Iteration of quadratic maps on matrix algebras

We study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics

Prolonged drug release from hot melt extruded solid dosage forms for oral application

Trabalho Final de Mestrado Integrado, Ciências Farmacêuticas, 2020, Universidade de Lisboa, Faculdade de Farmácia.A via de administração oral é a mais conveniente e utilizada para a administração de diversos fármacos. É ainda a via preferencial dos pacientes devido às suas numerosas vantagens. Contudo, a baixa biodisponibilidade demonstrada (que é altamente dependente da solubilidade em água e permeabilidade intestinal) consiste na maior dificuldade relativamente à formulação de formas farmacêuticas para aplicação oral. Isto, aliado ao facto de aproximadamente 90% das substâncias ativas nos primeiros estádios de desenvolvimento estarem incluídas nas classes II e IV do Sistema de Classificação Biofarmacêutico (significando que são fracamente solúveis em água e apresentam ou elevada ou reduzida permeabilidade), torna essencial criar ou melhorar métodos capazes de contrariar esta tendência. Como exemplo, cita-se a preparação de dispersões sólidas amorfas. Estas consistem num sistema no qual uma ou mais substâncias ativas, normalmente hidrofóbicas, estão dispersas, preferencialmente a nível molecular, numa matriz polimérica amorfa inerte, comummente hidrofílica, no estado sólido. As dispersões sólidas aumentam a área superficial disponível para a dissolução, aumentando ainda a molhabilidade das partículas e porosidade, permitindo o aumento da biodisponibilidade do fármaco. Adicionalmente, um outro desafio é a preparação de formulações de libertação prolongada de substâncias ativas fracamente solúveis em água. Para tal, pode proceder-se à incorporação da substância ativa num polímero solúvel ao qual poderão ser adicionados outros excipientes de modo a controlar a libertação. De entre as técnicas de preparação das dispersões sólidas, inclui-se a extrusão por fusão. Esta técnica permite a incorporação de substâncias ativas num transportador polimérico termoplástico, podendo ainda conter outros excipientes. Após a extrusão, obtém-se uma solução ou dispersão, conduzindo à conversão dos elementos iniciais num produto amorfo. Este produto é, então, expelido através da fieira (“die”) de modo a produzir um extrudido de densidade e forma uniformes. Assim, aumenta-se o perfil de dissolução da substância ativa com baixa solubilidade aquosa e portanto, a sua biodisponibilidade. Resumidamente, o presente estudo focar-se-á nos polímeros empregues na formulação de dispersões sólidas de libertação prolongada para administração oral, através da extrusão por fusão.The oral route consists in the most convenient and extensively employed route for the administration of various drugs. Additionally, it is patients first choice owing to its numerous advantages. Nevertheless, active pharmaceutical ingredients poor bioavailability (which is highly dependent on water solubility and intestinal permeability) lies as the main hurdle concerning the design of oral solid dosage forms. This, allied with the fact that approximately 90% of drugs in early-stages development demonstrate to have low aqueous solubility associated with either high or low permeability (meaning they are included in BCS classes II or IV, respectively), makes it imperative to create or improve methods capable of facing this tendency. One of those techniques is the preparation of amorphous solid dispersions (SDs). An amorphous SD occurs when one or more active ingredients, usually hydrophobic, are dispersed in an amorphous inert polymer carrier, commonly hydrophilic, at solid state and preferably at a molecular level. SDs improve the effective surface area available for dissolution, usually possess particles with high wettability and porosity thus, allowing the enhancement of drugs bioavailability. Additionally, other challenge consists in the formulation of poorly aqueous soluble drugs for prolonged drug delivery. In order to solve this, the API can be incorporated in a soluble polymer to which will be added other excipients to control the drug release, which can also be accomplished by the preparation of SDs. Regarding their manufacturing process, SDs can be formulated by a great number of techniques, including Hot-Melt Extrusion (HME). HME allows the embedment of active ingredients in a thermoplastic polymeric carrier, possibly containing other manufacturing excipients. After processing, it is obtained a molecular level mixing solution or dispersion, leading to the conversion of the initial elements into an amorphous product, which will be pressured through a die to form an extrudate of uniform shape and density, thus enhancing the dissolution of the initial drug and therefore, its bioavailability. Briefly, the present study will emphasize polymers applied in the formulation of prolonged drug release solid dispersions for oral administration, employing HME.Com o patrocínio da Faculté de Pharmacie de Lille

Fast-Forward Video Based on Semantic Extraction

Thanks to the low operational cost and large storage capacity of smartphones and wearable devices, people are recording many hours of daily activities, sport actions and home videos. These videos, also known as egocentric videos, are generally long-running streams with unedited content, which make them boring and visually unpalatable, bringing up the challenge to make egocentric videos more appealing. In this work we propose a novel methodology to compose the new fast-forward video by selecting frames based on semantic information extracted from images. The experiments show that our approach outperforms the state-of-the-art as far as semantic information is concerned and that it is also able to produce videos that are more pleasant to be watched.Comment: Accepted for publication and presented in 2016 IEEE International Conference on Image Processing (ICIP

Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards

In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of dephasing mechanisms in such chaotic billiards. Physical implementations of these billiards range from quantum dots of graphene to topological insulators structures. We show, in particular, that the role of finite crossover fields between the universal symmetries quickly leaves the conductance to the asymptotic limit of unitary ensembles. Furthermore, we show that the dephasing mechanisms strikingly lead Dirac billiards from the extreme quantum regime to the semiclassical Gaussian regime