The two gap transitions in Ge1−x_{1-x}Snx_x: effect of non-substitutional complex defects

The existence of non-substitutional $\beta$-Sn defects in Ge$_{1-x}$Sn$_{x}$ was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B 81, 155204 (2010)], which established that although most Sn enters substitutionally ($\alpha$-Sn) in the Ge lattice, a second significant fraction corresponds to the Sn-vacancy defect complex in the split-vacancy configuration ( $\beta$-Sn ), in agreement with our previous theoretical study [Ventura et al., Phys. Rev. B 79, 155202 (2009)]. Here, we present our electronic structure calculation for Ge$_{1-x}$Sn$_{x}$, including substitutional $\alpha$-Sn as well as non-substitutional $\beta$-Sn defects. To include the presence of non-substitutional complex defects in the electronic structure calculation for this multi-orbital alloy problem, we extended the approach for the purely substitutional alloy by Jenkins and Dow [Jenkins and Dow, Phys. Rev. B 36, 7994 (1987)]. We employed an effective substitutional two-site cluster equivalent to the real non-substitutional $\beta$-Sn defect, which was determined by a Green's functions calculation. We then calculated the electronic structure of the effective alloy purely in terms of substitutional defects, embedding the effective substitutional clusters in the lattice. Our results describe the two transitions of the fundamental gap of Ge$_{1-x}$Sn$_{x}$ as a function of the total Sn-concentration: namely from an indirect to a direct gap, first, and the metallization transition at higher $x$. They also highlight the role of $\beta$-Sn in the reduction of the concentration range which corresponds to the direct-gap phase of this alloy, of interest for optoelectronics applications.Comment: 11 pages, 9 Figure

Selecting the number of categories of the lymph node ratio in cancer research: A bootstrap-based hypothesis test

The high impact of the lymph node ratio as a prognostic factor is widely established in colorectal cancer, and is being used as a categorized predictor variable in several studies. However, the cut-off points as well as the number of categories considered differ considerably in the literature. Motivated by the need to obtain the best categorization of the lymph node ratio as a predictor of mortality in colorectal cancer patients, we propose a method to select the best number of categories for a continuous variable in a logistic regression framework. Thus, to this end, we propose a bootstrap-based hypothesis test, together with a new estimation algorithm for the optimal location of the cut-off points called BackAddFor, which is an updated version of the previously proposed AddFor algorithm. The performance of the hypothesis test was evaluated by means of a simulation study, under different scenarios, yielding type I errors close to the nominal errors and good power values whenever a meaningful difference in terms of prediction ability existed. Finally, the methodology proposed was applied to the CCR-CARESS study where the lymph node ratio was included as a predictor of five-year mortality, resulting in the selection of three categories.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Basque Government through the Consolidated Research Group MATHMODE (IT1294-19) from the Departamento de Educación, Política Lingüística y Cultura del Gobierno Vasco, the BERC 2018-2021 program and the SPRI Elkartek project 3KIA (KK-2020/00049); by the Spanish Government through the Ministerio de Ciencia, Innovación y Universidades: BCAM Severo Ochoa accreditation SEV-2017-0718 and by Ministerio de Economía y Competitividad and FEDER under research grants MTM2014-55966-P, MTM2016-74931-P and MTM2017-89422-P; and by Xunta de Galicia (Centro singular de investigación de Galicia accreditation 2019-2022) and the EU (ERDF), Ref. ED431G2019/06. Financial support for data collection was provided in part by grants from the Instituto de Salud Carlos III, (PS09/00314, PS09/00910, PS09/00746, PS09/00805, PI09/90460, PI09/90490, PI09/90453, PI09/90441, PI09/90397, and the thematic networks REDISSEC - Red de Investigación en Servicios de Salud en Enfermedades Crónicas), co-funded by European Regional Development Fund/European Social Fund (ERDF/ESF “Investing in your future”); and the Research Committee of the Hospital Galdakao

Sample size impact on the categorisation of continuous variables in clinical prediction

Recent advances in information technologies are generating a growth in the amount of available biomedical data. In this paper, we studied the impact sample size may have on the categorisation of a continuous predictor variable in a logistic regression setting. Two different approaches to categorise predictor variables were compared.MINECO: MTM2011-28285-C02-01, MTM2013-40941-P, MTM2014-55966-P. Basque Government: IT620-13. University of the Basque Country UPV/EHU: UFI11/52 Agrupamento INBIOMED from DXPCTSUG-FEDER unha maneira de facer Europa (2012/273)

Level shifts in a panel data based unit root test. An application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.

