arXiv subjects

Jun-ichi Inoue

Publications and source records attributed to Jun-ichi Inoue.

At least 37 records · Page 2Linked to original sources

arXiv2011

Optimization of artificial flockings by means of anisotropy measurements

An effective procedure to determine the optimal parameters appearing in artificial flockings is proposed in terms of optimization problems. We numerically examine genetic algorithms (GAs) to determine the optimal set of parameters such as the weights for three essential interactions in BOIDS by Reynolds (1987) under `zero-collision' and `no-breaking-up' constraints. As a fitness function (the energy function) to be maximized by the GA, we choose the so-called the $γ$-value of anisotropy which can be observed empirically in typical flocks of starling. We confirm that the GA successfully finds the solution having a large $γ$-value leading-up to a strong anisotropy. The numerical experience shows that the procedure might enable us to make more realistic and efficient artificial flocking of starling even in our personal computers. We also evaluate two distinct types of interactions in agents, namely, metric and topological definitions of interactions. We confirmed that the topological definition can explain the empirical evidence much better than the metric definition does.

physics.bio-ph↗

arXiv2011

Response of double-auction markets to instantaneous Selling-Buying signals with stochastic Bid-Ask spread

Statistical properties of order-driven double-auction markets with Bid-Ask spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the so-called {\it Madhavan-Richardson-Roomans model} (MRR for short) to simulate the stochastic process of the price-change in empirical data sets (say, EUR/JPY or USD/JPY exchange rates) in which the Bid-Ask spread fluctuates in time. We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour ('non-monotonic' behaviour) of the response function $R(l)$ ($l$ denotes the difference of times at which the response function is evaluated) calculated from the data. Especially, we confirm that the stochastic nature of the Bid-Ask spread causes apparent deviations from a linear relationship between the $R(l)$ and the auto-correlation function $C(l)$, namely, $R(l) \propto -C(l)$. To make the microscopic model of double-auction markets having stochastic Bid-Ask spread, we use the minority game with a finite market history length and find numerically that appropriate extension of the game shows quite similar behaviour of the response function to the empirical evidence. We also reveal that the minority game modeling with the adaptive ('annealed') look-up table reproduces the non-linear relationship $R(l) \propto -f(C(l))$ ($f(x)$ stands for a non-linear function leading to '$λ$-shapes') more effectively than the fixed (`quenched') look-up table does.

q-fin.TR↗

arXiv2011

Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.

cond-mat.dis-nn↗

arXiv2010

Statistical mechanics of digital halftoning

We consider the problem of digital halftoning from the view point of statistical mechanics. The digital halftoning is a sort of image processing, namely, representing each grayscale in terms of black and white binary dots. The digital halftoning is achieved by making use of the threshold mask, namely, for each pixel, the halftoned binary pixel is determined as black if the original grayscale pixel is greater than or equal to the mask value and is determined as white vice versa. To determine the optimal value of the mask on each pixel for a given original grayscale image, we first assume that the human-eyes might recognize the black and white binary halftoned image as the corresponding grayscale one by linear filters. The Hamiltonian is constructed as a distance between the original and the recognized images which is written in terms of the threshold mask. We are confirmed that the system described by the Hamiltonian is regarded as a kind of antiferromagnetic Ising model with quenched disorders. By searching the ground state of the Hamiltonian, we obtain the optimal threshold mask and the resulting halftoned binary dots simultaneously. From the power-spectrum analysis, we find that the binary dots image is physiologically plausible from the view point of human-eyes modulation properties. We also propose a theoretical framework to investigate statistical performance of inverse digital halftoning, that is, the inverse process of halftoning. From the Bayesian inference view point, we rigorously show that the Bayes-optimal inverse-halftoning is achieved on a specific condition which is very similar to the so-called Nishimori line in the research field of spin glasses.

cond-mat.dis-nn↗

arXiv2010

On-line trading as a renewal process: Waiting time and inspection paradox

We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. The basic method of our approach depends on the so-called renewal-reward theorem. Assuming that the stochastic process modelling the price change is a renewal process, we use the theorem to calculate the average waiting time of the process. The so-called ``inspection paradox'' is discussed, which, in general, means that the average durations is shorter than the average waiting time.

q-fin.ST↗

arXiv2010

Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems

Manipulating the topological properties of insulators, encoded in invariants such as the Chern number and its generalizations, is now a major issue for realizing novel charge/spin responses in electron systems. We propose that a simple optical means --subjecting to a driving laser field with circular polarization, can be fruitfully incorporated to this end. Taking as a prototypical example the two-band insulator first considered by Haldane, we show how the electron system can be tuned through phases associated with different Chern numbers as the laser intensity is adiabatically swept; i.e., a photo-induced analog of the quantum Hall plateau transition. The implications of our findings includes the possibility of laser-tuning a conventional insulator into a quantum spin Hall system.

