Tight Polynomial Bounds for Loop Programs in Polynomial Space

We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of polynomially-bounded variables, and on a weak programming language for which we have recently shown that tight bounds for polynomially-bounded variables are computable. These bounds are sets of multivariate polynomials. While their computability has been settled, the complexity of this program-analysis problem remained open. In this paper, we show the problem to be PSPACE-complete. The main contribution is a new, space-efficient analysis algorithm. This algorithm is obtained in a few steps. First, we develop an algorithm for univariate bounds, a sub-problem which is already PSPACE-hard. Then, a decision procedure for multivariate bounds is achieved by reducing this problem to the univariate case; this reduction is orthogonal to the solution of the univariate problem and uses observations on the geometry of a set of vectors that represent multivariate bounds. Finally, we transform the univariate-bound algorithm to produce multivariate bounds.

MVMOO: Mixed variable multi-objective optimisation

In many real-world problems there is often the requirement to optimise multiple conflicting objectives in an efficient manner. In such problems there can be the requirement to optimise a mixture of continuous and discrete variables. Herein, we propose a new multi-objective algorithm capable of optimising both continuous and discrete bounded variables in an efficient manner. The algorithm utilises Gaussian processes as surrogates in combination with a novel distance metric based upon Gower similarity. The MVMOO algorithm was compared to an existing mixed variable implementation of NSGA-II and random sampling for three test problems. MVMOO shows competitive performance on all proposed problems with efficient data acquisition and approximation of the Pareto fronts for the selected test problems.

Solving Generalized Equations with Bounded Variables and Multiple Residuated Operators

This paper studies the resolution of sup-inequalities and sup-equations with bounded variables such that the sup-composition is defined by using different residuated operators of a given distributive biresiduated multi-adjoint lattice. Specifically, this study has analytically determined the whole set of solutions of such sup-inequalities and sup-equations. Since the solvability of these equations depends on the character of the independent term, the resolution problem has been split into three parts distinguishing among the bottom element, join-irreducible elements and join-decomposable elements.

Measuring Income-Related Inequalities in Health in Multi-Country Analysis

Health inequalities remain a cause of concern for policymakers across the world. However, the measurement and monitoring of health inequalities over time and across countries remain a research challenge. The concentration index is one of the most popular measurement tools, however, it presents several drawbacks, especially for bounded variables, which are discussed in this study. Results from the European Community Household Panel dataset and the Statistics of Income and Living Conditions for Europe suggest that there is evidence of persistent socioeconomic inequalities in health in Europe. Further, results show the need of reporting both absolute and relative inequalities for appropriately monitoring and comparing trends in health inequalities across countries.

Mutiny on the Boundary: Methods for Bounded Quantitative Variables

Many quantitative variables in psychological research, assessment, and testing have bounds, but boundedness often is ignored by researchers. Ignoring bounds can result in miss-estimation, miss-specified models, and improper statistical inference. This tutorial introduces concepts and models for analyzing quantitative random variables that have one or more bounds. These variables fall into two groups: Those where the bounds are “absolute”, and “limited” variables whose bounds are “censored” or “truncated”. This tutorial explains which techniques are suited to dealing with specific types of bounded variables and how to deal with boundary cases, and provides a guide to resources for using these techniques effectively.