|
|
 Âûïóñê 72
- Gorelov M. The «value at risk» principle in hierarchical game
The two-player hierarchical game is considered. The bottom level player’s payoff is supposed to depend on random factor. The top level player is supposed to know the set of possible values of uncertain factors and probability measure on this set. And he assumes that the bottom level player knows the realized value of random factor when he chooses his control. The optimality principle is new. It is supposed that top level player wishes to obtain maximal possible result with prescribed probability. In such a way the model permits to take into account the inclination to risk of the top level player. Open loop and closed loop models are investigated. In both cases the original setting of the problem contains non elementary operation of choice of a set of negligible values of uncertain factors. The obtained results permit to replace this operation by the operation of calculating of mathematical expectation of random value. In both models the problem of calculating of maximal guaranteed result of top level player and search of his optimal strategy is reduced to calculating a minimax on “finite-dimensional” sets.
- Bibikov P., Streltsova I. On contact integral calabi invariant
The paper is about the problem of the global invariants construction for the action of the group of contact diffeomorphisms on itself by conjugations. The integral invariant is obtained for this action. This invariant is the analogue of the Calabi invariant for the groups of symplectomorphisms of the unit disk. We normalize Cartan form for a given contact diffeomorphism and then consider the volume form on our compact manifold. This volume form is constructed with the help of the normalized Cartan form. The volume of our manifold in relation to this form is our integral invariant.
- Zhozhikashvili A. The equivalence of the two orderings of a set of morphisms with a common domain
In previous works, the author proposed a mathematical language for describing the rules in artificial intelligence. A single production acts over a set of situation, taking one situation as a source and generating the another situation as the result of its application. The concept of pattern for a generalized description of similar situations is important in this theory. Both the situation and the pattern are coded in the proposed language by morphisms of the appropriately chosen category. Samples can be ordered by a degree of generality. Two methods of such ordering could be considered. We can assume that the first pattern is more general than the second one if the second can be obtained by specifying the first. We also can assume that the first pattern is more general than the second if each situation, suitable for the first pattern, is suitable for the second one. These two ways of ordering are close but not identical. The reformulation of these two definitions in the language of a category theory leads to the mathematical problem of comparing of two ways of ordering a certain set of morphisms. An article is devoted to an investigation of this problem.
- Glushchenko A. On development of neural network learning rate calculation method to adjust linear controllers online solving nonlinear plant control problem
The problem of a neural network learning rate calculation for online training process is considered. The network is a part of a neural tuner used to adjust linear P-/PI-controllers parameters in real time. Its outputs are the controller parameters values. The problem under consideration is closely related to a control system sustainability estimation, as too high learning rates might make the system unstable. So we propose an approach based on the second Lyapunov’s method to calculate learning rate upper acceptance limit for different situations without knowing the plant model. Modeling and laboratory experiments have been conducted using typical plants of heating furnaces and DC drives classes to prove the method reliability. Having analyzed obtained results, the conclusion can be made that for both plant classes learning rate estimations allow to keep the control system stable. At the same time, constant usage of maximum allowed value of the learning rate during the online training process may result in the plant energy efficiency decrease.
- Fedin G. Applying the robust approach for the transportation hubs with access roads location problem in the geographical region with existing transportation system
This paper presents the problem of transportation hubs location with access to roads within the existing regional transportation system. In this problem the decision maker minimizes the total cost, which includes expenses for constructing transportation hubs, building access roads for different means of transport to transportation hubs and transporting cargo between clients and transportation hubs. The goals of this paper are: 1) to classify formulations of various transportation hubs location problems; 2) to review most recent scientific papers considering these problems; 3) to formulate a new problem of hubs location with access roads as a mixed-integer linear programming problem and robust optimization one; 4) to test a proposed model on a transport system of a part of Russia. Our numerical tests confirm that both mixed-integer linear programming problem and robust optimization problem stated in this article can be solved for real-size transportation networks via standard optimizations software on a personal computer in short time.
- Vasilyev I., Chebotarev P. Making a typology of scientists on the basis of bibliometric data
In this paper, we propose a set of indicators for solving the problem of differentiation and stratification of scientists on the basis of bibliometric data using cluster analysis. The indicators include three standard citation indexes and five structural indexes characterizing the citation curve of a researcher. The latter indicators are defined in terms of increments of the annual citation rate, which characterize the time convexity of the total number of references. Ward's hierarchical clustering algorithm is applied to some sets of mathematicians, physicists, and psychologists with high citation rates. The analysis of the obtained results allows one not only to describe several stable types of scientists, but also to study the differences between distinct groups of scientists in various scientific disciplines. For mathematicians and physicists, three groups, “youth”, “luminaries”, and “inertial”, can be clearly distinguished, regardless of the way of clustering. The proportions of the corresponding groups are relatively stable and similar. In addition, among the mathematicians, a group “precocious” manifests itself, while among physicists, we observe a group of scholars who “caught the wave”. For psychologists, the clusters are essentially different. In many cases, the cluster structures revealed with and without standard citation indexes turn out to be similar.
- Malyshenko V., Malyshenko K. Modeling of the enterprise financial standing in the framework of the developing regional stock market fundamental analysis
The system of enterprise financial stability types for the investment assessment of potential objects has been developed on the base of the enterprises of the sanatorium and resort complex of Greater Yalta. This system can be used as the basis for obtaining objective information under conditions of limited application of stock market analytical methods. The information on investment objects severely restricted or have a form not-acceptable for the implementation of traditional analytical methods. The restricted stock market data about prices of financial assets of issuer (not submitted to the stock market) limits the application of forecasting methods. In this situation, a "hybrid" approach that combines the well-known coefficients of financial statements and methods of technical analysis provides more precisely prediction of complex financial stability.
- Samartsev A., Ivaschenko V., Rezchikov A. et al. Multiagental model of process of evacuation of people from industrial premises in case of emergency
A model of Fire Emergency Evacuation process from industrial premises based on the theory of multi-agent systems is proposed in this paper. The distinctive feature of the proposed model is in combining the formal description of agents physical interactions using an adaptive model of partially elastic collision with the rules defining the agents behavior. The correction of agents speed at each step of modeling time allows to reduce the time of their moving towards the exit from the premise. The model allows to investigate people locations and their movings in the fire emergency situation and to find the evacuation time. The proposed model can be used as a basis for finding directions of people evacuation and developing fire emergency evacuation plans.
|
|
