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Showing papers in "International Journal of Computer Mathematics in 2014"


Journal ArticleDOI
TL;DR: A wise strategy for step setting, which considers the information of firefly's personal and the global best positions, and shows that the modified algorithm enhances the performance of the basic firefly algorithm.
Abstract: Firefly algorithm is a bio-inspired optimization algorithm which has been empirically demonstrated to perform well on many optimization problems. However, it can easily get trapped in the local optima and causes low precision. Therefore, improvement of this disadvantage is the very important. In this paper, we propose a wise strategy for step setting, which considers the information of firefly's personal and the global best positions. The results show that the modified algorithm enhances the performance of the basic firefly algorithm.

65 citations


Journal ArticleDOI
TL;DR: Applying monotone iterative techniques and Lyapunov functional techniques, sufficient conditions are established for the global asymptotic stability of both virus-free and virus equilibria of the model.
Abstract: We propose a delayed SIRS computer virus propagation model. Applying monotone iterative techniques and Lyapunov functional techniques, we establish sufficient conditions for the global asymptotic stability of both virus-free and virus equilibria of the model.

48 citations


Journal ArticleDOI
TL;DR: A new type of contraction on a metric space endowed with a graph is introduced and fixed point theorems that generalize some of the results related with G-contraction for a directed graph G are proved.
Abstract: We introduce a new type of contraction on a metric space endowed with a graph and prove fixed point theorems that generalize some of the results related with G-contraction for a directed graph G. Examples are given to justify that our contractions are more general than many others in this area.

44 citations


Journal ArticleDOI
TL;DR: A new ear recognition method based on curvelet transform based on k-NN (k-nearest neighbour) is utilized as a classifier which shows encouraging performance.
Abstract: Ear is a relatively new biometric among others. Many methods have been used for ear recognition to improve the performance of ear recognition systems. In continuation of these efforts, we propose a new ear recognition method based on curvelet transform. Features of the ear are computed by applying Fast Discrete Curvelet Transform via the wrapping technique. Feature vector of each image is composed of an approximate curvelet coefficient and second coarsest level curvelet coefficients at eight different angles. k-NN (k-nearest neighbour) is utilized as a classifier. The proposed method is experimented on two ear databases from IIT Delhi. Results achieved using the proposed method on publicly available ear database are up to 97.77% which show encouraging performance.

43 citations


Journal ArticleDOI
Sizhong Zhou1
TL;DR: It is proved that every (0, mf−m+m+1)-digraph has a ( 0, f)-factorization k-orthogonal to H if f(x)≥3k−2 for each x∈V(D).
Abstract: Let D be a digraph with vertex set V(D) and arc set A(D) and let f=(f−, f+) be a pair of functions defined on V(D). Let H be a km-subdigraph of D. In this paper, it is proved that every (0, mf−m+1)-digraph has a (0, f)-factorization k-orthogonal to H if f(x)≥3k−2 for each x∈V(D).

41 citations


Journal ArticleDOI
TL;DR: A new sophisticated technique to solve a coupled system of fractional order partial differential equations by reducing the coupled system under consideration to a system of easily solvable algebraic equations without discretizing the system is developed.
Abstract: We study legendre polynomials in case of more than one variable and develop new operational matrices of fractional order integrations as well as fractional order differentiations. Based on these operational matrices, we develop a new sophisticated technique to solve a coupled system of fractional order partial differential equations. Our technique reduces the coupled system under consideration to a system of easily solvable algebraic equations without discretizing the system. As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique matches well with the exact solutions of the problems. We also study error analysis graphically.

40 citations


Journal ArticleDOI
TL;DR: An implicit second-order finite difference scheme, which is unconditionally stable, is employed to discretize fractional advection–diffusion equations with constant coefficients and is proved to be convergent unconditionally to the solution of the linear system.
Abstract: An implicit second-order finite difference scheme, which is unconditionally stable, is employed to discretize fractional advection–diffusion equations with constant coefficients. The resulting systems are full, unsymmetric, and possess Toeplitz structure. Circulant and skew-circulant splitting iteration is employed for solving the Toeplitz system. The method is proved to be convergent unconditionally to the solution of the linear system. Numerical examples show that the convergence rate of the method is fast.

