Department of Information and Computer Sciences, School of Engineering,
/ Graduate School of Science and Engineering,
Saitama University


Graduate School of Science and Engineering, Saitama University,
255 Shimo-Okubo, Sakura-ku, Saitama City, 338-8570, Japan

Research Interests

I have interests in various stochastic phenomena, including their mathematical structures and applications. From the viewpoint of statistical physics (and of mathematics), I have mainly studied stochastic processes. I believe that mathematical tools should be developed furthermore, and the developed mathematical tools could also lead to new useful algorithms for information processing..

Up to now, I have investigated the mathematical structures behind stochastic processes describing chemical reactions in small systems, such as cells, mainly using algebraic methods. In addition, based on the algebraic discussions, a new nonlinear Kalman filter for stochastic differential equations has been proposed.

I have also studied about a geometric phase (a fiber bundle) in counting statistics. In the counting statistics, quantities related to the number of transitions in stochastic processes are calculated. I have mainly developed discussions of cyclic- and noncyclic-nonadiabatic geometric phases for classical stochastic processes, and applied them to pump current problems in small systems and entropy-production problems in nonequilibrium statistical physics.

My current research topics are as follows:

My research topics include analysis of stochastic processes in biological issues, complex networks, and disordered urn model.

Publications (refereed journal papers only)

(under preparation or submitted)


  1. Jun Ohkubo,
    "Numerical methods to evaluate Koopman matrix from system equations",
    J. Phys. A: Math. Theor. Vol. 55, Number 22, Article No. 224007, pp. 1-20 (2022, June).
    Preprint: arXiv:2111.07213

  2. Jun Ohkubo,
    "Connection among stochastic Hamilton-Jacobi-Bellman equation, path-integral, and Koopman operator on nonlinear stochastic optimal control",
    J. Phys. Soc. Jpn. Vol. 90, No. 10, Article No. 104802, pp. 1-9 (2021, October).
    Preprint: arXiv:2012.05514

  3. Kotaro Furuya, Jun Ohkubo,
    "Semi-supervised learning combining backpropagation and STDP: STDP enhances learning by backpropagation with a small amount of labeled data in a spiking neural network",
    J. Phys. Soc. Jpn. Vol. 90, No. 7, Article No. 074802, pp. 1-9 (2021, July).
    Preprint: arXiv:2102.10530

  4. Yuka Hasama, Yoshiaki Saito, and Jun Ohkubo,
    "Water storage and drainage in perlite in container cultivation",
    SICE Journal of Control, Measurement, and System Integration Vol. 14, No. 2, pp. 104-110 (2021, April).

  5. Jun Ohkubo,
    "Combinatorics for calculating expectation values of functions in systems with evolution governed by stochastic differential equations",
    J. Stat. Mech. Vol. 2021, Article No. 013401, pp. 1-18 (2021, January).
    Preprint: arXiv:2005.04393

  6. Jun Ohkubo,
    "Making birth-death processes from backward Fokker-Planck equations for computing expectations in Langevin systems",
    J. Phys. Soc. Jpn. Vol. 89, No. 4, Article No. 044004, pp. 1-6 (2020, March).
    Preprint: arXiv:1906.00125

  7. Tomohiro Yokota, Makiko Konoshima, Hirotaka Tamura, and Jun Ohkubo,
    "Derivation of QUBO formulations for sparse estimation",
    J. Phys. Soc. Jpn. Vol. 89, No. 3, Article No. 034801, pp. 1-5 (2020, February).
    Preprint: arXiv:2001.03715

  8. Jun Ohkubo and Yuuki Arai,
    "Duality in stochastic processes from the viewpoint of basis expansions",
    J. Stat. Mech. Vol. 2019, Article No. 063202, pp.1-13 (2019, June).
    Preprint: arXiv:1902.01050

  9. Go Sato, Makiko Konoshima, Takuya Ohwa, Hirotaka Tamura, and Jun Ohkubo,
    "Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions",
    Phys. Rev. E Vol. 99, Issue 4, Article No. 042106, pp. 1-5 (2019, April).
    Preprint: arXiv:1811.03829

  10. Jun Ohkubo,
    "On dualities for SSEP and ASEP with open boundary conditions",
    J. Phys. A: Math. Theor. Vol. 50, Number 9, Article No. 095004, pp. 1-21 (2017, March).
    Preprint: arXiv:1606.05447

  11. Jun Ohkubo,
    "Duality-based calculations for transition probabilities in stochastic chemical reactions",
    Phys. Rev. E Vol. 95, Issue 2, Article No. 023304, pp. 1-7 (2017, February).
    Preprint: arXiv:1509.07193

  12. Jun Ohkubo,
    "Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes",
    Phys. Rev. E Vol. 92, Issue 4, Article No. 043302, pp. 1-9 (2015, October).
    Preprint: arXiv:1402.2025

