arXiv research

We introduce and study the space of \emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize con…

Curves inscribe rectangles with positive area.

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then introduce a notion of "being asymptotically isoperimetric" for a family of finite a…

Study new Ricci bounds for metric measure spaces, preserving properties under time changes.

Study measures non-smooth spaces using Ricci curvature, proving volume properties.

We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $Λ$ on the power set of $\mathbb{N}$. Each $E\in\cate$ has a least monotone cover in $\catf$, the collection of monotone subsets of $\cate$, an…

This paper analyzes the conflict between Hamming loss and subset accuracy in multi-label classification.

Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because they fit well with modern parallel computing architectures. We propose a simple me…

Study of regular points in extremal subsets of Alexandrov spaces.

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

New measure defined for Brakke flow, linking classical and new definitions.

We generalize subset currents on hyperbolic groups to surfaces.

A new approach to sensitivity analysis without the Sobol decomposition.

Reconstructing manifold structure from boundary light observations.

New subsets without interior support Poincaré inequalities, expanding previous results.

Study shows stability of travel time data reconstruction from closed subsets.

A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact hereditarily Baire Preiss-Simon space $X$ into a regular space $Y$ the scattere…

New set type with no uniformly perfect subsets.

Researchers expand on best subset selection theory, identifying key complexities.

Improved space management in iterative clustering reduces subset growth without sacrificing performance.

In this article we extend a euclidean result of David and Semmes to the Heisenberg group by giving a sufficient condition for a $k$-Ahlfors-regular subset to have big pieces of bilipschitz images of subsets of $\R^k$. This Carleson type condition measures how well the set can be approximated by the Heisenberg $k$-plane…

Optimizes kernel discrepancies by selecting subsets efficiently.

Extends Dirac operator results to foliations with invariant measures.

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.

Expected centre of mass for random embeddings is constant.

Uniform rectifiability proven for sets with Poincaré inequalities.

Study geodesically complete spaces with upper curvature bound.

We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured laminations in S, equipped with its natural Lebesgue measure. We prove that, for any 3-man…

The paper solves a problem of prescribing curvature measures on convex domains.

Study permeable sets and their dimensions, with applications to fractals.

JOBS recovers signals from bootstrapped subsets of measurements.

This paper improves volatility forecasting using dynamic subset selection in genetic programming.

We prove that the ring $\Aff{\R}{M}$ of all polynomials defined on a real algebraic variety $M\subset\R^n$ is dense in the Hilbert space $L^2(M,e^{-|x|^2}\deμ)$, where $\deμ$ denotes the volume form of $M$ and $\deν=e^{-|x|^2}\deμ$ the Gaussian measure on $M$.

Study shows a subset of foliations on $\mathbb{P}^n$ has all singular points linearizable.

Approximates measures on curved spaces using Dirac measures.

Maximal representations show strong entropy rigidity.

Study convexity properties of gradient map on probability measures.

The paper studies the moduli space of generalized Cantor sets and their properties.

The paper shows how almost isoperimetric domains are close to spheres.

Study geometrically measures to decide if modular companions are conformally equivalent.

We describe Information Forests, an approach to classification that generalizes Random Forests by replacing the splitting criterion of non-leaf nodes from a discriminative one -- based on the entropy of the label distribution -- to a generative one -- based on maximizing the information divergence between the class-con…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

Abstract: Determines Lamé coefficients from boundary measurements.

The paper tackles Best-of-K Bandit game, aiming to identify the highest reward subset with minimal queries.

In this work a new way to calculate the multivariate joint entropy is presented. This measure is the basis for a fast information-theoretic based evaluation of gene relevance in a Microarray Gene Expression data context. Its low complexity is based on the reuse of previous computations to calculate current feature rele…

Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.

Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitable non convex subset of R^2 equipped with the l^\infty-norm and the Lebesgue measure. Combining many such spaces gives a (non…

In this paper, we consider generic corank 2 sub-Riemannian structures, and we show that the Spherical Hausdorf measure is always a C^1-smooth volume, which is in fact generically C^2- smooth out of a stratified subset of codimension 7. In particular, for rank 4, it is generically C^2 . This is the continuation of a pre…