Construction of irreducible polynomials through rational transformations

Let $\mathbb F_q$ be the finite field with $q$ elements, where $q$ is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over $\mathbb F_q$ of high degree using rational transformations. In particular, given a divisor $D>2$ of $q+1$ and an irreducible polynomial $f\in \mathbb F_{q}[x]$ of degree $n$ such that $n$ is even or $D\not \equiv 2\pmod 4$, we show how to obtain from $f$ a sequence $\{f_i\}_{i\ge 0}$ of irreducible polynomials over $\mathbb F_q$ with $\mathrm{deg}(f_i)=n\cdot D^{i}$.Comment: 21 pages; comments are welcome

Accountability and corruption : political institutions matter

Using a cross-country panel, Lederman, Loayza, and Soares examine the determinants of corruption, paying particular attention to political institutions that increase political accountability. Previous empirical studies have not analyzed the role of political institutions, even though both the political science and the theoretical economics literature have indicated their importance in determining corruption. The main theoretical hypothesis guiding the authors?empirical investigation is that political institutions affect corruption through two channels: political accountability and the structure of the provision of public goods. The results suggest that political institutions are extremely important in determining the prevalence of corruption: democracy, parliamentary systems, political stability, and freedom of the press are all associated with lower corruption. In addition, the authors show that common findings of the earlier empirical literature on the determinants of corruption?elated to openness and legal tradition?o not hold once political variables are taken into account.Corruption&Anitcorruption Law,Decentralization,Pharmaceuticals&Pharmacoeconomics,Public Sector Corruption&Anticorruption Measures,Poverty Monitoring&Analysis,National Governance,Governance Indicators,Pharmaceuticals&Pharmacoeconomics,Corruption&Anitcorruption Law,Public Sector Corruption&Anticorruption Measures

Introducing Quantified Cuts in Logic with Equality

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method generating lemmas of the form $\forall x_1\ldots\forall x_n.A$. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to the TSTP proof database. It is shown that the extension of the method to handle equality and quantifier-blocks leads to a substantial improvement of the old algorithm

Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is constrained to a (not necessarily bounded) convex domain by a local time on the boundary. These equations include the subclass of reflected self-stabilizing diffusions that drift towards their mean via a convolution of the solution law with a stabilizing potential. Firstly, we establish existence and uniqueness results for this class and address the propagation of chaos. We work with a broad class of coefficients, including drift terms that are locally Lipschitz in spatial and measure variables. However, we do not rely on the boundedness of the domain or the coefficients to account for these non-linearities and instead use the self-stabilizing properties. We prove a Freidlin-Wentzell type Large Deviations Principle and an Eyring-Kramer's law for the exit-time from subdomains contained in the interior of the reflecting domain.Comment: 41 page

