Search

Meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility. Especially the tremendous progress in processor technology within recent years relativizes the increase in computation time due to the inherent search algorithm. Nevertheless meshfree approximation schemes are still faced with some challenges, like imposition of Dirichlet boundary conditions, robustness of the algorithm and accuracy. The recent developed Optimal Transportation Meshfree (OTM) method seemed to overcome most of these problems. In this paper the OTM solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation. However this scheme is not stable for some examples of application. Hence an investigation is conducted which shows that the reason for this instability is due to underintegration. Based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the Finite Element Method. In contrast to the original publication, the OTM algorithm is derived here from the principle of virtual work. Local maximum entropy shape functions are used which possess a weak Kronecker- δ property. This enables a direct imposition of Dirichlet boundary conditions if the boundary is convex. The limitations of this basis function are also addressed in this paper. Additionally, the search algorithm presented fulfills basic topological requirements. Several examples are investigated demonstrating the improved behavior of the stabilized OTM algorithm. [ABSTRACT FROM AUTHOR]

Evolutionary multi-objective optimization (EMO) algorithms are actively used for answering optimization problems with multiple contradictory objectives and scheming interpretable and precise real-time applications. A majority of existing EMO algorithms performs better on two or three objectives non-dominated problems; however, they meet complications in managing and maintaining a set of optimal solutions to multi-objective optimization problems. This paper proposes a search space-based multi-objective evolutionary algorithm (SSMOEA) for multi-objective optimization problems. To accomplish the potential of the search space-based method for solving multi-objective optimization problems and to reinforce the selection procedure toward the ideal direction while sustaining an extensive and uniform distribution of solutions is our key objective. To the best of our knowledge, this paper is the first attempt to propose a search space-based multi-objective evolutionary algorithm for multi-objective optimization. The experimental setup used showed that the proposed algorithm is good and competitive in comparison to the existing EMO algorithms from the viewpoint of finding a scattered and estimated solution set in multi-objective optimization problems. SSMOEA can achieve a good trade-off between search space convergence and search space diversity in the appropriate experimental setup. [ABSTRACT FROM AUTHOR]

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors x ∈ R d , the concept has been extended to cover many other types of problems. A noteable example is low-rank matrix recovery. Many methods used for recovery rely on solving convex programs. A particularly nice trait of compressed sensing is its geometrical intuition. In recent papers, a classical optimality condition has been used together with tools from convex geometry and probability theory to prove beautiful results concerning the recovery of signals from Gaussian measurements. In this paper, we aim to formulate a geometrical condition for stability and robustness, i.e. for the recovery of approximately structured signals from noisy measurements. We will investigate the connection between the new condition with the notion of restricted singular values , classical stability and robustness conditions in compressed sensing, and also to important geometrical concepts from complexity theory. We will also prove the maybe somewhat surprising fact that for many convex programs, exact recovery of a signal x 0 immediately implies some stability and robustness when recovering signals close to x 0 . [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of computing the 2-vertex-connected components of directed graphs. We present a new algorithm for solving this problem in O ( n m ) time. Furthermore, we show that the old algorithm of Erusalimskii and Svetlov runs in O ( n m 2 ) time. In this paper, we investigate the relationship between 2-vertex-connected components and dominator trees. We also consider three applications of our new algorithm, which are approximation algorithms for problems that are generalization of the problem of approximating the smallest 2-vertex-connected spanning subgraph of 2-vertex-connected directed graph. [ABSTRACT FROM AUTHOR]

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we present an efficient framework for the evaluation of subdivision schemes with polynomial reproduction property. For all interested rational parameters between 0 and 1 with the same denominator, their exact limit positions on the subdivision curve can be obtained by solving a system of linear equations. When the framework is applied to binary and ternary 4-point interpolatory subdivision schemes, we find that the corresponding coefficient matrices are strictly diagonally dominant, and so the evaluation processes are robust. For any individual irrational parameters between 0 and 1, its approximate value is computed by a recursive algorithm which can attain an arbitrary error bound. For surface schemes generalizing univariate subdivision schemes with polynomial reproduction property, exact evaluation methods can also be derived by combining Stam’s method with that of this paper. [ABSTRACT FROM AUTHOR]

