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This paper which depended on the foundation of back strip method has established mathematic model to simulate stratum burial history, which considered the computation of stratum skeleton depth based on max depth and the equation-depth point on the procedure to recover stratum by stripping each layer, and put forward the enhanced restoration method taking layers group as studying object. Finally, the method has been applied to build the computer model and program automatic back strip algorithm successfully. Experiments have proved that the method is accurate, applicable, and extensible under the conditions of various complex strata. [ABSTRACT FROM AUTHOR]

This paper proposes and evaluates a near admissible heuristic search strategy and its application to a kind of flexible manufacturing system (FMS) scheduling in a Petri net framework. Petri nets can concisely model the strict precedence constraint, multiple kinds of resources, and concurrent activities. To cope with the complexities for scheduling of FMS with alternative routings, this paper proposes an admissible heuristic function based on the execution of P-timed Petri nets and presents an improved dynamic weighting A* strategy using the proposed heuristic function. The search scheme does not need to predict the depth of solution in advance and the quality of the search result is also controllable. Some numerical experiments are carried out to demonstrate usefulness of the algorithm. [ABSTRACT FROM AUTHOR]

The results of testing formula simplification tools are presented in the first part of this paper. In the second part, an algorithm for constructing canonical forms of linear semi-algebraic formulas is described. The main result of the study is the definition of the canonical form of a linear semi-algebraic formula that has the property of uniqueness and other useful properties. An algorithm for constructing such a formula is described. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning. [ABSTRACT FROM AUTHOR]

A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis. [ABSTRACT FROM AUTHOR]

The authors study small vibrations of a mixture (emulsion) of two weakly viscous compressible fluids, construct a macroscopic (homogenized) model of emulsion, and establish convergence (with respect to a small parameter) of solutions of the original boundary value problem for a two-phase fluid to solutions of the corresponding homogenized problem. The paper also describes the results of qualitative analysis of the spectrum of the macroscopic acoustic equation (the dynamical Darcy's law), as well as typical spectral pictures obtained by numerical experiments. [ABSTRACT FROM AUTHOR]

The 0-1 Principle of Knuth and its many variants are well-known in the context of comparator networks. However, the comparator model is not the strongest model of computation obeying such principles. This paper studies another natural model of computation, the Min-Max model, that obeys all known 0-1 Principles. More important, it is the strongest model obeying certain variants of the 0-1 Principle. [ABSTRACT FROM AUTHOR]

This paper focuses on Benders decomposition techniques and Monte Carlo sampling (importance sampling) for solving two-stage stochastic linear programs with recourse, a method first introduced by Dantzig and Glynn [7]. The algorithm is discussed and further developed. The paper gives a complete presentation of the method as it is currently implemented. Numerical results from test problems of different areas are presented. Using small test problems, we compare the solutions obtained by the algorithm with universe solutions. We present the solutions of large-scale problems with numerous stochastic parameters, which in the deterministic formulation would have billions of constraints. The problems concern expansion planning of electric utilities with uncertainty in the availabilities of generators and transmission lines and portfolio management with uncertainty in the future returns. [ABSTRACT FROM AUTHOR]

A popular numerical method to compute sum of squares (SOS of polynomials) decompositions for polynomials is to transform the problem into semi-definite programming (SDP) problems and then solve them by SDP solvers. In this paper, we focus on reducing the sizes of inputs to SDP solvers to improve the efficiency and reliability of those SDP based methods. Two types of polynomials, convex cover polynomials and split polynomials, are defined. A convex cover polynomial or a split polynomial can be decomposed into several smaller sub-polynomials such that the original polynomial is SOS if and only if the sub-polynomials are all SOS. Thus the original SOS problem can be decomposed equivalently into smaller sub-problems. It is proved that convex cover polynomials are split polynomials and it is quite possible that sparse polynomials with many variables are split polynomials, which can be efficiently detected in practice. Some necessary conditions for polynomials to be SOS are also given, which can help refute quickly those polynomials which have no SOS representations so that SDP solvers are not called in this case. All the new results lead to a new SDP based method to compute SOS decompositions, which improves this kind of methods by passing smaller inputs to SDP solvers in some cases. Experiments show that the number of monomials obtained by our program is often smaller than that by other SDP based software, especially for polynomials with many variables and high degrees. Numerical results on various tests are reported to show the performance of our program. [ABSTRACT FROM AUTHOR]

