2063 research outputs found
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MAXIMAL OPERATORS ON THE INFINITE-DIMENSIONAL TORUS
Get PDFWe study maximal operators related to bases on the infinite- dimensional torus Tω. For the normalized Haar measure dx on Tω it is known that MR0, the maximal operator associated with the dyadic basis R0, is of weak type (1,1), but MR, the operator associated with the natural general basis R, is not. We extend the latter result to all q ∈ [1, ∞). Then we find a wide class of intermediate bases R0 ⊂ R′ ⊂ R, for which maximal functions have controlled, but sometimes very peculiar behavior. Precisely, for given q0 ∈ [1, ∞) we construct R′ such that M R′ is of restricted weak type (q, q) if and only if q belongs to a predetermined range of the form (q0,∞] or [q0,∞]. Finally, we study the weighted setting, considering the Muckenhoupt ARp (Tω) and reverse Hölder RHRr (Tω) classes of weights associated with R. For each p ∈ (1,∞) and each w ∈ ARp (Tω) we obtain that MR is not bounded on Lq(w) in the whole range q ∈ [1, ∞). Since we are able to show that
ARp (Tω)= RHRr (Tω), p∈(1,∞) r∈(1,∞)
the unboundedness result applies also to all reverse Hölder weights
HARDY TYPE INEQUALITIES FOR THE FRACTIONAL RELATIVISTIC OPERATOR
Get PDFWe prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringe
Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission
Get PDFMathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model
Generalized Maximum Entropy for Supervised Classification
Get PDFThe maximum entropy principle advocates to
evaluate events’ probabilities using a distribution that maximizes
entropy among those that satisfy certain expectations’ constraints. Such principle can be generalized for arbitrary decision
problems where it corresponds to minimax approaches. This
paper establishes a framework for supervised classification based
on the generalized maximum entropy principle that leads to
minimax risk classifiers (MRCs). We develop learning techniques
that determine MRCs for general entropy functions and provide
performance guarantees by means of convex optimization. In
addition, we describe the relationship of the presented techniques
with existing classification methods, and quantify MRCs performance in comparison with the proposed bounds and conventional
methods.RYC-2016-1938
Implementing the Cumulative Difference Plot in the IOHanalyzer
Get PDFThe IOHanalyzer is a web-based framework that enables an easy visualization and comparison of the quality of stochastic optimization algorithms. IOHanalyzer offers several graphical and statistical tools analyze the results of such algorithms. In this work, we implement the cumulative difference plot in the IOHanalyzer. The cumulative difference plot is a graphical approach that compares two samples through the first-order stochastic dominance. It improves upon other graphical approaches with the ability to distinguish between a small magnitude of difference and high uncertainty.The data science and artificial intelligence chair for digitalized industry and services, Telecom Paris, Institut Polytechnique de Paris,
Research Groups 20192021 (IT1244-19),
Spanish Ministry of Economy and Competitiveness, through the research project PID2019-106453GAI00/AEI/10.13039/501100011033
Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation
Get PDFIn this article, we present a general methodology to combine the Discontinuous Petrov-Galerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We rst introduce a semidiscretization in space with a DPG method rede ning the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to e ciently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators
On the Construction of Pareto-Compliant Combined Indicators
Get PDFThe most relevant property that a quality indicator (QI) is expected to have is Pareto compliance, which means that every time an approximation set strictly dominates another in a Pareto sense, the indicator must reflect this. The hypervolume indicator and its variants are the only unary QIs known to be Pareto-compliant but there are many commonly used weakly Pareto-compliant indicators such as R2, IGD+,andɛ+. Currently, an open research area is related to finding new Pareto-compliant indicators whose preferences are different from those of the hypervolume indicator. In this article, we propose a theoretical basis to combine existing weakly Pareto-compliant indicators with at least one being Pareto-compliant, such that the resulting combined indicator is Pareto-compliant as well. Most importantly, we show that the combination of Paretocompliant QIs with weakly Pareto-compliant indicators leads to indicators that inherit properties of the weakly compliant indicators in terms of optimal point distributions. The consequences of these new combined indicators are threefold: (1) to increase the variety of available Pareto-compliant QIs by correcting weakly Pareto-compliant indicators, (2) to introduce a general framework for the combination of QIs, and (3) to generate new selection mechanisms for multiobjective evolutionary algorithms where it is possible to achieve/adjust desired distributions on the Pareto front
Polynomial averages and pointwise ergodic theorems on nilpotent groups
Get PDFWe establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on -finite measure spaces. We also establish corresponding maximal inequalities on for and -variational inequalities on for . This gives an affirmative answer to the Furstenberg--Bergelson--Leibman conjecture in the linear case for all polynomial ergodic averages in discrete nilpotent groups of step two.
Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative, nilpotent setting.
In particular, we develop what we call a \textit{nilpotent circle method} that allows us to adapt some of the ideas of the classical circle method to the setting of nilpotent groups.Juan de la Cierva Incorporación 2019, Grant Number IJC2019-039661-I
BERC 2022-2025 progra
Mesoscopic simulations of inertial drag enhancement and polymer migration in viscoelastic solutions flowing around a confined array of cylinders
Get PDFWe study the flow around a periodic array of cylinders using a mesoscopic viscoelastic fluid that mimics polymeric solutions. We model our fluid employing a novel mesoscopic method based on Smoothed Dissipative Particle Dynamics and FENE springs. We characterize the static and dynamic properties of our model solutions and compare the results with theoretical predictions based on the Zimm model. After rheological characterization of the modeled solutions, we simulate the flow around a confined array of cylinders. The balance between inertia and elasticity in our simulations is studied using a wide range of Reynolds (Re) and Weissenberg (Wi) numbers. We find that increasing the flow rate reduces the drag coefficient on the cylinder up to a critical Re corresponding to a minimum. Thereafter, inertia becomes dominant and we encounter drag enhancement for all the solutions studied, including the Newtonian solvent. With the use of simple model for the viscous and inertial contributions to drag, we conclude that inertial effects are driving the increase in the drag experienced by the cylinder. In our simulations, we also observe migration of polymer chains away from the channel walls and in the wake of the cylinder. We conclude that stress gradients induced by the curvature of streamlines and convection of the depleted layers at the walls as the principal mechanisms driving the migration of chains. We find the extent of the migration correlates well with the viscoelastic Mach number (Ma = ReWi) suggesting that both elastic and inertial effects play a role in this phenomenon
The strange case of shear-thinning in non-Brownian suspensions
Get PDFShear thinning is generally reported in Brownian suspensions where it is understood to arise from a decrease in the
relative contribution of entropic forces. However it has also been often reported in experiments with non-colloidal sys-
tems and nominally-Newtonian matrices at high volume fractions. In spite of the generality of the observations, its or-
igin is still a matter of debate and the behaviour is dif cult to reproduce in numerical simulations where shear
thickening is typically observed instead.
Several explanations have been proposed in recent years ranging from hidden non-Newtonian effects in the small in-
terparticle gaps (Vázquez-Quesada et al., Phys. Rev. Lett. 117 (10), 108001 (2016), J. Non- Newt. Fluid Mech. 248, 1-7
(2017)), excluded volume effects (Chatté et al. Soft Matter,14, 879-89 (2018)) and variable friction coef cients (Chatté
et al.Soft Matter,14, 879-89 (2018); Tanner et al.Rheol. Acta 57:635–643 (2018); Lobry et al. J. Fluid Mech., 860,
682–710 (2019)). Another possibility that has emerged recently is related to slip occurring in the interparticle gaps
at the liquid-solid interface (Kroupa et al. Phys. Chem. Chem. Phys., 19, 5979-5984 (2017); Vázquez-Quesada et al.,
Phys. Rev. Fluids 3 (12), 123302 (2018); Kumar et al.J. Non-Newt. Fluid Mech., 281, 104312 (2020)). In this talk I
will review some of these issues and recent theories developed in this context