X-ray properties and evolution of high-redshift AGN, and the gas content of host galaxies

In this thesis, I have investigated the evolution of the high-redshift (z > 3) AGN population by collecting data from some of the major Chandra and XMM-Newton surveys. The final sample (141 sources) is one of the largest selected at z> 3 in the X- rays and it is characterised by a very high redshift completeness (98%). I derived the spectral slopes and obscurations through a spectral anaysis and I assessed the high-z evolution by deriving the luminosity function and the number counts of the sample. The best representation of the AGN evolution is a pure density evolution (PDE) model: the AGN space density is found to decrease by a factor of 10 from z=3 to z=5. I also found that about 50% of AGN are obscured by large column densities (logNH > 23). By comparing these data with those in the Local Universe, I found a positive evolution of the obscured AGN fraction with redshift, especially for luminous (logLx > 44) AGN. I also studied the gas content of z < 1 AGN-hosting galaxies and compared it with that of inactive galaxies. For the first time, I applied to AGN a method to derive the gas mass previously used for inactive galaxies only. AGN are found to live preferentially in gas-rich galaxies. This result on the one hand can help us in understanding the AGN triggering mechanisms, on the other hand explains why AGN are preferentially hosted by star-forming galaxies.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Higher-order regularization and morphological techniques for image segmentation

La segmentación de imágenes es un campo importante de la visión computacional y una de las áreas de investigación más activas, con aplicaciones en comprensión de imágenes, detección de objetos, reconocimiento facial, vigilancia de vídeo o procesamiento de imagen médica. La segmentación de imágenes es un problema difícil en general, pero especialmente en entornos científicos y biomédicos, donde las técnicas de adquisición imagen proporcionan imágenes ruidosas. Además, en muchos de estos casos se necesita una precisión casi perfecta. En esta tesis, revisamos y comparamos primero algunas de las técnicas ampliamente usadas para la segmentación de imágenes médicas. Estas técnicas usan clasificadores a nivel de pixel e introducen regularización sobre pares de píxeles que es normalmente insuficiente. Estudiamos las dificultades que presentan para capturar la información de alto nivel sobre los objetos a segmentar. Esta deficiencia da lugar a detecciones erróneas, bordes irregulares, configuraciones con topología errónea y formas inválidas. Para solucionar estos problemas, proponemos un nuevo método de regularización de alto nivel que aprende información topológica y de forma a partir de los datos de entrenamiento de una forma no paramétrica usando potenciales de orden superior. Los potenciales de orden superior se están popularizando en visión por computador, pero la representación exacta de un potencial de orden superior definido sobre muchas variables es computacionalmente inviable. Usamos una representación compacta de los potenciales basada en un conjunto finito de patrones aprendidos de los datos de entrenamiento que, a su vez, depende de las observaciones. Gracias a esta representación, los potenciales de orden superior pueden ser convertidos a potenciales de orden 2 con algunas variables auxiliares añadidas. Experimentos con imágenes reales y sintéticas confirman que nuestro modelo soluciona los errores de aproximaciones más débiles. Incluso con una regularización de alto nivel, una precisión exacta es inalcanzable, y se requeire de edición manual de los resultados de la segmentación automática. La edición manual es tediosa y pesada, y cualquier herramienta de ayuda es muy apreciada. Estas herramientas necesitan ser precisas, pero también lo suficientemente rápidas para ser usadas de forma interactiva. Los contornos activos son una buena solución: son buenos para detecciones precisas de fronteras y, en lugar de buscar una solución global, proporcionan un ajuste fino a resultados que ya existían previamente. Sin embargo, requieren una representación implícita que les permita trabajar con cambios topológicos del contorno, y esto da lugar a ecuaciones en derivadas parciales (EDP) que son costosas de resolver computacionalmente y pueden presentar problemas de estabilidad numérica. Presentamos una aproximación morfológica a la evolución de contornos basada en un nuevo operador morfológico de curvatura que es válido para superficies de cualquier dimensión. Aproximamos la solución numérica de la EDP de la evolución de contorno mediante la aplicación sucesiva de un conjunto de operadores morfológicos aplicados sobre una función de conjuntos de nivel. Estos operadores son muy rápidos, no sufren de problemas de estabilidad numérica y no degradan la función de los conjuntos de nivel, de modo que no hay necesidad de reinicializarlo. Además, su implementación es mucho más sencilla que la de las EDP, ya que no requieren usar sofisticados algoritmos numéricos. Desde un punto de vista teórico, profundizamos en las conexiones entre operadores morfológicos y diferenciales, e introducimos nuevos resultados en este área. Validamos nuestra aproximación proporcionando una implementación morfológica de los contornos geodésicos activos, los contornos activos sin bordes, y los turbopíxeles. En los experimentos realizados, las implementaciones morfológicas convergen a soluciones equivalentes a aquéllas logradas mediante soluciones numéricas tradicionales, pero con ganancias significativas en simplicidad, velocidad y estabilidad. ABSTRACT Image segmentation is an important field in computer vision and one of its most active research areas, with applications in image understanding, object detection, face recognition, video surveillance or medical image processing. Image segmentation is a challenging problem in general, but especially in the biological and medical image fields, where the imaging techniques usually produce cluttered and noisy images and near-perfect accuracy is required in many cases. In this thesis we first review and compare some standard techniques widely used for medical image segmentation. These techniques use pixel-wise classifiers and introduce weak pairwise regularization which is insufficient in many cases. We study their difficulties to capture high-level structural information about the objects to segment. This deficiency leads to many erroneous detections, ragged boundaries, incorrect topological configurations and wrong shapes. To deal with these problems, we propose a new regularization method that learns shape and topological information from training data in a nonparametric way using high-order potentials. High-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher order potential defined over many variables is computationally infeasible. We use a compact representation of the potentials based on a finite set of patterns learned fromtraining data that, in turn, depends on the observations. Thanks to this representation, high-order potentials can be converted into pairwise potentials with some added auxiliary variables and minimized with tree-reweighted message passing (TRW) and belief propagation (BP) techniques. Both synthetic and real experiments confirm that our model fixes the errors of weaker approaches. Even with high-level regularization, perfect accuracy is still unattainable, and human editing of the segmentation results is necessary. The manual edition is tedious and cumbersome, and tools that assist the user are greatly appreciated. These tools need to be precise, but also fast enough to be used in real-time. Active contours are a good solution: they are good for precise boundary detection and, instead of finding a global solution, they provide a fine tuning to previously existing results. However, they require an implicit representation to deal with topological changes of the contour, and this leads to PDEs that are computationally costly to solve and may present numerical stability issues. We present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension. We approximate the numerical solution of the contour evolution PDE by the successive application of a set of morphological operators defined on a binary level-set. These operators are very fast, do not suffer numerical stability issues, and do not degrade the level set function, so there is no need to reinitialize it. Moreover, their implementation is much easier than their PDE counterpart, since they do not require the use of sophisticated numerical algorithms. From a theoretical point of view, we delve into the connections between differential andmorphological operators, and introduce novel results in this area. We validate the approach providing amorphological implementation of the geodesic active contours, the active contours without borders, and turbopixels. In the experiments conducted, the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions, but with significant gains in simplicity, speed, and stability.

