Friday, December 7. 2018
THE CONCEPT OF DESIGNING AN INTELLECTUAL ROBOT CONTROL SYSTEM BASED ON THE MATHEMATICAL MODEL OF COGNITIVE DIGITAL AUTOMATA
V.V.Kozhevnikov1, B.M.Kostishko1, M.Yu.Leontev1, E.R.Mingachev1, S.V.Pavlov2, V.V.Prikhodko1
1S.P. Kapitsa Technological Research Institute of Ulyanovsk State University, Ulyanovsk, Russia 2Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia
Received: 10 November 2018; accepted in revised form: 04 December 2018
Abstract. An intellectual control system (ICS) to control robots can be built (designed) on the basis of the mathematical model of cognitive digital automata (CDA). The intellectual control system in this case is a software and hardware complex, where the mathematical model of the CDA determines the control system as an intellectual one. The cognitive ability of the mathematical model is determined by the possibility of forming new knowledge based on the knowledge gained at the training stage. The creativity of a mathematical model is determined by the ability to construct sequences (logical chains) of generating new knowledge. A specific feature of the mathematical model of the CDA consists in the fact that the description of the neural network (NN) structure serves as the initial structural scheme of automata, and the logical function "NOT-AND-OR" is used as the neuron model. The mathematical apparatus of Petri nets (PN) is proposed as a tool to construct the mathematical model of the CDA. The structure, composition and algorithm of functioning of the robot’s intellectual control system based on the mathematical model of the CDA is discussed in the paper. In accordance with the algorithm, the ICS operates in three modes: training, manual and automatic control. Training a mathematical model of the CDA can be performed both in the manual mode and in the automatic control mode. The possibility of learning in the automatic control mode, in its turn, provides the possibility of regenerating knowledge and, accordingly, the possibility of cognitive control.
Keywords: intellectual control system, robots, cognitive automata, artificial intelligence, neural networks, machine learning, cognition, thinking, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
c 2018 European Society of Computational
Methods in Sciences and Engineering
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Monday, November 12. 2018
NICOLETA E. TARFULEA DEPARTMENT OF MATHEMATICS, PURDUE UNIVERSITY NORTHWEST, USA
Abstract. HIV can infect cells via cell-to-cell and virus-to-cell transmissions. These two types of transmission may occur in a combined way and enable viral spread. In this paper, we investigate analytically and numerically the influence of these two transmission modes, as well as the viral loss due to infection of T-cells. We introduce, analyze, and compare three mathematical models and show that viral loss due to infection of cells has little effect on the dynamics of HIV. Moreover, we show that additional conditions for the steady state stability are needed when virus-to-cell-transmission is included and a critical value for this parameter is provided. Numerical simulations illustrate the theoretical results and further investigate the differences between these systems.
c 2018 European Society of Computational
Methods in Sciences and Engineering
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Monday, October 15. 2018
N. Chaabane1,a, B. Rivierea, Mikhail Sekachevb and Henri Calandrab aCAAM department, Rice University bTotal E&P Research & Technology USA, LLC 1E-mail: nc33@rice.edu
Abstract: In [7], a sequential approach was
introduced to solve the Biot system where the pressure and displacement
variables are decoupled. A stabilization term was added and the discontinuous
Galerkin method was used to discretize the equations in space and the backward
Euler method was used to discretize the equations in time. The convergence of
the method was established both theoretically and numerically. In this work, we
run several numerical experiments to further validate this approach. Cases with
more complex boundary conditions and realistic input parameters are solved. We
also carry out a strong scalability analysis to show the efficiency of this
method on supercomputers.
c 2018 European Society of Computational
Methods in Sciences and Engineering
Keywords: Poroelasticity; Biot system;
Discontinuous Galerkin; Barry-Mercer; sequential method; parallel
implementation
Mathematics Subject Classiffication: 65M60
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Monday, September 3. 2018
R. Boonklurb1, A. Duangpan2 and T. Treeyaprasert3 1,2Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand 3Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Pathumthani 12120, Thailand
Received 10 January 2018; accepted in revised form 27 August 2018
Abstract: We propose a modified finite integration method (FIM) by using the Chebyshev polynomial, to construct the first order integral matrix for solving linear differential equations in one and two dimensions. The grid points for the computation are generated by the zeros of the Chebyshev polynomial of a certain degree. We implement our method with several examples arose from real-world applications. In comparison with the finite difference method and the traditional FIMs (trapezoidal and Simpson's rules), numerical computations show that our modified FIM using Chebyshev nodes require the less computational cost to achieve significant improvement in accuracy.