32 citations


Journal ArticleDOI
TL;DR: Different methods to model driving patterns with a stochastic approach are proposed, some of them employing standard vehicle sensors, while others require non-conventional sensors (for instance, global positioning system or inertial reference system).
Abstract: Perfect knowledge of future driving conditions can be rarely assumed on real applications when optimally splitting power demands among different energy sources in a hybrid electric vehicle. Since performance of a control strategy in terms of fuel economy and pollutant emissions is strongly affected by vehicle power requirements, accurate predictions of future driving conditions are needed. This paper proposes different methods to model driving patterns with a stochastic approach. All the addressed methods are based on the statistical analysis of previous driving patterns to predict future driving conditions, some of them employing standard vehicle sensors, while others require non-conventional sensors (for instance, global positioning system or inertial reference system). The different modelling techniques to estimate future driving conditions are evaluated with real driving data and optimal control methods, trading off model complexity with performance.

31 citations


Journal ArticleDOI
TL;DR: This paper designs a certificateless authenticated AGKA scheme, which does not require certificates to guarantee the authenticity of public keys yet avoids the inherent escrow problem of identity-based cryptosystems.
Abstract: A recent primitive known as asymmetric group key agreement (AGKA) allows a group of users to negotiate a common encryption key which is accessible to any entities and corresponds to different decryption keys, each of which is only computable by one group member. This concept makes it easy to construct distributed and one-round group key agreement protocols. However, this existing instantiation depends on public key infrastructure (PKI) associated with certificate management, or it is only secure against passive adversaries. This paper addresses this concern by designing a certificateless authenticated AGKA scheme, which does not require certificates to guarantee the authenticity of public keys yet avoids the inherent escrow problem of identity-based cryptosystems. Using simple binding techniques, the proposed scheme can be raised to the same trust level as that using the traditional PKI. We show that the proposed protocol is secure provided that the underlying k-bilinear Diffie–Hellman exponent problem is...

28 citations


Journal ArticleDOI
TL;DR: It is shown that the proposed control scheme can guarantee tracking performance of the robotic manipulators system, in the sense that all variables of the closed-loop system are bounded and the effect due to the external disturbance and approximate error of radical basis function (RBF) NNs on the tracking error can be converged to zero in an infinite time.
Abstract: In this paper, an adaptive neural network (NN) switching control strategy is proposed for the trajectory tracking problem of robotic manipulators. The proposed system comprises an adaptive switching neural controller and the associated robust compensation control law. Based on the Lyapunov stability theorem and average dwell-time approach, it is shown that the proposed control scheme can guarantee tracking performance of the robotic manipulators system, in the sense that all variables of the closed-loop system are bounded and the effect due to the external disturbance and approximate error of radical basis function (RBF) NNs on the tracking error can be converged to zero in an infinite time. Finally, simulation results on a two-link robotic manipulator show the feasibility and validity of the proposed control scheme.

28 citations


Journal ArticleDOI
TL;DR: The effect of sRNAs on the stability and bifurcation of genetic regulatory networks mediated by small RNAs with multiple delays is shown, and sufficient conditions for the local stability of two-gene genetic Regulatory networks in the parameter space are presented.
Abstract: In this paper, we study the stability, bifurcation and periodic oscillation of two-gene regulatory networks mediated by small RNAs (sRNAs) with multiple delays. We first show the effect of sRNAs on the stability and bifurcation of genetic regulatory networks. Then we present sufficient conditions for the local stability of two-gene genetic regulatory networks in the parameter space, and assess critical values of the Hopf bifurcation. Although such networks may have multiple delays, sRNAs, positive feedbacks and different connection strengths among two genes, their stability and bifurcation depend on the sum of all time delays among all elements (including both mRNAs and proteins). Furthermore, the period of oscillations increases with the time delay, and in the case of larger delay, the amplitude of oscillations is robust against the change in the delay. Two examples are employed to illustrate the theorems developed in this study.

Journal ArticleDOI
TL;DR: A new implicit compact difference scheme is constructed for the fourth-order fractional diffusion-wave system by the method of order reduction, and two simple and accurate formulae of discretization for the derivative boundary conditions are obtained.
Abstract: In this paper, a new implicit compact difference scheme is constructed for the fourth-order fractional diffusion-wave system by the method of order reduction. The temporal Caputo fractional derivative is discretized by an L1 scheme. The spatial derivative of order 4 is reduced to one of order 2 by order reduction. Then, the reduced derivative of order 2 is discretized by a difference formula of order 4. Using order reduction, two simple and accurate formulae of discretization for the derivative boundary conditions are obtained. And a new way of proving the stability and convergence of the scheme is presented in this paper. Some numerical results demonstrate the accuracy and efficiency of our new scheme.

