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 Applied Mathematics - A Journal of Chinese Universities   [SJR: 0.275]   [H-I: 8]   [0 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1993-0445 - ISSN (Online) 1005-1031    Published by Springer-Verlag  [2355 journals]
• Feature selection of ultrahigh-dimensional covariates with survival
outcomes: a selective review
• Authors: Hyokyoung Grace Hong; Yi Li
Pages: 379 - 396
Abstract: Abstract Many modern biomedical studies have yielded survival data with high-throughput predictors. The goals of scientific research often lie in identifying predictive biomarkers, understanding biological mechanisms and making accurate and precise predictions. Variable screening is a crucial first step in achieving these goals. This work conducts a selective review of feature screening procedures for survival data with ultrahigh dimensional covariates. We present the main methodologies, along with the key conditions that ensure sure screening properties. The practical utility of these methods is examined via extensive simulations. We conclude the review with some future opportunities in this field.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3547-8
Issue No: Vol. 32, No. 4 (2017)

• The convergence ball and error analysis of the two-step Secant method
• Authors: Rong-fei Lin; Qing-biao Wu; Min-hong Chen; Yasir Khan; Lu Liu
Pages: 397 - 406
Abstract: Abstract Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order, we obtain an estimate of the radius of the convergence ball for the two-step secant method. Moreover, we also provide an error estimate that matches the convergence order of the two-step secant method. At last, we give an application of the proposed theorem.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3487-3
Issue No: Vol. 32, No. 4 (2017)

• New normalized nonlocal hybrid level set method for image segmentation
• Authors: Qiong Lou; Jia-lin Peng; De-xing Kong; Chun-lin Wang
Pages: 407 - 421
Abstract: Abstract This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3345-3
Issue No: Vol. 32, No. 4 (2017)

• Image segmentation by level set evolution with region consistency
constraint
• Authors: Li Zhong; Yuan-feng Zhou; Xiao-feng Zhang; Qiang Guo; Cai-ming Zhang
Pages: 422 - 442
Abstract: Abstract Image segmentation is a key and fundamental problem in image processing, computer graphics, and computer vision. Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation. However, poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation. In this paper, we present a region consistency constraint term to measure the regional consistency on both sides of the boundary, this term defines the boundary of the image within a range, and hence increases the stability of the level set model. The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary. Furthermore, this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour. The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3534-0
Issue No: Vol. 32, No. 4 (2017)

• Derivatives and differentials for multiplicative intuitionistic fuzzy
information
• Authors: Shan Yu; Ze-shui Xu; Shou-sheng Liu
Pages: 443 - 461
Abstract: Abstract By using the unsymmetrical scale instead of the symmetrical scale, the multiplicative intuitionistic fuzzy sets (MIFSs) reflect our intuition more objectively. Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number (MIFN) and is based on the unbalanced scale (i.e., Saaty’s 1-9 scale). In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively, in this paper, we firstly propose two new basic operational laws for MIFNs, which are the subtraction law and the division law. Secondly, we describe the change values of MIFNs when considering them as variables, classify these change values based on the basic operational laws for MIFNs, and depict the convergences of sequences of MIFNs by the subtraction and division laws. Finally, we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities, derivatives and differentials, and also give their application in selecting the configuration of a computer.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3479-3
Issue No: Vol. 32, No. 4 (2017)

• Boundedness of Hausdorff operators on the power weighted Hardy spaces
• Authors: Jie-cheng Chen; Shao-yong He; Xiang-rong Zhu
Pages: 462 - 476
Abstract: Abstract In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space $$H_{{{\left X \right }^\alpha }}^1({R^2})( - 1 \leqslant \alpha \leqslant 0)$$ , defined by $${H_{\Phi ,A}}f(x) = \int {_{{R^2}}} \Phi (u)f(A(u)x)du,$$ , where Φ ∈ L loc 1(R 2), A(u) = (a ij (u)) i,j=1 2 is a 2 × 2 matrix, and each a i,j is a measurable function. We obtain that H Φ,A is bounded from $$H_{{{\left X \right }^\alpha }}^1({R^2})( - 1 \leqslant \alpha \leqslant 0)$$ to itself, if $$\int {_{{R^2}}} \left {\Phi (u)} \right \left {\det \;{A^{ - 1}}(u)} \right {\left\ {A(u)} \right\ ^{ - \alpha }}\;\ln \;(1 + \frac{{{{\left\ {{A^{ - 1}}(u)} \right\ }^2}}}{{\left {\det \;{A^{ - 1}}(u)} \right }})du < \infty .$$ . This result improves some known theorems, and in some sense it is sharp.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3523-3
Issue No: Vol. 32, No. 4 (2017)

