Showing papers in "International Journal of Computer Mathematics in 2016"
TL;DR: This work presents a set of Elliptic Curve Cryptography optimizations for point and field arithmetic which are used in the design and implementation of a security and capability-based access control mechanism (DCapBAC) on smart objects, based on a lightweight and flexible design.
Abstract: In recent years, the increasing development of wireless communication technologies and IPv6 is enabling a seamless integration of smart objects into the Internet infrastructure. This extension of technology to common environments demands greater security restrictions, since any unexpected information leakage or illegitimate access to data could present a high impact in our lives. Additionally, the application of standard security and access control mechanisms to these emerging ecosystems has to face new challenges due to the inherent nature and constraints of devices and networks which make up this novel landscape. While these challenges have been usually addressed by centralized approaches, in this work we present a set of Elliptic Curve Cryptography optimizations for point and field arithmetic which are used in the design and implementation of a security and capability-based access control mechanism DCapBAC on smart objects. Our integral solution is based on a lightweight and flexible design that allows this functionality is embedded on resource-constrained devices, providing the advantages of a distributed security approach for Internet of Things IoT in terms of scalability, interoperability and end-to-end security. Additionally, our scheme has been successfully validated by using AVISPA tool and implemented on a real scenario over the Jennic/NXP JN5148 chipset based on a 32-bit RISC CPU. The results demonstrate the feasibility of our work and show DCapBAC as a promising approach to be considered as security solution for IoT scenarios.
115 citations
TL;DR: The g-extra conditional diagnosability ofhypercubes is determined and sequential -diagnosis algorithms for hypercubes with low time complexities under the Preparata, Metze, and Chien (PMC) model and the MM* model which is a special case of the Maeng and Malek (MM) model are proposed.
Abstract: The conditional diagnosis is a very important measure of the reliability and the fault-tolerance of networks. The ‘condition’ means that no faulty set contains all neighbours of any node. Under this assumption, for any system G, every component of has more than 1 node, where F is the faulty set of G. The g-extra conditional diagnosability is defined under the assumption that every component of has more than nodes. ‘A system with at most t faulty nodes is defined as sequentially t-diagnosable if at least one faulty node can be repaired, so that the testing can be continued using the repaired node to eventually diagnose all faulty nodes’ [E.P. Duarte Jr., R.P. Ziwich, and L.C.P. Albini, A survey of comparison-based system-level diagnosis, ACM Comput. Surv. 433 2011, article 22]. To increase the degree of the sequential t-diagnosability of a system, sequential -diagnosis strategy is proposed in this paper. It is allowed that there are at most k misdiagnosed nodes. In this paper, we determine the g-extra conditional diagnosability of hypercubes and propose sequential -diagnosis algorithms for hypercubes with low time complexities under the Preparata, Metze, and Chien PMC model and the MM* model which is a special case of the Maeng and Malek MM model.
98 citations
TL;DR: The stability and convergence of the compact difference scheme in a new norm are proved by the energy method.
Abstract: In this paper, a second-order backward differentiation formula compact difference scheme with the truncation error of order 1+α(0<α<1) for time and 4 for space to fractional-order Volterra equation is considered. The integral term is treated by means of the second-order convolution quadrature suggested by Lubich and fourth-order accuracy compact approximation is applied for the second-order space derivative. The stability and convergence of the compact difference scheme in a new norm are proved by the energy method. Numerical experiments that are in total agreement with our analysis are reported.
43 citations
TL;DR: It is found that the local discontinuous Galerkin (LDG) method can actually achieve convergence rate equals .
Abstract: In this paper, we study the local discontinuous Galerkin LDG method for some time-fractional fourth-order differential equations. The method was recently employed to solve the problem and shown to converge with order . We find that the LDG method can actually achieve convergence rate equals . The claims are justified by numerical tests.