Empirical evidence shows that repositories of business process models used in industrial practice contain significant amounts of duplication. This duplication arises for example when the repository covers multiple variants of the same processes or due to copy-pasting. Previous work has addressed the problem of efficiently retrieving exact clones that can be refactored into shared subprocess models. This paper studies the broader problem of approximate clone detection in process models. The paper proposes techniques for detecting clusters of approximate clones based on two well-known clustering algorithms: DBSCAN and Hierarchical Agglomerative Clustering (HAC). The paper also defines a measure of standardizability of an approximate clone cluster, meaning the potential benefit of replacing the approximate clones with a single standardized subprocess. Experiments show that both techniques, in conjunction with the proposed standardizability measure, accurately retrieve clusters of approximate clones that originate from copy-pasting followed by independent modifications to the copied fragments. Additional experiments show that both techniques produce clusters that match those produced by human subjects and that are perceived to be standardizable. [ABSTRACT FROM AUTHOR]

Abstract In this paper we show that it is possible to estimate the backward error for the approximation of the matrix exponential on-the-fly , without the need to precompute in high precision quantities related to specific accuracies. In this way, the scaling parameter s and the degree m of the truncated Taylor series (the underlying method) are adapted to the input matrix and not to a class of matrices sharing some spectral properties, such as with the classical backward error analysis. The result is a very flexible method which can approximate the matrix exponential at any desired accuracy. Moreover, the risk of overscaling, that is the possibility to select a value s larger than necessary, is mitigated by a new choice as the sum of two powers of two. Finally, several numerical experiments in MATLAB with data in double and variable precision and with different tolerances confirm that the method is accurate and often faster than available good alternatives. [ABSTRACT FROM AUTHOR]

Abstract This paper mainly investigates the numerical implementation issue of fractional order systems. First, a pattern of fixed pole schemes are developed to approximate fractional integrator/differentiator, whose common is that the poles keep constant for different α. Then, two solutions are proposed to improve the approximation performance around α = 0. Afterwards, the simulation schemes are introduced for two kinds of fractional order systems. In those schemes, the configuration problem of nonzero initial value is considered. Finally, a fair and solid comparison to the classical approximation methods is presented, demonstrating the effectiveness and efficiency of the elaborated algorithms. Highlights • A universal fixed pole approximation algorithm is derived for fractional integrator/differentiator. • The improvement is made to achieve a better performance with smaller order. • Two approximation schemes are presented for implementing fractional transfer function model. • Three approximation schemes are proposed for implementing fractional state space model. • The configuration of nonzero initial system state is discussed for fractional order system. [ABSTRACT FROM AUTHOR]

Highlights • A framework for convexifying MINLP problems containing signomial functions and twice-differentiable functions is presented. • Lifting transformation schemes based on power, exponential and α BB-type reformulations is used. • The transformations used in the framework are obtained by solving an optimization problem in a preprocessing step. • The reformulations technique is included in a global algorithm that can solve any twice-differentiable MINLP problem. Abstract In this paper, a framework for reformulating nonconvex mixed-integer nonlinear programming (MINLP) problems containing twice-differentiable (C 2) functions to convex relaxed form is discussed. To provide flexibility and for utilizing more effective transformation strategies, the twice-differentiable functions can be partitioned into convex, signomial and general nonconvex functions. The latter two can then be convexified using lifting transformations in combination with approximations using piecewise linear functions (PLFs). However, since there are many degrees of freedom in how to select the set of transformations, an optimization-based method is proposed for finding an optimal set. The lifting transformations are based on single-variable power and exponential transformations for signomials. For nonconvex C 2-functions the α reformulation (α R) technique as well as more generally the method of difference of convex functions can be applied. In the α R, the α BB convex underestimator can be used. The framework is utilized in the α signomial global optimization (α SGO) algorithm to find the ϵ -global solution to a nonconvex problem by iteratively updating the approximations provided by the PLFs. The framework can also be used to directly obtain a convex relaxation of any nonconvex MINLP problem of the specified type to a determined accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables. [ABSTRACT FROM AUTHOR]

In this paper, we consider the matrix equation A X A H + C Y C H = F , where A , C and F are given matrices with appropriate sizes and [ X , Y ] is an unknown Hermitian and generalized skew-Hamiltonian matrix pair. Based on matrix differential calculus and projection theorem in inner product spaces, we exploit the best approximate solution [ X ̂ , Y ̂ ] in the set S to a given matrix pair [ X ∗ , Y ∗ ] , where S signifies the least-squares Hermitian and generalized skew-Hamiltonian solution set of the matrix equation A X A H + C Y C H = F . The analytical expression of the best approximate solution is presented by applying the canonical correlation decomposition and the generalized singular value decomposition. Finally, a numerical algorithm and an illustrated example are given. [ABSTRACT FROM AUTHOR]

