Convex Dynamics and Applications

This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. \textit{Digital halftoning} is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A corollary of the theorem is that for \textit{error diffusion}, one of the methods of digital halftoning, averages of colors of the printed dots converge to averages of the colors taken from the same dots of the actual images. Digital printing is a special case of a much wider class of scheduling problems to which the theorem applies. Convex dynamics has roots in classical areas of mathematics such as symbolic dynamics, Diophantine approximation, and the theory of uniform distributions.Comment: LaTex with 9 PostScript figure

Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.Comment: To appear in Journal of Statistical Physic

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Impact of maternal education on response to lifestyle interventions to reduce gestational weight gain: Individual participant data meta-Analysis

Objectives To identify if maternal educational attainment is a prognostic factor for gestational weight gain (GWG), and to determine the differential effects of lifestyle interventions (diet based, physical activity based or mixed approach) on GWG, stratified by educational attainment. Design Individual participant data meta-Analysis using the previously established International Weight Management in Pregnancy (i-WIP) Collaborative Group database (https://iwipgroup.wixsite.com/collaboration). Preferred Reporting Items for Systematic reviews and Meta-Analysis of Individual Participant Data Statement guidelines were followed. Data sources Major electronic databases, from inception to February 2017. Eligibility criteria Randomised controlled trials on diet and physical activity-based interventions in pregnancy. Maternal educational attainment was required for inclusion and was categorised as higher education ( 65tertiary) or lower education ( 64secondary). Risk of bias Cochrane risk of bias tool was used. Data synthesis Principle measures of effect were OR and regression coefficient. Results Of the 36 randomised controlled trials in the i-WIP database, 21 trials and 5183 pregnant women were included. Women with lower educational attainment had an increased risk of excessive (OR 1.182; 95% CI 1.008 to 1.385, p =0.039) and inadequate weight gain (OR 1.284; 95% CI 1.045 to 1.577, p =0.017). Among women with lower education, diet basedinterventions reduced risk of excessive weight gain (OR 0.515; 95% CI 0.339 to 0.785, p = 0.002) and inadequate weight gain (OR 0.504; 95% CI 0.288 to 0.884, p=0.017), and reduced kg/week gain (B-0.055; 95% CI-0.098 to-0.012, p=0.012). Mixed interventions reduced risk of excessive weight gain for women with lower education (OR 0.735; 95% CI 0.561 to 0.963, p=0.026). Among women with high education, diet based interventions reduced risk of excessive weight gain (OR 0.609; 95% CI 0.437 to 0.849, p=0.003), and mixed interventions reduced kg/week gain (B-0.053; 95% CI-0.069 to-0.037,p<0.001). Physical activity based interventions did not impact GWG when stratified by education. Conclusions Pregnant women with lower education are at an increased risk of excessive and inadequate GWG. Diet based interventions seem the most appropriate choice for these women, and additional support through mixed interventions may also be beneficial

Global report on preterm birth and stillbirth (2 of 7): discovery science

<p>Abstract</p> <p>Background</p> <p>Normal and abnormal processes of pregnancy and childbirth are poorly understood. This second article in a global report explains what is known about the etiologies of preterm births and stillbirths and identifies critical gaps in knowledge. Two important concepts emerge: the continuum of pregnancy, beginning at implantation and ending with uterine involution following birth; and the multifactorial etiologies of preterm birth and stillbirth. Improved tools and data will enable discovery scientists to identify causal pathways and cost-effective interventions.</p> <p>Pregnancy and parturition continuum</p> <p>The biological process of pregnancy and childbirth begins with implantation and, after birth, ends with the return of the uterus to its previous state. The majority of pregnancy is characterized by rapid uterine and fetal growth without contractions. Yet most research has addressed only uterine stimulation (labor) that accounts for <0.5% of pregnancy.</p> <p>Etiologies</p> <p>The etiologies of preterm birth and stillbirth differ by gestational age, genetics, and environmental factors. Approximately 30% of all preterm births are indicated for either maternal or fetal complications, such as maternal illness or fetal growth restriction. Commonly recognized pathways leading to preterm birth occur most often during the gestational ages indicated: (1) inflammation caused by infection (22-32 weeks); (2) decidual hemorrhage caused by uteroplacental thrombosis (early or late preterm birth); (3) stress (32-36 weeks); and (4) uterine overdistention, often caused by multiple fetuses (32-36 weeks). Other contributors include cervical insufficiency, smoking, and systemic infections. Many stillbirths have similar causes and mechanisms. About two-thirds of late fetal deaths occur during the antepartum period; the other third occur during childbirth. Intrapartum asphyxia is a leading cause of stillbirths in low- and middle-income countries.</p> <p>Recommendations</p> <p>Utilizing new systems biology tools, opportunities now exist for researchers to investigate various pathways important to normal and abnormal pregnancies. Improved access to quality data and biological specimens are critical to advancing discovery science. Phenotypes, standardized definitions, and uniform criteria for assessing preterm birth and stillbirth outcomes are other immediate research needs.</p> <p>Conclusion</p> <p>Preterm birth and stillbirth have multifactorial etiologies. More resources must be directed toward accelerating our understanding of these complex processes, and identifying upstream and cost-effective solutions that will improve these pregnancy outcomes.</p

Magnetization Reversal Of Ferromagnetic Nanoparticles Induced By A Stream Of Polarized Electrons

The remagnetization of ferromagnetic Fe3O4 nanoparticles of several thousand cubic nanometers by spin-polarized current is investigated. For this purpose, magnetite nanoparticles are synthesized and deposited on a conductive nonmagnetic substrate. The remagnetization is conducted in high-vacuum scanning tunneling microscope (STM). The STM tip from magnetized iron wire constitutes one electrode while the ferromagnetic nanoparticle on the graphite surface represents the second electrode. The measured threshold value of remagnetization current (Ithresh=9 nA) is the lowest value of current at which remagnetization occurs. The change in nanoparticle magnetization is detected by the effect of giant magnetic resistance, specifically, the dependence of the weak polarized current (

CONVEX DYNAMICS AND APPLICATIONS

Abstract. This paper proves a theorem about bounding orbits of a time dependent dynamical system. The maps that are involved are examples in convex dynamics, by which we mean the dynamics of piecewise isometries where the pieces are convex. The theorem came to the attention of the authors in connection with the problem of digital halftoning. Digital halftoning is a family of printing technologies for getting full color images from only a few different colors deposited at dots all of the same size. The simplest version consist in obtaining grey scale images from only black and white dots. A corollary of the theorem is that for error diffusion, one of the methods of digital halftoning, averages of colors of the printed dots converge to averages of the colors taken from the same dots of the actual images. Digital printing is a special case of a much wider class of scheduling problems to which the theorem applies. Convex dynamics has roots in classical areas of mathematics such as symbolic dynamics, Diophantine approximation, and the theory of uniform distributions. 1