Nonlinear Estimates in Anisotropic Gevrey Spaces

2002 Mathematics Subject Classification: 35G20, 47H30

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

A PDE model for computing the optical flow

[EN] In this paper we present a new model for optical flow calculation using a variational formulation which preserves discontinuities of the flow much better than classical methods. We study the Euler-Lagrange equations asociated to the variational problem. In the case of quadratic energy, we show the existence and uniqueness of the corresponding evolution problem. Since our method avoid linearization in the optical flow constraint, it can recover large displacement in the scene. We avoid convergence to irrelevant local minima by embedding our method into a linear scale-space framework and using a focusing strategy from coarse to fine scales.

Numerical simulation of the evolution of viscous rotating drops

In this contribution we simulate numerically the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity ? or constant angular momentum L, surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. In the lecture we will describe the numerical method we have used to solve the PDE system that describes the evolution of the drop (3D boundary element method). We will also present the results we have obtained, paying special attention to the stability/instability of the equilibrium shapes.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

Prognostic Value Of Dna And Mrna E6/e7 Of Human Papillomavirus In The Evolution Of Cervical Intraepithelial Neoplasia Grade 2.

This study aimed at evaluating whether human papillomavirus (HPV) groups and E6/E7 mRNA of HPV 16, 18, 31, 33, and 45 are prognostic of cervical intraepithelial neoplasia (CIN) 2 outcome in women with a cervical smear showing a low-grade squamous intraepithelial lesion (LSIL). This cohort study included women with biopsy-confirmed CIN 2 who were followed up for 12 months, with cervical smear and colposcopy performed every three months. Women with a negative or low-risk HPV status showed 100% CIN 2 regression. The CIN 2 regression rates at the 12-month follow-up were 69.4% for women with alpha-9 HPV versus 91.7% for other HPV species or HPV-negative status (P < 0.05). For women with HPV 16, the CIN 2 regression rate at the 12-month follow-up was 61.4% versus 89.5% for other HPV types or HPV-negative status (P < 0.05). The CIN 2 regression rate was 68.3% for women who tested positive for HPV E6/E7 mRNA versus 82.0% for the negative results, but this difference was not statistically significant. The expectant management for women with biopsy-confirmed CIN 2 and previous cytological tests showing LSIL exhibited a very high rate of spontaneous regression. HPV 16 is associated with a higher CIN 2 progression rate than other HPV infections. HPV E6/E7 mRNA is not a prognostic marker of the CIN 2 clinical outcome, although this analysis cannot be considered conclusive. Given the small sample size, this study could be considered a pilot for future larger studies on the role of predictive markers of CIN 2 evolution.

