The structure of alternative tableaux

In this paper we study alternative tableaux introduced by Viennot [X. Viennot, Alternative tableaux, permutations and partially asymmetric exclusion process, talk in Cambridge, 2008]. These tableaux are in simple bijection with permutation tableaux, defined previously by Postnikov [A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764v1 [math.CO], 2006].We exhibit a simple recursive structure for alternative tableaux, from which we can easily deduce a number of enumerative results. We also give bijections between these tableaux and certain classes of labeled trees. Finally, we exhibit a bijection with permutations, and relate it to some other bijections that already appeared in the literature.     

Existence of optimal solutions for general stochastic linear complementarity problems

In this paper we show the solvability of the expected residual minimization (ERM) formulation for the general stochastic linear complementarity problem (SLCP) under mild assumptions. The properties of the ERM formulation are dependent on the choice of NCP functions. We focus on the ERM formulations defined by the “min” NCP function and the penalized FB function, both of which are nonconvex programs on the nonnegative orthant.     

Ekeland’s variational principle for vectorial multivalued mappings in a uniform space

In this paper, we establish Ekeland’s variational principle and an equilibrium version of Ekeland’s variational principle for vectorial multivalued mappings in the setting of separated, sequentially complete uniform spaces. Our approaches and results are different from those in Chen et al. (2008), Hamel (2005), and Lin and Chuang (2010) [13], [14] and [15]. As applications of our results, we study vectorial Caristi’s fixed point theorems and Takahashi’s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated, sequentially complete uniform space. We also apply our results to study maximal element theorems, which are unified methods of several variational inclusion problems. Our results contain many known results in the literature Fang (1996) [21], and will have many applications in nonlinear analysis.     

A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems.     

Parametric aggregation in ordered weighted averaging

Incorporating further information into the ordered weighted averaging (OWA) operator weights is investigated in this paper. We first prove that for a constant orness the minimax disparity model [13] has unique optimal solution while the modified minimax disparity model [16] has alternative optimal OWA weights. Multiple optimal solutions in modified minimax disparity model provide us opportunity to define a parametric aggregation OWA which gives flexibility to decision makers in the process of aggregation and selecting the best alternative. Finally, the usefulness of the proposed parametric aggregation method is illustrated with an application in metasearch engine.     

Viscosity method for hierarchical fixed point and variational inequalities with applications

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.     

视差自由立体显示中莫尔条纹消除的研究进展

视差自由立体显示中视差生成元件参数的不合理设定会导致影响三维图像的莫尔条纹产生。因此,莫尔条纹消除是视差自由立体显示中的关键问题之一。本文简单介绍了3种视差自由立体显示原理。综述了视差自由立体显示中的避免莫尔条纹产生和莫尔条纹最小化2种莫尔条纹消除技术,着重介绍了莫尔条纹最小化技术,包括工程实验、莫尔条纹图像仿真、余弦光栅叠加模型近似分析和序数方程方法和傅里叶分析方法的一致性分析等技术。其中后2种技术给出了视差自由立体显示中莫尔条纹最小化的详细理论分析和解释,并为其他视差自由立体显示技术提供了设计依据。     

Enterprise security economics: A self‐defense versus cyber‐insurance dilemma

We propose a model that optimizes enterprise investments in cybersecurity using expected utility theory. The model allows computing (a) investment in self‐defense to reduce the risk of security breaches, (b) investment in cyber insurance to transfer the residual risk to insurance companies, and (c) investment in forensic readiness to make the insured firms capable of generating provable insurance claims about security breaches. A three‐phase–based model of vulnerability rate evolution over time is proposed and used to estimate the different planned security expenditures throughout the investment horizon. At the starting time of investment, a decision maker invests to cover the existing risk of breach and periodically spends to cover the additional risk observed due to the release of new vulnerabilities. In this work, the intermediate tranches are determined while considering three different attitudes of decision makers, namely, optimistic, pessimistic, and realistic. An analysis is conducted to assess the performance of the proposed models.     

A Penalized Likelihood Method for Classification With Matrix-Valued Predictors

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.