This paper concerns a two-field reduced basis algorithm for the metamodelling of parametrized one-way coupled thermoelasticity problems based on the constitutive relation error (CRE) estimation. The coupled system consists of parametrized thermal diffusion and elastostatic equations which are explicitly coupled in a one-way manner. The former can be solved in advance independently and the latter can be solved afterwards using the solution of the former. For the fast and accurate analysis of the coupled system, we developed an algorithm that can choose adaptively the number of reduced basis functions of the temperature field to approximate the CRE equality of the mechanical field. We compute approximately the upper bound for the true errors of displacement and stress fields in energy norms. To enable this, a two-field greedy sampling strategy is adopted to construct the displacement and stress fields in an efficient manner. The computational efficiency of the proposed approach is demonstrated with computing the effective coefficient of thermal expansion of heterogeneous materials. [ABSTRACT FROM AUTHOR]

Fractional order systems become increasingly popular due to their versatility in modelling and control applications across various disciplines. However, the bottleneck in deploying these tools in practice is related to their implementation on real-life systems. Numerical approximations are employed but their complexity no longer match the attractive simplicity of the original fractional order systems. This paper proposes a low-order, computationally stable and efficient method for direct approximation of general order (fractional order) systems in the form of discrete-time rational transfer functions, e.g. processes, controllers. A fair comparison to other direct discretization methods is presented, demonstrating its added value with respect to the state of art. [ABSTRACT FROM AUTHOR]

A string T of length m is periodic in P of length p if P is a substring of T and T [ i ] = T [ i + p ] for all 0 ≤ i ≤ m − p − 1 and m ≥ 2 p . The shortest such prefix, P , is called the period of T (i.e., P = T [ 0 . . p − 1 ] ). In this paper we investigate the period recovery problem. Given a string S of length n , find the primitive period(s) P such that the distance between S and a string T that is periodic in P is below a threshold τ . We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O ( n log ⁡ n ) -time algorithm, where τ is given as ⌊ n ( 2 + ϵ ) p ⌋ , for ϵ > 0 . For the edit distance case, τ = ⌊ n ( 3.75 + ϵ ) p ⌋ and ϵ > 0 , we provide an O ( n 4 / 3 ) -time algorithm. [ABSTRACT FROM AUTHOR]

An exact run in a string T is a non-empty substring of T that is a repetition of a smaller substring possibly followed by a prefix of it. Finding maximal exact runs in strings is an important problem and therefore a well-studied one in the area of stringology. For a given string T of length n , finding all maximal exact runs in the string can be done in O ( n log ⁡ n ) time on general ordered alphabets or O ( n ) time on integer alphabets. In this paper, we investigate the maximal approximate runs problem: for a given string T and a number k , find non-empty substrings T ′ of T such that changing at most k letters in T ′ transforms them into a maximal exact run. We present an O ( n k 2 log 2 ⁡ k + o c c ) algorithm to solve this problem, where occ is the number of substrings found. [ABSTRACT FROM AUTHOR]

The Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method is a popular iterative approximation method in structural reliability analysis. However, it may pose numerical instability and result in divergence in the face of high nonlinearity. In the present paper, two adjusting parameters are included in this method and a generalization of HL-RF is proposed. The represented parameters are to control the convergence of the sequence especially when nonlinearity increases. The proposed algorithm actually improves the performance of HL-RF in convergence, while it remains as simple as HL-RF to implement without any need to merit functions or line search processes, needed in many approximation methods. Through various numerical examples, the robustness and efficiency of the proposed algorithm in highly nonlinear cases have been shown. [ABSTRACT FROM AUTHOR]

The algorithm by Al-Mohy and Higham (2011) [2] computes an approximation to e A b for given A and b , where A is an n -by- n matrix and b is, for example, a vector of dimension n . It uses a scaling together with a truncated Taylor series approximation to the exponential of the scaled matrix. In this paper, a method is developed for estimating the roundoff error of the computed solution. An asymptotic expansion of this error for small values of the unit roundoff is the basis of the method. The roundoff error is further expressed in terms of sums of rounding errors, which occur during the computation. A second approximation to e A b , which is computed with a lower precision than the first one, is used to evaluate these rounding errors in practice. The result is an upper bound on the normwise relative roundoff error. Further, an algorithm is proposed for computing the error bound. The cost for performing this algorithm depends on the type of problem and the accuracy, which is required for the error estimate. In case that all computations are performed with standard precisions, this cost can be expressed in terms of the number of computed matrix-vector products and is bounded from above by two times the cost for computing e A b . [ABSTRACT FROM AUTHOR]