In the present paper, we propose several kinds of adaptively relaxed iterative algorithms with a new step size for solving the split feasibility problem in real Hilbert spaces. The proposed algorithms never terminate, while the known algorithms existing in the literature may terminate. Several weak and strong convergence theorems of the proposed algorithms have been established. Some numerical experiments are also included to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multi-step hybrid extragradient algorithm by combining Korpelevich's extragradient method, the viscosity approximation method, the hybrid steepest-descent method, Mann's iteration method and the gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a solution of the convex minimization problem (CMP) with constraints of several problems: finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and the fixed point problem of a strictly pseudocontractive mapping. In the meantime, we also prove the strong convergence of the proposed algorithm to the unique solution of a hierarchical variational inequality problem (over the fixed point set of a strictly pseudocontractive mapping) with constraints of finitely many GMEPs, finitely many variational inclusions and the CMP. The results presented in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In recent years, convex optimization methods were successfully applied for various image processing tasks and a large number of first-order methods were designed to minimize the corresponding functionals. Interestingly, it was shown recently in Grewenig et al. () that the simple idea of so-called 'superstep cycles' leads to very efficient schemes for time-dependent (parabolic) image enhancement problems as well as for steady state (elliptic) image compression tasks. The 'superstep cycles' approach is similar to the nonstationary (cyclic) Richardson method which has been around for over sixty years. In this paper, we investigate the incorporation of superstep cycles into the projected gradient method. We show for two problems in compressive sensing and image processing, namely the LASSO approach and the Rudin-Osher-Fatemi model that the resulting simple cyclic projected gradient algorithm can numerically compare with various state-of-the-art first-order algorithms. However, due to the nonlinear projection within the algorithm convergence proofs even under restrictive assumptions on the linear operators appear to be hard. We demonstrate the difficulties by studying the simplest case of a two-cycle algorithm in ℝ with projections onto the Euclidean ball. [ABSTRACT FROM AUTHOR]

Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely used concept of efficiency has to be redefined for these problems. The use of interactive procedures can somehow ease this complexity, allowing the decision maker to learn about the problem itself, and to look for his most preferred solution. Reference point schemes can be adapted to stochastic problem, by asking the decision maker to provide, not only desirable levels for the objectives, but also the desired probability to achieve these values. In this paper, we analyze the different kinds of achievement scalarizing functions that can be used in this environment, and we study the efficiency (in the stochastic sense) of the different solutions obtained. As a result, a synchronous interactive method is proposed for a class of stochastic multiobjective problems, where only the objective functions are random. Several solutions can be generated by this new method, making use of the same preferential information, using the different achievement scalarizing functions. The preferential information (levels and probabilities for the objectives) is incorporated into the achievement scalarizing functions in a novel way to generate the new solutions. The special case of linear normal problems is addressed separately. The performance of the algorithm is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we focus on real-life settings that require the development of new models of flowshop scheduling problems, where job processing times can increase with the number of processed jobs due to the aging effect and decrease by the allocation of additional resource. We analyse the makespan minimization flowshop problem with such model and also with the aging effect only. We prove that the considered problems and their special cases are still polynomially solvable under given conditions, and on their basis, we provide optimal polynomial time solution algorithms. [ABSTRACT FROM AUTHOR]

Numerical calculations with finite-difference time-domain (FDTD) on metallic nanostructures in a broad optical spectrum require an accurate approximation of the permittivity of dispersive materials. In this paper, we present the algorithms behind B-CALM (Belgium-California Light Machine), an open-source 3D-FDTD solver operating on Graphical Processing Units with multi-pole dispersion models. Our modified architecture shows a reduction in computing times for multi-pole dispersion models. We benchmark B-CALM by computing the absorption efficiency of a metallic nanosphere on a broad spectral range with a six-poles Drude-Lorentz model and compare it with Mie theory. [ABSTRACT FROM AUTHOR]

