Performance information

• Koopman Analysis of Combinatorial Optimization Problems with Replica Exchange Monte Carlo Method
  Tatsuya Naoi; Tatsuya Kishimoto; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：94, Number：2, First page：024801-1, Last page：024801-8, Feb. 2025, [Reviewed], [Last, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.94.024801
  DOI ID：10.7566/jpsj.94.024801, ISSN：0031-9015, eISSN：1347-4073, 共同研究・競争的資金等ID：36619934
• Aspects of Importance Sampling in Parameter Selection for Neural Networks Using Ridgelet Transform
  Hikaru Homma; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：93, Number：12, First page：124001-1, Last page：124001-6, Dec. 2024, [Reviewed], [Last, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.93.124001
  DOI ID：10.7566/jpsj.93.124001, ISSN：0031-9015, eISSN：1347-4073, 共同研究・競争的資金等ID：35825151
• Compression of the Koopman matrix for nonlinear physical models via hierarchical clustering
  Tomoya Nishikata; Jun Ohkubo
  Nonlinear Theory and Its Applications, IEICE, Volume：15, Number：4, First page：938, Last page：953, Oct. 2024, [Reviewed], [Last, Corresponding]
  Institute of Electronics, Information and Communications Engineers (IEICE), English, Scientific journal
  DOI：https://doi.org/10.1587/nolta.15.938
  DOI ID：10.1587/nolta.15.938, eISSN：2185-4106, 共同研究・競争的資金等ID：36619934
• Attention-enhanced reservoir computing
  Felix Köster; Kazutaka Kanno; Jun Ohkubo; Atsushi Uchida
  Physical Review Applied, Volume：22, Number：1, First page：014039-1, Last page：014039-12, Jul. 2024, [Reviewed]
  American Physical Society (APS), English, Scientific journal
  DOI：https://doi.org/10.1103/physrevapplied.22.014039
  DOI ID：10.1103/physrevapplied.22.014039, eISSN：2331-7019, 共同研究・競争的資金等ID：43806931
• Improvement of System Identification of Stochastic Systems via Koopman Generator and Locally Weighted Expectation
  Yuki Tahara; Kakutaro Fukushi; Shunta Takahashi; Kayo Kinjo; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：93, Number：7, First page：073401-1, Last page：073401-9, Jul. 2024, [Reviewed], [Last, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.93.074006
  DOI ID：10.7566/jpsj.93.074006, ISSN：0031-9015, eISSN：1347-4073, 共同研究・競争的資金等ID：43806931
• Extraction of nonlinearity in neural networks with Koopman operator
  Naoki Sugishita; Kayo Kinjo; Jun Ohkubo
  Journal of Statistical Mechanics: Theory and Experiment, Volume：2024, Number：7, First page：073401-1, Last page：073401-22, Jul. 2024, [Reviewed], [Last, Corresponding]
  IOP Publishing, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/ad5713
  DOI ID：10.1088/1742-5468/ad5713, eISSN：1742-5468, 共同研究・競争的資金等ID：36619934
• Characterization of Locality in Spin States and Forced Moves for Optimizations
  Yoshiki Sato; Makiko Konoshima; Hirotaka Tamura; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：93, Number：4, First page：044802-1, Last page：044802-7, Apr. 2024, [Reviewed], [Last, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.93.044802
  DOI ID：10.7566/jpsj.93.044802, ISSN：0031-9015, eISSN：1347-4073
• Redundant basis interpretation of Doi-Peliti method and an application　　　　　　　　　　　　　　　
  Shunta Takahashi; Jun Ohkubo
  J. Stat. Phys., Volume：190, Number：10, First page：159-1, Last page：159-18, Oct. 2023, [Reviewed], [Last, Corresponding]
  English, Scientific journal
  DOI：https://doi.org/10.1007/s10955-023-03180-w
  DOI ID：10.1007/s10955-023-03180-w, 共同研究・競争的資金等ID：36619934
• Embedding stochastic differential equations into neural networks via dual processes
  Naoki Sugishita; Jun Ohkubo
  Journal of Statistical Mechanics: Theory and Experiment, Volume：2023, Number：9, First page：093201-1, Last page：093201-15, Sep. 2023, [Reviewed], [Last, Corresponding]
  Abstract
  
  We propose a new approach to constructing a neural network for predicting expectations of stochastic differential equations. The proposed method does not need data sets of inputs and outputs; instead, the information obtained from the time-evolution equations, i.e. the corresponding dual process, is directly compared with the weights in the neural network. As a demonstration, we construct neural networks for the Ornstein–Uhlenbeck process and the noisy van der Pol system. The remarkable feature of learned networks with the proposed method is the accuracy of inputs near the origin. Hence, it would be possible to avoid the overfitting problem because the learned network does not depend on training data sets.
  IOP Publishing, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/acf126
  DOI ID：10.1088/1742-5468/acf126, eISSN：1742-5468, 共同研究・競争的資金等ID：35825151
• Statistics for Stochastic Differential Equations and Approximations of Resolvent
  Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：92, Number：7, First page：074006-1, Last page：074006-10, Jul. 2023, [Reviewed], [Lead, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.92.074006
  DOI ID：10.7566/jpsj.92.074006, ISSN：0031-9015, eISSN：1347-4073, 共同研究・競争的資金等ID：36619934
• Efficient Correlation-based Discretization of Continuous Variables for Annealing Machines
  Yuki Furue; Makiko Konoshima; Hirotaka Tamura; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：92, Number：4, First page：044802-1, Last page：044802-7, Apr. 2023, [Reviewed], [Last, Corresponding]
  Physical Society of Japan, English, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.92.044802
  DOI ID：10.7566/jpsj.92.044802, ISSN：0031-9015, eISSN：1347-4073
• Numerical methods to evaluate Koopman matrix from system equations
  Jun Ohkubo
  Journal of Physics A: Mathematical and Theoretical, Volume：55, Number：22, First page：224007-1, Last page：224007-20, May 2022, [Reviewed], [Lead, Corresponding]
  Abstract
  
  The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous methods in the Koopman operator approach. The EDMD employs a data set of snapshot pairs and a specific dictionary to evaluate an approximation for the Koopman operator, i.e., the Koopman matrix. In this study, we focus on stochastic differential equations, and a method to obtain the Koopman matrix is proposed. The proposed method does not need any data set, which employs the original system equations to evaluate some of the targeted elements of the Koopman matrix. The proposed method comprises combinatorics, an approximation of the resolvent, and extrapolations. Comparisons with the EDMD are performed for a noisy van der Pol system. The proposed method yields reasonable results even in cases wherein the EDMD exhibits a slow convergence behavior.