Data is growing at an exponential pace. To cope with this data explosion, we need effective data processing and analysis techniques. Feature selection is selecting a subset of features from a dataset that still provides most of the useful information. Various tools are available as underlying framework for this process however, Rough Set Theory is the most prominent tool due to its analysis friendly nature. Majority of Rough Set based feature selection algorithms use positive region based dependency measure as the sole criteria to select feature subset. Calculating positive region requires calculation of lower approximation which consequently involves indiscernibility relation. In this paper, new definitions of two Rough Set preliminaries i.e. lower and upper rough set approximation are proposed. New definitions of approximations are computationally less expensive as compared to the conventional. The proposed redefinitions showed 42.78% decrease in execution time for redefined lower approximation and 43.06% decrease in case of redefined upper approximation, for five publicly available datasets while maintaining 100% accuracy. Finally based on these redefined approximations we proposed a feature selection algorithm, which when compared with state of the art techniques showed significant increase in performance without the affecting the accuracy. [ABSTRACT FROM AUTHOR]

Sweep coverage provides solutions for the applications in wireless sensor networks, where periodic monitoring is sufficient instead of continuous monitoring. The objective of the sweep coverage problem is to minimize the number of sensors required in order to guarantee sweep coverage for a given set of points of interest on a plane. Instead of using only mobile sensors for sweep coverage, use of both static and mobile sensors can be more effective in terms of energy utilization. In this paper, we introduce two variations in sweep coverage problem, where energy consumption by the sensors is taken into consideration. First, an energy efficient sweep coverage problem is proposed, where the objective is to minimize energy consumption by a set of sensors (mobile and/or static) with guaranteed sweep coverage. We prove that the problem is NP-hard and cannot be approximated within a factor of 2. An 8-approximation algorithm is proposed to solve the problem. A 2-approximation algorithm is also proposed for a special case. Second, an energy restricted sweep coverage problem is proposed, where the objective is to find the minimum number of mobile sensors to guarantee sweep coverage subject to the condition that the energy consumption by a mobile sensor in a given time period is bounded. We propose a ( 5 + 2 α ) -approximation algorithm to solve this NP-hard problem. [ABSTRACT FROM AUTHOR]

Systems of reaction–diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular, self-diffusion is a nonlinear term that models overcrowding of a particular species. The nonlinearity complicates attempts to construct efficient and accurate numerical approximations of the underlying systems of equations. In this paper, a new nonlinear splitting algorithm is designed for a partial differential equation that incorporates self-diffusion. We present a general model that incorporates self-diffusion and develop a numerical approximation. The numerical analysis of the approximation provides criteria for stability and convergence. Numerical examples are used to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

An edge-bicolored graph G = ( V , R ∪ B ) is called Red/Blue-split graph if there exists a partition I B and I R of V such that I B and I R are independent sets in ( V , B ) and ( V , R ) , respectively. Red/Blue-split graphs generalize several well studied graph classes including split graphs, bipartite graphs and König–Egerváry graphs. In this paper we consider the algorithmic complexity of various optimization problems like minimum edge (or vertex) deletion and maximum edge (or vertex) induced subgraph related to Red/Blue split graphs. All these problems are NP -hard and thus we look at them from algorithmic paradigms that are meant for coping with NP -hardness. We obtain various hardness as well as algorithmic results for these problems in the realm of approximation algorithms and parameterized complexity. The main tool we use to obtain all our results is polynomial time transformations between appropriate problems. On the way, we also resolve some problems related to inapproximability about certain optimization problems mentioned by Korach et al. (2006) [17] . [ABSTRACT FROM AUTHOR]

Evaluation of objective function for problems of structural optimization is generally considered as computationally expensive and can take from few seconds to hours or even days. After certain number of solutions has been evaluated during optimization, artificial neural networks (ANNs) can be trained and used to approximate the objective function. The number of training points depends on the character and topology of objective function, but the most important factor is the dimensionality of objective function. Similarly as the performance of optimization algorithms, requirements on training data for ANNs are affected by so called “curse of dimensionality”. To achieve the same precision of ANN approximation over n-dimensional space, the number of training points grows exponentially with the number of dimensions. This paper presents a feasibility study of using ANNs for approximation of objective function for problems solved by structural optimization with respect to the number of optimization variables. The goal of this study was to find the maximum number of dimensions, where it is feasible to use ANNs for approximation of objective function. Test problem with varying number of optimization variables was used to assess the feasibility of using ANN. [ABSTRACT FROM AUTHOR]

