In evolutionary theory, a key issue in selection theory is the expected time for a given amount of allele frequency change to occur. Crow and Kimura, by assuming weak selection, presented explicit results for several important cases of the directional selection and of the stochastic process. Those results played an important role in the theory of population genetics. In this paper, first we show that the weak selection assumption can be removed from most of the results of Crow and Kimura, and then we generalize those results to the most general selection model. Next, we estimate the errors of the deterministic formulae produced by proving that the deterministic formulae are limits of the corresponding stochastic formulae when the size of the population tends to infinity. Finally, we present a result which removes the restriction of Kimura’s corresponding results for a favourite recessive selection model, and we also observe that the conclusion made by Kimura about the favourite dominant selection might not be correct.

The after-tax net present value for 27 swine breeding systems composed of Duroc, Hampshire, and Yorkshire breeds were simulated and ordered using stochastic dominance analysis. The concept of the value of information was expanded to develop the concept of the willingness to pay to adopt a new technology. For producers not currently using the dominant system, estimates of the allowable present value cost of adoption are reported and used to explain diverse production practices.

A whole-farm, stochastic and dynamic simulation model was developed to predict biophysical and economic performance of grazing dairy systems. Several whole-farm models simulate grazing dairy systems, but most of them work at a herd level. This model, named e-Dairy, differs from the few models that work at an animal level, because it allows stochastic behaviour of the genetic merit of individual cows for several traits, namely, yields of milk, fat and protein, live weight (LW) and body condition score (BCS) within a whole-farm model. This model accounts for genetic differences between cows, is sensitive to genotype × environment interactions at an animal level and allows pasture growth, milk and supplements price to behave stochastically. The model includes an energy-based animal module that predicts intake at grazing, mammary gland functioning and body lipid change. This whole-farm model simulates a 365-day period for individual cows within a herd, with cow parameters randomly generated on the basis of the mean parameter values, defined as input and variance and co-variances from experimental data sets. The main inputs of e-Dairy are farm area, use of land, type of pasture, type of crops, monthly pasture growth rate, supplements offered, nutritional quality of feeds, herd description including herd size, age structure, calving pattern, BCS and LW at calving, probabilities of pregnancy, average genetic merit and economic values for items of income and costs. The model allows to set management policies to define: dry-off cows (ceasing of lactation), target pre- and post-grazing herbage mass and feed supplementation. The main outputs are herbage dry matter intake, annual pasture utilisation, milk yield, changes in BCS and LW, economic farm profit and return on assets. The model showed satisfactory accuracy of prediction when validated against two data sets from farmlet system experiments. Relative prediction errors were <10% for all variables, and concordance correlation coefficients over 0.80 for annual pasture utilisation, yields of milk and milk solids (MS; fat plus protein), and of 0.69 and 0.48 for LW and BCS, respectively. A simulation of two contrasting dairy systems is presented to show the practical use of the model. The model can be used to explore the effects of feeding level and genetic merit and their interactions for grazing dairy systems, evaluating the trade-offs between profit and the associated risk.

We consider the early carcinogenesis model originally proposed as a deterministicreaction-diffusion system. The model has been conceived to explore the spatial effectsstemming from growth regulation of pre-cancerous cells by diffusing growth factormolecules. The model exhibited Turing instability producing transient spatial spikes incell density, which might be considered a model counterpart of emerging foci of malignantcells. However, the process of diffusion of growth factor molecules is by its nature astochastic random walk. An interesting question emerges to what extent the dynamics of thedeterministic diffusion model approximates the stochastic process generated by the model.We address this question using simulations with a new software tool called sbioPN (spatialbiological Petri Nets). The conclusion is that whereas single-realization dynamics of thestochastic process is very different from the behavior of the reaction diffusion system,it is becoming more similar when averaged over a large number of realizations. The degreeof similarity depends on model parameters. Interestingly, despite the differences, typicalrealizations of the stochastic process include spikes of cell density, which however arespread more uniformly and are less dependent of initial conditions than those produced bythe reaction-diffusion system.

