集值映射向量优化的Benson真有效性

本文首先将单值映射的锥次类凸概念推广到集值映射，并对锥次类凸集值映射给出几个等价刻划和一个择一性定理。然后，利用这些概念与结果来确定拓扑线性空间中带集值映射的向量优化问题的Ｂｅｎｓｏｎ真有效性，获得两个标量化结果和两个Ｌａｇｒａｎｇｅ乘子定理，在定义了一个适当的集值Ｌａｇｒａｎｇｅ映射并对其引入真鞍点的概念之后，又建立了Ｂｅｎｓｏｎ真有效性的一个充分条件和一个充要条件，最后还讨论了两个对偶问题。     

Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps

This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained     

Continuous and Discrete Clebsch Variational Principles

The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group via a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be eliminated, if and only if the velocity map is a Lie algebra action, thereby producing the Euler–Poincaré (EP) equation for the vector space variables. In this case, the map from the canonical variables on the Lie group to the vector space is the standard momentum map defined using the diamond operator. We apply the Clebsch method in examples of the rotating rigid body and the incompressible Euler equations. Along the way, we explain how singular solutions of the EP equation for the diffeomorphism group (EPDiff) arise as momentum maps in the Clebsch approach. In the case of finite-dimensional Lie groups, the Clebsch variational principle is discretized to produce a variational integrator for the dynamical system. We obtain a discrete map from which the variables on the cotangent bundle of a Lie group may be eliminated to produce a discrete EP equation for elements of the vector space. We give an integrator for the rotating rigid body as an example. We also briefly discuss how to discretize infinite-dimensional Clebsch systems, so as to produce conservative numerical methods for fluid dynamics.      

GRASP and path relinking hybridizations for the point matching-based image registration problem

In the last decade, image registration has proven to be a very active research area when tackling computer vision problems, especially in medical applications. In general, image registration methods aim to find a transformation between two images taken under different conditions. Point matching is an image registration approach based on searching for the right pairing of points between the two images, which involves a combinatorial optimization problem. From this matching, the registration transformation can be inferred by means of numerical methods.     

Automated Segmentation and Registration of Dermatological Images

During the last years, there has been a significant increase in the level of interest in image morphology, full-color image processing, image data compression, image recognition and knowledge based analysis systems for medical images. The present paper describes the implementation and tests the efficiency of algorithms dealing with the issues of segmentation and registration of digital images containing skin lesions. Those steps are considered of great importance in computer based characterization systems as they are responsible for the isolation of pathological findings and the matching of sequential images during follow-up studies in medical imaging. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As an application, we prove a Bernstein theorem which says that if the image of the Gauss map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends the previous theorems obtained by B. Palmer [Pa] and Y.L. Xin [Xin1] where they assume that the image of the Gauss map is bounded. We also prove a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional spaces. Received July 4, 1997 / Accepted October 9, 1997     

Pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature

In this paper, we use heat flow method to prove the existence of pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature, which is a generalization of Eells–Sampson’s existence theorem. Furthermore, when the target manifold has negative sectional curvature, we analyze horizontal energy of geometric homotopy of two pseudo-harmonic maps and obtain that if the image of a pseudo-harmonic map is neither a point nor a closed geodesic, then it is the unique pseudo-harmonic map in the given homotopic class. This is a generalization of Hartman’s theorem.     

带动量项的高阶幂法解高阶马尔科夫链的极限概率分布向量

针对高阶马尔科夫链的极限概率分布问题,本文提出了两种带动量项的高阶幂法,并在一定条件下建立了所提算法的收敛性定理.数值实验结果表明动量项能够有效改善原幂法的计算效率.     

Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps

In the framework of locally convex topological vector spaces, we establish a scalarization theorem, a Lagrange multiplier theorem and duality theorems for superefficiency in vector optimization involving nearly subconvexlike set-valued maps.     

A least deviation method for priority derivation in group decision making with incomplete reciprocal preference relations

In this paper, based on the transfer relationship between reciprocal preference relation and multiplicative preference relation, we proposed a least deviation method (LDM) to obtain a priority vector for group decision making (GDM) problems where decision-makers' (DMs') assessments on alternatives are furnished as incomplete reciprocal preference relations with missing values. Relevant theorems are investigated and a convergent iterative algorithm about LDM is developed. Using three numerical examples, the LDM is compared with the other prioritization methods based on two performance evaluation criteria: maximum deviation and maximum absolute deviation. Statistical comparative study, complexity of computation of different algorithms, and comparative analyses are provided to show its advantages over existing approaches.     

