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• Multiple Optical Coherence Tomography (OCT) scanned sequences. • The procedure consists in a registration, an average and a filtering of the above OCT images (for this last step the Sampling Kantorovich (SK) algorithm has been used). • The retinal network has been detected by the application of an hybrid segmentation procedure (introduced in the present paper) based on classical Otsu and Phansalkar methods. The aim of this article is to provide an improvement in the reconstruction and visualization of retinal superficial capillary plexus and choriocapillaris images from healthy subjects. The implemented method uses multiple Optical Coherence Tomography (OCT) scanned sequences, performs a registration, an average and a filtering on them using for this last step the Sampling Kantorovich operator (SK). The resulting images are then analyzed with some well known methods in literature to quantitatively evaluate the improvement achieved by the proposed technique. Also fluoroangiography and histological images are introduced as reference to support the reliability and the goodness of the results. [ABSTRACT FROM AUTHOR]

Kernel ridge regression (KRR) is a popular scheme for non-linear non-parametric learning. However, existing implementations of KRR require that all the data is stored in the main memory, which severely limits the use of KRR in contexts where data size far exceeds the memory size. Such applications are increasingly common in data mining, bioinformatics, and control. A powerful paradigm for computing on data sets that are too large for memory is the streaming model of computation , where we process one data sample at a time, discarding each sample before moving on to the next one. In this paper, we propose StreaMRAK - a streaming version of KRR. StreaMRAK improves on existing KRR schemes by dividing the problem into several levels of resolution, which allows continual refinement to the predictions. The algorithm reduces the memory requirement by continuously and efficiently integrating new samples into the training model. With a novel sub-sampling scheme, StreaMRAK reduces memory and computational complexities by creating a sketch of the original data, where the sub-sampling density is adapted to the bandwidth of the kernel and the local dimensionality of the data. We present a showcase study on two synthetic problems and the prediction of the trajectory of a double pendulum. The results show that the proposed algorithm is fast and accurate. [ABSTRACT FROM AUTHOR]

Since unity step size could guarantee the fastest convergence and more detailed analysis for the affine projection (AP) algorithm, a statistical tracking behavior of AP algorithm is discussed in this paper. Deterministic recursive equations are derived for the mean weight error and mean-square error. All the possible correlations between the adaptive filtering coefficients and the past measurement noise are considered as well. [ABSTRACT FROM AUTHOR]

The edge-neighbor-scattering number (ENS) is an alternative invulnerability measure of networks such as the vertices represent spies or virus carriers. Let G = ( V , E ) be a graph and e be any edge in G . The open edge-neighborhood of e is N ( e ) = { f ∈ E ( G ) | f ≠ e , e and f are adjacent}, and the closed edge-neighborhood of e is N [ e ] = N ( e ) ∪ { e } . An edge e in G is said to be subverted when N [ e ] is deleted from G . An edge set X ⊆ E ( G ) is called an edge subversion strategy of G if each of the edges in X has been subverted from G . The survival subgraph is denoted by G / X . An edge subversion strategy X is called an edge-cut-strategy of G if the survival subgraph G / X is disconnected, or is a single vertex, or is ϕ . The ENS of a graph G is defined as E N S ( G ) = max X ⊆ E ( G ) { ω ( G / X ) − | X | } , where X is any edge-cut-strategy of G, ω ( G / X ) is the number of the components of G / X . It is proved that the problem of computing the ENS of a graph is NP-complete. In this paper, we give a polynomial algorithm of ENS of trees. [ABSTRACT FROM AUTHOR]

In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index. To make use of its sparsity, this paper provides a simple and efficient algorithm for index reduction of large scale DAEs system. We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTFs). We also present the extended signature matrix method with the block fixed point iteration and its complexity results. Furthermore, a range of nontrivial problems are demonstrated by our algorithm. [ABSTRACT FROM AUTHOR]

