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This paper proposes a low-cost, penalty parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous Galerkin (IPDG) formulation to weakly impose the continuity of the velocity function. However, despite its advantage of symmetry, the symmetric IPDG formulation requires a lot of computational effort to choose an optimal penalty parameter and compute different trace terms. To reduce such effort, we replace the derivatives of the velocity function with its weak derivatives computed by the geometric data of elements. Therefore, our modified EG (mEG) method is a penalty parameter-free numerical scheme that has reduced computational complexity and conserves the optimal convergence orders. Moreover, we achieve pressure robustness for the mEG method by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. The theoretical results are confirmed through numerical experiments with two- and three-dimensional examples. [ABSTRACT FROM AUTHOR]

As we know that, the parameterized Uzawa (PU) method can be very efficient when used to solve the standard saddle point problem, especially, when we have good and accurate estimation of preconditioned Schur complement matrix. In this paper, by taking full use of the special structure of coefficient matrix arising from complex Helmholtz equations, two types of optimized PU (OPU) methods are discussed theoretically and experimentally. Specifically, the convergence factors of these two OPU methods are less than 0.172, and the optimal result of first OPU method can reach 0.0396 with σ 1 ≥ σ 2 > 0 , which is currently the best theoretical result in the literatures. Moreover, the second OPU method has better computational advantages compared with the first OPU method as it avoids the inverse computation of W at each step, indicating the less CPU time will be costed by the second OPU method. In addition, the optimal parameters involved in our algorithms consist of constants, reducing the computational complexity associated with parameter selection. Finally, numerical results are given, not only show the effectiveness of OPU methods, but also confirm the rationality of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider and analyze the stability of three implicit/explicit (IMEX) schemes for the time-dependent natural convection problem, these considered numerical schemes contain the first order backward Euler scheme, second order Crank-Nicolson IMEX scheme and BDF2-AB2 combination. All numerical schemes deal with the linear terms implicitly and the nonlinear terms explicitly. Then the original nonlinear problem is split into two linearized subproblems with constant coefficient matrixes, which reduces the computational complexity and saves a lot of storage. The biggest feature of this paper is to establish the unconditional stability of three IMEX schemes for incompressible flows, which improves and supplements the published theoretical findings. Finally, some numerical examples are provided to show the performances of the considered numerical schemes. [ABSTRACT FROM AUTHOR]

In this paper, several local and parallel finite element algorithms are proposed and analyzed for the 2D/3D stationary inductionless incompressible magnetohydrodynamic (MHD) equations. The core concept is to guarantee the charge-conservation property by choosing mixed finite element spaces in H 0 (div , Ω) × L 0 2 (Ω) to approximate (J , ϕ) , meantime combining the idea of domain decomposition method to realize parallel operation. The characteristic of the proposed algorithms is that the computational complexity is greatly reduced while ensuring the accuracy of the numerical simulation. With the local a prior estimate as the technical means of theoretical analysis, we give the error estimates of the algorithms. Finally, several numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an efficient dimension splitting method is applied to the two-dimensional (2D) and three-dimensional (3D) Cahn-Hilliard type equations with significant applications in physical, biological and computer science. The proposed method can greatly reduce the storage requirements and computational complexity in two and three dimensions, and preserve the high precision and mass conservation. The dimension splitting method is based on auxiliary variables for spatial derivative terms and the operator splitting approach. It converts the 2D or 3D problem into a series of one-dimensional (1D) problems which can be solved by using multi-thread. The stability and accuracy of the proposed method are improved by a local stabilizing approach and extrapolation. The analyses of discrete energy and discrete mass conservation property are shown. Numerical examples confirm the advantages of proposed method. And a variety of simulations, such as the phase separations, curvature driven flows, diblock copolymers, tumor growth and volume restoration, are performed with respect to practical applications. • Dimension splitting method for Cahn-Hilliard type equations. • The global stability is achieved by the local stability of solving each sub-problem. • Fourth-order mass conservative scheme based on the compact differencing and extrapolation. • A large number of numerical examples for practical applications. [ABSTRACT FROM AUTHOR]

