Related papers: Kneser's method of neighbors

A set of vertices $S$ is a \emph{determining set} of a graph $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The \emph{determining number} of $G$ is the minimum cardinality of a determining set of $G$. This…

The concept of tensor rank, introduced in the twenties, has been popularized at the beginning of the seventies. This has allowed to carry out Factor Analysis on arrays with more than two indices. The generic rank may be seen as an upper…

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…

G.L. Watson \cite{watson1, watson2} introduced a set of transformations, called Watson transformations by most recent authors, in his study of the arithmetic of integral quadratic forms. These transformations change an integral quadratic…

The $k$-nearest neighbour ($k$-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the $k$-NN classifier. In this…

In this paper, we are interested in the interplay between integral ternary quadratic forms and class numbers. This is partially motivated by a question of Petersson.

This article continues and completes our previous work [14] J. Phys. Commun. 2 (2018) 025007. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the…

A significantly faster algorithm is presented for the original kNN mode seeking procedure. It has the advantages over the well-known mean shift algorithm that it is feasible in high-dimensional vector spaces and results in uniquely, well…

In this paper we study the identifiability of specific forms (symmetric tensors), with the target of extending recent methods for the case of $3$ variables to more general cases. In particular, we focus on forms of degree $4$ in $5$…

C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Assuming just a few elementary facts in field theory and the exclusion-inclusion formula, we show how one see the…

$K$-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of $K$-NN, learning an appropriate distance metric…

This is an algorithm for finding neighbors when the objects can freely move and have no predefined position. The query consists in finding neighbors for a center location and a given radius. Space is discretized in cubic cells. This…

In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…

This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a…

In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN).…

Let $K$ be a quartic CM field, that is, a totally imaginary quadratic extension of a real quadratic number field. In a 1962 article titled On the classfields obtained by complex multiplication of abelian varieties, Shimura considered a…

Machine learning has revolutionized many fields of science and technology. Through the $k$-Nearest Neighbors algorithm, we develop a model-independent classifier, where the algorithm can classify phases of a model to which it has never had…

We introduce a class of depth-based classification procedures that are of a nearest-neighbor nature. Depth, after symmetrization, indeed provides the center-outward ordering that is necessary and sufficient to define nearest neighbors. Like…