This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability obtained by Ignatovand Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed point of Suzuki’s generalized nonexpansive mappings. We establish some weak and strong convergence theorems in a uniformly convex Banach space. We also provide examples to illustrate the convergence behavior of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm is presented to solve the nonlinear fourth-order differential equations with complicated boundary conditions. The approach combines the Quasi-Newton’s method and the simplified reproducing kernel method. It is worth mentioning that the Quasi-Newton’s method is proposed for solving the nonlinear differential equations for the first time. Meanwhile, the simplified reproducing kernel method is applied to solve the linear equations which are obtained from the conversion of the Quasi-Newton’s method, avoiding the time-consuming Schmidt orthogonalization process. Moreover, the reproducing kernel space and its reproducing kernel are reasonably simple as no considering of the complicated boundary conditions. Furthermore the present scheme is employed successfully on some numerical examples. [ABSTRACT FROM AUTHOR]

This paper addresses the average consensus problem of multi-agent systems with general linear dynamics via event-triggered communications. It is shown how the design of both the control law and the trigger functions depends on parameters of the overall system, and an algorithm is proposed to estimate these parameters in a distributed fashion that does not imply an increase in the number of the communications between agents. As a result, it yields an adaptive control law and an update of the trigger functions’ parameters only at event times. Proofs of asymptotic convergence to average consensus and existence of positive lower bound for the inter-event intervals are provided. Numerical simulations show the effectiveness of the proposed approach and how it compares to constant values of the parameters. [ABSTRACT FROM AUTHOR]

Uncertain differential equation is a type of differential equation driven by Liu process and has been widely applied to many fields especially to uncertain finance. Unfortunately, the analytic solutions of uncertain differential equations cannot always be obtained. So far, some numerical methods have been investigated. This paper designs a new numerical algorithm for solving uncertain differential equations via Milne method. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a fractional thermal wave model for a bi-layered spherical tissue. Implicit finite difference method is employed to obtain the solution of the direct problem. The inverse analysis for simultaneously estimating the Caputo fractional derivative and the relaxation time parameters is implemented by means of the Levenberg–Marquardt method. Compared with the experimental data, we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment. We have also discussed the effect of the fractional derivative, the relaxation time parameters, the initial guess as well as the sensitivity problem. All the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective. [ABSTRACT FROM AUTHOR]

In order to compute meaningful approximations of the solutions of large-scale linear inverse ill-posed problems, some form of regularization should be employed. Cimmino and Landweber methods are well-known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems, despite their usually slow convergence. The goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods. In particular, we provide insight and algorithmic details about the simplified topological ε-algorithm applied to slow-converging iterative regularization methods. The results of many numerical experiments and comparisons with other methods are also displayed. [ABSTRACT FROM AUTHOR]

The sequential block-iterative scheme based on Landweber’s method is a general iterative one for image reconstruction. In this paper, we give the finite termination convergence for this scheme, which provides an approach to choose relaxation coefficients. Furthermore, sufficient and necessary convergence conditions are also established for the sequential block-iterative scheme case. [ABSTRACT FROM AUTHOR]

In this paper, we present an accelerated gradient based algorithm by minimizing certain criterion quadratic function for solving the generalized Sylvester-transpose matrix equation A X B + C X T D = F . The idea is from (Ding and Chen, 2005; Niu et al., 2011; Wang et al., 2012) in which some efficient algorithms were developed for solving the Sylvester matrix equation and the Lyapunov matrix equation. On the basis of the information generated in the previous half-step, we further introduce a relaxation factor to obtain the solution of the generalized Sylvester-transpose matrix equation. We show that the iterative solution converges to the exact solution for any initial value provided that some appropriate assumptions. Finally, some numerical examples are given to illustrate that the introduced iterative algorithm is efficient. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new filled function, and give an efficient criterion to choose its two parameters appropriately. An algorithm for unconstrained global optimization is developed from this new filled function. numerical results with a comparison on many test problems show that this algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

A new statistical analysis model is used to analyze the pseudo affine projection (PAP) algorithm with the optimal step-size in this paper. By setting the weight error to be zero in the direction of the adaptive weight update, the optimal step-size is obtained. Two assumptions for the direction vector are proposed, which simplify the analysis of the convergence behavior for the optimal step-size PAP algorithm. Under this condition, deterministic recursive equations for the weight error and for the mean-square error are derived in the direction of the adaptive weight update. Simulation results are provided to corroborate the analytical results. [ABSTRACT FROM AUTHOR]