Journal ArticleDOI
TL;DR: It is shown that the IST is an effective mathematical tool for solving the whole hierarchy of nonisospectral nonlinear partial differential equations with self-consistent sources.
Abstract: In this paper, a nonisospectral and variable-coefficient KdV equation hierarchy with self-consistent sources is derived from the related linear spectral problem. Exact solutions of the KdV equation hierarchy are obtained through the inverse scattering transformation (IST). It is shown that the IST is an effective mathematical tool for solving the whole hierarchy of nonisospectral nonlinear partial differential equations with self-consistent sources.

Journal ArticleDOI
TL;DR: The mollification regularization method is given to solve an inverse source problem for a fractional diffusion equation that is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data.
Abstract: In the present paper, we consider an inverse source problem for a fractional diffusion equation. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We give the mollification regularization method to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, a new a posteriori parameter choice rule is also proposed and a good error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.

Journal ArticleDOI
TL;DR: The numerical solutions for a class of fractional advection–diffusion equations with a kind of new generalized time-fractional derivative proposed last year are discussed in a bounded domain and the stability of numerical scheme is investigated.
Abstract: In the current paper, the numerical solutions for a class of fractional advection–diffusion equations with a kind of new generalized time-fractional derivative proposed last year are discussed in a bounded domain. The fractional derivative is defined in the Caputo type. The numerical solutions are obtained by using the finite difference method. The stability of numerical scheme is also investigated. Numerical examples are solved with different fractional orders and step sizes, which illustrate that the numerical scheme is stable, simple and effective for solving the generalized advection–diffusion equations. The order of convergence of the numerical scheme is evaluated numerically, and the first-order convergence rate has been observed.

Journal ArticleDOI
TL;DR: The iterative sequence produced by the PPHSS method is proved to be convergent to the unique solution of the saddle-point problem when the iteration parameters satisfy a proper condition.
Abstract: By utilizing the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration technique, we establish a parameterized PHSS (PPHSS) iteration method for non-Hermitian positive semidefinite linear saddle-point systems. The PPHSS method is essentially a two-parameter iteration which covers standard PHSS iteration and can extend the possibility to optimize the iterative process. The iterative sequence produced by the PPHSS method is proved to be convergent to the unique solution of the saddle-point problem when the iteration parameters satisfy a proper condition. In addition, for a special case of the PPHSS iteration method, we derive the optimal iteration parameter and the corresponding optimal convergence factor. Numerical experiments demonstrate the effectiveness and robustness of the PPHSS method both used as a solver and as a preconditioner for Krylov subspace methods.

Journal ArticleDOI
TL;DR: This estimate gives an analytical comparison of the eigenvector centrality of G with thecentrality of L(G) in terms of some irregularity measure of G.
Abstract: Given a network G, it is known that the Bonacich centrality of the bipartite graph B(G) associated with G can be obtained in terms of the centralities of the line graph L(G) associated with G and the centrality of the network G+gr (whose adjacency matrix is obtained by adding to the adjacency matrix A(G) the diagonal matrix D=bij, where bii is the degree of node i in G) and conversely. In this contribution, we use the centrality of G to estimate the centrality of G+gr and show that the error committed is bounded by some measure of the irregularity of G. This estimate gives an analytical comparison of the eigenvector centrality of G with the centrality of L(G) in terms of some irregularity measure of G.

Journal ArticleDOI
TL;DR: A new symmetric successive over-relaxation method to find solution of the large sparse augmented linear systems, which is the extension of the symmetrical successive overrelaxations iteration method.
Abstract: In this paper, we present a new symmetric successive over-relaxation method to find solution of the large sparse augmented linear systems, which is the extension of the symmetric successive overrelaxation iteration method. The convergence analysis of our method is also studied. Furthermore, the functional equation between the parameters and the eigenvalues of the relevant iteration matrix is obtained. Finally, numerical computations are presented to show the effectiveness of our algorithm.

