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Dr Alexander Plakhov

WIMCS Research Fellow and Lecturer

Specialist Subjects: Dynamical Systems, billiards, Monge-Kantorovich optimal mass transportation, Newton's problem of minimal resistance and aerodynamics of motion in rarefied media, scattering and integrability of classical Hamiltonian systems, Coxeter groups, stochastic approximation, spectrum of random matrices, probabilistic methods in graph theory, artificial neural networks, learning algorithms and application to REM sleep modeling.

List of Publications

 

  1. On multi-particle systems on a straight line with a triangular scattering reflection. Russ. Math. Surv. 37, 133-134 (1982).
  2. Scattering in multi-particle systems on the line with polynomial descent of potential. In Functional Analysis and its Applications in Mechanics and Probability Theory, Moscow University press, 72-78, in Russian (1984).
  3. Scattering in multi-particle systems on the line. Preprint No 918-85, Academy of Science of the USSR, 49 pp., in Russian (1985).
  4. Scattering mapping of classical Hamiltonian systems. Ph.D. Thesis. Moscow State University, in Russian (1986).
  5. Electromagnetic structure and scattering of neutrinos in an isotropic medium (with V. N. Oraevsky, V. B. Semikoz and Ya. A. Smorodinsky). Sov. Phys.-JETP 66, 890-896 (1987).
  6. Solitary waves in paramagnetic media (with S. A. Semenov). In Studies on Dynamic Properties of Distributed Media, Moscow, p. 30-40, in Russian (1989).
  7. Models of memory in a network of coupled oscillators (with S. A. Semenov and O. I. Fisun). In Applications Aspects of Analysis of Distributed Systems, Moscow, p. 11-21, in Russian (1990).
  8. Oscillatory model of neural networks (with O. I. Fisun). Math. Modeling 3, 48-54, in Russian (1991).
  9. Topological models of associative memory in neural networks (with S. A. Semenov). In Dynamic Processes in Complicated Systems, ed. L.N. Lupichev, Moscow, p. 29-43, in Russian (1991).
  10. A circular neural network supporting information waves (with S. A. Semenov). Europhys. Lett. 18, 201-206 (1992).
  11. A modified unlearning procedure for reaching perfect storage in neural networks (with S. A. Semenov). In Processes and Structures in Open Systems, ed. L.N. Lupichev, Moscow, p. 50-56, in Russian (1992).
  12. Short-term memory in a sparse clock neural network (with S. A. Semenov). J. Phys. I France 3, 767-776 (1993).
  13. An unlearning-type procedure for the self-correction of Hebbian connectivity (with S. A. Semenov). Neural Network World 4, 405-412 (1993).
  14. Neural networks: Iterative unlearning algorithm converging to the projector rule matrix (with S. A. Semenov). J. Phys. I France 4, 253-260 (1994).
  15. Unlearning dynamics in the Hopeld neural network. Izv. Vuzov - Radiofysika 37, 1104-1115, in Russian (1994).
  16. Convergence theorems of iterative learning algorithms for attractor neural networks (with S. A. Semenov). In Nonlinear Phenomena in Open Systems, ed. L.N. Lupichev, Moscow, p. 93-105, in Russian (1995).
  17. On the asymptotic behavior of a class of random matrix iterations. Fund. Appl. Math. 1, 1009-1018, in Russian (1995).
  18. On the distribution of eigenvalues in some ensembles of large random matrices. Fund. Appl. Math. 3, 903-923, in Russian (1997).
  19. Limit behavior of the spectrum in a class of large random matrices. Func. Anal. Appl. 31, 140-142 (1997).
  20. Scattering and Coxeter groups (with A. M. Stepin). Russ. Math. Surv. 53, 401-402 (1998).
  21. Parameter adaptation in stochastic optimization (with L.B. Almeida, T. Langlois, and J. D. Amaral). In On-Line Learning in Neural Networks, D. Saad (ed.), Cambridge University Press, 111-134 (1998).
  22. Scattering in multiparticle and billiard dynamical systems (with A. M. Stepin). Sbornik: Math. 190, 1005-1033 (1999).
  23. Newton's problem of a body of minimal aerodynamic resistance. Dokl. Akad. Nauk 390, 314-317 (2003).
  24. Newton's problem of the body of minimal resistance with a bounded number of collisions. Russ. Math. Surv. 58, 191-192 (2003).
  25. A stochastic approximation algorithm with step size adaptation (with Pedro Cruz). J. of Math. Sci. 120, 964-973 (2004).
  26. Relation between the Kendall and Spearman coefficients and concordance graphs. J. of Math. Sci. 120, 988-994 (2004).
  27. Newton's problem of minimal resistance for bodies containing a half-space. J. Dynam. Control Syst. 10, 247-251 (2004).
  28. Newton's problem of the body of minimum mean resistance. Sbornik: Math. 195, 1017-1037 (2004).
  29. Precise solutions of the one-dimensional Monge-Kantorovich problem. Sbornik: Math. 195, 1291-1307 (2004).
  30. Bodies of minimal aerodynamic resistance in dilute media with thermal motion of the particles. Doklady Math. 72, 495-498 (2005).
  31. Newton's aerodynamic problem in media of chaotically moving particles (with Delm Torres). Sbornik: Math. 196, 885-933 (2005).
  32. Optimal control of Newton-type problems of minimal resistance (with Delm Torres). Rend. Sem. Mat. Univ.Pol.Torino 64, 79-95 (2006).
  33. Billiards in unbounded domains reversing the direction of motion of a particle. Russ. Math. Surv. 61, 179-180 (2006).
  34. Problems of maximal mean resistance on the plane with Paulo Gouveia). Nonlinearity 20, 2271-2287 (2007).
  35. A stochastic approximation algorithm with multiplicative step size adaptation (with Pedro Cruz).
  36. Billiards and two-dimensional problems of optimal resistance.
  37. Billiards, optimal mass transport and problems of optimal aerodynamic resistance.

PhD Agregacao

 

Mathematical and Physical Sciences

Aberystwyth University

Tel: 01970622771

Fax: 01970622826

Email: axp@aber.ac.uk