On unconditionally positivity preserving DG schemes for shallow water flows with shock capturing by adaptive filtering procedures

In this work, we present an unconditionally positivity preserving implicit time integration scheme for the DG method applied to shallow water flows. For locally refined grids with very small elements, the ODE resulting from space discretization is stiff and requires implicit or partially implicit time stepping. However, for simulations including wetting and drying or regions with small water height, severe time step restrictions have to be imposed due to positivity preservation. Nevertheless, as implicit time stepping demands a significant amount of computational time in order to solve a large system of nonlinear equations for each time step we need large time steps to obtain an efficient scheme. In this context, we propose a novel approach to the strategy of positivity preservation. This new technique is based on the so-called Patankar trick and guarantees non-negativity of the water height for any time step size while still preserving conservativity. Due to this modification, the implicit scheme can take full advantage of larger time steps and is therefore able to beat explicit time stepping in terms of CPU time. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detecting Curves of Symmetry in Images Via Hough Transform

The Hough transform is a standard pattern recognition technique introduced between the 1960s and the 1970s for the detection of straight lines, circles, and ellipses with several applications including the detection of symmetries in images. Recently, based on algebraic geometry arguments, the procedure has been extended to the automated recognition of special classes of algebraic plane curves. This allows us to detect curves of symmetry present in images, that is, curves that recognize midpoints maps of various shapes extracted by an ad hoc symmetry algorithm, here proposed. Further, in the case of straight lines, the detection of lines of symmetry allows us, by a pre-processing step of the image, to improve the efficiency of the recognition algorithm on which the Hough transform technique is founded, without loss of generality and additional computational costs.     

Sparse recovery by the standard Tikhonov method

It is a common belief that the Tikhonov scheme with the -penalty fails to reconstruct a sparse structure with respect to a given system {ϕ _i }. However, in this paper we present a procedure for the sparse recovery, which is totally based on the standard Tikhonov method. This procedure consists of two steps. At first the Tikhonov scheme is used as a sieve to find the coefficients near ϕ _i , which are suspected to be non-zero. Within this step the performance of the standard Tikhonov method is controlled in some sparsity promoting space rather than in the original Hilbert one. In the second step of the proposed procedure, the coefficients with indices selected in the previous step are estimated by means of the data functional strategy. The choice of the regularization parameter is a crucial issue for both steps. We show that a recently developed parameter choice rule called the balancing principle can be effectively used here. We also present the results of computational experiments giving the evidence of the reliability of our approach.     

Multiobjective improved spatial fuzzy c-means clustering for image segmentation combining Pareto-optimal clusters

In this paper, we propose a grayscale image segmentation method based on a multiobjective optimization approach that optimizes two complementary criteria (region and edge based). The region-based fitness used is the improved spatial fuzzy c-means clustering measure that is shown performing better than the standard fuzzy c-means (FCM) measure. The edge-based fitness used is based on the contour statistics and the number of connected components in the image segmentation result. The optimization algorithm used is the multiobjective particle swarm optimization (MOPSO), which is well suited to handle continuous variables problems, the case of FCM clustering. In our case, each particle of the swarm codes the centers of clusters. The result of the multiobjective optimization technique is a set of Pareto-optimal solutions, where each solution represents a segmentation result. Instead of selecting one solution from the Pareto front, we propose a method that combines all solutions to get a better segmentation. The combination method takes place in two steps. The first step is the detection of high-confidence points by exploiting the similarity between the results and the membership degrees. The second step is the classification of the remaining points by using the high-confidence extracted points. The proposed method was evaluated on three types of images: synthetic images, simulated MRI brain images and real-world MRI brain images. This method was compared to the most widely used FCM-based algorithms of the literature. The results demonstrate the effectiveness of the proposed technique.     

Constrained derivative-free optimization on thin domains

Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.     

