The minimax estimations of the scalar product ⟨l, x(N)⟩ are obtained on the basis of observations y(k) = H(k)x(k) + η(k) up to N − 1 moment assuming that l ∈ L ⊆ Rn, x(k) is a solution of the difference equation S(k + 1)x(k + 1) = A(k)x(k) + f(k), x(0) = f0 with some rectangular matrix S(k) of rank p(k), f0, f(k) – are unknown vectors, η(k) – is random vector with unknown correlation matrix R(k), M η(k) ≡ 0.
Все статьи журнала
Журнал:
The estimate for the assymetry of a face of a man by its 3D model is proposed in the paper. It contains the detailed algorithm constructed for this estimate calculation. The used face modes are obtained by a methof of 3D scanning and are represented in the form of points cloud. The problem of detection of a face symmentry plane is solved. The algorithm was tested on 200 samples of face models. This testing shows the stability of the proposed estimate.
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Global optimization problems associated with cryptographic analysis of asymmetric ciphers. The aim of this article is to establish relation between well-known problems of cryptographic analysis and global optimization problems which can be associated with SAT representation of cryptographic algorithms where bits of key is part of SAT solution string. There was constructions SAT forms for factorization problem, SAT forms for logarithmic problem and logarithmic problem on elliptic curves.
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The double inequality V CD(S) ≤ Kl(S) < V CD(S) log l is proven, where V CD(S) is the Vapnik —Chervonenkis Dimension of some collection of general recursive functions, Kl(S) is the Kolmogorov’s complexity of this collection S, l is the length of data set (sample) which is shattered by S. The novel pV CD approach for V CD estimation based on above inequality is suggested.
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The automatic classification (cluster analysis) complex algorithm, that was especially developed for intellectual complex-organized data handling and decision support problems, is described.
It includes: the m-local optimization algorithm with the predetermined classification performance criterion, the informative parameters selection algorithm, the initial fragmentation algorithm, the missing observation filling algorithm.
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The analysis and forecasting within the loosely-formalized multivariate control system, consisting of sufficiently large number of a priori non-structured objects, problem solution method is proposed. As a forecasting model for each object the markovian chain with rstates, where r - the number of structural units (classes), is used.
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Authors describe the technique developed by them of predicate word's possible deep syntactic valences. S characteristics's values's automatic retrieval, Initial data are elements of lexicographic interpretation. The idea of algorithm of recognition of semantic valencies's role orientations is in more detail considered.
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All groups concidered in this paper are finite. The main aim in this note is receipt bounds of derived π-length for a π-soluble group depending on nilpotent π-length and derived length of π-Hall subgroups.
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In this paper,we consider the problems arising when input-output operations are planed. The main factors defining data processing on input-output stage are presented. The new approach to resolve above problems are presented.
Журнал:
In this paper,we consider the problems arising when input-output operations are planed. The main factors defining data processing on input-output stage are presented. The new approach to resolve above problems are presented.
Журнал:
The paper considers approach to the image recognition problem that is based on random Gibbs fields. Estimation of parameters of Gibbs models. One of the possible approach to this problem is maximum
entropy principle. According to this principle we should seek such distribution which is as non-informative as available prior information. the paper suggests another approach, which seeks such distributions, for which maximum and minimum values of probabilities of random object is attained.
Журнал:
We consider an approach to the learning by precedents problem based on the minimization of the required function model complexity. Such notions as function model, function class template, function model complexity, function complexity are introduced. The described method is used to solve the problem of pseudo-Boolean function reconstruction by precedents.
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By a stochastic Leontief type equation we mean a special class of stochastic differential equations in the Ito form, in which both in the left-hand and right-hand sides there are rectangular real matrices that form a singular pencil. Besides, in the right-hand side there are a deterministic summand, depending only on time, and impulse action. It is supposed that the diffusion coefficient of the system is given by a matrix depending only on time.
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Let $G$ be a finite unitary reflection group acting on the $n$-dimensional unitary space $U^n.$ Then $G$ acts on the polynomial ring $R = C[x_1,\dots,x_n]$ in a natural manner and there exists $n$-tuple $m_1 \ge m_2 \ge \dots \ge m_n$ of positive integers, such that the algebra $I^G$ of all $G$-invariant polynomials is generated by $n$ algebraically independent homogeneous polynomials $f_1(x_1,\dots, x_n),\dots, f_n(x_1,\dots,x_n) \in I^G$ with deg $f_i = m_i$ (a system of basic invariants of group $G$) [1].
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Let $m$ be the usual Lebesgue measure on $\mathbb{R}_+ = [0,+\infty)$. Dealing with symmetric (rearrangement invariant) spaces $\mathbf{E}$ on the standard measure space $(\mathbb{R}_+,m)$, we treat the following embeddings:
$$
\mathbf{L}_1\cap\mathbf{L}_\infty \subseteq \mathbf{\Lambda}^0_{\widetilde{V}}\subseteq \mathbf{E}^0\subseteq \mathbf{E}\subseteq \mathbf{E}^{11}\subseteq \mathbf{M}_{V_*} \subseteq \mathbf{L}_1+\mathbf{L}_\infty ,
$$
Журнал:
Let $A$ be a linear dissipative operator with dense domain $\mathfrak{D}(A)$ in Hilbert space $\mathfrak{H}$ and $−i \in \rho(A)$. We consider the self-adjoint operators $B = iR−iR^\ast−2R^\ast R, \widetilde{B} = iR−iR^\ast−2RR^\ast,$ where $R = (A + iI)^{−1}.$ Let $Q = \sqrt{B}, \widetilde{Q} = \sqrt{\widetilde{B}}, \mathfrak{H}_1 = \overline{Q\mathfrak{H}}, \mathfrak{H}_1 = \overline{\widetilde{Q}\mathfrak{H}}.$
Журнал:
Let $G_1$ and $G_2$ be two joined bodies with masses $m_1$ and $m_2$. Each of them has a cavity partially filled with homogeneous incompressible viscous fluids situated in domains $\Omega_1$ and $\Omega_2$ with free boundaries $\Gamma_1(t)$, $\Gamma_2(t)$ and rigit parts $S_1$, $S_2$. Let $\rho_1$, $\rho_2$ be densities of fluids. We suppose that the system oscillates (with friction) near the points $O_1$, $O_2$ which are spherical hinges.
