Related papers: Projection-Forcing Multisets of Weight Changes
We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the…
This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where…
We regard Forcing Notions P adding real numbers and the algebras of P-measurable sets. As for Cohen- and Random-Forcing we can show that each analytic set is P-measurable using Solovay's Unfolding Trick for infinite games. To show this we…
We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.
We prove various iteration theorems for forcing classes related to subproper and subcomplete forcing, introduced by Jensen. In the first part, we use revised countable support iterations, and show that 1) the class of subproper,…
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
Let $\mathbf d=(d_j)_{j\in\mathbb I_m}\in\mathbb N^m$ be a finite sequence (of dimensions) and $\alpha=(\alpha_i)_{i\in\mathbb I_n}$ be a sequence of positive numbers (of weights), where $\mathbb I_k=\{1,\ldots,k\}$ for $k\in\mathbb N$. We…
Let $\mathcal{M}$ be a set with $M$ elements, let $\psi :\mathcal{M}\to\mathcal{M}$ be a bijective involution, and let~$\boldsymbol{\mathcal{X}}_{\psi}$ be the set of sequences $(x_1,\dots,x_M)\in\mathcal{M}^M$ with the property that…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
Delsarte showed that for any projective linear code over a finite field of characteristic p with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = (p^s)u and w2 = (p^s)(u+1). Moreover, he showed that…
The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…
We discuss some highlights of our computer-verified proof of the construction, given a countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying $\mathit{ZFC}+\neg\mathit{CH}$ and $\mathit{ZFC}+\mathit{CH}$.…
In 1942 I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a positive linear combination of the Gegenbauer polynomials. In this paper we extend Schoenberg's theorem for…
In this paper we ask when it is possible to transform a given sequence into a frame or a lower semi frame by multiplying the elements by numbers. In other words, we ask when a given sequence is a weighted frame or a weighted lower semi…
Data analysis in high energy physics has to deal with data samples produced from different sources. One of the most widely used ways to unfold their contributions is the sPlot technique. It uses the results of a maximum likelihood fit to…