基于颜色和方向特征区域对比度的显著性检测模型

视觉显著性检测是很多计算机视觉任务的重要步骤,提出了一种基于颜色、方向特征和空间位置关系相结合的区域对比显著性检测算法.首先用基于图论的算法将图像分割成若干区域,结合区域间颜色特征和空间对比度计算出颜色显著图.同时采用基于纹理特征的算法分割图像,通过方向特征和空间对比度得到方向显著图.最后将二者结合得到最终显著图.在国际现有公开测试集上进行仿真实验,并与其它显著性检测方法进行对比,检测结果更加准确、合理,证明此算法切实可行.     

Continuous-Time Generalized Fractional Programming Problems. Part I: Basic Theory

This study, that will be presented as two parts, develops a computational approach to a class of continuous-time generalized fractional programming problems. The parametric method for finite-dimensional generalized fractional programming is extended to problems posed in function spaces. The developed method is a hybrid of the parametric method and discretization approach. In this paper (Part I), some properties of continuous-time optimization problems in parametric form pertaining to continuous-time generalized fractional programming problems are derived. These properties make it possible to develop a computational procedure for continuous-time generalized fractional programming problems. However, it is notoriously difficult to find the exact solutions of continuous-time optimization problems. In the accompanying paper (Part II), a further computational procedure with approximation will be proposed. This procedure will yield bounds on errors introduced by the numerical approximation. In addition, both the size of discretization and the precision of an approximation approach depend on predefined parameters.     

A fast and robust method for damage detection of truss structures

Use of optimization search algorithms is recognized as an efficient method for solving structural damage identification problems. Although these algorithms demonstrated their robustness to identify the location and extent of multiple damages in structural systems, they impose so much computational efforts to the damage assessing process that it reduces their attraction. In this paper by utilizing the concept of residual force vector, an efficient approach based on a Truss Element Damage Index (TEDI) is defined to assist in a fast and reliable prediction of damaged elements. Based on the proposed technique, the first step focuses on location detection of most probable damaged members. The healthy members will then be eliminated from the total list of variables. This can reduce the computational effort significantly. In the second step to identify damaged locations and severities, the Genetic Algorithm is employed to search for the optimum solution in the new search space resulted from the first step. Three test examples are considered to investigate the efficiency of proposed method for damage identification.     

A novel statistical approach for detection of suspicious regions in digital mammogram

In this paper, we propose a novel algorithm to detect the suspicious regions on digital mammograms that based on the Fisher information measure. The proposed algorithm is tested different types and categories of mammograms (fatty, fatty-glandular and dense glandular) within mini-MIAS database (Mammogram Image Analysis Society database (UK)). The proposed method is compared with a different segmentation based information theoretical methods to demonstrate their effectiveness. The experimental results on mammography images showed the effectiveness in the detection of suspicious regions. This study can be a part of developing a computer-aided decision (CAD) system for early detection of breast cancer.     

Fast color transfer from multiple images

Color transfer between images uses the statistics information of image effectively.We present a novel approach of local color transfer between images based on the simple statistics and locally linear embedding.A sketching interface is proposed for quickly and easily specifying the color correspondences between target and source image.The user can specify the correspondences of local region using scribes,which more accurately transfers the target color to the source image while smoothly preserving the boundaries,and exhibits more natural output results.Our algorithm is not restricted to one-to-one image color transfer and can make use of more than one target images to transfer the color in different regions in the source image.Moreover,our algorithm does not require to choose the same color style and image size between source and target images.We propose the sub-sampling to reduce the computational load.Comparing with other approaches,our algorithm is much better in color blending in the input data.Our approach preserves the other color details in the source image.Various experimental results show that our approach specifies the correspondences of local color region in source and target images.And it expresses the intention of users and generates more actual and natural results of visual effect.     

Method of Moments Estimators and Multi–step MLE for Poisson Processes

We introduce two types of estimators of the finite–dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and Multi–step MLE. It is shown that the estimators of the method of moments are consistent and asymptotically normal and the Multi–step MLE are consistent and asymptotically efficient. The construction of Multi–step MLE–process is done in two steps. First we construct a consistent estimator by the observations on some learning interval and then this estimator is used for construction of One–step and Two–step MLEs. The main advantage of the proposed approach is its computational simplicity.     

