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- Skorokhodov V. The problem of finding the threshold value in ergodic resource network
Resource network is a graphical model of diffusion proposed earlier in the literature. Every node of the network stores some amount of “resource”. This resource disseminates through networks according to the specified rules. Earlier it was proved that if the total amount of resource in the network does not exceed some threshold value that the diffusion process is equivalent to the random walk in the related Markov chain. The problem of finding the threshold value in ergodic resource network is considered. It is shown that this problem is reduced to solving of system of equations, which describes the principles of redistribution of resource for each node of a network. The $O(n^3)$ complexity algorithm for finding the threshold value in arbitrary ergodic network is developed.
- Zheleznov K. Analysis problem solution with disturbance both in input and output
The conventional approach to disturbances suggests that input and output disturbances are independent. This assumption can lead to inaccurate estimation when input and output disturbances originates from a common source. New tracking problem solution method for linear systems with identical disturbance in both system's input and output is suggested. Our technique is based on semi-definite programming and scalar optimixation. Its higher effectiveness in comparison with conventional method is shown on example task from COMPleib.
- Tikhonov A. Analysis of web structure using generalized navigational routes
Online search engines play an increasingly pervasive role in navigating users to the web pages of their interest. Given the ambitions of any major search engine to be a “one-stop service" for all user needs, it is important to understand the ways users find content on the Web. The proposed way of generalized description of navigational patterns used to learn the ways users approach different pages on the Web depending on the characteristics of these pages. We conducted a comprehensive large-scale study of navigational profiles of different web pages and found that the Web consists of several typical non-overlapping clusters formed by pages of similar ranges of incoming traffic. These clusters can be characterized by the functionality and the purpose of their pages. This approach is useful for finding user tasks that can be supported by search systems but not currently covered by them.
- Barabanov I., Novikov D. Continuous-time dynamic models of mob excitation
The mob excitation control problem is considered using the continuous-time modification of well-known threshold model of collected behavior introduced by Granovetter. Every agent decides whether to participate in a collective action or to be passive. Here we investigate the case when there is a number of agents which are active by default. These agents are called here “provokers”. We analyze the possibility to control the final state of the whole mob. The desired state of the mob is achieved by introducing an appropriate number of “provokers” at each moment of control.
- Gorelov M. Hierarchical games under uncertainty
The two-players hierarchical game is considered. The payoff function of low-level player (agent) depends on a random variable. The low-lever player knows the value of this variable at the moment of decision making. And high-level player (principal) knows only probability distribution on the domain when making his decision. We obtain the optimal strategy for the principal under the assumption that she is trying to maximize the guaranteed payoff. This results are tightly coupled with some work in the theory of contracts.
- Rogatkin A. Estimation of rare events probability in mob behavior
We developå a collective behavior model proposed in [2]. The model is a generalization of the M. Granovetter’s conformity threshold behavior model for the case of uncertainty in agents’ threshold values. We estimate the probability of exit of a system from a given set of states (i.e. in mob excitation) using an asymptotic result derived in [8]. Theoretical estimations of large deviations type are refined using numerical estimations obtained with the help of statistical simulations. Obtained results allow us to estimate stability of excitation prevention in the cases when the probabilities of events are too small for using statistical simulations. We give recommendations on the choice of parameters which guarantee a given probability threshold of exit of the system from a given set of states.
- Lazarev A., Bronnikov S., Gerasimov A., Musatova E., Petrov A., Ponomarev K., Kharlamov M., Khusnullin N., Yadrentsev D. Mathematical modeling of the astronaut training scheduling
Astronauts training is a long-term, complex and expensive process that lasts from two to three years and require individual approach to each participant. The paper presents an attempt to formalize this process. We consider a set of related problems of the astronaut training scheduling. The first problem is to distribute qualifications for various onboard systems between astronauts, i.e. to determine the set of tasks for each astronaut. The second problem is to determine start moments for all considered tasks. For this issue a mathematical models based on integer linear programming and constraint programming are proposed. Computational results of the implemented models and experiments on real data are presented.
- Belyavskyi A., Tomashevich S. Passivity-based method for quadrotor control
In the paper we consider the passification-based adaptive control system for stabilization of a quadrotor. We propose an algorithm of altitude and rotation angle which does not require any information about the parameters of the quadrotor. Also our algorithm takes into account the mutual influence of the quadrotor's pitch and roll. We designed the stabilization system using PD-controller and feedback linearization method. Results of simulation are presented and compared with results of two alternative methods.
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