  IOP Publishing, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8121/ac663b
  DOI ID：10.1088/1751-8121/ac663b, ISSN：1751-8113, eISSN：1751-8121, 共同研究・競争的資金等ID：35825151;24613319
• Connection among Stochastic Hamilton–Jacobi–Bellman Equation, Path-Integral, and Koopman Operator on Nonlinear Stochastic Optimal Control
  Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：90, Number：10, First page：104802, Last page：104802, Oct. 2021, [Reviewed], [Lead, Corresponding]
  Physical Society of Japan, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.90.104802
  DOI ID：10.7566/jpsj.90.104802, ISSN：0031-9015, eISSN：1347-4073
• Semi-Supervised Learning Combining Backpropagation and STDP: STDP Enhances Learning by Backpropagation with a Small Amount of Labeled Data in a Spiking Neural Network
  Kotaro Furuya; Jun Ohkubo
  Journal of the Physical Society of Japan, Volume：90, Number：7, First page：074802, Last page：074802, Jul. 2021, [Reviewed], [Last]
  Physical Society of Japan, Scientific journal
  DOI：https://doi.org/10.7566/jpsj.90.074802
  DOI ID：10.7566/jpsj.90.074802, ISSN：0031-9015, eISSN：1347-4073
• Water storage and drainage in perlite in container cultivation
  Yuka Hasama; Yoshiaki Saito; Jun Ohkubo
  SICE Journal of Control, Measurement, and System Integration, Volume：14, Number：2, First page：104, Last page：110, Jun. 2021, [Reviewed], [Last]
  Informa UK Limited, Scientific journal
  DOI：https://doi.org/10.1080/18824889.2021.1896642
  DOI ID：10.1080/18824889.2021.1896642, ISSN：1882-4889, eISSN：1884-9970
• Combinatorics for calculating expectation values of functions in systems with evolution governed by stochastic differential equations
  Jun Ohkubo
  Journal of Statistical Mechanics: Theory and Experiment, Volume：2021, Number：1, First page：013401, Last page：013401, Jan. 2021, [Reviewed], [Lead, Corresponding]
  IOP Publishing, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/abd029
  DOI ID：10.1088/1742-5468/abd029, eISSN：1742-5468, 共同研究・競争的資金等ID：24613319
• Making Birth–Death Processes from Backward Fokker–Planck Equations for Computing Expectations in Langevin Systems　　　　　　　　　　　　　　　
  Jun Ohkubo
  J. Phys. Soc. Jpn., Volume：89, Number：4, First page：044004-1, Last page：044004-6, Apr. 2020, [Reviewed], [Lead, Corresponding]
  English, Scientific journal
  共同研究・競争的資金等ID：24613319
• Derivation of QUBO Formulations for Sparse Estimation　　　　　　　　　　　　　　　
  Tomohiro Yokota; Makiko Konoshima; Hirotaka Tamura; Jun Ohkubo
  J. Phys. Soc. Jpn., Volume：89, Number：3, First page：034801-1, Last page：034801-5, Mar. 2020, [Reviewed], [Last, Corresponding]
  English, Scientific journal
• Duality in stochastic processes from the viewpoint of basis expansions　　　　　　　　　　　　　　　
  Jun Ohkubo; Yuuki Arai
  Volume：2019, First page：063202-1, Last page：063202-13, Jun. 2019, [Reviewed], [Lead, Corresponding]
  English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/ab1dd9
  DOI ID：10.1088/1742-5468/ab1dd9
• Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions　　　　　　　　　　　　　　　
  Go Sato; Makiko Konoshima; Takuya Ohwa; Hirotaka Tamura; Jun Ohkubo
  Phys. Rev. E, Volume：99, Number：4, First page：042106-1, Last page：042106-5, Apr. 2019, [Reviewed]
  English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.99.042106
  DOI ID：10.1103/PhysRevE.99.042106
• On dualities for SSEP and ASEP with open boundary conditions　　　　　　　　　　　　　　　
  J. Ohkubo
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：50, Number：9, First page：095004-1, Last page：095004-21, Mar. 2017, [Reviewed]
  Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have a unified discussion about duality relations with open boundaries. As for the symmetric simple exclusion process (SSEP), more general results than those from previous studies are obtained. It is clarified that not only the absorbing sites, but also additional sites-called copying sites-are needed for the boundaries in the dual process for the SSEP. The role of the copying sites is to conserve information about the particle states on the boundary sites. Similar discussions are applied to the asymmetric simple exclusion process (ASEP), in which the q-analogues are employed, and it is clarified that the ASEP with open boundaries has a complicated dual process on the boundaries.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8121/aa56f8
  DOI ID：10.1088/1751-8121/aa56f8, ISSN：1751-8113, eISSN：1751-8121, Web of Science ID：WOS:000395504300003
• Duality-based calculations for transition probabilities in stochastic chemical reactions　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：95, Number：2, First page：023304-1, Last page：023304-7, Feb. 2017, [Reviewed]
  An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time evolutions of the original reaction system, the dual process is dealt with. Usually, if one changes rate constants of the original reaction system, the direct time evolutions should be performed again, using the new rate constants. On the other hands, only one solution of an extended dual process can be reused to calculate the transition probabilities for various rate constant cases. The idea is demonstrated in a parameter estimation problem for the Lotka-Volterra system.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.95.023304
  DOI ID：10.1103/PhysRevE.95.023304, ISSN：2470-0045, eISSN：2470-0053, Web of Science ID：WOS:000402251400004
• Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：92, Number：4, First page：043302-1, Last page：043302-9, Oct. 2015, [Reviewed]
  An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.92.043302
  DOI ID：10.1103/PhysRevE.92.043302, ISSN：2470-0045, eISSN：2470-0053, Web of Science ID：WOS:000362445700015
• Karlin-McGregor-like formula in a simple time-inhomogeneous birth-death process　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：47, Number：40, First page：405001-1, Last page：405001-11, Oct. 2014, [Reviewed]
  Algebraic discussions are developed to derive transition probabilities for a simple time-inhomogeneous birth-death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases. As a result, an expression based on the Charlier polynomials is obtained, which can be considered as an extension of a famous Karlin-McGregor representation for a time-homogeneous birth-death process.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/47/40/405001
  DOI ID：10.1088/1751-8113/47/40/405001, ISSN：1751-8113, eISSN：1751-8121, Web of Science ID：WOS:000343240400003
• Lie Algebraic Discussions for Time-Inhomogeneous Linear Birth-Death Processes with Immigration　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF STATISTICAL PHYSICS, Volume：157, Number：2, First page：380, Last page：391, Oct. 2014, [Reviewed]
  Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without immigration have been studied by using a generating function approach, the processes with immigration are here analyzed by Lie algebraic discussions. As a result, a restriction for time-inhomogeneity of the birth-death process is understood from the viewpoint of the finiteness of the dimensionality of the Lie algebra.
  SPRINGER, English, Scientific journal
  DOI：https://doi.org/10.1007/s10955-014-1068-x
  DOI ID：10.1007/s10955-014-1068-x, ISSN：0022-4715, eISSN：1572-9613, Web of Science ID：WOS:000341710800010
• Basics of Counting Statistics　　　　　　　　　　　　　　　
  Jun Ohkubo
  IEICE TRANSACTIONS ON COMMUNICATIONS, Volume：E96B, Number：11, First page：2733, Last page：2740, Nov. 2013, [Reviewed], [Invited]
  In this paper, we briefly review the scheme of counting statistics, in which a probability of the number of monitored or target transitions in a Markov jump process is evaluated. It is generally easy to construct a master equation for the Markov jump process, and the counting statistics enables us to straightforwardly obtain basic equations of the counting statistics from the master equation; the basic equation is used to calculate the cumulant generating function of the probability of the number of target transitions. For stationary cases, the probability is evaluated from the eigenvalue analysis. As for the nonstationary cases, we review a numerical integration scheme to calculate the statistics of the number of transitions.
  IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG, English, Scientific journal
  DOI：https://doi.org/10.1587/transcom.E96.B.2733
  DOI ID：10.1587/transcom.E96.B.2733, ISSN：0916-8516, eISSN：1745-1345, CiNii Articles ID：130003385116, Web of Science ID：WOS:000327168100004
• Extended duality relations between birth-death processes and partial differential equations　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：46, Number：37, First page：375004-1, Last page：375004-11, Sep. 2013, [Reviewed]
  Duality relations between continuous-state and discrete-state stochastic processes with continuous time have already been studied and used in various research fields. We propose extended duality relations which enable us to derive discrete-state stochastic processes from arbitrary diffusion-type partial differential equations. The derivation is based on the Doi-Peliti formalism, and it will be clarified that additional states for the discrete-state stochastic processes must be considered in some cases.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/46/37/375004
  DOI ID：10.1088/1751-8113/46/37/375004, ISSN：1751-8113, Web of Science ID：WOS:000324071400005
• Algebraic Probability, Classical Stochastic Processes, and Counting Statistics　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：82, Number：8, First page：084001-1, Last page：084001-7, Aug. 2013, [Reviewed]
  We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can be reformulated in terms of the algebraic probability. This reformulation immediately gives the Doi-Peliti formalism, which has been frequently used in nonequilibrium physics. As an application of the reformulation, we give a derivation of basic equations for counting statistics, which plays an important role in nonequilibrium physics.
