Применение асимптотических методов в автоматизированном проектировании технических объектов
The problem of small sample size, i.e. absence of required quantity of empirical data for decision making of rational constructive-technically, in case of computer-aided design of elements, nodes and technical objects’ devices is considered. Randomization approach for blur factor’s determination of nonparametric decision rules is suggested. The approach of Laplace’s method in using cores’ asymptotic bound in case of static model is considered.
Using the weak asymptotic method, we approximate a triangular system of conservation laws arising from the so-called generalized pressureless gas dynamics by a diagonal linear system. Then, we apply the usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how the delta shock wave naturally arises along the characteristics. Also, we propose a procedure that could be applied to more general systems of conservation laws.
We construct a global smooth approximate solution to a multidimensional scalar conservation law describing the shock wave formation process for initial data with small variation. In order to solve the problem, we modify the method of characteristics by introducing “new characteristics”, nonintersecting curves along which the (approximate) solution to the problem under study is constant. The procedure is based on the weak asymptotic method, a technique which appeared to be rather powerful for investigating nonlinear waves interactions.
The Euromicro Conference on Digital System Design (DSD) addresses all aspects of (embedded, pervasive and high-performance) digital and mixed hardware/software system engineering, down to microarchitectures, digital circuits and VLSI techniques. It is a discussion forum for researchers and engineers from academia and industry working on state-of-the-art investigations, development and applications. It focuses on advanced circuit and system design and design automation concepts, paradigms, methods and tools, as well as on modern implementation technologies from full custom in nanometer technology nodes to FPGA and to multicore infrastructures. Compiler assisted ASIP, CMP, SMP, SMT, DSP-VLIW, GPU and platform based system design research results are welcome. Design and Verification Languages and Standards, High Level Synthesis, Efficiency, Density, Signal Integrity, Testability, Timing Analysis and Timing Closure, Asynchronous Techniques, Reconfigurable Architectures, Power Consumption, Computational Power Speed and Performance, Productive Design Technology and Engineering Flows, Manufacturability, Cost, Reliability, Error Resilience, Complexity, or Process Variability issues, Modeling, Design Experiences are covered in DSD.
The paper is discussing a method of increasing the reliability of on-board electronic equipment at the early stages of its design. Authors offer to evaluate and provide deterministic reserves for thermal, mechanical and electrical loads to electronic components using special simulation software. Determinacy of reserves loads on the electronic components is achieved by a result of complex modeling as additional indicators of reliability. The main methods of reliability indicators calculation conducted in enterprises are probabilistic, which are averaged and do not lend themselves to practical verification during testing. Complex modeling of destabilizing effects on the printing circuit board of designed on-board equipment allows to achieve the required reserves on the electrical, thermal and mechanical loads with respect to the maximum permissible temperatures, vibration and shock acceleration in the electronic components, which leads to the guaranteed provision of high levels of reliability.
Probabilistic neural network (PNN) is the well-known instance-based learning algorithm, which is widely used in various pattern classification and regression tasks, if rather small number of instances for each class is available. The known disadvantage of this network is its insufficient classification computational complexity. The common way to overcome this drawback is the reduction techniques with selection of the most typical instances. Such approach causes the shifting of the estimates of the class probability distribution, and, in turn, the decrease of the classification accuracy. In this paper we examine another possible solution by replacing the Gaussian window and the Parzen kernel to the orthogonal series Fejér kernel and using the naïve assumption about independence of features. It is shown, that our approach makes it possible to achieve much better runtime complexity in comparison with either original PNN or its modification with the preliminary clustering of the training set.
In this paper we examine the maintenance decision support in classification of the dangerous situations discovered by the monitoring system. This task is reduced to the contextual multi-armed bandit problem. We highlight small sample size problem appeared in this task due to the rather rare failures. The novel algorithm based on the nearest neighbor search is proposed. An experimental study is provided for several synthetic datasets with the situations described by either simple features or grayscale images. It is shown, that our algorithm outperforms the well-known contextual multi-armed methods with the Upper Confidence Bound and softmax random search strategies.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.