Sintomas neuropsiquiátricos e declínio cognitivo

Introdução: Os sintomas Neuropsiquiátricos (SNP) são manifestações comuns que afectam quase todas as pessoas que sofrem da doença de Alzheimer. O objectivo principal deste trabalho passa por relatar a prevalência dos diferentes SNP, utilizando uma prova especifica para esse efeito, o Neuropsychiatric Inventory – Questionnaire (NPI-Q), numa amostra de idosos recolhida junto da população geral, em instituições que recebem idosos (em diferentes valências) do Concelho de Coimbra. É igualmente nosso objectivo verificar se existe uma associação significativa entre o declínio cognitivo, avaliado através de uma prova de rastreio cognitivo, o Mini Mental State Examination (MMSE) junto do idoso e a gravidade (atribuída) dos SNP e o grau de perturbação causado pelos mesmos aos cuidadores informais dos idosos. Ao explorar esta associação e eventual papel preditivo da gravidade e grau de perturbação dos SNP para o declínio cognitivo, consideramos potenciais associações entre os SNP e o declínio e diferentes variáveis sociodemográficas, a sintomatologia depressiva e ansiosa. Importará controlar estas variáveis nas análises preditivas, no caso de encontrarmos associações estatisticamente significativas. Pretendemos, igualmente, controlar o eventual papel da simulação (teste Rey-15 Item Test/Rey 15), caso se encontre presente neste estudo. Metodologia: A amostra incluiu 52 idosos (média de idades, M = 80,1; Desvio-padrão, DP = 6,89; variação = 66 - 93) sob resposta social em diferentes instituições do Concelho de Coimbra que aceitaram responder voluntariamente (ou cujos familiares/cuidadores concederam o respectivo consentimento) a uma bateria de testes (incluindo algumas questões sociodemográficas, o MMSE, o Geriatric Anxiety Inventory/GAI a Geriatric Depression Scale/GDS, o Rey-15 e o NPI-Q. Resultados: A maioria dos sujeitos não sofria de declínio cognitivo (65%; n = 34), verificando-se, em oposição a outros estudos, que as percentagens de sujeitos com SNP eram inferiores. Os SNP mais prevalentes foram a Ansiedade (34,6%; n = 18) e a Irritabilidade (34,6%; n = 18). Verificou-se não existirem associações estatisticamente significativas entre a gravidade dos sintomas (NPI-Q) e grau de perturbação dos mesmos (NPI-Q), de acordo com os cuidadores informais, e a presença de declínio cognitivo nos idosos (MMSE). Também não se verificaram associações estatisticamente significativas entre a gravidade dos sintomas (NPI-Q) e grau de perturbação dos mesmos (NPI-Q), de acordo com os cuidadores informais e as variáveis sociodemográficas. Não foram encontradas associações entre a sintomatologia depressiva e ansiosa avaliada junto dos idosos e a gravidade dos SNP e grau de perturbação associado de acordo com os seus cuidadores informais. Conclusão/Discussão: Ao contrário do que poderia ser esperado, não se encontrou uma associação entre o declínio cognitivo, avaliado junto dos idosos, e a presença de SNP de acordo com os cuidadores informais. Vários motivos se podem associar a este resultado não significativo, como o facto da nossa amostra apresentar uma percentagem reduzida de idosos com declínio cognitivo, o tamanho reduzido da nossa amostra ou até mesmo o facto dos SNP terem sido avaliados por auxiliares da instituição que podem não possuir a formação necessária para os avaliar. Um dado igualmente relevante foi a ausência de associações significativas entre as medidas dos SNP e a sintomatologia depressiva/ansiosa e algumas variáveis sociodemográficas. Importa, em estudos futuros, com uma amostra maior, verificar se este padrão de resultados se mantém e, eventualmente, comparar os resultados obtidos depois do NPI-Q ser respondido por clínicos, familiares e auxiliares dos idosos. / Introduction: Neuropsychiatric symptoms (NPS) are common manifestations that afflict almost all Alzheimer’s disease patients. The main goal of this work was to present the prevalence of different NPS, using a specific test, the Neuropsychiatric Inventory – Questionnaire (NPI-Q), in a sample of elderly from the general population, under social answer in different institutions from Coimbra Council. Moreover, we want to verify if there is a significant association between the cognitive decline, assessed with a cognitive screening test, the Mini Mental State Examination (MMSE) administered to the elderly and the (attributed) severity of the NPS and distress caused by the symptoms, assessed by the informal caregiver of the elderly. While exploring this association and the potential predictive role of the severity and distress caused by the NPS to the cognitive decline, we also considered the potential associations between the NPS and the decline, different sociodemographic variables and depressive/anxious symptoms. It will be important to control these variables, if significant associations are found. We also wish to control the potential role of simulation (assessed by the Rey-15 Item Test/Rey 15), if we found that it is present in our sample. Methodology: Our sample comprises 52 elderly (mean age, M = 80,1; Standard deviation, SD = 6,89; range = 66 - 93) under social answer in different institutions from Coimbra Council who accepted to fill in voluntarily a test battery or whose relatives/caregivers gave consent, including some sociodemographic questions, the MMSE, the Geriatric Anxiety Inventory/GAI, the Geriatric Depression Scale/GDS, the Rey-15 and NPI-Q. Results: It was possible to verify that most of the subjects did not suffer from cognitive decline (65%; n = 34). We also verified, in opposition to other studies, that the percentage of elderly with NPS was lower, with the most prevalent being anxiety (34,6%; n = 18) and irritability (34,6%; n = 18). There were no statistically significant associations between symptoms severity (NPI-Q) and distress caused by them (NPI-Q), according to the informal caregivers and the presence of cognitive decline in the elderly (MMSE). Moreover, there were no significant associations between symptoms severity and associated distress (NPI-Q) and the sociodemographic variables of the study. There were no associations between depressive and anxious symptoms in the elderly and the symptoms severity and associated distress (NPI-Q) assessed by the informal caregivers. Conclusion/Discussion: Contrary to what would be expected, we did not find an association between cognitive decline in the elderly and the presence of NPS according to the informal caregivers. Several reasons can explain this non significant result, like the fact that our sample presents a low percentage of elderly with cognitive decline, the reduced sample size our even the fact that NPS were assessed by the assistant workers of the institutions that might no possess the necessary knowledge to assess them. Other relevant result was the absence of significant associations between the NPS measures and depressive/anxious symptoms and some demographic variables. In future studies, with a larger sample it will be important to verify if these patterns of results are maintained and, eventually, it would be interesting to compare the results found after the NPI-Q has been answered by clinicians, family members and institution’s assistants

