Dense forests and Danzer sets

A set $Y\subseteq\mathbb{R}^d$ that intersects every convex set of volume $1$ is called a Danzer set. It is not known whether there are Danzer sets in $\mathbb{R}^d$ with growth rate $O(T^d)$. We prove that natural candidates, such as discrete sets that arise from substitutions and from cut-and-project constructions, are not Danzer sets. For cut and project sets our proof relies on the dynamics of homogeneous flows. We consider a weakening of the Danzer problem, the existence of uniformly discrete dense forests, and we use homogeneous dynamics (in particular Ratner's theorems on unipotent flows) to construct such sets. We also prove an equivalence between the above problem and a well-known combinatorial problem, and deduce the existence of Danzer sets with growth rate $O(T^d\log T)$, improving the previous bound of $O(T^d\log^{d-1} T)$

A Danzer set for Axis Parallel Boxes

We present concrete constructions of discrete sets in $\mathbb{R}^d$ ($d\ge 2$) that intersect every aligned box of volume $1$ in $\mathbb{R}^d$, and which have optimal growth rate $O(T^d)$

Inhibition of Melanoma Angiogenesis by Telomere Homolog Oligonucleotides

Telomere homolog oligonucleotides (T-oligos) activate an innate telomere-based program that leads to multiple anticancer effects. T-oligos act at telomeres to initiate signaling through the Werner protein and ATM kinase. We wanted to determine if T-oligos have antiangiogenic effects. We found that T-oligo-treated human melanoma (MM-AN) cells had decreased expression of vascular endothelial growth factor (VEGF), VEGF receptor 2, angiopoeitin-1 and -2 and decreased VEGF secretion. T-oligos activated the transcription factor E2F1 and inhibited the activity of the angiogenic transcription factor, HIF-1α. T-oligos inhibited EC tubulogenesis and total tumor microvascular density matrix invasion by MM-AN cells and ECs in vitro. In melanoma SCID xenografts, two systemic T-oligo injections decreased by 60% (P<.004) total tumor microvascular density and the functional vessels density by 80% (P <.002). These findings suggest that restriction of tumor angiogenesis is among the host's innate telomere-based anticancer responses and provide further evidence that T-oligos may offer a powerful new approach for melanoma treatment.National Institutes of Health (CA10515); American Skin Associatio

Estudio de factibilidad para la instalacion de una planta elaboradora de envases de vidrio en la Septima Region

283 p.El presente informe analiza la factibilidad técnica y económica para la instalación de una fábrica de envases de vidrio en la Región del Maule. El estudio comprende cuatro partes fundamentales: a) Examen de las condiciones del mercado regional de envases viñeros. b) Aspectos técnicos, considerando tamaño del proyecto,fuentes de abastecimiento de insumos, proceso industrial, especificaciones de la planta, decisión de ubicación y costos de inversión y de producción. c) Financiamiento de la inversión y proyección económica y financiera. d) Determinación de indicadores económicos de evaluación. Los aspectos principales de estos análisis son los siguientes: Mercado El estudio del mercado de envases de vidrio se ha hecho tomando como referencia la embotellacion regional de vinos, que actualmente representa unos 180 millones de litros anuales de un. total de 300 millones de litros producidos en la región en 1983. Las estimaciones hechas indican que para esta capacidad de embotellacion se haría necesario emplear unos 30 millones de envases diversos (unas 19.000 ton. de vidrio) entre botellas y garrafas, teniendo en cuenta el re torno y la quiebra de estas, pero sin considerar los envases existentes entre los usuarios. El mercado nacional de envases viñeros, abastecido en este momento por las empresas Cristal Chile y Cristalerías Toro, representa actualmente un volumen de 10.000 ton. De vidrio, de las cuales aproximadamente unas 1.500 ton. se destinan a la Séptima Región. Se estima que con un cese de las importaciones de botellas la oferta nacional ascendería a unas 21.000 ton., en tanto que la demanda en el país es de 28.000 ton. Considerando la oferta nacional para la Región del Maule y tomando en cuenta los envases que se mantienen circulando en el mercado (aproximadamente 4.200 ton.), la demanda insatisfecha en l

Heart failure in obesity:From early detection to the role in clinically overt disease

Obesity significantly increases the risk of developing heart failure. With current diagnostic techniques, it is currently difficult to recognize signs of cardiac dysfunction and heart failure in people with obesity. The overall goal of this thesis is to study signs of early cardiac dysfunction and to investigate the role of speckle tracking echocardiography and biomarkers in the early detection of cardiac dysfunction in people with obesity. In this thesis, we have shown that measurements such as left atrium strain and left ventricular global longitudinal strain, measured by speckle tracking echocardiography, better and earlier detect signs of cardiac dysfunction in people with obesity. Abnormalities in strain parameters are already visible, while no abnormalities are found in conventional echocardiographic parameters. Furthermore, we found that in a large proportion of people with obesity, cardiac dysfunction is reversible one year after bariatric surgery. In a panel of 92 biomarkers, we found that people with obesity have elevated markers related to inflammation, fibrosis, and atherosclerosis. In 78% of the examined biomarkers, there was a significant change one year after bariatric surgery. In people where cardiac dysfunction persisted one year after bariatric surgery, biomarkers related to inflammation and insulin resistance were found to be important predictors for the persistence of cardiac dysfunction. These results are important, especially considering the increasing prevalence of obesity worldwide and the associated risk of heart failure. Early and accurate detection of signs of heart failure can ultimately lead to earlier treatment and patient management. The results in this thesis show that there are better methods for detecting heart failure in people with severe obesity, which is important for clinical practice and can be applied