The paper presents a polynomial-time algorithm for rescheduling traffic when one track of a double-track railway becomes unavailable, the remaining track has a siding, and there are two categories of trains—priority trains such as passenger trains and ordinary trains such as the majority of freight trains. The presented algorithm minimises the negative effect, caused by the track blockage, first for the priority trains and then for the ordinary trains on the set of all schedules optimal for the priority trains.

In this work, we study the optimal risk sharing problem for an insurer between himself and a reinsurer in a dynamical insurance model known as the Kramer–Lundberg risk process, which, unlike known models, models not per claim reinsurance but rather periodic reinsurance of damages over a given time interval. Here we take into account a natural upper bound on the risk taken by the reinsurer. We solve optimal control problems on an infinite time interval for mean-variance optimality criteria: a linear utility functional and a stationary variation coefficient. We show that optimal reinsurance belongs to the class of total risk reinsurances. We establish that the most profitable reinsurance is the stop-loss reinsurance with an upper limit. We find equations for the values of parameters in optimal reinsurance strategies.

The design problems of robust static controllers for discrete-time systems with norm- bounded parametric uncertainties and random input disturbances are considered. The con- trollers under consideration stabilize the plant for all possible values of uncertainty from a given set of parameters and also guarantee a desired suppression level for random exogenous disturbances. A numerical example is given.

In order to solve robust PageRank problem a saddle-point Mirror Descent algorithm for solving convex-concave optimization problems is enhanced and studied. The algorithm is based on two proxy functions, which use specificities of value sets to be optimized on (min-max search). In robust PageRank case the ones are entropy-like function and square of Euclidean norm. The saddle-point Mirror Descent algorithm application to robust PageRank leads to concrete complexity results, which are being discussed alongside with illustrative numerical example.

The paper is concerned with scheduling the two-way traffic between two stations connected by a single-track railway with a siding. It is shown that if, for each station, the order in which trains leave this station is known or can be found, then for various objective functions an optimal schedule can be constructed in polynomial time using the method of dynamic programming. Based on this result, the paper also presents a polynomial-time algorithm minimising the weighted number of late trains.

A weakening of the property covariance named self-covariance is defined. Sels-covariant solutions are positively homogenous and satisfy a "restricted" translation covariance so that feasible shifts are only the solution vectors and their multipliers. A description of all non-empty, single-valued,efficient,anonytmous, weakly and self-covariant solutions inn the class of two-person games is given. As demonstrated below, among them there exist just three solutions admitting consistent extensions in the Davis--Maschler sense. They are the equal share solution, the stansdard solution, and the constrained ergalitarian solution for super-additive two-person games. For the third solution mentioned, characterizations of some consistent extensions to the class of all TU games are given.

This work is devoted to the problems of information transmission with frequency shift keying and fast frequency hopping in special channels where the signal/noise ratio is low, and a high energy interfering signal is present. We propose a demodulation algorithm that is significantly more stable to the influence of a powerful interfering signal as compared to other known algorithms. Under these conditions, we show a statistical criterion that lets one significantly reduce error probability on the demodulator’s output. For the chosen criterion we prove several lemmas that let us speed up the demodulation algorithm. Computer modeling results show that the proposed demodulation algorithm has better correcting ability under a powerful interfering signal than previously known ones.

We analyze the methods of stochastic and fuzzy comparison and ordering of random and fuzzy variables. We find simple formulas for computing a number of comparisons and establish the interrelations between various comparisons. We propose and study a new approach to comparing histograms of discrete random (fuzzy) variables based on computing a “directed” minimal transformation that maps one of the compared variables into another. We apply the method of minimal transformations to solving the problem of optimal reduction of discrete random (fuzzy) variables to unimodal form which is considered in the context of ranking the histograms of universities constructed by USE (Unified State Exam) results. We propose a model of “perfect” admission for high school graduates and show that the distribution of admitted graduates to a university in this model will be unimodal under sufficiently general assumptions on the preference function.

We consider an optimal portfolio selection problem to track a riskless reference portfolio. Portfolio management strategies are compared taking into account the investor’s temporal preferences. We investigate stochastic optimality of the strategy that minimizes the expected long-run cost, deriving an asymptotical upper (almost sure) estimate for the difference between the values of the objective functional corresponding to the optimal strategy and for any admissible control.

Time consistency is one of the most important properties of solutions in cooperative differential games. This paper uses the core as a cooperative solution of the game. We design a strong time-consistent subset of the core. The design method of this subset is based on a special class of imputation distribution procedures (IDPs).

We study the recognition problem for composite objects based on a probabilistic model of a piecewise regular object with thousands of alternative classes. Using the model’s asymptotic properties, we develop a new maximal likelihood enumeration method which is optimal (in the sense of choosing the most likely reference for testing on every step) in the class of “greedy” algorithms of approximate nearest neighbor search. We show experimental results for the face recognition problem on the FERET dataset. We demonstrate that the proposed approach lets us reduce decision making time by several times not only compared to exhaustive search but also compared to known approximate nearest neighbors techniques.

The paper is concerned with scheduling trains moving in both directions between two stations connected by a single-track railway with a siding. The paper presents dynamic programming based algorithms which minimizes two objective functions: maximum lateness and total weighted completion time. The complexity of these algorithms is O(n2).

This paper considers a network game as follows. In each node of a network, economy is described by the simple two-period Romer’s model of endogenous growth with production and knowledge externalities. The sum of knowledge levels in the neighbor nodes causes an externality in the production of each network node. The concept of node type is introduced and a corresponding typology of networks is suggested. As demonstrated below, all inner equilibria of the game are determined by this typology. For several typologies, the equilibrium knowledge levels are found in explicit form for the nodes that have different positions in the network.

This paper derives upper and lower bounds of the price in the optimal stopping problem for a consistent random sequence in the case of finite horizon. As is demonstrated below, the bounds can be found by solving the maximax and maximin setups of optimal stopping problems. For these setups, we obtain conditions under which 1) a recurrent relation is satisfied for the upper (lower) truncated sequence of optimal stopping prices; 2) an optimality criterion is constructed for the stopping times; 3) the structure and invariance of the optimal stopping times are established. Some examples with explicit solutions of the maximax and maximin setups of optimal stopping problems are given.