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.7566/JPSJ.82.084001
  DOI ID：10.7566/JPSJ.82.084001, ISSN：0031-9015, Web of Science ID：WOS:000322374300017
• Noncyclic geometric phase in counting statistics and its role as an excess contribution　　　　　　　　　　　　　　　
  Jun Ohkubo
  Journal of Physics A: Mathematical and Theoretical, Volume：46, Number：28, First page：285001-1, Last page：285001-12, Jul. 2013, [Reviewed]
  We propose an application of fiber bundles to counting statistics. The framework of the fiber bundles gives a splitting of a cumulant generating function for a current in a stochastic process, i.e., contributions from the dynamical phase and the geometric phase. We will show that the introduced noncyclic geometric phase is related to kinds of excess contributions, which have been investigated a lot in nonequilibrium physics. Using a specific nonequilibrium model, the characteristics of the noncyclic geometric phase are discussed
  in particular, we reveal differences between a geometric contribution for the entropy production and the 'excess entropy production' which has been used to discuss the second law of steady-state thermodynamics. © 2013 IOP Publishing Ltd.
  English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/46/28/285001
  DOI ID：10.1088/1751-8113/46/28/285001, ISSN：1751-8113, J-Global ID：201302225888380171, CiNii Articles ID：120005307059, SCOPUS ID：84879896789
• One-parameter extension of the Doi-Peliti formalism and its relation with orthogonal polynomials　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：86, Number：4, First page：042102-1, Last page：042102-4, Oct. 2012, [Reviewed]
  An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.86.042102
  DOI ID：10.1103/PhysRevE.86.042102, ISSN：1539-3755, CiNii Articles ID：120004945140, PubMed ID：23214630, Web of Science ID：WOS:000310196800003
• Counting statistics for genetic switches based on effective interaction approximation　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF CHEMICAL PHYSICS, Volume：137, Number：12, First page：125102-1, Last page：125102-6, Sep. 2012, [Reviewed]
  Applicability of counting statistics for a system with an infinite number of states is investigated. The counting statistics has been studied a lot for a system with a finite number of states. While it is possible to use the scheme in order to count specific transitions in a system with an infinite number of states in principle, we have non-closed equations in general. A simple genetic switch can be described by a master equation with an infinite number of states, and we use the counting statistics in order to count the number of transitions from inactive to active states in the gene. To avoid having the non-closed equations, an effective interaction approximation is employed. As a result, it is shown that the switching problem can be treated as a simple two-state model approximately, which immediately indicates that the switching obeys non-Poisson statistics. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754537]
  AMER INST PHYSICS, English, Scientific journal
  DOI：https://doi.org/10.1063/1.4754537
  DOI ID：10.1063/1.4754537, ISSN：0021-9606, CiNii Articles ID：120004873983, PubMed ID：23020350, Web of Science ID：WOS:000309428500034
• Nonparametric model reconstruction for stochastic differential equations from discretely observed time-series data　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：84, Number：6, First page：066702-1, Last page：066702-9, Dec. 2011, [Reviewed]
  A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion coefficients in advance. In order to perform the nonparametric estimation, a maximum likelihood method is combined with a concept based on a kernel density estimation. In order to deal with discrete observation or sparsity of the time-series data, a local linearization method is employed, which enables a fast estimation.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.84.066702
  DOI ID：10.1103/PhysRevE.84.066702, ISSN：1539-3755, CiNii Articles ID：120003779166, PubMed ID：22304215, Web of Science ID：WOS:000298139000008
• Approximation scheme based on effective interactions for stochastic gene regulation　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：83, Number：4, First page：041915-1, Last page：041915-9, Apr. 2011, [Reviewed]
  Since gene regulatory systems sometimes contain only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme for dealing with the stochasticity of the gene regulatory systems. Using an effective interaction concept, original master equations can be reduced to simpler master equations, which can be solved analytically. We apply the approximation scheme to self-regulating systems with monomer or dimer interactions, and a two-gene system with an exclusive switch. The approximation scheme can recover the bistability of the exclusive switch adequately.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.83.041915
  DOI ID：10.1103/PhysRevE.83.041915, ISSN：1539-3755, CiNii Articles ID：120003338851, PubMed ID：21599208, Web of Science ID：WOS:000290116100008
• Long-tail behavior in locomotion of Caenorhabditis elegans　　　　　　　　　　　　　　　
  Jun Ohkubo; Kazushi Yoshida; Yuichi Iino; Naoki Masuda
  JOURNAL OF THEORETICAL BIOLOGY, Volume：267, Number：2, First page：213, Last page：222, Nov. 2010, [Reviewed]
  The locomotion of Caenorhabditis elegans exhibits complex patterns. In particular, the worm combines mildly curved runs and sharp turns to steer its course. Both runs and sharp turns of various types are important components of taxis behavior. The statistics of sharp turns have been intensively studied. However, there have been few studies on runs, except for those on klinotaxis (also called weathervane mechanism), in which the worm gradually curves toward the direction with a high concentration of chemicals; this phenomenon was discovered recently. We analyzed the data of runs by excluding sharp turns. We show that the curving rate obeys long-tail distributions, which implies that large curving rates are relatively frequent. This result holds true for locomotion in environments both with and without a gradient of NaCl concentration; it is independent of klinotaxis. We propose a phenomenological computational model on the basis of a random walk with multiplicative noise. The assumption of multiplicative noise posits that the fluctuation of the force is proportional to the force exerted. The model reproduces the long-tail property present in the experimental data. (C) 2010 Elsevier Ltd. All rights reserved.
  ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, English, Scientific journal
  DOI：https://doi.org/10.1016/j.jtbi.2010.08.020
  DOI ID：10.1016/j.jtbi.2010.08.020, ISSN：0022-5193, eISSN：1095-8541, Web of Science ID：WOS:000283334100009
• Noncyclic and nonadiabatic geometric phase for counting statistics　　　　　　　　　　　　　　　
  Jun Ohkubo; Thomas Eggel
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：43, Number：42, First page：425001-1, Last page：425001-11, Oct. 2010, [Reviewed]
  We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the counting statistics can be interpreted as a 'phase', and it is generally divided into two parts: the dynamical phase and a remaining one. It has already been shown that for cyclic evolution the remaining phase corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan phase. We here show that the remaining phase has also an interpretation as a geometric phase even in noncyclic and nonadiabatic evolution.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/43/42/425001
  DOI ID：10.1088/1751-8113/43/42/425001, ISSN：1751-8113, Web of Science ID：WOS:000282518000001
• A direct numerical method for obtaining the counting statistics for stochastic processes　　　　　　　　　　　　　　　
  Jun Ohkubo; Thomas Eggel
  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, Volume：2010, Number：6, First page：P06013-1, Last page：P06013-9, Jun. 2010, [Reviewed]
  We propose a direct numerical method for calculating the statistics for the numbers of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary moments of the probability distribution of the number of transitions are in principle calculated by solving numerically a system of coupled differential equations. As an example, a two-state model with a time-dependent transition matrix is considered and the first, second and third moments of the current are calculated. This calculation scheme is applicable for any stochastic process with a finite state space, and it would be helpful for studying current statistics for nonequilibrium systems.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/2010/06/P06013
  DOI ID：10.1088/1742-5468/2010/06/P06013, ISSN：1742-5468, Web of Science ID：WOS:000281744100018
• Duality in Interacting Particle Systems and Boson Representation　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF STATISTICAL PHYSICS, Volume：139, Number：3, First page：454, Last page：465, May 2010, [Reviewed]
  In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and annihilation operators. For some stochastic processes, duality relations have been known, which connect continuous time Markov processes with discrete state space and those with continuous state space. We clarify that using a generating function approach and the Doi-Peliti method, a birth-death process (or discrete random walk model) is naturally connected to a differential equation with continuous variables, which would be interpreted as a dual Markov process. The key point in the derivation is to use bosonic coherent states as a bra state, instead of a conventional projection state. As examples, we apply the scheme to a simple birth-coagulation process and a Brownian momentum process. The generator of the Brownian momentum process is written by elements of the SU(1,1) algebra, and using a boson realization of SU(1,1) we show that the same scheme is available.
