Uniform Approximation by Rational Functions Which All Satisfy the Same Algebraic Differential Equation

AbstractWe prove that given two disjoint compact setsK1andK2in the complex plane, without any holes in them, there exists a sequencepn(z) of rational functions, all of them satisfying one and the same algebraic differential equation, such thatpn(z) converges uniformly to 1 onK1and uniformly to 0 onK2

Using network analysis for the prediction of treatment dropout in patients with mood and anxiety disorders: a methodological proof-of-concept study

There are large health, societal, and economic costs associated with attrition from psychological services. The recently emerged, innovative statistical tool of complex network analysis was used in the present proof-of-concept study to improve the prediction of attrition. Fifty-eight patients undergoing psychological treatment for mood or anxiety disorders were assessed using Ecological Momentary Assessments four times a day for two weeks before treatment (3,248 measurements). Multilevel vector autoregressive models were employed to compute dynamic symptom networks. Intake variables and network parameters (centrality measures) were used as predictors for dropout using machine-learning algorithms. Networks for patients differed significantly between completers and dropouts. Among intake variables, initial impairment and sex predicted dropout explaining 6% of the variance. The network analysis identified four additional predictors: Expected force of being excited, outstrength of experiencing social support, betweenness of feeling nervous, and instrength of being active. The final model with the two intake and four network variables explained 32% of variance in dropout and identified 47 out of 58 patients correctly. The findings indicate that patients’ dynamic network structures may improve the prediction of dropout. When implemented in routine care, such prediction models could identify patients at risk for attrition and inform personalized treatment recommendations.This work was supported by the German Research Foundation National Institute (DFG, Grant nos. LU 660/8-1 and LU 660/10-1 to W. Lutz). The funder of the study had no role in study design, data collection, data analysis, data interpretation, or writing of the manuscript. The corresponding author had access to all data in the study and had final responsibility for the decision to submit for publication. Dr. Hofmann receives financial support from the Alexander von Humboldt Foundation (as part of the Humboldt Prize), NIH/NCCIH (R01AT007257), NIH/NIMH (R01MH099021, U01MH108168), and the James S. McDonnell Foundation 21st Century Science Initiative in Understanding Human Cognition - Special Initiative. (LU 660/8-1 - German Research Foundation National Institute (DFG); LU 660/10-1 - German Research Foundation National Institute (DFG); Alexander von Humboldt Foundation; R01AT007257 - NIH/NCCIH; R01MH099021 - NIH/NIMH; U01MH108168 - NIH/NIMH; James S. McDonnell Foundation 21st Century Science Initiative in Understanding Human Cognition - Special Initiative)Accepted manuscrip

Agallas De Cecidoses Eremita Curtis Y Eucecidoses Minutanus Brèthes (lepidoptera: Cecidosidae) En Magdalena, Prov. De Buenos Aires: Muestreo Preliminar Y Fauna Asociada

In Argentina, five galling species of the family Cecidosidae (Lepidoptera), including Cecidoses eremita Curtis and Eucecidoses minutanus Brèthes, have been cited. This note reports a preliminary study of their galls in "molles" (Schinus longifolius (Lindl.) Speg.) of Magdalena (Buenos Aires, Argentina). In April 2013, galls of C. eremita and E. minutanus were censused in randomly selected "molles". In April and December 2013, randomly selected galls were then collected and transported to our laboratory in hermetic bags, and conserved at -18 °C until examination. Maximum diameter and wall thickness of collected galls were measured. About 84% of the observed "molles" (103/123) had galls of C. eremita and/or E. minutanus. The median of galls per tree was 12 (Q1=6; Q3=22). Eucecidoses minutanus had galls with smaller diameter (U11;53= 583; P<0.05) and thinner wall (U10;52=506.5; P<0..05) than C. eremita. In open galls, we found Pseudoescorpionida, Araneae (Segestriidae and Salticidae), and larvae of Lepidoptera and Hymenoptera. Within closed galls, we found adults of Torymidae and Chalcidoidea, and larvae of Ichneumonoidea. © 2016, Universidade Estadual de Campinas UNICAMP. All rights reserved.16