Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

The Polynomial Eigenvalue Problem is Well Conditioned for Random Inputs

We compute the exact expected value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian distribution, showing that in general this problem is quite well conditioned.The first author's work was partially supported by Agencia Nacional de Investigación e Innovación (ANII), Uruguay, and by CSIC group 618, Universidad de La República, Uruguay. The second author's work was partially supported by MTM2017-83816-P and MTM2017-90682-REDT from Spanish Ministry of Science MICINN and by 21.SI01.64658 from Universidad de Cantabria and Banco de Santander

The multipliers of periodic points in one-dimensional dynamics

It will be shown that the smooth conjugacy class of an $S-$unimodal map which does not have a periodic attractor neither a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M.Shub and D.Sullivan for smooth expanding maps of the circle

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

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

Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.Comment: 72 pages, revised version 12/10/2010, to be published in Nonlinearit

Study protocol: differential effects of diet and physical activity based interventions in pregnancy on maternal and fetal outcomes--individual patient data (IPD) meta-analysis and health economic evaluation.

© 2014 Ruifrok et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.BACKGROUND: Pregnant women who gain excess weight are at risk of complications during pregnancy and in the long term. Interventions based on diet and physical activity minimise gestational weight gain with varied effect on clinical outcomes. The effect of interventions on varied groups of women based on body mass index, age, ethnicity, socioeconomic status, parity, and underlying medical conditions is not clear. Our individual patient data (IPD) meta-analysis of randomised trials will assess the differential effect of diet- and physical activity-based interventions on maternal weight gain and pregnancy outcomes in clinically relevant subgroups of women. METHODS/DESIGN: Randomised trials on diet and physical activity in pregnancy will be identified by searching the following databases: MEDLINE, EMBASE, BIOSIS, LILACS, Pascal, Science Citation Index, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, and Health Technology Assessment Database. Primary researchers of the identified trials are invited to join the International Weight Management in Pregnancy Collaborative Network and share their individual patient data. We will reanalyse each study separately and confirm the findings with the original authors. Then, for each intervention type and outcome, we will perform as appropriate either a one-step or a two-step IPD meta-analysis to obtain summary estimates of effects and 95% confidence intervals, for all women combined and for each subgroup of interest. The primary outcomes are gestational weight gain and composite adverse maternal and fetal outcomes. The difference in effects between subgroups will be estimated and between-study heterogeneity suitably quantified and explored. The potential for publication bias and availability bias in the IPD obtained will be investigated. We will conduct a model-based economic evaluation to assess the cost effectiveness of the interventions to manage weight gain in pregnancy and undertake a value of information analysis to inform future research. SYSTEMATIC REVIEW REGISTRATION: PROSPERO 2013: CRD42013003804.This study was funded by the National Institute for Health Research (NIHR) HTA (Health Technology Assessment) UK programme 12/01

Esomeprazole for the treatment of erosive esophagitis in children: an international, multicenter, randomized, parallel-group, double-blind (for dose) study

<p>Abstract</p> <p>Background</p> <p>Acid suppression with a proton pump inhibitor is standard treatment for gastroesophageal reflux disease and erosive esophagitis in adults and increasingly is becoming first-line therapy for children aged 1-17 years. We evaluated endoscopic healing of erosive esophagitis with esomeprazole in young children with gastroesophageal reflux disease and described esophageal histology.</p> <p>Methods</p> <p>Children aged 1-11 years with endoscopically or histologically confirmed gastroesophageal reflux disease were randomized to esomeprazole 5 or 10 mg daily (< 20 kg) or 10 or 20 mg daily (≥ 20 kg) for 8 weeks. Patients with erosive esophagitis underwent an endoscopy after 8 weeks to assess healing of erosions.</p> <p>Results</p> <p>Of 109 patients, 49% had erosive esophagitis and 51% had histologic evidence of reflux esophagitis without erosive esophagitis. Of the 45 patients who had erosive esophagitis and underwent follow-up endoscopy, 89% experienced erosion resolution. Dilation of intercellular space was reported in 24% of patients with histologic examination.</p> <p>Conclusions</p> <p>Esomeprazole (0.2-1.0 mg/kg) effectively heals macroscopic and microscopic erosive esophagitis in this pediatric population with gastroesophageal reflux disease. Dilation of intercellular space may be an important histologic marker of erosive esophagitis in children.</p> <p>Trial Registration</p> <p>D9614C00097; ClinicalTrials.gov identifier NCT00228527.</p

Erratum to: Study protocol: differential effects of diet and physical activity based interventions in pregnancy on maternal and fetal outcomes: individual patient data (IPD) meta-analysis and health economic evaluation.

Erratum to: Study protocol: differential effects of diet and physical activity based interventions in pregnancy on maternal and fetal outcomes: individual patient data (IPD) meta-analysis and health economic evaluatio

Learning to live together: mutualism between self-splicing introns and their hosts

Group I and II introns can be considered as molecular parasites that interrupt protein-coding and structural RNA genes in all domains of life. They function as self-splicing ribozymes and thereby limit the phenotypic costs associated with disruption of a host gene while they act as mobile DNA elements to promote their spread within and between genomes. Once considered purely selfish DNA elements, they now seem, in the light of recent work on the molecular mechanisms regulating bacterial and phage group I and II intron dynamics, to show evidence of co-evolution with their hosts. These previously underappreciated relationships serve the co-evolving entities particularly well in times of environmental stress