Informatica

The characteristics of the polymodallocally strictly monotone pseudoboolean functions and ones having constancy sets are investigated in this paper; the searchal algorithms for their optimization are proposed; analytical investigation of the proposed algorithms effectiveness is carried out. The paper is a continuation of the authors' researches which were begun before.

Error bounds are developed for a class of quadratic programming problems. The absolute error between an approximate feasible solution, generated via a dual formulation, and the true optimal solution is measured. Furthermore, these error bounds involve considerably less work computationally than existing estimates.

Identification problems of linear dynamic systems in the class of parametric mathematical models are considered. A method of calculating of guaranteed estimates of indefinite parameters is proposed. The method is based on the specific semiinfinite extremal problems solution.

Models for determining the electromagnetic fields are considered. The models consist of system of the Maxwell equations in the complete form and in the quasi-stationary approximation. Using the quasi-stationary approximation in media containing nonconducting subdomains is non correct from the physical point of view and give rise to a number of additional mathematical problems. The solutions of the Maxwell equations in the complete form and in the quasi-stationary approximation are compared. Initial boundary value problems are considered for conducting, nonconducting and mixed media. The conditions ensuring the closeness of solutions are established. The estimates are obtained in terms of input data of the problem. In particular, it has been proved that as the ratio of the characteristic rate to the light velocity tends to zero the strength of electric field in the conducting part and the strength of magnetic field in the entire domain, corresponding to the complete problem, converge to the ones corresponding to the approximate problem.

The binary logic functions “AND” and “OR” are realized by the model of a nonlinear stationary dendritic branch. The neuron with such dendrites is a complex logic system performing a great number of elementary logic operations.

In this paper open-loop three-level Stackelberg strategies in deterministic, sequential decision-making problems for linear continuous-time singular systems and quadratic cost function are studied. Necessary conditions under which the existence of open-loop Stackelberg strategies are derived. The analytical solution of three-level open-loop Stackelberg problem is given by means of the eigenvector method. An example is given to illustrate the proposed method.

The smoothing constant λ is the most important characteristic of the nonparametric Parzen window classifier (PWC). The PWC tends to a one-nearest neighbour classifier as λ tends to zero and to a parametric linear Eucliden distance classifier as λ tends to infinity. An asymptotic probability of misclassification of the PWC decreases with the decrease in λ. A sensitivity of the PWC to a finiteness of the training data depends on a true-intrinsic dimensionality of the data, and it increases with the decrease in the value of λ. It is proposed to determine an optimal value of the smoothing constant from a smoothed empirical graph of the dependence of an expected probability of misclassification on the value of λ. The graph can be estimated by means of leaving-one-out or hold-out methods simultaneously for a number of values of λ chosen from the interval (0.001–1000) in a logarithmic scale.