38 citations
TL;DR: A new computational method based on the second kind Chebyshev wavelets (SKCWs) together with the Galerkin method is proposed for solving a class of stochastic heat equation and the results reveal that the proposed method is very accurate and efficient.
Abstract: In this paper, a new computational method based on the second kind Chebyshev wavelets SKCWs together with the Galerkin method is proposed for solving a class of stochastic heat equation. For this purpose, a new stochastic operational matrix for the SKCWs is derived. A collocation method based on block pulse functions is employed to derive a general procedure for forming this matrix. The SKCWs and their operational matrices of integration and stochastic Ito-integration are used to transform the under consideration problem into the corresponding linear system of algebraic equations which can be simply solved to achieve the solution of the problem. The proposed method is very convenient for solving such problems, since the initial and boundary conditions are taken into account automatically. Moreover, the efficiency of the proposed method is shown for some concrete examples. The results reveal that the proposed method is very accurate and efficient.
36 citations
TL;DR: The novel compact alternating direction implicit (ADI) scheme is proposed for solving the time-fractional subdiffusion equation in two space dimensions and the unique solvability, unconditionally stability and convergence of the scheme are proved.
Abstract: In this paper, a novel compact alternating direction implicit ADI scheme is proposed for solving the time-fractional subdiffusion equation in two space dimensions. The established scheme is based on the modified L1 method in time and the compact finite difference method in space. The unique solvability, unconditionally stability and convergence of the scheme are proved. The derived compact ADI scheme is coincident with the one for 2D integer order parabolic equation when the , where is the order of the Riemann–Liouville derivative operator. In addition, the novel ADI scheme is used to solve the 2D modified fractional diffusion equation, and the corresponding stability and convergence results are also given. Numerical results are provided to verify the theoretical analysis.
33 citations
TL;DR: By developing several theorems, which incorporate the Adomian polynomials, the Laplace transformation of nonlinear expressions is made possible and the proposed approach is analytical, accurate, and free of integration.
Abstract: A technique for extending the Laplace transform method to solve nonlinear differential equations is presented. By developing several theorems, which incorporate the Adomian polynomials, the Laplace transformation of nonlinear expressions is made possible. A number of well-known nonlinear equations including the Riccati equation, Clairaut's equation, the Blasius equation and several other ones involving nonlinearities of various types such as exponential and sinusoidal are solved for illustration. The proposed approach is analytical, accurate, and free of integration.
33 citations
TL;DR: Seasonally forced epidemic models with and without vector dynamics are analysed and it is concluded that the models give basically the same information when the authors replace, in the SIR model, the human infectivity by a function of both human and mosquito infectivities.
Abstract: Dengue fever dynamics show seasonality, with the disease transmission being higher during the warmer seasons. In this paper, we analyse seasonally forced epidemic models with and without vector dynamics. We assume small seasonal effects and obtain approximations for the real response of each state variable and also for the corresponding amplitude and phase via decomposition of the sinusoidal forcing into imaginary exponential functions. The analysis begins with the simplest susceptible-infected-susceptible SIS model, followed by the simplest model with vector dynamics, susceptible-infected-susceptible for hosts and uninfected-vector SISUV. Finally, we compare the more complex susceptible-infected-recovered SIR and susceptible-infected-recovered for hosts and uninfected-vector SIRUV models and conclude that the models give basically the same information when we replace, in the SIR model, the human infectivity by a function of both human and mosquito infectivities.
32 citations
TL;DR: A new privacy-preserving location-sharing system for mOSN is presented, which is flexible to support a variety of location-based applications, in that it enables location- sharing between both trusted social relations and untrusted strangers.
