QuasiGeostrophic Diagnosis of Mixed-Layer Dynamics Embedded in a Mesoscale Turbulent Field

A quasigeostrophic model is developed to diagnose the three-dimensional circulation, including the vertical velocity, in the upper ocean from high-resolution observations of sea surface height and buoyancy. The formulation for the adiabatic component departs from the classical surface quasigeostrophic framework considered before since it takes into account the stratification within the surface mixed layer that is usually much weaker than that in the ocean interior. To achieve this, the model approximates the ocean with two constant stratification layers: a finite-thickness surface layer (or the mixed layer) and an infinitely deep interior layer. It is shown that the leading-order adiabatic circulation is entirely determined if both the surface streamfunction and buoyancy anomalies are considered. The surface layer further includes a diabatic dynamical contribution. Parameterization of diabatic vertical velocities is based on their restoring impacts of the thermal wind balance that is perturbed by turbulent vertical mixing of momentum and buoyancy. The model skill in reproducing the three-dimensional circulation in the upper ocean from surface data is checked against the output of a high-resolution primitive equation numerical simulation

Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

Nonlinear evolution of harmonically forced perturbations on a wingtip vortex

Wingtip vortices are created by flying airplanes due to lift generation. The vortex interaction with the trailing aircraft has sparked researchers’ interest to develop an efficient technique to destroy these vortices. Different models have been used to describe the vortex dynamics and they all show that, under real flight conditions, the most unstable modes produce a very weak amplification. Another linear instability mechanism that can produce high energy gains in short times is due to the non-normality of the system. Recently, it has been shown that these non-normal perturbations also produce this energy growth when they are excited with harmonic forcing functions. In this study, we analyze numerically the nonlinear evolution of a spatially, pointwise and temporally forced perturbation, generated by a synthetic jet at a given radial distance from the vortex core. This type of perturbation is able to produce high energy gains in the perturbed base flow (10^3), and is also a suitable candidate for use in engineering applications. The flow field is solved for using fully nonlinear three-dimensional direct numerical simulation with a spectral multidomain penalty method model. Our novel results show that the nonlinear effects are able to produce locally small bursts of instability that reduce the intensity of the primary vortex.

Switching Patterns and Steady-State Analysis of Grid-Connected and Stand-Alone Single-Stage Boost-Inverters for PV Applications

Renewable or sustainable energy (SE) sources have attracted the attention of many countries because the power generated is environmentally friendly, and the sources are not subject to the instability of price and availability. This dissertation presents new trends in the DC-AC converters (inverters) used in renewable energy sources, particularly for photovoltaic (PV) energy systems. A review of the existing technologies is performed for both single-phase and three-phase systems, and the pros and cons of the best candidates are investigated. In many modern energy conversion systems, a DC voltage, which is provided from a SE source or energy storage device, must be boosted and converted to an AC voltage with a fixed amplitude and frequency. A novel switching pattern based on the concept of the conventional space-vector pulse-width-modulated (SVPWM) technique is developed for single-stage, boost-inverters using the topology of current source inverters (CSI). The six main switching states, and two zeros, with three switches conducting at any given instant in conventional SVPWM techniques are modified herein into three charging states and six discharging states with only two switches conducting at any given instant. The charging states are necessary in order to boost the DC input voltage. It is demonstrated that the CSI topology in conjunction with the developed switching pattern is capable of providing the required residential AC voltage from a low DC voltage of one PV panel at its rated power for both linear and nonlinear loads. In a micro-grid, the active and reactive power control and consequently voltage regulation is one of the main requirements. Therefore, the capability of the single-stage boost-inverter in controlling the active power and providing the reactive power is investigated. It is demonstrated that the injected active and reactive power can be independently controlled through two modulation indices introduced in the proposed switching algorithm. The system is capable of injecting a desirable level of reactive power, while the maximum power point tracking (MPPT) dictates the desirable active power. The developed switching pattern is experimentally verified through a laboratory scaled three-phase 200W boost-inverter for both grid-connected and stand-alone cases and the results are presented.

