New data inversion formulae in confocal scanning microscopy

Whereas the resolving power of an ordinary optical microscope is determined by the classical Rayleigh distance, significant super-resolution, i.e. resolution improvement beyond that Rayleigh limit, has been achieved by confocal scanning light microscopy. Furthermore is has been shown that the resolution of a confocal scanning microscope can still be significantly enhanced by measuring, for each scanning position, the full diffraction image by means of an array of detectors and by inverting these data to recover the value of the object at the focus. We discuss the associated inverse problem and show how to generalize the data inversion procedure by allowing, for reconstructing the object at a given point, to make use also of the diffraction images recorded at other scanning positions. This leads us to a whole family of generalized inversion formulae, which contains as special cases some previously known formulae. We also show how these exact inversion formulae can be implemented in practice.

Extended formulations, nonnegative factorizations, and randomized communication protocols

An extended formulation of a polyhedron P is a linear description of a polyhedron Q together with a linear map π such that π(Q)=P. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis’ factorization theorem (Yannakakis in J Comput Syst Sci 43(3):441–466, 1991) provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of $$P$$P equals the nonnegative rank of its slack matrix S. Moreover, Yannakakis also shows that the nonnegative rank of S is at most 2^c, where c is the complexity of any deterministic protocol computing S. In this paper, we show that the latter result can be strengthened when we allow protocols to be randomized. In particular, we prove that the base-2 logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation. Using Yannakakis’ factorization theorem, this implies that the base-2 logarithm of the smallest size of an extended formulation of a polytope P equals the minimum complexity of a randomized communication protocol computing the slack matrix of P in expectation. We show that allowing randomization in the protocol can be crucial for obtaining small extended formulations. Specifically, we prove that for the spanning tree and perfect matching polytopes, small variance in the protocol forces large size in the extended formulation.

Approximation limits of linear programs (beyond hierarchies)

We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^1/2-ε)-approximations for CLIQUE require LPs of size 2^nΩ(ε). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov's [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.

On the extension complexity of combinatorial polytopes

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors. Using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs, including those used in quantum information and suspensions of cubic planar graphs.

Sorting under partial information (without the ellipsoid algorithm)

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P), the binary logarithm of the number of linear extensions of P. In a breakthrough paper, Jeff Kahn and Jeong Han Kim (STOC 1992) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present: an O(n2) algorithm performing O(log n·log e(P)) comparisons; an O(n2.5) algorithm performing at most (1+ε) log e(P) + Oε(n) comparisons; an O(n2.5) algorithm performing O(log e(P)) comparisons. All our algorithms are simple to implement. © 2010 ACM.

A toolset for the analysis of et-lotos specifications

info:eu-repo/semantics/published

A simulator of real-time systems specified in et-lotos

info:eu-repo/semantics/published

Observatoire des usages étudiants universitaires d’un système éducatif de gestion intégré

Les universités recourent de plus en plus souvent à des plateformes technologiques afin d’administrer les processus éducatifs et faciliter les tâches administratives des étudiants. Cependant, ces changements sont conséquents et engendrent souvent de nombreuses difficultés d’implémentation. C’est dans ce cadre qu’un Observatoire des usages étudiants d’un système éducatif de gestion intégré a été créé. Cet observatoire a pour missions d’identifier les facteurs de satisfaction et de fournir des recommandations à l’université. Plusieurs méthodologies (groupes de discussion, tests d’utilisabilité, questionnaires) ont été utilisées. Les résultats montrent que ce sont les difficultés et insatisfactions dues au système utilisé et aux informations présentes sur ce système qui influencent négativement l’acceptabilité du système. La création d’un tel observatoire permet tout à la fois d’étudier l’acceptabilité et la satisfaction des utilisateurs, de différencier l’impact des facteurs personnels et techniques, de s’interroger sur les processus d’évaluation des outils lors de leur implémentation.

Qu’est-ce qui motive les utilisateurs d’un système de gestion des apprentissages ?

info:eu-repo/semantics/nonPublished

How to beat the Rayleigh limit?

The problem of achieving super-resolution, i.e. resolution beyond the classical Rayleigh distance of half a wavelength, is a real challenge in several imaging problems. The development of computer-assisted instruments and the possibility of inverting the recorded data has clearly modified the traditional concept of resolving power of an instrument. We show that, in the framework of inverse problem theory, the achievable resolution limit arises no longer from a universal rule but instead from a practical limitation due to noise amplification in the data inversion process. We analyze under what circumstances super-resolution can be achieved and we show how to assess the actual resolution limits in a given experiment, as a function of the noise level and of the available a priori knowledge about the object function. We emphasize the importance of the a priori knowledge of its effective support and we show that significant super-resolution can be achieved for "subwavelength sources", i.e. objects which are smaller than the probing wavelength.

Health networks: Actors, professional relationships, and controversies

In recent years international policies have aimed to stimulate the use of information and communication technologies (ICT) in the field of health care. Belgium has also been affected by these developments and, for example, health electronic regional networks ("HNs") are established. Thanks to a qualitative case study we have explored the implementation of such innovations (HN) to better understand how health professionals collaborate through the HN and how the HN affect their relationships. Within the HNs studied a common good unites the actors: the continuity of care for a better quality of care. However behind this objective of continuity of care other individual motivations emerge. Some controversies need also to be resolved in order to achieve cooperative relationships. HNs have notably to take national developments into account. These developments raise the question of the control of medical knowledge and medical practice. Professional issues, and not only practical changes, are involved in these innovations. © 2008 The authors and IOS Press. All rights reserved.

Is the Species Flock Concept Operational? The Antarctic Shelf Case

There has been a significant body of literature on species flock definition but not so much about practical means to appraise them. We here apply the five criteria of Eastman and McCune for detecting species flocks in four taxonomic components of the benthic fauna of the Antarctic shelf: teleost fishes, crinoids (feather stars), echinoids (sea urchins) and crustacean arthropods. Practical limitations led us to prioritize the three historical criteria (endemicity, monophyly, species richness) over the two ecological ones (ecological diversity and habitat dominance). We propose a new protocol which includes an iterative fine-tuning of the monophyly and endemicity criteria in order to discover unsuspected flocks. As a result nine « full » species flocks (fulfilling the five criteria) are briefly described. Eight other flocks fit the three historical criteria but need to be further investigated from the ecological point of view (here called « core flocks »). The approach also shows that some candidate taxonomic components are no species flocks at all. The present study contradicts the paradigm that marine species flocks are rare. The hypothesis according to which the Antarctic shelf acts as a species flocks generator is supported, and the approach indicates paths for further ecological studies and may serve as a starting point to investigate the processes leading to flock-like patterning of biodiversity. © 2013 Lecointre et al.

Superresolution: an ill-posed problem in Fourier optics

info:eu-repo/semantics/published

The Superresolution Problem in Doppler Difference Laser Anemometry

info:eu-repo/semantics/published

Sufficient Conditions for the Existence of Bound States in a Potential without Spherical Symmetry

We give in this paper several suffieient conditions for the existence of negative energy bound states in a purely attractive potential without spherical symmetry. These conditions generalize the condition obtained recently by K. Chadan and A. Martin (C. R. Acad. Sci. Paris290 (1980), 151), and can ensure the existence of n bound states. For the spherically symmetric case, one gets simple formulae which are also new.