This paper deals with design parameter selection of a discrete-time neural second order sliding mode controller for unknown nonlinear systems, based on bacterial foraging optimization. First, a neural identifier is proposed in order to obtain a mathematical model for the unknown discrete-time nonlinear systems, then a novel second order sliding mode controller is proposed. Finally, both, the neural identifier and the controller are optimized using bacterial foraging algorithm. In order to illustrate the applicability of the proposed scheme, simulation results are included for a Van der Pol oscillator. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlinear matrix equations X + A * X q A = Q ( 0 < q ≤ 1 ) and X − A * X q A = Q ( q > 1 ) . Necessary and sufficient conditions for the (unique) existence of Hermitian positive definite solutions of these equations are derived. Effective iterative algorithms are also provided to obtain the unique solution of X + A * X q A = Q ( 0 < q ≤ 1 ) and the minimal and maximal Hermitian positive definite solutions of X − A * X q A = Q ( q > 1 ) . Numerical examples are included to illustrate the efficiency of the presented iteration algorithms. [ABSTRACT FROM AUTHOR]

Class of algorithms referring to the affine projection algorithms (APA) applies updates to the weights in a direction that is orthogonal to the most recent input vectors. This speeds up the convergence of the algorithm over that of the normalized least mean square (NLMS) algorithm, especially for highly colored input processes. In this paper a new statistical analysis model is used to analyze the APA class of algorithms with unity step size. Four assumptions are made, which are based on the direction vector for the APA class. Under these assumptions, deterministic recursive equations for the weight error and for the mean-square error are derived. We also analyze the steady-state behavior of the APA class. The new model is applicable to input processes that are autoregressive as well as autoregressive-moving average, and therefore is useful under more general conditions than previous models for prediction of the mean square error of the APA class. Simulation results are provided to corroborate the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, by applying particular structure of the real representations of quaternion matrices and the Moore–Penrose generalized inverse, we derive the expressions of the minimal norm least squares solution, the pure imaginary least squares solution, and the real least squares solution for the quaternion matrix equation A X = B . The resulting formulas only involve real matrices, which are simpler than those reported in (Yuan et al., 2013). The corresponding algorithms only perform real arithmetic which also consider particular structure of the real representations of quaternion matrices, therefore are very efficient and easily understood. Numerical examples are provided to illustrate the efficiency of our algorithms. [ABSTRACT FROM AUTHOR]

Application of evolutionary computation techniques is relatively novel for machine learning. Motivated by different types of evolutionary computation techniques, different types of automatic programming were proposed. Biogeography-Based Optimization (BBO) is a new evolutionary algorithm that is inspired by the science of biogeography and has been shown to be competitive to other population-based algorithms. Inspired by biogeography theory and previous results, in this paper Biogeography-Based Programming (BBP) is proposed as a new type of automatic programming for creating polynomial regression models. In order to show the effectiveness of the proposed BBP, a number of experiments were carried out on a suite set of benchmark functions and the results were also compared with several existing automatic programming algorithms. Furthermore, sensitivity analysis was performed for the parameter settings of the proposed BBP. The results indicate that the proposed model is promising in terms of success rate and accuracy and it performs better than other algorithms investigated in this consideration. [ABSTRACT FROM AUTHOR]

This paper mainly consider the construction of efficient Uzawa-type algorithms for solving the nonlinear saddle-point problem (NSPP). Two nonlinear inexact Uzawa hybrid algorithms based on one-step Newton method are proposed for solving the NSPPs. By using the so-called energy-norm, the convergence of the proposed algorithms is verified under some practical conditions. In addition, some numerical results are reported to illustrate the behavior of the considered algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a fast proximal point algorithm (PPA) is proposed for solving ℓ 1 -minimization problem arising from compressed sensing. The proposed algorithm can be regarded as a new adaptive version of customized proximal point algorithm, which is based on a novel decomposition for the given nonsymmetric proximal matrix M . Since the proposed method is also a special case of the PPA-based contraction method, its global convergence can be established using the framework of a contraction method. Numerical results illustrate that the proposed algorithm outperforms some existing proximal point algorithms for sparse signal reconstruction. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of smoothing functions. Some favorable properties of the functions are investigated. By using the proposed functions, the affine variational inequality problem (AVI) is reformulated as a system of parameterized smooth equations. A Newton method with a projection-type testing procedure is proposed to solve the equations. Under mild assumptions, we show that the algorithm may find a maximally complementary solution to the monotone AVI in a finite number of iterations. Preliminary numerical results indicate that the proposed smoothing functions are valuable. [ABSTRACT FROM AUTHOR]

