The Legendre Formula in Clifford Analysis

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Transition matrices characterizing a certain totally discontinuous map of the interval

We study a totally discontinuous interval map defined in [0,1] which is associated to a deformation of the shift map on two symbols 0−1. We define a sequence of transition matrices which characterizes the effect of the interval map on a family of partitions of the interval [0,1]. Recursive algorithms that build the sequence of matrices and their left and right eigenvectors are deduced. Moreover, we compute the Artin zeta function for the interval map.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.

Modifications in the correlation function in poly(vinyl alcohol)/silica hybrid wet gels

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Biodegradable Nanoparticles Containing Benzopsoralens: An Attractive Strategy for Modifying Vascular Function in Pathological Skin Disorders

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Loss of DNA polymerase zeta enhances spontaneous tumorigenesis.

Mammalian genomes encode at least 15 distinct DNA polymerases, functioning as specialists in DNA replication, DNA repair, recombination, or bypass of DNA damage. Although the DNA polymerase zeta (polzeta) catalytic subunit REV3L is important in defense against genotoxins, little is known of its biological function. This is because REV3L is essential during embryogenesis, unlike other translesion DNA polymerases. Outstanding questions include whether any adult cells are viable in the absence of polzeta and whether polzeta status influences tumorigenesis. REV3L-deficient cells have properties that could influence the development of neoplasia in opposing ways: markedly reduced damage-induced point mutagenesis and extensive chromosome instability. To answer these questions, Rev3L was conditionally deleted from tissues of adult mice using MMTV-Cre. Loss of REV3L was tolerated in epithelial tissues but not in the hematopoietic lineage. Thymic lymphomas in Tp53(-/-) Rev3L conditional mice occurred with decreased latency and higher incidence. The lymphomas were populated predominantly by Rev3L-null T cells, showing that loss of Rev3L can promote tumorigenesis. Remarkably, the tumors were frequently oligoclonal, consistent with accelerated genetic changes in the absence of Rev3L. Mammary tumors could also arise from Rev3L-deleted cells in both Tp53(+/+) and Tp53(+/-) backgrounds. Mammary tumors in Tp53(+/-) mice deleting Rev3L formed months earlier than mammary tumors in Tp53(+/-) control mice. Prominent preneoplastic changes in glandular tissue adjacent to these tumors occurred only in mice deleting Rev3L and were associated with increased tumor multiplicity. Polzeta is the only specialized DNA polymerase yet identified that inhibits spontaneous tumor development.

14-3-3 ZETA OVEREXPRESSION SERVES AS A NOVEL MOLECULAR SWITCH TURNING TGF-BETA FROM TUMOR SUPPRESSOR TO TUMOR PROMOTER

TGF-β plays an important role in differentiation and tissue morphogenesis as well as cancer progression. However, the role of TGF-β in cancer is complicate. TGF-β has primarily been recognized as tumor suppressor, because it can directly inhibit cell proliferation of normal and premalignant epithelial cell. However, in the last stage of tumor progression, TGF-β functions as tumor promoter to enhance tumor cells metastatic dissemination and expands metastatic colonies. Currently, the mechanism of how TGF-β switches its role from tumor suppressor to promoter still remains elusive. Here we identify that overexpression of 14-3-3ζ inhibits TGF-β’s cell cytostatic program through destabilizing p53 in non-transformed human mammary epithelial cells. Mechanistically, we found that 14-3-3ζ overexpression leads to 14-3-3σ downregulation, thereby activates PI3K/Akt signaling pathway and degrades p53, and further inhibits TGF-β induced p21 expression and cell cytostatic function. In addition, we found that overexpression of 14-3-3ζ promotes TGF-β induced breast cancer cells bone metastatic colonization through stabilizing Gli2, which is an important co-transcriptional factor for p-smad2 to activate PTHrP expression and bone osteolytic effect. Taken together, we reveal a novel mechanism that 14-3-3ζ dictates the tumor suppressor or metastases promoter activities of TGF-β signaling pathway through switching p-smad2 binding partner from p53 to Gli2. The expected results will not only provide us the better understanding of the important role of 14-3-3ζ in the early stage of breast cancer development, but also deeply impact our knowledge of signaling mechanisms underlying the complex roles of TGF-β in cancer, which will give us a more accurate strategy to determine when and how anti-TGF-β targeted therapy might be effective.

Transcriptional activation of human adult alpha-globin genes by hypersensitive site-40 enhancer: function of nuclear factor-binding motifs occupied in erythroid cells.

