Showing papers in "International Journal of Computer Mathematics in 2008"
TL;DR: A Chebyshev finite difference method has been proposed in order to solve linear and nonlinear second-order Fredholm integro-differential equations to demonstrate the validity and applicability of the presented technique.
Abstract: A Chebyshev finite difference method has been proposed in order to solve linear and nonlinear second-order Fredholm integro-differential equations. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a nonuniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique.
76 citations
TL;DR: A remarkably good correspondence between the number of simulated and registered HIV cases is found, indicating that the approach to modelling the dynamics of HIV spreading through a sexual network is a valid approach that opens up completely new ways of reasoning about various medication scenarios.
Abstract: We propose a new way to model HIV infection spreading through the use of dynamic complex networks. The heterogeneous population of HIV exposure groups is described through a unique network degree probability distribution. The time evolution of the network nodes is modelled by a Markov process and gives insight in HIV disease progression. The results are validated against historical data of AIDS cases in the USA as recorded by the Center of Disease Control. We find a remarkably good correspondence between the number of simulated and registered HIV cases, indicating that our approach to modelling the dynamics of HIV spreading through a sexual network is a valid approach that opens up completely new ways of reasoning about various medication scenarios.
73 citations
TL;DR: An introduction to the use of support vector (SV) learning machines used as a data mining tool applied to buildings energy consumption data from a measurement campaign and introduces a perturbation in one of the influencing variables to detect a model change.
Abstract: For the purpose of energy conservation, we present in this paper an introduction to the use of support vector (SV) learning machines used as a data mining tool applied to buildings energy consumption data from a measurement campaign. Experiments using a SVM-based software tool for the prediction of the electrical consumption of a residential building is performed. The data included 1 year and 3 months of daily recordings of electrical consumption and climate data such as temperatures and humidities. The learning stage was done for a first part of the data and the predictions were done for the last month. Performances of the model and contributions of significant factors were also derived. The results show good performances for the model. The second experiment consists of model re-estimations on a 1-year daily recording dataset lagged at 1-day time intervals in such a way that we derive temporal series of influencing factors weights along with model performance criteria. Finally, we introduce a perturbation in one of the influencing variables to detect a model change. Comparing contributing weights with and without the perturbation, the sudden contributing weight change could have diagnosed the perturbation. The important point is the ease of the production of many models. This method announces future research work in the exploitation of possibilities of this 'model factory'.
70 citations
TL;DR: A numerical technique is presented for the solution of nonlinear system of second-order boundary value problems by expanding the required approximate solution as the elements of cubic B-spline scaling function using the operational matrix of derivative.
Abstract: A numerical technique is presented for the solution of nonlinear system of second-order boundary value problems. This method uses the cubic B-spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B-spline scaling function. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results.
62 citations
TL;DR: A numerical method for solving the generalized (retarded or advanced) pantograph equation with constant and variable coefficients under mixed conditions is presented, based on the truncated Taylor polynomials.
Abstract: A numerical method for solving the generalized (retarded or advanced) pantograph equation with constant and variable coefficients under mixed conditions is presented. The method is based on the truncated Taylor polynomials. The solution is obtained in terms of Taylor polynomials. The method is illustrated by studying an initial value problem. IIIustrative examples are included to demonstrate the validity and applicability of the technique. The results obtained are compared to the known results.
52 citations
TL;DR: This paper proposes and validate numerically a set of novel adaptive strategies for synchronization and consensus of complex networks of dynamical systems where the adaptation law is based on, respectively, global and local information at the network nodes.
Abstract: The aim of this paper is to propose and validate numerically a set of novel adaptive strategies for synchronization and consensus of complex networks of dynamical systems. We present both centralized and decentralized strategies where the adaptation law is based on, respectively, global and local information at the network nodes. All the proposed adaptive techniques are then validated using computer simulations on ensembles of two types of oscillators: Kuramoto and Rossler. We show that, in both cases, synchronization can be achieved with the adaptive gains reaching asymptotically finite steady-state values.
51 citations
TL;DR: Bayesian networks are revealed to be the best all-round technique for this type of study, as they combine a powerful interpretative capacity with a predictive capacity that is comparable to that of the best available techniques.