Further progress in pair-density functional theory (sometimes called 2-DFT) hinges on the development of computationally facile and quantitatively accurate models for the kinetic energy functional. In this paper we perform computational tests for two of the simplest models, the generalized Weizsäcker kinetic energy functional and its spin-resolved extension. Both of these models perform very poorly for atoms. The higher-order Weizsäcker functionals (based on the three-electron distribution function) perform better, but are still not successful. This suggests that an alternative approach for designing kinetic energy functionals of the pair density is needed. [ABSTRACT FROM AUTHOR]

In this paper, a new mathematical model is proposed for inter- and intra-cell layout problem in cellular manufacturing system. A binary particle swarm optimization algorithm with a new heuristic approach for satisfying the constraints of model is implemented to solve the proposed model. Also, a variable neighborhood search is applied for finding better local optimal solutions. Some sensitivity analyses are carried out to find the best values of PSO parameters. To prove the efficiency of the proposed algorithm, various numerical examples in small, medium, and large sizes in both perfect geometric shapes and random placements are generated and solved. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm using binary trees is developed to detect the change points of a data set in which the data are assumed to be normally distributed. Usual BIC-type criteria are considered in the binary searching procedures when the number of change points is unknown. The algorithm is also extended to the switching regression models. Simulation study confirms that our algorithm is efficient compared with the ML-method. A real data example also verifies that the proposed procedure is appropriate. [ABSTRACT FROM AUTHOR]

Abstract  Suppressed fuzzy c-means (s-FCM) clustering was introduced in Fan et al. (Pattern Recogn Lett 24:1607–1612, 2003) with the intention of combining the higher speed of hard c-means (HCM) clustering with the better classification properties of fuzzy c-means (FCM) algorithm. The authors modified the FCM iteration to create a competition among clusters: lower degrees of memberships were diminished according to a previously set suppression rate, while the largest fuzzy membership grew by swallowing all the suppressed parts of the small ones. Suppressing the FCM algorithm was found successful in the terms of accuracy and working time, but the authors failed to answer a series of important questions. In this paper, we clarify the view upon the optimality and the competitive behavior of s-FCM via analytical computations and numerical analysis. A quasi competitive learning rate (QLR) is introduced first, in order to quantify the effect of suppression. As the investigation of s-FCM’s optimality did not provide a precise result, an alternative, optimally suppressed FCM (Os-FCM) algorithm is proposed as a hybridization of FCM and HCM. Both the suppressed and optimally suppressed FCM algorithms underwent the same analytical and numerical evaluations, their properties were analyzed using the QLR. We found the newly introduced Os-FCM algorithm quicker than s-FCM at any nontrivial suppression level. Os-FCM should also be favored because of its guaranteed optimality. [ABSTRACT FROM AUTHOR]

In this paper high order Parzen windows stated by means of basic window functions are studied for understanding some algorithms in learning theory and randomized sampling in multivariate approximation. Learning rates are derived for the least-square regression and density estimation on bounded domains under some decay conditions on the marginal distributions near the boundary. These rates can be almost optimal when the marginal distributions decay fast and the order of the Parzen windows is large enough. For randomized sampling in shift-invariant spaces, we consider the situation when the sampling points are neither i.i.d. nor regular, but are noised from regular grids by probability density functions. The approximation orders are estimated by means of the regularity of the approximated function and the density function and the order of the Parzen windows. [ABSTRACT FROM AUTHOR]

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the MM is used in the sub-domain where the MM is required to obtain high accuracy, and the FEM is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the MM and FEM when overcome their shortcomings. [ABSTRACT FROM AUTHOR]

In this paper, we study an extension of the Linear Multiple Choice Knapsack (LMCK) Problem that considers two objectives. The problem can be used to find the optimal allocation of an available resource to a group of disjoint sets of activities, while also ensuring that a certain balance on the resource amounts allocated to the activity sets is attained. The first objective maximizes the profit incurred by the implementation of the considered activities. The second objective minimizes the maximum difference between the resource amounts allocated to any two sets of activities. We present the mathematical formulation and explore the fundamental properties of the problem. Based on these properties, we develop an efficient algorithm that obtains the entire nondominated frontier. The algorithm is more efficient than the application of the general theory of multiple objective linear programming (MOLP), although there is a close underlying relationship between the two. We present theoretical findings which provide insight into the behavior of the algorithm, and report computational results which demonstrate its efficiency for randomly generated problems. [ABSTRACT FROM AUTHOR]

