Related papers: On weighted mean matrices whose $l^p$ norms are de…
We obtain a priori estimates in $L^p(\omega)$ for the generalized Beltrami equation, provided that the coefficients are compactly supported $VMO$ functions with the expected ellipticity condition, and the weight $\omega$ lies in the…
We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$…
With the success of deep neural networks (NNs) in a variety of domains, the computational and storage requirements for training and deploying large NNs have become a bottleneck for further improvements. Sparsification has consequently…
We establish a modified pointwise convex body domination for vector-valued Haar shifts in the nonhomogeneous setting, strengthening and extending the scalar case developed in arXiv:2309.13943. Moreover, we identify a subclass of shifts,…
We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (i.e., scoring matrices). In the simple version,…
We observe that a sequence satisfies Lucas congruences modulo $p$ if and only if its values modulo $p$ can be described by a linear $p$-scheme, as introduced by Rowland and Zeilberger, with a single state. This simple observation suggests…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
Sufficient conditions on associated parameters $p,b$ and $c$ are obtained so that the generalized and \textquotedblleft{normalized}\textquotedblright{} Bessel function $u_p(z)=u_{p,b,c}(z)$ satisfies $|(1+(zu''_p(z)/u'_p(z)))^2-1|<1$ or…
In this note we provide and analyze a simple method that given an $n \times d$ matrix, outputs approximate $\ell_p$-Lewis weights, a natural measure of the importance of the rows with respect to the $\ell_p$ norm, for $p \geq 2$. More…
We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$-th moments ($0<p\leq 1$) of nonnegative generalized $U$-statistics with constant not dependent on $p$. In…
The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…
The paper deals with the computation of the rank and the identifiability of a specific ternary form. Often, one knows some short Waring decomposition of a given form, and the problem is to determine whether the decomposition is minimal and…
We consider weighted operators acting on $L^p(\mathbb{R}^d)$ and show that they depend continuously on the weight $w\in A_p(\mathbb{R}^d)$ in the operator topology. Then, we use this result to estimate $L^p_w(\mathbb{T})$ norm of…
This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for…
Linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the…
Let $G$ be a discrete group, let $p\ge1$, and let $\omega$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $\omega$ for $\ell^p(G,\omega)$ to be a Banach algebra admitting a norm-controlled…
We settle an open problem of several years standing by showing that the least-squares mean for positive definite matrices is monotone for the usual (Loewner) order. Indeed we show this is a special case of its appropriate generalization to…
We study the generalizations of the known equivalent reformulations of condition moderate growth from the single weight sequence to the weight matrix setting. This condition, also known in the literature under the name stability under…