In this paper we consider relations between the principal iterations from the Padé family of Kenney and Laub for computing the matrix sign function and the principal iterations from the reciprocal Padé family of Greco, Iannazzo and Poloni, and the dual Padé family of Ziȩtak. We show global convergence of the principal reciprocal Padé iterations and the principal dual Padé iterations. We adopt the dual Padé family of iterations, to which the Newton method belongs, for computing the unitary polar factor of a nonsingular matrix. We present numerical experiments with the scaled Newton method of Higham for computing the unitary polar factor, which show how the quality of the computed inverses of matrices in the scaled Newton method affects the accuracy of the computed polar factorization of a nonsingular matrix. It indicates that assumptions, under which the backward stability of the scaled Newton method has been proved in the literature, cannot be weaker. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new algorithm for the computation of the common solution to the complex conjugate matrix equation system A i X B i + C i X ¯ D i = E i , i = 1 , 2 , … , N . The algorithms only need finite iteration steps, requiring only real computation. Furthermore, the algorithm can be extended to solve a more general complex matrix equation system. Two numerical examples are given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A class of differential quadratic programming problems in finite dimensional spaces is introduced in this paper. First, the existence of solutions for the differential quadratic programming problem is established under some suitable assumptions. Second, an algorithm for solving the differential quadratic programming problem is given and the convergence analysis for the algorithm is shown. Finally, some numerical experiments are reported to verify the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Fractional calculus and fractional differential equations are popular in describing anomalous diffusion, ground water flow and transport, and the price fluctuation in finance, etc. Some numerical methods are developed to solve the fractional ordinary differential equations. However, for most of these methods it seems that we always have to make a trade-off between efficiency and accuracy because of the non-local properties of fractional operators. In other words, for ensuring the accuracy, usually the computation cost is hard to accept; on the other hand if the computation cost is reduced then the accuracy is greatly lost. Based on the idea of equidistributing meshes, this paper designs efficient numerical schemes, which have linearly increasing computation cost with time t but not losing the accuracy at the same time. Error estimates for the proposed schemes are performed; and the numerical examples demonstrate the efficacy of our algorithms. [ABSTRACT FROM AUTHOR]

The parameterized inexact Uzawa methods have been used to solve some of the symmetric saddle point problems. In this paper, a new preconditioned parameterized inexact Uzawa method is presented to solve indefinite saddle point problems. After preconditioning, theoretical analyses show that the iteration method converges under certain conditions. So we propose three new algorithms based on these conditions. Numerical experiments are provided to show the effectiveness of the proposed preconditioner and all these algorithms have fantastic convergence rates by choosing optimal parameters. [ABSTRACT FROM AUTHOR]

A large class of iterative methods for solving nonlinear monotone systems is developed in recent years. In this paper we propose some new FR type directions in the frame of algorithm which is a combination of conjugate gradient approach and hyperplane projection technique. Derivative-free, function-value-based line search combined with projection procedure is used for globalization strategy. Numerical performances of methods with different search directions are compared. [ABSTRACT FROM AUTHOR]

In this paper, a D–N alternating algorithm based on the natural boundary reduction (NBR) is discussed to solve exterior three dimensional (3-D) Poisson problem with prolate spheroid artificial boundary. By the principle of the natural boundary reduction, we obtain the natural integral equation on prolate spheroid artificial boundary, suggest a D–N alternating algorithm, and analysis its convergence of the algorithm. Finally, some numerical examples are presented to show the effectiveness of this method. [ABSTRACT FROM AUTHOR]

