A complete set of covariants of the four qubit system

We obtain a complete and minimal set of 170 generators for the algebra of SL(2,\C)^{\times 4}-covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective Hilbert space. Also, this sheds some light on the local unitary invariants, and provides all the possible building blocks for the construction of entanglement measures for such a system.Comment: 14 pages, IOP macros; slightly expanded versio

Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

Lp solutions of backward stochastic differential equations

AbstractIn this paper, we are interested in solving backward stochastic differential equations (BSDEs for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions in Lp p>1, extending the results of El Karoui et al. (Math. Finance 7(1) (1997) 1) to the case where the monotonicity conditions of Pardoux (Nonlinear Analysis; Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic Publishers, Dordrecht, pp. 503–549) are satisfied. We consider both a fixed and a random time interval. In the last section, we obtain, under an additional assumption, an existence and uniqueness result for BSDEs on a fixed time interval, when the data are only in L1

Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

Nasal Carriage of Staphylococcus Aureus and Cross-Contamination in a Surgical Intensive Care Unit: Efficacy of Mupirocin Ointment

A six month prospective study was carried out in a surgical intensive care unit (SICU) of a university hospital to assess the incidence and routes of exogenous colonization by Staphylococcus aureus. A total of 157 patients were included in the study. One thousand one hundred and eleven specimens (nasal, surgical wound swabs, tracheal secretions obtained on admission and once a week thereafter, and all clinical specimens) were collected over a four month period from patients without nasal decontamination (A). They were compared with 729 specimens collected over a two month period from patients treated with nasal mupirocin ointment (B). All S. aureus strains were typed by restriction fragment length polymorphism (RFLP) pulsed-field gel electrophoresis after SmaI macrorestriction. The nasal colonization rates on admission were 25.5 and 32.7% in groups A and B, respectively. Thirty-one untreated patients (31.3%) and three patients (5.1%) treated with nasal ointment, acquired the nasal S. aureus in the SICU (P = 0.00027). Nasal carriers were more frequently colonized in the bronchopulmonary tract (Bp) and surgical wound (Sw) (62%) than patients who were not nasal carriers (14%) (P < 0.00001). The patterns were identical for nasal, Bp and Sw strains from the same patient. RFLP analysis characterized seven epidemic strains of methicillin-resistant S. aureus (MRSA) which colonized 60% of group A and 9% of group B patients (P < 0.00001). The bronchopulmonary tract infection rate was reduced in group B (P = 0.032). In conclusion, in an SICU, nasal carriage of S. aureus appeared to be the source of endogenous and cross- colonization. The use of nasal mupirocin ointment reduced the incidence of Bp and Sw colonization, as well as the MRSA infection rate

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Defects quantization in industrial radiographs by image processing

This paper refers to the industrial application of image processing using Non Destructive Testing by radiography . The various problems involved by the conception of a numerical tool are described . This tool intends to help radiograph experts to quantify defects and to follow up their evolution, using numerical techniques . The sequences of processings that achieve defect segmentation and quantization are detailed. They are based on the thorough knowledge of radiographs formation techniques . The process uses various methods of image analysis, including textural analysis and morphological mathematics. The interface between the final product and users will occur in an explicit language, using the terms of radiographie expertise without showing any processing details . The problem is thoroughly described : image formation, digitization, processings fitted to flaw morphology and finally product structure in progress .Cet article a pour sujet l'application industrielle du traitement d'image au contrôle non destructif par radiographie . Il décrit les différents problèmes posés par la conception d'un outil informatique ayant pour but de faciliter et d'améliorer la tâche d'expertise du radiographe pour la quantification et la suivi des défauts au cours du temps . Cet outil doit permettre à l'expert radiographe, néophyte en traitement d'image, d'utiliser pleinement les possibilités offertes par les techniques numériques . Des chaînes de traitement robustes, conduisant à la segmentation et à la quantification des défauts sont détaillées . Elles s'appuient sur la connaissance approfondie des techniques de formation de la radiographie . Les traitements retenus sont essentiellement basés sur l'analyse de texture et la morphologie mathématique . Les échanges entre l'utilisateur et le produit final se feront dans le vocabulaire de l'expert radiographe assurant la transparence des traitements . Le problème est décrit dans son intégralité : la formation de l'image, la numérisation, le choix de méthodes de traitement robustes et adaptées à l'aspect morphologique des défauts, et enfin la structure du produit en cours de réalisation

On the Effectiveness of Contracts as Test Oracles in the Detection and Diagnosis of Faults in Concurrent Object-Oriented Software

Design by Contract (DbC) is a software development methodology that focuses on clearly defining the interfaces between components to produce better quality object-oriented software. The idea behind DbC is that a method defines a contract stating the requirements a client needs to fulfill to use it, the precondition, and the properties it ensures after its execution, the postcondition. Though there exists ample support for DbC for sequential programs, applying DbC to concurrent programs presents several challenges. Using Java as the target programming language, this paper tackles such challenges by augmenting the Java Modelling Language (JML) and modifying the JML compiler to generate Runtime Assertion Checking (RAC) code to support DbC in concurrent programs. We applied our solution in a carefully designed case study on a highly concurrent industrial software system from the telecommunications domain to assess the effectiveness of contracts as test oracles in detecting and diagnosing functional faults in concurrent software. Based on these results, clear and objective requirements are defined for contracts to be effective test oracles for concurrent programs whilst balancing the effort to design them. Main results include that contracts of a realistic level of completeness and complexity can detect around 76% of faults and reduce the diagnosis effort for such faults by at least ten times. We, therefore, show that DbC can not only be applied to concurrent software but can also be a valua