interval in the past. With this simplified model we can analytically compute interspike interval histograms, and show how the resonance between noise and delay arises. The resonance is also observed when such elements are coupled through delayed interaction.

Web of Science

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 COMPUTER SOC  

We propose here a new model of encryption of binary data taking advantage of the complexity of dynamics of a model motivated by a neural network with delays. In this scheme, the encryption process is a coupling dynamics with various time delays between different bits (or neurons) in the original data. A simple example has been investigated to show that such a model may possess useful characteristics as an encryption scheme.

DOI： 10.1109/IJCNN.2000.861505

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

Noise and time delay are two elements that are associated with many natural systems, and often they are sources of complex behaviors. Understanding of this complexity is yet to be explored, particularly when both elements are present. As a step to gain insight into such complexity for a system with both noise and delay, we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives. A Langevin equation with delay and a random-walk model whose transition probability depends on a fixed time-interval past (delayed random walk model) are the subjects of in depth focus. As well as considering relations between these two types of models, we derive an approximate Fokker-Planck equation for delayed stochastic systems and compare its solution with numerical results. © 2000 The American Physical Society.

DOI： 10.1103/PhysRevE.61.1247

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We propose here a new model of encryption of binary data taking advantage of the complexity associated with delayed dynamics. In this scheme, the encryption process is a coupling dynamics with various time delays between different bits in the original data. It is shown that decoding of the encrypted data is extremely difficult without a complete knowledge of coupling manner with associated delays for all bits of the data.

DOI： 10.1016/S0010-4655(99)00279-9

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

本稿ではランジュバン方程式に「遅れ」の効果入れて拡張した確率微分方程式に対応するフォッカープランク方程式を近似的に導出する。手法としては拡張されたランジュバン方程式に近似的に対応するランダムウオークを使い、それを近似的に時間と空間について展開することによってフォッカープランク方程式を得る。このようなランダムウオークは遷移確率が一定の遅れを持った過去の位置によって決まるようなランダムウオーク(Delayed Random Walk)である。またここで得られたフォッカープランク方程式はちょうど遅れ時間と同じ時間離れた2点におけるジョイント確率分布の時間発展方程式として限られている。この式を定常状態において明示的に解き、数値計算の結果とくらべたところノイズの「大きさ」にくらべて十分に小さい「ドリフト」係数では有用な結果を確認した。

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人 日本応用数理学会  

DOI： 10.11540/bjsiam.8.1_46

CiNii Books

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We propose and study here a simple model of computer network traffic that can exhibit a phase transition from a low to high congestion state measured in terms of average travel time of packets as a function of the packet creation rate in the network. In the model, packets are generated with destination addresses, and are transferred from one router to another toward their destinations. The routers are capable of queuing packets and autonomously selecting a path to the next router for a packet. Through simulations on a two-dimensional lattice model network, we found that the phase transition point into the congestion phase depends on how each router chooses a path for the packets in its queue. In particular, an appropriate randomness in path selection can shift the onset of traffic congestion to accommodate more packets in the model network. © 1998 The American Physical Society.

DOI： 10.1103/PhysRevE.58.193

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback system with delay and noise. We successfully test the method with a time series generated by a discrete Langevin equation with delay.

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback system with delay and noise. We successfully test the method with a time series generated by a discrete Langevin equation with delay.

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of its correlation function. We investigate a model whose transient and stationary oscillatory behavior is analytically tractable. The correspondence of the model with a Langevin equation with delay is also considered. © 1997 The American Physical Society.

DOI： 10.1103/PhysRevE.55.R1255

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/BFb0031853

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1063/1.166134

Web of Science

PubMed

記述言語：英語   掲載種別：研究論文（学術雑誌）  

本論文では、Cowanによって提唱されたニューラルネットワークマスター方程式によって確率動作するニューラルネットの解析をする一手法について考察する。ここでは三つの状態をとるニューロンからなるネットワークを外積表記されたニューラルネットワークマスター方程式を用いて解析する。この解析ではネットワークのモーメントの力学階層式を導き、この階層式を近似する一方法としてネットワーク活動を平均場の中におかれた一つ、もしくは二つの擬似ニューロンによって表現する方法を提案する。これらの近似を単純な構造を持つネットワークに適用し、モンテカーロシミュレーションとの比較を行なった。

記述言語：英語   掲載種別：研究論文（学術雑誌）  

We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined. © 1995 Plenum Publishing Corporation.

