Nash multiplicity sequences and Hironaka's order function

When X is a d-dimensional variety defined over a field k of characteristic zero, a constructive resolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.The authors were partially supported by MTM2015-68524-P. The third author was supported by BES-2013-062656

Nash multiplicity sequences and Hironaka's order function

Producción CientíficaWhen X is a d-dimensional variety defined over a field k of characteristic zero, a constructive resolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.Ministerio de Economía, Industria y Competitividad (Project MTM2015-68524-P

Nash multiplicities and resolution invariants

Producción CientíficaThe Nash multiplicity sequence was defined by M. Lejeune-Jalabert as a non-increasing sequence of integers attached to a germ of a curve inside a germ of a hypersurface. M. Hickel generalized this notion and described a sequence of blow ups which allows us to compute it and study its behavior. In this paper, we show how this sequence can be used to compute some invariants that appear in algorithmic resolution of singularities. Moreover, this indicates that these invariants from constructive resolution are intrinsic to the variety since they can be read in terms of its space of arcs. This result is a first step connecting explicitly arc spaces and algorithmic resolution of singularities

Nash multiplicities and resolution invariants

The Nash multiplicity sequence was defined by Lejeune-Jalabert as a non-increasing sequence of integers attached to a germ of a curve inside a germ of a hypersurface. Hickel generalized this notion and described a sequence of blow ups which allows us to compute it and study its behavior. In this paper, we show how this sequence can be used to compute some invariants that appear in algorithmic resolution of singularities. Moreover, this indicates that these invariants from constructive resolution are intrinsic to the variety since they can be read in terms of its space of arcs. This result is a first step connecting explicitly arc spaces and algorithmic resolution of singularitie

Aldehydes as photoremovable directing groups: synthesis of pyrazoles by a photocatalyzed [3+2] cycloaddition/norrish type fragmentation sequence

A straightforward methodology for the regioselective synthesis of pyrazoles has been developed by a domino sequence based on a photoclick cycloaddition followed by a photocatalyzed oxidative deformylation reaction. Distinguishing features of this protocol include an unprecedented photoredox-catalyzed Norrish type fragmentation under green-light irradiation and the use of α,β-unsaturated aldehydes as synthetic equivalents of alkynes, where the aldehyde is acting as a novel photoremovable directing groupThis work was supported by the MINECO (CTQ2014-53894-R and CTQ2017-85454-C2-2-P) and FEDER/MICIU (PGC2018-098660-B-I00) of Spain. L.O.-R. thanks MINECO for a FPI fellowship, and A.P.-E. thanks CAM for a postdoctoral fellowshi

Catalytic Asymmetric Synthesis of Bicycloprolines by a 1,3-Dipolar Cycloaddition/Intramolecular Alkylation Strategy

This document is the Accepted Manuscript version of a Published Work that appeared in final form inJournal of Organic Chemistry, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1021/acs.joc.6b01100 to Published Work, see http://pubs.acs.org/page/policy/articlesonrequest/index.htmlThe diastereoselective one-pot synthesis of hexahydrocyclopenta [b] pyrrole derivatives (bicycloprolines) has been achieved by base-mediated reactions of (E)-tert-butyl 6-bromo-2-hexenoate with α-imino esters. The catalytic asymmetric version of this process has been efficiently achieved using the CuI/(R)-DTBM-Segphos complex as a catalyst following a two-step 1,3-dipolar cycloaddition/intramolecular alkylation sequence.Financial support of this work by the Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional (MINECO CTQ2012-35790 and MINECO/FEDER CTQ2015-66954-P) are gratefully acknowledged. M.G.-E. and A.P.-E. thank the MICINN for predoctoral fellowship

Molecular method for the characterization of Coxiella burnetii from clinical and environmental samples: variability of genotypes in Spain

BACKGROUND: Coxiella burnetii is a highly clonal microorganism which is difficult to culture, requiring BSL3 conditions for its propagation. This leads to a scarce availability of isolates worldwide. On the other hand, published methods of characterization have delineated up to 8 different genomic groups and 36 genotypes. However, all these methodologies, with the exception of one that exhibited limited discriminatory power (3 genotypes), rely on performing between 10 and 20 PCR amplifications or sequencing long fragments of DNA, which make their direct application to clinical samples impracticable and leads to a scarce accessibility of data on the circulation of C. burnetii genotypes. RESULTS: To assess the variability of this organism in Spain, we have developed a novel method that consists of a multiplex (8 targets) PCR and hybridization with specific probes that reproduce the previous classification of this organism into 8 genomic groups, and up to 16 genotypes. It allows for a direct characterization from clinical and environmental samples in a single run, which will help in the study of the different genotypes circulating in wild and domestic cycles as well as from sporadic human cases and outbreaks. The method has been validated with reference isolates. A high variability of C. burnetii has been found in Spain among 90 samples tested, detecting 10 different genotypes, being those adaA negative associated with acute Q fever cases presenting as fever of intermediate duration with liver involvement and with chronic cases. Genotypes infecting humans are also found in sheep, goats, rats, wild boar and ticks, and the only genotype found in cattle has never been found among our clinical samples. CONCLUSIONS: This newly developed methodology has permitted to demonstrate that C. burnetii is highly variable in Spain. With the data presented here, cattle seem not to participate in the transmission of C. burnetii to humans in the samples studied, while sheep, goats, wild boar, rats and ticks share genotypes with the human population

Si l@s estudiantes universitari@s no eligen ingenierías que las ingenierías vayan al colegio

La pandemia provocada por el virus SARS-CoV-2 ha puesto de manifiesto la imperiosa necesidad de construir una sociedad basada en el conocimiento. Otros grandes retos sociales como son revertir el cambio climático y la conservación y/o recuperación del entorno natural hacen énfasis en la necesidad de un desarrollo sostenible e igualitario. En este sentido es necesario concienciar a las nuevas generaciones del papel primordial que deben jugar las ingenieras e ingenieros en el desarrollo futuro como motores de ese cambio necesario. Sin embargo, el número de estudiantes de ingenierías disminuye paulatinamente, siendo además profesiones copadas mayoritariamente por hombres. En el presente proyecto se plantea ir a colegios e institutos de la Comunidad de Madrid a realizar actividades que pongan de manifiesto lo que la ingeniería puede hacer por la sociedad, presentado por los y las estudiantes de ingeniería química de la UCM que servirán de referentes tanto femeninos como masculinos para las generaciones venideras

Non-productive angiogenesis disassembles Aß plaque-associated blood vessels

The human Alzheimer’s disease (AD) brain accumulates angiogenic markers but paradoxically, the cerebral microvasculature is reduced around Aß plaques. Here we demonstrate that angiogenesis is started near Aß plaques in both AD mouse models and human AD samples. However, endothelial cells express the molecular signature of non-productive angiogenesis (NPA) and accumulate, around Aß plaques, a tip cell marker and IB4 reactive vascular anomalies with reduced NOTCH activity. Notably, NPA induction by endothelial loss of presenilin, whose mutations cause familial AD and which activity has been shown to decrease with age, produced a similar vascular phenotype in the absence of Aß pathology. We also show that Aß plaque-associated NPA locally disassembles blood vessels, leaving behind vascular scars, and that microglial phagocytosis contributes to the local loss of endothelial cells. These results define the role of NPA and microglia in local blood vessel disassembly and highlight the vascular component of presenilin loss of function in AD

Competencias básicas para la aplicación de la medicina regenerativa en la clínica de pequeños animales

Depto. de Medicina y Cirugía AnimalFac. de VeterinariaFALSEsubmitte