Abstract: This article proposes a methodology for the analysis of the causes and types of workplace accidents (in this paper we focus specifically on floor-level falls). The approach is based on machine learning techniques: Bayesian networks trained using different algorithms (with and without a priori information), classification trees, support vector machines and extreme learning machines. The results obtained using the different techniques are compared in terms of explanatory capacity and predictive potential, both factors facilitating the development of risk prevention measures. Bayesian networks are revealed to be the best all-round technique for this type of study, as they combine a powerful interpretative capacity with a predictive capacity that is comparable to that of the best available techniques. Moreover, the Bayesian networks force experts to apply a scientific approach to the construction and progressive enrichment of their models and also enable the basis to be laid for an accident prevention policy that is solidly grounded. Furthermore, the procedure enables better variable definition, better structuring of the data capture, coding, and quality control processes.
49 citations
TL;DR: Examples show that the level set method combined with the asymptotic analysis is robust for the shape optimization problems, and it allows us to identify the better solution compared to the purelevel set method exclusively based on the boundary variation technique.
Abstract: A class of shape optimization problems is solved numerically by the level set method combined with the topological derivatives for topology optimization. Actually, the topology variations are introduced on the basis of asymptotic analysis, by an evaluation of extremal points (local maxima for the specific problem) of the so-called topological derivatives introduced by Sokolowski and Zochowski [J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37(4) (1999), pp. 1251-1272] for elliptic boundary value problems. Topological derivatives are given for energy functionals of linear boundary value problems. We present results, including numerical examples, which confirm that the application of topological derivatives in the framework of the level set method really improves the efficiency of the method. Examples show that the level set method combined with the asymptotic analysis is robust for the shape optimization problems, and it allows us to identify the better solution compared to the pure level set method exclusively based on the boundary variation technique.
40 citations
TL;DR: An efficient and robust preconditioner, based on the Calderón formulae, is developed, for the solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape.
Abstract: The solution of the two-dimensional scattering problem for an homogeneous dielectric cylinder of arbitrary shape is considered. The numerical approach is based on a two-field system of integral equations solved by a Krylov subspace method. To accelerate and to improve the convergence of this solver, an efficient and robust preconditioner, based on the Calderon formulae, is developed. Several numerical simulations, for a wide range of physical parameters, validating the choice of this preconditioner are presented.
39 citations
TL;DR: A unified LMI approach is developed to establish sufficient conditions for the coupled neural networks to be globally synchronized, where the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required.
Abstract: In this paper, we deal with the synchronization problem for an array of linearly coupled neural networks with simultaneous presence of both the discrete and unbounded distributed time-delays By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several linear matrix inequalities (LMIs) are feasible Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to establish sufficient conditions for the coupled neural networks to be globally synchronized, where the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required It is also shown that the synchronization of coupled neural networks with bounded distributed delays is just a special case of our main results A numerical example is provided to show the usefulness of the proposed global synchronization condition
35 citations
TL;DR: By suitably choosing the parameters most of the previous known methods for homogeneous and non-homogeneous cases can be obtained from this method and a new high accuracy scheme is obtained.
Abstract: Second-order parabolic partial differential equations are solved by using a new three level method based on non-polynomial cubic spline in the space direction and finite difference in the time direction. Stability analysis of the method has been carried out and we have shown that our method is unconditionally stable. It has been shown that by suitably choosing the parameters most of the previous known methods for homogeneous and non-homogeneous cases can be obtained from our method. We also obtain a new high accuracy scheme of O(k4+h4). Numerical examples are given to illustrate the applicability and efficiency of the new method.
TL;DR: Numerical results of the algorithm, corres-ponding to the Moore– Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse.
Abstract: An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A{2, 3}s and A{2, 4}s are characterized in terms of matrix products (R*A)†R* and T*(AT*)†, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corres-ponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse.
TL;DR: A fixed point theorem is proved which allows the introduction of a suitable balanced quasi-metric on the set of all words over an alphabet to develop an application for the study of probabilistic divide and conquer algorithms.