The sparse representation of a multiple measurement vector (MMV) is an important problem in compressed sensing theory, the old alternating direction method (ADM) is an optimization algorithm that has recently become very popular due to its capabilities to solve large-scale or distributed problems. The MMV–ADM algorithm to solve the MMV problem by ADM has been proposed by H. Lu, et al. (2011)[24], but the theoretical result about the convergence of matrix iteration sequence generated by the algorithm is left as a future research topic. In this paper, based on the subdifferential property of the two-norm for vector, a shrink operator associated with matrix is established. By using the operator, a convergence theorem is proved, which shows the MMV–ADM algorithm can recover the jointly sparse vectors. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of absolute value equations associated with circular cone (CCAVE for short), which is a generalization of the absolute value equations discussed recently in the literature, analogously to the fact that circular cone is the very generalization of the second-order cone. We show that the CCAVE is equivalent to a class of circular cone linear complementarity problems, and hence generalize the well-known equivalence between absolute value equations and linear complementarity problems. Useful properties of the generalized differential of the absolute value function over the circular cone are investigated, which helps to propose a generalized Newton method for solving the CCAVE. The convergence of this method is established under mild conditions, as well as the efficiency of which is illustrated by some preliminary numerical results. [ABSTRACT FROM AUTHOR]

This paper describes a practical simulation-based algorithm, which we call the Stochastic Grid Bundling Method (SGBM) for pricing multi-dimensional Bermudan (i.e. discretely exercisable) options. The method generates a direct estimator of the option price, an optimal early-exercise policy as well as a lower bound value for the option price. An advantage of SGBM is that the method can be used for fast approximation of the Greeks (i.e., derivatives with respect to the underlying spot prices, such as delta, gamma, etc.) for Bermudan-style options. Computational results for various multi-dimensional Bermudan options demonstrate the simplicity and efficiency of the algorithm proposed. [ABSTRACT FROM AUTHOR]

Recently, many researches have tackled chaos optimization algorithms (COAs) as an attractive method of global optimization. Considering the statistical property such as the probability density function (PDF) of the chaotic sequences, the search ability of COA can improve the global searching capability by escaping the local solutions than classical stochastic optimization algorithms. This paper proposes a novel method for global optimization using spatiotemporal map to improve the performance of the COA. The experimental results of typical nonlinear multimodal benchmark functions optimization show that spatiotemporal COA map (SCOA) improves the convergence and high efficiency compared to five hybrid optimization algorithms, which are the Monte Carlo-BFGS algorithm (MC-BFGS), Logistic map based chaos-BFGS algorithm (LM-BFGS), Skew Tent map based chaos-BFGS algorithm (STM-BFGS), COA based on the Logistic map (LM-COA) and COA based on the Skew Tent map (STM-COA). [ABSTRACT FROM AUTHOR]

An automated exploration of datapath for power-delay tradeoff in high level synthesis (HLS) driven by bacterial foraging optimization algorithm (BFOA) is proposed in this paper. The proposed exploration approach is simulated to operate in the feasible temperature range of an actual Escherichia coli ( E. coli ) bacterium in order to mimic its biological lifecycle. The proposed work transforms a regular BFOA into an adaptive DSE framework that is capable to explore power-performance tradeoffs during HLS. The key sub-contributions of the proposed methodology are as follows: (a) Novel chemotaxis driven exploration drift algorithm; (b) Novel multi-dimensional bacterium encoding scheme to handle the DSE problem; (c) A novel replication algorithm customized to the DSE problem for manipulating the position of the bacterium by keeping the resource information constant (useful for inducing exploitative ability in the algorithm); (d) A novel elimination-dispersal (ED) algorithm to introduce diversity during the exploration process; (e) Adaptive mechanisms such as resource clamping and step size clamping to handle boundary outreach problem during exploration. Finally, results indicated an average improvement in QoR of > 35% and reduction in runtime of > 4% compared to recent approaches. [ABSTRACT FROM AUTHOR]

This paper deals with the merging problem of segments of a composite Bézier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (Woźny and Lewanowicz, 2009) [12]to compute the control points of the merged curve. Thanks to using fast schemes of evaluation of certain connections involving Bernstein and dual Bernstein polynomials, the complexity of our algorithm is significantly less than complexity of other merging methods. [ABSTRACT FROM AUTHOR]

