Gradual computerisation and verification of mathematics : MathLang's path into Mizar

There are many proof checking tools that allow capturing mathematical knowledge into formal representation. Those proof systems allow further automatic verifica- tion of the logical correctness of the captured knowledge. However, the process of encoding common mathematical documents in a chosen proof system is still labour- intensive and requires comprehensive knowledge of such system. This makes the use of proof checking tools inaccessible for ordinary mathematicians. This thesis provides a solution for the computerisation of mathematical documents via a num- ber of gradual steps using the MathLang framework. We express the full process of formalisation into the Mizar proof checker. The first levels of such gradual computerisation path have been developing well before the course of this PhD started. The whole project, called MathLang, dates back to 2000 when F. Kamareddine and J.B. Wells started expressing their ideas of novel approach for computerising mathematical texts. They mainly aimed at developing a mathematical framework which is flexible enough to connect existing, in many cases different, approaches of computerisation mathematics, which allows various degrees of formalisation (e.g., partial, full formalisation of chosen parts, or full formalisation of the entire doc- ument), which is compatible with different mathematical foundations (e.g., type theory, set theory, category theory, etc.) and proof systems (e.g., Mizar, Isar, Coq, HOL, Vampire). The first two steps in the gradual formalisation were developed by F. Kamareddine, J.B. Wells and M. Maarek with a small contribution of R. Lamar to the second step. In this thesis we develop the third level of the gradual path, which aims at capturing the rhetorical structure of mathematical documents. We have also integrated further steps of the gradual formalisation, whose final goal is the Mizar system. We present in this thesis a full path of computerisation and formalisation of math- ematical documents into the Mizar proof checker using the MathLang framework. The development of this method was driven by the experience of computerising a number of mathematical documents (covering different authoring styles)

Stochastic Improvement of Cyclic Railway Timetables

Real-time railway operations are subject to stochastic disturbances. However, a railway timetable is a deterministic plan. Thus a timetable should be designed in such a way that it can cope with the stochastic disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called “Zaanlijnâ€. The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable.Railway Timetabling;Stochastic Optimization;Robustness

Modeling the influence of environmental relative humidity on the elastic properties of unitarian hemp fibres

International audienceIn view of the production of high performance composites reinforced with plant-based fibres, it is essential to account for the high variability and the dependence of the fibre’s mechanical properties to moisture conditions in the design tools and models. This study proposes several empirical formula with probability distribution functions determined using experimental data sets to predict the evolution and the scattering of thetensile properties of elementary hemp fibres as a function of environmental relative humidity. In the present work, we also compare the experimentally determined median values of elastic modulus to the predictions of state-of-the-art micromechanical models. The comparisonshows that the available models are unable to predict the tensile modulus as a function of humidity in good agreement with experimental measurements. This discrepancy is due to the lack of knowledge of the ultrastructure and arrangement of the cell wall components, theirinteraction with water and their evolution under mechanical loading and by this way to the relatively far-reaching hypotheses formulated to derive the micromechanical model

Strong selection and high mutation supply characterize experimental Chlorovirus evolution

Characterizing how viruses evolve expands our understanding of the underlying fundamental processes, such as mutation, selection and drift. One group of viruses whose evolution has not yet been extensively studied is the Phycodnaviridae, a globally abundant family of aquatic large double-stranded (ds)DNA (dsDNA) viruses. Here we studied the evolutionary change of Paramecium bursaria chlorella virus 1 during experimental coevolution with its algal host. We used pooled genome sequencing of six independently evolved populations to characterize genomic change over five time points. Across six experimental replicates involving either strong or weak demographic fluctuations, we found single nucleotide polymorphisms (SNPs) at sixty-seven sites. The occurrence of genetic variants was highly repeatable, with just two of the SNPs found in only a single experimental replicate. Three genes A122/123R, A140/145R and A540L showed an excess of variable sites, providing new information about potential targets of selection during Chlorella–Chlorovirus coevolution. Our data indicated that the studied populations were not mutation-limited and experienced strong positive selection. Our investigation highlighted relevant processes governing the evolution of aquatic large dsDNA viruses, which ultimately contributes to a better understanding of the functioning of natural aquatic ecosystems

Quality of Life in rural and urban populations in Lebanon using SF-36 Health Survey

BACKGROUND: Measuring health status in a population is important for the evaluation of interventions and the prediction of health and social care needs. Quality of life (QoL) studies are an essential complement to medical evaluation but most of the tools available in this area are in English. In order to evaluated QoL in rural and urban areas in Lebanon, the short form 36 health survey (SF-36) was adapted into Arabic. METHODS: SF-36 was administered in a cross-sectional study, to collect sociodemographic and environmental variables as well as self reported morbidity. We analysed a representative sample containing 1632 subjects, from whom we randomly picked 524 subjects aged 14 years and over. The translation, cultural adaptation and validation of the SF-36 followed the International Quality of Life Assessment methodology. Multivariate analysis (generalized linear model) was performed to test the effect of habitat (rural on urban areas) on all domains of the SF-36. RESULTS: The rate of missing data is very low (0.23% of items). Item level validation supported the assumptions underlying Likert scoring. SF-36 scale scores showed wide variability and acceptable internal consistency (Cronbach's alpha >0.70), factor analysis yielded patterns of factor correlation comparable to that found in the U.S.A and France. Patients resident in rural areas had higher vitality scores than those in urban areas. Older people reported more satisfaction with some domains of life than younger people, except for physical functioning. The QoL of women is poorer than men; certain symptoms and morbidity independently influence the domains of SF-36 in this population. CONCLUSION: The results support the validity of the SF-36 Arabic version. Habitat has a minor influence on QoL, women had a poor QoL, and health problems had differential impact on QoL

Hybrid resolution approaches for dynamic assignment problem of reusable containers

In this study, we are interested in the reusing activities of reverse logistics. We focus on the dynamic assignment of reusable containers problem (e.g. gas bottles, beverages, pallets, maritime containers, etc.). The objective is to minimize the collect, reloading, storage and redistribution operations costs over a fixed planning horizon taking into account the greenhouse gas emissions. We present a new generic Mixed Integer Programming (MIP) model for the problem. The proposed model was solved using the IBM ILOG CPLEX optimization software; this method yield exact solutions, but it is very time consuming. So we adapted two hybrid approaches using a genetic algorithm to solve the problem at a reduced time (The second hybrid approach is enhanced with a local search procedure based on the Variable Neighborhood Search VNS). The numerical results show that both developed hybrid approaches generate high-quality solutions in a moderate computational time, especially the second hybrid method