Journal ArticleDOI
TL;DR: This work presents a closed-form analysis for evaluating queueing/system-time distributions using an inversion method which is based on the roots of associated characteristic equation and presents several numerical examples.
Abstract: With the advent of highly integrated transmission networks, the transmission of data, such as audio, video, video streaming are transmitted over a common medium in smaller file sizes. These files have variable transmission time requirement which is of deterministic in nature. Further, the traffic generated from various sources is bursty and correlated. This particular scenario can be best modelled as a single-server queueing system with arrivals following a Markovian arrival process and service-time deterministic distribution taking one of the N possible values. For this model, we present a closed-form (in terms of roots) analysis for evaluating queueing/system-time distributions using an inversion method which is based on the roots of associated characteristic equation. Several numerical examples are presented with complete discussion.

Journal ArticleDOI
TL;DR: This paper considers the local discontinuous Galerkin (LDG) finite element method for one-dimensional time-fractional Fisher's equation, and proves that the method is stable, and the numerical solution converges to the exact one with order O(hk+1+τ2−α), where h, τ and k are the space step sizes, time step size, polynomial degree, respectively.
Abstract: In this paper, we consider the local discontinuous Galerkin (LDG) finite element method for one-dimensional time-fractional Fisher's equation, which is obtained from the standard one-dimensional Fisher's equation by replacing the first-order time derivative with a fractional derivative (of order α, with 0<α<1). The proposed LDG is based on the LDG finite element method for space and finite difference method for time. We prove that the method is stable, and the numerical solution converges to the exact one with order O(hk+1+τ2−α), where h, τ and k are the space step size, time step size, polynomial degree, respectively. The numerical experiments reveal that the LDG is very effective.

Journal ArticleDOI
TL;DR: A new three-term conjugate gradient (TTCG) method is developed by applying the Powell symmetrical technique to the Hestenes–Stiefel method, which satisfies both the sufficient descent property and the conjugacy condition, which do not rely on any line search.
Abstract: The conjugate gradient method is one of the most effective methods to solve the unconstrained optimization problems In this paper, we develop a new three-term conjugate gradient (TTCG) method by applying the Powell symmetrical technique to the Hestenes–Stiefel method The proposed method satisfies both the sufficient descent property and the conjugacy condition , which do not rely on any line search Under the standard Wolfe line search, the global convergence of the proposed method is also established The numerical results also show that the proposed method is very effective and interesting by comparing with other TTCG methods using a classical set of test problems

Journal ArticleDOI
TL;DR: This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential.
Abstract: This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and compared with Pade state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.

Journal ArticleDOI
TL;DR: A novel variational model for removing multiplicative noise is proposed which is inherently equivalent to a combination of the classical total variation regularizer and a nonconvex regularizer, and an alternating iteration process in which two coupling minimization problems are solved.
Abstract: A novel variational model for removing multiplicative noise is proposed in this paper. In the model, a novel regularization term is elaborately designed which is inherently equivalent to a combination of the classical total variation regularizer and a nonconvex regularizer. The proposed regularization term, on the one hand, can better remove the noise in homogeneous regions of a noisy image and, on the other hand, can preserve edge details of the image during the denoising process. In order to solve the model efficiently, we design an alternating iteration process in which two coupling minimization problems are solved. For each of the two minimization problems, the existence and uniqueness of their solutions are proved under some necessary assumptions. Numerical results are reported to demonstrate the effectiveness of the proposed regularization term for multiplicative noise removal.

Journal ArticleDOI
TL;DR: It is proved that the VCP4 problem is NP-hard for cubic graphs and sharp lower and upper bounds on ψ4(G) for cubic graph are given and a 2-approximation algorithm for the V CP4 problem in cubic graphs is proposed.
Abstract: A subset F of vertices of a graph G is called a vertex cover Pk set if every path of order k in G contains at least one vertex from F. Denote by ψk(G) the minimum cardinality of a vertex cover Pk set in G. The vertex cover Pk (VCPk) problem is to find a minimum vertex cover Pk set. It is easy to see that the VCP2 problem corresponds to the well-known vertex cover problem. In this paper, we restrict our attention to the VCP4 problem in cubic graphs. The paper proves that the VCP4 problem is NP-hard for cubic graphs. Further, we give sharp lower and upper bounds on ψ4(G) for cubic graphs and propose a 2-approximation algorithm for the VCP4 problem in cubic graphs.

