Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Hypertension, poor glycemic control, and microalbuminuria in Cuban Americans with type 2 diabetes

Purpose: To investigate to what degree the presence of hypertension (HTN) and poor glycemic control (GC) influences the likelihood of having microalbuminuria (MAU) among Cuban Americans with type 2 diabetes (T2D).Methods: A cross-sectional study conducted in Cuban Americans (n = 179) with T2D. Participants were recruited from a randomly generated mailing list purchased from KnowledgeBase Marketing, Inc. Blood pressure (BP) was measured twice and averaged using an adult size cuff. Glycosylated hemoglobin (A1c) levels were measured from whole blood samples with the Roche Tina-quant method. First morning urine samples were collected from each participant to determine MAU by a semiquantitative assay (ImmunoDip).Results: MAU was present in 26% of Cuban Americans with T2D. A significantly higher percentage of subjects with MA had HTN (P = 0.038) and elevated A1C (P = 0.002) than those with normoalbuminuria. Logistic regression analysis showed that after controlling for covariates, subjects with poor GC were 6.76 times more likely to have MAU if they had hypertension compared with those without hypertension (P = 0.004; 95% confidence interval [CI]: 1.83, 23.05). Conclusion: The clinical significance of these findings emphasizes the early detection of MAU in this Hispanic subgroup combined with BP and good GC, which are fundamentals in preventing and treating diabetes complications and improving individuals’ renal and cardiovascular outcomes.

Tamed and Compatible Symplectic Forms on Four-Dimensional Almost Complex Lie Algebras

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved and will give some insights on the proof. The key for the proof is translating the problem into a Linear Algebra setting. This is a joint work with Dr. Draghici.

An investigation by AFM and TEM of the mechanism of anodic formation of nanoporosity in n-InP in KOH

The early stages of nanoporous layer formation, under anodic conditions in the absence of light, were investigated for n-type InP with a carrier concentration of ∼3× 1018 cm-3 in 5 mol dm-3 KOH and a mechanism for the process is proposed. At potentials less than ∼0.35 V, spectroscopic ellipsometry and transmission electron microscopy (TEM) showed a thin oxide film on the surface. Atomic force microscopy (AFM) of electrode surfaces showed no pitting below ∼0.35 V but clearly showed etch pit formation in the range 0.4-0.53 V. The density of surface pits increased with time in both linear potential sweep and constant potential reaching a constant value at a time corresponding approximately to the current peak in linear sweep voltammograms and current-time curves at constant potential. TEM clearly showed individual nanoporous domains separated from the surface by a dense ∼40 nm InP layer. It is concluded that each domain develops as a result of directionally preferential pore propagation from an individual surface pit which forms a channel through this near-surface layer. As they grow larger, domains meet, and the merging of multiple domains eventually leads to a continuous nanoporous sub-surface region.

Recovering Natural History: Modeling Cardiovascular Biomarkers in the Presence of Endogenous Medication Use

Thesis (Ph.D.)--University of Washington, 2016-08

Tile-Based Two-Dimensional Phase Unwrapping for Digital Holography Using a Modular Framework

A variety of physical and biomedical imaging techniques, such as digital holography, interferometric synthetic aperture radar (InSAR), or magnetic resonance imaging (MRI) enable measurement of the phase of a physical quantity additionally to its amplitude. However, the phase can commonly only be measured modulo 2π, as a so called wrapped phase map. Phase unwrapping is the process of obtaining the underlying physical phase map from the wrapped phase. Tile-based phase unwrapping algorithms operate by first tessellating the phase map, then unwrapping individual tiles, and finally merging them to a continuous phase map. They can be implemented computationally efficiently and are robust to noise. However, they are prone to failure in the presence of phase residues or erroneous unwraps of single tiles. We tried to overcome these shortcomings by creating novel tile unwrapping and merging algorithms as well as creating a framework that allows to combine them in modular fashion. To increase the robustness of the tile unwrapping step, we implemented a model-based algorithm that makes efficient use of linear algebra to unwrap individual tiles. Furthermore, we adapted an established pixel-based unwrapping algorithm to create a quality guided tile merger. These original algorithms as well as previously existing ones were implemented in a modular phase unwrapping C++ framework. By examining different combinations of unwrapping and merging algorithms we compared our method to existing approaches. We could show that the appropriate choice of unwrapping and merging algorithms can significantly improve the unwrapped result in the presence of phase residues and noise. Beyond that, our modular framework allows for efficient design and test of new tile-based phase unwrapping algorithms. The software developed in this study is freely available.

A parallel numerical solver using hierarchically tiled arrays

Solving linear systems is an important problem for scientific computing. Exploiting parallelism is essential for solving complex systems, and this traditionally involves writing parallel algorithms on top of a library such as MPI. The SPIKE family of algorithms is one well-known example of a parallel solver for linear systems. The Hierarchically Tiled Array data type extends traditional data-parallel array operations with explicit tiling and allows programmers to directly manipulate tiles. The tiles of the HTA data type map naturally to the block nature of many numeric computations, including the SPIKE family of algorithms. The higher level of abstraction of the HTA enables the same program to be portable across different platforms. Current implementations target both shared-memory and distributed-memory models. In this thesis we present a proof-of-concept for portable linear solvers. We implement two algorithms from the SPIKE family using the HTA library. We show that our implementations of SPIKE exploit the abstractions provided by the HTA to produce a compact, clean code that can run on both shared-memory and distributed-memory models without modification. We discuss how we map the algorithms to HTA programs as well as examine their performance. We compare the performance of our HTA codes to comparable codes written in MPI as well as current state-of-the-art linear algebra routines.