To improve computational efficiency, a new criss-cross algorithm based on the most-obtuse-angle pivoting index rule and deficient basis algorithm is proposed in this paper to solve linear programming problems. We do numerical test values with the 25 standard NETLIB problems, preliminary computational tests demonstrate that the new algorithm overcomes computational difficulties yielding from degeneracy, and reduces the number of iterations and the overall computation time. In addition, the new algorithm has greatly simplified unbound or infeasible conditions to make it more practical. So far, the numerical experimental results show that the new algorithm is promising and is able to implement under the sparse structure, in order to apply to large scale sparse problem. [ABSTRACT FROM AUTHOR]

A new definition of the filled function is presented in this paper. Based on the definition, a new filled function is presented, and a global optimization algorithm is developed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. The numerical experiments further show that the algorithm may solve higher dimensional global optimization problems. [ABSTRACT FROM AUTHOR]

This paper studies the existence of extremal solutions for nonlinear fractional differential equations with nonlinear integral boundary conditions and explores an explicit algorithm which converges to the extremal solutions of the problem at hand. An example is discussed for the illustration of the main work. [ABSTRACT FROM AUTHOR]

Scott (1970) [11] introduced qualitative fixed point techniques as a suitable mathematical tool for program verification. Inspired by the fact that the Scott mathematical tools do not include metric implements, Matthews (1994) [8] introduced the concept of partial metric space with the aim of reconciling the Scott fixed point techniques with metric spaces and proved a fixed point theorem for self-mappings in partial metric spaces providing, thus, quantitative techniques useful, in the spirit of Scott, in denotational semantics. Schellekens (1995) [10] showed that the original Scott ideas can be also applied to asymptotic complexity analysis of algorithms via quantitative fixed point techniques for self-mappings in quasi-metric spaces. Later on Cerdà-Uguet et al. (2012) [3] showed that, contrarily to the case of Matthews partial metric spaces, partial quasi-metrics are useful for modeling the algorithmic complexity by means of quantitative fixed point techniques that preserve the Scott ideas and Schellekens techniques concurrently. In the present paper, we focus our efforts on developing a quantitative fixed point technique, based on partial quasi-metric spaces, that allows us to provide a suitable mathematical tool for program verification and complexity analysis simultaneously and, in addition, preserves the Scott ideas and the essence of Matthews and Schellekens techniques. Moreover, we show its applicability to discuss the running time of computing an algorithm using a recursive denotational specification and the meaning of such an specification. [ABSTRACT FROM AUTHOR]

Differential Search method is recently proposed to solve box constrained global optimization problems. In this paper, we will further extend this method to solve generalized constrained optimization problems, particularly for structure design optimization problems. To handle the constraints, we first propose a novel dynamic S-type soft-threshold penalty method. Then, the original constrained optimization problem is transformed into a sequence of unconstrained optimization problems. The proposed method is mainly comprised of two steps: parameter iteration and solution iteration. The parameter iteration is to update the dynamic penalty parameter through a soft-threshold scheme and the solution iteration is to implement Differential Search algorithm to solve an unconstrained optimization problem. Two benchmark sets, CEC2006 and CEC2010, and four engineering structure design optimization problems are solved by our proposed algorithm as well as many other swarm-based algorithms proposed in recent literatures. Numerical results show that our method can achieve better performance but with fewer function evaluations comparing with the existing algorithms. [ABSTRACT FROM AUTHOR]