Journal ArticleDOI
TL;DR: The results obtained from this investigation have demonstrated the huge influence of the needle position on the flow characteristics, showing important hole to hole differences.
Abstract: In the present paper, a computational study has been performed in order to clarify the effects of the needle eccentricity in a real multihole microsac nozzle. This nozzle has been simulated at typical operating conditions of a diesel engine, paying special attention to the internal flow development and cavitation appearance within the discharge orifices. For that purpose, a multiphase flow solver based on a homogeneous equilibrium model with a barotropic equation of state has been used, introducing the turbulence effects by Reynolds-averaged Navier–Stokes methods with a re-normalization group k–ϵ model. The results obtained from this investigation have demonstrated the huge influence of the needle position on the flow characteristics, showing important hole to hole differences.

Journal ArticleDOI
TL;DR: In this paper, a graph matching strategy is used to construct aggregation-based coarsening for an algebraic two-grid method, and the effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection-diffusion coefficient matrix, and for problems from the Florida matrix market collection.
Abstract: A graph matching is used to construct aggregation-based coarsening for an algebraic two-grid method. Effects of inexact coarse grid solve is analysed numerically for a highly discontinuous convection–diffusion coefficient matrix, and for problems from the Florida matrix market collection. The proposed strategy is found to be more robust compared to a classical algebraic multi-grid approach based on strength of connections. Basic properties of two-grid method are outlined.

Journal ArticleDOI
TL;DR: This paper considers the coefficients in the mathematical model to be random variables, whose distribution and moments are unknown a priori, and need to be determined by comparison with experimental data, based on polynomial chaoses.
Abstract: When modelling biological processes, there are always errors, uncertainties and variations present. In this paper, we consider the coefficients in the mathematical model to be random variables, whose distribution and moments are unknown a priori, and need to be determined by comparison with experimental data. A stochastic spectral representation of the parameters and the solution stochastic process is used, based on polynomial chaoses. The polynomial chaos representation generates a system of equations of the same type as the original model. The inverse problem of finding the parameters is reduced to establishing the best-fit values of the random variables that represent them, and this is done using maximum likelihood estimation. In particular, in modelling biofilm growth, there are variations, measurement errors and uncertainties in the processes. The biofilm growth model is given by a parabolic differential equation, so the polynomial chaos formulation generates a system of partial differential equation...

Journal ArticleDOI
TL;DR: This work investigates uncertainty propagation in the context of high-end complex simulation codes, whose runtime on one configuration is on the order of the total limit of computational resources, and studies the use of lower-fidelity data generated by proper orthogonal decomposition-based model reduction using a Gaussian process approach.
Abstract: We investigate uncertainty propagation in the context of high-end complex simulation codes, whose runtime on one configuration is on the order of the total limit of computational resources. To this end, we study the use of lower-fidelity data generated by proper orthogonal decomposition-based model reduction. A Gaussian process approach is used to model the difference between the higher-fidelity and the lower-fidelity data. The approach circumvents the extensive sampling of model outputs – impossible in our context – by substituting abundant, lower-fidelity data in place of high-fidelity data. This enables uncertainty analysis while accounting for the reduction in information caused by the model reduction. We test the approach on Navier–Stokes flow models: first on a simplified code and then using the scalable high-fidelity fluid mechanics solver Nek5000. We demonstrate that the approach can give reasonably accurate while conservative error estimates of important statistics including high quantiles of the...

Journal ArticleDOI
TL;DR: A modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve an optimal control problem of switched systems with a continuous-time inequality constraint.
Abstract: In this paper, we consider an optimal control problem of switched systems with a continuous-time inequality constraint. Because of the complexity of this constraint, it is difficult to solve this problem by standard optimization techniques. To overcome this difficulty, the problem is divided into a bi-level optimization problem involving a combination of a continuous-time optimal control problem and a discrete optimization problem. Then, a modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve this bi-level optimization problem. Finally, a numerical example is presented to illustrate the efficiency of our method.

Journal ArticleDOI
TL;DR: The strong convergence of the split-step theta methods for non-autonomous stochastic differential equations under a linear growth condition on the diffusion coefficient and a one-sided Lipschitz condition is proved.
Abstract: In this paper, we first prove the strong convergence of the split-step theta methods for non-autonomous stochastic differential equations under a linear growth condition on the diffusion coefficient and a one-sided Lipschitz condition on the drift coefficient. Then, if the drift coefficient satisfies a polynomial growth condition, we further get the rate of convergence. Finally, the obtained results are supported by numerical experiments.