Maty's Biography of Abraham De Moivre, Translated, Annotated and Augmented

November 27, 2004, marked the 250th anniversary of the death of Abraham De Moivre, best known in statistical circles for his famous large-sample approximation to the binomial distribution, whose generalization is now referred to as the Central Limit Theorem. De Moivre was one of the great pioneers of classical probability theory. He also made seminal contributions in analytic geometry, complex analysis and the theory of annuities. The first biography of De Moivre, on which almost all subsequent ones have since relied, was written in French by Matthew Maty. It was published in 1755 in the Journal britannique. The authors provide here, for the first time, a complete translation into English of Maty's biography of De Moivre. New material, much of it taken from modern sources, is given in footnotes, along with numerous annotations designed to provide additional clarity to Maty's biography for contemporary readers.Comment: Published at http://dx.doi.org/10.1214/088342306000000268 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems

The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound $B$, a PDL formula $\varphi$ and a CFM $\mathcal{C}$, whether every existentially $B$-bounded MSC $M$ accepted by $\mathcal{C}$ satisfies $\varphi$. Recently, it was shown that this problem is PSPACE-complete. In the present work, we consider CRPDL over MSCs which is PDL equipped with the operators converse and repeat. The former enables one to walk back and forth within an MSC using a single path expression whereas the latter allows to express that a path expression can be repeated infinitely often. To solve the model checking problem for this logic, we define message sequence chart automata (MSCAs) which are multi-way alternating parity automata walking on MSCs. By exploiting a new concept called concatenation states, we are able to inductively construct, for every CRPDL formula $\varphi$, an MSCA precisely accepting the set of models of $\varphi$. As a result, we obtain that the model checking problem for CRPDL and CFMs is still in PSPACE

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R

The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from a q-> -1 limit of the dual q-Hahn polynomials. The Hopf algebra sl_{-1}(2) has four generators including an involution, it is also a q-> -1 limit of the quantum algebra sl_{q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of the -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl_{-1}(2) algebras, so that the Clebsch-Gordan coefficients of sl_{-1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.Comment: 15 pages, Some minor changes from version #

Utility functions predict variance and skewness risk preferences in monkeys.

Utility is the fundamental variable thought to underlie economic choices. In particular, utility functions are believed to reflect preferences toward risk, a key decision variable in many real-life situations. To assess the validity of utility representations, it is therefore important to examine risk preferences. In turn, this approach requires formal definitions of risk. A standard approach is to focus on the variance of reward distributions (variance-risk). In this study, we also examined a form of risk related to the skewness of reward distributions (skewness-risk). Thus, we tested the extent to which empirically derived utility functions predicted preferences for variance-risk and skewness-risk in macaques. The expected utilities calculated for various symmetrical and skewed gambles served to define formally the direction of stochastic dominance between gambles. In direct choices, the animals' preferences followed both second-order (variance) and third-order (skewness) stochastic dominance. Specifically, for gambles with different variance but identical expected values (EVs), the monkeys preferred high-variance gambles at low EVs and low-variance gambles at high EVs; in gambles with different skewness but identical EVs and variances, the animals preferred positively over symmetrical and negatively skewed gambles in a strongly transitive fashion. Thus, the utility functions predicted the animals' preferences for variance-risk and skewness-risk. Using these well-defined forms of risk, this study shows that monkeys' choices conform to the internal reward valuations suggested by their utility functions. This result implies a representation of utility in monkeys that accounts for both variance-risk and skewness-risk preferences

Test Station for Magnetization Measurements on Large Quantities of Superconducting Strands

In the superconducting main magnets of the Large Hadron Collider (LHC), persistent currents in the superconductor determine the field quality at injection field. For this reason it is necessary to check the magnetization of the cable strands during their production. During four years, this requires measurements of the width of the strand magnetization hysteresis loop at 0.5 T, 1.9 K, at a rate of up to eight samples per day. This paper describes the design, construction and the first results of a magnetization test station built for this purpose. The samples are cooled in a cryostat, with a 2-m long elliptic tail. This tail is inserted in a normal conducting dipole magnet with a field between ± 1.5 T. Racetrack pick-up coils, integrated in the cryostat, detect the voltage due to flux change, which is then integrated numerically. The sample holder can contain eight strand samples, each 20 cm long. The test station operates in two modes: either the sample is fixed while the external field is changed, or the sample is moved while the field remains constant. First results of calibration measurements with nickel and niobium are reported

Une synthèse des modèles de représentation des connaissances à base de Graphes Conceptuels et OWL

Nous présentons et comparons deux approches de modélisation, formelles et concrètes, pour représenter et manipuler des connaissances d’un domaine. Le modèle des graphes conceptuels permet de modéliser des connaissances en terme de graphes, basés sur un support. Cette approche de modélisation est intensionnelle, est munie d’une sémantique en logique du premier ordre, et fait l’hypothèse d’un monde fermé pour ses raisonnements. Le langage OWL permet de décrire des ontologies et des faits sur le Web, suivant une approche de modélisation extensionnelle. Il possède une sémantique issue des logiques de descriptions, et fait l’hypothèse d’un monde ouvert pour ses raisonnements

Definition and evaluation of a family of shape factors for off-line signature verification

In a real situation, the choice of the best representation for the implementation of a signature verification system able to cope with all types of handwriting is a very difficult task. This study is original in that the design of the integrated classifiers is based on a large number of individual classifiers (or signature representations) in an attempt to overcome in some way the need for feature selection. In fact, the cooperation of a large number of classifiers is justified only if the cost of individual classifiers is low enough . This is why the extended shadow code (ESC) used as a class of shape factors tailor-made for the signature verification problem seems a good choice for the design of integrated classifiers E(x) .Nous proposons dans cet article une voie à suivre pour tenter d'apporter une solution au problème complexe qu'est la définition d'un facteur de forme adapté au problème de la vérification automatique des signatures manuscrites. Le codage de la signature obtenu de la projection locale du tracé sur les segments d'un motif M(γ) est un compromis entre les approches globales où la silhouette de la signature est considérée comme un tout, et les approches locales où des mesures sont effectuées sur des portions spécifiques du tracé. Inspiré de ces deux familles d'approches, l'ESC est en fait une approche mixte qui permet d'effectuer des mesures locales sur la forme sans la segmenter en primitives élémentaires, une tâche très difficile en pratique. Ce travail porte principalement sur l'étude de l'influence de la résolution des motifs utilisés pour le codage de la signature (par la projection locale du tracé), et sur la définition d'un système de type multi-classifieurs pour tenter de rendre plus robuste la performance des systèmes de vérification de signatures

Asynchronous Games over Tree Architectures

We consider the task of controlling in a distributed way a Zielonka asynchronous automaton. Every process of a controller has access to its causal past to determine the next set of actions it proposes to play. An action can be played only if every process controlling this action proposes to play it. We consider reachability objectives: every process should reach its set of final states. We show that this control problem is decidable for tree architectures, where every process can communicate with its parent, its children, and with the environment. The complexity of our algorithm is l-fold exponential with l being the height of the tree representing the architecture. We show that this is unavoidable by showing that even for three processes the problem is EXPTIME-complete, and that it is non-elementary in general