2063 research outputs found
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Rotational smoothing
Get PDFRotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators regularizing in all directions. The gain of regularity is the result of rotating the directions where the corresponding operator performs the smoothing effect. In this paper we carry out a systematic study of the rotational smoothing for a class of operators that includes -vector-space Riesz potentials in with , and the convolution with fundamental solutions of elliptic constant-coefficient differential operators acting on -dimensional linear subspaces. Examples of the latter type of operators are the planar Cauchy transform in , or a solution operator for the transport equation in . The analysis of rotational smoothing is motivated by the resolution of some inverse problems under low-regularity assumptions
Linearization of holomorphic families of algebraic automor- phisms of the affine plane
Get PDFLet be a reductive group. We prove that a family of polynomial actions of on , holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular class of reductive group actions on is linearizable. The main step of our proof is to establish a certain restrictive Oka property for groups of equivariant algebraic automorphisms of
Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos
Get PDFWe investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.Marie Skłodowska-Curie grant agreement No. 79249
A two-stage approach for the spatio-temporal analysis of high-throughput phenotyping data
Get PDFHigh throughput phenotyping (HTP) platforms and devices are increasingly used for the characterization of growth and developmental processes for large sets of plant genotypes. Such HTP data require challenging statistical analyses in which longitudinal genetic signals need to be estimated against a background of spatio-temporal noise processes. We propose a two-stage approach for the analysis of such longitudinal HTP data. In a first stage, we correct for design features and spatial trends per time point. In a second stage, we focus on the longitudinal modelling of the spatially corrected data, thereby taking advantage of shared longitudinal features between genotypes and plants within genotypes. We propose a flexible hierarchical three-level P-spline growth curve model, with plants/plots nested in genotypes, and genotypes nested in populations. For selection of genotypes in a plant breeding context, we show how to extract new phenotypes, like growth rates, from the estimated genotypic growth curves and their first-order derivatives. We illustrate our approach on HTP data from the PhenoArch greenhouse platform at INRAE Montpellier and the outdoor Field Phenotyping platform at ETH Zürich.BERC 2018-2021
BCAM Severo Ochoa accreditation SEV-2017-0718)
EU H2020 grant agreement ID 731013 (EPPN2020)
PhenoCOOL (project no. 169542)
Efficient 5-axis CNC trochoidal flank milling of 3D cavities using custom-shaped cutting tools
Get PDFA novel method for trochoidal flank milling of 3D cavities bounded by free-form surfaces is proposed. Existing 3D trochoidal milling methods use on-market milling tools whose shape is typically cylindrical or conical, and is therefore not well-suited for meeting fine milling tolerances required for finishing of benchmark free-form surfaces like blades or blisks. In contrast, our variational framework incorporates the shape of the tool into the optimization cycle and looks not only for the trochoidal milling paths, but also for the shape of the tool itself. High precision quality is ensured by firstly designing flank milling paths for the side surfaces that delimit the motion space, in which the trochoidal milling paths are further computed. Additionally, the material removal rate is maximized with the cutter-workpiece engagement being constrained under a given tolerance. Our framework also supports multi-layer approach that is necessary to handle deep cavities. The ability and efficacy of the proposed method are demonstrated by several industrial benchmarks, showing that our approach meets fine machining tolerances using only a few trochoidal paths.RYC-2017-2264
COMPLETE CLASSIFICATION OF GLOBAL SOLUTIONS TO THE OBSTACLE PROBLEM
No full textThe characterization of global solutions to the obstacle problems in RN , or
equivalently of null quadrature domains, has been studied over more than 90 years. In this
paper we give a conclusive answer to this problem by proving the following long-standing
conjecture: The coincidence set of a global solution to the obstacle problem is either a half-
space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base
On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