Online identification of Takagi–Sugeno fuzzy models based on self-adaptive hierarchical particle swarm optimization algorithm

This paper presents an approach for online learning of Takagi–Sugeno (T-S) fuzzy models. A novel learning algorithm based on a Hierarchical Particle Swarm Optimization (HPSO) is introduced to automatically extract all fuzzy logic system (FLS)’s parameters of a T–S fuzzy model. During online operation, both the consequent parameters of the T–S fuzzy model and the PSO inertia weight are continually updated when new data becomes available. By applying this concept to the learning algorithm, a new type T–S fuzzy modeling approach is constructed where the proposed HPSO algorithm includes an adaptive procedure and becomes a self-adaptive HPSO (S-AHPSO) algorithm usable in real-time processes. To improve the computational time of the proposed HPSO, particles positions are initialized by using an efficient unsupervised fuzzy clustering algorithm (UFCA). The UFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system, enhancing the HPSO’s tuning. The approach is applied to identify the dynamical behavior of the dissolved oxygen concentration in an activated sludge reactor within a wastewater treatment plant. The results show that the proposed approach can identify nonlinear systems satisfactorily, and reveal superior performance of the proposed methods when compared with other state of the art methods. Moreover, the methodologies proposed in this paper can be involved in wider applications in a number of fields such as model predictive control, direct controller design, unsupervised clustering, motion detection, and robotics.     

Model-free conditional independence feature screening for ultrahigh dimensional data

Feature screening plays an important role in ultrahigh dimensional data analysis. This paper is concerned with conditional feature screening when one is interested in detecting the association between the response and ultrahigh dimensional predictors (e.g., genetic makers) given a low-dimensional exposure variable (such as clinical variables or environmental variables). To this end, we first propose a new index to measure conditional independence, and further develop a conditional screening procedure based on the newly proposed index. We systematically study the theoretical property of the proposed procedure and establish the sure screening and ranking consistency properties under some very mild conditions. The newly proposed screening procedure enjoys some appealing properties. (a) It is model-free in that its implementation does not require a specification on the model structure; (b) it is robust to heavy-tailed distributions or outliers in both directions of response and predictors; and (c) it can deal with both feature screening and the conditional screening in a unified way. We study the finite sample performance of the proposed procedure by Monte Carlo simulations and further illustrate the proposed method through two real data examples.     

Highway improvement project selection by the joint consideration of cost-benefit and risk criteria

Since highway improvement project selection requires screening thousands of road segments with respect to crashes for further analysis and final project selection, we provide a two-step project selection methodology and describe an application case to demonstrate its advantages. In the first step of the proposed methodology, we will use odds against observing a given crash count, injury count, run-off road count and so on as measures of risk and a multi-criteria pre-selection technique with the objective to decrease the number of prospective improvement locations. In the second step, the final project selection is accomplished based on a composite efficiency measure of estimated cost, benefit and hazard assessment (odds) under budget constraints. To demonstrate the two-step methodology, we will analyze 4 years of accident data at 23?000 locations where the final projects are selected out of several hundred of potential locations.     

基于拟线性化方法的非线性系统闭环反馈控制保辛算法

提出了一种求解非线性系统闭环反馈控制问题的保辛算法．首先,通过拟线性化方法将非线性系统最优控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代格式求解．然后,通过作用量变分原理与生成函数构造了保辛的数值算法,且该算法保持了原Hamilton系统的辛几何性质．最后,通过时间步的递进完成状态与控制变量的更新,进而达到闭环控制的目的．数值算例表明:保辛算法具有较高的计算精度和较快的收敛速度．此外,将闭环反馈控制与开环控制分别应用于驱动小车上的倒立摆控制系统中,结果表明:在存在初始偏差的情况下,开环控制会导致稳定控制任务的失败,而闭环反馈控制能够在一段时间后消除初始偏差的影响,并使系统达到稳定状态．     

