Publications (59)24.3 Total impact
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ABSTRACT: Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute nonentropic measures of inequality such as Lorenz curve, Gini index and the recently introduced k index analytically from known distribution functions. We characterize the distribution functions of different quantities such as votes, journal citations, city size, etc. with suitable fits, compute their inequality measures and compare with the analytical results. A single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data, and fit better to two distinct functions with a single crossover point. Here we provide general formulas to calculate these inequality measures for the above cases. We attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures. Regarding the k index as an `extra dimension', both the lower and upper bounds of the Gini index are obtained as a function of the k index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices.arXiv: 1406.2874. 06/2014;  [Show abstract] [Hide abstract]
ABSTRACT: In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective behaviour of markets during a financial crisis through crosscorrelations between typical Japanese daily stocks by making use of multi dimensional scaling. We find that all the twodimensional points (stocks) shrink into a single small region when a economic crisis takes place. By using the properties of crosscorrelations in financial markets especially during a crisis, we next propose a theoretical framework to predict several timeseries simultaneously. Our model system is basically described by a variant of the multilayered Ising model with random fields as nonstationary time series. Hyperparameters appearing in the probabilistic model are estimated by means of minimizing the 'cumulative error' in the past market history. The justification and validity of our approaches are numerically examined for several empirical data sets.Journal of Physics Conference Series 09/2013; 473(1).  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of nonstationary behavior, and we provide empirical evidence against the wellestablished common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing us to take into account possible risk underestimations due to the nonoptimality of the portfolio weights being used in order to distinguish such nonoptimality effects from risk underestimations genuinely due to nonstationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices.· 1.87 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The transverse Ising model was introduced in 1960s to study an orderdisorder transition in hydrogenbonded ferroelectric systems. Later, a significant amount of efforts have been devoted to the study of transverse Ising models. As a result, a lot of basic properties of a zerotemperature quantum phase transition of quantum manybody systems, groundstate properties of a frustrated or disordered system in the presence of quantum fluctuations, and the nature of nonequilibrium dynamics of a quantum system driven by controlling quantum fluctuations have been so far clarified. Also the study of quantum computation and information processing using quantum fluctuations has progressed recently. After a brief historical introduction of the transverse Ising models, Chap. 1 presents a qualitative property of the models obtained by the simple mean field theory, and gives a summary of following chapters as well as a list of experimental systems well represented by the transverse Ising models.Lecture Notes in Physics 01/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We investigate crosscorrelations between typical Japanese stocks collected through Yahoo!Japan website ( http://finance.yahoo.co.jp/ ). By making use of multidimensional scaling (MDS) for the crosscorrelation matrices, we draw twodimensional scattered plots in which each point corresponds to each stock. To make a clustering for these data plots, we utilize the mixture of Gaussians to fit the data set to several Gaussian densities. By minimizing the socalled Akaike Information Criterion (AIC) with respect to parameters in the mixture, we attempt to specify the best possible mixture of Gaussians. It might be naturally assumed that all the twodimensional data points of stocks shrink into a single small region when some economic crisis takes place. The justification of this assumption is numerically checked for the empirical Japanese stock data, for instance, those around 11 March 2011.Econophysics of Systemic Risk and Network Dynamics. 01/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of nonstationary behavior, and we provide empirical evidence against the wellestablished common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing to take into account possible risk underestimations due to the nonoptimality of the portfolio weights being used in order to distinguish such nonoptimality effects from risk underestimations genuinely due to nonstationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices.Journal of Statistical Mechanics Theory and Experiment 05/2012; 2012(07). · 1.87 Impact Factor 
Conference Paper: Statistical mechanics of labor markets
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ABSTRACT: On the basis of statistical mechanics, we introduce a probabilistic model of labor markets for university graduates in Japan. In order to make a model of the market efficiently, we shall take into account the following assumptions. Namely, each company fixes the number of opening positions for newcomers and the number itself is independent of business year. The ability of gathering newcomers depends on the result of matching process in past business years. This fact means that the ability of the company is weaken if the company did not make their quota or the company gathered applicants too much over the quota. All labors, in particular, university graduates who are looking for their jobs can access the public information about the ranking of companies. By assuming the above essential key points, we construct the energy function of each company and describe the probability that an arbitrary company gets students at each business year by a BoltzmannGibbs distribution. We evaluate the relevant physical quantities such as the employment rate. We find that the system undergoes a phase transition from the `good employment phase' to `poor employment phase' with spontaneous symmetry breaking when one controls the degree of importance for the ranking. With the assistance of a chaotic map for the inflation rate given by Neugart (2004), we also attempt to draw the socalled Philips curve. The condition on which the longtime average of inflation rate becomes negative with high unemployment rate, which might be regard as an indicator for a sort of `crisis' is discussed.SICE Annual Conference (SICE), 2011 Proceedings of; 10/2011 