Many particulate processes in process and bioprocess engineering can be described with multi-dimensional population balances. Approximate moment methods are frequently used for their solution. In the present paper a new approach is presented, which is particular efficient when the number of internal coordinates is high. It combines the direct quadrature method of moments with monomial cubatures. With the new method the computational effort increases only polynomially, in the simplest case even only linearly with the number of internal coordinates, compared to an exponential increase for the well known Gausssian cubatures. The technique is evaluated for a five dimensional benchmark problem describing virus replication in continuous cell cultures. Furthermore, the algorithm is applied to analyze influenza virus replication in genetically modified cell lines. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new highly efficient two-step algorithm based on local Gauss integration for the 2D steady-state natural convection problem. The basic idea of the algorithm is to compute an initial approximation for the velocity, pressure and temperature based on a lowest equal-order finite element pair P 1 – P 1 – P 1 , then to solve a linear system based on a quadratic equal-order finite element pair P 2 – P 2 – P 2 on the same mesh. Next, we give the corresponding stability and convergence of the algorithm, which show that the new two-step algorithm has the same order convergence rate as the quadratic equal-order stabilized finite element method. Finally, some numerical examples show that the new method is efficient, reliable, has good precision and can save a lot of computational time compared with the quadratic equal-order stabilized method. [ABSTRACT FROM AUTHOR]

A vertex subset C of a connected graph G is called a connected k -path vertex cover ( C V C P k ) if every path on k vertices contains at least one vertex from C , and the subgraph of G induced by C is connected. This concept originated in the field of security and supervisory control. This paper studies the minimum (weight) C V C P k problem. We first show that the minimum weight C V C P k problem can be solved in time O ( n ) when the graph is a tree, and can be solved in time O ( r n ) when the graph is a uni-cyclic graph whose unique cycle has length r , where n is the number of vertices. Making use of the algorithm on trees, we present a k -approximation algorithm for the minimum (cardinality) C V C P k problem under the assumption that the graph has girth at least k . An example is given showing that performance ratio k is asymptotically tight for our algorithm. [ABSTRACT FROM AUTHOR]

We consider a variant of the well-known Longest Common Subsequence (LCS) problem for weighted sequences. A weighted sequence determines the probability for each symbol to occur at a given position of the sequence (such sequences are also called Position Weighted Matrices, PWM). Two possible such versions of the problem were proposed by (Amir et al., 2009 and 2010), they are called LCWS and LCWS2 (Longest Common Weighted Subsequence 1 and 2). We solve an open problem, stated in the paper by Amir et al., of the tractability of a log-probability version of LCWS2 problem for bounded alphabets, showing that it is NP-hard already for an alphabet of size 2. We also improve the ( 1 / | Σ | ) -approximation algorithm given by Amir et al. (where Σ is the alphabet): we show a polynomial-time approximation scheme (PTAS) for the LCWS2 problem using O ( n 5 ) space. We also give a simpler (1/2)-approximation algorithm for the same problem using only O ( n 2 ) space. [ABSTRACT FROM AUTHOR]

Although, the Hamiltonicity of solid grid graphs are polynomial-time decidable, the complexity of the longest cycle problem in these graphs is still open. In this paper, by presenting a linear-time constant-factor approximation algorithm, we show that the longest cycle problem in solid grid graphs is in APX. More precisely, our algorithm finds a cycle of length at least 2 n 3 + 1 in 2-connected n -node solid grid graphs. [ABSTRACT FROM AUTHOR]