In this paper, the unconditionally optimal H 1 -norm error estimate for a two-step fast L1 scheme is considered for a nonlinear subdiffusion equation, which involves the considerations of both the initial singularity of the solution and the computational complexity to evaluate the Caputo derivative. For the fully discrete scheme, we use the fast L1 scheme developed in [28] to speed up the evaluation of the Caputo derivative on nonuniform time step, employ the Galerkin finite element (FE) method to discretize the spatial direction, and take the Newton linearized method to approximate the nonlinear term. While the theory of the L 2 -norm error estimate is well studied, there are few works on the unconditional convergence of H 1 -norm error estimate of the linearized Galerkin FE scheme for nonlinear subdiffusion equations. The main reason is that it requires to find a suitable test function in the FE space. To this end, we here respectively take the time-discrete operator and Laplace operator as the suitable test function in the FE space, and combine an improved discrete fractional Grönwall inequality to achieve the unconditional error estimate in H 1 -norm. Numerical results are provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

The framework of this paper is the improvement of direct-forcing immersed boundary methods in presence of moving obstacles. In particular, motivations for the use of the Direct Forcing (DF) method can be found in the advantage of a fixed computational mesh for fluid–structure interaction problems. Unfortunately, the direct forcing approach suffers a serious drawback in case of moving obstacles: the well known spurious force oscillations (SFOs). In this paper, we strengthen previous analyses of the origin of the SFO through a rigorous numerical evaluation based on Taylor expansions. We propose a remedy through an easy-to-implement regularization process (regularized DF). Formally, this regularization is related to the blending of the Navier–Stokes solver with the interpolation, but no modification of the numerical scheme is needed. This approach significantly cuts off the SFOs without increasing the computational cost. The accuracy and the space convergence order of the standard DF method are conserved. This is illustrated on numerical and physical validation test cases ranging from the Taylor–Couette problem to a cylinder with an imposed sinusoidal motion subjected to a cross-flow. [ABSTRACT FROM AUTHOR]

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths which evolve through the indices of the matrix according to a suitable probability law. The computational complexity is proved in this paper to be significantly better than the classical Monte Carlo method, which allows the computation of much more accurate solutions. Furthermore, the positive features of the algorithm in terms of parallelism were exploited in practice to develop a highly scalable implementation capable of solving some test problems very efficiently using high performance supercomputers equipped with a large number of cores. For the specific case of shared memory architectures the performance of the algorithm was compared with the results obtained using an available Krylov-based algorithm, outperforming the latter in all benchmarks analyzed so far. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with symbolic regression of deterministic chaos systems using a GPA-ES system. A Lorenz attractor, Rössler attractor, Rabinovich–Fabrikant equations and a van der Pol oscillator are used as examples of deterministic chaos systems to demonstrate significant differences in the efficiency of the symbolic regression of systems described by equations of similar complexity. Within the paper, the source of this behavior is identified in presence of structures which are hard to be discovered during the evolutionary process due to the low probability of their occurrence in the initial population and by the low chance to produce them by standard evolutionary operators given by small probability to form them in a single step and low fitness function magnitudes of inter-steps when GPA tries to form them in more steps. This low magnitude of fitness function for particular solutions tends to eliminate them, thus increasing the number of needed evolutionary steps. As the solution of identified problems, modification of terminals and related crossover and mutation operators are suggested. [Copyright &y& Elsevier]

Abstract: Understanding the structure of diffusion flames is often complicated by the dependence of flame structure on the boundary conditions, e.g. composition, temperature and flow field (e.g., strain rate in a counterflow flame.) In this paper, the local carbon-to-oxygen atom ratio (C/O ratio) is applied as a variable to interpret the flame and soot zone structures of counterflow diffusion flames from numerical results with detailed chemical kinetics and transport. Radical pool and soot precursor zones are shown to be clearly delineated in C/O ratio space. The boundary of these two zones, as well as the flame location, are shown to be independent of both stoichiometric mixture fraction ( ) and strain rate when interpreted in C/O space. The kinetic ratio is used to study the characteristics of key chemical reactions and to identify regions of equilibrium for these reactions. The results of this paper indicate that the C/O ratio is a valuable variable for interpreting flame structure and soot precursor chemistry for diffusion flames. [Copyright &y& Elsevier]

Abstract: Designing a key distribution protocol with minimal computation and storage complexity is a challenging issue in secure multimedia multicast. In most of the multimedia multicast applications, the group membership requires secured dynamic key generation and updation operations that usually consume much of the computation time. In this paper, we propose a new GCD (Greatest Common Divisor) based Key Distribution Protocol which focuses on two dimensions. The first dimension deals with the reduction of computation complexity which is achieved in our protocol by performing fewer multiplication operations during the key updation process. To optimize the number of multiplication operations, the existing Karatsuba divide and conquer approach for multiplication is used in this proposed work. The second dimension aims at reducing the amount of information stored in the Group Center and group members while performing the update operation in the key content. The proposed algorithm which focuses on these two dimensions has been implemented and tested using a Cluster tree based key management scheme and has been found to produce promising results. Comparative analysis to illustrate the performance of various key distribution protocols is shown in this paper and it has been observed that this proposed algorithm reduces the computation and storage complexity significantly. [Copyright &y& Elsevier]