In this paper, the k-ἐ two-equation turbulence model has been used to simulate ice accumulation under ice cover along a river bend. A 2D depth-averaged numerical model has been developed in a nonorthogonal coordinate system with nonstaggered curvilinear grids. In this model, the contravariant velocity has been treated as an independent variable. To avoid the pressure oscillation in the nonstaggered grids, the momentum interpolation has been introduced to interpolate variables at the interface. The discretizatidn equations have been solved by using pressure correction algorithms. An equation has been developed for describing the deformation of ice jam bottom. The thickness distribution of ice accumulation (ice jam) along the bend has been simulated. The developed model has been applied to the experimental studies under different conditions earned out at the Hefei University of Technology. Results indicate that all simulated thickness of ice accumulation agrees reasonably well with the measured thickness of ice accumulation in laboratory. [ABSTRACT FROM AUTHOR]

In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions. In addition, we also propose a descent algorithm that is indeed derivative-free for solving the unconstrained minimization based on the merit functions from the proposed NCP functions. Numerical results for the test problems from MCPLIB indicate that the descent algorithm has better performance when the parameter p decreases in (1,+∞). This implies that the merit functions associated with p ∈ (1, 2), for example p = 1.5, are more effective in numerical computations than the Fischer-Burmeister merit function, which exactly corresponds to p = 2. [ABSTRACT FROM AUTHOR]

This paper aims to provide a general and effective theoretical calculative method for the operational states of the stator windings? closed-loop, self-circulating, CLSC evaporative cooling system for hydrogenerators. The object-oriented concept was used in dealing with the real circulating cooling loop so as to develop numerical simulation software. At the same time, the experiment was carried out in a cooling system model in order to verify the validity of the simulation. Comparative results show that the maximum relative errors between simulation and experimental results are less than 10%. In general, the mathematical model of the circulating system is satisfied and the algorithm of the numerical simulation is correct. The simulation accurately predicts the condition of the real electrical machine. [ABSTRACT FROM AUTHOR]

Macroscopic simulations of non-convex minimisation problems with enforced microstructures encounter oscillations on finest length scales-too fine to be fully resolved. The numerical analysis must rely on an essentially equivalent relaxed mathematical model. The paper addresses a prototype example, the scalar 2-well minimisation problem and its convexification and introduces a benchmark problem with a known (generalised)solution. For this benchmark, the stress error is studied empirically to asses the performance of adaptive finite element methods for the relaxed and the original minimisation problem. Despite the theoretical reliability-efficiency gap for the relaxed problem, numerical evidence supports that adaptive mesh-refining algorithms generate efficient triangulations and improve the experimental convergence rates optimally. Moreover, the averaging error estimators perform surprisingly accurate. [ABSTRACT FROM AUTHOR]

In a regression kink (RK) design with a finite sample, a confounding smooth nonlinear relationship between an assignment variable and an outcome variable around a threshold can be spuriously picked up as a kink and results in a biased estimate. In order to investigate how well RK designs handle such confounding nonlinearity, I firstly implement Monte Carlo (MC) simulations and then study the effect of fiscal equalization grants on local expenditure in Japan using an RK design. Results in both the MC simulations and the empirical application suggest that RK estimation without covariates can be easily biased, and this problem can be mitigated by adding observed covariates to the regressors. On the other hand, a smaller bandwidth or a higher-order polynomial, even a quadratic polynomial, tends to result in imprecise estimates although they may be able to reduce estimation bias. In sum, RK estimation with confounding nonlinearity often suffers from bias or imprecision, and estimates are credible only when relevant covariates are controlled for. I also examine how placebo RK estimation can effectively address these issues. [ABSTRACT FROM AUTHOR]

In this paper a nonlinear backward parabolic problem in one dimensional space is considered. Using a suitable iterative algorithm, the problem is converted to a linear backward parabolic problem. For the corresponding problem, the backward finite differences method with suitable grid size is applied. It is shown that if the coefficients satisfy some special conditions, this algorithm not only is convergent, but also is conditionally stable. Moreover, it is proved that the estimated values converge to the exact solution of the problem. All these approaches examined in some numerical examples. corresponding theorems for the convergency and stability of the solution are studied. [ABSTRACT FROM AUTHOR]

