Authors:Yi Gao; Ji-gen Peng; Shi-gang Yue Pages: 1 - 24 Abstract: Abstract Although Gaussian random matrices play an important role of measurement matrices in compressed sensing, one hopes that there exist other random matrices which can also be used to serve as the measurement matrices. Hence, Weibull random matrices induce extensive interest. In this paper, we first propose the l2,q robust null space property that can weaken the D-RIP, and show that Weibull random matrices satisfy the l2,q robust null space property with high probability. Besides, we prove that Weibull random matrices also possess the l q quotient property with high probability. Finally, with the combination of the above mentioned properties, we give two important approximation characteristics of the solutions to the l q -minimization with Weibull random matrices, one is on the stability estimate when the measurement noise e ∈ ℝ n needs a priori e 2 ≤ є, the other is on the robustness estimate without needing to estimate the bound of e 2. The results indicate that the performance of Weibull random matrices is similar to that of Gaussian random matrices in sparse recovery. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3430-2 Issue No:Vol. 33, No. 1 (2018)

Authors:Min-zhi Zhao; Dong Xu; Hui-zeng Zhang Pages: 25 - 34 Abstract: Abstract Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ ) and the stopping probabilities P(τ = τ A ) with A ∈ C, where τ A is the waiting time until the pattern A appears as a run. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3522-z Issue No:Vol. 33, No. 1 (2018)

Authors:Xin Deng; Xu-fei Tang; Shi-jie Wang; Xue-jun Wang Pages: 35 - 47 Abstract: Abstract In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let {X n , n ≥ 1} be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3423-1 Issue No:Vol. 33, No. 1 (2018)

Authors:Jing Zheng; Chang-qing Tong; Gui-jun Zhang Pages: 48 - 58 Abstract: Abstract Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term. Based on the mortality data of America from Human Mortality database (HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3349-7 Issue No:Vol. 33, No. 1 (2018)

Authors:Eungjune Shim; Youngjun Kim; Deukhee Lee; Byung Hoon Lee; Sungkyung Woo; Kunwoo Lee Pages: 59 - 70 Abstract: Abstract X-ray imaging is the conventional method for diagnosing the orthopedic condition of a patient. Computerized Tomography(CT) scanning is another diagnostic method that provides patient’s 3D anatomical information. However, both methods have limitations when diagnosing the whole leg; X-ray imaging does not provide 3D information, and normal CT scanning cannot be performed with a standing posture. Obtaining 3D data regarding the whole leg in a standing posture is clinically important because it enables 3D analysis in the weight bearing condition. Based on these clinical needs, a hardware-based bi-plane X-ray imaging system has been developed; it uses two orthogonal X-ray images. However, such methods have not been made available in general clinics because of the hight cost. Therefore, we proposed a widely adaptive method for 2D X-ray image and 3D CT scan data. By this method, it is possible to threedimensionally analyze the whole leg in standing posture. The optimal position that generates the most similar image is the captured X-ray image. The algorithm verifies the similarity using the performance of the proposed method by simulation-based experiments. Then, we analyzed the internal-external rotation angle of the femur using real patient data. Approximately 10.55 degrees of internal rotations were found relative to the defined anterior-posterior direction. In this paper, we present a useful registration method using the conventional X-ray image and 3D CT scan data to analyze the whole leg in the weight-bearing condition. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3459-2 Issue No:Vol. 33, No. 1 (2018)

Authors:P Indhumathi; A Leelamani Pages: 71 - 87 Abstract: In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3449-4 Issue No:Vol. 33, No. 1 (2018)

Authors:Zi-hao Wang; Hong-wei Lin; Chen-kai Xu Pages: 88 - 106 Abstract: Abstract We develop a data driven method (probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e., retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set. A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3536-6 Issue No:Vol. 33, No. 1 (2018)

Authors:Zhi-xiang Wu Pages: 107 - 126 Abstract: Abstract In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra ℍ. Although the category of all left ℍ-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra ℍ, and a series of weak Hopf algebras. Some results of [8] are generalized. PubDate: 2018-03-01 DOI: 10.1007/s11766-018-3327-0 Issue No:Vol. 33, No. 1 (2018)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)