An estimation of the stability and the localisability functions of multistable processes

Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability functions, and we prove the consistency of those two estimators. We illustrate these convergences with two classical examples, the Levy multistable process and the Linear Multifractional Multistable Motion

Localisable moving average stable and multistable processes

We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a ``tangent process'', in a suitable sense. We give general conditions on the kernel g defining the moving average which ensures that the process is localisable and we characterize the nature of the associated tangent processes. Examples include the reverse Ornstein-Uhlenbeck process and the multistable reverse Ornstein-Uhlenbeck process. In the latter case, the tangent process is, at each time t, a L\'evy stable motion with stability index possibly varying with t. We also consider the problem of path synthesis, for which we give both theoretical results and numerical simulations

The Hausdorff dimension of the range of the Lévy multistable processes

International audienceWe compute the Hausdorff dimension of the image X(E) of a non random Borel set E ⊂ [0, 1], where X is a Lévy multistable process in R. This extends the case where X is a classical stable Lévy process by letting the stability exponent α be a smooth function, which leads to non-homogeneous processes because their increments are not stationary and not necessarily independent. Contrary to the situation where the stability parameter is a constant, the dimension depends on the version of the multistable Lévy motion when the process has an infinite first moment

Neuromuscular fatigue in healthy muscle: Underlying factors and adaptation mechanisms

AbstractObjectivesThis review aims to define the concept of neuromuscular fatigue and to present the current knowledge of the central and peripheral factors at the origin of this phenomenon. This review also addresses the literature that focuses on the mechanisms responsible for the adaption to neuromuscular fatigue.MethodOne hundred and eighty-two articles indexed in PubMed (1954–2010) have been considered.ResultsNeuromuscular fatigue has central and peripheral origins. Central fatigue, preponderant during long-duration, low-intensity exercises, may involve a drop in the central command (motor, cortex, motoneurons) elicited by the activity of cerebral neurotransmitters and muscular afferent fibers. Peripheral fatigue, associated with an impairment of the mechanisms from excitation to muscle contraction, may be induced by a perturbation of the calcium ion movements, an accumulation of phosphate, and/or a decrease of the adenosine triphosphate stores. To compensate for the consequent drop in force production, the organism develops several adaptation mechanisms notably implicating motor units.ConclusionFatigue onset is associated with an alteration of the mechanisms involved in force production. Then, the interaction between central and peripheral mechanisms leads to a series of events that ultimately contribute to the observed decrease in force production

Evaluation of health promotion in schools: a realistic evaluation approach using mixed methods

http://www.biomedcentral.com/content/pdf/1471-2458-10-43.pdfInternational audienceBackground: Schools are key settings for health promotion (HP) but the development of suitable approaches for evaluating HP in schools is still a major topic of discussion. This article presents a research protocol of a program developed to evaluate HP. After reviewing HP evaluation issues, the various possible approaches are analyzed and the importance of a realistic evaluation framework and a mixed methods (MM) design are demonstrated. Methods/Design: The design is based on a systemic approach to evaluation, taking into account the mechanisms, context and outcomes, as defined in realistic evaluation, adjusted to our own French context using an MM approach. The characteristics of the design are illustrated through the evaluation of a nationwide HP program in French primary schools designed to enhance children's social, emotional and physical health by improving teachers' HP practices and promoting a healthy school environment. An embedded MM design is used in which a qualitative data set plays a supportive, secondary role in a study based primarily on a different quantitative data set. The way the qualitative and quantitative approaches are combined through the entire evaluation framework is detailed. Discussion: This study is a contribution towards the development of suitable approaches for evaluating HP programs in schools. The systemic approach of the evaluation carried out in this research is appropriate since it takes account of the limitations of traditional evaluation approaches and considers suggestions made by the HP research community

Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable Processes

International audienc