Discrete quadratic curvature energies

We present a family of discrete isometric bending models (IBMs) for triangulated surfaces in 3-space. These models are derived from an axiomatic treatment of discrete Laplace operators, using these operators to obtain linear models for discrete mean curvature from which bending energies are assembled. Under the assumption of isometric surface deformations we show that these energies are quadratic in surface positions. The corresponding linear energy gradients and constant energy Hessians constitute an efficient model for computing bending forces and their derivatives, enabling fast time-integration of cloth dynamics with a two- to three-fold net speedup over existing nonlinear methods, and near-interactive rates for Willmore smoothing of large meshes.     

Linear variational principle for convex vector maximization

For infinitely dimensional convex vector maximization problems, it is proved that there exists, under certain conditions, an arbitrarily small additive perturbation of the performance criterion by a linear continuous operator such that the perturbed problem has efficient solutions. The study was sponsored by the Ukrainian State Fund for Basic Research __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 105–114, March–April 2007.     

Robust control of polytopic systems by convex optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.     

Mesh Simplification Based on Super-Face and Genetic Algorithm in Reverse Engineering

Mesh simplification is one of the most important links in the context of reverse engineering. It is also an important consideration in computer graphics. This paper presents a novel and original method of triangular mesh reduction. A new concept of super-face is defined. In order to construct a super-face, a way to calculate the scattered point curvature is discussed. The growth of a seed point and the combination of different regions are also necessary for the construction of a super-face. When the hole left by the deletion of super-face is retriangulated a genetic algorithm is used that has been modified for our specific problem. Then the different weights to balance the optimisation of the new triangular mesh can be adjusted.     

基于波动方程的聚焦点控制照明叠前深度偏移

 基于波动方程的聚焦点控制照明叠前深度偏移技术借助于差分计算，把速度、密度等介质参数的影响体现在差分计算的矩阵方程中，能够自动适应速度场的任意变化，快速傅里叶变换的使用也加速了波场延拓的计算速度。因此此法兼具有限差分偏移方法和傅里叶偏移方法的优点，既可适应速度场的剧烈变化，又可保证对陡倾地层的成像效果，是目前针对复杂构造最有效的成像方法之一。对于单个聚焦点及其周围的成像步骤为：①采用矩形网格情况下绕射走时的有限差分计算方法生成合成算子；②应用合成算子来合成面炮震源和面波记录；③对合成的面炮震源和面波记录做傅里叶有限差分法波动方程叠前深度偏移，得到该聚焦点及其附近区域的成像结果。按照上述成像步骤，将震源波场和炮集记录依据相应的外推公式进行延拓，最终应用成像条件求取成像值。在地质目标处选取多个聚焦点，可以得到面向目标的控制照明偏移成像，在多个层位上选取多个聚焦点进行控制照明叠前深度偏移，可以得到整块区域的成像。通过对Marmousi模型的试算，取得了较好的效果。     

容纳矛盾逻辑系统与悖论

分析了目前各种容纳矛盾逻辑系统的不足,提出了正域、反域、不动域的概念,进而发现悖论是逻辑思维领域的不动点,建立了一个容纳矛盾的逻辑系统S,并给出了系统S的语义模型,证明了系统S的元定理.在系统S中,命题演算被分成3个独立的域,正域、反域中所有经典逻辑的定理与演算模式都是有效的;不动域是一个包含矛盾的域,在不动域中,可以证明悖论是一个定理.系统S与Da Costa的次协调逻辑系统Cn相比较,它不但可以容纳矛盾,并且可以把矛盾解释清晰.以此逻辑系统为基础,可以建立一个容纳矛盾的数学基础.     

一种改进选择算子的遗传算法在泊松曲线沉降预测模型中的应用

选择算子是遗传算法的重要算子之一,它对于种群的多样性和算法的收敛性具有重要的影响。本文对轮盘赌选择算子进行改进,将适应值分组应用于种群个体的选择中,提出适应度分组轮盘赌,并将该方法用于泊松曲线沉降预测模型的优化。实验结果表明,该算法为泊松曲线沉降预测模型的参数估计提供一种有效的方法。     

基于内在奖励的技能获取和组合方法

现有的内在奖励随着agent不断探索环境而逐渐消失,导致了agent无法利用内在奖励信号去指引agent寻找最优策略。为了解决这个问题,提出了一种基于内在奖励的技能获取和组合方法。该方法首先在agent与环境交互过程中寻找积极状态,在积极状态中筛选子目标;其次从初始状态到达子目标,子目标到达终止状态所产生的一条轨迹中发现技能,对技能中出现一个或者两个以上的子目标进行组合;最后用初始状态到子目标的距离和初始状态到子目标的累积奖励值对技能进行评估。该方法在Mujoco环境中取得了较高的平均奖励值,尤其是在外在奖励延迟的情况下,也能取得较好的平均奖励值。说明该方法提出的子目标和技能可以有效地解决内在奖励消失后,agent无法利用内在奖励信号学习最优策略的问题。     

An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow

In this paper we present a simple, general methodology for the generation of high-order operator decomposition (splitting) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described.