Precipitation forecast has been identified as one of the central issues in climate research. However, the underlying mechanisms of precipitation are far from being understood. In this paper, a new algorithm of forecasting precipitation based on law of conservation of mass in hydrological cycle is proposed and its feasibility is verified. The algorithm mainly include three steps: in the first step, the area we employ is divided into a number of sub-areas, the precipitation source and evaporation whereabouts equations for sub-regions are established, and the rationality of them can be verified by checking whether the precipitation source and evaporation equations meet a self-consistent relationship or not; in the second step, a conversion equation for sub-regional precipitation prediction will be established, which characterize the relationship between precipitation and evaporation in the sub-areas; in the last step, if the regional evaporation, precipitation and moisture divergence (convergence) function keep stable in a certain time scale, then precipitation forecast is achieved by evaporation anomalies and moisture divergence function, which can be predicted according to the prophase sea surface temperature and atmospheric circulation. Finally, the northern and southern hemispheres seasonal precipitation, evaporation and moisture divergence (convergence) weighting coefficients are calculated using this algorithm based on European centre for medium-range weather forecasts (ECMWF) interim re-analysis (ERA-Interim) dataset, which well verifies the feasibility of the algorithm. The obtained results may provide new insights for precipitation forecast in the future. [ABSTRACT FROM AUTHOR]

In this paper we are presenting some new approaches to the biological model of neural network, which is strictly based on Hodgkin–Huxley types of models. The first aspect was to introduce stochasticity into a model of dendritic structure of neuron already proposed in Hodgkin and Huxley (1952) by using Markov kinetic schemes (Destexhe et al., 1994). Second thing was to bring into this model a training algorithm which is based on the descent gradient method. Subsequently the trained neural network is supposed to solve a problem of noise removal from a given image. This study is supposed to underline potential of biologically realistic models of neural network, which – with a bit of invention – can be used like conventional artificial neural networks. [ABSTRACT FROM AUTHOR]

Dijkstra’s algorithm to solve the shortest path problem (SPP) is a very well-known algorithm. When applied to real situations, although the shortest path can be computed with Dijkstra’s algorithm, it is not always the one that is chosen. In traffic situations, for example, the driver may not know the exact length of the lanes or the shortest path to follow. Even more compelling is the fact that although the driver knows the shortest route, he/she may prefer choosing a different route. In this paper we present the new algorithm PEDA (Probabilistic Extension of Dijkstra’s Algorithm) which introduces probabilistic changes in the weight of the edges and also in the decisions when choosing the shortest path. When PEDA is applied to traffic flow, more realistic simulations, in which the shortest path is not always chosen, are obtained. This more accurately simulates the more normal behavior of drivers. As an example of an application, we introduce the ATISMART + model, an extension of the ATISMART model, where an accelerated-time simulation of car traffic in a smart city was described. In that previous work, all cars in the system used Dijkstra’s algorithm to choose improved ATISMART + model, for accelerated time simulations of traffic flow in smart cities, uses the new PEDA algorithm. The results obtained show that ATISMART + produces more realistic simulations considering different drivers’ behaviors. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings. The strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real Hilbert space. Our result generalizes several recent results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, a primal-dual quasi interior-point algorithm for inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The algorithm starts from an arbitrarily initial point. Then after finite iterations, the iteration points enter into the interior of the feasible region and the objective function is monotonically decreasing. Furthermore, the proposed algorithm is proved to possess global and superlinear convergence under mild conditions including a weak assumption of positive definiteness. Finally, some encouraging preliminary computational results are reported. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of conjugate gradient algorithms for training neural networks which is based on a new modified nonmonotone scheme proposed by Shi and Wang (2011). The utilization of a nonmonotone strategy enables the training algorithm to overcome the case where the sequence of iterates runs into the bottom of a curved narrow valley, a common occurrence in neural network training process. Our proposed class of methods ensures sufficient descent, avoiding thereby the usual inefficient restarts and it is globally convergent under mild conditions. Our experimental results provide evidence that the proposed nonmonotone conjugate gradient training methods are efficient, outperforming classical methods, proving more stable, efficient and reliable learning. [ABSTRACT FROM AUTHOR]

This paper, as a continued work of Huang and Cao (2014), discusses the multiscale computation of the radiative heat transfer in composite materials or porous media. A novel multiscale asymptotic expansion is presented, and an explicit rate of convergence is derived. We develop a multiscale algorithm for solving this kind of problem. A fully implicit scheme is carefully studied and an iterative algorithm is given. The convergence of the iterative algorithm is proved by the fixed point method. Numerical results confirm the efficiency and accuracy of this approach and show that the novel multiscale asymptotic expansion is essential for the radiative-dominated cases. [ABSTRACT FROM AUTHOR]