Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.

SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions

MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40

Weitzenböck Derivations and Classical Invariant Theory: I. Poincaré Series

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

The Lindelöf number greater than continuum is u-invariant

2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Relationship of Omega-3 Fatty Acids on C-Reactive Protein and Homocysteine in Haitian and African Americans with and without Type 2 Diabetes

Background: Omega-3 fatty acids (n-3) may be protective of cardiovascular risk factors for vulnerable populations. The purpose of this study was to assess the association between n-3 with, C-reactive protein (CRP), and homocysteine (HCY) in Black minorities with and without type 2 diabetes. Methods: A cross-sectional study was conducted with 406 participants: Haitian Americans (HA): n=238. African Americans (AA): n=172. Participants were recruited from a randomly generated mailing lists, local diabetes educators, community health practitioners and advertisements from 2008-2010. Sociodemographics and anthropometrics were collected and used to adjust analyses. All dietary variables were collected using the semi-quantitative food frequency questionnaire (FFQ) and used to quantify vitamin components. Blood was collected to measure CVD risk factors (blood lipids, HCY, and CRP). Results: African Americans had higher waist circumferences and C-reactive protein and consumed more calories as compared to Haitian Americans. Omega 3 fatty acid intake per calorie did not differ between these ethnicities, yet African Americans with low n-3 intake were three times more likely to have high C-reactive protein as compared to their counterparts [OR=3. 32 (1. 11, 9. 26) p=0.031]. Although homocysteine did not differ by ethnicity, African Americans with low omega 3 intake (<1 g/day) were four times as likely to have high homocysteine (>12 mg/L) as compared to their counterparts, adjusting for confounders [OR=4.63 (1.59, 12.0) p=0.004]. Consumption of n-3 by diabetes status was not associated with C-reactive protein or homocysteine levels. Conclusions: Consumption of n-3 may be protective of cardiovascular risk factors such as C-r

The effects of dietary omega-3 fatty acids on brain function are sex, age and brain-region specific

Omega (n)-3 polyunsaturated fatty acids (PUFA) have beneficial effects in neuropsychiatric illnesses. The goals of this thesis were to determine the effects of feeding diets varying in n-3 PUFA on brain fatty acid composition, and neurotrophin and myelin-related gene expression of the brain in an age, sex, and region-specific manner. A diet high in n-3 PUFA altered phospholipid docosahexaenoic acid (DHA) and oleic acid composition in an age, sex, and region-specific manner. Diet had no effect on the mRNA expression of brain-derived neurotrophic factor (BDNF) and tropomyosin-receptor kinase-B (TrkB); however, stearoyl-CoA desaturase-1 (SCD1) and myelin basic protein (MBP) gene expression increased in offspring fed a diet high in n-3 PUFA in an age, sex, and region-specific manner. DHA treatment to ex vivo cerebral cortical cells showed an increase in BDNF, TrkB, SCD1, and MBP mRNA expression compared to control cells. The mRNA expression of BDNF and SCD1 was higher in DHA treated cells compared to arachidonic acid treated cells. Overall, the data presented in this thesis suggests that the potential benefits of n-3 PUFA on brain function are sex, age and brain-region specific.

Experimental data of CO2, CO3, Omega calcite saturation, pH values, alpha and epsilon fractionation factors, and Dd18O calctite-water

The oxygen isotopic composition (d18O) of calcium carbonate of planktonic calcifying organisms is a key tool for reconstructing both past seawater temperature and salinity. The calibration of paloeceanographic proxies relies in general on empirical relationships derived from field experiments on extant species. Laboratory experiments have more often than not revealed that variables other than the target parameter influence the proxy signal, which makes proxy calibration a challenging task. Understanding these secondary or "vital" effects is crucial for increasing proxy accuracy. We present data from laboratory experiments showing that oxygen isotope fractionation during calcification in the coccolithophore Calcidiscus leptoporus and the calcareous dinoflagellate Thoracosphaera heimii is dependent on carbonate chemistry of seawater in addition to its dependence on temperature. A similar result has previously been reported for planktonic foraminifera, supporting the idea that the [CO3]2- effect on d18O is universal for unicellular calcifying planktonic organisms. The slopes of the d18O/[CO3]2- relationships range between -0.0243 per mil/(µmol/kg) (calcareous dinoflagellate T. heimii) and the previously published -0.0022 per mil/(µmol/kg) (non-symbiotic planktonic foramifera Orbulina universa), while C. leptoporus has a slope of -0.0048 per mil/(µmol/kg). We present a simple conceptual model, based on the contribution of d18O-enriched [HCO3]- to the [CO3]2- pool in the calcifying vesicle, which can explain the [CO3]2- effect on d18O for the different unicellular calcifiers. This approach provides a new insight into biological fractionation in calcifying organisms. The large range in d18O/[CO3]2- slopes should possibly be explored as a means for paleoreconstruction of surface [CO3]2-, particularly through comparison of the response in ecologically similar planktonic organisms.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Solvency considerations in the gamma-omega surplus model

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent.