We introduce and study a new general split feasibility problem (GSFP) in a Hilbert space. This problem generalizes the split feasibility problem (SFP). The GSFP extends the SFP with a nonlinear continuous operator. We apply the preconditioning methods to increase the efficiency of the CQ algorithm, two general preconditioning CQ algorithms for solving the GSFP are presented. We also propose a new inexact method to approximate the preconditioner. The convergence theorems are established under the projections with respect to special norms. Some numerical results illustrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

Deterministic collect algorithms are presented that are adaptive to total contention and are efficient with respect to both the number of registers used and the step complexity. One of them has optimal O( k) step and O( n) space complexities, but assumes that processes’ identifiers are in O( n), where n is the total number of processes in the system and k is the total contention. The step complexity of an unrestricted name space variant of this algorithm remains O( k), but its space complexity increases to O( n 2). [ABSTRACT FROM AUTHOR]

In this paper, we examine the performance of the TROLL stacked-time algorithm in the simulation of large scale overlapping generations (OLG) models. At each period of time, the number of equations is proportional to the individual length of lifetime. The model size and the data requirements may thus be very large. Given the repetitive structure of the equations, we show how TROLL specific macrocommands can be used to explode a generic version (in which the lifetime is parameterized) into a complete model. A similar technique applies to explode the initial dataset on the whole simulation horizon. The stability properties of the model are derived and the stacked-time algorithm performances are checked for a large scale model with endogenous labour supply and uncertain lifetime. It turns out that TROLL performances are very attractive even for a system of 300000 simultaneous equations. [ABSTRACT FROM AUTHOR]

A new method named as Statistical Average Algorithm is developed for solving the structural dynamic compound inverse problem, which means to identify structural parameters with unknown input or to inverse input time history with unknown structural parameters. By taking the mechanical characteristic of the ground motion as an additional condition, an iterative algorithm based on the least-squares technique is developed so that the input process and structural parameters can be correctly determined using only output measurements. The procedure of the proposed method is discussed in detail, and a mathematical proof is presented as well in the appendix. A practical input situation such as earthquake, ambient vibration is considered in the numerical examples to verify the accuracy, reliability and robustness of the proposed algorithm. Considering the background of the practical application, both of the noise-free and noise-included output responses are considered in the numerical examples. In all cases, the proposed method identifies the structural parameters and reconstructs the input process rationally. [ABSTRACT FROM AUTHOR]

For linear processes with independent identically distributed innovations that are regularly varying with tail index α ∈ (0, 2), we study the functional convergence of the joint partial-sum and partial-maxima processes. We derive a functional limit theorem under certain assumptions on the coefficients of the linear processes, which enable the functional convergence in the space of ℝ2-valued càdlàg functions on [0, 1] with the Skorokhod weak M2 topology.We also obtain a joint convergence in the M2 topology on the first coordinate and in theM1 topology on the second coordinate. [ABSTRACT FROM AUTHOR]

Based on the alternating direction method of multipliers (ADMM), we develop three numerical algorithms incrementally for solving the optimal control problems constrained by random Helmholtz equations. First, we apply the standard Monte Carlo technique and finite element method for the random and spatial discretization, respectively, and then ADMM is used to solve the resulting system. Next, combining the multi-modes expansion, Monte Carlo technique, finite element method, and ADMM, we propose the second algorithm. In the third algorithm, we preprocess certain quantities before the ADMM iteration, so that nearly no random variable is in the inner iteration. This algorithm is the most efficient one and is easy to implement. The error estimates of these three algorithms are established. The numerical experiments verify the efficiency of our algorithms. [ABSTRACT FROM AUTHOR]

