arXiv research

The study shows finite measure-preserving isometry groups for certain metric measure spaces.

The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.

Unified theory of measure-preserving diffusions on manifolds.

Study shows infinite-dimensional third bounded cohomology for non-orientable surfaces.

In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…

Compact embeddings for invariant functions in metric-measure spaces.

The paper studies curvature measures and volume-preserving flows on convex bodies.

Extends Lipschitz functions while preserving local constants.

BiLipschitz mappings can be extended to preserve area.

We prove two rigidity results for automorphism groups of the spaces ML(S) of measured laminations on a closed hyperbolic surface S and PML(S) of projective measured laminations on this surface. The results concern the homeomorphisms of ML(S) that preserve the geometric intersection between laminations and the homeomorp…

This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.

We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation of resulting risk measures from the properti…

Paper proves curvature conditions are preserved in metric spaces.

We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.

An algorithm preserves topological features in dimensionality reduction.

Derives stochastic and dissipative dynamics preserving Gibbs measure.

In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…

Characterizes measures preserving compound mixed renewal process properties.

The paper introduces new volume measures and volume comparison inequalities for Lorentzian spaces.

We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concre…

Transformers preserve support and can approximate any continuous map.

Study curvatures of diffeomorphisms on non-orientable surfaces.

New risk measure extensions preserve key properties.

We consider a connected smooth $n$-dimensional manifold $M$ endowed with a volume form $Ω$, and we show that an open subset $U$ of $R^n$ of Lebesgue measure $\Vol (U)$ embeds into $M$ by a smooth volume preserving embedding whenever the volume condition $\Vol (U) \le \Vol (M,Ω)$ is met.

Suppose M is a noncompact connected 2-manifold and m is a good Radon measure of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the group of homeomorphisms of M equipped with the compact-open topology and let H(M; m)_0 denote the identity component of the subgroup consisting of m-preserving homeomo…

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new ev…

Paper improves privacy-preserving measurement of advertising incrementality.

We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N finite, or having infinity-Ricci curvature bounded below by K, for K a real number. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein space P_2(X) of probability measur…

A new framework explains why early pruning works well.

We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry.

Proposes a privacy-preserving system for federated learning of road networks.

Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving homeomorphisms of M equipped with the compact-open topology and H_E(M; m) denote the subgroup consisting of all h in H(M; m) which fix the ends of M. Each h in H_E(M; m) mov…

Normal-bundle bootstrap generates new data preserving geometric structure.

The paper uses EVT to improve tail risk measures under ambiguity sets.

In this paper angular curvature measures are investigated. Our first result is a complete classification of translation-invariant angular smooth curvature measures on $\mathbb{R}^n$. Subsequently, we use this result to show that the class of angular curvature measures on a Riemannian manifold is preserved by both the p…

Proposes an accuracy-preserving calibration method for DNNs.

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping cl…

Handlebody groups are rigid under measure equivalence.

A new copula, the checkerboard copula, maximizes entropy and preserves dependence.

Constructs a support-preserving homotopy for differential forms with boundary decay estimates.

Proposes a hierarchical clustering method for positive and negative dissimilarities.

Study graph products of groups, classifying them up to measure equivalence and rigidity.

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…

The Bakry-Emery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the Bakry-Emery tensor. We show that the Bakry-Emery tensor is nondecreasing under a Riemannia…

Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action of G satisfies a nonwandering hypothesis, then the action has a global fixed po…

An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the di…

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action of the fundamental group on a probability space. We show that integral foliated s…

A new measure of causal influence quantifies intrinsic contributions in DAGs.