Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.

Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

On the Iwasawa decomposition

La decomposizione di Iwasawa è una particolare decomposizione di un gruppo di Lie semisemplice G in cui i fattori sono sottogruppi chiusi di G. In questa tesi si analizza nello specifico la decomposizione di Iwasawa del gruppo SL(2,R), dandone alcune rilevanti applicazioni algebriche e topologiche (Capitolo 2). Alcune di queste sono ad esempio l'omeomorfismo di SL(2,R) con l'interno di un toro solido e l'esistenza di un unico omomorfismo continuo (quello banale) da SL(2,R) al gruppo additivo di R. Vengono poi studiate le classi di coniugio degli elementi di SL(2,R) in termini dei sottogruppi che compaiono nella decomposizione di Iwasawa e l'azione di SL(2,R) sul semipiano superiore del piano complesso, da cui è possibile ricavare una dimostrazione alternativa della decomposizione di Iwasawa. Il Capitolo 1 raccoglie il materiale introduttivo utile ad una lettura autocontenuta della tesi; in particolare vengono introdotti i gruppi topologici GL(n,F) e SL(n,F) (dove F indica un campo), l'azione di un gruppo su un insieme e l'esponenziale di matrici. Infine nel Capitolo 3 viene estesa la dimostrazione della decomposizione di Iwasawa ai gruppi SL(n,R) e SL(n,C).

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Efficacy Of Ethylene-diamine-tetra-acetic Acid Associated With Chlorhexidine On Intracanal Medication Removal: A Scanning Electron Microscopy Study.

The aim of this study was to evaluate the effectiveness of 17% ethylene-diamine-tetra-acetic acid (EDTA) used alone or associated with 2% chlorhexidine gel (CHX) on intracanal medications (ICM) removal. Sixty single-rooted human teeth with fully formed apex were selected. The cervical and middle thirds of each canal were prepared with Gates Glidden drills and rotary files. The apical third was shaped with hand files. The specimens were randomly divided into two groups depending on the ICM used after instrumentation: calcium hydroxide Ca(OH)(2) +CHX or Ca(OH)(2) +sterile saline (SS). After seven days, each group was divided into subgroups according to the protocol used for ICM removal: instrumentation and irrigation either with EDTA, CHX+EDTA, or SS (control groups). All specimens were sectioned and processed for observation of the apical thirds by using scanning electron microscopy. Two calibrated evaluators attributed scores to each specimen. The differences between the protocols for ICM removal were analyzed with Kruskal-Wallis and Mann-Whitney U tests. Friedman and Wilcoxon signed rank tests were used for comparison between the score of debris obtained in each root canal third. Remains of Ca(OH)(2) were found in all specimens independently of the protocol and ICM used (P > 0.05). Seventeen percent EDTA showed the best results in removing ICM when used alone (P < 0.05), particularly in those associated with CHX. It was concluded that the chelating agent 17% EDTA significantly improved the removal of ICM when used alone. Furthermore, the type of the vehicle associated with Ca(OH)(2) also plays a role in the ICM removal.

Metals And (metallo)proteins Identification In Vitreous Humor Focusing On Post-mortem Biochemistry.

This work describes the evaluation of metals and (metallo)proteins in vitreous humor samples and their correlations with some biological aspects in different post-mortem intervals (1-7 days), taking into account both decomposing and non-decomposing bodies. After qualitative evaluation of the samples involving 26 elements, representative metal ions (Fe, Mg and Mo) are determined by inductively coupled plasma mass spectrometry after using mini-vial decomposition system for sample preparation. A significant trend for Fe is found with post-mortem time for decomposing bodies because of a significant increase of iron concentration when comparing samples from bodies presenting 3 and 7 days post-mortem interval. An important clue to elucidate the role of metals is the coupling of liquid chromatography with inductively coupled plasma mass spectrometry for identification of metals linked to proteins, as well as mass spectrometry for the identification of those proteins involved in the post-mortem interval.