Abstract: Compared with traditional online social networks OSNs, mobile OSNs mOSNs take a step further in that they provide the location-based services, and location-sharing is a fundamental component of mOSN However, without privacy protection, users may be hesitant to share their locations In this paper, we present a new privacy-preserving location-sharing system for mOSN, which is flexible to support a variety of location-based applications, in that it enables location-sharing between both trusted social relations and untrusted strangers It allows user to dynamically change his sharing decryption key when to add or revoke a friend We further propose a security improved system, which can be secure against neighborhood attacks In our proposed systems, threat models are further analysed and users’ location privacy is proved secure Implementation and evaluation show that they are efficient and practical
30 citations
TL;DR: It is proved that the difference scheme is unconditionally stable, and the difference solution converges to the exact one with second order accuracy in both the space and time dimensions.
Abstract: The present work is mainly devoted to studying the fractional nonlinear Schrodinger equation with wave operator. We first derive two conserved quantities of the equation, and then develop a three-level linearly implicit difference scheme. This scheme is shown to be conserves the discrete version of conserved quantities. Using energy method, we prove that the difference scheme is unconditionally stable, and the difference solution converges to the exact one with second order accuracy in both the space and time dimensions. Numerical experiments are performed to support our theoretical analysis and demonstrate the accuracy, discrete conservation laws and effectiveness for long-time simulation.
29 citations
TL;DR: An efficient semi-numerical method is proposed for solving nonlinear singular boundary value problems (BVPs) arising in various physical models using a modification of the Adomian decomposition method (ADM).
Abstract: An efficient semi-numerical method is proposed for solving nonlinear singular boundary value problems BVPs arising in various physical models. We proposed a modification of the Adomian decomposition method ADM. The technique depends on transforming the BVPs to Fredholm integral equations before establishing the recursive scheme for the solution components of a specific solution. The major advantage of the proposed method over the classical ADM or modified ADM is that it provides not only better numerical results but also avoids unnecessary computation for determining the unknown parameters. Moreover, the proposed technique overcomes the singularity issue at the origin . Furthermore, the convergence analysis of the proposed method is established. Two singular examples are examined to demonstrate the accuracy, applicability, and generality of the proposed method.
TL;DR: This paper proposes a new secure and privacy-preserving navigation protocol based on vehicular cloud, which resolves the limitations of previous approaches and is highly efficient because it does not rely on bilinear pairing operations unlike prior secure navigation protocols in the literature.
Abstract: Vehicular cloud is the new paradigm of vehicular ad hoc networks VANETs, which not only takes the recent advance of vehicular technology, but also keeps up with the trend of cloud computing for big data processing and complicated intelligent analysis over VANET environments. In this paper, we present a model for secure navigation systems based on vehicular cloud, which fully utilizes the advantages of cloud computing. In particular, we make up for the limitations of prior VANET-based secure navigation protocols and provide a stronger notion of security for secure navigation services in terms of insider threats and data leakage points of view. We propose a new secure and privacy-preserving navigation protocol based on vehicular cloud, which resolves the limitations of previous approaches. Moreover, the proposed protocol is highly efficient because it does not rely on bilinear pairing operations unlike prior secure navigation protocols in the literature. We demonstrate comprehensive analysis to confirm the fulfilment of the security objectives and the efficiency of the proposed protocol.
TL;DR: These integrals are further applied in proving two theorems on Saigo–Maeda fractional integral operators, and some consequent results and special cases are pointed out in the concluding section.
Abstract: The purpose of this paper is to compute two unified fractional integrals involving the product of two H-functions, a general class of polynomials and Appell function . These integrals are further applied in proving two theorems on Saigo–Maeda fractional integral operators. Some consequent results and special cases are also pointed out in the concluding section.
TL;DR: In this paper, a predator-prey population model with prey gathering together for defence purposes is considered, and the authors characterize the system behavior, establishing that ultimately either only the susceptible prey survive, or the disease becomes endemic, but the predators are wiped out.
