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THE MUCKENHOUPT CONDITION
Get PDFThe goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, and pose several conjectures and partial results related to the duality of the Hardy-Littlewood maximal operator. Furthermore, we give an overview of the theory applied to weighted variable Lebesgue and Morrey spaces
Uniform maximal Fourier restriction for convex curves
No full textWe extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the curve. The improvement over M\"{u}ller, Ricci, and Wright and Ramos is given by the removal of the regularity condition on the curve. This requires the choice of an appropriate measure for each curve, that is suggested by an affine invariant construction of Oberlin in \cite{MR1960918}. As corollaries, we obtain a uniform Fourier restriction theorem for arbitrary convex curves and a result on the Lebesgue points of the Fourier transform on the curve.CRC 1060 \emph{The Mathematics of Emergent Effects} at the University of Bonn, funded through the Deutsche Forschungsgemeinschaf
Effects of confinement-induced non-Newtonian lubrication forces on the rheology of a dense suspension
No full textIn this work, we propose a functionalised bi-viscous lubrication model to study the material properties of concentrated non-Brownian suspensions and explore the possible confinement-induced non-Newtonian effects of the lubricant in the rheological response of this type of suspensions. From tribological studies, it is well-known that even macroscopically Newtonian liquids under strong confinement might exhibit properties which deviate significantly from their bulk behaviour. When two surfaces separated by an extremely small gap (still large compared to the molecular size) are sheared, strong shear-thinning of the lubricant viscosity at low shear-rates is observed, in spite of its Newtonian-like bulk response. This is connected to a significant increase of the zero-shear-rate viscosity under extreme confinement. We start from an effective lubrication algorithm recently proposed and develop a new gap-size-dependent interparticle bi-viscous lubrication model, able to capture qualitatively the main phenomenology of confined lubricants. We solve the lubrication interaction between particles iteratively via a semi-implicit splitting scheme. Since the handling of lubrication is made implicitly here, the method copes efficiently with large increases of the inter-particle effective viscosities, which would otherwise lead to simulation blow-up or the use of vanishing time-steps in standard explicit schemes. We analyse the rheological response of the suspension systematically in terms of model parameters. In contrast to pure Newtonian lubrication interactions, distinct shear-thinning and shear-thickening regimes in the relative suspension viscosity are observed, which are discussed in terms of particle microstructure coupled with the complex rheology of the confined lubricant. In addition, normal-stress response is negative in both and , which is difficult to achieve with standard contact frictional models
Hammering at the entropy: A generic-guided approach to learning polymeric rheological constitutive equations using PINNs.
Get PDFWe present a versatile framework that employs Physics-Informed Neu-
ral Networks (PINNs) to discover the entropic contribution that leads to
the constitutive equation for the extra-stress in rheological models of poly-
mer solutions. In this framework the training of the Neural Network is
guided by an evolution equation for the conformation tensor which is
GENERIC-compliant. We compare two training methodologies for the
data-driven PINN constitutive models: one trained on data from the an-
alytical solution of the Oldroyd-B model under steady-state rheometric
flows (PINN-rheometric), and another trained on in-silico data gener-
ated from complex flow CFD simulations around a cylinder that use the
Oldroyd-B model (PINN-complex). The capacity of the PINN models to
provide good predictions are evaluated by comparison with CFD simula-
tions using the underlying Oldroyd-B model as a reference. Both models
are capable of predicting flow behavior in transient and complex condi-
tions; however, the PINN-complex model, trained on a broader range of
mixed flow data, outperforms the PINN-rheometric model in complex flow
scenarios. The geometry agnostic character of our methodology allows us
to apply the learned PINN models to flows with different topologies than
the ones used for training
A macroscopic clock model to solve the paradox of Schrödinger’s cat
Get PDFWe propose detecting the moment an atom emits a photon by means of a nearly classical macroscopic clock and discuss its viability. It is shown that what happens in such a measurement depends on the relation between the clock’s accuracy and the width of the energy range available to the photon. Implications of the analysis for the long standing Schrödinger’s cat problem are reported
A stochastic programming model for ambulance (re)location–allocation under equitable coverage and multi-interval response time
