Zeta regularized determinants for conic manifolds

We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.     

On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph $K_n$ are constructed for $n=q+1$ with any odd prime power $q$ such that either $q\equiv 1(mod4)$ or $q=2^h?1$. The arithmetic restriction $n=q+1$ is due to the fact that the vertices of $K_n$ in the construction are the points of a conic $\Omega$ in the finite plane of order $q$. Here we work on the Euclidean plane and describe an analogous construction where the role of $\Omega$ is taken by a regular $n$-gon. This allows us to remove the above constraints and construct one-factorizations of $K_n$ for every even $n\ge 6$.     

Characterizing an optimal input in perturbed convex programming

When every feasible stable perturbation of data results in a non-improvement of the optimal value function, then we talk about an ‘optimal input’ or an ‘optimal selection of data”. In this paper we describe such data for convex programs using perturbed saddle points. Research partly supported by Natural Sciences and Engineering Council of Canada and le Ministère de l'Education du Québec (F.C.A.C.). Presented in part at the Third Symposium on Mathematical Programming with Data Perturbations, The George Washington University, Washington, D.C. (May 21–22, 1981).     

Shape controlled interpolatory ternary subdivision

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges.     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.     

Segment-based region of interest generation for pedestrian detection in far-infrared images

We present a region of interest (ROI) generation method specialized for nighttime pedestrian detection using far-infrared (FIR) images. Because pedestrians typically appear brighter than background in FIR images, previous research efforts primarily attempted to extract ROIs based on the intensity threshold. However this approach has problems resulting from the intensity variances of pedestrians due to their clothing and, especially in urban scenarios, and other heat sources that emit more heat than the pedestrians. In this paper, we propose a novel ROI generation method that is based on combining image segments instead of using the intensity threshold. In order to minimize dependence on brightness, we utilize the low-frequency characteristics of FIR images. As a result, our proposed method generates a small number of ROIs at an acceptable miss rate and the generated ROIs provide advantages for classification because the pedestrians are satisfactorily arranged within a bounding box. Experiments conducted indicate that our proposed method performs reliably in urban scenarios.     

一类锥模型非单调信赖域算法及收敛性分析

本文对无约束优化问题提出了一类基于锥模型的非单调信赖域算法.二次模型非单调信赖域算法是新算法的特例.在适当的条件下,证明了算法的全局收敛性及Q-二次收敛性.     

Interior projection-like methods for monotone variational inequalities

We propose new interior projection type methods for solving monotone variational inequalities. The methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms, and are based on using non Euclidean projection-like maps. We prove global convergence results and establish rate of convergence estimates. The projection-like maps are given by analytical formulas for standard constraints such as box, simplex, and conic type constraints, and generate interior trajectories. We then demonstrate that within an appropriate primal-dual variational inequality framework, the proposed algorithms can be applied to general convex constraints resulting in methods which at each iteration entail only explicit formulas and do not require the solution of any convex optimization problem. As a consequence, the algorithms are easy to implement, with low computational cost, and naturally lead to decomposition schemes for problems with a separable structure. This is illustrated through examples for convex programming, convex-concave saddle point problems and semidefinite programming.The work of this author was partially supported by the United States–Israel Binational Science Foundation, BSF Grant No. 2002-2010.