Geodesics for a class of distances in the space of probability measures

In this paper, we study the characterization of geodesics for a class of distances between probability measures introduced by Dolbeault, Nazaret and Savar e. We first prove the existence of a potential function and then give necessary and suffi cient optimality conditions that take the form of a coupled system of PDEs somehow similar to the Mean-Field-Games system of Lasry and Lions. We also consider an equivalent formulation posed in a set of probability measures over curves

When are Stochastic Transition Systems Tameable?

A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Decisive Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs for short) are needed. In this article, we provide a framework to perform both the qualitative and the quantitative analysis of STSs. First, we define various notions of decisiveness (inherited from [1]), notions of fairness and of attractors for STSs, and make explicit the relationships between them. Then, we define a notion of abstraction, together with natural concepts of soundness and completeness, and we give general transfer properties, which will be central to several verification algorithms on STSs. We further design a generic construction which will be useful for the analysis of {\omega}-regular properties, when a finite attractor exists, either in the system (if it is denumerable), or in a sound denumerable abstraction of the system. We next provide algorithms for qualitative model-checking, and generic approximation procedures for quantitative model-checking. Finally, we instantiate our framework with stochastic timed automata (STA), generalized semi-Markov processes (GSMPs) and stochastic time Petri nets (STPNs), three models combining dense-time and probabilities. This allows us to derive decidability and approximability results for the verification of these models. Some of these results were known from the literature, but our generic approach permits to view them in a unified framework, and to obtain them with less effort. We also derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page

Le prince héritier à Sparte

In each of the two Spartan royal families, a precise dynastic nomos regulates successions. The first son who is born after his father’s accession is considered from childhood as the heir apparent. He is exempted from the agôgè; when he has reached adulthood, he may be chosen as commander-in-chief of the civic army. Such a situation, which is exceptional among Greek kingships, is probably linked with the fact that the Spartan dyarchy is an element of the constitutional kosmos of the city

Discriminative Parameter Estimation for Random Walks Segmentation

The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner. However, one of the main drawbacks of using the RW algorithm is that its parameters have to be hand-tuned. we propose a novel discriminative learning framework that estimates the parameters using a training dataset. The main challenge we face is that the training samples are not fully supervised. Speci cally, they provide a hard segmentation of the images, instead of a proba- bilistic segmentation. We overcome this challenge by treating the opti- mal probabilistic segmentation that is compatible with the given hard segmentation as a latent variable. This allows us to employ the latent support vector machine formulation for parameter estimation. We show that our approach signi cantly outperforms the baseline methods on a challenging dataset consisting of real clinical 3D MRI volumes of skeletal muscles.Comment: Medical Image Computing and Computer Assisted Interventaion (2013

Frequency of the Congenital Transmission of Trypanosoma cruzi: A Systematic Review and Meta-Analysis

BACKGROUND: Chagas disease is caused by the parasite Trypanosoma cruzi and is endemic in much of Latin America. With increased globalisation and immigration, it is a risk in any country, partly through congenital transmission. The frequency of congenital transmission is unclear. OBJECTIVE: To assess the frequency of congenital transmission of T. cruzi. SEARCH STRATEGY: PubMed, Journals@Ovid Full Text, EMBASE, CINAHL, Fuente Academica and BIREME databases were searched using seven search terms related to Chagas disease or T. cruzi and congenital transmission. SELECTION CRITERIA: The inclusion criteria were the following: Dutch, English, French, Portuguese or Spanish language; case report, case series or observational study; original data on congenital T. cruzi infection in humans; congenital infection rate reported or it could be derived. This systematic review included 13 case reports/series and 51 observational studies. DATA COLLECTION AND ANALYSIS: Two investigators independently collected data on study characteristics, diagnosis and congenital infection rate. The principal summary measure - the congenital transmission rate - is defined as the number of congenitally infected infants divided by the number of infants born to infected mothers. A random effects model was used. MAIN RESULTS: The pooled congenital transmission rate was 4.7% (95% confidence interval: 3.9-5.6%). Countries where T. cruzi is endemic had a higher rate of congenital transmission compared with countries where it is not endemic (5.0% versus 2.7%). CONCLUSIONS: Congenital transmission of Chagas disease is a global problem. Overall risk of congenital infection in infants born to infected mothers is about 5%. The congenital mode of transmission requires targeted screening to prevent future cases of Chagas disease.Fil: Howard, Elizabeth J.. University of Tulane; Estados UnidosFil: Xiong, Xu. University of Tulane; Estados UnidosFil: Carlier, Yves. Université Libre de Bruxelles; BélgicaFil: Sosa-estani, Sergio Alejandro. Dirección Nacional de Instituto de Investigación. Administración Nacional de Laboratorio e Instituto de Salud. Instituto Nacional de Parasitología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Buekens, Pierre. University of Tulane; Estados Unido

Prior Knowledge, Random Walks and Human Skeletal Muscle Segmentation

International audienceIn this paper, we propose a novel approach for segmenting the skeletal muscles in MRI automatically. In order to deal with the absence of contrast between the different muscle classes, we proposed a principled mathematical formulation that integrates prior knowledge with a random walks graph-based formulation. Prior knowledge is repre- sented using a statistical shape atlas that once coupled with the random walks segmentation leads to an efficient iterative linear optimization sys- tem. We reveal the potential of our approach on a challenging set of real clinical data

Automatic skeletal muscle segmentation through random walks and graph-based seed placement

International audienceIn this paper we propose a novel skeletal muscle segmentation method driven from discrete optimization. We introduce a graphical model that is able to automatically determine appropriate seed positions with respect to the different muscle classes. This is achieved by taking into account the expected local visual and geometric properties of the seeds through a pair-wise Markov Random Field. The outcome of this optimization process is fed to a powerful graphbased diffusion segmentation method (random walker) that is able to produce very promising results through a fully automated approach. Validation on challenging data sets demonstrates the potentials of our method

Analysing Decisive Stochastic Processes

In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems and probabilistic vector addition systems with states. In this paper, we extend the concept of decisiveness to more general stochastic processes. This extension is non trivial as we consider stochastic processes with a potentially continuous set of states and uncountable branching (common features of real-time stochastic processes). This allows us to obtain decidability results for both qualitative and quantitative verification problems on some classes of real-time stochastic processes, including generalized semi-Markov processes and stochastic timed automat