Exponential Rosenbrock methods without order reduction when integrating nonlinear initial value problems

A technique is described in this paper to avoid order reduction when integrating reaction-diffusion initial boundary value problems with explicit exponential Rosenbrock methods. The technique is valid for any Rosenbrock method, without having to impose any stiff order conditions, and for general time-dependent boundary values. An analysis on the global error is thoroughly performed and some numerical experiments are shown which corroborate the theoretical results, and in which a big gain in efficiency with respect to applying the standard method of lines can be observed.Comment: 27 pages, 2 figure

Avoiding order reduction with explicit Runge-Kutta exponential methods in nonlinear initial boundary value problems

In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary conditions can be constructed, that may imply increasing the number of stages and therefore, the computational cost seems bigger than the technique which is suggested here, which just adds some terms with information on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here

Exponential quadrature rules without order reduction for integrating linear initial boundary value problems

In this paper a technique is suggested to integrate linear initial boundary value problems with exponential quadrature rules in such a way that the order in time is as high as possible. A thorough error analysis is given both for the classical approach of integrating the problem first in space and then in time and for doing it in the reverse order in a suitable manner. Time-dependent boundary conditions are considered with both approaches and full discretization formulas are given to implement the methods once the quadrature nodes have been chosen for the time integration and a particular (although very general) scheme is selected for the space discretization. Numerical experiments are shown which corroborate that, for example with the suggested technique, order 2s is obtained when choosing the s nodes of the Gaussian quadrature rule

Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods

We study some of the main features of Fractional Step Runge-Kutta-Nystr¨om methods when they are used to integrate Initial-Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention in the order reduction phenomenon, which appears if classical boundary conditions are taken at the internal stages. This drawback is specially hard when time dependent boundary conditions are considered. In this paper we present an efficient technique, very simple and computationally cheap, which allows us to avoid the order reduction; such technique consists of modifying the boundary conditions for the internal stages of the method

Integrated analysis of mismatch repair system in malignant astrocytomas

This is an open-access article distributed under the terms of the Creative Commons Attribution License.-- et al.Malignant astrocytomas are the most aggressive primary brain tumors with a poor prognosis despite optimal treatment. Dysfunction of mismatch repair (MMR) system accelerates the accumulation of mutations throughout the genome causing uncontrolled cell growth. The aim of this study was to characterize the MMR system defects that could be involved in malignant astrocytoma pathogenesis. We analyzed protein expression and promoter methylation of MLH1, MSH2 and MSH6 as well as microsatellite instability (MSI) and MMR gene mutations in a set of 96 low- and high-grade astrocytomas. Forty-one astrocytomas failed to express at least one MMR protein. Loss of MSH2 expression was more frequent in low-grade astrocytomas. Loss of MLH1 expression was associated with MLH1 promoter hypermethylation and MLH1 -93G>A promoter polymorphism. However, MSI was not related with MMR protein expression and only 5% of tumors were MSI-High. Furthermore, the incidence of tumors carrying germline mutations in MMR genes was low and only one glioblastoma was associated with Lynch syndrome. Interestingly, survival analysis identified that tumors lacking MSH6 expression presented longer overall survival in high-grade astrocytoma patients treated only with radiotherapy while MSH6 expression did not modify the prognosis of those patients treated with both radiotherapy and chemotherapy. Our findings suggest that MMR system alterations are a frequent event in malignant astrocytomas and might help to define a subgroup of patients with different outcome.This work was supported by Fondo de Investigación Sanitaria (FIS PI 10/00219), Instituto de Estudios de Ciencias de la Salud de Castilla y León IECSCYL and Junta de Castilla y León y Fondo Social Europeo (Orden EDU/330/2008).Peer Reviewe

Psychometric network analysis of the Patient Health Questionnaire-4 (PHQ-4) in Paraguayan general population

Background: Depression and anxiety are two of the most prevalent and disabling mental disorders worldwide, both in the general population and in outpatient clinical settings. Objective: This study aimed to analyze the psychometric properties of the Patient Health Questionnaire-4 (PHQ-4) based on network analysis metrics. Methods: A total of 911 Paraguayans (23.71% women and 76.29% men; mean age 31.25 years, SD = 10.63), selected by non-probabilistic convenience sampling, participated in the study. Network analysis was used to evaluate the internal structure, reliability, and measurement invariance between men and women. Results: The results revealed that the PHQ-4 is a unidimensional measure through Exploratory Graph Analysis (EGA). Reliability, through structural consistency, identified that 100% of the time, only a single dimension was obtained, and all items remained stable, as they were always replicated within the empirical dimension. The unidimensional structure has shown evidence of configural invariance; therefore, the network structure functioned equally among the different sex groups. Conclusion: The PHQ-4 presented optimal preliminary evidence of validity based on its internal structure, reliability, and invariance between sexes. Therefore, it may be useful as an accurate and brief measure of anxiety and depressive symptoms in the Paraguayan context