Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

The Annual Condition of Education Report, 2002

Statistics about public edcuation in the state of Iowa including graduation rates, No Child Left Behind Act,

A model for physical activity, bahaviour and energy expenditure assessment in real-life condition

RésuméL'origine de l'obésité, qui atteint des proportions épidémiques, est complexe. Elle est liée au mode de vie et au comportement des individus par rapport à l'activité physique, expression des choix individuels et de l'interaction avec l'environnement. Les mesures du comportement au niveau de l'activité physique des individus face à leur environnement, la répartition des types d'activité physique, la durée, la fréquence, l'intensité, et la dépense énergétique sont d'une grande importance. Aujourd'hui, il y a un manque de méthodes permettant une évaluation précise et objective de l'activité physique et du comportement des individus. Afin de compléter les recherches relatives à l'activité physique, à l'obésité et à certaines maladies, le premier objectif du travail de thèse était de développer un modèle pour l'identification objective des types d'activité physique dans des conditions de vie réelles et l'estimation de la dépense énergétique basée sur une combinaison de 2 accéléromètres et 1 GPS. Le modèle prend en compte qu'une activité donnée peut être accomplie de différentes façons dans la vie réelle. Les activités quotidiennes ont pu être classées en 8 catégories, de sédentaires à actives, avec une précision de 1 min. La dépense énergétique a pu peut être prédite avec précision par le modèle. Après validation du modèle, le comportement des individus de l'activité physique a été évalué dans une seconde étude. Nous avons émis l'hypothèse que, dans un environnement caractérisé par les pentes, les personnes obèses sont tentées d'éviter les pentes raides et de diminuer la vitesse de marche au cours d'une activité physique spontanée, ainsi que pendant les exercices prescrits et structurés. Nous avons donc caractérisé, par moyen du modèle développé, le comportement des individus obèses dans un environnement vallonné urbain. La façon dont on aborde un environnement valloné dans les déplacements quotidiens devrait également être considérée lors de la prescription de marche supplémentaire afin d'augmenter l'activité physique.SummaryOrigin of obesity, that reached epidemic proportion, is complex and may be linked to different lifestyle and physical activity behaviour. Measurement of physical activity behaviour of individuals towards their environment, the distribution of physical activity in terms of physical activity type, volume, duration, frequency, intensity, and energy expenditure is of great importance. Nowadays, there is a lack of methods for accurate and objective assessment of physical activity and of individuals' physical activity behaviour. In order to complement the research relating physical activity to obesity and related diseases, the first aim of the thesis work was to develop a model for objective identification of physical activity types in real-life condition and energy expenditure based on a combination of 2 accelerometers and 1 GPS device. The model takes into account that a given activity can be achieved in many different ways in real life condition. Daily activities could be classified in 8 categories, as sedentary to active physical activity, within 1 min accuracy, and physical activity patterns determined. The energy expenditure could be predicted accurately with an accuracy below 10%. Furthermore, individuals' physical activity behaviour is expression of individual choices and their interaction with the neighbourhood environment. In a second study, we hypothesized that, in an environment characterized by inclines, obese individuals are tempted to avoid steep positive slopes and to decrease walking speed during spontaneous outdoor physical activity, as well as during prescribed structured bouts of exercise. Finally, we characterized, by mean of the developed model, the physical activity behaviour of obese individuals in a hilly urban environment. Quantifying how one tackles hilly environment or avoids slope in their everyday displacements should be also considered while prescribing extra walking in free-living conditions in order to increase physical activity.

Stochastic stability and the evolution of coordination in spatially structured populations.

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs. Specifically, such strategies are shown to be "stochastically stable" (a refinement of evolutionary stability). Here, we extend the notion of stochastic stability to biological models of continuous phenotypes at a mutation-selection-drift balance. This allows us to make a unique prediction for long-term evolution in games with multiple equilibria. We show how genetic relatedness due to limited dispersal and scaled to account for local competition can crucially affect the stochastically-stable outcome of coordination games. We find that positive relatedness (weak local competition) increases the chance the payoff dominant strategy is stochastically stable, even when it is not risk dominant. Conversely, negative relatedness (strong local competition) increases the chance that strategies evolve that are neither payoff nor risk dominant. Extending our results to large multiplayer coordination games we find that negative relatedness can create competition so extreme that the game effectively changes to a hawk-dove game and a stochastically stable polymorphism between the alternative strategies evolves. These results demonstrate the usefulness of stochastic stability in characterizing long-term evolution of continuous phenotypes: the outcomes of multiplayer games can be reduced to the generic equilibria of two-player games and the effect of spatial structure can be analyzed readily.

The Annual Condition of Education Report, 2003

Statistics about public education in the state of Iowa including graduation rates and No Child Left Behind Act.

Condition of Iowa Community Colleges, 2003

Enrollment, Human Resource, Economic Development, and Financial Information of the Community Colleges for Fiscal Year 2003.

Assessing dystrophies and other muscle diseases at the nanometer scale by atomic force microscopy.

AIM: Atomic force microscopy nanoindentation of myofibers was used to assess and quantitatively diagnose muscular dystrophies from human patients. MATERIALS & METHODS: Myofibers were probed from fresh or frozen muscle biopsies from human dystrophic patients and healthy volunteers, as well as mice models, and Young's modulus stiffness values were determined. RESULTS: Fibers displaying abnormally low mechanical stability were detected in biopsies from patients affected by 11 distinct muscle diseases, and Young's modulus values were commensurate to the severity of the disease. Abnormal myofiber resistance was also observed from consulting patients whose muscle condition could not be detected or unambiguously diagnosed otherwise. DISCUSSION & CONCLUSION: This study provides a proof-of-concept that atomic force microscopy yields a quantitative read-out of human muscle function from clinical biopsies, and that it may thereby complement current muscular dystrophy diagnosis.

A repeated GGA motif is critical for the activity and stability of the riboregulator RsmY of Pseudomonas fluorescens.

The riboregulator RsmY of Pseudomonas fluorescens strain CHA0 is an example of small regulatory RNAs belonging to the global Rsm/Csr regulatory systems controlling diverse cellular processes such as glycogen accumulation, motility, or formation of extracellular products in various bacteria. By binding multiple molecules of the small regulatory protein RsmA, RsmY relieves the negative effect of RsmA on the translation of several target genes involved in the biocontrol properties of strain CHA0. RsmY and functionally related riboregulators have repeated GGA motifs predicted to be exposed in single-stranded regions, notably in the loops of hairpins. The secondary structure of RsmY was corroborated by in vivo cleavage with lead acetate. RsmY mutants lacking three or five (out of six) of the GGA motifs showed reduced ability to derepress the expression of target genes in vivo and failed to bind the RsmA protein efficiently in vitro. The absence of GGA motifs in RsmY mutants resulted in reduced abundance of these transcripts and in a shorter half-life (< or = 6 min as compared with 27 min for wild type RsmY). These results suggest that both the interaction of RsmY with RsmA and the stability of RsmY strongly depend on the GGA repeats and that the ability of RsmY to interact with small regulatory proteins such as RsmA may protect this RNA from degradation.

Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.