During exploration and pre-feasibility studies of a typical petroleum project many analyses are required to support decision making. Among them is reservoir lithofacies modeling, preferably using uncertainty assessment, which can be carried out with geostatistical simulation. The resulting multiple equally probable facies models can be used, for instance, in flow simulations. This allows assessing uncertainties in reservoir flow behavior during its production lifetime, which is useful for injector and producer well planning. Flow, among other factors, is controlled by elements that act as flow corridors and barriers. Clean sand channels and shale layers are examples of such reservoir elements that have specific geometries. Besides simulating the necessary facies, it is also important to simulate their shapes. Object-based and process-based simulations excel in geometry reproduction, while variogram-based simulations perform very well at data conditioning. Multiple-point geostatistics (MPS) combines both characteristics, consequently it was employed in this study to produce models of a real-world reservoir that are both data adherent and geologically realistic. This work aims at illustrating how subsurface information typically available in petroleum projects can be used with MPS to generate realistic reservoir models. A workflow using the SNESIM algorithm is demonstrated incorporating various sources of information. Results show that complex structures (e.g. channel networks) emerged from a simple model (e.g. single branch) and the reservoir facies models produced with MPS were judged suitable for geometry-sensitive applications such as flow simulations. [ABSTRACT FROM AUTHOR]

Let S be a set of n points in the unit square [0,1], one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cover at least a positive constant area (about 0.09). This is a first step towards the solution of a longstanding conjecture that the rectangles in such a packing can jointly cover an area of at least 1/2. [ABSTRACT FROM AUTHOR]

Medial axis transform of a pocket with free-form closed boundaries is a completed, compact representation of the pocket geometric shape and topology. It is very useful to multiple cutters selection and their tool paths generation for CNC machining of complex pockets. In the past decades, much research has been successfully conducted on the topic of finding the medial axis of a shape domain bounded with a polygon or simple geometries, e.g., lines and circles. Currently, more pockets with free-form boundaries are adopted in mechanical parts; however, the prior medial axis generation methods cannot handle this type of pockets well, resulting in long computation time and low medial axis accuracy. To address this problem, an efficient, accurate approach to calculating the medial axis transforms of these pockets is proposed in this work. An original optimization model of bisectors is established, and a new optimization method-the hybrid global optimization method-is developed to efficiently and accurately solve the optimization model of bisectors. The new optimization model and solver have been applied to many examples, and the testing results have demonstrated the advantages of this innovative approach over the prior medial axis methods. It can be an effective solution to the medial axis transforms of complex pockets. [ABSTRACT FROM AUTHOR]

We introduce an explicit algorithm for solving nonsmooth equilibrium problems in finite-dimensional spaces. A particular iteration proceeds in two phases. In the first phase, an orthogonal projection onto the feasible set is replaced by projections onto suitable hyperplanes. In the second phase, a projected subgradient type iteration is replaced by a specific projection onto a halfspace. We prove, under suitable assumptions, convergence of the whole generated sequence to a solution of the problem. The proposed algorithm has a low computational cost per iteration and, some numerical results are reported. [ABSTRACT FROM AUTHOR]

In a classical risk model with zero initial capital and unknown claim-size distribution, we consider the statistical problem of estimating uniformly in t the (unknown) finite-time survival probability φ( t) at time t, given a sample of claim sizes. We construct an empirical estimator of the function φ(·) based on the sample of claim sizes, and using a functional approach we establish asymptotic statistical properties of our estimator with respect to supremum norm. We also consider numerical evaluation of finite-time survival probabilities and their empirical counterparts using the fast Fourier transform algorithm, and we carry out small-scale simulation studies of the behaviour of our estimator. [ABSTRACT FROM AUTHOR]

We introduce polylinking networks, which is a flow model based on polylinking systems that generalizes the classical flow model of Ford and Fulkerson on acyclic networks and has applications in the context of wireless networks. More precisely, a flow model recently introduced by Avestimehr et al. (Proceedings of the Allerton conference on communication, control, and computing ) used in the context of wireless information networks is a special case of the presented model. We define a notion of source-destination cut and derive a max-flow min-cut theorem. Additionally, we present various properties of polylinking networks that can be seen as generalizations of properties for classical flows. Using submodular function minimization and submodular flow algorithms, one can efficiently determine a maximum flow, a minimum source-destination cut, as well as a minimum cost flow. These algorithms lead to new efficient algorithms for the information flow model. [ABSTRACT FROM AUTHOR]