Abstract: We consider a predator–prey population model with prey gathering together for defence purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behaviour, establishing that ultimately either only the susceptible prey survive, or the disease becomes endemic, but the predators are wiped out. Another alternative is that the disease is eradicated, with sound prey and predators thriving at an equilibrium or through persistent population oscillations. Finally, the populations can thrive together, with the endemic disease. The only impossible alternative in these circumstances is predators thriving just with infected prey. But this follows from the model assumptions, in that infected prey are too weak to sustain themselves. A mathematical peculiarity of the model is the singularity-free reformulation, which leads to three entirely new dependent variables to describe the system. The model is then extended to encompass the situation in which ingestion of diseased prey is fatal for the predators and to the cases where the predators find the infected prey less palatable.
TL;DR: This work proposes a new approach to model the correlation as a hyperbolic function of a stochastic process, which is much more realistic to model real- world phenomena and could be used in many financial application fields.
Abstract: It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that correlation is not a deterministic quantity. In this work, we propose a new approach to model the correlation as a hyperbolic function of a stochastic process. Our general approach provides a stochastic correlation which is much more realistic to model real-world phenomena and could be used in many financial application fields. Furthermore, it is very flexible: any mean-reverting process with positive and negative values can be regarded and no additional parameter restrictions appear which simplifies the calibration procedure. As an example, we compute the price of a Quanto applying our new approach. Using our numerical results we discuss concisely the effect of considering stochastic correlation on pricing the Quanto.
TL;DR: An efficient identity-based encryption (IBE) scheme over lattice that is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model and the public key size is shorter than that of the known constructions.
Abstract: An efficient identity-based encryption IBE scheme over lattice is proposed in this paper. Under the hardness of the learning with errors LWE problem, the proposed scheme is semantic secure against adaptive chosen identity and chosen plaintext attack in the standard model. To improve the efficiency of the lattice-based IBE scheme, unlike the identity string is encoded into a matrix by a group of public matrices in several known constructions, the identity string of l bits is encoded into a vector with the help of vectors in this paper. With the help of this idea, we achieve the private key extraction of IBE scheme at the same lattice. Then, the public key of the proposed scheme only consists of one matrix and vectors, compared with that the public keys of the known lattice-based IBE schemes all consist as a group of matrices. Hence, the public key size of this scheme is shorter than that of the known constructions.
TL;DR: This paper presents a family of three-parameter derivative-free iterative methods with and without memory for solving nonlinear equations, based on the new fourth-order method without memory, and demonstrates the efficiency and the performance of the presented methods.
Abstract: In this paper, we present a family of three-parameter derivative-free iterative methods with and without memory for solving nonlinear equations. The convergence order of the new method without memory is four requiring three functional evaluations. Based on the new fourth-order method without memory, we present a family of derivative-free methods with memory. Using three self-accelerating parameters, calculated by Newton interpolatory polynomials, the convergence order of the new methods with memory are increased from 4 to 7.0174 and 7.5311 without any additional calculations. Compared with the existing methods with memory, the new method with memory can obtain higher convergence order by using relatively simple self-accelerating parameters. Numerical comparisons are made with some known methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods.
TL;DR: The proposed approach to use optimized conditions obtained by a stochastic technique based on the covariance matrix adaptation evolution strategy for the solution of the gravitational potential equation for the data acquired from the geological survey of Chicxulub crater.
Abstract: Many engineering and scientific problems need to solve boundary value problems for partial differential equations or systems of them. For most cases, to obtain the solution with desired precision and in acceptable time, the only practical way is to harness the power of parallel processing. In this paper, we present some effective applications of parallel processing based on hybrid CPU/GPU domain decomposition method. Within the family of domain decomposition methods, the so-called optimized Schwarz methods have proven to have good convergence behaviour compared to classical Schwarz methods. The price for this feature is the need to transfer more physical information between subdomain interfaces. For solving large systems of linear algebraic equations resulting from the finite element discretization of the subproblem for each subdomain, Krylov method is often a good choice. Since the overall efficiency of such methods depends on effective calculation of sparse matrix–vector product, approaches that use graphics processing unit GPU instead of central processing unit CPU for such task look very promising. In this paper, we discuss effective implementation of algebraic operations for iterative Krylov methods on GPU. In order to ensure good performance for the non-overlapping Schwarz method, we propose to use optimized conditions obtained by a stochastic technique based on the covariance matrix adaptation evolution strategy. The performance, robustness, and accuracy of the proposed approach are demonstrated for the solution of the gravitational potential equation for the data acquired from the geological survey of Chicxulub crater.
