Asymptotics for generating functions of the Fuss-Catalan numbers

We consider a certain class of polynomials with coefficients in Z_M, all of which admit a unique zero. We prove that the zero of each of those can be given by a (multiple) sum involving the coefficients and a vectorial generalization of the Fuss-Catalan numbers. We also consider the sequence of the partial sums of the generating function of the d -Fuss- Catalan numbers. Using the holonomy of this sequence, we study its asymptotic behaviour. The main difference from the known case d = 2 is, in that one, we have a “closed” expression for the generating function.The research of the authors were partially financed by Portuguese Funds through Fundação para a Ciência e a Tecnologia within the Projects UIDB/00013/2020 and UIDP/00013/2020

A two obstacles coupled problem

We consider a system of an evolutionary variational inequality of two obstacles type, depending on the temperature, coupled with the heat equation. We prove existence of solution of this system and we present examples that motivated this work. In particular, with additional assumptions on the data, we prove that solutions of this problem are also solutions of a similar problem where the convex set is of gradient constraint type (that depends on the temperature), improving a previous result.This research was partially supported by CMAT - Centro de Matemática da Universidade do Minho, financed by the Strategic Project PEst-OE/MAT/UI0013/2014

Convergence of convex sets with gradient constraint

Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação (POCTI), União Europeia (UE). Fundo Europeu de Desenvolvimento Regional - (Portugal/FEDER-EU)

A diffusion problem with gradient constraint depending on the temperature

We consider a system of a variational inequality with gradient constraint depending on the temperature, coupled with the heat equation. We prove existence of solution of this system by approximating it by a system of equations and using a fixed point argument.Fundação para a Ciência e a Tecnologia (FCT) - Pluriannual Funding Program, projecto UT-Austin/MAT/0035/2008.Centro de Matemática da Universidade do Minh

Reversible cerebral vasoconstriction syndrome – A narrative revision of the literature

AbstractReversible Cerebral Vasoconstriction Syndrome (RCVS) is a not very well known clinical-imaging entity; it is characterized by thunderclap headache, which mimics an aneurysmal subarachnoid haemorrhage, and a diffuse and segmental constriction of cerebral arteries, that resolves spontaneously within 3 months. The pathophysiology remains unknown. The female gender is the more affected and more than half of cases occur in the puerperium or after exposure to vasoactive substances. Typically, RCVS is self-limited and has a benign course, although it may have more serious complications with permanent neurologic sequelae and death. Treatment is predominantly supportive and directed to the symptoms

Towards an interpretable advertisement click prediction

In the new era of computational advertising, Click prediction models are used to anticipate a click response and guide marketers’ decisions about whom to target and how to personalize. The more prediction tasks achieve impressive performances, the more trust is put in black models to make important decisions in a business domain. Due to the complexity and lack of transparency of the models, posterior explanation methods are needed to identify features’ contributions that envision a global explanation of the model. This thesis develops an advertisement Click prediction using a supervised machine learning framework and uses the KernelSHAP method to provide feature importance insights on the predictions made by the model. The thesis aims to answer: 1) how can marketers integrate Click prediction in their businesses; 2) which are the most impactful features for a click response; 3) how advertisement categories differ from an overall model. For that purpose, is used a publicly available ADS dataset (2016) to train a neural network. The results showed the overall model performance is not substantially different from a segmented categories performance. The output of KernelSHAP showed that even though the visual content is impactful for the likelihood of a Click for all models, each category has its own feature importance pattern influenced by the product the category promotes. The performance metrics presented a high ratio of true negative to true positive due to a class imbalance problem. To mitigate the cost of misclassification is suggested an individual analysis that better fit target business model.Na era da publicidade computacional, os modelos de previsão Clique são utilizados para antecipar uma resposta de clique e guiar decisões­chave como a quem publicitar. Quanto mais preciso é o desempenho, mais confiança é depositada em modelos para tomar decisões importantes num domínio empresarial. Devido à complexidade e falta de transparência dos modelos, são necessários métodos de explicação posteriores para identificar como cada atributo contribuiu para a previsão. Esta tese desenvolve um modelo aprendizagem automática que prevê o Clique em anúncios e utiliza o método KernelSHAP que explica quais os atributos mais relevantes à previsão. A tese tem como objetivo responder a: 1) como podem os profissionais de publicidade integrar a previsão de clique nos seus negócios; 2) quais são as características mais impactantes para obter um Clique; 3) como as categorias de publicidade diferem de um modelo global. Para esse efeito, é utilizado um conjunto de dados publicamente disponível ­ ADS(2016)­ para treinar uma rede neural. Os resultados mostraram que o desempenho global do modelo não é substancialmente diferente do desempenho segmentado de categorias. Os resultados do KernelSHAP mostraram que, embora o conteúdo visual seja impactante para a probabilidade de um Clique em todos os modelos, cada categoria tem o seu próprio padrão de atributos mais importantes para a classificação. Estes são influenciados pelo produto que a categoria promove. As métricas de avaliação apresentam uma discrepância entre previsões corretas entre classes. Para mitigar o custo de uma classificação errada, sugere­se uma análise individual que melhor se ajuste ao modelo de negócio

Intermolecular Covalent Interactions:A Quantitative Molecular Orbital Perspective