A solar radiation forecasting model can be utilized is a scientific contrivance for investigating future viability of solar energy potentials. In this paper, a wavelet-coupled support vector machine (W-SVM) model was adopted to forecast global incident solar radiation based on the sunshine hours ( S t ), minimum temperature ( T max ), maximum temperature ( T max ), windspeed ( U ), evaporation ( E ) and precipitation ( P ) as the predictor variables. To ascertain conclusive results, the merit of the W-SVM was benchmarked with the classical SVM model. For daily forecasting, sixteen months of data (01-March-2014 to 30-June-2015) partitioned into the train (65%) and test (35%) set for the three metropolitan stations (Brisbane City, Cairns Aero and Townsville Aero) were utilized. Data were decomposed into their wavelet sub-series by discrete wavelet transformation algorithm and summed up to create new series with one approximation and four levels of detail using Daubechies-2 mother wavelet. For daily forecasting, six model scenarios were formulated where the number of input was increased and the forecast was assessed by statistical metrics (correlation coefficient r ; Willmott’s index d ; Nash-Sutcliffe coefficient E NS ; peak deviation P dv ), distribution statistics and prediction errors (mean absolute error MAE ; root mean square error RMSE ; mean absolute percentage error MAPE ; relative root mean square error RMSE ). Results for daily forecasts showed that the W-SVM model outperformed the classical SVM model for optimum input combinations. A sensitivity analysis with single predictor variables yielded the best performance with S t as an input, confirming that the largest contributions for forecasting solar energy is derived from the sunshine hours per day compared to the other prescribed inputs. All six inputs were required in the optimum W-SVM for Brisbane and Cairns stations to yield r = 0.928, d = 0.927, E NS = 0.858, P dv = 1.757%, MAE = 1.819 MJ m −2 and r = 0.881, d = 0.870, E NS = 0.762, P dv = 9.633%, MAE = 2.086 MJ m −2 , respectively. However, for Townsville, the time-series of S t , T min and T max and E were required in the optimum model to yield r = 0.858, d = 0.886, E NS = 0.722, P dv = 10.282% and MAE = 2.167 MJ m −2 . In terms of the relative model errors over daily forecast horizon, W-SVM model was the most accurate precise for Townsville ( RRMSE = 12.568%; MAPE = 12.666%) followed by Brisbane (13.313%; 13.872%) and Cairns (14.467%; 15.675%) weather stations. A set of alternative models developed over the monthly, seasonal and annual forecast horizons verified the long-term forecasting skill, where lagged inputs of T max , T min , E , P and VP for Roma Post Office and Toowoomba Regional stations were employed. The wavelet-coupled model performed well, with r = 0.965, d = 0.964, P dv = 2.249%, RRMSE = 5.942% and MAPE = 4.696% (Roma) and r = 0.958, d = 0.943, P dv = 0.979%, RRMSE = 7.66% and MAPE = 6.20% (Toowoomba). Accordingly, the results conclusively ascertained the importance of wavelet-coupled SVM predictive model as a qualified stratagem for short and long-term forecasting of solar energy for assessment of solar energy prospectivity in this study region. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of positivity preservation in numerical algorithms for simulating fiber suspension flows. In contrast to fiber orientation models based on the Advani–Tucker evolution equations for even-order orientation tensors, the probability distribution function of fiber orientation is approximated using the Galerkin discretization of the Fokker–Planck equation with Fourier basis functions or spherical harmonics. This procedure leads to a natural generalization of orientation tensor models replacing ad hoc closure approximations by Galerkin equations for the fine-scale components. After introducing an operator splitting approach to solving the discretized Fokker–Planck equation, we present conditions and correction techniques that guarantee physically correct distribution functions. As the reader will see, the derivation of these conditions is independent of the space dimension and their applicability is not limited to the simulation of fiber suspensions. [ABSTRACT FROM AUTHOR]

Various papers have analyzed the noisy optimization of convex functions. This analysis has been made according to several criteria used to evaluate the performance of algorithms: uniform rate, simple regret and cumulative regret. We propose an iterative optimization framework, a particular instance of which, using Hessian approximations, provably (i) reaches the same rate as Kiefer–Wolfowitz algorithm when the noise has constant variance, (ii) reaches the same rate as Evolution Strategies when the noise variance decreases quadratically as a function of the simple regret, (iii) reaches the same rate as Bernstein-races optimization algorithms when the noise variance decreases linearly as a function of the simple regret. [ABSTRACT FROM AUTHOR]

Being the unbalanced version of the famous Min s – t Cut problem, the Min k -Size s – t Cut problem asks to find a k -size s – t cut with the minimum capacity, where a k -size s – t cut means an s – t cut with its s -side having size at most k . This problem is fundamental and has extensive applications, especially in community identification in social and information networks. It is known that the Min k -Size s – t Cut problem is NP-hard and can be approximated within O ( log ⁡ n ) , where n is the number of vertices in the input graph. In this paper, we give a new approximation algorithm for the Min k -Size s – t Cut problem based on the parametric flow technique. The algorithm is very simple and has only three lines to state. Its approximation ratio is k + 1 k + 1 − k ⁎ , where k ⁎ is the size of the s -side of an optimal solution. [ABSTRACT FROM AUTHOR]

