Identification of the parameters of a convection diffusion system

Computational algorithms are proposed for the realization of gradient methods based on the solution of direct and conjugate problems in weak formulations for some complex inverse problems of the recovery of parameters of multicomponent parabolic distributed systems. The approach proposed makes it unnecessary to set up Lagrange functionals in explicit form and to use the Green function. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 42–63, January–February 2009.     

A fast cellular method of matrix multiplication

This paper proposes a cellular method of matrix multiplication. The method reduces the multiplicative and additive complexities of well-known matrix multiplication algorithms by 12.5%. The computational complexities of cellular analogs of such algorithms are estimated. A fast cellular analog is presented whose multiplicative and additive complexities are equal to ≈0.382n³ multiplications and ≈1.147n³ additions, respectively, where n is the order of the matrices being multiplied. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 55–59, May–June 2008.     

Topological-Like Features in Diagrammatical Quantum Circuits

In this paper, we revisit topological-like features in the extended Temperley–Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We describe these quantum circuits and derive characteristic equations for them with the help of topological-like operations. Furthermore, we comment on known diagrammatical approaches to quantum information phenomena from the perspectives of both tensor categories and topological quantum field theories. Moreover, we remark on the proposal for categorical quantum physics and information as described by dagger ribbon categories. The main results in this paper had been presented at the workshop “Cats, Kets and Cloisters” (Computing Laboratory, Oxford University, July 17–23, 2006). Categorical quantum physics and information is proposed as described by dagger ribbon categories. The functor between Abramsky and Coecke’s categorical quantum mechanics and the extended Temperley–Lieb categorical approach is recognized as the same type as those defining topological quantum field theories. On the one hand, fundamental objects in the physical world may be string-like (even brane-like) and satisfy the braid statistics. On the other hand, fundamental particles at the Planck energy scale (or quasi-particles of many-body systems) may obey the braid statistics and have an effective (or a new internal) degree of freedom called the “twist spin”. The name “categorical quantum physics and information” hereby refers to quantum physics and information which can be recast in terms of the language of categories. This is a simple and intuitional generalization of the name “categorical quantum mechanics”. The latter does not yet recognize conformal field theories, topological quantum field theories, quantum gravity and string theories which have been already described in the categorical framework by different research groups. Besides, the proposal categorical quantum physics and information is strongly motivated by the present study in quantum information phenomena and theory. It is aimed at setting up a theoretical platform on which both categorical quantum mechanics and topological quantum computing by Freedman, Larsen and Wang are allowed to stand.     

Models and information technologies for decision support during structural and technological changes

Models, numerical algorithms, and database and software components aimed at decision support during the elaboration of energy-saving measures are considered. Modern methods of nonsmooth optimization are applied to solve relevant optimization problems. The paper partially uses the results of the studies within the framework of the Energy-Saving Program. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 26–49, March–April 2009.     

Construction and Methods of Learning of Bayesian Networks

Methods of learning Bayesian networks from databases, basic concepts of Bayesian networks, basic methods of learning, methods of learning parameters, and the structures of a network and hidden parameters are considered. Basic definitions and key concepts with illustrative examples are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 133–147, July–August 2005.     

Accelerated simulation of failure probability of a system consisting of elements with considerably differing reliability

The failure probability of a system in a given time interval is investigated. Failure and repair distribution functions are assumed to be of a general form. A new accelerated simulation method is proposed that makes it possible to construct estimates with bounded relative root-mean-square errors for systems consisting of components with frequency-different reliability. A numerical example is given. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 48–58, November–December, 1999.     

Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier–Stokes Equations

The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in time of these schemes well combines with the high accuracy in space of spectral methods.     

Finding maximum (in modulus) complex-conjugate eigenvalues of arbitrarily high dimension

Algorithms of determining maximum (in modulus) complex-conjugate eigenvalues are considered as applied to finding eigenvalues of high-dimension matrices according to the Khilenko method. An advantage of the algorithms is that the amount of calculation does not increase exponentially with the dimension of matrices. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 104–110, March–April 2006.     

