A Geometric Lower Bound Theorem

We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of chordality. Further, for C^2-convex bodies, asymptotically tight lower bounds on the g-numbers of the approximating polytopes are given, in terms of their Hausdorff distance from the convex body.Comment: 26 pages, 6 figures, to appear in Geometric and Functional Analysi

Reciprocal maximum likelihood degrees of diagonal linear concentration models

We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model L ⊆ Cn of dimension r is equal to (-2)rχM(1/2), where χM is the characteristic polynomial of the matroid M associated to L. In particular, this establishes the polynomiality of the rmld for general diagonal linear concentration models, positively answering a question of Sturmfels, Timme, and Zwiernik

Recommendations for ophthalmologic practice during the easing of COVID-19 control measures

In the context of the COVID-19 pandemic, this paper provides recommendations for medical eye care during the easing of control measures after lockdown. The guidelines presented are based on a literature review and consensus among all Spanish Ophthalmology Societies regarding protection measures recommended for the ophthalmologic care of patients with or without confirmed COVID-19 in outpatient, inpatient, emergency and surgery settings. We recommend that all measures be adapted to the circumstances and availability of personal protective equipment at each centre and also highlight the need to periodically update recommendations as we may need to readopt more restrictive measures depending on the local epidemiology of the virus. These guidelines are designed to avoid the transmission of SARS-CoV-2 among both patients and healthcare staff as we gradually return to normal medical practice, to prevent postoperative complications and try to reduce possible deficiencies in the diagnosis, treatment and follow-up of the ophthalmic diseases. With this update (5th) the Spanish Society of Ophthalmology is placed as one of the major ophthalmology societies providing periodic and systematized recommendations for ophthalmic care during the COVID-19 pandemic

Viceversos: Trasvases metodológicos en el paisaje (entre Geografía, Sociología y Arquitectura)

El objetivo de la Red ha sido compartir metodologías de detección, análisis y proyecto en la interacción entre sociedad y paisaje en áreas específicas del Levante español, metodologías que pudieran ser ensayadas por estudiantes de Sociología, Arquitectura y Geografía en la Universidad de Alicante en el marco de sus prácticas de campo en sus asignaturas de Grado.El ámbito socio-geográfico preciso ha sido el término municipal de Sella en la Marina Baixa, incluyendo unos valles del término municipal de Benimantell cuyo acceso natural se produce desde Sella. Los objetivos básicos de las metodologías compartidas se han referido a cómo el paisaje semiabandonado y abancalado junto a ríos y acequias presenta trazas identitarias aprovechables (sendas de montaña que conectan masías, enclaves geomorfológicos, fincas en desuso, cuencas visuales, masas forestales…) para encontrar nuevos usos y formas de habitar el espacio natural, o formas de paisaje convertible en aula de escuela primaria, o formas lúdico-musicales de disfrute en la naturaleza.El trabajo de los integrantes de la Red consistió en diseñar los protocolos de interacción para situaciones flexibles dentro de los cronogramas formativos reglados (Grados de Sociología, Arquitectura, Geografía) definiendo sesiones de colaboración, desplazamientos al lugar, metodologías compartidas y encuentros para debatir los resultados. Los resultados de la experiencia se han llegado a publicar por el momento en dos comunicaciones en Congresos y Jornadas de Redes en la UA

Slavery and the african cultural legacy in the Caribbean

Con autorización de la editorial para este libro.[EN] The purpose of this book is to raise awareness among a wide audience of one of the most significant and shameful phenomena for humanity, as was the enslavement of over twelve and a half million Africans who were brought to America and forced to work and live as slaves. Many countries participated in the slave trade at different times and withvaried intensity (Great Britain, Portugal, France, Spain, Denmark, Netherlands, Germany, United States...).[ES] El propósito de esta obra es dar a conocer a un público amplio uno de los fenómenos de mayor trascendencia y vergüenza para la humanidad como fue la esclavización de más de doce millones y medio de africanos que fueron trasladados a América, obligados a trabajar y vivir como esclavos. Muchos países participaron en la trata de esclavos en distintos momentos y con diferente intensidad (Gran Bretaña, Portugal, Francia, España, Dinamarca, Países Bajos, Alemania, Estados Unidos…).Connected Worlds: The Caribbean, Origin of Modern World. This project has received funding from the European Union´s Horizon 2020 research and innovation programme under the Marie Sklodowska Curie grant agreement Nº 823846. This project is directed by professor Consuelo Naranjo Orovio, Institute of History-CSIC.Peer reviewe

Gestión del conocimiento. Perspectiva multidisciplinaria. Volumen 17

El libro “Gestión del Conocimiento. Perspectiva Multidisciplinaria”, Volumen 17 de la Colección Unión Global, es resultado de investigaciones. Los capítulos del libro, son resultados de investigaciones desarrolladas por sus autores. El libro es una publicación internacional, seriada, continua, arbitrada, de acceso abierto a todas las áreas del conocimiento, orientada a contribuir con procesos de gestión del conocimiento científico, tecnológico y humanístico. Con esta colección, se aspira contribuir con el cultivo, la comprensión, la recopilación y la apropiación social del conocimiento en cuanto a patrimonio intangible de la humanidad, con el propósito de hacer aportes con la transformación de las relaciones socioculturales que sustentan la construcción social de los saberes y su reconocimiento como bien público

Polytopes and C1C^1-convex bodies

International audienceThe face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity.Nous étudions les nombres de faces de polytopes simpliciaux qui se rapprochent de $C^1$-corps convexes dans la métrique Hausdorff. Plusieurs résultats structurels sur le skeleta de ces polytopes sont recherchées et utilisées pour calculer un théorème limite inférieure de cette classe de polytopes. Cela résout partiellement une conjecture formulée par Kalai en 1994: si une suite $\{P_n\}_{n=0}^{\infty}$ de polytopes simpliciaux converge vers une $C^1$-corps convexe dans la distance Hausdorff, puis les entrées du $g$-vecteur de $P_n$ convergent vers l’infini

Polytopes and C1C^1-convex bodies

The face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity

Polytopes and C1C^1-convex bodies

The face numbers of simplicial polytopes that approximate $C^1$-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity.Nous étudions les nombres de faces de polytopes simpliciaux qui se rapprochent de $C^1$-corps convexes dans la métrique Hausdorff. Plusieurs résultats structurels sur le skeleta de ces polytopes sont recherchées et utilisées pour calculer un théorème limite inférieure de cette classe de polytopes. Cela résout partiellement une conjecture formulée par Kalai en 1994: si une suite $\{P_n\}_{n=0}^{\infty}$ de polytopes simpliciaux converge vers une $C^1$-corps convexe dans la distance Hausdorff, puis les entrées du $g$-vecteur de $P_n$ convergent vers l’infini

The Lower Bound Theorem for polytopes that approximate C¹-convex bodies

The face numbers of simplicial polytopes that approximate C¹-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence {Pn} ∞ n=0 of simplicial polytopes converges to a C¹-convex body in the Hausdorff distance, then the entries of the g-vector of Pn converge to infinity