Approximability and exact resolution of the multidimensional binary vector assignment problem

In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets \(V^1, V^2, \ldots , V^m\), each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset \(V^i\). To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by Open image in new window , and the restriction of this problem where every vector has at most c zeros by Open image in new window . Open image in new window was only known to be Open image in new window -hard, even for Open image in new window . We show that, assuming the unique games conjecture, it is Open image in new window -hard to Open image in new window -approximate Open image in new window for any fixed Open image in new window and Open image in new window . This result is tight as any solution is a Open image in new window -approximation. We also prove without assuming UGC that Open image in new window is Open image in new window -hard even for Open image in new window . Finally, we show that Open image in new window is polynomial-time solvable for fixed Open image in new window (which cannot be extended to Open image in new window ).     

On the <Emphasis Type="Italic">m</Emphasis>-clique free interval subgraphs polytope: polyhedral analysis and applications

In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results.     

New lower bounds for the second variable Zagreb index

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randi?, the second Zagreb and the modified Zagreb indices.     

On the relationship between compliance with recommendations on the audit committee of codes of good practices and financial reporting quality

Codes of good practices provide a soft alternative to the hard legislation approach to corporate governance. These codes include a set of recommendations that companies are expected to follow in order to enhance governance structures and practices. Some of these recommendations specifically aim to improve the effectiveness of the audit committee. We investigate the relationship between the level of compliance with recommendations on the audit committee of the Spanish Unified Code and financial reporting quality, as measured by discretionary accruals and by the opinion of the audit report. We use a sample of companies listed in the Spanish stock market for the years between 2007 and 2013. Results show a strong and positive relationship between the level of compliance with recommendations and the quality of financial reporting. We also report significant results for some specific recommendations. These results are robust to various checks. Therefore, the level of compliance with recommendations on the audit committee might provide a feasible and reliable indicator of the quality of financial reports released by the company.     

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.     

Subset sum problems with digraph constraints

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees.     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.     

Contract design and insurance fraud: an experimental investigation

This paper experimentally examines the impact of contract design on insurance fraud. We test how fraud behavior varies for insurance contracts with full coverage, a straight deductible or claim-dependent premiums (bonus-malus contracts), in a setup where rational and selfish individuals have an incentive to always claim the maximum possible indemnity. We find a substantial impact of contractual arrangements: Deductible contracts lead to a greater extent to claim build-up than full coverage contracts. In contrast, bonus-malus contracts that entail the same net gains from fraud as deductible contracts do not increase claim build-up. Thus, our results indicate that bonus-malus contracts may be superior to deductible contracts for behavioral reasons.     

Advancing Social Capital Measurement: Using General Social Survey Cycles to Develop an Efficient Survey Instrument

The General Social Survey (GSS) has provided significant insight about the state of societies around the world through the International Social Survey Programme (ISSP). Although broadly applicable, in this study the context for developing a new social capital survey instrument covers the Canadian GSS since 1985. Questions in the GSS are often used by researchers who are interested in specific questions or themes for use in some form of re-sampling. Given significant social and relational themes, GSS cycles from 1985 to 2013 were reviewed using a social capital framework to produce a new Social Capital GSS survey instrument. A process of vetting and sorting questions led to development of a 41 question instrument that includes 16 demographic and context variables and 25 social network and trust variables. After testing and refinement, the instrument was used with a randomly sampled group across selected East Hamilton Census Tracts that are differentiated by median income and a standard deviation above and below respectively (n?=?97).     

Effects of a Mindfulness Task on Women’s Sexual Response

Mindfulness-based interventions are effective at improving symptoms of sexual dysfunction in women. The mechanisms by which mindfulness improves sexual function are less clear. The main objective of our study was to investigate the impact of a mindfulness task on sexual response in women. Forty-one women (mean age = 27.2, SD = 5.6) participated in two laboratory sessions that each included two erotic films and one attention task that were presented in counterbalanced order. Both attention tasks consisted of a six-minute audio recording of either a modified body scan, focusing on genital arousal sensations (mindfulness condition), or a visualization exercise. Subjective and genital sexual arousal were measured continuously during stimulus presentation. The mindfulness task led to greater subjective and lower genital arousal. The agreement of subjective and genital sexual arousal (i.e., concordance) was greater in the mindfulness condition. Trait mindfulness was related to lower sexual arousal but also greater sexual concordance in women. Mindfulness-based interventions that encourage women to focus on physical arousal sensations in the here and now may be associated with women’s improved sexual function by enhancing feelings of sexual arousal during sexual activity and by increasing concordance between subjective and genital sexual arousal.