cond-mat.mtrl-sci↗

arXiv2010

Numerical study on the emergence of anisotropy in artificial flocks: A BOIDS modeling and simulations of empirical findings

In real flocks, it was revealed that the angular density of nearest neighbors shows a strong {\it anisotropic structure} of individuals by very recent extensive field studies by Ballerini et al [{\it Proceedings of the National Academy of Sciences USA} {\bf 105}, pp.1232-1237 (2008)]. In this paper, we show that this empirical evidence in real flocks, namely, the structure of anisotropy also emerges in an artificial flock simulation based on the {\it BOIDS} by Reynolds [{\it Computer Graphics} {\bf 21}, pp.25-34 (1987)]. We numerically find that appropriate combinations of the weights for just only three essential factors of the BOIDS, namely, `Cohesion', `Alignment' and `Separation' lead to a strong anisotropy in the flock. This result seems to be highly counter-intuitive and also provides a justification of the hypothesis that the anisotropy emerges as a result of self-organization of interacting intelligent agents (birds for instance). To quantify the anisotropy, we evaluate a useful statistics (a kind of {\it order parameters} in statistical physics), that is to say, the so-called $γ$-value defined as an inner product between the vector in the direction of the lowest angular density of flocks and the vector in the direction of the moving of the flock. Our results concerning the emergence of the anisotropy through the $γ$-value might enable us to judge whether an arbitrary flock simulation seems to be {\it realistic} or not.

physics.bio-ph↗

arXiv2010

Simultaneous Bayesian inference of motion velocity fields and probabilistic models in successive video-frames described by spatio-temporal MRFs

We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by spatio-temporal Markov random fields. Preliminary to construction of our procedure, we find that mean-field variables in the iteration diverge due to improper normalization factor of regularization terms appearing in the posterior. To avoid this difficulty, we rescale the regularization term by introducing a scaling factor and optimizing it by means of minimization of the mean-square error. We confirm that the optimal scaling factor stabilizes the mean-field iterative process of the motion velocity estimation. We next attempt to estimate the optimal values of hyper-parameters including the regularization term, which define our probabilistic model macroscopically, by using the Boltzmann-machine type learning algorithm based on gradient descent of marginal likelihood (type-II likelihood) with respect to the hyper-parameters. In our framework, one can estimate both the probabilistic model (hyper-parameters) and motion velocity fields simultaneously. We find that our motion estimation is much better than the result obtained by Zhang and Hanouer (1995) in which the hyper-parameters are set to some ad-hoc values without any theoretical justification.

cs.CV↗

arXiv2010

A Gibbs distribution that learns from GA dynamics

A general procedure of average-case performance evaluation for population dynamics such as genetic algorithms (GAs) is proposed and its validity is numerically examined. We introduce a learning algorithm of Gibbs distributions from training sets which are gene configurations (strings) generated by GA in order to figure out the statistical properties of GA from the view point of thermodynamics. The learning algorithm is constructed by means of minimization of the Kullback-Leibler information between a parametric Gibbs distribution and the empirical distribution of gene configurations. The formulation is applied to the solvable probabilistic models having multi-valley energy landscapes, namely, the spin glass chain and the Sherrington-Kirkpatrick model. By using computer simulations, we discuss the asymptotic behaviour of the effective temperature scheduling and the residual energy induced by the GA dynamics.

cs.NE↗

arXiv2010

Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method

In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range ($d(=\infty)$-dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding $(d+1)$-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some `non-monotonic' behaviour in its time evolution.

cond-mat.dis-nn↗

arXiv2010

Quantum phase transition in a disordered long-range transverse Ising antiferromagnet

We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum case. For the pure case applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in the Trotter direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick (SK) type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to para phase occurs. Analytical studies for the phase transitions are discussed in detail in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.

cond-mat.stat-mech↗

arXiv2008

A Novel Quantum Transition in a Fully Frustrated Transverse Ising Antiferromagnet

We consider a long-range Ising antiferromagnet (LRIAF) put in a transverse field. Applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in Trotter time direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We also discuss the phase diagram for the Sherrington-Kirkpatrick (SK) model with the same LRIAF bias, also in presence of a transverse field. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the antiferromagnet. This glass order eventually gets destroyed as the thermal or quantum fluctuations increased beyond their threshold values and the transition to para phase occurs. Indications of this novel phase transition are discussed. Because of the presence of full frustration, this surrogate property of the LRIAF for incubation of stable spin glass phase in it (induced by addition of a small disorder) should enable eventually the study of classical and quantum spin glass phases by using some perturbation theory with respect to the disorder.