Abstract: This paper proposes a block-edge-based Single-Pass Perceptual Embedded Zero-tree Coding (SPPEZC) method. SPPEZC combines two novel compression concepts, called Block-Edge Detection (BED) and the Low-Complexity and Low-Memory Entropy Coder (LLEC), for coding efficiency and quality. Because the edge information can provide beneficial cues for preserving the perceptual quality of compressed images, this paper presents an effective combinative coding scheme, called Single-Pass Perceptual Embedded Zero-tree Coding (SPPEZC), which integrates the improved LLEC and the block-edge information. This approach provides improved perceptual quality in compressed images. Based on the block-edge information, this paper proposes an adaptive architecture for adjusting the quantization table and subsequently coding the quantized coefficients with the LLEC. The proposed SPPEZC approach was implemented and evaluated on both PC-based and DSP-based embedded platforms. Experimental results and comparisons demonstrate that the proposed SPPEZC technique provides computational efficiency as well as satisfactory perceptual quality in compressed images. [Copyright &y& Elsevier]

Abstract This paper presents a fast singular boundary method (SBM) for three-dimensional (3D) Helmholtz equation. The SBM is a boundary-type meshless method which incorporates the advantages of the boundary element method (BEM) and the method of fundamental solutions (MFS). It is easy-to-program, and attractive to the problems with complex geometries. However, the SBM is usually limited to small-scale problems, because of the operation count of O (N 3) with direct solvers or O (N 2) with iterative solvers, as well as the memory requirement of O (N 2). To overcome this drawback, this study makes the first attempt to employ the precorrected-FFT (PFFT) to accelerate the SBM matrix–vector multiplication at each iteration step of the GMRES for 3D Helmholtz equation. Consequently, the computational complexity can be reduced from O (N 2) to O (N l o g N) or O (N). Three numerical examples are successfully tested on a desktop computer. The results clearly demonstrate the accuracy and efficiency of the developed fast PFFT-SBM strategy. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we have designed a simple method for the inverse scattering problem of stratified ocean waveguide. The simple approach applies the bisection technique in parallel to estimate the boundaries of inhomogeneous media from the received partial data. In addition, the algorithm only involves the matrix–vector operations and possesses the optimal computation complexity in both two and three dimensions. In practice, it is easy to carry out, robust against noise and capable of reconstructing the penetrable obstacles of different locations and shapes. We can consider the simple method as a direct and straightforward process to supply satisfactory initial positions for the implementation of any existing more refined but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers. [ABSTRACT FROM AUTHOR]

For the dynamic load identification for stochastic structures, ill-posedness and randomness are main causes that lead to instability and low accuracy. Monte-Carlo simulation (MCS) method is a robust and effective random simulation technique for the dynamic load identification problems of stochastic structures. However, it needs large computational cost and is also inefficient for practical engineering applications because of the requirement of a large quantity of samples. In order to improve its computational efficiency, this paper proposes a novel computational algorithm for the dynamic load identification of stochastic structures. First, the newly developed algorithm transforms dynamic load identification problems for stochastic structures into equivalent deterministic dynamic load identification problems. Second, a new regularization method is proposed to realize the deterministic dynamic load identification. Third, the assessments of the statistics of identified loads are obtained based on statistical theory. Finally, the stability and robustness of the proposed algorithm are well validated by two engineering examples. It is demonstrated that the newly developed regularization method outperforms the traditional Tikhonov regularization method in computational accuracy. Moreover, the newly proposed algorithm can significantly improve the computational efficiency of MCS and is very stable and effective in solving the dynamic load identification for stochastic structures. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose an ordinal optimization (OO) theory-based algorithm to solve the yet to be explored distributed state estimation with continuous and discrete variables problems (DSECDP) of large distributed power systems. The proposed algorithm copes with a huge amount of computational complexity problem in large distributed systems and obtains a satisfactory solution with high probability based on the OO theory. There are two contributions made in this paper. First, we have developed an OO theory-based algorithm for DSECDP in a deregulated environment. Second, the proposed algorithm is implemented in a distributed power system to select a good enough discrete variable solution. We have tested the proposed algorithm for numerous examples on the IEEE 118-bus and 244-bus with four subsystems using a 4-PC network and compared the results with other competing approaches: Genetic Algorithm, Tabu Search, Ant Colony System and Simulated Annealing methods. The test results demonstrate the validity, robustness and excellent computational efficiency of the proposed algorithm in obtaining a good enough feasible solution. [Copyright &y& Elsevier]

