Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Collagen I–mediated up-regulation of N-cadherin requires cooperative signals from integrins and discoidin domain receptor 1

Tumor cells undergo epithelial-to-mesenchymal transition (EMT) to convert from a benign to a malignant phenotype. Our recent focus has been signaling pathways that promote EMT in response to collagen. We have shown that human pancreatic cancer cells respond to collagen by up-regulating N-cadherin, which promotes tumor growth, invasion, and metastasis. Initial characterization showed that knocking down c-Jun NH2-terminal kinase prevented N-cadherin up-regulation and limited tumor growth and invasion in a mouse model for pancreatic cancer. The current study was designed to understand the pathway from collagen to N-cadherin up-regulation. Initiation of the signal requires two collagen receptors, α2β1 integrin and discoidin domain receptor (DDR) 1. Each receptor propagates signals through separate pathways that converge to up-regulate N-cadherin. Focal adhesion kinase (FAK)–related protein tyrosine kinase (Pyk2) is downstream of DDR1, whereas FAK is downstream of α2β1 integrin. Both receptor complexes rely on the p130 Crk-associated substrate scaffold. Interestingly, Rap1, but not Rho family guanosine triphosphatases, is required for the response to collagen I

Ergodicity of certain cocycles over certain interval exchanges

We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters

Metabolic Alterations in Pancreatic Cancer Progression

Pancreatic cancer is the third leading cause of cancer-related deaths in the USA. Pancreatic tumors are characterized by enhanced glycolytic metabolism promoted by a hypoxic tumor microenvironment and a resultant acidic milieu. The metabolic reprogramming allows cancer cells to survive hostile microenvironments. Through the analysis of the principal metabolic pathways, we identified the specific metabolites that are altered during pancreatic cancer progression in the spontaneous progression (KPC) mouse model. Genetically engineered mice exhibited metabolic alterations during PanINs formation, even before the tumor development. To account for other cells in the tumor microenvironment and to focus on metabolic adaptations concerning tumorigenic cells only, we compared the metabolic profile of KPC and orthotopic tumors with those obtained from KPC-tumor derived cell lines. We observed significant upregulation of glycolysis and the pentose phosphate pathway metabolites even at the early stages of pathogenesis. Other biosynthetic pathways also demonstrated a few common perturbations. While some of the metabolic changes in tumor cells are not detectable in orthotopic and spontaneous tumors, a significant number of tumor cell-intrinsic metabolic alterations are readily detectable in the animal models. Overall, we identified that metabolic alterations in precancerous lesions are maintained during cancer development and are largely mirrored by cancer cells in culture conditions

MUC16-mediated activation of mTOR and c-Myc reprograms pancreatic cancer metabolism.

MUC16, a transmembrane mucin, facilitates pancreatic adenocarcinoma progression and metastasis. In the current studies, we observed that MUC16 knockdown pancreatic cancer cells exhibit reduced glucose uptake and lactate secretion along with reduced migration and invasion potential, which can be restored by supplementing the culture media with lactate, an end product of aerobic glycolysis. MUC16 knockdown leads to inhibition of mTOR activity and reduced expression of its downstream target c-MYC, a key player in cellular growth, proliferation and metabolism. Ectopic expression of c-MYC in MUC16 knockdown pancreatic cancer cells restores the altered cellular physiology. Our LC-MS/MS based metabolomics studies indicate global metabolic alterations in MUC16 knockdown pancreatic cancer cells, as compared to the controls. Specifically, glycolytic and nucleotide metabolite pools were significantly decreased. We observed similar metabolic alterations that correlated with MUC16 expression in primary tumor tissue specimens from human pancreatic adenocarcinoma cancer patients. Overall, our results demonstrate that MUC16 plays an important role in metabolic reprogramming of pancreatic cancer cells by increasing glycolysis and enhancing motility and invasiveness

Silibinin-mediated metabolic reprogramming attenuates pancreatic cancer-induced cachexia and tumor growth.

