Localized large sums of random variables

We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.Comment: 8 pages; small changes suggested by the referee. To appear in Stat. Prob. Letter

The distribution of integers with at least two divisors in a short interval

Let H(x,y,z) be the number of integers $\le x$ with a divisor in (y,z] and let H_1(x,y,z) be the number of integers $\le x$ with exactly one such divisor. When y and z are close, it is expected that H_1(x,y,z) H(x,y,z), that is, an integer with a divisor in (y,z] usually has just one. We determine necessary and sufficient conditions on y and z so that H_1(x,y,z) H(x,y,z). In doing so, we answer an open question from the paper "The distribution of integers with a divisor in a given interval", math.NT/0401223.Comment: 12 pages; minor corrections; added abstract and affiliation informatio

Fast and strongly localized observation for the Schrödinger equation

International audienceWe study the exact observability of systems governed by the Schrödinger equation in a rectangle with homogeneous Dirichlet (respectively Neumann) boundary conditions and with Neumann (respectively Dirichlet) boundary observation. Generalizing previous results of Ramdani, Takahashi, Tenenbaum and Tucsnak, we prove that these systems are exactly observable in arbitrarily small time. Moreover, we show that the above results hold even if the observation regions have arbitrarily small measures. More precisely, we prove that in the case of homogeneous Neumann boundary conditions with Dirichlet boundary observation, the exact observability property holds for every observation region whith non empty interior. In the case of homogeneous Dirichlet boundary conditions with Neumann boundary observation, we show that the exact observability property holds if and only if the observation region has an open intersection with an edge of each direction. Moreover, we give explicit estimates for the blow-up rate of the observability constants as the time and (or) the size of the observation region tend to zero. The main ingredients of the proofs are an effective version of a theorem of Beurling and Kahane on non harmonic Fourier series and an estimate for the number of lattice points in the neighbourhood of an ellipse

The selective peroxisome proliferator-activated receptor alpha modulator (SPPARM) paradigm : conceptual framework and therapeutic potential: A consensus statement from the International Atherosclerosis Society (IAS) and the Residual Risk Reduction Initiative (R3i) Foundation

In the era of precision medicine, treatments that target specific modifiable characteristics of high-risk patients have the potential to lower further the residual risk of atherosclerotic cardiovascular events. Correction of atherogenic dyslipidemia, however, remains a major unmet clinical need. Elevated plasma triglycerides, with or without low levels of high-density lipoprotein cholesterol (HDL-C), offer a key modifiable component of this common dyslipidemia, especially in insulin resistant conditions such as type 2 diabetes mellitus. The development of selective peroxisome proliferator-activated receptor alpha modulators (SPPARM) offers an approach to address this treatment gap. This Joint Consensus Panel appraised evidence for the first SPPARM agonist and concluded that this agent represents a novel therapeutic class, distinct from fibrates, based on pharmacological activity, and, importantly, a safe hepatic and renal profile. The ongoing PROMINENT cardiovascular outcomes trial is testing in 10,000 patients with type 2 diabetes mellitus, elevated triglycerides, and low levels of HDL-C whether treatment with this SPPARM agonist safely reduces residual cardiovascular risk.Peer reviewe

Residual vascular risk in diabetes – will the SPPARM alpha concept hold the key?

No abstract available

Motivation for youth participation in sport and physical activity: relationships to culture, self-reported activity levels, and gender

The purpose of the present investigation was to compare participation motives of youth in competitive sport versus physical activity using culture, self-reported physical activity levels, and gender as independent variables. Participants were 1,472 boys (n=822) and girls (n=650) from the United States, Australia, and New Zealand. Three self-report inventories were administered to all participants to determine the amount and frequency of participation as well as participation motives for competitive sport and physical activity. Results from principal component factor analyses revealed stability across cultures in the four factors describing competitive motives (i.e., competition, social/energy, fitness/fun, teamwork) as well as from the four factors describing physical activity motives (i.e., intrinsic, extrinsic, fitness, energy release) accounting for 44% and 51% of the variance, respectively. Results from the 3 x 2 x 3 (Physical Activity Frequency x Gender x Culture) MANOVA's on the competitive sport and physical activity questionnaires revealed significant multivariate main effects for all three independent variables for both questionnaires. Post hoc tests indicated that all four factors were related to these main effects across competitive and physical activity motives. Results are discussed in terms of the differing motives for sport and physical activity and the importance of understanding the particular social milieu in which these activities occur