线性空间中具有集到集映射的向量极值问题的Lagrange乘子定理

本文在没有任何拓扑结构的条件下，即在非常一般的线性空间中，首先利用Ｍｏｒｒｉｓ序列定义了集到集凸映射的概念，其次证明了集到集映射的Ｆａｒｋａｓ－Ｍｉｎｋｏｗｓｋｉ定理，然后讨论了具有集到集映射的向量极值问题的Ｌａｇｒａｎｇｅ乘子定理。     

Loose saddle points of set-valued maps in topological vector spaces

We give a new existence theorem for loose saddle point of set-valued map having values in a partially ordered topological vector space which is based on continuity and quasiconvexity- quasiconcavity of its scalarized maps. Moreover, we prove a new saddle point theorem for vector-valued functions in locally convex topological vector spaces under weak condition that is the semicontinuity of two function scalarization.     

A novel image encryption algorithm based on a 3D chaotic map

Recently [Solak E, Çokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405-1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259-1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749-761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.     

Convexity of Multi-valued Momentum Maps

A famous theorem of Atiyah, Guillemin and Sternberg states that, given a Hamiltonian torus action, the image of the momentum map is a convex polytope. We prove that this result can be extended to the case in which the action is non-Hamiltonian. Our generalization of the theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and its image is the product of a convex polytope along a rational subspace times the orthogonal vector space. We also prove that this decomposition in direct product is stable under small equivariant perturbations of the symplectic structure; this, in particular, means that the property of being Hamiltonian is locally stable. The technique developed allows us to extend the result to any compact group action and also to deduce that any symplectic n-torus action, with fixed points, on a compact 2n-dimensional manifold, is Hamiltonian.     

Pseudo-holomorphic maps and bubble trees

This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable singularity theorem. The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of maps from a “bubble tree”—a map from a wedge Σ V S² V S² V ... →N. The main result is that the images of these renormalized maps converge in L^1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents a homology class then the limiting map represents this class.     

低分辨率医学图像的多图谱分割方法

基于多图谱的图像分割方法因其分割精度高和鲁棒性强,在医学图像分割领域被广泛研究,主要包含图像配准和标签融合两个步骤.目前对多图谱分割方法的研究通常都是在图谱图像和待分割目标图像具有相同分辨率的情况下展开的.然而,由于受图像采集时间,采集设备等影响,临床实践中采集的影像大多是低分辨率数据,使得目前在影像研究中广泛使用的方法无法有效应用于临床实践.因此,针对这一问题,我们结合图像超分辨率恢复方法,提出了精确鲁棒的低分辨率医学图像的多图谱分割方法,实验结果显示提出的方法显著地提高了多图谱分割方法的分割精度.     

On the domain invariance of countably condensing vector fields

Using homotopy theory, we give the domain invariance theorem for countably condensing vector fields, where the notion of countably condensing maps is due to Väth. A starting point of this investigation is that there is a symmetric characteristic set for a countably condensing map.     

On a characterization of convexity-preserving maps, Davidon’s collinear scalings and Karmarkar’s projective transformations

In a recent paper, the authors have proved results characterizing convexity-preserving maps defined on a subset of a not-necessarily finite dimensional real vector space as projective maps. The purpose of this note is three-fold. First, we state a theorem characterizing continuous, injective, convexity-preserving maps from a relatively open, connected subset of an affine subspace of ℝ ^m into ℝ ⁿ as projective maps. This result follows from the more general results stated and proved in a coordinate-free manner in the above paper, and is intended to be more accessible to researchers interested in optimization algorithms. Second, based on that characterization theorem, we offer a characterization theorem for collinear scalings first introduced by Davidon in 1977 for deriving certain algorithms for nonlinear optimization, and a characterization theorem for projective transformations used by Karmarkar in 1984 in his linear programming algorithm. These latter two theorems indicate that Davidon’s collinear scalings and Karmarkar’s projective transformations are the only continuous, injective, convexity-preserving maps possessing certain features that Davidon and Karmarkar respectively desired in the derivation of their algorithms. The proofs of these latter two theorems utilize our characterization of continuous, injective, convexity-preserving maps in a way that has implications to the choice of scalings and transformations in the derivation of optimization algorithms in general. The third purpose of this note is to point this out. Received: January 2000 / Accepted: November 2000?Published online January 17, 2001     

一种基于物体质心的图像自动化校准方法

图像校准是将任意相邻两图像都具有公共部分的一列图像合成一副全图的图像处理过程.而图像自动化校准的难点在于对一组图像公共部分特征信息的提取和自动匹配,尤其是自动匹配和图像校准的误差分析.本文基于放射变换不变性,给出了一种基于特征信息质心的自动匹配方法,与目前国际上主流特征提取和特征校准方法相比,本文方法较准确,且适用于卫星图片及一些MRI和CT 图片.本文方法的另一优点是具有线性计算复杂度.     

集值映射向量优化问题的ε—超有效解

本文引进了集值映射向量优化问题的ε－超有效解概念,并在集值映射为近似广义锥次似凸的假设下,建立了关于ε－超有效解的标量化定理和Lagrange乘子定理。