Littérature et mathématiques : introduction à une approche interdisciplinaire

L’aventure que nous avons entreprise il y a plus de cinq ans afin d’explorer des oeuvres littéraires dans une perspective interdisciplinaire français et mathématiques vient notamment de notre passion commune pour l’univers créatif de ces deux disciplines. Il est bien connu que l’oeuvre littéraire offre un terreau fertile pour donner forme à diverses interprétations, pour se questionner et pour réfléchir aux propositions des auteurs. Cependant, ce n’est peut-être pas cette expérience créative que vous avez vécue des mathématiques ; pourtant, sans cet espace d’imaginaire, peu de nouvelles solutions à des problèmes de la vie quotidienne verraient le jour. C’est pourquoi, dans ce dossier, nous avons privilégié une entrée plus directe dans les textes littéraires par les mathématiques afin de démontrer que lier littérature et mathématiques s’avère un jeu indéniablement inépuisable de fantaisie pour autant que des oeuvres s’y prêtent

Computing Distances between Probabilistic Automata

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L with negation and L without negation, by the modal operator. Using flow networks, we show how to compute the relations in PTIME. This allows the definition of an efficiently computable non-discounted distance between the states of a PA. A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions. We compare our notions of distance to others previously defined and illustrate our approach on various examples. We also show that our distance is not expansive with respect to process algebra operators. Although L without negation is a suitable logic to characterise epsilon-(bi)simulation on deterministic PAs, it is not for general PAs; interestingly, we prove that it does characterise weaker notions, called a priori epsilon-(bi)simulation, which we prove to be NP-difficult to decide.Comment: In Proceedings QAPL 2011, arXiv:1107.074

A model of evaluative opinion to encourage greater transparency and justification of interpretation in post-mortem forensic toxicology

Over the past decades, the calls to improve the robustness of interpretation in forensic science have increased in magnitude. Forensic toxicology has seen limited progress in this regard. In this work, we propose a transparent interpretive pathway for use in postmortem forensic toxicology cases. This process allows the selection of the interpretive methodology based on the amount of previous information that is available for the drug(s) in question. One approach is an assessment of various pharmacological and circumstantial considerations resulting in a toxicological significance score (TSS), which is particularly useful in situations where limited information about a drug is available. When there is a robust amount of case data available, then a probabilistic approach, through the evaluation of likelihood ratios by the forensic toxicologist and of prior probabilities by the fact finder, is utilized. This methodology provides a transparent means of making an interpretive decision on the role of a drug in the cause of death. This will allow the field of forensic toxicology to take a step forward in using best practice in evaluative reporting, a tool already used by many other forensic science disciplines.</p

Litt.et.Maths : explorer des albums de littérature dans une perspective interdisciplinaire français et mathématiques

Le français et les mathématiques, tant au primaire qu’au secondaire, sont les deux disciplines centrales des programmes de formation actuels. Ces disciplines scolaires occupent plus de 60 % du temps d’enseignement, d’apprentissage et d’évaluation, et elles sont sources des principales difficultés et des principaux troubles d’apprentissage des élèves. Afin de réconcilier ces deux disciplines souvent considérées comme opposées et difficiles, et de les faire apprécier par des élèves parfois réticents, nous avons mis sur pied à l’automne 2012 un laboratoire interdisciplinaire littérature et mathématiques nommé Litt.et.Maths

Reliable Reconstruction of Fine-Grained Proofs in a Proof Assistant

International audienceWe present a fast and reliable reconstruction of proofs generated by the SMT solver veriT in Isabelle. The fine-grained proof format makes the reconstruction simple and efficient. For typical proof steps, such as arithmetic reasoning and skolemization, our reconstruction can avoid expensive search. By skipping proof steps that are irrelevant for Isabelle, the performance of proof checking is improved. Our method increases the success rate of Sledgehammer by halving the failure rate and reduces the checking time by 13%. We provide a detailed evaluation of the reconstruction time for each rule. It reveals that the runtime is influenced by both simple rules that appear very often and common complex rules

Reliable Reconstruction of Fine-Grained Proofs in a Proof Assistant

International audienceWe present a fast and reliable reconstruction of proofs generated by the SMT solver veriT in Isabelle. The fine-grained proof format makes the reconstruction simple and efficient. For typical proof steps, such as arithmetic reasoning and skolemization, our reconstruction can avoid expensive search. By skipping proof steps that are irrelevant for Isabelle, the performance of proof checking is improved. Our method increases the success rate of Sledgehammer by halving the failure rate and reduces the checking time by 13%. We provide a detailed evaluation of the reconstruction time for each rule. It reveals that the runtime is influenced by both simple rules that appear very often and common complex rules

Seventeen Provers under the Hammer

International audienceOne of the main success stories of automatic theorem provers has been their integration into proof assistants. Such integrations, or "hammers," increase proof automation and hence user productivity. In this paper, we use Isabelle/HOL's Sledgehammer tool to find out how useful modern provers are at proving formulas in higher-order logic. Our evaluation follows in the steps of Böhme and Nipkow's Judgment Day study from 2010, but instead of three provers we use 17, including SMT solvers and higher-order provers. Our work offers an alternative yardstick for comparing modern provers, next to the benchmarks and competitions emerging from the TPTP World and SMT-LIB

