Related papers: Monotone rearrangement does not increase generaliz…
We construct bisymmetric, strictly increasing binary operations on real intervals which are not continuous. This answers a natural question in the theory of bisymmetric and mean-type operations by showing that continuity may fail for…
Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the…
A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is…
We are interested in the long-time behaviour of the kinetic Vicsek equation, rigorously derived as the mean-field limit~\cite{bolley2012meanfield} of a coupled system of~$N$ stochastic differential equations describing particles moving at…
We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…
We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading…
We present results from four independent models of a granular assembly subjected to tapping. We find that the steady-state packing fraction as a function of the tapping intensity is nonmonotonic. In particular, for high tapping intensities,…
Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable…
In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell…
We make some improvements to our previous results. First, we prove a version of our volume growth theorem which does not require any assumption on the first Betti number. Second, we show that our local regularity theorem only requires a…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
We provide lower bounds for the norms of embeddings between $\boldsymbol{\gamma}$-weighted Anchored and ANOVA spaces of $s$-variate functions with mixed partial derivatives of order one bounded in $L_p$ norm ($p\in[1,\infty]$). In…
By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.
The backreaction of nonlinear inhomogeneities to the cosmic expansion is analyzed in the framework of general relativity with a cosmological constant. By defining the spatially averaged matter energy density, we find that the cosmological…
We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows…
We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$…
The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a…
The main results of this paper provide VMO-type estimates for the quadratic tilt-excess on varifolds with critical generalized mean curvature. These estimates apply to varifolds with "almost-integral" density which are close to a…
In many problems, a sensible estimator of a possibly multivariate monotone function may itself fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid…
In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study…