On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desired tolerance. While the first algorithm is conceptually simpler and more efficient, it is not guaranteed to converge for objective functions that are not strictly convex. This shortcoming is overcome in the second algorithm, which uses an additional outer proximal iteration, and, which is proven to converge under mild assumptions. Two examples are given to demonstrate the theoretical usefulness of the optimality conditions as well as the high efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on Signal Processing. In previous versions, the example in Section VI.B contained some mistakes and inaccuracies, which have been fixed in this versio

Model-Based Security Testing

Security testing aims at validating software system requirements related to security properties like confidentiality, integrity, authentication, authorization, availability, and non-repudiation. Although security testing techniques are available for many years, there has been little approaches that allow for specification of test cases at a higher level of abstraction, for enabling guidance on test identification and specification as well as for automated test generation. Model-based security testing (MBST) is a relatively new field and especially dedicated to the systematic and efficient specification and documentation of security test objectives, security test cases and test suites, as well as to their automated or semi-automated generation. In particular, the combination of security modelling and test generation approaches is still a challenge in research and of high interest for industrial applications. MBST includes e.g. security functional testing, model-based fuzzing, risk- and threat-oriented testing, and the usage of security test patterns. This paper provides a survey on MBST techniques and the related models as well as samples of new methods and tools that are under development in the European ITEA2-project DIAMONDS.Comment: In Proceedings MBT 2012, arXiv:1202.582

Why highly expressed proteins evolve slowly

Much recent work has explored molecular and population-genetic constraints on the rate of protein sequence evolution. The best predictor of evolutionary rate is expression level, for reasons which have remained unexplained. Here, we hypothesize that selection to reduce the burden of protein misfolding will favor protein sequences with increased robustness to translational missense errors. Pressure for translational robustness increases with expression level and constrains sequence evolution. Using several sequenced yeast genomes, global expression and protein abundance data, and sets of paralogs traceable to an ancient whole-genome duplication in yeast, we rule out several confounding effects and show that expression level explains roughly half the variation in Saccharomyces cerevisiae protein evolutionary rates. We examine causes for expression's dominant role and find that genome-wide tests favor the translational robustness explanation over existing hypotheses that invoke constraints on function or translational efficiency. Our results suggest that proteins evolve at rates largely unrelated to their functions, and can explain why highly expressed proteins evolve slowly across the tree of life.Comment: 40 pages, 3 figures, with supporting informatio

Robust methods of building regression models : an application to the housing sector.

This article studies robustification strategies for the linear model in the presence of outliers. The advantages of an internal analysis of the robustness of least squares for a given sample are pointed out. The application of this methodology is illustrated by building an explicit model of the determinants of rental housing values in the Madrid Metropolitan Area.Outliers; Influential observations; Robust regression; Cook distance; Hedonic price function; Housing market;