Related papers: Constructing/analyzing differential distributed la…

The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…

A celebrated result by M. Davis, H. Putnam, J. Robinson, and Y. Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this…

Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly…

A method for constructing distributions on the non negative integers as discrete analogue of continuous distributions on the non negative real is presented. A justification of the definition of discrete self decomposable laws is provided.…

When $\mathbb{Z}^d$ is represented as a finite disjoint union of translated integer sublattices, the translated sublattices must possess some special properties. Such a representation is called a \emph{lattice tiling}. We develop a…

In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…

A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…

We prove identities generating higher dimensional vector partitions. We derive theorems for integer lattice points in the 2D first quadrant, then generalize the approach to find 3D and $n$-space lattice point vector region extensions. We…

The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…

In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently states that the incomparability graph of the boolean…

This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they…

We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The efficacy of the…

Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…

We show that the number $p\_d$ of non-similar perfect $d$-dimensional lattices satisfies eventually the inequalities$e^{d^{1-\epsilon}}<p\_d<e^{d^{3+\epsilon}}$ for arbitrary smallstrictly positive $\epsilon$.

We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We…

Let $P_r(n)$ be the set of partitions of n with non negative rth differences. Let $\lambda$ be a partition chosen uniformly at random among the set $P_r(n)$. Let $d(\lambda)$ be a positive rth difference chosen uniformly at random in…

We first show that the tilings of a general domain form a lattice which we then undertake to decompose and generate without any redundance. To this end, we study extensively the relatively simple case of hexagons and their deformations. We…

A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of…

This article is the second part of an essay dedicated to lattices freely generated by posets within a variety. The first part dealt with four easy varieties while this part is concerned with finitely generated varieties. Here we present a…