Abstract: A new mathematical model is introduced for the study of the domain of words. We do it by means of the introduction of a suitable balanced quasi-metric on the set of all words over an alphabet. It will be shown that this construction has better quasi-metric and topological properties than several classical constructions. We also prove a fixed point theorem which allows us to develop an application for the study of probabilistic divide and conquer algorithms.
TL;DR: To partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease.
Abstract: A multivariate function f(x1,..., xN) can be evaluated via interpolation if its values are given at a finite number nodes of a hyperprismatic grid in the space of independent variables x1, x2,..., xN. Interpolation is a way to characterize an infinite data structure (function) by a finite number of data approximately. Hence it leaves an infinite arbitrariness unless a mathematical structure with finite number of flexibilities is imposed for the unknown function. Imposed structure has finite dimensionality. When the dimensionality increases unboundedly, the complexities grow rapidly in the standard methods. The main purpose here is to partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula. As a result, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease.
TL;DR: A new class of equations of Lane–Emden or Emden–Fowler type is considered, which is based on the coefficient of y′ rewritten in terms of a new function ϕ (x) such that the equation can be solved in Terms of ϕ.
Abstract: Singular initial value problems are investigated. We consider a new class of equations of Lane-Emden or Emden-Fowler type. The coefficient of y' rewritten in terms of a new function ϕ (x) such that the equation can be solved in terms of ϕ. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method.
TL;DR: Genetic Algorithm with different logic structures for price breaks has been developed and implemented for a multi-item inventory control system of breakable items like the items made of glass, mud, porcelain, etc.
Abstract: Genetic Algorithm (GA) with different logic structures for price breaks has been developed and implemented for a multi-item inventory control system of breakable items like the items made of glass, mud, porcelain, etc. with all unit discount (AUD), incremental quantity discount (IQD) and a combination of these discounts. Here, AUD and IQD on purchasing price with two price breaks are allowed. Also, demand and breakability of the items are stock-dependent. Shortages are not allowed. Replenishment is instantaneous. Selling price is a mark-up of the purchasing cost. For storage, warehouse capacity is limited. For the present model, GA has been developed in real code representation using Roulette wheel selection, arithmetic crossover and uniform mutation. This algorithm has been implemented successfully to find the optimum order quantities for the above inventory control system to achieve the maximum possible profit. The algorithm and the inventory model have been illustrated numerically and some sensitivity ...
TL;DR: Two new second- and fourth-order methods based on a septic non-polynomial spline function for the numerical solution of sixth-order two-point boundary value problems are presented and give better approximations than existing polynomial spline and finite difference methods up to order four and has a lower computational cost.
Abstract: Two new second-and fourth-order methods based on a septic non-polynomial spline function for the numerical solution of sixth-order two-point boundary value problems are presented. The spline function is used to derive some consistency relations for computing approximations to the solution of this problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods up to order four and has a lower computational cost. Convergence analysis of these two methods is discussed. Three numerical examples are included to illustrate the practical use of our methods as well as their accuracy compared with existing spline function methods.
TL;DR: A numerical scheme arising from the use of a fourth order rational approximants to the matrix-exponential term in a three-time level recurrence relation is proposed for the numerical solution of the one-dimensional sine-Gordon (SG) equation already known from the bibliography.
Abstract: A numerical scheme arising from the use of a fourth order rational approximants to the matrix-exponential term in a three-time level recurrence relation is proposed for the numerical solution of the one-dimensional sine-Gordon (SG) equation already known from the bibliography. The method for its implementation uses a predictor-corrector scheme in which the corrector is accelerated by using the already evaluated corrected values modified predictor-corrector scheme. For the implementation of the corrector, in order to avoid extended matrix evaluations, an auxiliary vector was successfully introduced. Both the predictor and the corrector schemes are analysed for stability. The predictor-corrector/modified predictor-corrector (P-C/MPC) schemes are tested on single and soliton doublets as well as on the collision of breathers and a comparison of the numerical results with the corresponding ones in the bibliography is made. Finally, conclusions for the behaviour of the introduced MPC over the standard P-C scheme are derived.
TL;DR: A nonlinear explicit scheme is proposed for numerically solving first-order singular or singularly perturbed autonomous initial-value problems (IVP) of the form y ′=f(y), based on the local approximation of the function f(y) by a second-order Taylor expansion.