Correlation Between Testosterone And Psa Kinetics In Metastatic Prostate Cancer Patients Treated With Diverse Chemical Castrations.

To assess total testosterone and prostatic-specific antigen (PSA) kinetics among diverse chemical castrations, advanced-stage prostate cancer patients were randomized into three groups of 20: Group 1, Leuprolide 3.75 mg; Group 2, Leuprolide 7.5 mg; and Group 3, Goserelin 3.6 mg. All groups were treated with monthly application of the respective drugs. The patients' levels of serum total testosterone and PSA were evaluated at two time periods: before the treatment and 3 months after the treatment. Spearman's rank correlation coefficient was utilized to verify the hypothesis of linear correlation between total testosterone and PSA levels. At the beginning the patients' age, stage, grade, PSA, and total testosterone were similar within the three groups, with median age 72, 70, and 70 years in Groups 1, 2, and 3, respectively. Three months after the treatment, patients who received Leuprolide 7.5 mg presented significantly lower median total testosterone levels compared with Goserelin 3.6 mg and Leuprolide 3.75 mg (9.5 ng/dL vs. 20.0 ng/dL vs. 30.0 ng/dL, respectively; p = .0072), while those who received Goserelin 3.6 mg presented significantly lower PSA levels compared with Leuprolide 7.5 mg and Leuprolide 3.75 mg (0.67 vs. 1.86 vs. 2.57, respectively; p = .0067). There was no linear correlation between total testosterone and PSA levels. Overall, regarding castration levels of total testosterone, 28.77% of patients did not obtain levels ≤50 ng/dL and 47.80% did not obtain levels ≤20 ng/dL. There was no correlation between total testosterone and PSA kinetics and no equivalence among different pharmacological castrations.

Aplicação do escore MELD em pacientes submetidos a transplante de fígado: análise retrospectiva da sobrevida e dos fatores preditivos a curto e longo prazo

BACKGROUND: The model for end-stage liver disease (MELD) was developed to predict short-term mortality in patients with cirrhosis. There are few reports studying the correlation between MELD and long-term posttransplantation survival. AIM: To assess the value of pretransplant MELD in the prediction of posttransplant survival. METHODS: The adult patients (age >18 years) who underwent liver transplantation were examined in a retrospective longitudinal cohort of patients, through the prospective data base. We excluded acute liver failure, retransplantation and reduced or split-livers. The liver donors were evaluated according to: age, sex, weight, creatinine, bilirubin, sodium, aspartate aminotransferase, personal antecedents, brain death cause, steatosis, expanded criteria donor number and index donor risk. The recipients' data were: sex, age, weight, chronic hepatic disease, Child-Turcotte-Pugh points, pretransplant and initial MELD score, pretransplant creatinine clearance, sodium, cold and warm ischemia times, hospital length of stay, blood requirements, and alanine aminotransferase (ALT >1,000 UI/L = liver dysfunction). The Kaplan-Meier method with the log-rank test was used for the univariable analyses of posttransplant patient survival. For the multivariable analyses the Cox proportional hazard regression method with the stepwise procedure was used with stratifying sodium and MELD as variables. ROC curve was used to define area under the curve for MELD and Child-Turcotte-Pugh. RESULTS: A total of 232 patients with 10 years follow up were available. The MELD cutoff was 20 and Child-Turcotte-Pugh cutoff was 11.5. For MELD score > 20, the risk factors for death were: red cell requirements, liver dysfunction and donor's sodium. For the patients with hyponatremia the risk factors were: negative delta-MELD score, red cell requirements, liver dysfunction and donor's sodium. The regression univariated analyses came up with the following risk factors for death: score MELD > 25, blood requirements, recipient creatinine clearance pretransplant and age donor >50. After stepwise analyses, only red cell requirement was predictive. Patients with MELD score < 25 had a 68.86%, 50,44% and 41,50% chance for 1, 5 and 10-year survival and > 25 were 39.13%, 29.81% and 22.36% respectively. Patients without hyponatremia were 65.16%, 50.28% and 41,98% and with hyponatremia 44.44%, 34.28% and 28.57% respectively. Patients with IDR > 1.7 showed 53.7%, 27.71% and 13.85% and index donor risk <1.7 was 63.62%, 51.4% and 44.08%, respectively. Age donor > 50 years showed 38.4%, 26.21% and 13.1% and age donor <50 years showed 65.58%, 26.21% and 13.1%. Association with delta-MELD score did not show any significant difference. Expanded criteria donors were associated with primary non-function and severe liver dysfunction. Predictive factors for death were blood requirements, hyponatremia, liver dysfunction and donor's sodium. CONCLUSION: In conclusion MELD over 25, recipient's hyponatremia, blood requirements, donor's sodium were associated with poor survival.

