Related papers: Counting or producing all fixed cardinality transv…
Given a connected graph $G=(V,E)$, a set $S\subseteq V$ is a $k$-metric generator for $G$ if for any two different vertices $u,v\in V$, there exist at least $k$ vertices $w_1,...,w_k\in S$ such that $d_G(u,w_i)\ne d_G(v,w_i)$ for every…
We construct a special type of antichain (i. e., a family of subsets of a set, such that no subset is contained in another) using group-theoretical considerations, and obtain an upper bound on the cardinality of such an antichain. We apply…
Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively.
We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…
We show how to convert any clustering into a prediction set. This has the effect of converting the clustering into a (possibly overlapping) union of spheres or ellipsoids. The tuning parameters can be chosen to minimize the size of the…
When defining the amount of additive structure on a set it is often convenient to consider certain sumsets; Calculating the cardinality of these sumsets can elucidate the set's underlying structure. We begin by investigating finite sets of…
All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…
The problem of clustering a set of points moving on the line consists of the following: given positive integers n and k, the initial position and the velocity of n points, find an optimal k-clustering of the points. We consider two…
A generating function is derived that counts the number of diagrams in an arbitrary scalar field theory. The number of graphs containing any number $n_j$ of $j$-point vertices is given. The count is also used to obtain the number of…
We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the…
We study properties of the set of subsums for a convergent series $ k_1 \sin x + \dots + k_m \sin x +\dots + k_1\sin x^n +\dots + k_m \sin x^n + \dots $, where $k_1, k_2, k_3,\dots,k_m$ are fixed positive integers and $0<x<1$. Depends on…
Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be…
Cantor's diagonal method is traditionally used to prove the uncountability of the set of all infinite binary sequences. This paper analyzes the expressive limits of this method. It is shown that under any constructive application --…
A parametrization of the Kasner indices in terms of a continuous parameter is constructed by exploiting their representation as trilinear coordinates. This provides a clear picture of their variation through their entire range vis a vis…