A simple stochastic model for evolution, based upon the need to pass a sequence of n critical steps is applied to both terrestrial and extraterrestrial origins of life. In the former case, the time at which humans have emerged during the habitable period of Earth suggests a value of n=4. Progressively adding earlier evolutionary transitions gives an optimum fit when n=5, implying either that their initial transitions are not critical or that habitability began around 6 Ga ago. The origin of life on Mars or elsewhere within the Solar System is excluded by the latter case and the simple anthropic argument is that extraterrestrial life is scarce in the Universe because it does not have time to evolve. Alternatively, the timescale can be extended if the migration of basic progenotic material to Earth is possible. If extra transitions are included in the model to allow for Earth migration, then the start of habitability needs to be even earlier than 6 Ga ago. Our present understanding of Galactic habitability and dynamics does not exclude this possibility. We conclude that Galactic punctuated equilibrium, proposed as a way round the anthropic problem, is not the only way of making life more common in the Galaxy.

We study molecular motor-induced microtubule self-organization in dilute and semi-dilutefilament solutions. In the dilute case, we use a probabilistic model of microtubuleinteraction via molecular motors to investigate microtubule bundle dynamics. Microtubulesare modeled as polar rods interacting through fully inelastic, binary collisions. Ourmodel indicates that initially disordered systems of interacting rods exhibit anorientational instability resulting in spontaneous ordering. We study the existence anddynamic interaction of microtubule bundles analytically and numerically. Our resultsreveal a long term attraction and coalescing of bundles indicating a clear coarsening inthe system; microtubule bundles concentrate into fewer orientations on a slow logarithmictime scale. In semi-dilute filament solutions, multiple motors can bind a filament toseveral others and, for a critical motor density, induce a transition to an ordered phasewith a nonzero mean orientation. Motors attach to a pair of filaments and walk along thepair bringing them into closer alignment. We develop a spatially homogenous, mean-fieldtheory that explicitly accounts for a force-dependent detachment rate of motors, which inturn affects the mean and the fluctuations of the net force acting on a filament. We showthat the transition to the oriented state can be both continuous and discontinuous whenthe force-dependent detachment of motors is important.

Les problèmes actuels en mécanique dans le domaine ferroviaire font intervenir de manièreintensive des non-linéarités, que ce soit dans le comportement des composants du système(ex. ballast...), ou aux interfaces. Par ailleurs, la prise en compte de l’aléatoire dansla modélisation devient incontournable, tant pour les sollicitations du système que pourla variabilité de ses caractéristiques. Ces deux tendances sont illustrées sur desexemples de problématiques actuelles : dynamique des véhicules et de l’infrastructure,crissement...

In the building domain, components or equipment are often subjected to severeenvironmental conditions. In order to predict the reliability and the life-time of suchequipment, accelerated life testing can be carried out. Severe conditions are applied toaccelerate the ageing of the components and the reliability at nominal conditions is thendeduced considering that these nominal conditions are not constant but stochastic. In thispaper, the accelerated life testing of photovoltaic modules is carried out at severemodule temperature levels. The module power losses are monitored and the limit state isdetermined when a threshold power is reached. The stochastic data and the reliability aresimulated during a period of twenty years. Finally, the life time of the component isevaluated.

Les prothèses de hanche en biocéramique sont résistantes à l'usure mais, du fait de leur fragilité intrinsèque, sont susceptibles de se rompre. Le phénomène de décoaptation, séparation de faible amplitude de la tête et de la cupule, a été mis en évidence lors de la marche, et le choc mécanique en résultant peut fortement augmenter les risques de rupture. Un modèle par éléments-finis a été développé et les résultats ont été exploités afin de simuler l'évolution de la probabilité de rupture de cupules en zircone au cours du temps. Les résultats s'accordent bien avec l'expérience, même si des améliorations sont nécessaires afin de prendre en compte l'érosion des surfaces de contact.