This thesis reports detailed quantum chemical investigations on the nature and strength of intermolecular interactions in DmZ•••A– complexes, mediated via atoms Z of groups 15–17 in the periodic table, based on quantitative Kohn-Sham molecular orbital theory. In the first stage, accurate ab initio benchmark and density functional theory (DFT) validation studies have been done. For each type of bond, pnictogen bond (PnB) and chalcogen bond (ChB), and, for comparison, halogen bond (XB) and hydrogen bonds (HB), accurate trends in bond length and strength are computed, based on a consistent set of data from our validated relativistic DFT approach. The main purpose is to provide a unified picture of chalcogen bonds and pnictogen bonds, together with hydrogen bonds and halogen bonds. The analyses herein reveal that the intramolecular interactions have a strong covalent component and are certainly not dominantly electrostatic in nature, as it is incorrectly suggested by the sigma-hole model whose weaknesses are consistently exposed. The findings in this thesis work thus suggest that the commonly accepted designation "Non-Covalent Interactions (NCI)" for the pertinent intermolecular interactions does not properly cover their nature and it is proposed to replace this designation with the more appropriate "Intermolecular Covalent Interactions (ICI)"

Biopolymers valorization using biocompatible ionic liquids for biomedical applications

In the last decades, biopolymers received much attention, especially due to its inherent properties, such as biodegradability, biocompatibility and biological properties. However, they showed some limitations in a wide range of applications, mainly in the biomedical field, due to their low solubility in water and in biocompatible organic solvents. To overcome this, ionic liquids (ILs) as low-melting organic salts appeared as an alternative dissolution agent, mainly due to their peculiar properties, which can be tuned according to the adequate selection of the cation and anion. In this context, this thesis aims the development of polymeric structures via biopolymer dissolution using innovative biocompatible ILs. ILs containing pharmaceutically acceptable drugs – namely lidocaine, procaine, and ibuprofen with anaesthetic and anti-inflammatory effects, respectively – were synthesized to enhance the therapeutic properties of the produced biopolymeric structures. This way, the IL will have a double role, it will act as a solvent for the biopolymer dissolution as well as a therapeutic agent, for example for topical delivery of anaesthetic and anti-inflammatory drugs. Different protic ionic liquids, which are ILs that are not fully ionized, have been successfully synthetized by acid-base reactions, using active pharmaceutical drugs as a cation (lidocaine or procaine) combined with carboxylate anions, namely acetate, propionate, hexanoate or ibuprofenate (anti-inflammatory properties). They have been characterized by spectroscopic techniques (1H NMR, FTIR) to assess their structure, thermal analysis (TGA, DSC) to evaluate their thermal stability, and viscosity studies. The prepared ILs have been tested as dissolution agents for different biopolymers, namely chitin-glucan complex (CGC) and chitosan. In general, the prepared ILs containing acetate or propionate anions seemed to be capable to dissolve the CGC biopolymer (1 wt. %). The obtained polymeric structures have been characterized by adequate methods to study their morphology (SEM), composition (FTIR), thermal (TGA, DSC) and mechanical properties depending on their form (films or gels). FTIR studies suggested the obtained films were composed mainly by lidocaine free base and the obtained gel was composed mainly by procaine free base. In general, all prepared polymeric structures showed lower thermal stability than the CGC biopolymer. The obtained gel exhibited a viscous behaviour, whereas films exhibited hydrophilic surface and, poor mechanical properties which limits their potential for application

An architecture for an effective usage of data mining in business intelligence systems

Business Intelligence (BI) is one emergent area of the Decision Support Systems (DSS) discipline. Over the last years, the evolution in this area has been considerable. Similarly, in the last years, there has been a huge growth and consolidation of the Data Mining (DM) field. DM is being used with success in BI systems, but a truly DM integration with BI is lacking. Therefore, a lack of an effective usage of DM in BI can be found in some BI systems. An architecture that pretends to conduct to an effective usage of DM in BI is presented

Análise do efeito da fadiga muscular no senso de posição articular do joelho

Projeto de Graduação apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de Licenciada em FisioterapiaObjetivo: Determinar o efeito da fadiga muscular no Senso de Posição Articular (SPA) do joelho e comparar acuidade propriocetiva entre amplitudes de teste, membro preferido e não-preferido e entre géneros. Métodos: Participaram neste estudo 33 adultos saudáveis. A fadiga foi induzida através do levantar e sentar de uma cadeira. O SPA foi avaliado pelo método de reposicionamento ativo, para as posições de 20º e 45º de flexão, através de um sistema de centrais inerciais. Resultados: O erro de reposicionamento aumentou com a fadiga aos 45º no membro preferido (p=0.030). O erro de reposicionamento é maior aos 45º do que aos 20º, com diferenças significativas no membro não-preferido (p=0.018) antes da fadiga e no membro preferido (p=0.020) depois da fadiga. A dominância não influenciou o SPA em repouso, mas depois da fadiga o membro preferido apresentou erros de posicionamento superiores na amplitude de 45º (p=0.039). Não existem diferenças relacionadas com o género (p>0.05). Conclusão: A fadiga afeta o SPA. O erro de reposicionamento é maior em amplitudes intermédias do que em amplitudes extremas. O membro preferido é mais afetado pela fadiga e não existem diferenças no SPA inerentes ao género.Aim: To determine the effect of muscle fatigue on knee joint position sense (JPS) and compare the proprioceptive acuity between test amplitudes, dominant and non-dominant limb and genders. Methods: The sample consisted of 33 healthy subjects. Fatigue was induced by a sit to stand task. JPS was evaluated by active repositioning method, to the ranges of 20º and 45º of flexion, using a central inertial system. Results: Reposition error increased with fatigue at the range of 45º in the dominant limb (p=0.030). The reposition error is higher at 45º than at 20º, with significant differences in the non-dominant limb before fatigue (p=0.018) and in the dominant limb (p=0.020) after fatigue. Dominance did not influenced JPS at rest, but after fatigue the dominant limb showed higher reposition errors at the range of 45º (p=0.034). There are no differences related to gender (p>0.05). Conclusion: Muscle fatigue affects JPS. The reposition error is higher at intermediate ranges than in limit ranges. Fatigue affects mainly the dominant limb and there are no differences in the JPS between gender.N/