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 Âûïóñê 64
- Pyanykh A. Modified multistage bidding model with a countable set of states
A simplified financial market model with two players bidding for one unit of a risky asset for several consecutive stages is considered. First Player (an insider) is informed about the liquidation price of the asset which can take any value in $\Z_+$. At the same time Second Player knows only probability distribution $\p$ of the price and that First Player is an insider. At each bidding stage the players place integer bids. The higher bid wins and one unit of the asset is transacted to the winning player at the cost equal to a convex combination of the bids with some coefficient $\beta$. After each stage the bids are announced to the players. In this paper we obtain a solution to an infinitely long zero-sum game for distributions $\p$ with finite variation. The optimal strategy of the insider player generates a non-symmetric random walk of the asset price which supports the hypothesis that stock price fluctuations have a strategic origin.
- Rezchikov A., Kushnokov V., Ivaschenko V., Tsesarskiy L., Bogomolov A., Filimonyuk L., Adamovich K. Analysis and forecast of air transportation safety: system dynamics modeling
We developed a complex of system dynamics models intended to analyze and forecast key safety characteristics of an air transportation system. The models use the graph of causal relationships where graph nodes represent characteristics of the transportation system and links represent causal relationships between different characteristics. The graph defines a system of nonlinear differential equations. The regression parameters were estimated from official historical data since 1992 to 2009 years. The causal graph includes system variables such as the number of incidents per year and external parameters such as average pilot flying hours etc. The quality of the model was evaluated on 2010-2013 years incidents statistics in CIS. Our model was able to predict the number of incidents with reasonable accuracy. The additional analysis shows that the system obtained can demonstrate chaotic behavior under specific parameter values. The proposed model can reveal trends in the analyzed safety characteristics of an air transportation system.
- Emelianova Ju. Stabilization of Nonlinear 2D- Fornasini--Marchesini System
The paper considers nonlinear 2D-system described by Fornasini-Marchesini state-space model. Sufficient conditions for the property of exponential stability are developed in terms of vector Lyapunov functions and a converse stability theorem is proved. A form of passivity, termed exponential passivity, is defined and used together with a vector storage function. This technique makes it possible to develop a new control law design algorithm to guarantee exponential stability of the system. As an example the algorithm is applied to a physically relevant case of systems with nonlinear actuator dynamics. Further research will focus on two directions. In earlier work linear Fornasini-Marchesini model was applied to a high-precision rolling system. The results of this paper can be useful to devise a nonlinear control system that will improve the efficiency. Other possible application is related to discrete approximation of Darboux differential equations systems which leads to Fornasini-Marchesini equations. Our results can be applied to problems of this sort.
- Application of multi-agent technologies to transportatIon problem with time windows and multiple depots
In this paper a multi-agent approach to MDVRP (Multiple Depot Vehicle Routing Problem with Time Windows) problem is presented. The multi-agent system consists of interacting trucks, depots and orders interacting in an artificial environment. Truck agents are seeking to maximize the number of orders delivered with minimal route cost. Order agents are looking for a truck with minimal tariff. Depot agents are in charge for the whole coordination. Every agent can interact only with agents in its local neighborhood. The performance of the system depends on the number of messages processed by every agent. Delaney triangulation based scene structure is proposed to limit the intensity of agent negotiations. The system was evaluated on a number of testbed problems known from literature. It's shown that solutions obtained by the method proposed is worse by 10-30% from best known solutions, but the method is quick enough and then can be applied in real-time systems.
- Edge scaling of computing systems
The problem we consider is how to increase a parallelization potential of tasks in a computing system not extending the number of its processor units. Our approach is to introduce additional links to initial system topology but preserve all existing links, addressing and routing policies. We provide a general formulation of the proposed approach and detailed description for systems with hypercube topology. In an edge scaled hypercube the conventional addressing scheme is enhanced by inverse addressing. We demonstrate that bisection bandwidth of the modified network is twice as high as of conventional hypercube and the diameter is twice as low. We obtain the scalability functions of a limit parallelization and a topological scalability on tasks with limited path length between branches. The proposed network modification can be applied to a limited k-dimensional fragment of the network with adaptive k selection. The impact on reliability of such systems will be covered in future research.
- Information equilibrium in dynamic model of collective behavior in a competitive market
The article presents a dynamic model of reflexive behavior which provides a unified approach to description of interactions of Cournot/Stackelberg agents in a competitive market in the absence of common knowledge. The approach based on game theory and the theory of collective behavior with incomplete information. The model is a conventional Cournout output competition with linear costs and the inverse demand function. Rational agents in the model have incorrect initial beliefs about marginal costs of their competitors. We investigate two cases: (1) all agents act simultaneously and (2) first agent is a Stackelberg leader. We study repeated interactions when the agents dynamically update their actions and beliefs based on observed actions of their competitors. A unified procedure of beliefs update is provided for both cases. Necessary and sufficient conditions for the convergence of dynamic processes to the equilibrium with true beliefs are obtained. The results are illustrated with numerical examples.
- Consensus in social networks with complex structure of social actors
We study opinion dynamics in network structures of a special type: each node consists of two agents interacting among themselves. The external agent interacts with the rest of the network and the internal agent interacts only with the external one. For example, every external agent has a personal advisor who doesn’t participate directly in the negotiations. We investigate properties of the consensus arising in these network structures under conventional de Groot opinion dynamics model and how the final influences depends on the mutual trust between external and internal agents. The analytical solution for the vector of final influences was obtained. We show that the final influence of a node depends monotonically on the trust between external and internal agents. It was shown for the two-node case under what conditions the internal parameters of a node are more important than the external ones. Our results can potentially be extended to the networks where nodes have more complex internal structure.
- Patients admission process analysis in a large clinic by collective multivariate expertise methods
The article describes multivariate expertise methods applied to analyse the hospitalization process in a large clinic (N.N. Burdenko’s Scientific Research Neurosurgery Institute of Health Ministry of Russia, as an example). More than 7000 operations are performed in the clinic every year and the end-to-end treatment process requires optimization. We consider different aspects of the treatment process: admission in the emergency department, multiple characteristics of stay in surgical wards and surgery unit itself. Our goal was to reduce the admission and surgery waiting times. Our approach was to formally organize collective expertise involving both the clinic staff and external specialists as the experts. The formal expertise procedure revealed some solutions that were difficult to foresee on the common sense basis. We use data provided by the hospital information system to evaluate the effect of various implemented proposals. The formal collective expertise reduced the waiting time significantly and becomes a solid foundation for further optimization decisions such as hiring additional nurse.
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