The line balancing problem consits in assigning tasks to stations in orderto respect precedence constraints and cycle time constraints. In thispaper, the cycle time is fixed and the objective is to minimize the numberof stations. We propose to use metaheuristics based on simulated annealingby exploiting the link between the line balancing problem and the binpacking problem. The principle of the method lies in the combinationbetween a metaheuristic and a bin packing heuristic. Two representationsof a solution and two neighboring systems are proposed and the methods arecompared with results from the literature. They are better or similar totabu search based algorithm.


Even over a 75-year horizon, forecasts of PAYGO pension finances are misleadingly optimistic. Infinite horizon forecasts are necessary, but are they possible? We build on earlier stochastic forecasts of the US Social Security trust fund which model key demographic and economic variables as historical time series, and use the fitted models to generate Monte Carlo simulations of future fund performance. Using a 500-year stochastic projection, effectively infinite with discounting, we find a fund balance of −5.15 per cent of payroll, compared to the −3.5 per cent of the 2004 Trustees‘ Report, probably reflecting different mortality projections. Our 95 per cent probability bounds are −10.5 and −1.3 per cent. Such forecasts, which reflect only ‘routine’ uncertainty, have many problems but nonetheless seem worthwhile.

We consider a classic competing-species model with the rates changed to include Gaussian white noise. We show that if the noise is not too large, then the stochastic version is ergodic. An explicit relation between the noise and the original competing-species parameters gives a sufficient condition for ergodicity.

De plus en plus fréquemment, l'analyse modale d'une structure en laboratoire est complétée, voire remplacée, par une analyse modale de la structure "en service". Les sollicitations du système sont alors presque toujours inconnues. On pratique alors un mode d'analyse dit "purement stochastique". Les caractéristiques modales identifiées sont alors également de nature stochastique. Les taux d'amortissement, qui déjà, dans des conditions déterministes, sont souvent obtenus avec une faible précision, se trouvent alors fortement sujets à caution. Il est donc souhaitable d'assortir ces résultats d'une fourchette de validité statistique, et cela sans avoir recours à une coûteuse campagne statistique de résultats. Certains auteurs (Viberg, Jansson, ...) ont montré que la procédure d'identification elle-même est capable de fournir cette fourchette. Leur approche est ici mise en application dans le cas de l'identification des amortissements et est prolongée dans le cadre de l'approche stochastique de Van Overshee-De Moor. Deux validations en simulation, et une validation expérimentale sont présentées.

Nous étudions ici la lubrification d'un palier dans une zone très localisée où l'épaisseur du film est particulièrement faible. Le problème ainsi posé est un problème de lubrification élastohydrodynamique rugueuse où il y a de fortes variations relatives d'épaisseur de film. Nous comparons les résultats obtenus dans cette situation par les équations de Navier-Stokes d'une part et par l'équation de Reynolds d'autre part. Puis nous regardons les influences mutuelles des différentes fréquences spatiales de la rugosité et du film lubrifiant.Les travaux en lubrification sont nombreux. Nous rappelons le classement bien connu des situations de lubrification, explicité sur une courbe de Stribeck, qui ordonne selon les épaisseurs croissantes de film, la lubrification limite, la lubrification mixte et la lubrification en film complet. Ceci nous conduit à considérer notre situation micro-élastohydrodynamique comme intermédiaire entre les lubrifications limite et mixte. Nous proposons ensuite une revue bibliographique montrant les deux approches, statistiques et déterministes, utilisées généralement pour intégrer la rugosité dans les équations de la lubrification élastohydrodynamique. Nous justifions ainsi le choix d'une approche déterministe pour notre étude.Les hypothèses et les méthodes utilisées par notre modèle étant ainsi précisées, nous présentons alors les résultats concernant les deux objectifs cités précédemment.