PARAFAC: uma ferramenta quimiométrica para tratamento de dados multidimensionais. Aplicações na determinação direta de fármacos em plasma humano por espectrofluorimetria

Since the last decade, the combined use of chemometrics and molecular spectroscopic techniques has become a new alternative for direct drug determination, without the need of physical separation. Among the new methodologies developed, the application of PARAFAC in the decomposition of spectrofluorimetric data should be highlighted. The first objective of this article is to describe the theoretical basis of PARAFAC. For this purpose, a discussion about the order of chemometric methods used in multivariate calibration and the development of multi-dimensional methods is presented first. The other objective of this article is to divulge for the Brazilian chemical community the potential of the combination PARAFAC/spectrofluorimetry for the determination of drugs in complex biological matrices. For this purpose, two applications aiming at determining, respectively, doxorrubicine and salicylate in human plasma are presented.

Produção de serapilheira e decomposição do material foliar em um cerradão na Estação Ecológica de Jataí, município de Luiz Antônio, SP, Brasil

We estimate litter production and leaf decomposition rate in a cerradão area, physiognomy little studied and very threatened in São Paulo State. During the period of study, litter production was 5646.9 kg.ha-1.year-1, which the 'leaf' fraction corresponded to 4081.2 kg.ha¹.year¹; the 'branch' fraction, to 1066.1 kg.ha-1.year-1; the 'reproductive structures' fraction, to 434.1 kg.ha-1.year-1; and the 'miscellaneous' fraction to 65.5 kg.ha-1.year-1. Litter production was highly seasonal and negatively correlated with relative humidity and air temperature. Leaf production was negatively correlated with relative humidity, rainfall, and air temperature. There was no significant difference between litter production found in this study and those in two other sites with cerradão and semideciduous forest, but these physiognomies differed significantly from the cerrado sensu stricto. Leaf decomposition rate (K) was 0.56. Half-life of the decomposing material was 1.8 years and turnover time was 2.3 years.

Hipotaxe e Gramaticalização: uma Análise das Construções de Tempo e de Condição

This paper studies complex sentences with temporal hypotatic clauses and with conditional hypotatic clauses in order to investigate the degree of grammaticalization shown by these two kinds of utterances. Our hypothesis is that the more the hypotatic clause is integrated to the nuclear clause, the greater is the degree of grammaticalization. Such degree of integration was measured according to three groups of factors, and the results show that, regarding two of the variables evaluated, the conditional clauses are the most integrated to their nucleus, but, in another rank of evaluation, the temporal clauses are the most integrated ones. Considering that this study is based on a functionalist view, the results may be interpreted according to the principle that there is a competition of motivations in the use of language, so that each utterance reflects the balance of such forces.

Tua imensa torcida e bem feliz... da relação torcedor com o clube

Universidade Estadual de Campinas . Faculdade de Educação Física

Variabilidade da frequencia cardiaca : estudo das influencias autonomicas sobre suas caracteristicas temporal e espectral em halterofilistas e sedentarios

Universidade Estadual de Campinas. Faculdade de Educação Física