• When q theory meets large losses risks and agency conflicts
• Authors: Ying Wang; Wen-li Huang; Sheng-hong Li
Pages: 477 - 492
Abstract: Abstract We incorporate large losses risks into the DeMarzo et al.(2012) model of dynamic agency and the q theory of investment. The large losses risks induce losses costs and losses arising from agency conflicts during the large losses prevention process. Both of them reduce firm’s value, distort investment policy and generate a deeper wedge between the marginal and average q. In addition, we study the implementation of the contract to enhance the practical utility of our model. The agent optimally manages the firm’s cash flow and treats the cash reservation and credit line as the firm’s financial slack, and hedges the productivity shocks and large losses shocks via futures and insurance contracts, respectively.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3509-1
Issue No: Vol. 32, No. 4 (2017)

• Competitive analysis of price online inventory problem with cost function
• Authors: Shu-guang Han; Jiu-ling Guo; Lu-ping Zhang; Jue-liang Hu
Pages: 493 - 502
Abstract: Abstract In this paper, a new price is given to the online decision maker at the beginning of each day. The trader must decide how many items to purchase according to the current price. We present three variants and an online algorithm based on cost function. The competitive ratio of the online algorithm is given for each variant, which is a performance measure of an online algorithm. More importantly, we show that the online algorithm is optimal.
PubDate: 2017-12-01
DOI: 10.1007/s11766-017-3280-3
Issue No: Vol. 32, No. 4 (2017)

• Self-normalization: Taming a wild population in a heavy-tailed world
• Authors: Qi-man Shao; Wen-xin Zhou
Pages: 253 - 269
Abstract: Abstract The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student’s t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical problems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robustness property of Studentization/self-normalization against heavy-tailed sampling distributions. This paper gives an overview of the salient progress of self-normalized limit theory, from Student’s t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one- and two-sample U-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3552-y
Issue No: Vol. 32, No. 3 (2017)

• On the rate of complete convergence for weighted sums of NSD random
variables and an application
Pages: 270 - 280
Abstract: Abstract In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3437-0
Issue No: Vol. 32, No. 3 (2017)

• Bounds on partial derivatives of NURBS surfaces
• Authors: Guo-jin Wang; Hui-xia Xu; Qian-qian Hu
Pages: 281 - 293
Abstract: Abstract In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3429-0
Issue No: Vol. 32, No. 3 (2017)

• A correlative classifiers approach based on particle filter and sample set
for tracking occluded target
• Authors: Kang Li; Fa-zhi He; Hai-ping Yu; Xiao Chen
Pages: 294 - 312
Abstract: Abstract Target tracking is one of the most important issues in computer vision and has been applied in many fields of science, engineering and industry. Because of the occlusion during tracking, typical approaches with single classifier learn much of occluding background information which results in the decrease of tracking performance, and eventually lead to the failure of the tracking algorithm. This paper presents a new correlative classifiers approach to address the above problem. Our idea is to derive a group of correlative classifiers based on sample set method. Then we propose strategy to establish the classifiers and to query the suitable classifiers for the next frame tracking. In order to deal with nonlinear problem, particle filter is adopted and integrated with sample set method. For choosing the target from candidate particles, we define a similarity measurement between particles and sample set. The proposed sample set method includes the following steps. First, we cropped positive samples set around the target and negative samples set far away from the target. Second, we extracted average Haar-like feature from these samples and calculate their statistical characteristic which represents the target model. Third, we define the similarity measurement based on the statistical characteristic of these two sets to judge the similarity between candidate particles and target model. Finally, we choose the largest similarity score particle as the target in the new frame. A number of experiments show the robustness and efficiency of the proposed approach when compared with other state-of-the-art trackers.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3466-8
Issue No: Vol. 32, No. 3 (2017)