Modelo para distribuição de recursos nos municípios brasileiros baseado na lei de diretrizes orçamentárias, análise multicritério e programação linear

The municipal management in any country of the globe requires planning and allocation of resources evenly. In Brazil, the Law of Budgetary Guidelines (LDO) guides municipal managers toward that balance. This research develops a model that seeks to find the balance of the allocation of public resources in Brazilian municipalities, considering the LDO as a parameter. For this using statistical techniques and multicriteria analysis as a first step in order to define allocation strategies, based on the technical aspects arising from the municipal manager. In a second step, presented in linear programming based optimization where the objective function is derived from the preference of the results of the manager and his staff. The statistical representation is presented to support multicriteria development in the definition of replacement rates through time series. The multicriteria analysis was structured by defining the criteria, alternatives and the application of UTASTAR methods to calculate replacement rates. After these initial settings, an application of linear programming was developed to find the optimal allocation of enforcement resources of the municipal budget. Data from the budget of a municipality in southwestern Paraná were studied in the application of the model and analysis of results.

Algoritmo paralelo para determinação de autovalores de matrizes hermitianas

Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.

Modelos linear e não linear em análises genéticas para sobrevivência de crias de ovinos da raça Santa Inês.

Resumo: Registros de sobrevivência do nascimento ao desmame de 3846 crias de ovinos da raça Santa Inês foram analisados por modelos de reprodutor linear e não linear (modelo de limiar), para estimar componentes de variância e herdabilidade. Os modelos usados para sobrevivência, analisada como característica da cria, incluíram os efeitos fixos de sexo, da combinação tipo de nascimento-criação da cria e da idade da ovelha ao parto, efeito da covariável peso da cria ao nascer e efeitos aleatórios de reprodutor, da classe rebanho-ano-estação e do resíduo. Componentes de variância para o modelo linear foram estimados pelo método da máxima verossimilhança restrita (REML) e para o modelo não linear por uma aproximação da máxima verossimilhança marginal (MML), pelo programa CMMAT2. O coeficiente de herdabilidade (h2) estimado pelo modelo de limiar foi de 0,29, e pelo modelo linear, 0,14. A correlação de ordem de Spearman entre as capacidades de transmissão dos reprodutores, com base nos dois modelos foi de 0,96. As estimativas de h2 obtidas indicam a possibilidade de se obter, por seleção, ganho genético para sobrevivência. [Linear and nonlinear models in genetic analyses of lamb survival in the Santa Inês hair sheep breed]. Abstract: Records of 3,846 lambs survival from birth to weaning of Santa Inês hair sheep breed, were analyzed by linear and non linear sire models (threshold model) to estimate variance components and heritability (h2). The models that were used to analyze survival, considered in this study as a lamb trait, included the fixed effects of sex of the lamb, combination of type of birth-rearing of lamb, and age of ewe, birth weight of lamb as covariate, and random effects of sire, herd-year-season and residual. Variance components were obtained using restricted maximum likelihood (REML), in linear model and marginal maximum likelihood in threshold model through CMMAT2 program. Estimate of heritability (h2) obtained by threshold model was 0.29 and by linear model was 0.14. Rank correlation of Spearman, between sire solutions based on the two models was 0.96. The obtained estimates in this study indicate that it is possible to acquire genetic gain to survival by selection.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

Caffeine Intake and its Association with Disease Progression, Sleep Quality and Anxiety Symptoms and Nutritional Alterations in People Living with HIV in the Miami Adult Studies on HIV Cohort

Miami-Dade County has approximately 27,000 people living with HIV (PLWH), and the highest HIV incidence in the nation. PLWH have reported several types of sleep disturbances. Caffeine is an anorexic and lipolytic stimulant that may adversely affect sleep patterns, dietary intakes and body composition. High caffeine consumption (>250 mg. per day or the equivalent of >4 cups of brewed coffee) may also affect general functionality, adherence to antiretroviral treatment (ART) and HIV care. This study assess the relationship of high caffeine intake with markers of disease progression, sleep quality, insomnia, anxiety, nutritional intakes and body composition. A convenience sample of 130 PLWH on stable ART were recruited from the Miami Adult Studies on HIV (MASH) cohort, and followed for three months. After consenting, questionnaires on Modified Caffeine Consumption (MCCQ), Pittsburg Insomnia Rating Scale (PIRS), Pittsburg Sleep Quality Index (PSQI), Generalized Anxiety Disorder-7 (GAD-7), socio-demographics, drug and medication use were completed. CD4 count, HIV viral load, anthropometries, and body composition measures were obtained. Mean age was 47.89±6.37 years, 60.8% were male and 75.4% were African-Americans. Mean caffeine intake at baseline was 337.63 ± 304.97 mg/day (Range: 0-1498 mg/day) and did not change significantly at 3 months. In linear regression, high caffeine consumption was associated with higher CD4 cell count (β=1.532, P=0.049), lower HIV viral load (β=-1.067, P=0.048), higher global PIRS (β=1.776, P=0.046), global PSQI (β=2.587, P=0.038), and GAD-7 scores (β=1.674, P=0.027), and with lower fat mass (β=-0.994, P=0.042), energy intakes (β=-1.643, P=0.042) and fat consumption (β=-1.902, P=0.044), adjusting for relevant socioeconomic and disease progression variables. Over three months, these associations remained significant. The association of high caffeine with lower BMI weakened when excluding users of other anorexic and stimulant drugs such as cocaine and methamphetamine, suggesting that caffeine in combination, but not alone, may worsen their action. In summary, high caffeine consumption was associated with better measures of disease progression; but was also detrimental on sleep quality, nutritional intakes, BMI and body composition and associated with insomnia and anxiety. Large scale studies for longer time are needed to elucidate the contribution of caffeine to the well-being of PLWH.