Related papers: The Homogeneous Approximation Property and the Com…

We prove a homological stability theorem for certain complements of symmetric spaces. This is a variant of a conjecture by Vakil and Matchett Wood for subspaces of $\mathrm{Sym}^n(X)$ where $X$ is an open manifold admitting a boundary. To…

Recently, inhomogeneous generalisations of the Friedmann-Lemaitre-Robertson-Walker cosmological models have gained interest in the astrophysical community and are more often employed to study cosmological phenomena. However, in many papers…

Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong…

In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set this has already been done using the notion of…

With the aim to improve the performance of feature matching, we present an unsupervised approach to fuse various local descriptors in the space of homographies. Inspired by the observation that the homographies of correct feature…

Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object…

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability…

A profound link between Homogeneous Dynamics and Diophantine Approximation is based on an observation that Diophantine properties of a real matrix $B$ are encoded by the corresponding lattice $\Lambda_B$ translated by a multi-parameter…

Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…

Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…

In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…

We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and…

For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…

The concept of frames, initially introduced by Duffin and Schaeffer, gained substantial recognition decades later when Daubechies, Grossman, and Meyer highlighted its significance. Since then, frame theory has become a fundamental and…

In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we will show that those combined extensions can be made if we…

Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity…

Let $\Gamma$ be a countable discrete group. We show that $\Gamma$ has the approximation property if and only if $\Gamma$ is exact and for any operator space $S \subseteq \K(H)$ we have $\Cu(\Gamma)^{\Gamma} \otimes S = (\Cu(\Gamma) \otimes…

In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…

Let $H$ be an infinite-dimensional separable Hilbert space and let $(X,d,\mu)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scale. We prove that every bounded continuous tight frame…

We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…