We use the vectors of small angular displacement
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The solution finding of the linear programming problem with incomplete information and reconstruction of model parameters is investigated.
Журнал:
In the paper, we study the Cauchy problem for the differential second-order equation in Hilbert space $\mathscr{H} = H_1 \oplus H_2$ of the following form
$$\mathscr{C}\frac{d^2u}{dt^2} + \mathscr{B}_0u = f(t),\quad u(0) = u^0,\quad u^\prime(0) = u^1,$$
$$
\mathscr{C} =
\left(
\begin{matrix}
I_1& 0\\
0& A
\end{matrix},
\right),\quad
\mathscr{B}_0 =
\left[
\left(
\begin{matrix}
0& 0\\
0& N
\end{matrix}
\right)
+
\left(
Журнал:
Let a rigid immovable vessel be partially filled with an ideal incompressible stratified fluid.
We assume that in an equilibrium state the density of a fluid is a function of the vertical variable
$x_3$, i.e., $\rho_0 = \rho_0(x_3)$. In this case the gravitational field with constant acceleration $\overrightarrow{g} = −g\overrightarrow{e_3}$ acts
on the fluid, here $g > 0$ and $\overrightarrow{e_3}$ is unit vector of the vertical axis $Ox_3$, which is directed opposite
Журнал:
In this paper, consider the n-person normal form game under uncertainty. Many coalition related concepts of equilibrium or solutions have been introduced for n-person normal form games. The main initial motivation for the inception of this direction of research is to overcome one of the drawbacks of Nash equilibrium (NE), namely, NE is not immune against coalition deviation. A coalition may improve the payoff of all its members by collectively deviating from NE. In this article, the Coalitional Equilibrium (CE), is introduced for normal form games under uncertainty.
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The sufficient conditions of the existence of Berge equilibrium situation in noncooperative game of many persons in normal form are established. On the basis of these conditions the existence of Berge equilibrium situation in mixed strategies (by compact sets of strategies of players and continuity of their payoff functions) is proved. Let us consider the history of the appearance of the Berge equilibrium notion.
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Necessary familiar concepts from fuzzy numbers theory and interval systems are presented in the article, namely, concepts of: a fuzzy number; the carrier and the membershi function of fuzzy number; a discrete and continual fuzzy number; an interval matrix; low and upper bounds of an interval matrix; a middle matrix; a matrix of radiuses; an interval vector; low and upper bounds of an interval vector; a middle vector; the vector of radiuses.
Журнал:
Let $G$ be a finite unitary reflection group acting on the $n$-dimensional unitary
space $U^n$. The algebra $I^G$ of $G$-invariant polynomials is generated by n algebraically independent
homogeneous polynomials $f_1(x_1, . . . , x_n), . . . , f_n(x_1, . . . , x_n)$ of degrees $m_1 \leqslant m_2 \leqslant · · · \leqslant m_n$ (a
system of basic invariants of group $G$) [1]. According to [4] (cf. [2]) a system ${f_1, . . . , f_n}$ of
basic invariants is said to be canonical if it satisfies the following system of partial differential
Журнал:
Problem of exploration finite graphs by three agents is considered. Constructed an algorithm for exploration undirected graphs with $O (n^2)$ (n is amount of nodes of graph) time and space complexities. Two agents (which move on graph) needs two different colors (in total three colors) for graph exploration. An algorithm is based on depth-first traversal method.
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In this paper dynamical system with fixed switching points is considered. Existence conditions for a solution of a structural and parametric optimization problem in a class of structural controls and sufficient conditions for optimality are proved. A numerical method for structural optimization of linear system with quadratic functional is created.
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Considered the mathematical model of the flow of the river Tisza in view the maximum cost flows. Determined of the value of maximum flows by the method of bandwidth analysis. Provided recommendations on further use of this method.
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Formula of the evaluating of multiple integrals with using Lagrange polynomial interlineation was submitted. Cubature formula is investigated in the case when information about function is set of values on lines in $G = [-1, 1]^2$ on the class of functions with condition $|f^{(p_1, p_2)} (x, y)| \le M$. The estimation of error of approaching of the cubature formula is presented.
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We introduce strategies for parallelizing a sequential local elimination algorithm for sparse discrete optimization problems. The local elimination procedure exploits the structure of the underlying problem graph using extended elimination tree. We propose to use hybrid Master-Worker scheme where worker processors (GPUs) solve concurrently subproblems corresponding to super-nodes of extended elimination tree that are generated by a single master process (CPU).
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Authors propose an algorithm of computing block-tree structure for sparse matrices. Finkelshtein’s algorithm for constructing quasiblock structures is modified and implemented. Preliminary benchmarking with test problems was done. Quality of computed quasiblock structures is investigated.