Abstract: Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods I, Numer. Math. 56 (1989) 157–177; O. Axelsson, P.S. Vassilevski, Algebraic multilevel preconditioning methods II, SIAM J. Numer. Anal. 27 (1990) 1569–1590] on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant in the so-called strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. More precisely, the value of the upper bound for is a part of the construction of various multilevel extensions of the related two-level methods. In this paper algebraic two-level and multilevel preconditioning algorithms for second-order elliptic boundary value problems are constructed, where the discretization is done using Rannacher–Turek non-conforming rotated bilinear finite elements on quadrilaterals. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The proposed variants of the hierarchical two-level basis are first introduced in a rather general setting. Then, the parameters involved are studied and optimized. The major contribution of the paper is the derived estimates of the constant in the strengthened CBS inequality which is shown to allow the efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver. [Copyright &y& Elsevier]

In this paper, linearly implicit predictor–corrector methods are proposed for solving space-fractional reaction–diffusion equations with non-smooth initial data. The methods are based on Matrix Transfer Technique for spatial discretization and are shown to be unconditionally stable. It is observed that the linearly implicit predictor–corrector method derived by using (1,1)-Padé approximation to matrix exponential function incurs oscillatory behavior for some time steps. These oscillations are due to high frequency components present in the solution and are diminished as the order of the space-fractional derivative decreases (slow diffusion). We present a priori reliability constraint to avoid these unwanted oscillations and generalize the constraints for all ( m , m ) -Padé approximants, m ∈ Z + , to the matrix exponential functions. These time stepping constraints are seen to be dependent on the order of the space-fractional derivative. The linearly implicit predictor–corrector method based on the (0,2)-Padé approximations to the matrix exponential function is shown to be oscillation-free for any time step. Error estimates are obtained for the methods and are theoretically shown to be second-order convergent. Computational complexity of the algorithms is discussed for solving multidimensional space-fractional reaction–diffusion systems. Several numerical experiments are performed to support our theoretical observations and to show the effectiveness, reliability, and efficiency of the methods. [ABSTRACT FROM AUTHOR]

We study the approximation of determinant for large scale matrices with low computational complexity. This paper develops a generalized stochastic polynomial approximation frame as well as a stochastic Legendre approximation algorithm to calculate log-determinants of large-scale positive definite matrices based on the prior eigenvalue distributions. The generalized frame is implemented by weighted L 2 orthogonal polynomial expansions with an efficient recursion formula and matrix–vector multiplications. So the proposed scheme is efficient both in computational complexity and data storage. Respective error bounds are given in theory which guarantee the convergence of the proposed algorithms. We illustrate the effectiveness of our method by numerical experiments on both synthetic matrices and counting spanning trees. [ABSTRACT FROM AUTHOR]

This paper presents a deep analysis of a time-dependent Schrödinger equation with fractional time derivative. After the discretization of the spatial operator the equation is reformulated in terms of a special system of fractional differential equations; it occurs that the eigenvalues of the coefficient matrix lay on the boundary of the stability region of fractional differential equations. The main difficulties in solving this system are hence related to the simultaneous presence of persisting oscillations (possibly with high frequency as it is typical with Schrödinger equations) and a persisting memory (as a consequence of the fractional order); moreover, an accurate spatial discretization gives rise to systems of large to very large size, involving a noteworthy computational complexity. By means of a theoretical analysis the exact solution is split into two or three terms (depending on the order of the fractional derivative), thus to face the numerical computation by different and suitably selected methods: direct evaluation of matrix functions for the terms characterized by smooth behaviour but with persistent memory and a step-by-step strategy, in conjunction with matrix function, for the oscillating term. In both cases, Krylov subspace methods are employed for the computation of matrix functions and convergence results are presented. [ABSTRACT FROM AUTHOR]

This paper focuses on providing the computation methods for the backward time tempered fractional Feynman–Kac equation, being one of the models recently proposed in Wu et al. (2016). The discretization for the tempered fractional substantial derivative is derived, and the corresponding finite difference and finite element schemes are designed with well established stability and convergence. The performed numerical experiments show the effectiveness of the presented schemes. [ABSTRACT FROM AUTHOR]