Get PDFIn this article we consider direct and inverse problems for α-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of directional antilocality as introduced by Y. Ishikawa in the 80s. We consider the Dirichlet problem for these operators on the respective “domain of dependence of the operator” and in several, adapted function spaces. This formulation allows one to avoid natural “gauges” which would else have to be considered in the study of the associated inverse problems. Exploiting the directional antilocality of these operators we complement the investigation of the direct problem with infinite data and single measurement uniqueness results for the associated inverse problems. Here, due to the only directional antilocality, new geometric conditions arise on the measurement domains. We discuss both the setting of symmetric and a particular class of non-symmetric nonlocal elliptic operators, and contrast the corresponding results for the direct and inverse problems. In particular for only “one-sided operators” new phenomena emerge both in the direct and inverse problems: For instance, it is possible to study the problem in data spaces involving local and nonlocal data, the unique continuation property may not hold in general and further restrictions on the measurement set for the inverse problem arise
SPH simulations of thixo-viscoplastic fluid flow past a cylinder
Get PDFThixotropic materials are complex fluids that display time-dependent viscosity and/or yield-stress response upon the application of a fixed deformation, while recovering their original structured-state when the deformation is discontinued. Thixotropic effects are presents in many different systems and applications, ranging from food products, such as ketchup, to metals, such as molten aluminum. In this work we present a first attempt to simulate the rheological properties of thixo-viscoplastic flows using a Smoothed Particle Hydrodynamic (SPH) method. The study set up is a 2D flow around a circular cylinder as well as a simple shear flow between parallel plates to validate our numerical results. SPH solutions are compared with simulations performed using the open-source Finite Volume Method solver RheoTool, based on OpenFOAM. The viscoplastic model used in this work is the Papanastasiou model combined with a recently developed microstructural one, in order to include thixotropy. In this thixo-viscoplastic framework, we analyze the flow properties in terms of yield-fronts, streamlines and structure-parameter fields at different Bingham and Thixotropy numbers, through microstructural thixotropic and yield-stress parameters variation. Obtained results show an important novelty: an asymmetry in the thixo-viscoplastic flow around the cylinder
Predictive Maintenance of Floating Offshore Wind Turbine Mooring Lines using Deep Neural Networks
Get PDFThe recent massive deployment of onshore wind farms has caused controversy to arise mainly around the issues of land occupation, noise and visual pollution and impact on wildlife. Fixed offshore turbines, albeit beneficial in those aspects, become economically unfeasible when installed far away from coastlines. The possibility of installing floating offshore wind turbines is currently hindered by their excessive operation and maintenance costs. We have developed a comprehensive model to help companies plan their operations in advance by detecting failure in mooring lines in almost real time using supervised deep learning techniques. Given the lack of real data, we have coupled numerical methods and OpenFAST simulations to build a dataset containing the displacements and rotations of a turbine's floating platform across all directions. These time series and their corresponding frequency spectra are used to obtain a set of key statistical parameters, including means and standard deviations, peak frequencies, and several relevant momenta. We have designed and trained a Deep Neural Network to understand and distinguish amongst a series of common failure modes for mooring lines considering a range of metocean and structural conditions. We have obtained promising results when monitoring severe changes in the line's mass and damping using short time spans, achieving a 95.7\% validation accuracy when detecting severe biofouling failure
Changes in Social and Clinical Determinants of COVID-19 Outcomes Achieved by the Vaccination Program: A Nationwide Cohort Study
Get PDFBackground: The objective of this study was to assess changes in social and clinical
determinants of COVID-19 outcomes associated with the first year of COVID-19 vaccination rollout in
the Basque population. Methods: A retrospective study was performed using the complete database
of the Basque Health Service (n = 2,343,858). We analyzed data on age, sex, socioeconomic status,
the Charlson comorbidity index (CCI), hospitalization and intensive care unit (ICU) admission, and
COVID-19 infection by Cox regression models and Kaplan–Meier curves. Results: Women had a
higher hazard ratio (HR) of infection (1.1) and a much lower rate of hospitalization (0.7). With older
age, the risk of infection fell, but the risks of hospitalization and ICU admission increased. The higher
the CCI, the higher the risks of infection and hospitalization. The risk of infection was higher in
high-income individuals in all periods (HR = 1.2–1.4) while their risk of hospitalization was lower in
the post-vaccination period (HR = 0.451). Conclusion: Despite the lifting of many control measures
during the second half of 2021, restoring human mobility patterns, the situation could not be defined
as syndemic, clinical determinants seeming to have more influence than social ones on COVID-19
outcomes, both before and after vaccination program implementation