Article: STATPHYSKolkata VII
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ABSTRACT: In the past two decades, a series of international conferences on Statistical Physics, going by the name Statphys Kolkata, have been organized in Kolkata (previously Calcutta) at roughly threeyear intervals, the first one being held in 1992–93. The seventh of this series, Statphys Kolkata VII (http://www.saha.ac.in/cmp/stat.vii/index.php) was held from 26–30 November 2010. This meeting was organized as part of the Silver Jubilee Celebration of the Satyendra Nath Bose National Centre for Basic Sciences, Kolkata, in collaboration with the Saha Institute of Nuclear Physics, Kolkata. In Statphys Kolkata VII, a few topics of current interest such as Collective behavior and emergent phenomena, Systems far from equilibrium, Soft matter, and Quantum critical phenomena were given special emphasis, while various other issues of Statistical Physics were also addressed. We were happy to note that the conference attracted a large number of participants, and the talk and poster sessions generated a lot of discussions, arguments and collaborations. The articles appearing in this proceedings are based on the invited talks and selected poster presentations. We would like to thank the Journal of Physics Conference Series, IOP, for publishing the proceedings of the conference, and the referees for their prompt and active support. The proceedings of the earlier Statphys Kolkata conferences have appeared in Physica A, vol 384 (2007); Physica A, vol 346 (2005); Physica A, vol 318 (2003); Physica A, vol 270 (1999); Physica A, vol 224 (1996); and Physica A, vol 186 (1992). We would like to take this opportunity to thank all the members of the organizing committee (especially Dr Anjan Kumar Chandra for extensive allround help), and acknowledge the Centre for Applied Mathematics and Computational Science (CAMCS, Saha Institute of Nuclear Physics, Kolkata) and Satyendra Nath Bose National Centre for Basic Sciences, Kolkata, for their financial support. Jayanta Kumar Bhattacharjee, Bikas K Chakrabarti, JunIchi Inoue and Parongama SenConvenors and Editors of the proceedingsJournal of Physics Conference Series 05/2011; 297(1):011001.  [Show abstract] [Hide abstract]
ABSTRACT: As a mathematical model of associative memories, the Hopfield model was now wellestablished and a lot of studies to reveal the patternrecalling process have been done from various different approaches. As wellknown, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the inputoutput 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 patternrecalling processes of the Hopfield model governed by the Glauberdynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantummechanical variant. In this paper, in terms of the stochastic process of quantummechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantummechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which nonextensive 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 builtin patterns under the influence of quantummechanical noise.Journal of Physics Conference Series 03/2011;  [Show abstract] [Hide abstract]
ABSTRACT: We attempt to reconstruct macroscopic properties of a stochastic labor market from the view point of its microscopic descriptions. Especially, we derive the socalled Philips curve which generally possesses a universal fitting form: (inflation rate) = (unemployment rate) c + b, b, c < 0. To check the validity of our probabilistic modeling, we compare our numerical results with the corresponding empirical evidence in Japanese labor markets from 1970's to 2000's.01/2011;  [Show abstract] [Hide abstract]
ABSTRACT: 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 humaneyes 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 powerspectrum analysis, we find that the binary dots image is physiologically plausible from the view point of humaneyes 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 Bayesoptimal inversehalftoning is achieved on a specific condition which is very similar to the socalled Nishimori line in the research field of spin glasses. Comment: 20 pages, 27 figures, using revtex411/2010;  [Show abstract] [Hide abstract]
ABSTRACT: Statistical properties of orderdriven doubleauction markets with BidAsk spread are investigated through the dynamical quantities such as response function. We first attempt to utilize the socalled {\it MadhavanRichardsonRoomans model} (MRR for short) to simulate the stochastic process of the pricechange in empirical data sets (say, EUR/JPY or USD/JPY exchange rates) in which the BidAsk spread fluctuates in time. We find that the MRR theory apparently fails to simulate so much as the qualitative behaviour ('nonmonotonic' 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 BidAsk spread causes apparent deviations from a linear relationship between the $R(l)$ and the autocorrelation function $C(l)$, namely, $R(l) \propto C(l)$. To make the microscopic model of doubleauction markets having stochastic BidAsk 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') lookup table reproduces the nonlinear relationship $R(l) \propto f(C(l))$ ($f(x)$ stands for a nonlinear function leading to '$\lambda$shapes') more effectively than the fixed (`quenched') lookup table does.Journal of Economic Interaction and Coordination 11/2010; · 0.57 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: 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 `zerocollision' and `nobreakingup' constraints. As a fitness function (the energy function) to be maximized by the GA, we choose the socalled the $\gamma$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 $\gamma$value leadingup 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.Computing Research Repository  CORR. 11/2010; 
Conference Paper: Quantum annealing via transverse interaction with XYtype anisotropy