An enhanced version of a stochastic SParse Approximate Inverse (SPAI) preconditioner for general matrices is presented in this paper. This method is used in contrast to the standard deterministic preconditioners computed by the Modified SParse Approximate Inverse Preconditioner (MSPAI). Thus we present a Monte Carlo preconditioner that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough approximate matrix inverse first, which can further be optimized by an iterative filter process and a parallel refinement, to enhance the accuracy of the inverse and the preconditioner respectively. The advantage of the proposed approach is that finding the sparse Monte Carlo matrix inversion has a computational complexity linear of the size of the matrix, it is inherently parallel and thus can be obtained very efficiently for large matrices and can be used also as an efficient preconditioner while solving systems of linear algebraic equations. The behaviour of the proposed algorithm is studied and its performance measured, evaluated and compared with MSPAI. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel variational model for salt and pepper noise removal, and an efficient numerical algorithm for solving it. The proposed model features the use of an approximating function of l 0 norm to measure the closeness of the reconstructed and observed images at the pixels which are not the candidates of the noisy pixels. In addition, the total variation (TV) of the image on the entire image domain is minimized for edge-preserving smoothing. When solving the proposed minimization problem, to reduce the computational complexity from the expression of the approximating function, we use the dual forms of both TV and data terms, and find the solution of the corresponding primal–dual problem. Numerous experiments on real images, and comparisons with TV-L2, TV-L1, and adaptive median filter (AMF) indicate the effectiveness and robustness of the proposed method in salt and pepper noise removal. [ABSTRACT FROM AUTHOR]

In this paper, we present two novel symbolic computational algorithms to solve periodic pentadiagonal (PP) linear systems. These two algorithms are based on a special matrix decomposition and the use of any fast pentadiagonal linear solver, respectively. Some numerical examples are given in order to demonstrate the performance of the proposed algorithms and their competitiveness with existing algorithms. All of the experiments are performed on a computer workstation with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, we focus on efficient second-order in time approximations of the Allen–Cahn and Cahn–Hilliard equations. First of all, we present the equations, generic second-order schemes (based on a mid-point approximation of the diffusion term) and some schemes already introduced in the literature. Then, we propose new ways of deriving second-order in time approximations of the potential term (starting from the main schemes introduced in Guillén-González and Tierra (2013)), yielding to new second-order schemes. For these schemes and other second-order schemes previously introduced in the literature, we study the constraints on the physical and discrete parameters that can appear to assure the energy-stability, unique solvability and, in the case of nonlinear schemes, the convergence of Newton’s method to the nonlinear schemes. Moreover, in order to save computational cost we have developed a new adaptive time-stepping algorithm based on the numerical dissipation introduced in the discrete energy law in each time step. Finally, we compare the behaviour of the schemes and the effectiveness of the adaptive time-stepping algorithm through several computational experiments. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as for one dimensional problems, for two dimensional problems, and for three dimensional problems, where is the number of degrees of freedom, and is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to for the one dimensional case, for the two dimensional case, and for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of and . Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. [Copyright &y& Elsevier]

Abstract: In this paper a new method is introduced for the estimation of modeling error resulting from homogenization of elastic heterogeneous bodies. The approach is similar to the well known explicit residual approximation error estimation. It is proved that besides the residuum of the equilibrium equation and interelement traction jump also a difference of stress divergences as well as traction jump along the material interfaces contribute to the modeling error estimate. Moreover, explicit specification and numerical evaluation of “stability” constants provide reasonable effectivity index of this error indicator. Selected numerical examples illustrate the promise of this approach. Therefore, the proposed methodology is a computationally inexpensive option for the other methods of modeling error assessment. [Copyright &y& Elsevier]

Abstract: Design of an optimal controller for higher-order or time-delay systems often leads to complex control algorithms. One of the possibilities of control of such processes is their approximation by a lower-order model with a time-delay (dead time). These time-delay processes can be effectively handled by the Model-based Predictive Control (MPC) method. The paper deals with design of an algorithm for adaptive predictive control of higher-order processes, which are approximated by a second-order model of the process with a time-delay. Most processes in industrial practice are characterized by nonlinear behavior and contain uncertainties. The adaptive control strategy is one of the possible approaches to optimal control of such systems. The proposed adaptive predictive controller for control of the time-delay system was tested and verified by simulation of a model of a laboratory heat exchanger which was obtained from measured experimental data. [Copyright &y& Elsevier]

Abstract: Catalysts are omnipresent in the chemical industry. Understanding of catalytic chemical reactions is crucial for a rational development of catalysts. The present paper describes approaches for simulating phenomena in heterogeneous catalysis on a molecular level. Modeling of porous structures and their fractal surfaces will be presented. Simulation of adsorption and diffusion of reactants and products inside the pores by means of various Monte Carlo and Molecular Dynamics algorithms is described, followed by quantum chemical methods for calculating reactions on the active centers. Optimization of pore structures and multiscaling procedures complete the picture. [Copyright &y& Elsevier]

