On the affine random walk on the torus

Let $\mu$ be a borelian probability measure on $\mathbf{G}:=\mathrm{SL}_d(\mathbb{Z}) \ltimes \mathbb{T}^d$. Define, for $x\in \mathbb{T}^d$, a random walk starting at $x$ denoting for $n\in \mathbb{N}$, $$\left\{\begin{array}{rcl} X_0 &=&x\\ X_{n+1} &=& a_{n+1} X_n + b_{n+1} \end{array}\right.$$ where $((a_n,b_n))\in \mathbf{G}^\mathbb{N}$ is an iid sequence of law $\mu$. Then, we denote by $\mathbb{P}_x$ the measure on $(\mathbb{T}^d)^\mathbb{N}$ that is the image of $\mu^{\otimes \mathbb{N}}$ by the map $\left((g_n) \mapsto (x,g_1 x, g_2 g_1 x, \dots , g_n \dots g_1 x, \dots)\right)$ and for any $\varphi \in \mathrm{L}^1((\mathbb{T}^d)^\mathbb{N}, \mathbb{P}_x)$, we set $\mathbb{E}_x \varphi((X_n)) = \int \varphi((X_n)) \mathrm{d}\mathbb{P}_x((X_n))$. Bourgain, Furmann, Lindenstrauss and Mozes studied this random walk when $\mu$ is concentrated on $\mathrm{SL}_d(\mathbb{Z}) \ltimes\{0\}$ and this allowed us to study, for any h\"older-continuous function $f$ on the torus, the sequence $(f(X_n))$ when $x$ is not too well approximable by rational points. In this article, we are interested in the case where $\mu$ is not concentrated on $\mathrm{SL}_d(\mathbb{Z}) \ltimes \mathbb{Q}^d/\mathbb{Z}^d$ and we prove that, under assumptions on the group spanned by the support of $\mu$, the Lebesgue's measure $\nu$ on the torus is the only stationary probability measure and that for any h\"older-continuous function $f$ on the torus, $\mathbb{E}_x f(X_n)$ converges exponentially fast to $\int f\mathrm{d}\nu$. Then, we use this to prove the law of large numbers, a non-concentration inequality, the functional central limit theorem and it's almost-sure version for the sequence $(f(X_n))$. In the appendix, we state a non-concentration inequality for products of random matrices without any irreducibility assumption

The speed of convergence in the renewal theorem

In this article we study a diophantine property of probability measures on R. We will always assume that the considered measures have an exponential moment and a drift. We link this property to the points in C close to the imaginary axis where the Fourier-Laplace transform of those measures take the value 1 and finally, we apply this to the study of the speed in Kesten's renewal theorem on R

Le théorème central limite pour la marche linéaire sur le tore et le théorème de renouvellement dans Rd\mathbb{R}^d

The first part of this thesis deals with the random walk on the torus $\mathbb{T}^d := \mathbb{R}^d / \mathbb{Z}^d$ defined by a probability measure on $\mathrm{SL}_d(\mathbb{Z})$.To study the Central Limit Theorem and the Law of the Iterated Logarithm, we apply Gordin's method. To do so, we use a result proved by Bourgain, Furmann, Lindenstrauss and Mozes to solve Poisson's equation at point's having good diophantine properties.In the second part, we study the walk on $\mathbb{R}^d \setminus\{0\}$ defined by the action of $\mathrm{SL}_d(\mathbb{R})$ and we prove a result about the rate of convergence in Guivarc'h and Le Page's renewal theorem.La première partie de cette thèse porte sur l'étude de la marche aléatoire sur le tore $\mathbb{T}^d:=\mathbb{R}^d/\mathbb{Z}^d$ définie par une mesure de probabilité $\mathrm{SL}_d(\mathbb{Z})$.Pour étudier le Théorème Central Limite et la loi du logarithme itéré, nous appliquons la méthode de Gordin qui consiste à se ramener à des martingales. Pour cela, nous utilisons un résultat de Bourgain, Furmann, Lindenstrauss et Mozes nous permettant de résoudre l'équation de Poisson pour des points ayant de bonnes propriétés diophantiennes.Dans la deuxième partie, nous étudions la marche sur $\mathbb{R}^d \setminus\{0\}$ définie par l'action de $\mathrm{SL}_d(\mathbb{R})$ et nous montrons un résultat de vitesse de convergence dans le théorème de renouvellement de Guivarc'h et Le Page