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ABSTRACT: We investigate quantum annealing (QA) via the transverse interaction with XYtype anisotropy to the ground state problems for a toy model system composed of 4 S=l/2 quantum spins interacting with antiferromagnetic interactions. By solving the Schrodinger equation for the toy model system, we find that the QA succeeds in deriving the ground state of the toy model system, if the target system does not have nontrivial degeneracy in the ground state. Then, we also And that the QA selectively obtains a desirable solution among the degenerate ground states by tuning the XYtype anisotropy appropriately, when the target system has nontrivial degeneracy in the ground state. Then, the spin wave theory also finds that the toy model indicates similar properties in an infinitevolume limit. Next, we find that the ground state of the target system can be obtained even if we start annealing procedure from states including excited states of the kinetic energy term, when we set the time interval to be large in solving the Schrodinger equation.SICE Annual Conference 2010, Proceedings of; 09/2010 
Chapter: QuantumMechanical Variant of the Thouless–Anderson–Palmer Equation for ErrorCorrecting Codes
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ABSTRACT: Statistical mechanics of information has been applied to problems in various research topics of information science and technology [1],[2]. Among those research topics, errorcorrecting code is one of the most developed subjects. In the research field of errorcorrecting codes, Nicolas Sourlas showed that the socalled convolutional codes can be constructed by spin glass with infinite range pbody interactions and the decoded message should be corresponded to the ground state of the Hamiltonian [3]. Ruján pointed out that the bit error can be suppressed if one uses finite temperature equilibrium states as the decoding result, instead of the ground state [4], and the socalled Bayesoptimal decoding at some specific condition was proved by Nishimori [5] and Nishimori and Wong [6]. Kabashima and Saad succeeded in constructing more practical codes, namely lowdensity parity check (LDPC) codes by using the infinite range spin glass model with finite connectivities [7]. They used the socalled TAP (Thouless–Anderson–Palmer) equations to decode the original message for a given parity check.07/2010: pages 283295;  [Show abstract] [Hide abstract]
ABSTRACT: 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.12321237 (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.2534 (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 counterintuitive and also provides a justification of the hypothesis that the anisotropy emerges as a result of selforganization 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 socalled $\gamma$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 $\gamma$value might enable us to judge whether an arbitrary flock simulation seems to be {\it realistic} or not. Comment: 7 pages, 11 figures, Proceedings of the Operational Research Society Simulation Workshop 2010 (SW10)04/2010;  [Show abstract] [Hide abstract]
ABSTRACT: A general procedure of averagecase 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 KullbackLeibler information between a parametric Gibbs distribution and the empirical distribution of gene configurations. The formulation is applied to the solvable probabilistic models having multivalley energy landscapes, namely, the spin glass chain and the SherringtonKirkpatrick model. By using computer simulations, we discuss the asymptotic behaviour of the effective temperature scheduling and the residual energy induced by the GA dynamics. Comment: 14 pages, 19 figures04/2010;  [Show abstract] [Hide abstract]
ABSTRACT: We numerically investigate a meanfield 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 spatiotemporal Markov random fields. Preliminary to construction of our procedure, we find that meanfield 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 meansquare error. We confirm that the optimal scaling factor stabilizes the meanfield iterative process of the motion velocity estimation. We next attempt to estimate the optimal values of hyperparameters including the regularization term, which define our probabilistic model macroscopically, by using the Boltzmannmachine type learning algorithm based on gradient descent of marginal likelihood (typeII likelihood) with respect to the hyperparameters. In our framework, one can estimate both the probabilistic model (hyperparameters) 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 hyperparameters are set to some adhoc values without any theoretical justification. Comment: 10 pages, 21 figures, using IEEEtran.cls04/2010; 
Article: Deterministic flows of orderparameters in stochastic processes of quantum Monte Carlo method
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ABSTRACT: In terms of the stochastic process of quantummechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infiniterange ($d(=\infty)$dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glaubertype 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 microscopiclaw. 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 statisticalmechanical 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 zerotemperature flow equation of image restoration measure showing some `nonmonotonic' behaviour in its time evolution. Comment: 14 pages, 6 figures, using jpconf.cls, Proceedings of IWSMI2010 in KyotoJournal of Physics Conference Series 04/2010;  [Show abstract] [Hide abstract]
ABSTRACT: In this talk, we attempt to make a microscopic modeling the firstpassage process (or the firstexit process) of the BUND future by minority game with market history. We find that the firstpassage process of the minority game with appropriate history length generates the same properties as the BTP future (the middle and long term Italian Government bonds with fixed interest rates), namely, both firstpassage time distributions have a crossover at some specific time scale as is the case for the MittagLeffler function. We also provide a macroscopic (or a phenomenological) modeling of the firstpassage process of the BTP future and show analytically that the firstpassage time distribution of a simplest mixture of the normal compound Poisson processes does not have such a crossover.03/2010;
Publication Stats
97  Citations  
24.30  Total Impact Points  
Top Journals
Institutions

1970–2013

Hokkaido University
 • Graduate School of Information Science and Technology
 • Graduate School of Engineering
Sapporo, Hokkaidō, Japan


2005–2010

Saha Institute of Nuclear Physics
 Theoretical Condensed Matter Physics Division
Calcutta, Bengal, India