Abstract: Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. In this paper, we introduce fundamental concepts and unique properties of adaptive networks through a brief, non-comprehensive review of recent literature on mathematical/computational modeling and analysis of such networks. We also report our recent work on several applications of computational adaptive network modeling and analysis to real-world problems, including temporal development of search and rescue operational networks, automated rule discovery from empirical network evolution data, and cultural integration in corporate merger. [Copyright &y& Elsevier]

Abstract: We investigate the qualitative behavior of chemical reaction mixtures in their time evolution, specifically when starting from initial conditions that are extremal in the sense that they cannot be extrapolated back in time without nonphysical, negative concentration values arising. Several extremal initial conditions will exist and the maxima and mutual intersections of the corresponding concentration time evolutions are of surprising complexity as to their ordering in time and in value, and as to the coincidences that may occur among them for special values of the rate constants. These extremal time evolutions also exhibit properties of mutual reciprocity that can be expressed by invariants involving their joint kinetics. Such invariants arise naturally, since they curtail the complexity of the coincidence analysis, e.g., by excluding certain intersections and by identifying the times at which certain maxima are reached. In this paper, we analyze the reversible–irreversible three-step linear sequential mechanism and provide charts of parametric subdomains and their boundary curves. Generally, such properties of simple linear and non-linear systems in fact reflect their unexpected complexity. We propose to use a special term for defining this phenomenon: simplexity. [Copyright &y& Elsevier]

Abstract: In the framework of the classical theory of Singularly Perturbed Systems (SPS) there exist two main types of invariant manifolds, i.e. fast and slow manifolds with their own intrinsic dynamics. There are many different methods for dimension and complexity reduction for mechanisms of chemical kinetics, based on the concept of slow invariant manifolds. For instance, most known and popular techniques such as Quasi-Steady State (QSSA) and Partial Equilibrium Approaches (PEA) as well as recently developed Intrinsic Low Dimensional Manifolds (ILDM) and Computational Singular Perturbation (CSP) methods have shown a potential to treat automatically very complex mechanisms comprising hundreds of chemically reacting species. In this respect, the importance of slow invariant manifolds has become more or less clear. However, the importance of fast invariant manifolds is much less transparent. Though without an accurate knowledge about fast manifolds (fast fibers in other terminology) slow manifolds cannot be appropriately identified. In this paper we shall discuss a concept of Singularly Perturbed Vector Fields (SPVF) that is a coordinate free theory of singularly perturbed systems with the main emphasis made on fast invariant manifolds and on the method which allows identification and evaluation of these objects. The importance of these objects in model reduction of mechanisms of chemical kinetics will be addressed. Motivation and application of the method will be demonstrated by a simple model example and by analysis of conventional QSSA and PEA methods. [Copyright &y& Elsevier]

Abstract: In this paper we present a conservative numerical method for the Cahn–Hilliard equation with Dirichlet boundary conditions in complex domains. The method uses an unconditionally gradient stable nonlinear splitting numerical scheme to remove the high-order time-step stability constraints. The continuous problem has the conservation of mass and we prove the conservative property of the proposed discrete scheme in complex domains. We describe the implementation of the proposed numerical scheme in detail. The resulting system of discrete equations is solved by a nonlinear multigrid method. We demonstrate the accuracy and robustness of the proposed Dirichlet boundary formulation using various numerical experiments. We numerically show the total energy decrease and the unconditionally gradient stability. In particular, the numerical results indicate the potential usefulness of the proposed method for accurately calculating biological membrane dynamics in confined domains. [Copyright &y& Elsevier]

Abstract: Weldlines are generally unavoidable during the process of injection mold filling with even moderate complexity when two or more melts meet, which greatly influence the quality of the products. In this paper, we propose a new method to numerically simulate the mold filling process and to capture the weldline adaptively based on the Level Set/Ghost method. The cases where the weldlines are caused by two melt fronts in the injection mold filling process are analyzed, and our special interest is devoted to confirming the position and the shape of the weldline depending on the new adaptive technique based on the level set function. The numerical results show that the proposed method is feasible to detect the influence of the inset size, the inset shape and the inset center place on the weldline. [Copyright &y& Elsevier]