  SPRINGER, English, Scientific journal
  DOI：https://doi.org/10.1007/s10955-009-9910-2
  DOI ID：10.1007/s10955-009-9910-2, ISSN：0022-4715, Web of Science ID：WOS:000276511500006
• Two Langevin equations in the Doi-Peliti formalism　　　　　　　　　　　　　　　
  Kazunori Itakura; Jun Ohkubo; Shin-ichi Sasa
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：43, Number：12, First page：125001-1, Last page：125001-12, Mar. 2010, [Reviewed]
  A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with the so-called Cole Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme X reversible arrow X + X is investigated as an illustrative example.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/43/12/125001
  DOI ID：10.1088/1751-8113/43/12/125001, ISSN：1751-8113, Web of Science ID：WOS:000275302300003
• Posterior Probability and Fluctuation Theorem in Stochastic Processes　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：78, Number：12, First page：123001-1, Last page：123001-4, Dec. 2009, [Reviewed]
  A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes' theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.78.123001
  DOI ID：10.1143/JPSJ.78.123001, ISSN：0031-9015, Web of Science ID：WOS:000272985600001
• Variational principle of counting statistics in master equations　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：80, Number：1, First page：012101-1, Last page：012101-4, Jul. 2009, [Reviewed]
  We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not an approximation, but a valid procedure in the present derivation. Hence, a variational principle in the counting statistics is naturally derived. In order to obtain the variational principle, we employ many independent replicas of the same system. In addition, the Euler-Maclaurin formula is used in order to connect the discrete and continuous properties of the system.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.80.012101
  DOI ID：10.1103/PhysRevE.80.012101, ISSN：1539-3755, Web of Science ID：WOS:000268616300115
• Current and fluctuation in a two-state stochastic system under nonadiabatic periodic perturbation　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF CHEMICAL PHYSICS, Volume：129, Number：20, First page：205102-1, Last page：205102-6, Nov. 2008, [Reviewed]
  We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that the periodic perturbation induces a so-called pump current, and the pump current and its fluctuation are calculated with the aid of the geometrical phase interpretation. We give a simple calculation recipe for the statistics of the current, especially in a nonadiabatic case. The calculation scheme is based on the nonadiabatic geometrical phase interpretation. Using the Floquet theory, the total current and its fluctuation are calculated, and it is revealed that the average of the current shows a stochastic-resonance-like behavior. In contrast, the fluctuation of the current does not show such behavior.
  AMER INST PHYSICS, English, Scientific journal
  DOI：https://doi.org/10.1063/1.3026510
  DOI ID：10.1063/1.3026510, ISSN：0021-9606, Web of Science ID：WOS:000262607100038
• Power-law behavior and condensation phenomena in disordered urn models　　　　　　　　　　　　　　　
  Jun-ichi Inoue; Jun Ohkubo
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：41, Number：32, First page：324020-1, Last page：324020-14, Aug. 2008, [Reviewed]
  We investigate the 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 the 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 rho(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 macro-economy, in particular the emergence of wealth differentials.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/41/32/324020
  DOI ID：10.1088/1751-8113/41/32/324020, ISSN：1751-8113, eISSN：1751-8121, Web of Science ID：WOS:000258023900022
• Approximation scheme for master equations: Variational approach to multivariate case　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF CHEMICAL PHYSICS, Volume：129, Number：4, First page：044108-1, Last page：044108-8, Jul. 2008, [Reviewed]
  We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large in such small systems. Although a Fokker-Planck equation obtained by the system size expansion includes the fluctuation effects, it needs large computational costs for complicated chemical reaction systems. In addition, discrete characteristics of the original master equation are neglected in the system size expansion scheme. It has been shown that the use of the second quantization description and a variational method achieves tremendous reduction in the dimensionality of the master equation approximately, without loss of the discrete characteristics. Here, we propose a new scheme for the choice of variational functions, which is applicable to multivariate cases. It is revealed that the new scheme gives better numerical results than old ones and the computational cost increases only slightly. (C) 2008 American Institute of Physics.
  AMER INST PHYSICS, English, Scientific journal
  DOI：https://doi.org/10.1063/1.2957462
  DOI ID：10.1063/1.2957462, ISSN：0021-9606, Web of Science ID：WOS:000258171500013
• Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems　　　　　　　　　　　　　　　
  N. A. Sinitsyn; J. Ohkubo
  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Volume：41, Number：26, First page：262002-1, Last page：262002-4, Jul. 2008, [Reviewed]
  Kepler and Kagan (1991 Phys. Rev. Lett. 66 847) derived a geometric phase shift in dissipative limit cycle evolution. This effect was considered as an extension of the geometric phase in classical mechanics. We show that the opposite is also true, namely, this geometric phase can be identified with the classical mechanical Hannay angle in an extended phase space. Our results suggest that this phase can be generalized to a stochastic evolution with an additional noise term in evolution equations.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1751-8113/41/26/262002
  DOI ID：10.1088/1751-8113/41/26/262002, ISSN：1751-8113, Web of Science ID：WOS:000256694000002
• Transition phenomena induced by internal noise and quasi-absorbing state　　　　　　　　　　　　　　　
  Jun Ohkubo; Nadav Shnerb; David A. Kessler
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：77, Number：4, First page：044002-1, Last page：044002-5, Apr. 2008, [Reviewed]
  We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Sec. Jpn. 72 (2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss the transition phenomenon by means of a random walk model and an effective model. The discussion makes it clear that quasi-absorbing states, which are produced by the change of the strength of the internal noise, play an important role in the transition phenomenon. Stabilizing the quasi-absorbing states causes bifurcation of the peaks in the stationary probability distribution discontinuously.
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.77.044002
  DOI ID：10.1143/JPSJ.77.044002, ISSN：0031-9015, Web of Science ID：WOS:000255110900012
• The stochastic pump current and the non-adiabatic geometrical phase　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, Volume：2008, Number：2, First page：P02011-1, Last page：P02011-12, Feb. 2008, [Reviewed]
  We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/2008/02/P02011
  DOI ID：10.1088/1742-5468/2008/02/P02011, ISSN：1742-5468, Web of Science ID：WOS:000254376400008
• Condensation phenomena with distinguishable particles　　　　　　　　　　　　　　　
  Jun Ohkubo
  PHYSICAL REVIEW E, Volume：76, Number：5, First page：051108-1, Last page：051108-6, Nov. 2007, [Reviewed]
  We study real-space condensation phenomena in types of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We study a stochastic process in the Ehrenfest class, i.e., particles in a site are distinguishable. In terms of the statistical mechanical analog, the Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify conditions for condensation phenomena in disordered cases in the Ehrenfest class. In addition, we discuss the preferential urn model as an example of the disordered urn model. It becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model. It is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.76.051108
  DOI ID：10.1103/PhysRevE.76.051108, ISSN：1539-3755, Web of Science ID：WOS:000251326100015
• A field theoretic approach to master equations and a variational method beyond the Poisson ansatz　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, Volume：2007, Number：9, First page：P09017-1, Last page：P09017-13, Sep. 2007, [Reviewed]
  We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the variational scheme developed gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network.