Pancreatic ductal adenocarcinoma (PDAC) is the fourth leading cause of cancer-related deaths in the US. Cancer-associated cachexia is present in up to 80% of PDAC patients and is associated with aggressive disease and poor prognosis. In the present studies we evaluated an anti-cancer natural product silibinin for its effectiveness in targeting pancreatic cancer aggressiveness and the cachectic properties of pancreatic cancer cells and tumors. Our results demonstrate that silibinin inhibits pancreatic cancer cell growth in a dose-dependent manner and reduces glycolytic activity of cancer cells. Our LC-MS/MS based metabolomics data demonstrates that silibinin treatment induces global metabolic reprogramming in pancreatic cancer cells. Silibinin treatment diminishes c-MYC expression, a key regulator of cancer metabolism. Furthermore, we observed reduced STAT3 signaling in silibinin-treated cancer cells. Overexpression of constitutively active STAT3 was sufficient to substantially revert the silibinin-induced downregulation of c-MYC and the metabolic phenotype. Our in vivo investigations demonstrate that silibinin reduces tumor growth and proliferation in an orthotopic mouse model of pancreatic cancer and prevents the loss of body weight and muscle. It also improves physical activity including grip strength and latency to fall in tumor-bearing mice. In conclusion, silibinin-induced metabolic reprogramming diminishes cell growth and cachectic properties of pancreatic cancer cells and animal models

Ergodic infinite group extensions of geodesic flows on translation surfaces

We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that certain concrete staircases, covers of square-tiled surfaces, are not ergodic in almost every direction. In contrast we show the almost sure ergodicity of other concrete staircases. An appendix provides a combinatorial approach for the study of square-tiled surfaces

SIRT1-NOX4 Signaling Axis Regulates Cancer Cachexia

Approximately one third of cancer patients die due to complexities related to cachexia. However, the mechanisms of cachexia and the potential therapeutic interventions remain poorly studied. We observed a significant positive correlation between SIRT1 expression and muscle fiber cross-sectional area in pancreatic cancer patients. Rescuing Sirt1 expression by exogenous expression or pharmacological agents reverted cancer cell-induced myotube wasting in culture conditions and mouse models. RNA-seq and follow-up analyses showed cancer cell-mediated SIRT1 loss induced NF-κB signaling in cachectic muscles that enhanced the expression of FOXO transcription factors and NADPH oxidase 4 (Nox4), a key regulator of reactive oxygen species production. Additionally, we observed a negative correlation between NOX4 expression and skeletal muscle fiber cross-sectional area in pancreatic cancer patients. Knocking out Nox4 in skeletal muscles or pharmacological blockade of Nox4 activity abrogated tumor-induced cachexia in mice. Thus, we conclude that targeting the Sirt1-Nox4 axis in muscles is an effective therapeutic intervention for mitigating pancreatic cancer-induced cachexia

Na mira do sucesso : estratégias de combate ao insucesso escolar de alunos estrangeiros

Trabalho de projeto de mestrado, Ciências da Educação (Área de especialização Formação de Adultos), Universidade de Lisboa, Instituto de Educação, 2017Considerando a importância da integração no contexto escolar e consequentemente no sucesso educativo, o presente trabalho projeto, desenvolvido no âmbito do Mestrado em Ciências da Educação, área de especialidade em Formação de Adultos, centra-se na integração de alunos estrangeiros no ensino português, assim como na dinamização de atividades de promoção do seu sucesso escolar. Deste modo, o relatório apresenta como principais temáticas a integração de estrangeiros em Portugal, o insucesso escolar dos alunos estrangeiros e as políticas educativas de combate a este fenómeno, culminando na definição e desenvolvimento de um projeto de combate ao insucesso escolar destinado a este público. O trabalho desenvolvido junto destes jovens nos últimos nove anos e o diagnóstico elaborado no Agrupamento de Escolas João de Barros permitiu compreender a importância de intervir junto da população estrangeira, fomentando o sucesso educativo e a integração no país de acolhimento, uma vez que a taxa de retenção destes jovens está muito acima dos seus colegas autóctones.Considering the importance of integration in the school context, and consequently in educational success, this project, developed in the scope of the master’s degree in Educational Sciences, specialization in Adult Education, focuses on foreign students’ integration at the Portuguese educational system and activities that could be developed to promote their school success. Therefore, the main themes of the report are the integration of foreigners in Portugal, the lack of academic experience from foreign students and educational policies to reduce this barrier, in order to define and develop a project to combat school failure among this cases. The work developed for the last nine years with this students, the diagnostic elaborated in João de Barros Group of Schools, allowed me to understand the importance of an intervention among foreign students, to foment educational success and integration in the host country, bearing in mind that the retention rate in those cases is far above the native students’ average