Abstract: A nonlinear explicit scheme is proposed for numerically solving first-order singular or singularly perturbed autonomous initial-value problems (IVP) of the form y'=f(y). The algorithm is based on the local approximation of the function f(y) by a second-order Taylor expansion. The resulting approximated differential equation is then solved without local truncation error. For the true solution the method has a local truncation error that behaves like either O(h3) or O(h4) according to whether or not some parameter vanishes. Some numerical examples are provided to illustrate the performance of the method. Finally, an application of the method for detecting and locating singularities is outlined.
TL;DR: A new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams that supports distinct site shapes, generality, efficiency, robustness and easy implementation is proposed.
Abstract: We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distance, convex distance functions, etc.) and is restricted to diagrams with connected Voronoi regions. The presented approach constructs a tree (a quadtree in 2D/an octree in 3D) which encodes in its nodes and in a compact way all the information required for generating an explicit representation of the boundaries of the Voronoi diagram approximation. Then, by using this hierarchical data structure a reconstruction strategy creates the diagram approximation. We also present the algorithms required for dynamically maintaining under the insertion or deletion of sites the Voronoi diagram approximation. The main features of our approach are its generality, efficiency, robustness and easy implementation.
TL;DR: Numerical simulation demonstrates that the efficiency and performance of the algorithm are improved and it is shown that IMSCOA provides more optimal results than the other methods, whether or not the problem is large scale.
Abstract: This paper reforms the Mutative Scale Chaos Optimization Algorithm (MSCOA). Numerical simulation demonstrates that the efficiency and performance of the algorithm are improved. An analysis of the Improved Mutative Scale Chaos Optimization Algorithm (IMSCOA) is also given. IMSCOA is applied to examples of economic load dispatch, considering both the valve point effect and transmission loss. The results are compared with those computed by other methods, including MSCOA and another effective chaos algorithm—CROA. It is shown that IMSCOA provides more optimal results than the other methods, whether or not the problem is large scale. This demonstrates the efficiency and practicability of IMSCOA in engineering practice.
TL;DR: It is shown that a parametric dual of ROMAN DOMINATION is in ℱ𝒫𝒯 and it is proved that this problem is W[2]-complete for general graphs, however, parameterized algorithms are presented for graphs of bounded treewidth and for planar graphs.
Abstract: We analyse the graph-theoretic formalization of ROMAN DOMINATION, dating back to the military strategy of the Emperor Constantine, from a parameterized perspective. More specifically, we prove that this problem is W[2]-complete for general graphs. However, parameterized algorithms are presented for graphs of bounded treewidth and for planar graphs. Moreover, it is shown that a parametric dual of ROMAN DOMINATION is in FPT.
TL;DR: An exact relation between the Fourier Transform of a signal and its Fractal Dimension is obtained and an electroencephalographic application involving fractal and spectral parameters is described.
Abstract: Fourier parameters display the spectral content of a signal and provide explicit representations in the frequency domain. In the case of electroencephalograms, the FFT algorithm was the only quantifying method used until the 1970s, but this analysis is not conclusive in most pathologies. Fractal techniques provide new tools for the processing of signals whose traces have a sophisticated geometric complexity. The fractal dimension is computed easily in our work by means of explicit formulae involving the time samples. In this paper we obtain, under some hypotheses, an exact relation between the Fourier Transform of a signal and its Fractal Dimension. In the last part of the paper, an electroencephalographic application involving fractal and spectral parameters is described.
TL;DR: It is proved that, in an n-star graph, all fault-free vertices but at most two form a connected component, and that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.
Abstract: In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n≥3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.
TL;DR: Using the Lyapunov–Krasovskii functional method and employing the convexity of the matrix equation, some new stability criteria are derived, which are expressed by a set of linear matrix inequalities.
Abstract: This paper is concerned with the global robust asymptotical stability for a class of cellular neural networks with time-varying delays and parameter uncertainties. By using the Lyapunov-Krasovskii functional method and employing the convexity of the matrix equation, some new stability criteria are derived, which are expressed by a set of linear matrix inequalities. To show the effectiveness and less conservatism of our method, two numerical examples are presented finally.