For two positive integers m , k and a connected graph G = ( V , E ) with a nonnegative vertex weight function w , the balanced m -connected k -partition problem, denoted as BC m P k , is to find a partition of V into k disjoint nonempty vertex subsets ( V 1 , V 2 , … , V k ) such that each G [ V i ] (the subgraph of G induced by V i ) is m -connected, and min 1 ≤ i ≤ k ⁡ { w ( V i ) } is maximized. The optimal value of BC m P k on graph G is denoted as β m ⁎ ( G , k ) , that is, β m ⁎ ( G , k ) = max ⁡ min 1 ≤ i ≤ k ⁡ { w ( V i ) } , where the maximum is taken over all m -connected k -partition of G . In this paper, we study the BC 2 P k problem on interval graphs, and obtain the following results. (1) For k = 2 , a 4/3-approximation algorithm is given for BC 2 P 2 on 4-connected interval graphs. (2) In the case that there exists a vertex v with weight at least W / k , where W is the total weight of the graph, we prove that the BC 2 P k problem on a 2 k -connected interval graph G can be reduced to the BC 2 P k − 1 problem on the ( 2 k − 1 ) -connected interval graph G − v . In the case that every vertex has weight at most W / k , we prove a lower bound β 2 ⁎ ( G , k ) ≥ W / ( 2 k − 1 ) for 2 k -connected interval graph G . (3) Assuming that weight w is integral, a pseudo-polynomial time algorithm is obtained. Combining this pseudo-polynomial time algorithm with the above lower bound, a fully polynomial time approximation scheme (FPTAS) is obtained for the BC 2 P k problem on 2 k -connected interval graphs. [ABSTRACT FROM AUTHOR]

In this paper we devise a new algorithm for completing surface with missing geometry and topology founded upon the theory and techniques of sparse signal recovery. The key intuition is that any meaningful 3D shape, represented as a discrete mesh, almost certainly possesses a low-dimensional intrinsic structure, which can be expressed as a sparse representation in some transformed domains. Instead of estimating the missing geometry directly, our novel method is to find this low-dimensional representation which describes the entire original shape. More specifically, we find that, for many shapes, the vertex coordinate function can be well approximated by a very sparse coefficient representation with respect to the dictionary comprising its Laplacian eigenfunctions, and it is then possible to recover this sparse representation from partial measurements of the original shape. Taking advantage of the sparsity cue, we advocate a novel variational approach for surface inpainting, integrating data fidelity constraints on the shape domain with coefficient sparsity constraints on the transformed domain. Because of the powerful properties of Laplacian eigenbasis, the inpainting results of our method tend to be smooth and globally coherent with the remaining shape. We demonstrate the performance of our new method via various examples in geometry restoration, shape repair, and hole filling. [ABSTRACT FROM AUTHOR]

Based on kernel-based approximation technique, we devise in this paper an efficient and accurate numerical scheme for solving a backward space–time fractional diffusion problem (BSTFDP). The kernels used in the approximation are the fundamental solutions of the space–time fractional diffusion equation expressed in terms of inverse Fourier transform of Mittag-Leffler functions. The use of Inverse fast Fourier transform (IFFT) technique enables an accurate and efficient evaluation of the fundamental solutions and gives a robust numerical algorithm for the solution of the BSTFDP. Since the BSTFDP is intrinsic ill-posed, we apply the standard Tikhonov regularization technique to obtain a stable solution to the highly ill-conditioned resultant system of linear equations. For choosing optimal regularization parameter, we combine the regularization technique with the generalized cross validation (GCV) method for an optimal placement of the source points in the use of fundamental solutions. Meanwhile, the proposed algorithm also speeds up the previous method given in Dou and Hon (2014). Several numerical examples are constructed to verify the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E 3 . This algorithm is based on “spherical” space subdivision. The main idea of the S-CH algorithm is to eliminate as many input points as possible before the convex hull construction. The experimental results show that only a very small number of points are used for the final convex hull calculation. Experiments made also proved that the proposed S-CH algorithm achieves a better time complexity in comparison with other algorithms in E 3 . [ABSTRACT FROM AUTHOR]

This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a low-dimensional stable invariant subspace of the associated Hamiltonian matrix. We give conditions on AREs to admit solutions of low numerical rank and show that these can be approximated via Hamiltonian eigenspaces. We discuss strategies on choosing the proper eigenspace that yields a good approximation, and different formulas for building the approximation itself. Similarities of our approach with several other methods for solving AREs are shown: closely related are the projection-type methods that use various Krylov subspaces and the qADI algorithm. The aim of this paper is merely to analyze the possibilities of computing approximate Riccati solutions from low-dimensional subspaces related to the corresponding Hamiltonian matrix and to explain commonalities among existing methods rather than providing a new algorithm. [ABSTRACT FROM AUTHOR]