DOI： 10.1007/BF02218819

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

© 1995 Massachusetts Institute of Technology. We study the stochastic behavior of a single self-exciting model neuron with additive noise, a system that has bistable stochastic dynamics. We use Langevin and Fokker-Planck equations to obtain analytical expressions for the stationary distribution of activities and for the crossing rate between two stable states. We adjust the parameters in these expressions to fit observed histograms of neural activity, thus obtaining what we call an "effective single neuron" for a given network. We construct an effective single neuron from an activity histogram of a representative hidden neuron in a recurrent learning network. We also compare our result with an effective single neuron previously obtained analytically through the adiabatic elimination approximation.

DOI： 10.1162/neco.1995.7.3.518

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

The fluctuations about the stable point in a delayed dynamical system are modeled as a delayed random walk: i.e., a random walk in which the transition probability depends on the position of the walker at a time in the past and transitions in the direction of the stable point are more probable. It is shown that, depending on the magnitude of the delay, the root mean square displacement X2(t) versus time interval approaches a limiting value in either an oscillatory or nonoscillatory fashion. This limiting value of X2(t) is a linear function of. © 1995 The American Physical Society.

DOI： 10.1103/PhysRevE.52.3277

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

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：LAWRENCE ERLBAUM ASSOC PUBL  

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

記述言語：英語   掲載種別：研究論文（学術雑誌）  

It is shown that the pupil latency can be estimated from pupil cycling measurements when the pupil light reflex is clamped with piecewise constant negative feedback. The solution of the mathematical model previously shown to describe these oscillations is utilized to develop a variety of strategies to estimate latency and to evaluate the effects of noise on these estimates. The results demonstrate that the pupil latency shows considerable variation.

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）  

A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations. © 1993 The American Physical Society.

DOI： 10.1103/PhysRevE.48.2259

Scopus

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：SPIE - INT SOC OPTICAL ENGINEERING  

It is shown that the pupil latency can be estimated from pupil cycling measurements when the pupil light reflex is clamped with piecewise constant negative feedback. The solution of the mathematical model previously shown to describe these oscillations is utilized to develop a variety of strategies to estimate latency and to evaluate the effects of noise on these estimates. The results demonstrate that the pupil latency shows considerable variation.

Web of Science

記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1119/1.15502

Web of Science

担当ページ：206   記述言語：日本語 著書種別：教科書・概説・概論

「安定」「正確」を求める現実社会は、じつは「不規則」や「不確実さ」に満ちている。そうした「不確実性」は、時に予想もしない効果をもたらしたり、有益な働きをしてくれる。トーナメント戦での番狂わせ、犯人追跡の意外な方法、免震制御、時間差による攻撃手段など。身近にある不安定現象を挙げながらその意外な効用を説く

記述言語：英語

CiNii Books

担当ページ：1-500   記述言語：日本語 著書種別：教科書・概説・概論

担当ページ：1-155   記述言語：日本語 著書種別：教科書・概説・概論

記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

CiNii Books

記述言語：日本語   出版者・発行元：一般社団法人電子情報通信学会  

本論文では、遅れ力学に現れる複雑さを利用して暗号化をおこなうモデルを提案する。この方式では暗号化のプロセスは暗号化するビット列のそれぞれのビットがお互いに遅れをともなって相互作用する力学系とする。この力学系の特性を数値計算によって調べたが、鍵、すなわち力学系を規定するパラメータ、の一部の変更が暗号化状態に多大な影響を及ぼすなどの暗号方式として望ましい性質の一部を持ち合わせていることが示された。

CiNii Books

記述言語：日本語   出版者・発行元：一般社団法人日本物理学会  

CiNii Books

記述言語：日本語   出版者・発行元：一般社団法人電子情報通信学会  

信号伝達の「遅れ」と「ノイズ(ゆらぎ)」は生体の情報処理にほほ普遍的に存在する要素である。最近、我々はこの2つの要素を同時に含む系の理論体系の一つとしてDelayed Random Walkの概念を提唱した。Delayed Random W alkはWalkerの有る地点での遷移確率が、ある1定の時間以前のWalkerの存在地点によって決まるようなRandom Walkである。この概念のもとで人間の重心制御のモデルを構築したが、ここではそのモデルをさらに発展させた、モデルを考察する。具体的には重心制御における空間的なThresholdを設け、それ以下での揺らぎについては強いフィードバックがかからないようなモデルとした。このモデルによる統計的な挙動と実験におけるデータとの比較について考察する。

CiNii Books

記述言語：日本語   出版者・発行元：一般社団法人電子情報通信学会  

本論文では、Cowanによって提唱されたニュ-ラルネットワ-クマスタ-方程式によって確率動作するニュ-ラルネットの解析をする一手法について考察する。ここでは二つの状態をとるニュ-ロンからなるネットワ-クを外積表記されたニュ-ラルネットワ-クマスタ-方程式を用いて解析する。この解析ではネットワ-クのモ-メントの力学階層式を導き、この階層式を近似する一方法としてネットワ-ク活動を平均場の中におかれた一つ、もしくは二つの擬似ニュ-ロンによって表現する方法を提案する。これらの近似を単純な構造を持つネットワ-クに適用し、モンテカ-ロシミュレ-ションとの比較を行なった。