A História da Escola Naval (1845-1910) Formação dos Oficiais de Marinha numa Época de Transição

A presente Dissertação de Mestrado, subordinada ao tema “A História da Escola Naval (1845-1910): Formação dos Oficiais de Marinha numa Época de Transição” tem como objetivo central responder à questão: “Como evoluiu o ensino ministrado na Escola Naval desde a sua criação até ao ano em que terminou o período monárquico?”. Para tal procedeu-se à análise do contexto da época que originou a necessidade da criação de um estabelecimento de ensino capaz de garantir a formação adequada aos futuros Oficiais da Armada portuguesa. De facto, após a criação da Escola Naval e em plena segunda metade do século XIX, ocorreram diversos acontecimentos de elevada importância que levaram a cabo um conjunto de reorganizações ao nível do ensino naval. Para tal contribuíram a evolução da tática e guerra naval e o desenvolvimento industrial e científico Europeu. Este último traduziu-se na evolução dos meios de propulsão (da vela ao vapor); o crescente desenvolvimento da artilharia, relacionado com a utilização do aço na construção dos navios (da madeira ao aço); e o aparecimento de torpedos, como arma naval inovadora. Este conjunto de acontecimentos foi tido em conta e adaptado ao ensino ministrado, sendo que estas inovações requeriam uma adaptação do plano de estudos dos alunos da Escola Naval. Para alcançar estes objetivos foi utilizada uma metodologia baseada na análise documental, tentando, sempre que possível, basear a informação apresentada em documentos diretamente relacionados com o tema. A fim de apresentar os resultados alcançados estruturou-se o trabalho em cinco capítulos: “Introdução”, “Ensino e Educação Superior no início do século XIX”, “A Escola Naval”, “Reformas da Escola Naval” e “Conclusão”. Após o término da investigação concluiu-se que as restruturações sofridas ao nível do ensino proporcionaram aos alunos, que concluíam o curso da Escola Naval, uma formação, cultura e saberes para se tornarem aptos a desempenhar as exigentes funções de Oficial de uma Armada em desenvolvimento.The purpose of the following Dissertation, entitled “The History of Naval School (1845-1910): Training of Navy Officers in a Season of Transition” was aimed at answering the question: “How has education developed at Naval School from its creation until the end of the monarchic period?”. For this, we proceeded to analyse the whole context of the era that gave rise to the need to create an educational institution capable of ensuring adequate training for future officers of Portuguese Navy. In fact, after the creation of the Naval School and in full second half of the nineteenth century, there were several events of high importance that carried out a series of reorganizations at the level of naval education. This trend evolution of tactics and naval warfare and European scientific and industrial development. The latter resulted in the evolution of the means of propulsion (sail to steam), the increasing development of artillery, related to the use of steel in ships construction (wood to steel), and the appearance of torpedoes, an innovative naval gun. This set of events was taken into account and adapted to the instruction given to students because these innovations requiring adaptation of the curriculum of the students of the Naval School. To achieve these goals it was used a methodology based on documentary analysis, trying wherever possible, to use information presented in documents directly related to the topic. In order to present the results the present dissertation was structured in five chapters: "Introduction", "Education and Higher Education in the early nineteenth century", "The Naval School", "Naval School Reforms" and "Conclusion". Upon completion of this investigation it was concluded that the restructuring suffered in the entire education level provided to students a good training, culture and knowledge to become able to perform the demanding tasks of a Navy in development