  13. Jun Ohkubo,
    "Karlin-McGregor-like formula in a simple time-inhomogeneous birth-death process",
    J. Phys. A: Math. Theor. Vol. 47, No. 40, Article No. 405001, pp. 1-11 (2014, October).
    Preprint: arXiv:1404.2703

  14. Jun Ohkubo,
    "Lie algebraic discussions for time-inhomogeneous linear birth-death processes with immigration",
    J. Stat. Phys. Vol. 157, No. 2, pp. 380-391 (2014, October).
    Preprint: arXiv:1404.5085

  15. Jun Ohkubo,
    "Basics of counting statistics", [INVITED PAPER]
    IEICE Trans. Commun. Vol. E96-B, No.11, pp. 2733-2740 (2013, November).

  16. Jun Ohkubo,
    "Extended duality relations between birth-death processes and partial differential equations",
    J. Phys. A: Math. Theor. Vol. 46, No. 37, Article No. 375004, pp. 1-11 (2013, September).
    Preprint: arXiv:1304.4293

  17. Jun Ohkubo,
    "Algebraic probability, classical stochastic processes, and counting statistics",
    J. Phys. Soc. Jpn. Vol. 82, No. 8, Article No. 084001, pp. 1-7 (2013, August).
    Preprint: arXiv:1210.6735

  18. Jun Ohkubo,
    "Noncyclic geometric phase in counting statistics and its role as an excess contribution",
    J. Phys. A: Math. Theor. Vol. 46, No. 28, Article No. 285001, pp. 1-12 (2013, July).
    Preprint: arXiv:1303.0623

  19. Jun Ohkubo,
    "One-parameter extension of the Doi-Peliti formalism and its relation with orthogonal polynomials",
    Phys. Rev. E Vol. 86, Issue 4, Article No. 042102, pp. 1-4 (2012, October).
    Preprint: arXiv:1206.0062

  20. Jun Ohkubo,
    "Counting statistics for genetic switches based on effective-interaction approximation",
    J. Chem. Phys. Vol. 137, Issue 12, Article No. 125102, pp. 1-6 (2012, September).
    Preprint: arXiv:1209.2217

  21. Jun Ohkubo,
    "Nonparametric model reconstruction for stochastic differential equations from discretely observed time-series data",
    Phys. Rev. E Vol.84, Issue 6, Article No. 066702, pp. 1-9 (2011, December).
    Preprint: arXiv:1107.0647

  22. Jun Ohkubo,
    "Approximation scheme based on effective interactions for stochastic gene regulation",
    Phys. Rev. E Vol. 83, Issue 4, Article No. 041915, pp. 1-9 (2011, April).
    Preprint: arXiv:1009.3085

  23. Jun Ohkubo and Thomas Eggel,
    "Noncyclic and nonadiabatic geometric phase for counting statistics",
    J. Phys. A: Math. Theor. Vol. 43, No. 42, Article No. 425001, pp. 1-11 (2010, October).
    Preprint: arXiv:1004.0075

  24. J. Ohkubo, K. Yoshida, Y. Iino, and N. Masuda,
    "Long-tail behavior in locomotion of Caenorhabditis elegans",
    J. Theor. Biol. Vol. 267, pp. 213-222 (2010, August).
    Preprint: arXiv:1008.3014

  25. Jun Ohkubo and Thomas Eggel,
    "A direct numerical method for obtaining the counting statistics for stochastic processes",
    J. Stat. Mech. Vol. 2010, Article No. P06013, pp.1-8 (2010, June).
    Preprint: arXiv:1002.4247

  26. Jun Ohkubo,
    "Duality in interacting particle systems and boson representation",
    J. Stat. Phys. Vol. 139, No. 3, pp. 454-465 (2010, April).
    Preprint: arXiv:0909.5290

  27. Kazunori Itakura, Jun Ohkubo, and Shin-ichi Sasa,
    "Two Langevin equations in the Doi-Peliti formalism",
    J. Phys. A: Math. Theor. Vol. 43, No. 12, Article No. 125001, pp. 1-12 (2010, March).
    Preprint: arXiv:0912.1652

  28. Jun Ohkubo,
    "Posterior Probability and Fluctuation Theorem in Stochastic Processes",
    J. Phys. Soc. Jpn. Vol. 78, No. 12, Article No. 123001, pp. 1-4 (2009, December).
    Preprint: arXiv:0909.5292

  29. Jun Ohkubo,
    "Variational principle of counting statistics in master equations",
    Phys. Rev. E Vol. 80, Issue 1, Article No. 012101, pp.1-4 (2009, July).
    Preprint: arXiv:0906.5187