TL;DR: A novel pinning scheme based on ControlRank (CR), which is a vertex centrality index exploring the link structure of the directed networks, is developed, which demonstrates that it is much more effective to pin the vertex with largest CR than pin the node with largest out-degree.
Abstract: By applying local feedback injections to a small fraction of network vertices, a dynamical network can be stabilized on a homogeneous equilibrium. However, different pinning strategies may lead to different performances. This paper develops a novel pinning scheme based on ControlRank (CR), which is a vertex centrality index exploring the link structure of the directed networks. Simulation study is given on a scale-free directed dynamical network, which demonstrates that it is much more effective to pin the vertex with largest CR than pin the vertex with largest out-degree.
TL;DR: The Chebyshev–Legendre method is derived for a class of optimal control problems governed by ordinary differential equations and the Legendre expansions of both the state and the control functions are used to approximate the control and state functions.
Abstract: In this paper, we derive the so-called Chebyshev-Legendre method for a class of optimal control problems governed by ordinary differential equations We use Legendre expansions to approximate the control and state functions and we employ the Chebyshev-Gauss-Lobatto (CGL) points as the interpolating points Thus the unknown variables of the equivalent nonlinear programming problems are the coefficients of the Legendre expansions of both the state and the control functions We evaluate the function values at the CGL nodes via the fast Legendre transform In this way, the fast Legendre transform can be utilized to save CPU calculation time Some numerical examples are given to illustrate the applicability and high accuracy of the Chebyshev-Legendre method in solving a wide class of optimal control problem
TL;DR: This paper revisits the problem of synchronization stability for general complex dynamical networks with coupling delays with a new delay-dependent criterion derived by introducing a new kind of Lyapunov–Krasovskii functional formulated in terms of a linear matrix inequality, which can be readily solved via standard software.
Abstract: This paper revisits the problem of synchronization stability for general complex dynamical networks with coupling delays. A new delay-dependent criterion is derived by introducing a new kind of Lyapunov-Krasovskii functional and is formulated in terms of a linear matrix inequality, which can be readily solved via standard software. This new criterion based on a delay fractioning approach is proved to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning. Furthermore, the resulting criterion is further extended to the synchronization stability analysis of complex dynamical networks with time-varying structured uncertainties. Two numerical examples are provided to show the effectiveness and advantage of the proposed results.
TL;DR: This paper addresses complex real-time networked control systems (NCSs) and finds that co-design of network and control is an effective approach to simplify the network behaviour and consequently to maximize the performance of the overall NCSs.
Abstract: This paper addresses complex real-time networked control systems (NCSs). From our recent effort in this area, a general framework is developed to deal with network complexity. When the complex traffic of real-time NCSs are treated as stochastic and bounded variables, simplified yet improved methods for robust stability and control synthesis can be developed to guarantee the stability of the systems. From the perspective of network design, over-provisioning of network capacity is not a general solution as it cannot provide any guarantee for predictive communication behaviour, which is a basic requirement for many real-time applications. Co-design of network and control is an effective approach to simplify the network behaviour and consequently to maximize the performance of the overall NCSs. To implement such a co-design, a queuing protocol is applied to obtain predictable network traffic behaviour. Then, the predictable network-induced delay is compensated through the controller design, and any dropped control packet is also estimated in real-time using past control packets. In this way, the network-induced delay can be limited within a single control period, significantly simplifying the network complexity as well as system analysis and design.
TL;DR: This paper presents the C 4 curves, which is the extension of the four-point approximating subdivision scheme developed by Siddiqi and Ahmad, and uses the Laurent polynomial method to analyse the smoothness of the new scheme.
Abstract: In this paper a new five-point approximating subdivision scheme is presented, generating the C4 curves, which is the extension of the four-point approximating subdivision scheme developed by Siddiqi and Ahmad. The limit function of the new five-point scheme has a support on [-5, 4]. The Laurent polynomial method is used to analyse the smoothness of the new scheme. The Holder exponent for the scheme is calculated. The usefulness of the scheme is illustrated in the examples.