Satellite imagery provides a unique opportunity for oceanic fronts' identification and the observation of the synoptic variability of the fronts. Top quality interpretative frontal maps are compiled by expert oceanographers from satellite and in situ data aided by numerical models of the ocean's circulation. To be used for the initialization and data assimilation in numerical models, these frontal maps have to be digitized and vectorized. Here, we present an algorithm that automatically recognizes oceanic structures (fronts, eddies, filaments) in frontal maps formatted as raster images. The algorithm is based on a formalized description of the structure of the frontal zone, the image vectorization, and the detection of significant structural elements based on the classification of these elements. The classification of the structural elements was first developed by analyzing once-a-week satellite-derived sea surface temperature (SST) images for the western North Atlantic from 2010. The structural elements are then recognized based on their invariant spatial characteristics and their positions relative to one another in any new SST image. The algorithm outputs a set of digital arrays that are vector descriptors of all the significant structural elements of the frontal map. [ABSTRACT FROM AUTHOR]

In this work, we aim to tackle one of the most devastating failure modes in reinforced concrete (RC) structures: the diagonal-tension failure. In order to study this phenomenon numerically, a model capable of dealing with both static and dynamic crack propagation as well as the natural transition of these two regimes is necessary. We chose a discrete cohesive model for concrete fracture, an interface bond-slip model for the deterioration between concrete and steel rebar, both combined with an insertion algorithm. The static process is solved by a dynamic relaxation (DR) method together with a modified technique to enhance the convergence rate. The same DR method is used to detect a dynamic process and switch to a dynamic calculation. The methodology is applied to model the experimental results of Carmona et al. (Engineering Fracture Mechanics 74:2788-2809, ), where the recognition of the transition to a dynamic fracture in a presumably static calculation is essential to reproduce the diagonal-tension failure observed. [ABSTRACT FROM AUTHOR]

Abstract  The design of erasure correcting codes and their decoding algorithms is now at the point where capacity achieving codes are available with decoding algorithms that have complexity that is linear in the number of information symbols. One aspect of these codes is that the overhead (number of coded symbols beyond the number of information symbols required to achieve decoding completion with high probability) is linear in k. This work considers a new class of random codes which have the following advantages: (i) the overhead is constant (in the range of 5 to 10), independent of the number of data symbols being encoded (ii) the probability of completing decoding for such an overhead is essentially one (iii) the codes are effective for a number of information symbols as low as a few tens (iv) the only probability distribution required is the uniform distribution. The price for these properties is that the decoding complexity is greater, on the order of k 3/2. However, for the lower values of k where these codes are of particular interest, this increase in complexity might be outweighed by their advantages. The parity check matrices of these codes are chosen at random as windowed matrices, i.e. for each column an initial starting position of a window of length w is chosen and the succeeding w positions are chosen at random as zero or one. It can be shown that it is necessary that w=O(k 1/2) for the probabilistic matrix rank properties to behave as a non-windowed random matrix. The sufficiency of the condition has so far been established by extensive simulation, although other arguments strongly support this conclusion. The properties of the codes described depend heavily on the rank properties of random matrices over finite fields. Known results on such matrices are briefly reviewed and several conjectures needed in the discussion of the code properties, are stated. The likelihood of the validity of the conjectures is supported through extensive experimentation. Mathematical proof of the conjectures would be of great value for their own interest as well of the particular coding application described here. [ABSTRACT FROM AUTHOR]

We develop the results on polynomial ergodicity of Markov chains and apply to the Metropolis–Hastings algorithms based on a Langevin diffusion. When a prescribed distribution p has heavy tails, the Metropolis–Hastings algorithms based on a Langevin diffusion do not converge to p at any geometric rate. However, those Langevin based algorithms behave like the diffusion itself in the tail area, and using this fact, we provide sufficient conditions of a polynomial rate convergence. By the feature in the tail area, our results can be applied to a large class of distributions to which p belongs. Then, we show that the convergence rate can be improved by a transformation. We also prove central limit theorems for those algorithms. [ABSTRACT FROM AUTHOR]

A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary point, and does not require the row vectors of A to be linearly independent. We prove that our algorithm is globally convergent under weak conditions. Preliminary numerical results demonstrate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments. [ABSTRACT FROM AUTHOR]

We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well. [ABSTRACT FROM AUTHOR]