cond-mat.stat-mech↗

arXiv2008

The distribution of first-passage times and durations in FOREX and future markets

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely, a distribution derived from the so-called Mittag-Leffler survival function and the Weibull distribution. For Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_ max, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type one if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other side, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results much more efficiently than a simple Weibull distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull-law for short times and do not have too heavy a tail.

q-fin.TR↗

arXiv2008

Bayes-optimal inverse halftoning and statistical mechanics of the Q-Ising model

On the basis of statistical mechanics of the Q-Ising model, we formulate the Bayesian inference to the problem of inverse halftoning, which is the inverse process of representing gray-scales in images by means of black and white dots. Using Monte Carlo simulations, we investigate statistical properties of the inverse process, especially, we reveal the condition of the Bayes-optimal solution for which the mean-square error takes its minimum. The numerical result is qualitatively confirmed by analysis of the infinite-range model. As demonstrations of our approach, we apply the method to retrieve a grayscale image, such as standard image `Lenna', from the halftoned version. We find that the Bayes-optimal solution gives a fine restored grayscale image which is very close to the original.

cond-mat.dis-nn↗

arXiv2008

Counting solutions for the CDMA multiuser MAP demodulator

We evaluate the average number of locally minimal solutions for maximum-{\it a-posteriori} (MAP) demodulation in code-division multiple-access (CDMA) systems. For this purpose, we use a sophisticated method to investigate the ground state properties for the Sherrington-Kirkpatrick-type (i.e. fully connected) spin glasses established by Tanaka and Edwards in 1980. We derive the number of locally minimal solutions as a function of several parameters which specify the CDMA multiuser MAP demodulator. We also calculate the distribution function of the normalized-energies for the locally minimum states. We find that for a small number of chip intervals (or equivalently a large number of users) and large noise level at the base station, the number of local minimum solutions becomes larger than that of the SK model. This provides us with useful information about the computational complexity of the MAP demodulator.

cond-mat.dis-nn↗

arXiv2008

Power-law behavior and condensation phenomena in disordered urn models

We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point of the power-law behavior and randomness; it is clarified that quenched random parameters play an important role in generating power-law behavior. We evaluate the occupation probability $P(k)$ with which an urn has $k$ balls by using the concept of statistical physics of disordered systems. In the disordered urn model belonging to the Monkey class, we find that above critical density $ρ_\mathrm{c}$ for a given temperature, condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large $k$ regime. We also discuss an interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials.

physics.soc-ph↗

arXiv2007

Queueing theoretical analysis of foreign currency exchange rates

We propose a useful approach for investigating the statistical properties of foreign currency exchange rates. Our approach is based on queueing theory, particularly, the so-called renewal-reward theorem. For the first passage processes of the Sony Bank US dollar/Japanese yen (USD/JPY) exchange rate, we evaluate the average waiting time which is defined as the average time that customers have to wait between any instant when they want to observe the rate (e.g. when they log in to their computer systems) and the next rate change. We find that the assumption of exponential distribution for the first-passage process should be rejected and that a Weibull distribution seems more suitable for explaining the stochastic process of the Sony Bank rate. Our approach also enables us to evaluate the expected reward for customers, i.e. one can predict how long customers must wait and how much reward they will obtain by the next price change after they log in to their computer systems. We check the validity of our prediction by comparing it with empirical data analysis.

physics.data-an↗

arXiv2007

Crossover between Levy and Gaussian regimes in first passage processes

We propose a new approach to the problem of the first passage time. Our method is applicable not only to the Wiener process but also to the non--Gaussian L$\acute{\rm e}$vy flights or to more complicated stochastic processes whose distributions are stable. To show the usefulness of the method, we particularly focus on the first passage time problems in the truncated L$\acute{\rm e}$vy flights (the so-called KoBoL processes), in which the arbitrarily large tail of the L$\acute{\rm e}$vy distribution is cut off. We find that the asymptotic scaling law of the first passage time $t$ distribution changes from $t^{-(α+1)/α}$-law (non-Gaussian L$\acute{\rm e}$vy regime) to $t^{-3/2}$-law (Gaussian regime) at the crossover point. This result means that an ultra-slow convergence from the non-Gaussian L$\acute{\rm e}$vy regime to the Gaussian regime is observed not only in the distribution of the real time step for the truncated L$\acute{\rm e}$vy flight but also in the first passage time distribution of the flight. The nature of the crossover in the scaling laws and the scaling relation on the crossover point with respect to the effective cut-off length of the L$\acute{\rm e}$vy distribution are discussed.

physics.data-an↗