CiNii Books

開催年月日： 2021年8月

記述言語：英語   会議種別：口頭発表（一般）  

開催地：Online (Coventry England)  

開催年月日： 2020年9月

記述言語：日本語   会議種別：口頭発表（一般）  

開催年月日： 2017年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2014年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2013年8月

記述言語：英語   会議種別：口頭発表（一般）  

We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential equation with time delayed feedback, which can be viewed as describing temporal non-locality.

開催年月日： 2011年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2011年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2010年12月

記述言語：英語   会議種別：口頭発表（一般）  

We would like to present here a rather peculiar observation during human stick balancing at his fingertip. It is observed that the balancing time improves when the subject moves objects with the other hand. This is particularly so for many subjects with medium skill of stick balancing. Based on this example, we would like to consider how this seemingly simple task is composed of intricate mixtures of feedback delay, fluctuations, and predictions. We will present some simple models of dynamics in which these factors lead to complex behaviors. It is inferred, from these examples, that the concept of "non-locality" could possibly play an important role in characterizing biological and physiological systems. © 2010 ISAROB.

開催年月日： 2010年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2010年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2008年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2007年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2007年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2004年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 2003年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 1998年12月

記述言語：英語   会議種別：口頭発表（一般）  

We propose here a new model of encryption of binary data taking advantage of the complexity of nonlinear dynamics with delays. In this scheme, the encryption process is a nonlinear coupling dynamics with various time delays between different bits in the original data. It is shown that the model has the following two properties : (1)A minor difference in the key leads to rather uncorrelated ciphertext. (2)An effect of change of multiple bits in the plaintext does not propagate to the ciphertext as a simple superposition of effects of each changed bit.

開催年月日： 1998年7月

記述言語：英語   会議種別：口頭発表（一般）  

本論文では、遅れ力学に現れる複雑さを利用して暗号化をおこなうモデルを提案する。この方式では暗号化のプロセスは暗号化するビット列のそれぞれのビットがお互いに遅れをともなって相互作用する力学系とする。この力学系の特性を数値計算によって調べたが、鍵、すなわち力学系を規定するパラメータ、の一部の変更が暗号化状態に多大な影響を及ぼすなどの暗号方式として望ましい性質の一部を持ち合わせていることが示された。

開催年月日： 1998年

記述言語：英語   会議種別：口頭発表（一般）  

開催年月日： 1997年

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

We present here a simple equation explicitly incorporating non-locality, which reproduces quantized energy levels of the bound states for the square well potentials. Introduction of this equation is motivated by studies of differential equation with time delayed feedback, which can be viewed as describing temporal non-locality.

記述言語：英語   会議種別：口頭発表（一般）  

We would like to present here a rather peculiar observation during human stick balancing at his fingertip. It is observed that the balancing time improves when the subject moves objects with the other hand. This is particularly so for many subjects with medium skill of stick balancing. Based on this example, we would like to consider how this seemingly simple task is composed of intricate mixtures of feedback delay, fluctuations, and predictions. We will present some simple models of dynamics in which these factors lead to complex behaviors. It is inferred, from these examples, that the concept of "non-locality" could possibly play an important role in characterizing biological and physiological systems. © 2010 ISAROB.

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

記述言語：英語   会議種別：口頭発表（一般）  

出願人：ソニー株式会社

出願番号：特願平10-300679  出願日：1998年10月

公開番号：特開2000-132094  公開日：2000年5月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平10-086757  出願日：1998年3月

公開番号：特開平11-282347  公開日：1999年10月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平9-295537  出願日：1997年10月

公開番号：特開平11-136283  公開日：1999年5月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平9-107565  出願日：1997年4月

公開番号：特開平10-302192  公開日：1998年11月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平8-131574  出願日：1996年5月

公開番号：特開平9-319721  公開日：1997年12月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平7-340262  出願日：1995年12月

公開番号：特開平9-179832  公開日：1997年7月

特許番号/登録番号：特許第3512080号  発行日：2004年1月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平7-011197  出願日：1995年1月

公開番号：特開平8-204812  公開日：1996年8月

J-GLOBAL

出願人：ソニー株式会社

出願番号：特願平7-011196  出願日：1995年1月

公開番号：特開平8-204808  公開日：1996年8月

J-GLOBAL

執筆者：本人以外