Riemann's Hypothesis

Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function.

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.

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.

Contribuciones de weierstrass a las funciones elípticas

Este trabajo de investigación de maestría contiene algunas reflexiones en torno a la emergencia histórica de la función de Weierstrass. Entre otros elementos interesantes, se prueba que dicha función se hubiera podido construir con los elementos disponibles en la época, es decir, los aportes de Abel, Jacobi y Liouville en el campo de las funciones elípticas. También se precisa la contribución original de Weierstrass en este campo, la cual consistió en fundar la teoría de las funciones elípticas sobre la base firme de los productos y las series infinitas; claro está, aprovechando las ventajas del lenguaje de la Variable Compleja.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.