Abstract: Frequent itemset mining from data streams is an important data mining problem with broad applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. However, it is also a difficult problem due to the unbounded, high-speed and continuous characteristics of streaming data. Therefore, extracting frequent itemsets from more recent data can enhance the analysis of stream data. In this paper, we propose an efficient algorithm, called Max-FISM (Maximal-Frequent Itemsets Mining), for mining recent maximal frequent itemsets from a high-speed stream of transactions within a sliding window. According to our algorithm, whenever a new transaction is inserted in the current window only its maximum itemset should be inserted into a prefix tree-based summary data structure called Max-Set for maintaining the number of independent appearance of each transaction in the current window. Finally, the set of recent maximal frequent itemsets is obtained from the current Max-Set. Experimental studies show that the proposed Max-FISM algorithm is highly efficient in terms of memory and time complexity for mining recent maximal frequent itemsets over high-speed data streams. [Copyright &y& Elsevier]

Abstract: The growing complexity of systems-on-chip (SoCs) pushes researchers to propose replacing the bus architecture by Networks-on-Chip (NoCs). The key advantages of NoCs are efficient exploitation of performance and scalability. Nowadays NoCs are a well established research topic and several implementations have been proposed. Some techniques are proposed to improve NoC performance in terms of latency and throughput while others are proposed to improve area utilization and power consumption. An important research in NoC design is the tradeoff between area/power and performance. In order to improve performance some techniques tend to increase the number of buffers. However this method increases area and power consumption. This paper introduces new router architecture, called the Flexible Router, which improves the performance of the overall network using the same amount of available buffers but in more efficient way. Therefore there is no need to increase the size of buffers or to use extra virtual channels (VCs) which cause high power consumption, area overheads, and complex logic. The Flexible Router provides a way to handle the requests to a busy buffer by other buffers in the router. It is observed that the Flexible router can achieve better performance in terms of increasing the saturation rate for Hotspot, Uniform, and Nearest-Neighbor traffic patterns, especially Hotspot with an 11.4% increase. Discussion about area overhead compared to the Base router and analysis of arriving out of order packets (side-effect) are also provided. [Copyright &y& Elsevier]

Abstract: As described in this paper, an encoder that generates drift-error-resilient coded bitstreams is proposed. The proposed drift-error-resilient bitstreams are generated using the TotalCoeff or the total amount of non-zero DCT coefficients to estimate the drift-error distortion. This estimated drift error distortion is then examined in the motion estimation process. Results show that our proposed method can decrease drift error effectively compared to the original encoder and that it can achieve comparable PSNR to a conventional drift-error-resilient encoder. The main advantage of the proposed method compared to a conventional drift-error-resilient encoder is that, comparable PSNR performance, lower complexity and memory usage can be achieved without implementing an open-loop transcoder at the encoder feedback loop. [Copyright &y& Elsevier]

Abstract: Having been widely used in a VoIP system, the ITU-T G.729 standard is of high computational complexity, a heavy load for a real-time operation on a low-end smart phone or other embedded devices even with the G.729A standard. In this paper, there are three methods proposed for an efficient complexity reduction of G.729A, i.e., a combined local optimal pulse method, employed to search an algebraic codebook, a discontinuous pitch estimation, used to analyze the open-loop pitch, and the hybrid two-stage vector quantization (HTVQ), assigned to quantize the line spectral frequency (LSF) coefficients. It is validated by experimental results that the improved version of G.729A can be easily implemented on a smart phone (312 MHz CPU, 64 MB RAM) in real-time operation. In total 80.94% of computational load can be thus eliminated in comparison with the G.729A and a satisfactory speech quality is maintained as intended, an excellent efficiency demonstration by the methods proposed. [Copyright &y& Elsevier]

Abstract: This paper proposed an improved version of the Particle Swarm Optimization (PSO) approach to solve Traveling Salesman Problems (TSP). This evolutionary algorithm includes two phases. The first phase includes Fuzzy -Means clustering, a rule-based route permutation, a random swap strategy and a cluster merge procedure. This approach firstly generates an initial non-crossing route, such that the TSP can be solved more efficiently by the proposed PSO algorithm. The use of sub-cluster also reduces the complexity and achieves better performance for problems with a large number of cities. The proposed Genetic-based PSO procedure is then applied to solve the TSP with better efficiency in the second phase. The proposed Genetic-based PSO procedure is applied to TSPs with better efficiency. Fixed runtime performance was used to demonstrate the efficiency of the proposed algorithm for the cases with a large number of cities. [Copyright &y& Elsevier]

Abstract: This paper aims at showing how the so-called mathematical kinetic theory for active particles can be properly developed to propose a new system biology approach. The investigation begins with an analysis of complexity in biological systems, continues with reviewing a general methodology to reduce complexity and furnishes the mathematical tools to describe the time evolution of such systems by capturing all their features. [Copyright &y& Elsevier]

