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On the residual dependence index of elliptical distributions

STATISTICS & PROBABILITY LETTERS 2010年第13-14期80卷 1070-1078页

作者： Hashorva, Enkelejd Univ Bern Dept Math Stat & Actuarial Sci CH-3012 Bern Switzerland

The residual dependence index of bivariate Gaussian distributions is determined by the correlation coefficient. This tail index is of certain statistical importance when extremes and related rare events of bivariate samples with asymptotic independent components are being modeled. In this paper we calculate the partial residual dependence indices of a multivariate elliptical random vector assuming that the associated random radius has distribution function in the Gumbel max-domain of attraction. Furthermore, we discuss the estimation of these indices when the associated random radius possesses a Weibull-tail distribution. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Partial residual dependence index Gumbel max-domain of attraction Weibull-tail distribution Elliptical distribution quadratic programming problem

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Distributed Gradient Method for Neural Network-Based Constrained k - Winners-Take-All

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2024年第6期11卷 5760-5772页

作者： Shi, Xiasheng Su, Yanxu Mu, Chaoxu Sun, Changyin Anhui Univ Engn Res Ctr Autonomous Unmanned Syst Technol Minist Educ Hefei 230601 Peoples R China Anhui Univ Anhui Prov Engn Res Ctr Unmanned Syst & Intelligen Hefei 230601 Peoples R China Anhui Univ Sch Artificial Intelligence Hefei 230601 Peoples R China Tianjin Univ Sch Elect & Informat Engn Tianjin 300072 Peoples R China

Thispaper studies the neural network-based distributed constrained k-winners-take-all (kWTA) problem, which aims to select k largest inputs from amount of inputs under two types of global coupled constraints. Namely, equality and inequality constrained kWTA problems. By selecting the proper parameter, the two constrained kWTA problems can be transformed into two continuous constrained quadratic programming problems. Subsequently, we propose a derivative feedback-based modified primal-dual fully distributed algorithm for the kWTA problem with a global coupled equality constraint by utilizing Karush-Kuhn-Tucker (KKT) conditions and the gradient flow method. In addition, the developed derivative feedback-based distributed neurodynamic method is initialization-free. Furthermore, the above method is revised via a maximal projection operator for the kWTA problem with a global coupled inequality constraint. The two methods are rigorously proved to asymptotically solve the distributed constrained kWTA models in accordance with LaSalle's invariance principle. The performance of our designed methods is tested via four simulation examples.

关键词： Neurons Convergence Neurodynamics Biological neural networks quadratic programming Task analysis Optimization Derivative feedback control k--winners-take-all neurodynamic method LaSalle's invariance principle quadratic programming problem

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Design of linkage mechanisms of partially rigid frames using limit analysis with quadratic yield functions

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2016年 88-89卷 68-78页

作者： Ohsaki, Makoto Tsuda, Seita Miyazu, Yuji Kyoto Univ Dept Architecture & Architectural Engn Nishikyo Ku Kyoto 6158540 Japan Okayama Prefectural Univ Dept Design & Technol 111 Kuboki Soja 7191197 Japan Hiroshima Univ Dept Architecture 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan

A method is presented for generating linkage mechanisms consisting of frame members. A quadratic programming problem is solved to obtain an infinitesimal mechanism allowing a hinge rotating about an axis in arbitrarily inclined direction. The problem is equivalent to a plastic limit analysis problem with quadratic yield functions with respect to member-end moments and axial force. The directions of hinges are obtained from the ratios of member-end moments along the local axes. A finite mechanism is generated by carrying out geometrically nonlinear analysis and adding hinges, if necessary. Effectiveness of the proposed method is demonstrated through examples of 3-dimensional mechanisms. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Linkage mechanism quadratic programming problem Plastic limit analysis Overconstrained mechanism Optimality conditions

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Exact asymptotics of component-wise extrema of two-dimensional Brownian motion

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EXTREMES 2020年第4期23卷 569-602页

作者： Debicki, Krzysztof Ji, Lanpeng Rolski, Tomasz Univ Wroclaw Math Inst Pl Grunwaldzki 2-4 PL-50384 Wroclaw Poland Univ Leeds Sch Math Woodhouse Lane Leeds LS2 9JT W Yorkshire England

We derive the exact asymptotics of P{ sup(t >= 0) (X-1(t) - mu(1)t) > u,sup(s >= 0) (X-2(s) - mu(2)s) > u }, u -> infinity. where (X-1(t),X-2(s))(t,s >= 0) is a correlated two-dimensional Brownian motion with correlation rho is an element of [- 1,1] and mu(1), mu(2) > 0. It appears that the play between rho and mu(1), mu(2) leads to several types of asymptotics. Although the exponent in the asymptotics as a function of rho is continuous, one can observe different types of prefactor functions depending on the range of rho, which constitute a phase-type transition phenomena.

关键词： Two-dimensional Brownian motion Exact asymptotics Component-wise extrema quadratic programming problem Generalised Pickands-Piterbarg constants

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On the cumulative Parisian ruin of multi-dimensional Brownian motion risk models

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SCANDINAVIAN ACTUARIAL JOURNAL 2020年第9期2020卷 819-842页

作者： Ji, Lanpeng Univ Leeds Sch Math Woodhouse Lane Leeds LS2 9JT W Yorkshire England

Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial capital tends to infinity. An asymptotic distribution for the conditional cumulative Parisian ruin time is also derived. The obtained results on the cumulative Parisian ruin can be seen as generalisations of some of the results derived in Dbicki et al. [(2018). Extremal behavior of hitting a cone by correlated Brownian motion with drift. Stochastic Processes and Their Applications 128, 4171-4206]. As a particular interesting case, the two-dimensional Brownian motion risk model is discussed in detail.