Dynamic Image Precompensation for Improving Visual Performance of Computer Users with Ocular Aberrations

With the progress of computer technology, computers are expected to be more intelligent in the interaction with humans, presenting information according to the user's psychological and physiological characteristics. However, computer users with visual problems may encounter difficulties on the perception of icons, menus, and other graphical information displayed on the screen, limiting the efficiency of their interaction with computers. In this dissertation, a personalized and dynamic image precompensation method was developed to improve the visual performance of the computer users with ocular aberrations. The precompensation was applied on the graphical targets before presenting them on the screen, aiming to counteract the visual blurring caused by the ocular aberration of the user's eye. A complete and systematic modeling approach to describe the retinal image formation of the computer user was presented, taking advantage of modeling tools, such as Zernike polynomials, wavefront aberration, Point Spread Function and Modulation Transfer Function. The ocular aberration of the computer user was originally measured by a wavefront aberrometer, as a reference for the precompensation model. The dynamic precompensation was generated based on the resized aberration, with the real-time pupil diameter monitored. The potential visual benefit of the dynamic precompensation method was explored through software simulation, with the aberration data from a real human subject. An "artificial eye'' experiment was conducted by simulating the human eye with a high-definition camera, providing objective evaluation to the image quality after precompensation. In addition, an empirical evaluation with 20 human participants was also designed and implemented, involving image recognition tests performed under a more realistic viewing environment of computer use. The statistical analysis results of the empirical experiment confirmed the effectiveness of the dynamic precompensation method, by showing significant improvement on the recognition accuracy. The merit and necessity of the dynamic precompensation were also substantiated by comparing it with the static precompensation. The visual benefit of the dynamic precompensation was further confirmed by the subjective assessments collected from the evaluation participants.

E-polynomial of SL(2,C)-character varieties of complex curves of genus 3.

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

A symbolic approach to nonlinearly perturbed heat equation

We consider a system described by the linear heat equation with adiabatic boundary conditions which is perturbed periodicaly. This perturbation is nonlinear and is characterized by a one-parameter family of quadratic maps. The system, depending on the parameters, presents very complex behaviour. We introduce a symbolic framework to analyze the system and resume its most important features.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

A study on the macroeconomics of climate change

This work aims at exploring the relationship between business cycles, having frequencies rooted in the short run, and climatic phenomena, which span longer time horizons. The ultimate goal is to provide a theoretical framework to address these questions: How could very long run considerations affect short run economic decisions? How short run and transitory decisions could exert a long lasting effect on climate? This is achieved by means of an off-the-shelf real business cycle (RBC) model augmented so as to include a climatic block. The economy is perturbed by a technology shock and an energy-price shock. In general, the model performs relatively well in reproducing the cyclical characteristics of the economic variables; however, it is not as successful in capturing the cyclical behavior of climatic variables. Finally, it proposes a set of policy experiments, all taking the form of an energy tax directly or indirectly linked to the climatic status. As a matter of fact the effect of any tax responsive to the business cycle shows positive aspects: when a technology shock hits the economy, it mitigates global warming with minor costs in terms of potential output losses. It also protects the economy from an increase in energy prices, sustaining a certain level of output despite the fall in fossil energy use.

Strategies to hijack MTs dysfunction in neurodegenerative tauopathies: Design and synthesis of novel CNS-disease-modifying tools

Neuronal microtubules assembly and dynamics are regulated by several proteins including (MT)-associated protein tau, whose aberrant hyperphosphorylation promotes its dissociation from MTs and its abnormal deposition into neurofibrillary tangles, a common neurotoxic hallmarks of neurodegenerative tauopathies. To date, no disease-modifying drugs have been approved to combat CNS tau-related diseases. The multifactorial etiology of these conditions represents one of the major limits in the discovery of effective therapeutic options. In addition, tau protein functions are orchestrated by diverse post-translational modifications among which phosphorylation mediated by PKs plays a leading role. In this context, conventional single-target therapies are often inadequate in restoring perturbed networks and fraught with adverse side-effects. This thesis reports two distinct approaches to hijack MT defects in neurons. The first is focused on the rational design and synthesis of first-in-class triple inhibitors of GSK-3β, FYN, and DYRK1A, three close-related PKs, which act as master regulators of aberrant tau hyperphosphorylation. A merged multi-target pharmacophore strategy was applied to simultaneously modulate all three targets and achieve a disease-modifying effect. Optimization of ARN25068 by a computationally and crystallographic driven SAR exploration, allowed to rationalize the key structural modifications to maintain a balanced potency against all three targets and develop a new generation of quite well-balanced analogs exhibiting improved physicochemical properties, a good in vitro ADME profile, and promising cell-based anti-tau phosphorylation activity. In Part II, MT-stabilizing compounds have been developed to compensate MT defects in tau-related pathologies. Intensive chemical effort has been devoted to scaling up BL-0884, identified as a promising MT-normalizing TPD, which exhibited favorable ADME-PK, including brain penetration, oral bioavailability, and brain pharmacodynamic activity. A suitable functionalization of the exposed hydroxyl moiety of BL-0884 was carried out to generate corresponding esters and amides possessing a wide range of applications as prodrugs and active targeting for cancer chemotherapy.