Abstract: This paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable. We mainly evaluate the system reliability that units of data can be sent from the source to the sink under both time threshold and budget . In particular, the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time. A simple algorithm is proposed to generate all lower boundary points for (), and the system reliability can then be computed in terms of such points by utilizing a union of subsets. Computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently. [Copyright &y& Elsevier]

Abstract: Two-terminal reliability, which is defined as the probability that there exists at least one path from source node to sink node, is an important performance measure in network system. However, it is well known that the complexity of exact two-terminal reliability evaluation is NP-hard. This paper considers a bounding algorithm for computing two-terminal reliability based on decomposition technique originally used in computing multi-state reliability. Compared with traditional bounding algorithms, the proposed algorithm requires neither all MPs/MCs to be enumerated in advance, nor all arcs to have the same state probabilities. It can sequentially improve the quality of approximation according to a predetermined value . Especially, it may be an exact algorithm if it runs into completion. An example shows that the proposed algorithm is practical and effective. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the fractal properties of the generalized Chaikin corner-cutting subdivision scheme with two arbitrary parameters. On the basis of the discussion of limit points on the limit curve, the fractal range of the scheme is obtained and illustrated. The results obtained suggest a clear direction for generating fractal curves by using this scheme. Two fractal examples and their complexity evaluation results obtained by using the box dimension are given. [Copyright &y& Elsevier]

Abstract: We develop a multilevel augmentation method for solving nonlinear boundary value problems. We first describe the multilevel augmentation method for solving nonlinear operator equations of the second kind which has been proposed in our recent paper Chen et al. (2011) , and then apply it to solving the nonlinear two-point boundary value problems of second-order differential equations. The theoretical analysis of convergence order and computational complexity are proposed. Finally numerical experiments are presented to confirm the theoretical estimates and illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract: Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability results related to two implementations of the Richardson Extrapolation (Active Richardson Extrapolation and Passive Richardson Extrapolation) are formulated and proved in this paper. An advanced atmospheric chemistry scheme, which is commonly used in many well-known operational environmental models, is applied in a long sequence of experiments in order to demonstrate the fact that [(a)] it is indeed possible to improve the accuracy of the numerical results when the Richardson Extrapolation is used (also when very difficult, badly scaled and stiff non-linear systems of ODEs are to be treated), [(b)] the computations can become unstable when the combination of the Trapezoidal Rule and the Active Richardson Extrapolation is used, [(c)] the application of the Active Richardson Extrapolation with the Backward Euler Formula is leading to a stable computational process, [(d)] experiments with different algorithms for solving linear systems of algebraic equations are very useful in the efforts to select the most suitable approach for the particular problems solved and [(e)] the computational cost of the Richardson Extrapolation is much less than that of the underlying numerical method when a prescribed accuracy has to be achieved. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate uniqueness problems of entire functions that share one value with one of their derivatives. Let be a non-constant entire function, and be positive integers. If and share 1 CM and , then , and assumes the form , where is a non-zero constant and . This result shows that a conjecture given by Brück is true when , where is an integer. [Copyright &y& Elsevier]

Abstract: When interactions among users of a system have to take place, for example, over the internet, establishing trust relationships among these users becomes crucial. However, the way this trust is established depends to a certain extent on the context where the interactions take place. Most of the time, trust is encoded as a numerical value that might not be very meaningful for a not very experienced user. In this paper we propose a model that takes into account the semantic and the computational sides of trust. This avoids users having to deal directly with the computational side; they instead deal with meaningful labels such as Bad or Good in a given context. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the four useful measurements of the complexity of a term, called the maximum depth, the minimum depth, the variable count, and the operation count. We construct a formula for the complexity of the superposition in terms of complexity of the inputs for each of these measurements. We also obtain formulas for the complexity of in terms of the complexity where is a compound term and is a generalized hypersubstitution. We apply these formulas to the theory of -strongly solid varieties, examining the -normalization chains of a variety with respect to these complexity measurements. [Copyright &y& Elsevier]

Abstract: In this paper, an inversion algorithm for a banded matrix is presented. The twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the decomposition, as is shown with the analysis of computing complexity and the numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with an NP-hard minimization problem, performing data allocation over multiple broadcast channels in the wireless environment. Our idea is to solve the discrete case of such a problem by the concept of gradient in the Euclidean space . The theoretical basis of the novel idea ensures the near-optimality of our solution. Furthermore, the experimental results show that the problem can be solved quickly. [Copyright &y& Elsevier]