Related papers: Exact bounds for efficient consistent matrices obt…

This paper describes a new mechanism that might help with defining pattern sequences, by the fact that it can produce an upper bound on the ensemble value that can persistently oscillate with the actual values produced from each pattern.…

The paper considers two main results. First one is the uniform bound for strong mixing coefficient of ARCH sequence. Second is the bound for maximum of residual empirical process in the same model. We illustrate their usefulness by proving…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…

The supporting vectors of a matrix A are the solutions of max || x ||_2 =1 {||Ax||_2^2}. The generalized supporting vectors of matrices A_1 , . . . , A_k are the solutions of max || x ||_2 =1 {||A_1x||_2^2 + ||A_2x||_2^2 + ... +…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…

This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…

This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…

We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…

The joint degree matrix of a graph gives the number of edges between vertices of degree i and degree j for every pair (i,j). One can perform restricted swap operations to transform a graph into another with the same joint degree matrix. We…

This paper studies the open problem of conformalized entry prediction in a row/column-exchangeable matrix. The matrix setting presents novel and unique challenges, but there exists little work on this interesting topic. We meticulously…

The spread of a matrix is defined as the maximum of distances between any two eigenvalues of that matrix. In this paper we investigate spread maximization as a function on compact convex subset of the set of real symmetric matrices. We…

Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x)…

We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…

It is known that a unitary matrix can be decomposed into a product of reflections, one for each dimension, and the Haar measure on the unitary group pushes forward to independent uniform measures on the reflections. We consider the sequence…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…