A modification of the decoding q-ary Sum Product Algorithm (q-SPA) was proposed for the nonbinary codes with small check density based on the permutation matrices. The algorithm described has a vector realization and operates over the vectors defined on the field GF(q), rather than over individual symbols. Under certain code parameters, this approach enables significant speedup of modeling.
The result on existence of a pure-strategy symmetric Bayesian Nash equilibrium in the war of attrition is generalized for fuzzy players’ actions and types.
We offer a general approach to describing power indices that account for preferences as suggested by F. Aleskerov. We construct two axiomatizations of these indices. Our construction generalizes the Laruelle-Valenciano axioms for Banzhaf (Penrose) and Shapley-Shubik indices. We obtain new sets of axioms for these indices, in particular, sets without the anonymity axiom.
An axiomatics of power indices in voting with quota was proposed. It relies on the additivity and dictator axioms. Established was an important property that the player’s power index is representable as the sum of contributions of the coalitions in which it is a pivot member. The coalition contributions are independent of the players’ weights or the quota. The general theorem of power index representation and the theorem of representation for a power index of anonymous players were formulated and proved.
We formulate the optimal control problem for a class of nonlinear objects that can be represented as objects with linear structure and state-dependent coefficients. The linear structure of the transformed nonlinear system and the quadratic quality functional let us, in the optimal control synthesis, to pass from Hamilton–Jacobi equations to a state-dependent Riccati equation. The main problem is the implementation of an optimal control problem is related to the search for solutions of this equation in the rate of the object functioning. This paper proposes a method of an algorithmic parameter optimization of the controller based on the use of the necessary conditions for the optimality of the considered control systems. The constructed algorithms can be used both for optimizing the non-stationary objects themselves, if the corresponding parameters are selected for this purpose, and for optimizing the entire managed system by means of the corresponding parametric adjustment of the regulators. The effectiveness of the developed algorithms is demonstrated by the example of medical treatment of patients with HIV.
In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs 1‖maxΣU j . In both cases, it is assumed that the processing of the first job starts at time zero and there is no idle time between the jobs. We show that problem 1‖max-ΣT j is polynomially solvable. For several special cases of problem 1‖maxΣT j , we present exact polynomial algorithms. Moreover, we give an exact pseudo-polynomial algorithm for the general case of the latter problem and an alternative exact algorithm.
We present the basic properties of the a new pattern analysis method in the system of parallel coordinates; results of the method do not depend on the ordering of data in the original sample of objects being analyzed. We prove that clusters obtained with this method do not overlap. We also show the possibility of representing objects of one cluster in the form of monotonically increasing/decreasing functions.
Для передачи по mesh-сети потоковых данных, предъявляющих высокие требования к качеству обслуживания, удобно использовать описанный в стандарте IEEE 802.11s механизм MCCA детерминированного доступа к среде. При использовании этого механизма станции резервируют для своих передач определенные периодически повторяющиеся интервалы времени, тем самым получая бесконкурентный доступ к каналу связи. Однако, чтобы обеспечить успешную доставку данных в условиях помех, необходимо устанавливать дополнительные резервирования под повторные попытки передачи. В работе построена аналитическая модель процесса передачи неординарного потока по многошаговым беспроводным сетям с помощью механизма MCCA. Модель позволяет определить наибольший период резервирований, при котором выполнены требования на время доставки и долю потерянных пакетов.
For the process of order (1,1) spatial autoregression, the consistency and asymptotic normality of the sign estimate were established. The relative asymptotic efficiency of the sign estimate relative to least- squares estimate was calculated, and its behavior under various distributions of the renewing field was considered.