  30. Jun Ohkubo,
    "Current and fluctuation in a two-state stochastic system under nonadiabatic periodic perturbation",
    J. Chem. Phys. Vol. 129, Issue 20, Article No. 205102, pp. 1-6 (2008, November).
    Preprint: arXiv:0712.4105

  31. Jun-ichi Inoue and Jun Ohkubo,
    "Power-law behavior and condensation phenomena in disordered urn models",
    J. Phys. A: Math. Theor. Vol. 41, No. 32, Article No. 324020, pp. 1-14 (2008, August).
    Preprint: arXiv:physics/0606068

  32. Jun Ohkubo,
    "Approximation scheme for master equations: Variational approach to multivariate case",
    J. Chem. Phys. Vol. 129, Issue 4, Article No. 044108, pp. 1-8 (2008, July).
    Preprint: arXiv:0806.4017

  33. N. A. Sinitsyn and J. Ohkubo,
    "Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems",
    J. Phys. A: Math. Theor. Vol. 41, No. 26, Article No. 262002, pp. 1-4 (2008, July).
    Preprint: arXiv:cond-mat/0805.2789

  34. Jun Ohkubo, Nadav Shnerb, and David A. Kessler,
    "Transition phenomena induced by internal noise and quasi-absorbing state", [Papers of Editors' Choice]
    J. Phys. Soc. Jpn. Vol. 77, No. 4, Article No. 044002, pp. 1-5 (2008, April).
    Preprint: arXiv:0709.0155

  35. Jun Ohkubo,
    "The stochastic pump current and the non-adiabatic geometrical phase",
    J. Stat. Mech. Vol. 2008, Article No. P02011, pp.1-12 (2008, February).
    Preprint: arXiv:0712.0432

  36. Jun Ohkubo,
    "Condensation phenomena with distinguishable particles",
    Phys. Rev. E Vol. 76, Issue 5, Article No. 051108, pp.1-6 (2007, November).
    Preprint: arXiv:0707.4519

  37. Jun Ohkubo,
    "A field theoretic approach to master equations and a variational method beyond the Poisson ansatz",
    J. Stat. Mech. Vol. 2007, , Article No. P09017, pp.1-13 (2007,September).
    Preprint: arXiv:0708.3713

  38. Jun Ohkubo,
    "Free energy of disordered urn models in the canonical ensemble",
    J. Phys. Soc. Jpn. Vol. 76, No. 9, Article No. 095002, pp.1-2 (2007, September).
    Preprint: arXiv:0705.2104

  39. Jun Ohkubo and Kazuyuki Tanaka,
    "Nonadditive volume and community detection problem in complex networks",
    J. Phys. Soc. Jpn. Vol. 75, No. 11, Article No. 115001, pp.1-2 (2006, November).

  40. Jun Ohkubo, Muneki Yasuda, and Kazuyuki Tanaka,
    "Replica analysis of preferential urn Model",
    J. Phys. Soc. Jpn. Vol. 75, No. 7, Article No. 074802, pp.1-6 (2006, July).
    Preprint: cond-mat/0601193
    (Erratum: Vol. 76, No. 4, Article No. 048001, pp.1 (2007, April))

  41. Jun Ohkubo, Muneki Yasuda, and Kazuyuki Tanaka,
    "Preferential urn model and nongrowing complex networks",
    Phys. Rev. E Vol. 72, No. 6, Article No. 065104(R), pp.1-4 (2005, December).

  42. Jun Ohkubo, Muneki Yasuda, and Kazuyuki Tanaka,
    "Statistical-mechanical iterative algorithms on complex networks",
    Phys. Rev. E Vol. 72, Issue 4, Article No. 046135, pp.1-8 (2005, October).
    Preprint: cond-mat/0507322

  43. Jun Ohkubo, Kazuyuki Tanaka, and Tsuyoshi Horiguchi,
    "Generation of complex bipartite graphs by using a preferential rewiring process",
    Phys. Rev. E Vol. 72, Issue 3, Article No. 036120, pp.1-10 (2005, September).

  44. Jun Ohkubo and Tsuyoshi Horiguchi,
    "Scale-free property of optimal network for packet flow by a packet routing control",
    Physica A Vol. 353, pp. 649-660 (2005, August).

  45. Jun Ohkubo and Tsuyoshi Horiguchi,
    "Complex networks by non-growing model with preferential rewiring process",
    J. Phys. Soc. Jpn. Vol. 74, No. 4, pp. 1334-1340 (2005, April).

  46. Jun Ohkubo, Tsuyoshi Kato, Hirohiko Kono, and Yuichi Fujimura,
    "Molecular alignment in a liquid induced by a nonresonant laser field: Molecular dynamics simulation",
    J. Chem. Phys. Vol. 120, Issue 19, pp. 9123-9132 (2004, May).

Curriculum vitae


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