POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Photovoltaic power forecast modeling with artificial neural networks

Dissertação de Mestrado, Engenharia Eletrónica e Telecomunicações, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2016

Diversity and Stability in Food Webs : Impacts of Non-Equilibrium Dynamics, Topology and Variation

With progressive climate change, the preservation of biodiversity is becoming increasingly important. Only if the gene pool is large enough and requirements of species are diverse, there will be species that can adapt to the changing circumstances. To maintain biodiversity, we must understand the consequences of the various strategies. Mathematical models of population dynamics could provide prognoses. However, a model that would reproduce and explain the mechanisms behind the diversity of species that we observe experimentally and in nature is still needed. A combination of theoretical models with detailed experiments is needed to test biological processes in models and compare predictions with outcomes in reality. In this thesis, several food webs are modeled and analyzed. Among others, models are formulated of laboratory experiments performed in the Zoological Institute of the University of Cologne. Numerical data of the simulations is in good agreement with the real experimental results. Via numerical simulations it can be demonstrated that few assumptions are necessary to reproduce in a model the sustained oscillations of the population size that experiments show. However, analysis indicates that species "thrown together by chance" are not very likely to survive together over long periods. Even larger food nets do not show significantly different outcomes and prove how extraordinary and complicated natural diversity is. In order to produce such a coexistence of randomly selected species—as the experiment does—models require additional information about biological processes or restrictions on the assumptions. Another explanation for the observed coexistence is a slow extinction that takes longer than the observation time. Simulated species survive a comparable period of time before they die out eventually. Interestingly, it can be stated that the same models allow the survival of several species in equilibrium and thus do not follow the so-called competitive exclusion principle. This state of equilibrium is more fragile, however, to changes in nutrient supply than the oscillating coexistence. Overall, the studies show, that having a diverse system means that population numbers are probably oscillating, and on the other hand oscillating population numbers stabilize a food web both against demographic noise as well as against changes of the habitat. Model predictions can certainly not be converted at their face value into policies for real ecosystems. But the stabilizing character of fluctuations should be considered in the regulations of animal populations.

Essays on employment / education, investment in education and student achievement

Méthodologie: Modèle de régression quantile de variable instrumentale pour données de Panel utilisant la fonction de production partielle

On the Wick product and Wong-Zakai approximations.

This thesis is a compilation of 6 papers that the author has written together with Alberto Lanconelli (chapters 3, 5 and 8) and Hyun-Jung Kim (ch 7). The logic thread that link all these chapters together is the interest to analyze and approximate the solutions of certain stochastic differential equations using the so called Wick product as the basic tool. In the first chapter we present arguably the most important achievement of this thesis; namely the generalization to multiple dimensions of a Wick-Wong-Zakai approximation theorem proposed by Hu and Oksendal. By exploiting the relationship between the Wick product and the Malliavin derivative we propose an original reduction method which allows us to approximate semi-linear systems of stochastic differential equations of the Itô type. Furthermore in chapter 4 we present a non-trivial extension of the aforementioned results to the case in which the system of stochastic differential equations are driven by a multi-dimensional fraction Brownian motion with Hurst parameter bigger than 1/2. In chapter 5 we employ our approach and present a “short time” approximation for the solution of the Zakai equation from non-linear filtering theory and provide an estimation of the speed of convergence. In chapters 6 and 7 we study some properties of the unique mild solution for the Stochastic Heat Equation driven by spatial white noise of the Wick-Skorohod type. In particular by means of our reduction method we obtain an alternative derivation of the Feynman-Kac representation for the solution, we find its optimal Hölder regularity in time and space and present a Feynman-Kac-type closed form for its spatial derivative. Chapter 8 treats a somewhat different topic; in particular we investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of semi-linear stochastic differential equations describing a predator-prey model perturbed by Gaussian noise.

Radical chemistry of the catechol/quinone system and its role in the control of lipid peroxidation and melanin biosynthesis

The catechol (1,2-dihydroxybenzene) is a privileged structural motif among natural antioxidants like flavonoids, owing to its reactivity with alkylperoxyl radicals due to the stability of the semiquinone radical. The exploration of the relevance and mechanism of this non-conventional antioxidant chemistry in heterogenous biomimetic systems (aqueous micelles and unilamellar liposomes) is explored for the first time in Chapter 1. Results show antioxidant behaviour that surpasses that of nature’s premiere antioxidant α-tocopherol and relies on the cross-dismutation of alkylperoxyl and hydroperoxyl radicals at the water-lipid interface with regeneration of the catechol function from the oxidized quinone. The design and synthesis of new biomimetic catechol-type antioxidants by conjugation of thiols (e.g. cysteine) with quinones highlighted an unusual 1,6-type regioselectivity, which had been previously reported but never fully rationalized. Owing to its importance both in nature and in the development of new antioxidants, we investigated it in detail in Chapter 2. We could prove the onsetting of a radical-chain mechanism intermediated by thiyl and thiosemiquinone radicals at the basis of the “anomalous nucleophilic addition” of thiols to ortho-quinones, which paves the way to better understanding of the chemistry of such systems. The oxidation of catechols to the corresponding quinones is also a key reaction in the biosynthesis of melanins, mediated by enzyme Tyrosinase.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Non-linear modelling of microwave devices embedding nano-ferroelectric materials for real-time reconfigurable transmitarray