Effects Of Therapeutic Approach On The Neonatal Evolution Of Very Low Birth Weight Infants With Patent Ductus Arteriosus.

To analyze the effects of treatment approach on the outcomes of newborns (birth weight [BW] < 1,000 g) with patent ductus arteriosus (PDA), from the Brazilian Neonatal Research Network (BNRN) on: death, bronchopulmonary dysplasia (BPD), severe intraventricular hemorrhage (IVH III/IV), retinopathy of prematurity requiring surgical (ROPsur), necrotizing enterocolitis requiring surgery (NECsur), and death/BPD. This was a multicentric, cohort study, retrospective data collection, including newborns (BW < 1000 g) with gestational age (GA) < 33 weeks and echocardiographic diagnosis of PDA, from 16 neonatal units of the BNRN from January 1, 2010 to Dec 31, 2011. Newborns who died or were transferred until the third day of life, and those with presence of congenital malformation or infection were excluded. Groups: G1 - conservative approach (without treatment), G2 - pharmacologic (indomethacin or ibuprofen), G3 - surgical ligation (independent of previous treatment). Factors analyzed: antenatal corticosteroid, cesarean section, BW, GA, 5 min. Apgar score < 4, male gender, Score for Neonatal Acute Physiology Perinatal Extension (SNAPPE II), respiratory distress syndrome (RDS), late sepsis (LS), mechanical ventilation (MV), surfactant (< 2 h of life), and time of MV. death, O2 dependence at 36 weeks (BPD36wks), IVH III/IV, ROPsur, NECsur, and death/BPD36wks. Student's t-test, chi-squared test, or Fisher's exact test; Odds ratio (95% CI); logistic binary regression and backward stepwise multiple regression. Software: MedCalc (Medical Calculator) software, version 12.1.4.0. p-values < 0.05 were considered statistically significant. 1,097 newborns were selected and 494 newborns were included: G1 - 187 (37.8%), G2 - 205 (41.5%), and G3 - 102 (20.6%). The highest mortality was observed in G1 (51.3%) and the lowest in G3 (14.7%). The highest frequencies of BPD36wks (70.6%) and ROPsur were observed in G3 (23.5%). The lowest occurrence of death/BPD36wks occurred in G2 (58.0%). Pharmacological (OR 0.29; 95% CI: 0.14-0.62) and conservative (OR 0.34; 95% CI: 0.14-0.79) treatments were protective for the outcome death/BPD36wks. The conservative approach of PDA was associated to high mortality, the surgical approach to the occurrence of BPD36wks and ROPsur, and the pharmacological treatment was protective for the outcome death/BPD36wks.

Evolution Of The Deaths Registry System In Brazil: Associations With Changes In The Mortality Profile, Under-registration Of Death Counts, And Ill-defined Causes Of Death.

This paper examines the spatial pattern of ill-defined causes of death across Brazilian regions, and its relationship with the evolution of completeness of the deaths registry and changes in the mortality age profile. We make use of the Brazilian Health Informatics Department mortality database and population censuses from 1980 to 2010. We applied demographic methods to evaluate the quality of mortality data for 137 small areas and correct for under-registration of death counts when necessary. The second part of the analysis uses linear regression models to investigate the relationship between, on the one hand, changes in death counts coverage and age profile of mortality, and on the other, changes in the reporting of ill-defined causes of death. The completeness of death counts coverage increases from about 80% in 1980-1991 to over 95% in 2000-2010 at the same time the percentage of ill-defined causes of deaths reduced about 53% in the country. The analysis suggests that the government's efforts to improve data quality are proving successful, and they will allow for a better understanding of the dynamics of health and the mortality transition.

Digestive Peptidase Evolution In Holometabolous Insects Led To A Divergent Group Of Enzymes In Lepidoptera.