The developmental stage- and erythroid lineage-specific activation of the human embryonic zeta- and fetal/adult alpha-globin genes is controlled by an upstream regulatory element [hypersensitive site (HS)-40] with locus control region properties, a process mediated by multiple nuclear factor-DNA complexes. In vitro DNase I protection experiments of the two G+C-rich, adult alpha-globin promoters have revealed a number of binding sites for nuclear factors that are common to HeLa and K-562 extracts. However, genomic footprinting analysis has demonstrated that only a subset of these sites, clustered between -130 and +1, is occupied in an erythroid tissue-specific manner. The function of these in vivo-occupied motifs of the alpha-globin promoters, as well as those previously mapped in the HS-40 region, is assayed by site-directed mutagenesis and transient expression in embryonic/fetal erythroid K-562 cells. These studies, together with our expression data on the human embryonic zeta-globin promoter, provide a comprehensive view of the functional roles of individual nuclear factor-DNA complexes in the final stages of transcriptional activation of the human alpha-like globin promoters by the HS-40 element.

Cellular protein kinase C isoform zeta regulates human parainfluenza virus type 3 replication.

Phosphorylation of the P proteins of nonsegmented negative-strand RNA viruses is critical for their function as transactivators of the viral RNA polymerases. Using unphosphorylated P protein of human parainfluenza virus type 3 (HPIV3) expressed in Escherichia coli, we have shown that the cellular protein kinase that phosphorylates P in vitro is biochemically and immunologically indistinguishable from cellular protein kinase C isoform zeta (PKC-zeta). Further, PKC-zeta is specifically packaged within the progeny HPIV3 virions and remains tightly associated with the ribonucleoprotein complex. The P protein seems also to be phosphorylated intracellularly by PKC-zeta, as shown by the similar protease digestion pattern of the in vitro and in vivo phosphorylated P proteins. The growth of HPIV3 in CV-1 cells is completely abrogated when a PKC-zeta-specific inhibitor pseudosubstrate peptide was delivered into cells. These data indicate that PKC-zeta plays an important role in HPIV3 gene expression by phosphorylating P protein, thus providing an opportunity to develop antiviral agents against an important human pathogen.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.

Doehlert Design-desirability Function Multi-criteria Optimal Separation Of 17 Phenolic Compounds From Extra-virgin Olive Oil By Capillary Zone Electrophoresis.

In Brazil, the consumption of extra-virgin olive oil (EVOO) is increasing annually, but there are no experimental studies concerning the phenolic compound contents of commercial EVOO. The aim of this work was to optimise the separation of 17 phenolic compounds already detected in EVOO. A Doehlert matrix experimental design was used, evaluating the effects of pH and electrolyte concentration. Resolution, runtime and migration time relative standard deviation values were evaluated. Derringer's desirability function was used to simultaneously optimise all 37 responses. The 17 peaks were separated in 19min using a fused-silica capillary (50μm internal diameter, 72cm of effective length) with an extended light path and 101.3mmolL(-1) of boric acid electrolyte (pH 9.15, 30kV). The method was validated and applied to 15 EVOO samples found in Brazilian supermarkets.

Effect Of Exercise Test On Pulmonary Function Of Obese Adolescents.

to investigate the pulmonary response to exercise of non-morbidly obese adolescents, considering the gender. a prospective cross-sectional study was conducted with 92 adolescents (47 obese and 45 eutrophic), divided in four groups according to obesity and gender. Anthropometric parameters, pulmonary function (spirometry and oxygen saturation [SatO2]), heart rate (HR), blood pressure (BP), respiratory rate (RR), and respiratory muscle strength were measured. Pulmonary function parameters were measured before, during, and after the exercise test. BP and HR were higher in obese individuals during the exercise test (p = 0.0001). SatO2 values decreased during exercise in obese adolescents (p = 0.0001). Obese males had higher levels of maximum inspiratory and expiratory pressures (p = 0.0002) when compared to obese and eutrophic females. Obese males showed lower values of maximum voluntary ventilation, forced vital capacity, and forced expiratory volume in the first second when compared to eutrophic males, before and after exercise (p = 0.0005). Obese females had greater inspiratory capacity compared to eutrophic females (p = 0.0001). Expiratory reserve volume was lower in obese subjects when compared to controls (p ≤ 0,05). obese adolescents presented changes in pulmonary function at rest and these changes remained present during exercise. The spirometric and cardiorespiratory values were different in the four study groups. The present data demonstrated that, in spite of differences in lung growth, the model of fat distribution alters pulmonary function differently in obese female and male adolescents.