Stochastic physics and representation of El Niño Southern Oscillation in climate models

El Niño-Southern Oscillation (ENSO) è il maggiore fenomeno climatico che avviene a livello dell’Oceano Pacifico tropicale e che ha influenze ambientali, climatiche e socioeconomiche a larga scala. In questa tesi si ripercorrono i passi principali che sono stati fatti per tentare di comprendere un fenomeno così complesso. Per prima cosa, si sono studiati i meccanismi che ne governano la dinamica, fino alla formulazione del modello matematico chiamato Delayed Oscillator (DO) model, proposto da Suarez e Schopf nel 1988. In seguito, per tenere conto della natura caotica del sistema studiato, si è introdotto nel modello lo schema chiamato Stochastically Perturbed Parameterisation Tendencies (SPPT). Infine, si sono portati due esempi di soluzione numerica del DO, sia con che senza l’introduzione della correzione apportata dallo schema SPPT, e si è visto in che misura SPPT porta reali miglioramenti al modello studiato.

Pipkiiα Is Widely Expressed In Hematopoietic-derived Cells And May Play A Role In The Expression Of Alpha- And Gamma-globins In K562 Cells.

Characterized for the first time in erythrocytes, phosphatidylinositol phosphate kinases (PIP kinases) belong to a family of enzymes that generate various lipid messengers and participate in several cellular processes, including gene expression regulation. Recently, the PIPKIIα gene was found to be differentially expressed in reticulocytes from two siblings with hemoglobin H disease, suggesting a possible relationship between PIPKIIα and the production of globins. Here, we investigated PIPKIIα gene and protein expression and protein localization in hematopoietic-derived cells during their differentiation, and the effects of PIPKIIα silencing on K562 cells. PIPKIIα silencing resulted in an increase in α and γ globins and a decrease in the proliferation of K562 cells without affecting cell cycle progression and apoptosis. In conclusion, using a cell line model, we showed that PIPKIIα is widely expressed in hematopoietic-derived cells, is localized in their cytoplasm and nucleus, and is upregulated during erythroid differentiation. We also showed that PIPKIIα silencing can induce α and γ globin expression and decrease cell proliferation in K562 cells.

The Clinical Impact Of Cerebellar Grey Matter Pathology In Multiple Sclerosis.

The cerebellum is an important site for cortical demyelination in multiple sclerosis, but the functional significance of this finding is not fully understood. To evaluate the clinical and cognitive impact of cerebellar grey-matter pathology in multiple sclerosis patients. Forty-two relapsing-remitting multiple sclerosis patients and 30 controls underwent clinical assessment including the Multiple Sclerosis Functional Composite, Expanded Disability Status Scale (EDSS) and cerebellar functional system (FS) score, and cognitive evaluation, including the Paced Auditory Serial Addition Test (PASAT) and the Symbol-Digit Modalities Test (SDMT). Magnetic resonance imaging was performed with a 3T scanner and variables of interest were: brain white-matter and cortical lesion load, cerebellar intracortical and leukocortical lesion volumes, and brain cortical and cerebellar white-matter and grey-matter volumes. After multivariate analysis high burden of cerebellar intracortical lesions was the only predictor for the EDSS (p<0.001), cerebellar FS (p = 0.002), arm function (p = 0.049), and for leg function (p<0.001). Patients with high burden of cerebellar leukocortical lesions had lower PASAT scores (p = 0.013), while patients with greater volumes of cerebellar intracortical lesions had worse SDMT scores (p = 0.015). Cerebellar grey-matter pathology is widely present and contributes to clinical dysfunction in relapsing-remitting multiple sclerosis patients, independently of brain grey-matter damage.

Dna Extraction From Filter-paper Spots Of Vaginal Samples Collected After Sexual Violence.

To detect the presence of male DNA in vaginal samples collected from survivors of sexual violence and stored on filter paper. A pilot study was conducted to evaluate 10 vaginal samples spotted on sterile filter paper: 6 collected at random in April 2009 and 4 in October 2010. Time between sexual assault and sample collection was 4-48hours. After drying at room temperature, the samples were placed in a sterile envelope and stored for 2-3years until processing. DNA extraction was confirmed by polymerase chain reaction for human β-globin, and the presence of prostate-specific antigen (PSA) was quantified. The presence of the Y chromosome was detected using primers for sequences in the TSPY (Y7/Y8 and DYS14) and SRY genes. β-Globin was detected in all 10 samples, while 2 samples were positive for PSA. Half of the samples amplified the Y7/Y8 and DYS14 sequences of the TSPY gene and 30% amplified the SRY gene sequence of the Y chromosome. Four male samples and 1 female sample served as controls. Filter-paper spots stored for periods of up to 3years proved adequate for preserving genetic material from vaginal samples collected following sexual violence.