arXiv subjects
Publications and source records attributed to Toru Ohira.
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.
We present here a new conjecture for the nature of the Mersenne prime numbers by connecting it with the Collatz-Kakutani problem. By introducing a natural path length on the basis of the Collatz-Kakutani tree, we conjecture that this path length of a Mersenne prime from the root of the Collatz-Kakutani tree is approximately proportional to the index of the Mersenne prime. We also discuss difference of behaviors between Mersenne numbers and Mersenne primes.
We are studying the effect of converting caught targets into new chasers in the context of the recently proposed `group chase and escape' problem. Numerical simulations have shown that this conversion can substantially reduce the lifetimes of the targets when a large number of them are initially present. At the same time, it also leads to a non-monotonic dependence on the initial number of targets, resulting in the existence of a maximum lifetime. As a counter effect for this conversion, we further introduce self-multiplying abilities to the targets. We found that the longest lifetime exists when suitable combination of these two effects is created.
We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are cases in which an optimal number of chasers exists for a given number of escapees (or targets) to minimize the cost of catching all targets. We have also found an indication of self-organized spatial structures formed by both groups.
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space" variable, which is opposite to the normal description of stochastic dynamics. Similarly with respect to non-locality, we discuss delayed and predictive dynamics which involve two points separated on the time axis. With certain combinations of fluctuations and non-locality in time, we observe a ``resonance'' effect. This is an effect similar to stochastic resonance, which has been discussed within the normal context of stochastic dynamics, but with different mechanisms. We discuss how these models may be developed to fit a broader context of generalized dynamical systems where fluctuations and non-locality are present in both space and time.
We present a simple dynamical model to address 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.
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".
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include 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 strengths in the time variable. Thus, they provide a different mechanism for ``stochastic resonance'', which has been discussed within the normal context of stochastic dynamics. In a broader context, we expect these simple models and associated behaviours may serve as one of the starting points to construct and investigate an extended classical dynamical theory where both the space and time variables are taken as stochastic. We need to explore if such approaches can be further developed for both classical and quantum applications.
Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of "resonant" effect takes place to keep the stability of the fixed point better with tuned bias and delay. We also briefly discuss the second model called sticky random walk, which is introduced to model string entanglement. Peculiar resonant effects with respect to these random walks are presented.
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.
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well as how far ahead in time to make them. Comparisons of these predictive dynamical models and corresponding delayed dynamical models are discussed.
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 assumption 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.
We study here a model of globally coupled units with adaptive interaction weights which 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 connection from such unit to almost all of the other units are especially strengthened. Such weight structure facilitates the coherent activity among units.
We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise'' and ``delay''. We demonstrate numerically and analytically that we can observe resonant phenomena between the oscillatory behavior due to noise and that due to delay.
We propose two dynamical models with delay taking advantage of their complex dynamics for information processing tasks. The first model incorporates coupled delayed dynamics of multiple bits, which is shown to have desirable properties as an encryption scheme. The second model is a single binary element with delayed stochastic transition, which presents a resonance behavior between noise and delay.
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.
We propose here an autonomous traffic signal control model based on analogy with neural networks. In this model, the length of cycle time period of traffic lights at each signal is autonomously adapted. We find a self-organizing collective behavior of such a model through simulation on a one-dimensional lattice model road: traffic congestion is greatly diffused when traffic signals have such autonomous adaptability with suitably tuned parameters. We also find that effectiveness of the system emerges through interactions between units and shows a threshold transition as a function of proportion of adaptive signals in the model.
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 discrete Langevin equation with delay.