  IOP PUBLISHING LTD, English, Scientific journal
  DOI：https://doi.org/10.1088/1742-5468/2007/09/P09017
  DOI ID：10.1088/1742-5468/2007/09/P09017, ISSN：1742-5468, Web of Science ID：WOS:000249982200019
• Free energy of disordered urn models in the canonical ensemble　　　　　　　　　　　　　　　
  Jun Ohkubo
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：76, Number：9, First page：095002-1, Last page：095002-2, Sep. 2007, [Reviewed]
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.76.095002
  DOI ID：10.1143/JPSJ.76.095002, ISSN：0031-9015, Web of Science ID：WOS:000249723300035
• Nonadditive volume and community detection problem in complex networks　　　　　　　　　　　　　　　
  Jun Ohkubo; Kazuyuki Tanaka
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：75, Number：11, First page：115001-1, Last page：115001-2, Nov. 2006, [Reviewed]
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.75.115001
  DOI ID：10.1143/JPSJ.75.115001, ISSN：0031-9015, Web of Science ID：WOS:000242210200050
• Replica analysis of preferential urn model　　　　　　　　　　　　　　　
  Jun Ohkubo; Muneki Yasuda; Kazuyuki Tanaka
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：75, Number：7, First page：074802-1, Last page：074802-6, Jul. 2006, [Reviewed]
  We analyze a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." In the replica analysis, we clarify that the preferential urn model with randomness shows a fat-tailed occupation distribution. We discuss the intuitive picture of the preferential urn model, a relationship between quenched and annealed systems, and a trial for the application of the preferential urn model to econophysics. The analytical treatments and results would be useful for various research fields such as complex networks, stochastic models, and econophysics.
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.75.074802
  DOI ID：10.1143/JPSJ.75.074802, ISSN：0031-9015, Web of Science ID：WOS:000240212900041
• Preferential urn model and nongrowing complex networks　　　　　　　　　　　　　　　
  J Ohkubo; M Yasuda; K Tanaka
  PHYSICAL REVIEW E, Volume：72, Number：6, First page：065104(R)-1, Last page：065104(R)-4, Dec. 2005, [Reviewed]
  A preferential urn model, which is based on the concept "the rich get richer," is proposed. From a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions, it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model. Furthermore, it is clarified that the preferential urn model with randomness generates a fat-tailed occupation distribution; the concept of the local temperature enables us to understand the fat-tailed occupation distribution intuitively. Since the preferential urn model is a simple stochastic model, it can be applied to research on not only the nongrowing complex networks, but also many other fields such as econophysics and social sciences.
  AMERICAN PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.72.065104
  DOI ID：10.1103/PhysRevE.72.065104, ISSN：1539-3755, Web of Science ID：WOS:000235065000004
• Statistical-mechanical iterative algorithms on complex networks　　　　　　　　　　　　　　　
  J Ohkubo; M Yasuda; K Tanaka
  PHYSICAL REVIEW E, Volume：72, Number：4, First page：046135-1, Last page：046135-8, Oct. 2005, [Reviewed]
  The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in Barabasi and Albert networks, but does not influence that in Erdos and Renyi networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barabasi-Albert's scale-free networks.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.72.046135
  DOI ID：10.1103/PhysRevE.72.046135, ISSN：2470-0045, eISSN：2470-0053, Web of Science ID：WOS:000232931200047
• Generation of complex bipartite graphs by using a preferential rewiring process　　　　　　　　　　　　　　　
  J Ohkubo; K Tanaka; T Horiguchi
  PHYSICAL REVIEW E, Volume：72, Number：3, First page：036120-1, Last page：036120-10, Sep. 2005, [Reviewed]
  It is important in computer science, sociology, and so on to investigate complex bipartite graphs from a viewpoint of statistical physics. We propose a model to generate complex bipartite graphs without growing; the bipartite graphs are assumed to have two sets of the fixed numbers of nodes and a fixed number of edges between nodes belonging to different sets of nodes. In this model, essential ingredients are a preferential rewiring process and a fitness distribution function. By using the preferential rewiring process, we confirm that a bipartite graph reaches a stationary state after a sufficiently long time has passed. We find that the obtained bipartite graph has a scale-free-like property when a suitable fitness distribution is used. It turns out that a condensation of edges takes place in the cases of certain fitness distributions.
  AMER PHYSICAL SOC, English, Scientific journal
  DOI：https://doi.org/10.1103/PhysRevE.72.036120
  DOI ID：10.1103/PhysRevE.72.036120, ISSN：2470-0045, eISSN：2470-0053, Web of Science ID：WOS:000232227800028
• Scale-free property of optimal network for packet flow by a packet routing control　　　　　　　　　　　　　　　
  J Ohkubo; T Horiguchi
  PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, Volume：353, Number：1-4, First page：649, Last page：660, Aug. 2005, [Reviewed]
  We investigate an optimal network structure for packet flow on large-scale networks. For this aim, we introduce a cost function which represents efficiency of the packet flow. Our strategy for obtaining an optimal network is to reconnect links in the network so as to minimize the defined cost function. We apply this strategy to a packet communication network in which a packet routing is controlled by using neural networks. We found that the optimal network shows a scale-free property for large degree k when the buffer-size distribution has a power-law form and the probability with which a node is chosen as a destination of a packet is proportional to the buffer size of the node. (c) 2005 Elsevier B.V. All rights reserved.
  ELSEVIER SCIENCE BV, English, Scientific journal
  DOI：https://doi.org/10.1016/j.physa.2005.01.020
  DOI ID：10.1016/j.physa.2005.01.020, ISSN：0378-4371, eISSN：1873-2119, Web of Science ID：WOS:000229915200045
• Complex networks by non-growing model with preferential rewiring process　　　　　　　　　　　　　　　
  J Ohkubo; T Horiguchi
  JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, Volume：74, Number：4, First page：1334, Last page：1340, Apr. 2005, [Reviewed]
  We propose a model for generating a scale-free-like network by means of only a preferential rewiring process with fitness parameter chosen from fitness distribution. By using the proposed rewiring process without growing, the network reaches a stationary state from an initial network with fixed numbers of nodes and edges. It turns out that the obtained network has a lot of isolated nodes and a giant cluster which has a scale-free-like property. We found that the obtained networks by choosing a suitable fitness distribution show some properties related to real metabolic networks.