In 2010, it was proved that the interval number and the convexity number on the monophonic convexity are NP-hard on general graphs (Dourado et al., 2010). In this paper, we extend this results on the monophonic convexity. We prove that deciding if the interval number is at most 2 and deciding if the percolation time is at most 1 are NP-complete problems even in bipartite graphs. We also prove that the convexity number is as hard to approximate as the maximum clique problem. Finally, we obtain polynomial time algorithms to determine the convexity number on hereditary graph classes such that the computation of the clique number is polynomial time solvable (as perfect graphs and planar graphs). [ABSTRACT FROM AUTHOR]

Typically, tasks of modeling complex systems are performed using a certain step size, and step size reduction can lead to an increase in working time. Additionally, with a low frame rate, the modeling process appears jerky. This situation can cause a problems with interpolation of frame. In this paper, an algorithm is presented for approximate assumption of the water front between flood modeling steps. An approach is described that produces smoother water front visualization instead of reducing the modeling step size. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking quantiles and range countings in wireless sensor networks. The quantiles and range countings are two important aggregations to characterize a data distribution. Let S ( t ) = ( d 1 , … , d n ) denote the multi-set of sensory data that have arrived until time t , which is a sequence of data orderly collected by nodes s 1 , s 2 , … , s k . One of our goals is to continuously track ϵ -approximate ϕ -quantiles ( 0 ≤ ϕ ≤ 1 ) of S ( t ) for all ϕ 's with efficient total communication cost and balanced individual communication cost. The other goal is to track ( ϵ , δ ) -approximate range countings satisfying the requirement of arbitrary precision specified by different users. In this paper, a deterministic tracking algorithm based on a dynamic binary tree is proposed to track ϵ -approximate ϕ -quantiles, whose total communication cost is O ( k / ϵ ⋅ log ⁡ n ⋅ log 2 ⁡ ( 1 / ϵ ) ) , where k is the number of the nodes in a network, n is the total number of the data, and ϵ is the user-specified approximation error. For range countings, a Bernoulli sampling based algorithm is proposed to track ( ϵ , δ ) -approximate range countings, whose total communication cost is O ( 2 ϵ 2 ln ⁡ 2 1 − 1 − δ + n c ) , where δ is the user-specified error probability, n c is the number of clusters. [ABSTRACT FROM AUTHOR]

Takagi–Sugeno–Kang (TSK) fuzzy systems have been widely applied for solving function approximation and regression-centric problems. Existing dynamic TSK models proposed in the literature can be broadly classified into two classes. Class I TSK models are essentially fuzzy systems that are limited to time-invariant environments. Class II TSK models are generally evolving systems that can learn in time-variant environments. This paper attempts to address the issues of achieving compact, up-to-date fuzzy rule bases and interpretable knowledge bases in TSK models. It proposes a novel rule pruning method which is simple, computationally efficient and biologically plausible. This rule pruning algorithm applies a gradual forgetting approach and adopts the Hebbian learning mechanism behind the long-term potentiation phenomenon in the brain. It also proposes a merging approach which is used to improve the interpretability of the knowledge bases. This approach can prevent derived fuzzy sets from expanding too many times to protect their semantic meanings. These two approaches are incorporated into a generic self-evolving Takagi–Sugeno–Kang fuzzy framework (GSETSK) which adopts an online data-driven incremental-learning-based approach. Extensive experiments were conducted to evaluate the performance of the proposed GSETSK against other established evolving TSK systems. GSETSK has also been tested on real world dataset using the high-way traffic flow density and Dow Jones index time series. The results are encouraging. GSETSK demonstrates its fast learning ability in time-variant environments. In addition, GSETSK derives an up-to-date and better interpretable fuzzy rule base while maintaining a high level of modeling accuracy at the same time. [ABSTRACT FROM AUTHOR]

Given an edge-weighted graph G = ( V , E ) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R . A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we consider the full Steiner tree problem when G is a unit disk graph. We present a 20-approximation algorithm for the full Steiner tree problem in G . As for λ -precise unit disk graphs we present a ( 10 + 1 λ ) -approximation algorithm, where λ is the length of the shortest edge in G . [ABSTRACT FROM AUTHOR]