Related papers: Bounds on Dimension Reduction in the Nuclear Norm

Local M-smoothers are interesting and important signal and image processing techniques with many connections to other methods. In our paper we derive a family of partial differential equations (PDEs) that result in one, two, and three…

: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we…

We prove a deterministic analogue of Rudelson's sampling theorem for sums of positive semidefinite matrices. Let $A_1,\dots,A_m$ be positive semidefinite \(d\times d\) matrices, and let $\lambda_1,\dots,\lambda_m \ge 0$ satisfy \[…

In this paper we consider non-anticommutative field theories in $\mathcal{N} =2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry…

A graph $G$ is $m$-minor-universal if every graph with at most $m$ edges (and no isolated vertices) is a minor of $G$. We prove that the $d$-dimensional hypercube, $Q_d$, is $\Omega\left(\frac{2^d}{d}\right)$-minor-universal, and that there…

We show that there exist scalar field theories with plausible one-particle states in general $D$ dimensional nonstationary curved spacetimes whose propagating modes are localized on $d\le D$ dimensional hypersurfaces, and the corresponding…

It is shown that if a C*-algebra has nuclear dimension $n$ then its Cuntz semigroup has the property of $n$-comparison. It then follows from results by Ortega, Perera, and Rordam that $\sigma$-unital C*-algebras of finite nuclear dimension…

In this paper we prove the Hausdorff dimension of the set of (nondegenerate) singular two-dimensional vectors with uniform exponent $\mu$ $\in$ (1/2, 1) is 2(1 -- $\mu$) when $\mu$ $\ge$ $\sqrt$ 2/2, whereas for $\mu$ \textless{} $\sqrt$…

Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models,…

At critical values of the scaling dimension $\lambda$, supermultiplets of the global ${\cal N}$-Extended one-dimensional Supersymmetry algebra induce $D$-module representations of finite superconformal algebras (the latters being identified…

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form $$[{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}],$$ where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all…

Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…

Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin…

We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\dots,A_{k}$ such that either each of these subsets has size $\Omega(n/k^{5})$ and, for every $i<j$, every element in $A_{i}$ is less than or equal…

We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most…

Let $\cal M$ denote the set ${\cal S}_{n, q}$ of $n \times n$ symmetric matrices with entries in ${\rm GF}(q)$ or the set ${\cal H}_{n, q^2}$ of $n \times n$ Hermitian matrices whose elements are in ${\rm GF}(q^2)$. Then $\cal M$ equipped…

We generalize the spacetime positive mass theorem to include multiple time dimensions. In particular, we show that the mass remains nonnegative in the sense that the energy $E$ is bounded from below by the trace norm of the linear momenta…

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…

A celebrated conjecture due to De Giorgi states that any bounded solution of the equation $\Delta u + (1-u^2) u = 0 \hbox{in} \R^N $ with $\pp_{y_N}u >0$ must be such that its level sets $\{u=\la\}$ are all hyperplanes, {\em \bf at least}…

Let $F$ be a totally real field, and $\mathbb{A}_F$ be the adele ring of $F$. Let us fix $N$ to be a positive integer. Let $\pi_1=\otimes\pi_{1,v}$ and $\pi_2=\otimes\pi_{2,v}$ be distinct cohomological cuspidal automorphic representations…