  PHYSICAL SOC JAPAN, English, Scientific journal
  DOI：https://doi.org/10.1143/JPSJ.74.1334
  DOI ID：10.1143/JPSJ.74.1334, ISSN：0031-9015, CiNii Articles ID：150000092053, Web of Science ID：WOS:000228562900038
• Molecular alignment in a liquid induced by a nonresonant laser field: Molecular dynamics simulation　　　　　　　　　　　　　　　
  J Ohkubo; T Kato; H Kono; Y Fujimura
  JOURNAL OF CHEMICAL PHYSICS, Volume：120, Number：19, First page：9123, Last page：9132, May 2004, [Reviewed]
  We carried out molecular dynamics (MD) simulations for a dilute aqueous solution of pyrimidine in order to investigate the mechanisms of field-induced molecular alignment in a liquid phase. An anisotopically polarizable molecule can be aligned in a liquid phase by the interaction with a nonresonant intense laser field. We derived the effective forces induced by a nonresonant field on the basis of the concept of the average of the total potential over one optical cycle. The results of MD simulations show that a pyrimidine molecule is aligned in an aqueous solution by a linearly polarized field of light intensity Isimilar to10(13) W/cm(2) and wavelength lambda=800 nm. The temporal behavior of field-induced alignment is adequately reproduced by the solution of the Fokker-Planck equation for a model system in which environmental fluctuations are represented by Gaussian white noise. From this analysis, we have revealed that the time required for alignment in a liquid phase is in the order of the reciprocals of rotational diffusion coefficients of a solute molecule. The degree of alignment is determined by the anisotropy of the polarizability of a molecule, light intensity, and temperature. We also discuss differences between the mechanisms of optical alignment in a gas phase and a liquid phase. (C) 2004 American Institute of Physics.
  AMER INST PHYSICS, English, Scientific journal
  DOI：https://doi.org/10.1063/1.1704631
  DOI ID：10.1063/1.1704631, ISSN：0021-9606, Web of Science ID：WOS:000221146400026

• 線形代数の半歩先 データサイエンス・機械学習に挑む前の30話　　　　　　　　　　　　　　　
  大久保 潤, [Single work]
  Mar. 2025
  ISBN：9784065386477, 共同研究・競争的資金等ID：36619934
• 確率的シミュレーション　　　　　　　　　　　　　　　
  大久保 潤, [Single work]
  Dec. 2023
  ISBN：9784627097216, 共同研究・競争的資金等ID：36619934
• ネットワーク科学の道具箱　　　　　　　　　　　　　　　
  林, 幸雄; 大久保, 潤; 藤原, 義久; 上林, 憲行; 小野, 直亮; 湯田, 聴夫; 相馬, 亘; 佐藤, 一憲, [Contributor]
  Dec. 2007
  Japanese, Total pages：viii, 212p
  CiNii Books：http://ci.nii.ac.jp/ncid/BA84306856
  ISBN：9784764903463, CiNii Books ID：BA84306856

• 組合せ最適化問題を高速に解くイジングマシンへのデータ解析手法の応用　　　　　　　　　　　　　　　
  直井 達也; 岸本 龍弥; 大久保 潤
  Mar. 2025
  Mar. 2025 - Mar. 2025, Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• 確率微分方程式の期待値計算における簡潔な表現に関する研究　　　　　　　　　　　　　　　
  岸本 龍弥; 大久保 潤
  Mar. 2025
  Mar. 2025 - Mar. 2025, Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• Koopman作用素によるデータと方程式情報の統合的な利用　　　　　　　　　　　　　　　
  太田 一郎; 小柳 尚太; 金城 佳世; 大久保 潤
  Mar. 2025
  Mar. 2025 - Mar. 2025, Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• Sliding Window を用いたカーネル拡張動的モード分解のオンライン化　　　　　　　　　　　　　　　
  櫻井 大和; 金城 佳世; 大久保 潤
  Mar. 2025
  Mar. 2025 - Mar. 2025, Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• 確率微分方程式を対象としたニューラルネットワーク中間層の可視化とKoopman解析　　　　　　　　　　　　　　　
  濱 晴矢; 大久保 潤
  Sep. 2024
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• オンライン拡張動的モード分解を用いた既知のKoopnan行列の更新　　　　　　　　　　　　　　　
  小柳 尚太; 大久保 潤
  Sep. 2024
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• オンラインEDMDにおける方程式の情報の利用　　　　　　　　　　　　　　　
  太田 一郎; 小柳 尚太; 金城 佳世; 大久保 潤
  Sep. 2024
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• アニーリングマシンにおける制約式を扱う2つの手法のレプリカ交換モンテカルロ法による比較　　　　　　　　　　　　　　　
  岸本 龍弥; 大久保 潤
  Sep. 2024
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• 双対過程における微分方程式系の解法としてのテンソル・トレイン形式　　　　　　　　　　　　　　　
  金城 佳世; 大久保 潤
  Sep. 2024
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• 生成子拡張動的モード分解を用いた決定論的レーザカオスの確率モデル化　　　　　　　　　　　　　　　
  福士 鶴太郎; 大久保 潤
  Sep. 2024
  Japanese, Oral presentation
  共同研究・競争的資金等ID：43806931
• リッジレット変換によるニューラルネットワークのパラメータ初期化手法の改良　　　　　　　　　　　　　　　
  本間 輝; 大久保 潤
  Sep. 2024
  Japanese, Oral presentation
  共同研究・競争的資金等ID：35825151
• Sliding Windowを用いたカーネル拡張動的モード分解のオンライン化　　　　　　　　　　　　　　　
  櫻井 大和; 大久保 潤
  Sep. 2024
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• レプリカ交換モンテカルロ法による組合せ最適化問題の解探索に対するKoopman解析　　　　　　　　　　　　　　　
  直井 達也; 大久保 潤
  Sep. 2024
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• Koopman作用素とテンソル・トレイン形式をニューラルネットワークに使う　　　　　　　　　　　　　　　
  大久保潤
  Jul. 2024, [Invited]
  Japanese, Invited oral presentation
  共同研究・競争的資金等ID：36619934
• Computing Statistics of Stochastic Differential Equations Via Tensor-Train Format　　　　　　　　　　　　　　　
  Kayo Kinjo; Jun Ohkubo
  2024 SIAM Conference on Nonlinear Waves and Coherent Structures, Jun. 2024
  Jun. 2024 - Jun. 2024, English, Poster presentation
  共同研究・競争的資金等ID：36619934
• Reservoir computing with attention mechanism;Improving chaotic time-series forecasting　　　　　　　　　　　　　　　
  Felix Koster; Kazutaka Kanno; Jun Ohkubo; Atsushi Uchida
  The First International Symposium on Photonic Computing, Mar. 2024
  Mar. 2024 - Mar. 2024, English, Poster presentation
• Probabilistic interpretation for leader-laggard relationship in mutually coupled synchronized semiconductor lasers　　　　　　　　　　　　　　　
  Jun Ohkubo; Kakutaro Fukushi; Yuuki Tahara; Kayo Kinjo
  The First International Symposium on Photonic Computing, Mar. 2024
  Mar. 2024 - Mar. 2024, English, Poster presentation
  共同研究・競争的資金等ID：43806931