Variable selection with LASSO regression for complex survey data

Variable selection is an important step to end up with good prediction models. LASSO regression models are one of the most commonly used methods for this purpose, for which cross-validation is the most widely applied validation technique to choose the tuning parameter (λ). Validation techniques in a complex survey framework are closely related to “replicate weights”. However, to our knowledge, they have never been used in a LASSO regression context. Applying LASSO regression models to complex survey data could be challenging. The goal of this paper is two-fold. On the one hand, we analyze the performance of replicate weights methods to select the tuning parameter for fitting LASSO regression models to complex survey data. On the other hand, we propose new replicate weights methods for the same purpose. In particular, we propose a new design-based cross-validation method as a combination of the traditional cross-validation and replicate weights. The performance of all these methods has been analyzed and compared by means of an extensive simulation study to the traditional cross-validation technique to select the tuning parameter for LASSO regression models. The results suggest a considerable improvement when the new proposal design-based cross-validation is used instead of the traditional crossvalidation.IT1456-22 PIF18/21

Estimation of cut-off points under complex-sampling design data

In the context of logistic regression models, a cut-off point is usually selected to dichotomize the estimated predicted probabilities based on the model. The techniques proposed to estimate optimal cut-off points in the literature, are commonly developed to be applied in simple random samples and their applicability to complex sampling designs could be limited. Therefore, in this work we propose a methodology to incorporate sampling weights in the estimation process of the optimal cut-off points, and we evaluate its performance using a real data-based simulation study. The results suggest the convenience of considering sampling weights for estimating optimal cut-off points.IT1294-19 BERC 2018-2021 KK-2020/00049 PIF18/21

A new approach to categorize continuous variables in prediction models: Proposal and validation

When developing prediction models for application in clinical practice, health practitioners usually categorise clinical variables that are continuous in nature. Although categorisation is not regarded as advisable from a statistical point of view, due to loss of information and power, it is a common practice in medical research. Consequently, providing researchers with a useful and valid categorisation method could be a relevant issue when developing prediction models. Without recommending categorisation of continuous predictors, our aim is to propose a valid way to do it whenever it is considered necessary by clinical researchers. This paper focuses on categorising a continuous predictor within a logistic regression model, in such a way that the best discriminative ability is obtained in terms of the highest area under the receiver operating characteristic curve (AUC). The proposed methodology is validated when the optimal cut points' location is known in theory or in practice. In addition, the proposed method is applied to a real data set of patients with an exacerbation of chronic obstructive pulmonary disease, in the context of the IRYSS-COPD study where a clinical prediction rule for severe evolution was being developed. The clinical variable PCO2 was categorised in a univariable and a multivariable setting.MINECO: MTM2010-14913, MTM2011-28285-C02-01 and MTM2013-40941-P. Basque Government: IT620-13, 2012111008. University of the Basque Country UPV/EHU: GIU10/21, UFI11/52. Agrupamento IN-BIOMED from DXPCTSUG-FEDER unha maneira de facer Europa (2012/273). Red IRYSS (Investigación en Resultados y Servicios Sanitarios)- of the Instituto de Salud Carlos III: G03/22

Los partidos de ámbito no estatal en Aragón : el Partido Aragonés y la Chunta Aragonesista

El objeto de este artículo consiste en mostrar de modo sucinto las trayectorias políticas y organizativas de los dos principales partidos de ámbito no estatal en Aragón: el Partido Aragonés (PAR) y la Chunta Aragonesista (CHA). Para ello, se hace énfasis en la importancia que los cambios en el entorno, especialmente el electoral, han tenido en la vida interna de ambos partidos, y, también, en la similitud de ambas trayectorias marcadas por un rápido crecimiento inicial y una importante erosión electoral una vez superado el umbral de la representación.The aim of this article is to describe the political and organizational evolution of the two main non state wide parties in Aragon: the Partido Aragonés (PAR) and the Chunta Aragonesista (CHA). The article focuses on the importance that the environmental changes, especially at the electoral arena, have had on the evolution of both parties. And also points out the similarities of their trajectories, deeply marked by a significant initial growth and steady electoral erosion once the representation threshold is achieved

Non-substitutional single-atom defects in the Ge_(1-x)Sn_x alloy

Ge_(1-x)Sn_x alloys have proved difficult to form at large x, contrary to what happens with other group IV semiconductor combinations. However, at low x they are typical examples of well-behaved substitutional compounds, which is desirable for harnessing the electronic properties of narrow band semiconductors. In this paper, we propose the appearance of another kind of single-site defect ($\beta-Sn$), consisting of a single Sn atom in the center of a Ge divacancy, that may account for these facts. Accordingly, we examine the electronic and structural properties of these alloys by performing extensive numerical ab-initio calculations around local defects. The results show that the environment of the $\beta$ defect relaxes towards a cubic octahedral configuration, facilitating the nucleation of metallic white tin and its segregation, as found in amorphous samples. Using the information stemming from these local defect calculations, we built a simple statistical model to investigate at which concentration these $\beta$ defects can be formed in thermal equilibrium. These results agree remarkably well with experimental findings, concerning the critical concentration above which the homogeneous alloys cannot be formed at room temperature. Our model also predicts the observed fact that at lower temperature the critical concentration increases. We also performed single site effective-field calculations of the electronic structure, which further support our hypothesis.Comment: 12 pages, 1 table, 16 figure