The complexity of quantified constraints using the algebraic formulation

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Fredholm conditions on non-compact manifolds: theory and examples

We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user's guide" to Fredholm conditions on particular classes of manifolds including asymptotically hyperbolic manifolds, asymptotically Euclidean (or conic) manifolds, and manifolds with poly-cylindrical ends. The reader interested in applications should be able read right away the results related to those examples, beginning with Section 5. Our general, theoretical results are that an operator adapted to the geometry is Fredholm if, and only if, it is elliptic and all its limit operators, in a sense to be made precise, are invertible. Central to our theoretical results is the concept of a Fredholm groupoid, which is the class of groupoids for which this characterization of the Fredholm condition is valid. We use the notions of exhaustive and strictly spectral families of representations to obtain a general characterization of Fredholm groupoids. In particular, we introduce the class of the so-called groupoids with Exel's property as the groupoids for which the regular representations are exhaustive. We show that the class of "stratified submersion groupoids" has Exel's property, where stratified submersion groupoids are defined by glueing fibered pull-backs of bundles of Lie groups. We prove that a stratified submersion groupoid is Fredholm whenever its isotropy groups are amenable. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. This fact is explored to yield Fredholm conditions not only in the above mentioned classes, but also on manifolds that are obtained by desingularization or by blow-up of singular sets

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

Revisão e verificação das propriedades psicométricas da dimensão instabilidade de humor do inventário dimensional clínico da personalidade

El presente estudio tuvo como objetivo examinar la dimensión Inestabilidad del Humor del Inventario Dimensional Clínico de la Personalidad (IDCP), y la investigación de sus propiedades psicométricas. Para ello se desarrollaron nuevos ítems que fueron aplicados a 230 participantes, con edades comprendidas entre 18 y 63 años (M=23,0, DP=9,44), la mayoría de sexo femenino (76,4%). Todos los participantes respondieron el IDCP, la versión brasileña de la versión revisada del Inventario de Personalidad NEO, y la versión brasileña del Inventario de Personalidad para el DSM-5 (PID-5). Como resultado, 306 nuevos ítems fueron desarrollados con base en cuatro fuentes de referencia, y seleccionados mediante análisis de contenido, y 27 ítems que conformaron la versión final para la aplicación de la dimensión. Después de recoger los datos y de realizar el análisis estadístico, la dimensión analizada constaba de tres factores, además de una puntuación total. Los coeficientes de consistencia interna fueron adecuados e iguales a 0,85 para el conjunto final de 16 ítems con un rango de variación entre 0,78 y 0,81 por cada factor. De otra parte, se encontraron las intracorrelaciones esperadas, así como correlaciones coherentes con los instrumentos utilizados. Los datos permiten inferir evidencias de validez de la escala revisada, así como una demostración satisfactoria de la consistencia interna.O presente estudo teve como objetivo revisar a dimensão Instabilidade de Humor do Inventário Dimensional Clínico da Personalidade (IDCP), investigando suas propriedades psicométricasPara tanto, novos itens foram desenvolvidos, para então serem aplicados. Participaram 230 sujeitos, com idade variando entre 18 e 63 anos (M=23,0; DP=9,44), sendo a maior parte do sexo feminino (76,4%). Todos os participantes responderam o IDCP, a versão brasileira do Inventário de Personalidade NEO-PI Revisado e a versão brasileira do Personality Inventory for DSM-5 (PID-5). Como resultado, foram desenvolvidos 306 novos itens com base em quatro fontes de referencia na área e selecionados, por meio de análise de conteúdo, 27 para compor a versão final de aplicação da dimensão. Após a coleta de dados e análises estatísticas, a dimensão revisada ficou composta por três fatores, além de um escore total. Os coeficientes de consistência interna mostraram-se adequados sendo igual a 0,85 para o conjunto final de 16 itens e variando de 0,78 e 0,81 por fator. Além disso, foram encontradas intracorrelações esperadas, bem como correlações coerentes com os instrumentos aplicados. Os dados permitem inferir evidências de validade para a dimensão revisada, além de demonstrar índices satisfatórios de consistência interna.The present study aimed to review the Mood Instability dimension of the Dimensional Clinical Personality Inventory (DCPI) and to examine its psychometric properties. To this end, new items were developed that were applied to 230 subjects, aged between 18 and 63 years (M = 23.0, SD = 9.44), with a majority of females (76.4%). All participants answered the DCPI, the Brazilian version of the NEO Personality Inventory-Revised and the Brazilian version of the Personality Inventory for DSM-5 (PID-5). As a result, 306 new items were developed based on four sources of reference in the area and selected by means of content analysis and 27 items to compose the final version of the dimension to be applied. After data collection and statistical analysis, the reviewed dimension was composed of three factors plus a total score. The internal consistency coefficients were adequate and equal to .85 for the final set of 16 items, with a variation range between .78 and .81 per factor. Moreover, the expected intracorrelations were found, as well as consistent correlations with the instruments used. Data allow inferring validity evidence for the scale reviewed, as well as demonstrating satisfactory internal consistency

On Maltsev Digraphs

This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio

Diabetes mellitus como mau preditor de prognóstico na insuficiência cardíaca avançada