Get PDFEmergency Medical Services are essential for health systems as their effective management can improve patient prognosis. Nevertheless, designing an optimized distribution of resources is a difficult task due to the complex nature of these systems. Moreover, locating the resources is particularly challenging in heterogeneous density territories where, in addition to their efficient management, the equity principle in the medical access of inhabitants of rural areas is also desirable. This paper approaches the ambulance (re)location–allocation problem in the geographical area of the Basque Country. The area has three major cities, which account for a third of the emergencies, while there are few emergencies in rural areas, with a sparse population. To that end, a two-stage stochastic 0-1 integer linear programming model that balances the response time between densely populated and isolated areas is proposed. Specifically, the model incorporates two relevant principles: (1) optimizing emergency attendance through the option of allocating ambulances via a multi-interval response time and (2) equitably responding to emergencies so remote areas are not neglected. Conducted experiments have been validated and indicate that the proposed model can improve the success rate in rural areas by 23 percentage points, while reducing the overall success rate by less than 9 percentage points.Spanish Ministry of Science and Innovation through the project PID2019-104933GB-I00/AEI/10.13039/501100011033
PRE2020-091984 Severo Ochoa grant from the Spanish Ministry of Science and Innovatio
Modeling spillover dynamics: understanding emerging pathogens of public health concern
Get PDFThe emergence of infectious diseases with pandemic potential is a major public health threat worldwide. The World Health Organization reports that about 60% of emerging infectious diseases are zoonoses, originating from spillover events. Although the mechanisms behind spillover events remain unclear, mathematical modeling offers a way to understand the intricate interactions among pathogens, wildlife, humans, and their shared environment. Aiming at gaining insights into the dynamics of spillover events and the outcome of an eventual disease outbreak in a population, we propose a continuous time stochastic modeling framework. This framework links the dynamics of animal reservoirs and human hosts to simulate cross-species disease transmission. We conduct a thorough analysis of the model followed by numerical experiments that explore various spillover scenarios. The results suggest that although most epidemic outbreaks caused by novel zoonotic pathogens do not persist in the human population, the rising number of spillover events can avoid long-lasting extinction and lead to unexpected large outbreaks. Hence, global efforts to reduce the impacts of emerging diseases should not only address post-emergence outbreak control but also need to prevent pandemics before they are established
Monitoring Mooring Lines of Floating Offshore Wind Turbines: Autoregressive Coefficients and Stacked Auto-Associative-Deep Neural Networks
No full textThis study introduces a pioneering monitoring system designed to mitigate operational costs and enhance the sustainability of Floating Offshore Wind Turbines (FOWT). The proposed framework combines Autoregressive models with a Stacked Auto-Associative-based Deep Neural Network (AANN-DNN) to detect and classify damages in mooring systems of FOWTs. By extracting damage-sensitive features (DSFs) using the AR models from time-series data and employing unsupervised learning in the auto-associative neural network, followed by supervised training with DNN, the approach demonstrates exceptional accuracy in damage identification and classification. Numerical simulations conducted using NREL’s OpenFAST software under diverse metocean conditions validate the method’s efficacy, offering a promising solution for efficient FOWT mooring line monitoring
How to Count Coughs: An Event-Based Framework for Evaluating Automatic Cough Detection Algorithm Performance
No full textChronic cough disorders are widespread and challenging to assess because they rely on subjective patient questionnaires about cough frequency. Wearable devices running Machine Learning (ML) algorithms are promising for quantifying daily coughs, providing clinicians with objective metrics to track symptoms and evaluate treatments. However, there is a mismatch between state-of-the-art metrics for cough counting algorithms and the information relevant to clinicians. Most works focus on distinguishing cough from non-cough samples, which does not directly provide clinically relevant outcomes such as the number of cough events or their temporal patterns. In addition, typical metrics such as specificity and accuracy can be biased by class imbalance. We propose using event-based evaluation metrics aligned with clinical guidelines on significant cough counting endpoints. We use an ML classifier to illustrate the shortcomings of traditional sample-based accuracy measurements, highlighting their variance due to dataset class imbalance and sample window length. We also present an open-source event-based evaluation framework to test algorithm performance in identifying cough events and rejecting false positives. We provide examples and best practice guidelines in event-based cough counting as a necessary first step to assess algorithm performance with clinical relevance.RYC2021-032853-
Geometry of two-body correlations in three-qubit states
No full textWe study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure states and extend this result by including the three-body correlations. Second, we consider mixed states and conjecture a tight nonlinear bound for all three-qubit states. Finally, within the created framework, we give criteria to detect different types of multipartite entanglement as well as characterize the rank of the quantum state