Multiple scattering in random mechanical systems and diffusion approximation

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P_h, depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that (P_h -I)/h converges for small h to a second order elliptic differential operator L on compactly supported functions and that the Markov chain process associated to P_h converges to a diffusion with infinitesimal generator L. Both P_h and L are selfadjoint (densely) defined on the space L2(H,{\eta}) of square-integrable functions over the (lower) half-space H in R^m, where {\eta} is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator L respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.Comment: 34 pages, 13 figure

Higher order approximation of isochrons

Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a linear approximation of isochrons. In this paper, we extend the method for obtaining partial derivatives of the phase function to arbitrary order, providing higher order approximations of isochrons. In particular, our method in order 2 can be applied to the study of dynamics of a stable oscillator subjected to stochastic perturbations, a topic that will be discussed in a future paper. We use the Stuart-Landau oscillator to illustrate the method in order 2

Relationships Between Subgingival Microbiota and GCF Biomarkers in Generalized Aggressive Periodontitis

Aim To examine relationships between subgingival biofilm composition and levels of gingival crevicular fluid (GCF) cytokines in periodontal health and generalized aggressive periodontitis (GAP). Materials and methods Periodontal parameters were measured in 25 periodontally healthy and 31 GAP subjects. Subgingival plaque and GCF samples were obtained from 14 sites from each subject. 40 subgingival taxa were quantified using checkerboard DNA-DNA hybridization and the concentrations of 8 GCF cytokines measured using Luminex. Cluster analysis was used to define sites with similar subgingival microbiotas in each clinical group. Significance of differences in clinical, microbiological and immunological parameters among clusters was determined using the Kruskal-Wallis test. Results GAP subjects had statistically significantly higher GCF levels of interleukin-1β (IL-1β) (p\u3c0.001), granulocyte-macrophage colony-stimulating factor (GM-CSF) (p\u3c0.01), and IL-1β/IL-10 ratio (p\u3c0.001) and higher proportions of Red and Orange complex species than periodontally healthy subjects. There were no statistically significant differences in the mean proportion of cytokines among clusters in the periodontally healthy subjects, while the ratio IL-1β/IL-10 (p\u3c0.05) differed significantly among clusters in the aggressive periodontitis group. Conclusions Different subgingival biofilm profiles are associated with distinct patterns of GCF cytokine expression. Aggressive periodontitis subjects were characterized by a higher IL-1β/IL-10 ratio than periodontally healthy subjects, suggesting an imbalance between pro- and anti-inflammatory cytokines in aggressive periodontitis

Zone trapping/merging zones in flow analysis: A novel approach for rapid assays involving relatively slow chemical reactions

AbstractA novel strategy for accomplishing zone trapping in flow analysis is proposed. The sample and the reagent solutions are simultaneously inserted into convergent carrier streams and the established zones merge together before reaching the detector, where the most concentrated portion of the entire sample zone is trapped. The main characteristics, potentialities and limitations of the strategy were critically evaluated in relation to an analogous flow system with zone stopping. When applied to the spectrophotometric determination of nitrite in river waters, the main figures of merit were maintained, exception made for the sampling frequency which was calculated as 189h−1, about 32% higher relatively to the analogous system with zone stopping. The sample inserted volume can be increased up to 1.0mL without affecting sampling frequency and no problems with pump heating or malfunctions were noted after 8-h operation of the system. In contrast to zone stopping, only a small portion of the sample zone is halted with zone trapping, leading to these beneficial effects

Evaluation and Validation of a Method for Determining Platelet Catecholamine in Patients with Obstructive Sleep Apnea and Arterial Hypertension

Background: Measurements of plasma and urinary catecholamine are susceptible to confounding factors that influence the results, complicating the interpretation of sympathetic nervous system (SNS) activity in the Obstructive sleep apnea (OSA) and arterial hypertension (HYP) conditions.Objective: in this study, we validated a test for platelet catecholamine and compared the catecholamine levels (adrenaline and noradrenaline) in urine, plasma and platelets in patients with OSA and HYP compared with controls.Methods: in the validation, 30 healthy, nonsmoking volunteers who were not currently undergoing treatment or medication were selected as the control group. One hundred fifty-four individuals (114 OSA, 40 non-OSA) were consecutively selected from the outpatient clinic of the Sleep Institute and underwent clinical, polysomnographic and laboratory evaluation, including the urinary, plasma and platelet levels of adrenaline (AD) and noradrenaline (NA). Patients were then allocated to groups according to the presence of OSA and/or hypertension.Results: A logistic regression model, controlled for age and BMI, showed that urinary AD and urinary NA were risk factors in the OSA+HYP group and the HYP group; however, the model showed higher levels of platelet NA for OSA without HYP. After 1 year of CPAP (continuous upper airway pressure) treatment, patients (n = 9) presented lower levels of urinary NA (p = 0.04) and platelet NA (p = 0.05).Conclusion: Urinary NA and AD levels were significantly associated with the condition of hypertension with and without OSA, whereas platelet NA with OSA without comorbidity. These findings suggest that platelet catecholamine levels might reflect nocturnal sympathetic activation in OSA patients without hypertension.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Associacao Fundo de Pesquisa a Psicobiologia (AFIP), BrazilConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Federal de São Paulo, Dept Psychobiol, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Cardiol, São Paulo, BrazilAssoc Fundo Incent & Pesquisa, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Psychobiol, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Cardiol, São Paulo, BrazilWeb of Scienc

Impact of Side Branch Predilation on Percutaneous Coronary Intervention in Complex Coronary Bifurcation Lesions

ABSTRACTBackgroundThe treatment of coronary bifurcation lesions with single stenting in the main vessel and provisional side branch stenting may be limited by the degree of anatomical/morphological complexity. Side branch predilation, a procedural step that is typically avoided, may be required to maintain side branch patency. The impact of side branch predilation on the immediate results of percutaneous coronary intervention in complex coronary bifurcation lesions was investigated.MethodsBetween May, 2008 and August, 2009, 59 patients with single coronary bifurcation lesions and significant involvement of the main and side branches were included in the study. The main exclusion criteria were the involvement of the left main coronary artery, ST-elevation acute myocardial infarction (< 72 hours) and in-stent restenosis.ResultsThe mean age of patients was 61.2±11 years, 25.4% were female, and 30.1% had diabetes mellitus. Lesions were most prevalent in the left anterior descending artery/diagonal branch (86.4%). During the procedure, 8.5% (5/59) of lesions had unsuccessful side branch predilation, and four of these bifurcations were treated with two stents. In the multivariate model, side branch stenosis at baseline was the only significant predictor of unsuccessful side branch predilation (odds ratio 1.15, 95%CI: 1.01–1.30; P=0.04), and side branch stenosis > 87.6% was identified as the most accurate cut-off value to predict failure in the receiver operating characteristic (ROC) curve.ConclusionsSide branch predilation was associated with immediate side branch failure in < 10% of cases, and the only significant predictor in the multivariate model was side branch stenosis severity (> 85%) at baseline

Billiards in a general domain with random reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord "picked at random" in ${\mathcal D}$, and we study the angle of intersection of the process with a $(d-1)$-dimensional manifold contained in ${\mathcal D}$.Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains