Related papers: Mora's holy grail: Algorithms for computing in loc…
Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a quantum algorithm of Arvind et al.…
We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarantees under natural regularity conditions on the convolution…
We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is…
Given a fine abelian group grading on a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero, with universal grading group $G$, it is shown that the induced grading by the free group $G/\tor(G)$ is…
Recent studies suggest that context-aware low-rank approximation is a useful tool for compression and fine-tuning of modern large-scale neural networks. In this type of approximation, a norm is weighted by a matrix of input activations,…
The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…
We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to…
We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
The aim of these notes is to collect and motivate the basic localization toolbox for the geometric study of ``spaces'', locally described by noncommutative rings and their categories of one-sided modules. We present the basics of Ore…
Let $(A,\m)$ be a Noetherian local ring, let $M$ be a finitely generated \CM $A$-module of dimension $r \geq 2$ and let $I$ be an ideal of definition for $M$. Set $L^I(M) = \bigoplus_{n\geq 0}M/I^{n+1}M$. In part one of this paper we showed…
We propose a localization formula for the chiral de Rham complex generalizing the well-known localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this…
An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
In this paper, we study the solving degrees for affine semi-regular sequences and their homogenized sequences. Some of our results are considered to give mathematically rigorous proofs of the correctness of methods for computing Gr\"{o}bner…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…
In the present paper MAPLE subroutines computing Milnor and Tyurina numbers of an isolated algebraic hypersurface singularity are presented and described in detail. They represents examples, and perhaps the first ones, of a MAPLE…