Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms

This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to ℝ2 that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by piecewise affine homeomorphisms, for some β ∈ (0,α) that only depends on α. The proof is constructive. We adapt the proof of simplicial approximation in the supremum norm, and measure the side lengths and angles of the triangulation over which the approximating homeomorphism is piecewise affine. The approximation in the supremum norm, and a control on the minimum angle and on the ratio between the maximum and minimum side lengths of the triangulation suffice to obtain approximation in the Hölder norm

Forward and Inverse Dynamics and Quasi-Static Analysis of Mechanizes with MATLAB®

There are many potential advantages of direct and inverse dynamic and quasi-static analysis of mechanisms, namely control the risk of slippage, improve stability, better adaptation to the environment, obtaining smooth movements and optimizing energy consumption. This chapter proposes new analysis methods and algorithms to bring new solutions to the mechanics of the machines under consideration. The methodology has been developed in modular programs thanks to the flexibility of MATLAB®

Neuropathological findings in fatal COVID-19 and their associated neurological clinical manifestations

9 p.Severe cases of Coronavirus Disease 2019 (COVID-19) can present with multiple neurological symptoms. The available neuropathological studies have described different lesions; the most frequent was the presence of neuroinflammation and vascular-related lesions. The objective of this study was to report the neuropathological studies performed in a medical institution, with abundant long intensive care unit stays, and their associated clinical manifestations. This is a retrospective monocentric case series study based on the neuropathological reports of 13 autopsies with a wide range of illness duration (13-108 days). A neuroinflammatory score was calculated based on the quantification of CD8- and CD68-positive cells in representative areas of the central nervous system. This score was correlated afterwards with illness duration and parameters related to systemic inflammation. Widespread microglial and cytotoxic T-cell activation was found in all patients. There was no correlation between the neuroinflammatory score and the duration of the illness; nor with parameters of systemic inflammation such as the peak of IL-6 or the HScore (a parameter of systemic macrophage activation syndrome). Two patients had global hypoxic ischaemic damage and five patients had subacute infarcts. One patient had many more brain vascular microthrombi compared to the others and multiple subacute pituitary infarcts. SARS-CoV-2 RNA was not detected with qRT-PCR. The proportion of brain lesions in severe COVID-19 patients could be related to illness duration. In our series, with abundant long hospitalisation stays, neuroinflammation was present in all patients and was more prominent between day 34 and day 45 after onset of symptoms. Clinical correlation showed that two patients with the highest neuroinflammatory scores had severe encephalopathies that were not attributable to any other cause. The second most frequent lesions were related to vascular pathology.Instituto de Salud Carlos IIICIBERONCInstituto Ramón y Cajal de Investigación SanitariaMerck, Sharp & Dohme (MSD

Late Cretaceous continental and marine vertebrate assemblages of the Laño Quarry (Basque-Cantabrian Region, Iberian Peninsula): an update

The vertebrate-bearing beds of the Laño quarry (Condado de Treviño) are among the most relevant sites from the Late Cretaceous of Europe. Geologically, Laño and the adjacent region are set on the southern limb of the South-Cantabrian Synclinorium (SE Basque-Cantabrian Region, northern Iberian Peninsula). The Laño sites were discovered in 1984; thousands of bones and teeth, including microfossils, have been collected during the prospection in the field and excavation campaigns. The vertebrate remains occur at two different stratigraphic horizons within a continental to shallow marine succession of Late Campanian-Maastrichtian age. The lower horizon contains the Laño 1 and Laño 2 sites, whereas the upper horizon contains the Albaina site. In the Laño sites, three fossiliferous beds (called L1A, L1B and L2) are known within an alluvial system composed mainly of fluvial sands and silts. The sedimentary structures are consistent with channel areas within an extensive braided river system. Based mainly on stratigraphic correlations, the fluvial beds of Laño are regarded as Late Campanian to Early Maastrichtian in age. These deposits have yielded a very diverse vertebrate assemblage, which consists of nearly 40 species, including actinopterygians, lissamphibians, lepidosaurs, turtles, crocodyliforms, dinosaurs, pterosaurs, and mammals. Seven genera and ten species have been erected to date in Laño. With reference to the marine vertebrate association of Albaina, it consists of at least 37 species, including sharks and rays, actinopterygians, mosasaurids, and plesiosaurs. Two genera and species of rhinobatoids (family indet.) and two new species of rhinobatids have been erected in Albaina. The fossil association indicates a Late (but not latest) Maastrichtian age. Recently, isolated turtle and dinosaur fossils have been discovered in the sublittoral beds of Albaina. The Laño quarry is one of the most noteworthy Campanian-Maastrichtian vertebrate localities of Europe by its taxonomic diversity, and provides useful information about the composition and affinities of both continental and marine vertebrate faunas from the latest Cretaceous of southwestern Europe.Los niveles con fósiles de vertebrados de la cantera de Laño (Condado de Treviño) se cuentan entre los más importantes del Cretácico Superior de Europa. Desde un punto de vista geológico, Laño y la región adyacente forman parte del flanco sur del Sinclinorio Subcantábrico (SE de la Región Vasco-Cantábrica). El descubrimiento de los niveles fosilíferos remonta a 1984; las prospecciones de campo y las campañas de excavación han proporcionado miles de huesos y dientes, incluyendo microfósiles. Los restos de vertebrados aparecen en dos horizontes estratigráficos diferentes formando parte de una sucesión continental a marina litoral de edad Campaniense superior a Maastrichtiense. El horizonte inferior contiene los yacimientos de Laño 1 y Laño 2, mientras que el superior contiene solo uno: Albaina. En los yacimientos de Laño, se reconocen tres niveles fosilíferos (llamados L1A, L1B y L2) formados en el seno de un sistema aluvial compuesto por arenas y limos fluviales. Las estructuras sedimentarias indican áreas de canal dentro de un sistema trenzado muy extendido. Según las correlaciones estratigráficas, los depósitos fluviales de Laño son de edad Campaniense superior a Maastrichtiense inferior. Estos depósitos han proporcionado una asociación muy diversa de vertebrados, que consiste en cerca de 40 especies, incluyendo actinopterigios, lisanfibios, lepidosaurios, tortugas, cocodrilos, dinosaurios, pterosaurios y mamíferos. En Laño se han definido hasta el momento siete géneros y diez especies. Por lo que respecta a la asociación de vertebrados marinos de Albaina, se han reconocido al menos 37 especies, que incluyen tiburones y rayas, actinopterigios, mosasaurios y plesiosaurios. Hasta la fecha se han definido en Albaina cuatro nuevos rinobatoideos: dos especies de rinobátidos y dos géneros y especies cuya familia es indeterminada. La asociación fósil es de edad Maastrichtiense superior no terminal. Recientemente se ha descrito el hallazgo de restos fósiles aislados de tortugas y dinosaurios en los niveles marinos de Albaina. La cantera de Laño es una de las localidades de vertebrados más destacadas del Campaniense-Maastrichtiense por su diversidad taxonómica, y proporciona información relevante sobre la composición y afinidades de las faunas de vertebrados continentales y marinos del Cretácico final del suroeste de Europa

Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm

The general picture that emerged by the end of 1990s from a large set of optical and X-ray, spectral and timing data was that the X-rays are produced in the innermost hot part of the accretion flow, while the optical/infrared (OIR) emission is mainly produced by the irradiated outer thin accretion disc. Recent multiwavelength observations of Galactic black hole transients show that the situation is not so simple. Fast variability in the OIR band, OIR excesses above the thermal emission and a complicated interplay between the X-ray and the OIR light curves imply that the OIR emitting region is much more compact. One of the popular hypotheses is that the jet contributes to the OIR emission and even is responsible for the bulk of the X-rays. However, this scenario is largely ad hoc and is in contradiction with many previously established facts. Alternatively, the hot accretion flow, known to be consistent with the X-ray spectral and timing data, is also a viable candidate to produce the OIR radiation. The hot-flow scenario naturally explains the power-law like OIR spectra, fast OIR variability and its complex relation to the X-rays if the hot flow contains non-thermal electrons (even in energetically negligible quantities), which are required by the presence of the MeV tail in Cyg X-1. The presence of non-thermal electrons also lowers the equilibrium electron temperature in the hot flow model to <100 keV, making it more consistent with observations. Here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid (thermal/non-thermal) hot flow model satisfies most of the constraints.Comment: 26 pages, 13 figures. To be published in the Space Science Reviews and as hard cover in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Performance of ALICE AD modules in the CERN PS test beam

Two modules of the AD detector have been studied with the test beam at the T10 facility at CERN. The AD detector is made of scintillator pads read out by wave-length shifters (WLS) coupled to clean fibres that carry the produced light to photo-multiplier tubes (PMTs). In ALICE the AD is used to trigger and study the physics of diffractive and ultra-peripheral collisions as well as for a variety of technical tasks like beam-gas background monitoring or as a luminometer. The position dependence of the modules' efficiency has been measured and the effect of hits on the WLS or PMTs has been evaluated. The charge deposited by pions and protons has been measured at different momenta of the test beam. The time resolution is determined as a function of the deposited charge. These results are important ingredients to better understand the AD detector, to benchmark the corresponding simulations, and very importantly they served as a baseline for a similar device, the Forward Diffractive Detector (FDD), being currently built and that will be in operation in ALICE during the LHC Runs 3 and 4.Peer reviewe

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding

Strange Resonance Production in p+p and Au+Au Collisions at RHIC Energies

Resonance yields and spectra from elementary p+p and Au+Au collisions at $\sqrt{s_{\rm NN}} =$ 200 GeV from the STAR experiment at RHIC are presented and discussed in terms of chemical and thermal freeze-out conditions. Thermal models do not adequately describe the yields of the resonance production in central Au+Au collisions. The approach to include elastic hadronic interactions between chemical freeze-out and thermal freeze-out suggests a time of $\Delta \tau>$5 fm/c.Comment: 4 pages, 7 figures, proceedings of the Quark Matter 2004, in Oakland, California, to be published in Journal of Physics G: Nuclear and Particle Physic

Identified particles at large transverse momenta in STAR in Au+Au collisions @ sqrt(s_NN) = 200 GeV

We report measurements of the ratios of identified hadrons (pi,K,p,Lambda) in Au+Au collisions at sqrt(s_NN) = 200 GeV as a function of both collision centrality and transverse momentum (p_T). Ratios of anti-baryon to baryon yields are independent of p_T within 2<p_T <6 GeV/c indicating that, for such a range, our measurements are inconsistent with theoretical pQCD calculations predicting a decrease due to a stronger contribution from valence quark scattering. For both strange and non-strange species, a strong baryon enhancement relative to meson yields is observed as a function of collision centrality in this intermediate p_T region, leading to p/pi and Lambda/K ratios greater than unity. The nuclear modification factor, R_cp (central relative to peripheral collisions), is used to illustrate the interplay between jet quenching and hadron production. The physics implications of these measurements are discussed with reference to different theoretical models.Comment: 5 pages, 4 figures. Proceedings of Quark Matter 2004 Conference, Jan 2004, Oakland, USA. Submitted to Journal of Physics