• 方程式とデータの融合へ向けて: 確率過程の双対性とKoopman作用素　　　　　　　　　　　　　　　
  大久保潤
  Oct. 2023, [Invited]
  Japanese, Invited oral presentation
  共同研究・競争的資金等ID：36619934
• 最適化問題におけるスピン状態の特徴付けとその応用　　　　　　　　　　　　　　　
  佐藤 芳樹; 此島 真喜子; 田村 泰孝; 大久保 潤
  Sep. 2023
  Japanese, Oral presentation
• モンテカルロサンプリングを用いない統計量の計算:双対過程における微分方程式系のテンソル・トレイン形式　　　　　　　　　　　　　　　
  金城 佳世; 大久保 潤
  Sep. 2023
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• カーネル法を用いた拡張動的モード分解へのオンライン学習の適用　　　　　　　　　　　　　　　
  櫻井 大和; 大久保 潤
  Sep. 2023
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• gEDMDを用いた相互結合レーザによる遅延カオス同期の確率モデル化　　　　　　　　　　　　　　　
  田原 悠暉; 大久保 潤
  Sep. 2023
  Japanese, Poster presentation
  共同研究・競争的資金等ID：43806931
• スパイク性を用いた回帰問題の性能向上に向けた正規化手法の提案　　　　　　　　　　　　　　　
  王子 周; 大久保 潤
  Sep. 2023
  Japanese, Poster presentation
• 量子的でない確率過程と量子的な手法の接点と応用　　　　　　　　　　　　　　　
  大久保潤
  Sep. 2023, [Invited]
  Japanese, Invited oral presentation
• 階層型クラスタリングを用いたKoopman作用素の低次元化による計算量削減　　　　　　　　　　　　　　　
  西方 智也; 大久保 潤
  Sep. 2023
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• 双対性を用いた確率微分方程式の統計量計算における基底関数の拡張　　　　　　　　　　　　　　　
  高橋 駿太; 大久保 潤
  Mar. 2023
  Japanese, Poster presentation
  共同研究・競争的資金等ID：36619934
• 確率微分方程式の統計量計算へのフロンティア法の利用と工夫　　　　　　　　　　　　　　　
  濱 晴矢; 大久保 潤
  Mar. 2023
  Japanese, Oral presentation
  共同研究・競争的資金等ID：35825269
• 双対性を利用した確率微分方程式のニューラルネットワークへの埋め込み　　　　　　　　　　　　　　　
  杉下 直輝; 大久保 潤
  Dec. 2022
  Japanese, Oral presentation
  共同研究・競争的資金等ID：35825151
• 記憶ユニットの初期化方法による関数近似性能への影響　　　　　　　　　　　　　　　
  寺澤 悠翔; 大久保 潤
  Dec. 2022
  Japanese, Oral presentation
  共同研究・競争的資金等ID：35825151
• アニーリングマシンにおける相関に基づく連続変数の離散化手法　　　　　　　　　　　　　　　
  古江 友樹; 此島 真喜子; 田村 泰孝; 大久保 潤
  Dec. 2022
  Japanese, Oral presentation
• 確率モデルにおけるポンプカレント現象の最適化と幾何学的描像　　　　　　　　　　　　　　　
  佐野 隆二; 大久保 潤
  Dec. 2022
  Japanese, Oral presentation
• スパイキングニューラルネットワークへの AdaBoost の適用と工夫　　　　　　　　　　　　　　　
  川口 雅也; 大久保 潤
  Sep. 2022
  Japanese, Oral presentation
• ホロノミック勾配法を用いた状態推定の連続時間系への適用　　　　　　　　　　　　　　　
  山本 陸; 大久保 潤
  Sep. 2022
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• 確率微分方程式における組合せ論的な統計量計算手法と計算コスト　　　　　　　　　　　　　　　
  大久保 潤
  Sep. 2022
  Japanese, Oral presentation
  共同研究・競争的資金等ID：35825269
• 確率微分方程式に対する組合せ論的計算と Crank-Nicolson 法　　　　　　　　　　　　　　　
  大久保 潤
  Sep. 2022
  Japanese, Oral presentation
  共同研究・競争的資金等ID：36619934
• Deep Learning Hybrid Models for Sentiment Analysis　　　　　　　　　　　　　　　
  Yunpeng Rong; Jun Ohkubo
  Nov. 2021
  English, Oral presentation
• スパイキングニューラルネットワークにおけるマルコフ情報源の符号化手法の検討　　　　　　　　　　　　　　　
  関根 清貴; 大久保 潤
  Oct. 2021
  Oral presentation
• 常微分方程式に基づくニューラルネットワークの複雑さと精度の数値的研究　　　　　　　　　　　　　　　
  江刺家 郁; 大久保 潤
  Oct. 2021
• イジング形式を用いた組み合わせ最適化問題の難しさの可視化と定量化　　　　　　　　　　　　　　　
  副島 圭市; 此島 真喜子; 田村 泰孝; 大久保 潤
  Oct. 2021
  Oral presentation
• 双対過程に基づくコンピューティングの展開　　　　　　　　　　　　　　　
  大久保 潤
  Aug. 2021, [Invited]
  Nominated symposium
• 誤差逆伝播法を用いたSNNにおける量子化の影響評価　　　　　　　　　　　　　　　
  渡辺 裕美; 大久保 潤
  Oct. 2020
  Japanese, Oral presentation
• Numerical experiments for iterative path-integral method under compound Poisson process　　　　　　　　　　　　　　　
  Hongrui Zhai; Jun Ohkubo
  Oct. 2020
  English, Oral presentation
• Estimation of Water Storage and Drainage of Perlite As Soil for Automated Planter Cultivation　　　　　　　　　　　　　　　
  Yuka Hasama; Yoshiaki Saito; Jun Ohkubo
  Sep. 2020 - Sep. 2020, English, Oral presentation
• 確率微分方程式における双対性を用いた期待値の計算　　　　　　　　　　　　　　　
  大久保 潤
  Mar. 2020 - Mar. 2020, Japanese, Oral presentation
• イジング計算機での利用に向けたl1ノルムのQUBO形式について　　　　　　　　　　　　　　　
  横田 知大; 此島 真喜子; 田村 泰孝; 大久保 潤
  Mar. 2020 - Mar. 2020, Japanese, Oral presentation
• プランタ栽培における含水状態および排水の計測　　　　　　　　　　　　　　　
  挾間 優佳; 齋藤 芳明; 大久保 潤
  Mar. 2020 - Mar. 2020, Japanese, Oral presentation
• ベイズ統計を用いた神経細胞軸索輸送の自動粒子追跡に関する研究　　　　　　　　　　　　　　　
  稗田 康洋; 大久保 潤; 林 久美子
  Mar. 2020 - Mar. 2020, Japanese, Oral presentation
• 双対を用いた計算について　　　　　　　　　　　　　　　
  大久保 潤
  Nov. 2019, [Invited]
  Japanese, Invited oral presentation
  共同研究・競争的資金等ID：24613319
• CEMアルゴリズムを用いたマルウェアのクラスタリング　　　　　　　　　　　　　　　
  レーナン トゥアンアン; 大久保 潤
  Oct. 2019 - Oct. 2019, Japanese, Oral presentation
• word2visualvec を応用したマルウェア亜種推定の枠組みの提案　　　　　　　　　　　　　　　
  横瀬 謙信; 大久保 潤
  Oct. 2019 - Oct. 2019, Japanese, Oral presentation
• 確率過程の双対性を利用したコンピューティング　　　　　　　　　　　　　　　
  大久保 潤
  Mar. 2019, [Invited], [Domestic conference]
  Japanese, Invited oral presentation
• イベント駆動型シミュレーションのサンプリング効率化について　　　　　　　　　　　　　　　
  大久保 潤
  Mar. 2019
  Japanese, Poster presentation
• 土壌の含水状態モデリング　　　　　　　　　　　　　　　
  挾間 優佳; 齋藤 芳明; 大久保 潤
  Mar. 2019 - Mar. 2019, Japanese, Oral presentation
• 強化学習における相互情報量を用いた探索行動の調整　　　　　　　　　　　　　　　
  小山 凱史; 大久保 潤
  Mar. 2019, Japanese, Oral presentation
• ReLU型関数のQUBO形式に関する数値的検証　　　　　　　　　　　　　　　
  佐藤 豪; 此島 真喜子; 大輪 拓也; 田村 泰孝; 大久保 潤
  Mar. 2019
  Japanese, Oral presentation
• 機械学習を利用するための考え方のポイント　　　　　　　　　　　　　　　
  大久保 潤
  Sep. 2018, [Invited], [Domestic conference]
  Japanese, Invited oral presentation
• fastTextを用いたマルウェア亜種判別　　　　　　　　　　　　　　　
  岩元 遼太; 大久保 潤
  Sep. 2018 - Sep. 2018, Japanese, Oral presentation
• 双対性と経路積分を用いた最適制御における補間法の利用　　　　　　　　　　　　　　　
  武田 雄介; 大久保 潤
  Sep. 2018 - Sep. 2018, Japanese, Oral presentation
• Computation based on Duality in Stochastic Processes and Its Application　　　　　　　　　　　　　　　
  Jun Ohkubo
  2018 International Symposium for Advanced Computing and Information Technology (ISACIT 2018), Aug. 2018, [Invited], [International conference]
  English, Keynote oral presentation
• 分割演算子法を用いた確率的勾配法の検討　　　　　　　　　　　　　　　
  鈴木 和磨; 大久保 潤
  Sep. 2017 - Sep. 2017, Japanese, Oral presentation