TL;DR: The meshless local radial point interpolation (MLRPI) method is applied to simulate three-dimensional wave equation subject to given appropriate initial and Neumann's boundary conditions to demonstrate reliable rates of convergence.
Abstract: In this article, the meshless local radial point interpolation MLRPI method is applied to simulate three-dimensional wave equation subject to given appropriate initial and Neumann's boundary conditions. The main drawback of methods in fully 3-D problems is the large computational costs. In the MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as a cube or a sphere. The point interpolation method with the help of radial basis functions is proposed to form shape functions in the frame of MLRPI. The local weak formulation using Heaviside step function converts the set of governing equations into local integral equations on local subdomains where Neumann's boundary condition is imposed naturally. A two-step time discretization technique with the help of the Crank-Nicolson technique is employed to approximate the time derivatives. Convergence studies in the numerical example show that the MLRPI method possesses reliable rates of convergence.
TL;DR: This work considers a model where an intervention directly affects the observation at its occurrence, but not the underlying mean, and then also enters the dynamics of the process via its dynamics.
Abstract: We study different approaches for modelling intervention effects in time series of counts, focusing on the so-called integer-valued GARCH models. A previous study treated a model where an intervention affects the non-observable underlying mean process at the time point of its occurrence and additionally the whole process thereafter via its dynamics. As an alternative, we consider a model where an intervention directly affects the observation at its occurrence, but not the underlying mean, and then also enters the dynamics of the process. While the former definition describes an internal change of the system, the latter can be understood as an external effect on the observations due to e.g. immigration. For our alternative model we develop conditional likelihood estimation and, based on this, tests and detection procedures for intervention effects. Both models are compared analytically and using simulated and real data examples. We study the effect of model misspecification and computational issues.
TL;DR: The problem of computing exact values or sharp bounds for the strong metric dimension of the rooted product of graphs and express these in terms of invariants of the factor graphs are studied.
Abstract: Let G be a connected graph. A vertex w strongly resolves two different vertices u,v of G if there exists a shortest u−w path, which contains the vertex v or a shortest v−w path, which contains the vertex u. A set W of vertices is a strong metric generator for G if every pair of different vertices of G is strongly resolved by some vertex of W. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. It is known that the problem of computing this invariant is NP-hard. According to that fact, in this paper we study the problem of computing exact values or sharp bounds for the strong metric dimension of the rooted product of graphs and express these in terms of invariants of the factor graphs.
TL;DR: An alternating direction implicit (ADI) scheme with second-order accuracy in both space and time is constructed and a preconditioner is proposed to improve the efficiency for the implementation of the scheme in this situation.
Abstract: In this paper, finite difference schemes for differential equations with both temporal and spatial fractional derivatives are studied. When the order of the time fractional derivative is in , an alternating direction implicit ADI scheme with second-order accuracy in both space and time is constructed. For equations with time fractional derivatives of order lying in , a scheme is derived and solved by the generalized minimal residual method. We also propose a preconditioner to improve the efficiency for the implementation of the scheme in this situation.
TL;DR: Based on two-grid discretizations, two local and parallel finite element algorithms for solving the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media are proposed.
Abstract: In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms.
TL;DR: These asymptotic orders of the errors on k and ω are derived and are demonstrated by several numerical experiments, which show that the efficiency and accuracy of this method significantly improve as the frequencies increase.
