Related papers: A Stability Result for Sparse Convolutions

In this paper, we study the Bresse system in a bounded domain with linear frictional dissipation working only on the veridical displacement. The longitudinal and shear angle displacements are free. Our first main result is to prove that,…

We prove a topological stability result for the actions of hyperbolic groups on their Bowditch boundaries. More precisely, we show that a sufficiently small perturbation of the standard boundary action, if assumed on each parabolic subgroup…

Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on…

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the…

We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a…

Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent groups. We prove three main theorems: (1) the rigid abelian…

High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…

In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…

We study families $\mathcal{F}\subseteq 2^{[n]}$ with restricted intersections and prove a conjecture of Snevily in a stronger form for large $n$. We also obtain stability results for Kleitman's isodiametric inequality and families with…

It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…

Let x be a signal to be sparsely decomposed over a redundant dictionary A, i.e., a sparse coefficient vector s has to be found such that x=As. It is known that this problem is inherently unstable against noise, and to overcome this…

Let F be a relatively free algebra of infinite rank. We say that F has the SMALL INDEX PROPERTY if any subgroup of Gamma=Aut(F) of index at most rank(F) contains the pointwise stabilizer Gamma_(U) of a subset U of F of cardinality less than…

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…

Let $X$ be a non-singular irreducible complex projective curve of genus $g\geq 2$. We use $(t,\ell)$-stability to prove the existence of coherent systems over $X$ that are $\alpha$-stable for all allowed $\alpha >0$.

We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $\phi_J$. For configurations with a fixed isotropic global stress tensor, we compute the…

Babai's conjecture states that, for any finite simple non-abelian group $G$, the diameter of $G$ is bounded by $(\log|G|)^{C}$ for some absolute constant $C$. We prove that, for any untwisted classical group $G$ of rank $r$ defined over a…

We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated…

We prove that half spaces are the only stable nonlocal $s$-minimal cones in $\mathbb{R}^3$, for $s\in(0,1)$ sufficiently close to $1$. This is the first classification result of stable $s$-minimal cones in dimension higher than two. Its…

We study the stability of Freund-Rubin compactifications, AdS_p x M_q, of p+q-dimensional gravity theories with a q-form field strength and no cosmological term. We show that the general AdS_p x S^q vacuum is classically stable against…