Models and algorithms for a staff scheduling problem

We present mathematical models and solution algorithms for a family of staff scheduling problems arising in real life applications. In these problems, the daily assignments to be performed are given and the durations (in days) of the working and rest periods for each employee in the planning horizon are specified in advance, whereas the sequence in which these working and rest periods occur, as well as the daily assignment for each working period, have to be determined. The main objective is the minimization of the number of employees needed to perform all daily assignments in the horizon. We decompose the problem into two steps: the definition of the sequence of working and rest periods (called pattern) for each employee, and the definition of the daily assignment to be performed in each working period by each employee. The first step is formulated as a covering problem for which we present alternative ILP models and exact enumerative algorithms based on these models. Practical experience shows that the best approach is based on the model in which variables are associated with feasible patterns and generated either by dynamic programming or by solving another ILP. The second step is stated as a feasibility problem solved heuristically through a sequence of transportation problems. Although in general this procedure may not find a solution (even if one exists), we present sufficient conditions under which our approach is guaranteed to succeed. We also propose an iterative heuristic algorithm to handle the case in which no feasible solution is found in the second step. We present computational results on real life instances associated with an emergency call center. The proposed approach is able to determine the optimal solution of instances involving up to several hundred employees and a working period of up to 6 months. Mathematics Subject Classification (2000): 90B70, 90C10, 90C27, 90C39, 90C57, 90C59     

An unsupervised context-sensitive change detection technique based on modified self-organizing feature map neural network

In this paper, we propose an unsupervised context-sensitive technique for change-detection in multitemporal remote sensing images. Here a modified self-organizing feature map neural network is used. Each spatial position of the input image corresponds to a neuron in the output layer and the number of neurons in the input layer is equal to the number of features of the input patterns. The network is updated depending on some threshold value and when the network converges, status of output neurons depict a change-detection map. To select a suitable threshold of the network, a correlation based and an energy based criteria are suggested. The proposed change-detection technique is unsupervised and distribution free. Experimental results, carried out on two multispectral and multitemporal remote sensing images, confirm the effectiveness of the proposed approach.     

Dynamical reconstruction of unknown inputs in nonlinear differential equations

We present an algorithm for the identification of an unknown but bounded input to a nonlinear finite-dimensional system, based on observations taken at discrete time instants and corrupted by observation errors. This algorithm is stable with respect to observation and computational errors.If we have the further information that the unknown input is a signal of bounded variation, then we can give explicit convergence estimates of the algorithm.     

Computing lower bounds on basket option prices by discretizing semi-infinite linear programming

The problem of finding static-arbitrage bounds on basket option prices has received a growing attention in the literature. In this paper, we focus on the lower bound case and propose a novel efficient solution procedure that is based on the separation problem. The computational burden of the proposed method is polynomial in the input data size. We also discuss the case of possibly negative weight vectors which can be applied to spread options.     

Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer-aided therapy

Segmenting the lesion regions from the ultrasound (US) images is an important step in the intra-operative planning of some computer-aided therapies. High-Intensity Focused Ultrasound (HIFU), as a popular computer-aided therapy, has been widely used in the treatment of uterine fibroids. However, such segmentation in HIFU remains challenge for two reasons: (1) the blurry or missing boundaries of lesion regions in the HIFU images and (2) the deformation of uterine fibroids caused by the patient’s breathing or an external force during the US imaging process, which can lead to complex shapes of lesion regions. These factors have prevented classical active contour-based segmentation methods from yielding desired results for uterine fibroids in US images. In this paper, a novel active contour-based segmentation method is proposed, which utilizes the correlation information of target shapes among a sequence of images as prior knowledge to aid the existing active contour method. This prior knowledge can be interpreted as a unsupervised clustering of shapes prior modeling. Meanwhile, it is also proved that the shapes correlation has the low-rank property in a linear space, and the theory of matrix recovery is used as an effective tool to impose the proposed prior on an existing active contour model. Finally, an accurate method is developed to solve the proposed model by using the Augmented Lagrange Multiplier (ALM). Experimental results from both synthetic and clinical uterine fibroids US image sequences demonstrate that the proposed method can consistently improve the performance of active contour models and increase the robustness against missing or misleading boundaries, and can greatly improve the efficiency of HIFU therapy.