Trypsins and chymotrypsins are well-studied serine peptidases that cleave peptide bonds at the carboxyl side of basic and hydrophobic l-amino acids, respectively. These enzymes are largely responsible for the digestion of proteins. Three primary processes regulate the activity of these peptidases: secretion, precursor (zymogen) activation and substrate-binding site recognition. Here, we present a detailed phylogenetic analysis of trypsins and chymotrypsins in three orders of holometabolous insects and reveal divergent characteristics of Lepidoptera enzymes in comparison with those of Coleoptera and Diptera. In particular, trypsin subsite S1 was more hydrophilic in Lepidoptera than in Coleoptera and Diptera, whereas subsites S2-S4 were more hydrophobic, suggesting different substrate preferences. Furthermore, Lepidoptera displayed a lineage-specific trypsin group belonging only to the Noctuidae family. Evidence for facilitated trypsin auto-activation events were also observed in all the insect orders studied, with the characteristic zymogen activation motif complementary to the trypsin active site. In contrast, insect chymotrypsins did not seem to have a peculiar evolutionary history with respect to their mammal counterparts. Overall, our findings suggest that the need for fast digestion allowed holometabolous insects to evolve divergent groups of peptidases with high auto-activation rates, and highlight that the evolution of trypsins led to a most diverse group of enzymes in Lepidoptera.

Effects Of Pde Type 5 Inhibitors On Left Ventricular Diastolic Dysfunction In Resistant Hypertension.

Resistant hypertension (RHTN) is a multifactorial disease characterized by blood pressure (BP) levels above goal (140/90 mmHg) in spite of the concurrent use of three or more antihypertensive drugs of different classes. Moreover, it is well known that RHTN subjects have high prevalence of left ventricular diastolic dysfunction (LVDD), which leads to increased risk of heart failure progression. This review gathers data from studies evaluating the effects of phosphodiesterase-5 (PDE-5) inhibitors (administration of acute sildenafil and short-term tadalafil) on diastolic function, biochemical and hemodynamic parameters in patients with RHTN. Acute study with sildenafil treatment found that inhibition of PDE-5 improved hemodynamic parameters and diastolic relaxation. In addition, short-term study with the use of tadalafil demonstrated improvement of LVDD, cGMP and BNP-32 levels, regardless of BP reduction. No endothelial function changes were observed in the studies. The findings of acute and short-term studies revealed potential therapeutic effects of IPDE-5 drugs on LVDD in RHTN patients.A Hipertensão arterial resistente (HAR) é uma doença multifatorial caracterizada por níveis pressóricos acima das metas (140/90 mmHg), a despeito de tratamento farmacológico otimizado de 3 ou mais fármacos anti-hipertensivos de diferentes classes. Pacientes diagnosticados como hipertensos resistentes apresentam alta prevalência de disfunção diastólica do ventrículo esquerdo (DDVE) que proporciona risco aumentado para insuficiência cardíaca. Esta revisão reúne dados de estudos prévios avaliando os efeitos dos inibidores de fosfodiesterase-5 (PDE-5) (administração aguda de sildenafil e de curto prazo de tadalafil) na função diastólica e nos parâmetros bioquímicos e hemodinâmicos em pacientes com HAR. O estudo agudo com sildenafil demonstrou que a inibição da PDE-5 melhorou os parâmetros hemodinâmicos e de relaxamento diastólico. Além disso, o estudo curto prazo com o uso de tadalafil revelou melhora da DDVE e dos níveis de GMPc e BNP-32, independente de redução de pressão arterial. A função endotelial não apresentou alteração com ambos os tratamentos. Os resultados dos estudos agudo e de curto prazo sugerem efeitos terapêuticos potenciais dos fármacos inibidores da PDE-5 na disfunção diastólica em pacientes com HAR.

Time evolution of the South Atlantic Magnetic Anomaly

The South Atlantic Magnetic Anomaly (SAMA) is one of the most outstanding anomalies of the geomagnetic field. The SAMA secular variation was obtained and compared to the evolution of other anomalies using spherical harmonic field models for the 1590-2005 period. An analysis of data from four South American observatories shows how this large scale anomaly affected their measurements. Since SAMA is a low total field anomaly, the field was separated into its nondipolar, quadrupolar and octupolar parts. The time evolution of the non-dipole/total, quadrupolar/total and octupolar/total field ratios yielded increasingly high values for the South Atlantic since 1750. The SAMA evolution is compared to the evolution of other large scale surface geomagnetic features like the North and the South Pole and the Siberia High, and this comparison shows the intensity equilibrium between these anomalies in both hemispheres. The analysis of non-dipole fields in historical period suggests that SAMA is governed by (i) quadrupolar field for drift, and (ii) quadrupolar and octupolar fields for intensity and area of influence. Furthermore, our study reinforces the possibility that SAMA may be related to reverse fluxes in the outer core under the South Atlantic region.