An Upper Bound to the Space Density of Interstellar Comets

Two well-studied white dwarfs with helium-dominated atmospheres (DBs) each possess less hydrogen than carried by a single average-mass comet. Plausibly, the wind rates from these stars are low enough that most accreted hydrogen remains with the star. If so, and presuming their nominal effective temperatures, then these DBs have been minimally impacted by interstellar comets during their 50 Myr cooling age; interstellar iceballs with radii between 10 m and 2 km contain less than 1% of all interstellar oxygen. This analysis suggests that most stars do not produce comets at the rate predicted by "optimistic" scenarios for the formation of the Oort cloud.Comment: Astronomical Journal, accepte

Psychological determinants of whole-body endurance performance

Background: No literature reviews have systematically identified and evaluated research on the psychological determinants of endurance performance, and sport psychology performance-enhancement guidelines for endurance sports are not founded on a systematic appraisal of endurance-specific research. Objective: A systematic literature review was conducted to identify practical psychological interventions that improve endurance performance and to identify additional psychological factors that affect endurance performance. Additional objectives were to evaluate the research practices of included studies, to suggest theoretical and applied implications, and to guide future research. Methods: Electronic databases, forward-citation searches, and manual searches of reference lists were used to locate relevant studies. Peer-reviewed studies were included when they chose an experimental or quasi-experimental research design, a psychological manipulation, endurance performance as the dependent variable, and athletes or physically-active, healthy adults as participants. Results: Consistent support was found for using imagery, self-talk, and goal setting to improve endurance performance, but it is unclear whether learning multiple psychological skills is more beneficial than learning one psychological skill. The results also demonstrated that mental fatigue undermines endurance performance, and verbal encouragement and head-to-head competition can have a beneficial effect. Interventions that influenced perception of effort consistently affected endurance performance. Conclusions: Psychological skills training could benefit an endurance athlete. Researchers are encouraged to compare different practical psychological interventions, to examine the effects of these interventions for athletes in competition, and to include a placebo control condition or an alternative control treatment. Researchers are also encouraged to explore additional psychological factors that could have a negative effect on endurance performance. Future research should include psychological mediating variables and moderating variables. Implications for theoretical explanations of endurance performance and evidence-based practice are described

Activity-Based Funding of Hospitals and Its Impact on Mortality, Readmission, Discharge Destination, Severity of Illness, and Volume of Care: A Systematic Review and Meta-Analysis

Background: Activity-based funding (ABF) of hospitals is a policy intervention intended to re-shape incentives across health systems through the use of diagnosis-related groups. Many countries are adopting or actively promoting ABF. We assessed the effect of ABF on key measures potentially affecting patients and health care systems: mortality (acute and post-acute care); readmission rates; discharge rate to post-acute care following hospitalization; severity of illness; volume of care. &nbsp; &nbsp; Methods: We undertook a systematic review and meta-analysis of the worldwide evidence produced since 1980. We included all studies reporting original quantitative data comparing the impact of ABF versus alternative funding systems in acute care settings, regardless of language. We searched 9 electronic databases (OVID MEDLINE, EMBASE, OVID Healthstar, CINAHL, Cochrane CENTRAL, Health Technology Assessment, NHS Economic Evaluation Database, Cochrane Database of Systematic Reviews, and Business Source), hand-searched reference lists, and consulted with experts. Paired reviewers independently screened for eligibility, abstracted data, and assessed study credibility according to a pre-defined scoring system, resolving conflicts by discussion or adjudication. &nbsp; &nbsp; Results: Of 16,565 unique citations, 50 US studies and 15 studies from 9 other countries proved eligible (i.e. Australia, Austria, England, Germany, Israel, Italy, Scotland, Sweden, Switzerland). We found consistent and robust differences between ABF and no-ABF in discharge to post-acute care, showing a 24% increase with ABF (pooled relative risk = 1.24, 95% CI 1.18–1.31). Results also suggested a possible increase in readmission with ABF, and an apparent increase in severity of illness, perhaps reflecting differences in diagnostic coding. Although we found no consistent, systematic differences in mortality rates and volume of care, results varied widely across studies, some suggesting appreciable benefits from ABF, and others suggesting deleterious consequences. &nbsp; &nbsp; Conclusions: Transitioning to ABF is associated with important policy- and clinically-relevant changes. Evidence suggests substantial increases in admissions to post-acute care following hospitalization, with implications for system capacity and equitable access to care. High variability in results of other outcomes leaves the impact in particular settings uncertain, and may not allow a jurisdiction to predict if ABF would be harmless. Decision-makers considering ABF should plan for likely increases in post-acute care admissions, and be aware of the large uncertainty around impacts on other critical outcomes