In this thesis work a nonlinear model for Interdigitated Capacitors (IDCs) based on ferroelectric materials, is proposed. Through the properties of materials such as Hafnium-Zirconium Oxide (HfZrO2), it is possible to realize tunable radiofrequency (RF) circuits. In particular, the model proposed in this thesis describes the use of an IDC, realized on a High-Resistivity silicon substrate, as a phase shifter for beam-steering applications. The model is obtained starting from already present experimental measurements, through which it is possible to identify a circuit model. The model is tested for both low power values and other power values using Harmonic Balance simulations, which show an excellent convergence of the model up to 40 dBm of input power. Furthermore, an array composed by two patches operating both at 2.55 GHz, which exploits the tunable properties of the HfZrO-based IDC is proposed. At 0dBm the model shows a 47° phase shift with polarization -1 V and 1 V which leads to a 11° steering of the main lobe of the array.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

Synthetic generation of amyloid PET images by non-linear dimensionality reduction inversion

Privacy issues and data scarcity in PET field call for efficient methods to expand datasets via synthetic generation of new data that cannot be traced back to real patients and that are also realistic. In this thesis, machine learning techniques were applied to 1001 amyloid-beta PET images, which had undergone a diagnosis of Alzheimer’s disease: the evaluations were 540 positive, 457 negative and 4 unknown. Isomap algorithm was used as a manifold learning method to reduce the dimensions of the PET dataset; a numerical scale-free interpolation method was applied to invert the dimensionality reduction map. The interpolant was tested on the PET images via LOOCV, where the removed images were compared with the reconstructed ones with the mean SSIM index (MSSIM = 0.76 ± 0.06). The effectiveness of this measure is questioned, since it indicated slightly higher performance for a method of comparison using PCA (MSSIM = 0.79 ± 0.06), which gave clearly poor quality reconstructed images with respect to those recovered by the numerical inverse mapping. Ten synthetic PET images were generated and, after having been mixed with ten originals, were sent to a team of clinicians for the visual assessment of their realism; no significant agreements were found either between clinicians and the true image labels or among the clinicians, meaning that original and synthetic images were indistinguishable. The future perspective of this thesis points to the improvement of the amyloid-beta PET research field by increasing available data, overcoming the constraints of data acquisition and privacy issues. Potential improvements can be achieved via refinements of the manifold learning and the inverse mapping stages during the PET image analysis, by exploring different combinations in the choice of algorithm parameters and by applying other non-linear dimensionality reduction algorithms. A final prospect of this work is the search for new methods to assess image reconstruction quality.

Correlation Between The Friedman Staging System And The Upper Airway Volume In Patients With Obstructive Sleep Apnea.

This study was designed to evaluate the correlation between computed tomography findings and data from the physical examination and the Friedman Staging System (FSS) in patients with obstructive sleep apnea (OSA). We performed a retrospective evaluation by reviewing the medical records of 33 patients (19 male and 14 female patients) with a mean body mass index of 30.38 kg/m(2) and mean age of 49.35 years. Among these patients, 14 presented with severe OSA, 7 had moderate OSA, 7 had mild OSA, and 5 were healthy. The patients were divided into 2 groups according to the FSS: Group A comprised patients with FSS stage I or II, and group B comprised patients with FSS stage III. By use of the Fisher exact test, a positive relationship between the FSS stage and apnea-hypopnea index (P = .011) and between the FSS stage and body mass index (P = .012) was found. There was no correlation between age (P = .55) and gender (P = .53) with the FSS stage. The analysis of variance test comparing the upper airway volume between the 2 groups showed P = .018. In this sample the FSS and upper airway volume showed an inverse correlation and were useful in analyzing the mechanisms of airway collapse in patients with OSA.