Le théorème central limite pour la marche linéaire sur le tore et le théorème de renouvellement dans Rd

The first part of this thesis deals with the random walk on the torus Td := Rd/Zd defined by a robability measure on SLd(Z). To study the Central Limit Theorem and the Law of the Iterated Logarithm, we apply Gordin’s method. To do so, we use a result proved by Bourgain, Furmann, Lindenstrauss and Mozes to solve Poisson’s equation at point’s having good diophantine properties.In the second part, we study the walk on Rd \ {0} defined by the action of SLd(R) and we prove a result about the rate of convergence in Guivarc’h and Le Page’s renewal theorem.La première partie de cette thèse porte sur l’étude de la marche aléatoire sur le tore Td := Rd/Zd définie par une mesure de probabilité SLd(Z). Pour étudier le Théorème Central Limite et la loi du logarithme itéré, nous appliquons la méthode de Gordin qui consiste à se ramener à des martingales. Pour cela, nous utilisons un résultat de Bourgain, Furmann, Lindenstrauss et Mozes nous permettant de résoudre l’équation de Poisson pour des points ayant de bonnes propriétés diophantiennes. Dans la deuxième partie, nous étudions la marche sur Rd\{0} définie par l’action de SLd(R) et nous montrons un résultat de vitesse de convergence dans le théorème de renouvellement de Guivarc’h et Le Page

Cultural Evolution from the Producers’ Standpoint

Standard approaches to cultural evolution focus on the recipients or consumers. This does not take into account the fitness costs incurred in producing the behaviors or artifacts that become cultural, i.e., widespread in a social group. We argue that cultural evolution models should focus on these fitness costs and benefits of cultural production particularly in the domain of “symbolic” culture. In this approach, cultural products can be considered as a part of the extended phenotype of producers, which can affect the fitness of recipients in a positive way (through cooperation) but also in a detrimental way (through manipulation and exploitation). Taking the producers’ perspective may help explain the specific features of many kinds of cultural products

Central vein catheter-related thrombosis in intensive care patients: incidence, risks factors, and relationship with catheter-related sepsis.

peer reviewed[en] OBJECTIVE: To evaluate the incidence and risk factors for catheter-related central vein thrombosis in ICU patients. DESIGN: Observational prospective multicenter study. SETTING: An 8-bed surgical ICU, a 10-bed surgical cardiovascular ICU, and a 10-bed medical-surgical ICU. PATIENTS: During an 18-month period, 265 internaljugular or subclavian catheters were included. Veins were explored by duplex scanning performed just before or < 24 h after catheter removal. Suspected risk factors of catheter-related central vein thrombosis were recorded. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Fifty-seven catheters were excluded from the analysis. Therefore 208 catheters were analyzed. Mean age of patients was 64+/-15 years, simplified acute physiologic score was 12+/-5, organ system failure score at insertion was 1+/-1, and mean duration of catheterization was 9+/-5 days. A catheter-related internal jugular or subclavian vein thrombosis occurred in 33% of the cases (42% [95% confidence interval (CI), 34 to 49%] and 10% [95% CI, 3 to 18%], respectively). Thrombosis was limited in 8%, large in 22%, and occlusive in 3% of the cases. Internal jugular route (relative risk [RR], 4.13; 95% CI, 1.72 to 9.95), therapeutic heparinization (RR 0.47; 95% CI, 0.23 to 0.99), and age >64 years (RR, 2.44; 95% CI, 2.05 to 3.19) were independently associated with catheter-related thrombosis. Moreover, the risk of catheter-related sepsis was 2.62-fold higher when thrombosis occurred (p=0.011). CONCLUSIONS: Catheter-related central vein thrombosis is a frequent complication of central venous catheterization in ICU patients and is closely associated with catheter-related sepsis

