Local distinguishability of quantum states in infinite dimensional systems

We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Microbiological Implications of Periurban Agriculture and Water Reuse in Mexico City

BACKGROUND: Recycled treated or untreated wastewater represents an important health challenge in developing countries due to potential water related microbiological exposure. Our aim was to assess water quality and health implications in a Mexico City periurban agricultural area. METHODOLOGY/PRINCIPAL FINDINGS: A longitudinal study in the Xochimilco wetland area was conducted, and 42 sites were randomly selected from 211, including irrigation water canals and effluents of treatment plants. Sample collection took place during rainy and dry seasons (2000-2001). Microbiological parameters (total coliforms, fecal coliforms, streptococci/enterococci, and bacteria other than Vibrio grown on TCBS), Helicobacter pylori, and physicochemical parameters including trihalomethanes (THM) were determined. Fecal coliforms and fecal streptococci are appropriate indicators of human or animal fecal contamination. Fecal coliform counts surpass Mexican and World Health Organization irrigation water guidelines. Identified microorganisms associated with various pathologies in humans and domestic animals comprise Escherichia coli, Klebsiella spp., Salmonella spp., Enterobacter spp., Enterococcus spp., and Pseudomonas spp; H. pylori was also present in the water. An environmental characteristic of the canal system showed high Total Organic Carbon content and relatively low dissolved oxygen concentration; residual chlorine as a disinfection control is not efficient, but THMs do not represent a problem. During the rainy season, temperature and conductivity were higher; in contrast, pH, dissolved oxygen, ammonia, and residual chlorine were lower. This is related with the continuous load of feces from human and animal sources, and to the aquatic systems, which vary seasonally and exhibit evidence of lower water quality in effluents from treatment plants. CONCLUSIONS/SIGNIFICANCE: There is a need for improvement of wastewater treatment systems, as well as more efficient monitoring, regulation, and enforcement procedures for wastewater disposal into bodies of water

Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization

Permanently going back and forth between the “quadratic world” and the “convexity world” in optimization

The objective of this work is twofold. Firstly, we propose a review of different results concerning convexity of images by quadratic mappings, putting them in a chronological perspective. Next, we enlighten these results from a geometrical point of view in order to provide new and comprehensive proofs and to immerse them in a more general and abstract context

Aportación metodológica para determinar el índice de calidad del medio ambiente urbano y edificado del Área Metropolitana de Barcelona

El presente trabajo está orientado hacia la determinación de una metodología que evalúa características socio-residenciales, diagnostica el estado de bienestar del medio ambiente urbano del Área Metropolitana de Barcelona (AMB), responde al estado en que se encuentran las viviendas pre-existentes al 2001. La investigación incorpora una aportación al enfoque de valoración inmobiliaria sustentada en técnicas de valores sociales como parte de un contexto integral. La orientación al desarrollo sostenible constituye dar un enfoque de valoración inmobiliaria, es decir, retomando el valor de uso como una combinación de valores urbanos y de satisfacción residencial en la base del análisis. La hipótesis de la investigación nace a partir de desarrollar una metodología sustentada en indicadores parciales (simples) idóneos para la obtención del Índice de Calidad Edificada del AMB obtenido por el método del indicador sintético de distancia DP2. El objetivo de la investigación es demostrar la validación del método del indicador sintético de distancia.This work is oriented towards the determination of a methodology to assess socio-residential characteristics, diagnoses the welfare state of the urban environment in the metropolitan area of Barcelona (AMB), responds to the state that are pre-existing dwellings to 2001 . The research incorporates a contribution to real estate valuation approach supported by techniques of social values as part of a comprehensive context. The sustainable development orientation is an approach to property valuation, returning the value in use as a combination of urban values and residential satisfaction in the analysis. The hypothesis of the research stems from developing a methodology supported by partial indicators (simple) suitable for obtaining Built Quality Index of AMB obtained by the method of the synthetic indicator DP2 away. The objective of this research is to demonstrate the validation of the method of the synthetic indicator away.Peer Reviewe

Social welfare and profit maximization from revealed preferences

Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity $O(m^2/\epsilon^2)$, where $\epsilon$ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of $O(\sqrt{mn})$ from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently)

New approximations for the cone of copositive matrices and its dual

We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C (resp. for its dual), thus complementing previous inner (resp. outer) approximations for C (for the dual). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to K-copositivity and K-complete positivity for a closed convex cone K, is straightforward.Comment: 8