• A novel enhancement method for low illumination images based on microarray
camera
• Authors: Jian-cheng Zou; Wen-qi Zheng; Zhi-hui Yang
Pages: 313 - 322
Abstract: Abstract It is difficult but important to get clear information from the low illumination images. In recent years the research of the low illumination image enhancement has become a hot topic in image processing and computer vision. The Retinex algorithm is one of the most popular methods in the field and uniform illumination is necessary to enhance low illumination image quality by using this algorithm. However, for the different areas of an image with contrast brightness differences, the illumination image is not smooth and causes halo artifacts so that it cannot retain the detail information of the original images. To solve the problem, we generalize the multi-scale Retinex algorithm and propose a new enhancement method for the low illumination images based on the microarray camera. The proposed method can well make up for the deficiency of imbalanced illumination and significantly inhibit the halo artifacts as well. Experimental results show that the proposed method can get better image enhancement effect compared to the multi-scale Retinex algorithm of a single image enhancement. Advantages of the method also include that it can significantly inhibit the halo artifacts and thus retain the details of the original images, it can improve the brightness and contrast of the image as well. The newly developed method in this paper has application potential to the images captured by pad and cell phone in the low illumination environment.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3458-8
Issue No: Vol. 32, No. 3 (2017)

• On vector variational-like inequalities and vector optimization problems
with ( G , α )-invexity
• Authors: Anurag Jayswal; Sarita Choudhury
Pages: 323 - 338
Abstract: Abstract The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3339-1
Issue No: Vol. 32, No. 3 (2017)

• Fusion-Riesz frame in Hilbert space
• Authors: Xue-bin Li; Shou-zhi Yang
Pages: 339 - 352
Abstract: Abstract Fusion-Riesz frame (Riesz frame of subspace) whose all subsets are fusion frame sequences with the same bounds is a special fusion frame. It is also considered a generalization of Riesz frame since it shares some important properties of Riesz frame. In this paper, we show a part of these properties of fusion-Riesz frame and the new results about the stabilities of fusion-Riesz frames under operator perturbation (simple named operator perturbation of fusion-Riesz frames). Moreover, we also compare the operator perturbation of fusion-Riesz frame with that of fusion frame, fusion-Riesz basis (also called Riesz decomposition or Riesz fusion basis) and exact fusion frame.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3448-x
Issue No: Vol. 32, No. 3 (2017)

• Hamilton-Souplet-Zhang’s gradient estimates for two weighted
nonlinear parabolic equations
• Authors: Bing-qing Ma; Guang-yue Huang
Pages: 353 - 364
Abstract: Abstract In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3500-x
Issue No: Vol. 32, No. 3 (2017)

• On fundamental solution for powers of the sub-Laplacian on the Heisenberg
group
• Authors: Hai-meng Wang; Qing-yan Wu
Pages: 365 - 378
Abstract: Abstract We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.
PubDate: 2017-09-01
DOI: 10.1007/s11766-017-3506-4
Issue No: Vol. 32, No. 3 (2017)

• Energy and Laplacian of fractal interpolation functions
• Authors: Xiao-hui Li; Huo-jun Ruan
Pages: 201 - 210
Abstract: Abstract In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5: Δu = 0 on SG {q 1, q 2, q 3}, and u(q i ) = a i , i = 1, 2, 3, where q i , i = 1, 2, 3, are boundary points of SG.
PubDate: 2017-06-01
DOI: 10.1007/s11766-017-3482-8
Issue No: Vol. 32, No. 2 (2017)

• Optimality conditions in set optimization employing higher-order radial
derivatives
• Authors: Guo-lin Yu
Pages: 225 - 236
Abstract: Abstract There are two approaches of defining the solutions of a set-valued optimization problem: vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated (weak) minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
PubDate: 2017-06-01
DOI: 10.1007/s11766-017-3414-7
Issue No: Vol. 32, No. 2 (2017)

• Competitive analysis of online inventory problem with interrelated prices
• Authors: Shu-guang Han; Jiu-ling Guo; Lu-ping Zhang; Jue-liang Hu; Yi-wei Jiang; Di-wei Zhou
Pages: 237 - 252
Abstract: Abstract This paper investigates the online inventory problem with interrelated prices in which a decision of when and how much to replenish must be made in an online fashion even without concrete knowledge of future prices. Four new online models with different price correlations are proposed in this paper, which are the linear-decrease model, the log-decrease model, the logarithmic model and the exponential model. For the first two models, the online algorithms are developed, and as the performance measure of online algorithm, the upper and lower bounds of competitive ratios of the algorithms are derived respectively. For the exponential and logarithmic models, the online algorithms are proposed by the solution of linear programming and the corresponding competitive ratios are analyzed, respectively. Additionally, the algorithm designed for the exponential model is optimal, and the algorithm for the logarithmic model is optimal only under some certain conditions. Moreover, some numerical examples illustrate that the algorithms based on the dprice-conservative strategy are more suitable when the purchase price fluctuates relatively flat.
PubDate: 2017-06-01
DOI: 10.1007/s11766-017-3360-4
Issue No: Vol. 32, No. 2 (2017)

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