• ガウシアングラフィカルモデルを用いた動画補修の提案　　　　　　　　　　　　　　　
  藤田 涼世; 大久保 潤
  Sep. 2017 - Sep. 2017, Japanese, Oral presentation
• 二値行列分解のためのイジングモデルの定式化　　　　　　　　　　　　　　　
  中村 崇人; 大久保 潤; 此島 真喜子; 田村 泰孝
  Sep. 2017 - Sep. 2017, Japanese, Oral presentation
• 確率微分方程式のモデル推定の双対性に基づいた数値計算法の提案　　　　　　　　　　　　　　　
  荒井 祐樹; 大久保 潤
  Sep. 2017 - Sep. 2017, Japanese, Oral presentation
• 機械学習を利用するための考え方のポイント　　　　　　　　　　　　　　　
  大久保 潤
  Oct. 2016, [Invited], [Domestic conference]
  Japanese, Invited oral presentation
• 非可換代数と双対確率過程 -- 量子系の手法で古典確率過程を扱う　　　　　　　　　　　　　　　
  大久保 潤
  May 2015, [Invited], [Domestic conference]
  Japanese, Invited oral presentation
• Toward useful and concise descriptions for dynamics in small systems　　　　　　　　　　　　　　　
  Jun Ohkubo
  Minisymposium "Stochastic processes on biological fluctuations" in the joint annual meeting of the Japanese society for mathematical biology and the society for mathematical biology (JSMB/SMB OSAKA 2014), Jul. 2014, [Invited], [International conference]
  English, Invited oral presentation
• Geometric phase discussions for counting statistics　　　　　　　　　　　　　　　
  2013 Taiwan International Workshop on Biological Physics and Complex Systems (BioComplex-Taiwan-2013), Jul. 2013, [Invited], [International conference]
  English, Invited oral presentation
• Application of quantum mechanical formulation to classical stochastic processes　　　　　　　　　　　　　　　
  Kyoto University-Durham University Joint International Symposium 2012: Emergence and Feedback in Physical and Social Systems, Nov. 2012, Various instutites and departments in Kyoto University and Durham University, [Invited], [International conference]
  English, Invited oral presentation
• Applications of concepts and methods in physics to stochasticity in networks　　　　　　　　　　　　　　　
  International Conference on Towards Mathematical Foundations of Complex Network Theory, Sep. 2012, [Invited], [International conference]
  English, Invited oral presentation
• 離散的に観測された時系列データからのモデル再構成　　　　　　　　　　　　　　　
  Jun. 2012, [Invited]
  Japanese, Invited oral presentation
• 計数統計とその周辺　　　　　　　　　　　　　　　
  Sep. 2011
  Japanese, Invited oral presentation
• 非平衡統計力学から見たナノデバイスの情報処理機能　　　　　　　　　　　　　　　
  Mar. 2011, [Invited]
  Japanese, Invited oral presentation

• THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS
• THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS
• THE PHYSICAL SOCIETY OF JAPAN

• Koopman作用素を用いたニューラルネットワークの構築とその応用　　　　　　　　　　　　　　　
  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Apr. 2021 - Mar. 2026
  Saitama University
  Grant amount(Total)：4160000, Direct funding：3200000, Indirect funding：960000
  Grant number：21K12045
  論文ID：48941158, 講演・口頭発表等ID：48233904
• Koopman作用素を用いたレーザダイナミクスの確率的挙動のモデル化　　　　　　　　　　　　　　　
  Apr. 2023 - Mar. 2025
  Grant amount(Total)：6500000, Direct funding：5000000, Indirect funding：1500000
  Grant number：23H04800
  論文ID：47171278, 講演・口頭発表等ID：48233912
• 方程式と双対性でつなぐ革新的データ処理技術の創出　　　　　　　　　　　　　　　
  Apr. 2022 - Mar. 2025
  Principal investigator
  論文ID：48941162, 書籍等出版物ID：49401649, 講演・口頭発表等ID：49544108
• 双対過程に基づくサンプリング不要な統計量計算手法のアルゴリズム論的解析と効率化　　　　　　　　　　　　　　　
  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Transformative Research Areas (A), Grant-in-Aid for Transformative Research Areas (A), Sep. 2021 - Mar. 2023
  Saitama University, Principal investigator
  Grant amount(Total)：5200000, Direct funding：4000000, Indirect funding：1200000
  Grant number：21H05843
  講演・口頭発表等ID：42312298
• 双対過程に基づくコンピューティングの展開　　　　　　　　　　　　　　　
  Oct. 2018 - Mar. 2022
  Principal investigator
  論文ID：40648210, 講演・口頭発表等ID：26885217
• 双対関係を利用した時系列データモデリング手法の構築　　　　　　　　　　　　　　　
  Apr. 2016 - Mar. 2020
  Principal investigator
  Competitive research funding
• 代数的確率論に基づく細胞内反応時系列データ解析手法の開発　　　　　　　　　　　　　　　
  2013 - 2015
  Principal investigator
  Competitive research funding
• Computational study of locomotion, learning, and memory using stochastic analysis methods　　　　　　　　　　　　　　　
  Ministry of Education, Culture, Sports, Science and Technology, Grants-in-Aid for Scientific Research(新学術領域研究(研究領域提案型)), 新学術領域研究(研究領域提案型), 2008 - 2012
  Naoki MASUDA; 大久保 潤, 東京大学, Coinvestigator not use grants
  Grant amount(Total)：33930000, Direct funding：26100000, Indirect funding：7830000
  (抄録なし)
  Competitive research funding, Grant number：20115009
• Development and applications of analytical methods for classical stochastic processes based on condensed matter physics　　　　　　　　　　　　　　　
  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), 2009 - 2011
  OHKUBO Jun, Principal investigator
  Grant amount(Total)：3380000, Direct funding：2600000, Indirect funding：780000
  Inthisstudy, analyticalmethodsforclassicalstochasticprocesseswerestudied. Basedonformalanalogieswithmethodsincondensedmatterphysics, thefollowingtwopointsweremainlyinvestigated, i. e.,(1) arelationshipbetweenquantummechanicalformalismandstochasticprocessesforchemicalreactionsandecosystems, and(2) basicsforcountingstatistics(itsrelationtogeometricphases, andproposalofanumericalmethod). Inaddition, anewapProximationschemeforgeneregulatorysystemswasproposed. Thesestudiesareexpectedtobeusefulnotonlyforphysics, butalsoforlifesciences.
  Competitive research funding, Grant number：21740283
• 確率的情報処理としての複雑ネットワークにおけるコミュニティ検出・制御理論の構築　　　　　　　　　　　　　　　
  2006 - 2006
  Principal investigator
  Competitive research funding, Grant number：06J05140

• 信号分析装置，信号分析方法及びコンピュータプログラム　　　　　　　　　　　　　　　
  Patent right
  Patent/Registration no：特許6112613