Abstract: In this paper, we consider the numerical computation of Hankel transform with weak singularities at the endpoints. By using the analytic continuation, we transform the integral into two line integrals in complex plane, which can be efficiently evaluated by some proper Gauss quadrature rules. The asymptotic orders of the errors on k and ω are derived. These asymptotic orders are demonstrated by several numerical experiments either for fixed k or for fixed ω, which show that the efficiency and accuracy of this method significantly improve as the frequencies increase.
TL;DR: It is proved that for any two connected graphs G and H, the bound is sharp and the k-path-connectivity of a graph G is a generalization of Dirac's notion.
Abstract: Dirac showed that in a -connected graph there is a path through all the k vertices. The k-path-connectivity of a graph G, which is a generalization of Dirac's notion, was introduced by Hager in 1986. Denote by the lexicographic product of two graphs G and H. In this paper, we prove that for any two connected graphs G and H. Moreover, the bound is sharp. We also derive an upper bound of , that is, .
TL;DR: A detection and prevention scheme that protects Android against privilege escalation attack that tries to get full access to all data and can detect and prevent new and unknown malware as well as currently known one.
Abstract: The users of smartphones are rapidly expanding worldwide. These devices have user's security-sensitive data and are ready to communicate with the outside world. Various kinds of malware are attacking smartphones, especially Android phones, but the existing Android security measure does not work satisfactorily. One-third of the current Android malware were privilege escalation attacks, which try to obtain root-privilege to fully compromise the Android security. We propose a detection and prevention scheme that protects Android against such privilege escalation attack that tries to get full access to all data. The proposed scheme monitors important system calls from an application process. If the system call must be called by privileged Android system components in normal operation, the scheme prevent it from executing. The scheme can detect and prevent new and unknown malware as well as currently known one.
TL;DR: This work proposes a class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations and proves the energy conservation, stability, and convergence of these schemes.
Abstract: In this work, we propose a class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrodinger equations. We prove the energy conservation, stability, and convergence of our schemes. In the proposed schemes, we only need to solve linear algebraic systems to obtain the numerical solutions. Numerical examples are presented to verify the accuracy, energy conservation, and stability of these schemes.
TL;DR: This paper completely determine the restricted (edge-)connectivity of .
Abstract: Augmented k-ary n-cube is proposed as a new interconnection network model by Xiang and Steward [Augmented k-ary n-cubes, Inform. Sci. 1811 2011, pp. 239–256]. For a connected graph G, an edge-cut vertex-cut S is called a restricted edge-cut restricted vertex-cut if G–S contains no isolated vertices. The restricted edge-connectivity restricted connectivity of G, denoted by , is the minimum cardinality over all restricted edge-cuts vertex-cuts of G. In this paper, we completely determine the restricted edge-connectivity of . Precisely, for ; for , for , for and , but does not have restricted vertex-cut.
TL;DR: Two recently proposed adaptations of the well-known Stahel–Donoho estimator of multivariate location and scatter for high-dimensional data are discussed and their performance is investigated.
Abstract: We discuss two recently proposed adaptations of the well-known Stahel–Donoho estimator of multivariate location and scatter for high-dimensional data. The first adaptation adjusts the calculation of the outlyingness of the observations while the second adaptation allows to give separate weights to each of the components of an observation. Both adaptations address the possibility that in higher dimensions most observations can be contaminated in at least one of its components. We then combine the two approaches in a new method and investigate its performance in comparison to the previously proposed methods.
TL;DR: The solution and analysis of Kuramoto–Sivashinsky equation by cubic Hermite collocation method is performed and a bound for maximum norm of the semi-discrete solution is derived by using Lyapunov functional.
Abstract: The solution and analysis of Kuramoto–Sivashinsky equation by cubic Hermite collocation method is performed and a bound for maximum norm of the semi-discrete solution is derived by using Lyapunov functional. Error estimates are also obtained for semi-discrete solutions and verified by numerical experiments.