Authors:Qi-man Shao; Wen-xin Zhou Pages: 253 - 269 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)

Authors:Habib Naderi; Mohammad Amini; Abolghasem Bozorgnia Pages: 270 - 280 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)

Authors:Guo-jin Wang; Hui-xia Xu; Qian-qian Hu Pages: 281 - 293 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)

Authors:Kang Li; Fa-zhi He; Hai-ping Yu; Xiao Chen Pages: 294 - 312 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)

Authors:Jian-cheng Zou; Wen-qi Zheng; Zhi-hui Yang Pages: 313 - 322 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: 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:Xue-bin Li; Shou-zhi Yang Pages: 339 - 352 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)

Authors:Bing-qing Ma; Guang-yue Huang Pages: 353 - 364 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: 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)

Authors:Zhi-ting Xu; Dan-xia Chen Pages: 127 - 146 Abstract: The aim of this paper is to study the dynamics of an SIS epidemic model with diffusion. We first study the well-posedness of the model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions connecting the disease-free equilibrium and the endemic equilibrium when R 0 > 1 and c > c*. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R 0 > 1 and c ∈ [0, c*). PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3460-1 Issue No:Vol. 32, No. 2 (2017)

Authors:De-xing Kong; Qi Liu Pages: 147 - 163 Abstract: In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the (1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem; while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3422-7 Issue No:Vol. 32, No. 2 (2017)

Authors:Yue Zhang; Chun-gang Zhu; Qing-jie Guo Pages: 164 - 182 Abstract: Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc´ıa-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface. Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3457-9 Issue No:Vol. 32, No. 2 (2017)

Authors:Asad Khan; Luo Jiang; Wei Li; Li-gang Liu Pages: 183 - 200 Abstract: 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. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3447-y Issue No:Vol. 32, No. 2 (2017)

Authors:Xiao-hui Li; Huo-jun Ruan Pages: 201 - 210 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)

Authors:Wen-sheng Wang Pages: 211 - 224 Abstract: In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-Itô-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging. PubDate: 2017-06-01 DOI: 10.1007/s11766-017-3160-x Issue No:Vol. 32, No. 2 (2017)

Authors:Guo-lin Yu Pages: 225 - 236 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)

Authors:Shu-guang Han; Jiu-ling Guo; Lu-ping Zhang; Jue-liang Hu; Yi-wei Jiang; Di-wei Zhou Pages: 237 - 252 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)

Authors:Yu Liu; Chen-dong Xu Pages: 1 - 13 Abstract: A new method for approximation of conic section by quartic Bézier curve is presented, based on the quartic Bézier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G 2 continuous spline approximation of conic section when using the subdivision scheme, and the effectiveness of this method is demonstrated by some numerical examples. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3434-3 Issue No:Vol. 32, No. 1 (2017)

Authors:Fan Zhang; Xue-ying Qin; Xue-mei Li; Fu-hua Cheng Pages: 53 - 67 Abstract: For a given set of data points in the plane, a new method is presented for computing a parameter value (knot) for each data point. Associated with each data point, a quadratic polynomial curve passing through three adjacent consecutive data points is constructed. The curve has one degree of freedom which can be used to optimize the shape of the curve. To obtain a better shape of the curve, the degree of freedom is determined by optimizing the bending and stretching energies of the curve so that variation of the curve is as small as possible. Between each pair of adjacent data points, two local knot intervals are constructed, and the final knot interval corresponding to these two points is determined by a combination of the two local knot intervals. Experiments show that the curves constructed using the knots by the new method generally have better interpolation precision than the ones constructed using the knots by the existing local methods. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3338-2 Issue No:Vol. 32, No. 1 (2017)

Authors:Yi-fen Ke; Chang-feng Ma Pages: 117 - 126 Abstract: In this paper, we propose and analyze an accelerated augmented Lagrangian method (denoted by AALM) for solving the linearly constrained convex programming. We show that the convergence rate of AALM is O(1/k 2) while the convergence rate of the classical augmented Lagrangian method (ALM) is O(1/k). Numerical experiments on the linearly constrained l 1−l 2 minimization problem are presented to demonstrate the effectiveness of AALM. PubDate: 2017-03-01 DOI: 10.1007/s11766-017-3381-z Issue No:Vol. 32, No. 1 (2017)