c 2018 European Society of Computational Methods in Sciences and Engineering Keywords: Finite integration method, Linear differential equations, Chebyshev polynomial. Mathematics Subject Classication: 65L05, 65L10, 65N30
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Monday, July 16. 2018
V.V. Kozhevnikov1, V.V. Prikhodko1, V.V. Svetukhin1, A.V. Zhukov1, A.N. Fomin1, M.Yu. Leontyev1, D.Ya. Vostretsov1, A.A. Sobolev1, V.I. Skrebtsov1, V.E. Kiryukhin1, V.V. Levschanov1, D.S. Lavygin1, E.M. Chavkin1, E.R. Mingachev1, R.G. Bildanov1, S.V. Pavlov2, V.N. Kovalnogov1
1 S.P. Kapitsa Research Institute of Technology (Technological Research Institute) of Ulyanovsk State University, Ulyanovsk, Russia 2 Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia
Received 29 June, 2018; accepted in revised form 17 July, 2018
Abstract Principal directions of developing the methods for designing intelligent systems of robot control assume technologies based on the use of artificial neural networks. The neural networks, where the model of a neuron was developed as the simplest processor element, performing the computation of the transfer function of a scalar product of an input data vector and a weight vector, can give interesting results regarding generation of dependencies and forecasting. However, their obvious drawback is the lack of an explicit algorithm of action. Memorization of information in the learning process occurs implicitly as a result of selection of the weight coefficients of the neural network, therefore the problem of cognition (the formation of new knowledge) on the basis of those obtained earlier in the learning process seems difficult to resolve. A positive solution to this problem will open the way to the creation of the full-fledged artificial mind. From this point of view the promising area is where the mathematical model of the neural networks is built on the basis of mathematical logic. The intelligent control system in this case is a software and hardware complex, where the mathematical model of the neural network identifies the control system as an intellectual one.
c 2018 European Society of Computational Methods in Sciences and Engineering
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Friday, April 6. 2018
R. Arcucciab1, L.Carracciuoloc and R.Toumid a: University of Naples Federico II, Naples, Italy b: Euro Mediterranean Center on Climate Change, Italy c: National Research Council, Naples, Italy d: Imperial College London, London, United Kingdom
Received 1 February, 2017; accepted in revised form 03 April, 2018
Abstract: Data Assimilation (DA) is an uncertainty quantication technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. As a crucial point into DA models is the ill conditioning of the covariance matrices involved, it is mandatory to introduce, in a DA software, preconditioning methods. Here we present rst results obtained introducing two dierent preconditioning methods in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea by using the Regional Ocean Modeling System (ROMS) with observations provided by the Group of High resolution sea surface temperature (GHRSST). We present the algorithmic strategies we employ and the numerical issues on data collected in two of the months which present the most signicant variability in water temperature: August and March.
c 2018 European Society of Computational Methods in Sciences and Engineering
Keywords: Data Assimilation, oceanographic data, Sea Surface Temperature, Caspian sea, ROMS Mathematics Subject Classication: 65Y05, 65J22, 68W10, 68U20 PACS: 02.70.-c
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Monday, March 26. 2018
O. Ozturk Department of Mathematics, Faculty of Arts and Sciences, Bitlis Eren University, 13000 Bitlis, Turkey
Received 10 October, 2016; accepted in revised form 22 March, 2018
Abstract: Fractional calculus and its generalizations are used for the solutions of some classes of differential equations and fractional differential equations. In this paper, our aim is to solve the radial Schrödinger equation given by the Makarov potential by the help of fractional calculus theorems. The related equation was solved by applying a fractional calculus theorem that gives fractional solutions of the second order differential equations with singular points. In the last section, we also introduced hypergeometric form of this solution.
© European Society of Computational Methods in Sciences and Engineering Keywords: Fractional calculus, Generalized Leibniz rule, Radial Schrödinger equation, Makarov potential Mathematics Subject Classification: 26A33, 34A08
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