关键词： Multi-dimensional Brownian motion cumulative Parisian ruin exact asymptotics ruin probability quadratic programming problem

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Asymptotics of multivariate conditional risk measures for Gaussian risks

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INSURANCE MATHEMATICS & ECONOMICS 2019年 86卷 205-215页

作者： Ling, Chengxiu Xian Jiaotong Liverpool Univ Dept Math Sci Suzhou 215123 Peoples R China Univ Lausanne Dept Actuarial Sci CH-1015 Lausanne Switzerland

This paper investigates accurate approximations of marginal moment excess, marginal conditional tail moment and marginal moment shortfall for multivariate Gaussian system risks. Based on the dimension reduction property via the quadratic programming problem, the super-exponential and polynomial convergence speeds are specified. Two interesting questions involved in risk management are well addressed, namely the minimal additional risk capital injection to avoid infinite risk contagion and a sufficient and necessary condition to alternate the convergence speeds. Numerical study and typical examples are given to illustrate the efficiency of our findings. Due to the flexible moment order, additional applications may involve in risk management, including tail mean-variance portfolio and multivariate conditional risk measures of tail covariance, tail skewness with dependence and extremal risk contagion under consideration. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Gaussian system risk Multivariate risk measures Risk contagion quadratic programming problem Marginal moment excess

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Collocation-Variational Approaches to the Solution to Volterra Integral Equations of the First Kind

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2022年第1期62卷 98-105页

作者： Bulatov, M., V Markova, E., V Russian Acad Sci Siberian Branch Matrosov Inst Syst Dynam & Control Theory Irkutsk 664033 Russia Russian Acad Sci Siberian Branch Melentiev Energy Syst Inst Irkutsk 664033 Russia

Volterra integral equations of the first kind on a bounded interval are considered. It is assumed that the kernel and the right-hand side of an equation are sufficiently smooth functions, the kernel does not vanish on the diagonal, while the right-hand side vanishes at the initial integration moment. For the numerical solution to such equations, single-step methods based on two-step quadrature rules are proposed. Discretization of this type yields an underdetermined system of linear algebraic equations, which has infinitely many solutions. The system is supplemented with the condition that the norm of the approximate solution is minimal in some analogues of a Sobolev space to uniquely determine the approximate solution at discretization nodes. Such methods are always stable in the case of a second-order approximation and converge to the exact solution with the second order. Numerical results produced by the proposed methods as applied to well-known test examples are presented.

关键词： Volterra integral equation of the first kind quadrature rules discretization quadratic programming problem

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Application of the Conjugate Gradient Method for Solving Unilateral Discrete Contact problems for an Elastic Half-Space

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2024年第11期64卷 2680-2695页

作者： Bobylev, A. A. Lomonosov Moscow State Univ Moscow 119991 Russia

problems of unilateral discrete contact between an elastic half-space and a rigid punch of finite size with a surface microrelief are considered. A variational formulation of the problems is obtained in the form of a boundary variational inequality using the Poincare-Steklov operator, which maps normal stresses into normal displacements on a part of the boundary of the elastic half-space. A minimization problem equivalent to the variational inequality is presented, as a result of the approximation of which a quadratic programming problem subject to equality and inequality constraints is obtained. To solve this problem, a new computational algorithm based on the conjugate gradient method is proposed, which includes three equations of punch equilibrium in the calculation. The algorithm belongs to the class of active set methods and takes into account the specifics of the set of constraints. Some patterns of contact interaction of surfaces with a regular microrelief are established.

关键词： unilateral discrete contact boundary variational inequality Poincare-Steklov operator quadratic programming problem conjugate gradient method

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Newton's Method for Minimizing a Convex Twice Differentiable Function on a Preconvex Set

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第3期58卷 322-327页

作者： Zabotin, V. I. Chernyaev, Yu. A. Kazan Natl Res Tech Univ Kazan 420111 Tatarstan Russia

The problem of minimizing a convex twice differentiable function on the set-theoretic difference between a convex set and the union of several convex sets is considered. A generalization of Newton's method for sol... 详细信息

关键词： Newton's method preconvex set quadratic programming problem necessary conditions for a local minimum convergence of algorithm

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Efficient Formulations for 1-SVM and their Application to Recommendation Tasks

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JOURNAL OF COMPUTERS 2006年第3期1卷 27-34页

作者： Yajima, Yasutoshi Kuo, Tien-Fang Tokyo Inst Technol Dept Ind Engn & Management Tokyo Japan

The present paper proposes new approaches for recommendation tasks based on one-class support vector machines (1-SVMs) with graph kernels generated from a Laplacian matrix. We introduce new formulations for the 1-SVM that can manipulate graph kernels quite efficiently. We demonstrate that the proposed formulations fully utilize the sparse structure of the Laplacian matrix, which enables the proposed approaches to be applied to recommendation tasks having a large number of customers and products in practical computational times. Results of various numerical experiments demonstrating the high performance of the proposed approaches are presented.

关键词： support vector machine Laplacian matrix graph kernel quadratic programming problem collaborative filtering recommender system

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