Seawater carbonate chemistry and elemental composition of purple sea urchin (Strongylocentrotus purpuratus) calcite in a laboratory experiment

Ocean acidification will likely have negative impacts on invertebrates producing skeletons composed of calcium carbonate. Skeletal solubility is partly controlled by the incorporation of "foreign" ions (e.g. magnesium) into the crystal lattice of these skeletal structures, a process that is sensitive to a variety of biological and environmental factors. Here we explore effects of life stage, oceanographic region of origin, and changes in the partial pressure of carbon dioxide in seawater (pCO2) on trace elemental composition in the purple sea urchin (Strongylocentrotus purpuratus). We show that, similar to other urchin taxa, adult purple sea urchins have the ability to precipitate skeleton composed of a range of biominerals spanning low- to high-Mg calcites. Mg / Ca and Sr / Ca ratios were substantially lower in adult spines compared to adult tests. On the other hand, trace elemental composition was invariant among adults collected from four oceanographically distinct regions spanning a range of carbonate chemistry conditions (Oregon, Northern California, Central California, and Southern California). Skeletons of newly settled juvenile urchins that originated from adults from the four regions exhibited intermediate Mg / Ca and Sr / Ca between adult spine and test endmembers, indicating that skeleton precipitated during early life stages is more soluble than adult spines and less soluble than adult tests. Mean skeletal Mg / Ca or Sr / Ca of juvenile skeleton did not vary with source region when larvae were reared under present-day, global-average seawater carbonate conditions (400 µatm; pHT = 8.02 ± 0.03 1 SD; Omega calcite = 3.3 ± 0.2 1 SD). However, when reared under elevated pCO2 (900 µatm; pHT = 7.73 ± 0.03; Omega calcite = 1.8 ± 0.1), skeletal Sr / Ca in juveniles exhibited increased variance across the four regions. Although larvae from the northern populations (Oregon, Northern California, Central California) did not exhibit differences in Mg or Sr incorporation under elevated pCO2 (Sr / Ca = 2.10 ± 0.06 mmol/mol; Mg / Ca = 67.4 ± 3.9 mmol/mol), juveniles of Southern California origin partitioned ~8% more Sr into their skeletons when exposed to higher pCO2 (Sr / Ca = 2.26 ± 0.08 vs. 2.09 ± 0.005 mmol/mol 1 SD). Together these results suggest that the diversity of carbonate minerologies present across different skeletal structures and life stages in purple sea urchins does not translate into an equivalent geochemical plasticity of response associated with geographic variation or temporal shifts in seawater properties. Rather, composition of S. purpuratus skeleton precipitated during both early and adult life history stages appears relatively robust to spatial gradients and predicted future changes in carbonate chemistry. An exception to this trend may arise during early life stages, where certain populations of purple sea urchins may alter skeletal mineral precipitation rates and composition beyond a given pCO2 threshold. This potential for geochemical plasticity during early development in contrast to adult stage geochemical resilience adds to the growing body of evidence that ocean acidification can have differing effects across organismal life stages.

Automatically Evolving Rotation-invariant Texture Image Descriptors by Genetic Programming

In computer vision, training a model that performs classification effectively is highly dependent on the extracted features, and the number of training instances. Conventionally, feature detection and extraction are performed by a domain-expert who, in many cases, is expensive to employ and hard to find. Therefore, image descriptors have emerged to automate these tasks. However, designing an image descriptor still requires domain-expert intervention. Moreover, the majority of machine learning algorithms require a large number of training examples to perform well. However, labelled data is not always available or easy to acquire, and dealing with a large dataset can dramatically slow down the training process. In this paper, we propose a novel Genetic Programming based method that automatically synthesises a descriptor using only two training instances per class. The proposed method combines arithmetic operators to evolve a model that takes an image and generates a feature vector. The performance of the proposed method is assessed using six datasets for texture classification with different degrees of rotation, and is compared with seven domain-expert designed descriptors. The results show that the proposed method is robust to rotation, and has significantly outperformed, or achieved a comparable performance to, the baseline methods.