O setor privado sem fins lucrativos e as políticas públicas de esporte e lazer (2008-2011) = : The non-profitable private sector and the public policies for sport and leisure (2008-2011)

Universidade Estadual de Campinas . Faculdade de Educação Física

Renin angiotensin system and cardiac hypertrophy after sinoaortic denervation in rats

OBJECTIVE: The aim of this study was to evaluate the role of angiotensin I, II and 1-7 on left ventricular hypertrophy of Wistar and spontaneously hypertensive rats submitted to sinoaortic denervation. METHODS: Ten weeks after sinoaortic denervation, hemodynamic and morphofunctional parameters were analyzed, and the left ventricle was dissected for biochemical analyses. RESULTS: Hypertensive groups (controls and denervated) showed an increase on mean blood pressure compared with normotensive ones (controls and denervated). Blood pressure variability was higher in denervated groups than in their respective controls. Left ventricular mass and collagen content were increased in the normotensive denervated and in both spontaneously hypertensive groups compared with Wistar controls. Both hypertensive groups presented a higher concentration of angiotensin II than Wistar controls, whereas angiotensin 1-7 concentration was decreased in the hypertensive denervated group in relation to the Wistar groups. There was no difference in angiotensin I concentration among groups. CONCLUSION: Our results suggest that not only blood pressure variability and reduced baroreflex sensitivity but also elevated levels of angiotensin II and a reduced concentration of angiotensin 1-7 may contribute to the development of left ventricular hypertrophy. These data indicate that baroreflex dysfunction associated with changes in the renin angiotensin system may be predictive factors of left ventricular hypertrophy and cardiac failure.

Selective Decrease of Components of the Creatine Kinase System and ATP Synthase Complex in Chronic Chagas Disease Cardiomyopathy

Background: Chronic Chagas disease cardiomyopathy (CCC) is an inflammatory dilated cardiomyopathy with a worse prognosis than other cardiomyopathies. CCC occurs in 30 % of individuals infected with Trypanosoma cruzi, endemic in Latin America. Heart failure is associated with impaired energy metabolism, which may be correlated to contractile dysfunction. We thus analyzed the myocardial gene and protein expression, as well as activity, of key mitochondrial enzymes related to ATP production, in myocardial samples of end-stage CCC, idiopathic dilated (IDC) and ischemic (IC) cardiomyopathies. Methodology/Principal Findings: Myocardium homogenates from CCC (N = 5), IC (N = 5) and IDC (N = 5) patients, as well as from heart donors (N = 5) were analyzed for protein and mRNA expression of mitochondrial creatine kinase (CKMit) and muscular creatine kinase (CKM) and ATP synthase subunits aplha and beta by immunoblotting and by real-time RT-PCR. Total myocardial CK activity was also assessed. Protein levels of CKM and CK activity were reduced in all three cardiomyopathy groups. However, total CK activity, as well as ATP synthase alpha chain protein levels, were significantly lower in CCC samples than IC and IDC samples. CCC myocardium displayed selective reduction of protein levels and activity of enzymes crucial for maintaining cytoplasmic ATP levels. Conclusions/Significance: The selective impairment of the CK system may be associated to the loss of inotropic reserve observed in CCC. Reduction of ATP synthase alpha levels is consistent with a decrease in myocardial ATP generation through oxidative phosphorylation. Together, these results suggest that the energetic deficit is more intense in the myocardium of CCC patients than in the other tested dilated cardiomyopathies.

Er : YAG laser, ultrasonic system, and curette produce different profiles on dentine root surfaces: An in vitro study

Objective: The aim of the present study was to compare the in vitro effects of the Er:YAG laser, an ultrasonic system, and manual curette on dentine root surface by roughness and micro-morphological analysis. Materials and Methods: Thirty-six flattened bovine roots were randomly assigned to one of the following groups: group 1 (n = 12): Er: YAG laser ( 2940 nm), 120 mJ/pulse, 10 Hz, 8.4 J/cm(2); group 2 ( n = 12): ultrasonic system; and group 3 ( n = 12): manual curette. The mean surface roughness (Ra) of each sample was measured using a profilometer before and after the treatments. The micro-morphology of the treated and untreated ( control) root surfaces was evaluated with scanning electron microscopy (SEM) at 50 x and 1000 x magnification. Results: Analysis with the profilometer showed that for equal times of instrumentation, the smoothest surfaces were produced by the Er: YAG laser and the ultrasonic system, followed by the curette ( p < 0.05). Morphological analyses demonstrated that treatment with the Er: YAG laser produced some areas with an irregular surface, craters, and ablation of the intertubular dentin. The smear layer was removed and dentine tubules were opened by both curettes and the ultrasonic system. The micro-morphology of the dentine root surface after ultrasonic treatment, however, demonstrated randomly distributed areas cratering. Conclusion: All instruments increased the roughness of the dentine root surface after treatment; however, the curette produced rougher surfaces than the other devices. SEM analysis revealed distinct root surface profiles produced by the three devices.