Nt-acetylation-independent turnover of SQUALENE EPOXIDASE 1 by Arabidopsis DOA10-like E3 ligases

The acetylation-dependent (Ac/)N-degron pathway degrades proteins through recognition of their acetylated N-termini (Nt) by E3 ligases called Ac/N-recognins. To date, specific Ac/N-recognins have not been defined in plants. Here we used molecular, genetic, and multiomics approaches to characterize potential roles for Arabidopsis (Arabidopsis thaliana) DEGRADATION OF ALPHA2 10 (DOA10)-like E3 ligases in the Nt-acetylation-(NTA)-dependent turnover of proteins at global- and protein-specific scales. Arabidopsis has two endoplasmic reticulum (ER)-localized DOA10-like proteins. AtDOA10A, but not the Brassicaceae-specific AtDOA10B, can compensate for loss of yeast (Saccharomyces cerevisiae) ScDOA10 function. Transcriptome and Nt-acetylome profiling of an Atdoa10a/b RNAi mutant revealed no obvious differences in the global NTA profile compared to wild type, suggesting that AtDOA10s do not regulate the bulk turnover of NTA substrates. Using protein steady-state and cycloheximide-chase degradation assays in yeast and Arabidopsis, we showed that turnover of ER-localized SQUALENE EPOXIDASE 1 (AtSQE1), a critical sterol biosynthesis enzyme, is mediated by AtDOA10s. Degradation of AtSQE1 in planta did not depend on NTA, but Nt-acetyltransferases indirectly impacted its turnover in yeast, indicating kingdom-specific differences in NTA and cellular proteostasis. Our work suggests that, in contrast to yeast and mammals, targeting of Nt-acetylated proteins is not a major function of DOA10-like E3 ligases in Arabidopsis and provides further insight into plant ERAD and the conservation of regulatory mechanisms controlling sterol biosynthesis in eukaryotes

228 Blood pressure in HIV-infected patients

ObjectifveTo determine the prevalence of hypertension in a cohort of HIV-infected patients (HIV+).MethodsHIV+ patients were enrolled consecutively at ambulatory cardiology consultation. We evaluated:cardiovascular risk factors,office blood pressure,24 hours ambulatory blood pressure monitoring (ABPM).We identified patients with known hypertension, masked hypertension and white-coat effect.Results258 HIV+ patients (mean age 49±7 ans, 91% men) were consecutively included in this study between 2005 and 2009. Cardiovascular risk factors were as follows: 52% had dyslipidemia, 51% were active smokers, 40% with known hypertension and 9% were diabetics. Body mass index of the entire cohort was 24±4kg/mΣ and 89% were under antiretrovirals. Data on blood pressure are depicted in Table 1. 19% (29) were discovered to have hypertension.ConclusionHypertension is frequent in HIV-infected patients and more and more common with aging. The number of non-dipper HIV+ was high in this cohort. Studies on the impact of HIV infection and antiretrovirals on the autonomic nervous system should be performed.ParametersN=258Office systolic BP, mmHg131±19Office diastolic BP, mmHg81±10Mean 24h-systolic BP, mmHg125±13Mean 24-diastolic BP, mmHg77±9Daytime systolic BP, mmHg129±13Daytime diastolic BP, mmHg80±9Nighttime systolic BP, mmHg115±17Nighttime diastolic BP, mmHg68±10BP profile in known hypertensive patientsN=103Number of patients with appropriate BP control, %45%Number of patients with white-coat effect, %17%Non dipper, %43% in known hypertensive patients 39% in unknown hypertensive patient