Finite Volume Discretization and Multilevel Methods in Flow Problems

This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier–Stokes equations. As is well known the use of staggered grids (e.g. MAC grids, Perić et al. Comput. Fluids, 16(4), 389–403, (1988)) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization (Faure et al. (2004a) Submitted, Perić et al. Comput. Fluids, 16(4), 389–403, (1988)), for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equations; the two-, and three-dimensional Navier–Stokes equations introducing new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere (see Faure et al. (2004a) Submitted and Faure et al. (2004b), in preparation).     

Direct methods of solving systems of linear algebraic ef ions with complex a-matrices

Algorithms of computer algebra are proposed for solving systems of linear algebraic equations with complex á- matrices. An analysis of roundoff errors for the computational schemes considered is given. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 144–156, March–April, 2000.     

Methods of detection of program bugs in computer systems

A problem of information protection in computer systems, namely, protection from program bugs, is considered. The existing methods of detection of viruses, program bugs, and other destructive program means are considered. The stages of bug life cycle are shown. A safety filter is proposed, i.e., a protection system based on an on-line multiparameter check of program execution. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 184–188, July–August, 1999.     

Fast retraining of SDM

The functioning of Kanerva’s Sparse Distributed Memory is examined under conditions of changes in data that are to be written at an address. To improve the efficiency of retraining, a modification of the Kanerva writing procedure is proposed. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 40–49, July–August, 1999.     

Systems Specification by Basic Protocols

Theoretical foundations of requirements formalization and verification based on basic protocols are presented. This approach uses the concept of an attributed transition system. Facets of an implementation of the system VRS are described together with some statistical results of using this tool in large-scale industrial projects. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–21, July–August 2005.     

Number of cyclically irreducible words in the alphabet of a free group of finite rank

It is shown that a formula that was independently obtained earlier for the number of cyclically irreducible words of length n in a symmetric alphabet of a finitely generated free group of rank k and the Whitney formula for a chromatic polynomial of a simple nonself-intersecting cycle of length n with a variable λ are mutually deducible from one another when λ = 2k. The necessary bijections differ for even and odd values of n. To the memory of William T. Tutte (05.14.1917–05.02.2002) __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 39–48, July–August 2007.     

Generalized linearly homogeneous production functions

The production functions are considered as functions of values of concave programming problems. Some properties of the functions, in particular, the property of homogeneity and linear homogeneity, are investigated. Examples of the construction of such functions are presented. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 124–132, September–October, 1999.     

Distinctive features of structural programming of synchronous sorting algorithms

Parallel (synchronous) algorithms of sorting arrays are considered. A modified synchronous sorting algorithm based on the pairwise exchange method is proposed and simulated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 122–133, September–October 2006.     

Solving combined inverse problems for multicomponent parabolic distributed systems

The paper outlines a technique to construct computational algorithms for solving combined inverse problems for multicomponent parabolic systems with main and natural inhomogeneous interface conditions. Frechet derivatives are obtained in explicit form for quadratic residual functionals to construct gradient computational algorithms. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 48–71, September–October 2007.     

A priori determination of bounds for the optimal value of variables in integer linear programming problems

The paper outlines a simple technique for determining a narrower interval containing the coordinates of the optimal solution to integer linear programming problems. Computational experiments show that the lengths of the given ranges of variables decreases by 30–90% on average. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 86–93, March–April 2006.     

Approximation processes for resolvent operators

We introduce general sequences of linear operators obtained from classical approximation processes which are useful in the approximation of the resolvent operators of the generators of suitable C ₀-semigroups. The main aim is the representation of the resolvent operators in terms of classical approximation operators. Work performed under the auspices of PRIN 2006–07 “Kolmogorov equations” (coordinator G. Da Prato)     

Moving Mesh Finite Element Methods for an Optimal Control Problem for the Advection-Diffusion Equation

An optimal control problem for the advection-diffusion equation is studied using a Lagrangian-moving mesh finite element method. The weak formulation of the model advection–diffusion equation is based on Lagrangian coordinates, and semi–discrete (in space) error estimates are derived under minimal regularity assumptions. In addition, using these estimates and Brezzi-Rappaz-Raviart theory, symmetric error estimates for the optimality system are derived. The results also apply for advection dominated problems