Rotation sets of billiards with one obstacle

We investigate the rotation sets of billiards on the $m$-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Detection of norovirus in saliva samples from acute gastroenteritis cases and asymptomatic subjects : Association with age and higher shedding in stool

Norovirus infections are a leading cause of acute gastroenteritis outbreaks worldwide and across all age groups, with two main genogroups (GI and GII) infecting humans. The aim of our study was to investigate the occurrence of norovirus in saliva samples from individuals involved in outbreaks of acute gastroenteritis in closed and semiclosed institutions, and its relationship with the virus strain, virus shedding in stool, the occurrence of symptoms, age, and the secretor status of the individual. Epidemiological and clinical information was gathered from norovirus outbreaks occurring in Catalonia, Spain during 2017-2018, and stool and saliva samples were collected from affected and exposed resident individuals and workers. A total of 347 saliva specimens from 25 outbreaks were analyzed. Further, 84% of individuals also provided a paired stool sample. For GII infections, norovirus was detected in 17.9% of saliva samples from symptomatic cases and 5.2% of asymptomatic individuals. Positivity in saliva occurred in both secretors and nonsecretors. None of the individuals infected by norovirus GI was positive for the virus in saliva. Saliva positivity did not correlate with any of the studied symptoms but did correlate with age ≥ 65 years old. Individuals who were positive in saliva showed higher levels of virus shedding in stool. Mean viral load in positive saliva was 3.16 ± 1.08 log10 genome copies/mL, and the predominance of encapsidated genomes was confirmed by propidium monoazide (PMA)xx-viability RTqPCR assay. The detection of norovirus in saliva raises the possibility of oral-to-oral norovirus transmission during the symptomatic phase and, although to a lesser extent, even in cases of asymptomatic infections

Latent tuberculosis infection, tuberculin skin test and vitamin D status in contacts of tuberculosis patients: a cross-sectional and case-control study

<p>Abstract</p> <p>Background</p> <p>Deficient serum vitamin D levels have been associated with incidence of tuberculosis (TB), and latent tuberculosis infection (LTBI). However, to our knowledge, no studies on vitamin D status and tuberculin skin test (TST) conversion have been published to date. The aim of this study was to estimate the associations of serum 25-hydroxyvitamin D₃(25[OH]D) status with LTBI prevalence and TST conversion in contacts of active TB in Castellon (Spain).</p> <p>Methods</p> <p>The study was designed in two phases: cross-sectional and case-control. From November 2009 to October 2010, contacts of 42 TB patients (36 pulmonary, and 6 extra-pulmonary) were studied in order to screen for TB. LTBI and TST conversion cases were defined following TST, clinical, analytic and radiographic examinations. Serum 25(OH)D levels were measured by electrochemiluminescence immunoassay (ECLIA) on a COBAS^®410 ROCHE^®analyzer. Logistic regression models were used in the statistical analysis.</p> <p>Results</p> <p>The study comprised 202 people with a participation rate of 60.1%. Only 20.3% of the participants had a sufficient serum 25(OH)D (≥ 30 ng/ml) level. In the cross-sectional phase, 50 participants had LTBI and no association between LTBI status and serum 25(OH)D was found. After 2 months, 11 out of 93 negative LTBI participants, without primary prophylaxis, presented TST conversion with initial serum 25(OH)D levels: a:19.4% (7/36): < 20 ng/ml, b:12.5% (4/32):20-29 ng/ml, and c:0%(0/25) ≥ 30 ng/ml. A sufficient serum 25(OH)D level was a protector against TST conversion a: Odds Ratio (OR) = 1.00; b: OR = 0.49 (95% confidence interval (CI) 0.07-2.66); and c: OR = 0.10 (95% CI 0.00-0.76), trends p = 0.019, adjusted for high exposure and sputum acid-fast bacilli positive index cases. The mean of serum level 25(OH)D in TST conversion cases was lower than controls,17.5 ± 5.6 ng/ml versus 25.9 ± 13.7 ng/ml (p = 0.041).</p> <p>Conclusions</p> <p>The results suggest that sufficient serum 25(OH)D levels protect against TST conversion.</p

A quasiperiodically forced skew-product on the cylinder without fixed-curves

In Fabbri et al. (2005) the Sharkovskiĭ Theorem was extended to periodic orbits of strips of quasiperiodic skew products in the cylinder. In this paper we deal with the following natural question that arises in this setting: Does Sharkovskiĭ Theorem hold when restricted to curves instead of general strips? We answer this question in the negative by constructing a counterexample: We construct a map having a periodic orbit of period 2 of curves (which is, in fact, the upper and lower circles of the cylinder) and without any invariant curve. In particular this shows that there exist quasiperiodic skew products in the cylinder without invariant curves. © 2016 Elsevier Lt

Finite-time scaling in local bifurcations.

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available