Métodos de Interpolación Basados en Funciones de Base Radial con Aplicaciones a la Reconstrucción de Imágenes

This article presents the Radial Base Functions (RBFs) as a functional interpolation method for implicit surface reconstruction from points cloud.  These methods allow not only to improve inaccuracies resulting from scanners, but also possible discontinuities that occur in the point clouds.  The complexity of three-dimensional objects makes reconstruction difficult since devices such as scanners do not always faithfully reproduce the objects, which can lead to information gaps or an incomplete reconstruction. Interpolation methods based on RBFs allow to correct these errors.  Three-dimensional surface reconstruction has wide applications in biomedical engineering, in the design of industrial parts, among others.  With the algorithm, we developed we have been able to make reconstructions of both explicit and implicit functions, in two and three dimensions.Keywords:  Radial Basis Functions, Three-dimensional reconstruction, Interpolation Methods

Familias de existencia y unicidad y operadores diferenciales

El presente trabajo conlleva al estudio de las familias de existencia y unicidad de operadores lineales acotados como una herramienta para manejar el problema abstracto de Cauchy, así como algunas aplicaciones con operadores diferenciales relacionados con familias de existencia. Por razones técnicas, hemos dividido este trabajo en tres capítulos y un apéndice. En el primer capítulo se estudian las integrales de Riemann y las transformadas de Laplace para funciones valuadas en un espacio de Banach, así como el teorema de acotamiento uniforme. El segundo capítulo es una presentación de las definiciones y propiedades básicas de la nueva familia de existencia así como su compañera familia de unicidad que incluye sus conexiones con el problema abstracto de Cauchy. El tercer y último capítulo se enfoca en el problema de cuando los operadores diferenciales, así como los operadores matriciales tienen familias E0 de existencia. En el apéndice se presentan los espacios de Sobolev y los teoremas de inmersión, temas que son necesarios para el desarrollo del tercer capítulo

Atrasentan and renal events in patients with type 2 diabetes and chronic kidney disease (SONAR): a double-blind, randomised, placebo-controlled trial

Background: Short-term treatment for people with type 2 diabetes using a low dose of the selective endothelin A receptor antagonist atrasentan reduces albuminuria without causing significant sodium retention. We report the long-term effects of treatment with atrasentan on major renal outcomes. Methods: We did this double-blind, randomised, placebo-controlled trial at 689 sites in 41 countries. We enrolled adults aged 18–85 years with type 2 diabetes, estimated glomerular filtration rate (eGFR)25–75 mL/min per 1·73 m 2 of body surface area, and a urine albumin-to-creatinine ratio (UACR)of 300–5000 mg/g who had received maximum labelled or tolerated renin–angiotensin system inhibition for at least 4 weeks. Participants were given atrasentan 0·75 mg orally daily during an enrichment period before random group assignment. Those with a UACR decrease of at least 30% with no substantial fluid retention during the enrichment period (responders)were included in the double-blind treatment period. Responders were randomly assigned to receive either atrasentan 0·75 mg orally daily or placebo. All patients and investigators were masked to treatment assignment. The primary endpoint was a composite of doubling of serum creatinine (sustained for ≥30 days)or end-stage kidney disease (eGFR <15 mL/min per 1·73 m 2 sustained for ≥90 days, chronic dialysis for ≥90 days, kidney transplantation, or death from kidney failure)in the intention-to-treat population of all responders. Safety was assessed in all patients who received at least one dose of their assigned study treatment. The study is registered with ClinicalTrials.gov, number NCT01858532. Findings: Between May 17, 2013, and July 13, 2017, 11 087 patients were screened; 5117 entered the enrichment period, and 4711 completed the enrichment period. Of these, 2648 patients were responders and were randomly assigned to the atrasentan group (n=1325)or placebo group (n=1323). Median follow-up was 2·2 years (IQR 1·4–2·9). 79 (6·0%)of 1325 patients in the atrasentan group and 105 (7·9%)of 1323 in the placebo group had a primary composite renal endpoint event (hazard ratio [HR]0·65 [95% CI 0·49–0·88]; p=0·0047). Fluid retention and anaemia adverse events, which have been previously attributed to endothelin receptor antagonists, were more frequent in the atrasentan group than in the placebo group. Hospital admission for heart failure occurred in 47 (3·5%)of 1325 patients in the atrasentan group and 34 (2·6%)of 1323 patients in the placebo group (HR 1·33 [95% CI 0·85–2·07]; p=0·208). 58 (4·4%)patients in the atrasentan group and 52 (3·9%)in the placebo group died (HR 1·09 [95% CI 0·75–1·59]; p=0·65). Interpretation: Atrasentan reduced the risk of renal events in patients with diabetes and chronic kidney disease who were selected to optimise efficacy and safety. These data support a potential role for selective endothelin receptor antagonists in protecting renal function in patients with type 2 diabetes at high risk of developing end-stage kidney disease. Funding: AbbVie

Familias de existencia y unicidad para el problema abstracto de Cauchy.

El presente trabajo conlleva al estudio de las familias de existencia y unicidad de operadores lineales acotados definidos sobre espacios de Banach como una herramienta para manejar el problema abstracto de Cauchy. En este trabajo se presenta un sistema de operadores más general, la familia de existencia para un operador lineal, de operadores lineales acotados de un espacio de Banach (puede ser diferente de) en como una nueva herramienta por tratar con problema abstracto de Cauchy. Esta idea es algo diferente de lo tradicional. También se estudia a su compañera familia de unicidad

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old