Related papers: Minimal clones generated by majority operations
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal…
A smallest generating set of a semigroup is a generating set of the smallest cardinality. Similarly, an irredundant generating set $X$ is a generating set such that no proper subset of $X$ is also a generating set. A semigroup $S$ is…
Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic component code and the generator polynomial of a second cyclic component code, an…
We study a recursively defined sequence which is constructed using the least common multiple. It has been conjectured that every term of that sequence is $1$ or a prime. In this paper we show that this claim is connected to a strong version…
This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions…
We determine the minimum possible critical exponent for all palindromes over finite alphabets.
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…
Given a clone C on a set A, we characterize the clone of operations on A which are local term operations of every ultrapower of the algebra $(A; C)$.
We treat two different topics on the log minimal model program, especially for four-dimensional log canonical pairs. (a) Finite generation of the log canonical ring in dimension four. (b) Abundance theorem for irregular fourfolds. We obtain…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We obtain tight bounds for the minimal number of generators of an ideal with bounded-degree generators in a polynomial ring $K[X_1,\dots,X_n],$ as well as a sharp quantification of the maximum possible size of a minimal generating set of…
In this paper we have studied the problem of scalar particles pair creation by an electric field in the presence of a minimal length. Two sets of exact solutions for the Klein Gordon equation are given in momentum space. Then the canonical…
Machine learning is applied to find proofs, with smaller or smallest numbers of nodes, for the classification of 4-nilpotent semigroups.
Let $S(n)$ be the infinite-type surface with infinite genus and $n \in \mathbb{N}$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\mod(S(n))$, is a Polish group that is not countably generated, but it…
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…
We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting as well as a recent extension by Cornu\'ejols and Y{\i}ld{\i}z. We show that…
We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have…
We construct a minimal generating set of the level 2 mapping class group of a nonorientable surface of genus $g$, and determine its abelianization for $g\ge4$.