Trabalho final de mestrado integrado em Medicina àrea científica de Cardiologia apresentado á Faculdade de Medicina da Universidade de CoimbraIntrodução: Insuficiência Cardíaca e Diabetes mellitus são duas entidades clínicas crónicas, interdependentes que coexistem e condicionam aumento significativo das taxas de mortalidade. Com o aumento da incidência destas duas patologias na sociedade atual, importa determinar os impactos e mecanismos que as interligam. Mas, o impacto da Diabetes em doentes hospitalizados por Insuficiência Cardíaca e/ou, em casos de Insuficiência Cardíaca Avançada, permanece ainda com contornos mal definidos e controversos, nomeadamente, quanto à influência prognóstica da Diabetes mellitus na sobrevivência destes doentes. Objetivo: Avaliar a Diabetes mellitus como preditor do prognóstico de doentes internados por Insuficiência Cardíaca Avançada. Metodologia: Realizou-se um estudo retrospetivo a partir de uma amostra retida de 339 doentes admitidos consecutivamente, entre janeiro de 2003 e junho de 2006, na unidade de tratamento de Insuficiência Cardíaca Avançada do Centro Hospitalar Universitário de Coimbra. Na análise, consideraram-se dois grupos contrastantes segundo a ausência (grupo A) ou evidência clínica de Diabetes mellitus (grupo B). Na análise de sobrevivência, o endpoint primário foi definido com base na mortalidade ou na ocorrência de efeitos adversos major, nomeadamente necessidade de transplante ou readmissão hospitalar, num tempo de seguimento clínico máximo de 6,3 anos (range 0-2306 dias, mediana 395,5 dias). Resultados: Da totalidade da amostra retida, 32,2% (n=109) dos elementos eram diabéticos. Este grupo incluiu maior número de indivíduos do sexo masculino [76,1 (n=83) versus 68,7% (n=158); p=0,099)] e de idosos (63,5±11,2 versus 56,6±15,4 anos, p<0,001). O diagnóstico de admissão mais frequente foi a Insuficiência Cardíaca Diabetes mellitus como mau preditor de prognóstico na Insuficiência Cardíaca Avançada? 3 crónica agudizada (89,0%, n=97) e as comorbilidades mais prevalentes: anemia (30,2%, n=26), doença tiroideia (20,9%, n=18), doença renal (48,9%, n=45), dislipidémia (60,7%, n=54), tabagismo (33.0% n=27) e doença arterial periférica (20,8%, n=16). Relativamente aos dados hemodinâmicos, os doentes do grupo B apresentam valores de tensão arterial sistólica na admissão mais elevados (117,6±24,4 versus 110,7±22,2 mmHg, p=0,017). Os valores de glicémia foram também significativamente mais elevados (193,9±92,9 versus 121,7±45,1mg/dL, p<0,001). A mortalidade intra-hospitalar foi de 7,8% no grupo A e 5,5% no grupo B, não tendo esta diferença significado estatístico. No follow-up, também não se registaram diferenças estatisticamente significativas relativamente à taxa de mortalidade (22,9 versus 31,6, p=0,098). A sobrevivência, expressa sob a forma de curvas Kaplan-Meyer, é pior (30,6%) no Grupo B a partir dos 4,3 anos de follow-up. Aos 6 meses e ao fim de um ano a sobrevivência é, para o Grupo A e B de 62,5 versus 67,9% e 48,8 versus 56,2%, respetivamente. Conclusões: Neste estudo, a Diabetes mellitus não se associou a um pior prognóstico em doentes com Insuficiência Cardíaca AvançadaTitle: Is Diabetes mellitus a poor predictor of prognosis in Advanced Heart Failure? Introduction: Heart Failure and Diabetes mellitus are two chronic and interdependent clinical conditions that coexist and commonly cause significant increase in mortality rates. With the increasing incidence of these two diseases in our society nowadays, it reveals to be important to determine the impacts and mechanisms that interrelate. But the impact of Diabetes in patients hospitalized for heart failure and / or in cases of Advanced Heart Failure, still remains ill-defined and controversial, particularly regarding the prognostic influence of Diabetes mellitus on survival of these patients. Objective: To evaluate the Diabetes mellitus as a predictor of prognosis of patients hospitalized for Advanced Heart Failure. Methods: We conducted a retrospective study from a retained sample of 339 patients admitted consecutively between January 2003 and June 2006 on the treatment unit of Advanced Heart Failure of the Centro Hospitalar Universitário de Coimbra. In the analysis, we considered two contrasting groups according to absence (group A) or clinical evidence of Diabetes mellitus (group B). In survival analysis, the primary endpoint was defined based on mortality or the occurrence of major adverse event, including the need for transplantation or hospital readmission in a clinical follow-up time of 6.3 years (range 0-2306 days, median 395.5 days). Results: Of the total sample, 32.2% (n=109) of the elements were diabetic. This group included more males [76.1 (n=83) versus 68.7% (n=158), p=0.099)] and elderly (63.5±11.2 versus 56.6±15.4 years, p<0.001). The most common admission diagnosis was chronic decompensated Heart Failure (89.0%, n=97) and the most prevalent comorbidities: anemia (30.2%, n=26), thyroid disease (20.9%, n=18), kidney disease Diabetes mellitus como mau preditor de prognóstico na Insuficiência Cardíaca Avançada? 5 (48.9%, n=45), dyslipidemia (60.7%, n=54), smoking (33.0% n=27) and peripheral arterial disease (20.8%, n=16). For hemodynamic data, patients in group B have values of systolic blood pressure higher at admission (117.6±24.4 versus 110.7±22.2 mmHg, p=0.017). The blood glucose values were also significantly higher (193.9±92.9 versus 121.7±45.1 mg/dL, p<0.001). The in-hospital mortality was 7.8% in group A and 5.5% in group B, and this difference is not statistically significant. At follow-up, also there were no statistically significant differences regarding the mortality rate (22.9 versus 31.6, p=0.098). Survival, expressed in the form of Kaplan-Meyer curves, it is worse (30.6%) in Group B from 4.3 years of follow-up. At 6 months and one year survival is in Group A and B 62.5 and 48.8 versus 67.9% vs. 56.2%, respectively. Conclusions: In this study, Diabetes mellitus was not associated with a worse prognosis in patients with Advanced Heart Failure