Related papers: Kneser's method of neighbors

The deductive method ruled mathematics for the last 2500 years, now it is the turn of the inductive method. Here we make a modest start by using the inductive method to discover and prove (rigorously) explicit generating functions for the…

In this work, an expansion of Guessab-Schmeisser two points formula for n-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several…

Suppose $V$ is an $n$-element set where for each $x \in V$, the elements of $V \setminus \{x\}$ are ranked by their similarity to $x$. The $K$-nearest neighbor graph is a directed graph including an arc from each $x$ to the $K$ points of $V…

We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains…

Estimation of the population size $n$ from $k$ i.i.d.\ binomial observations with unknown success probability $p$ is relevant to a multitude of applications and has a long history. Without additional prior information this is a notoriously…

The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…

This paper presents Clustering based on Near Neighbor Influence (CNNI), a new clustering algorithm which is inspired by the idea of near neighbor and the superposition principle of influence. In order to clearly describe this algorithm, it…

This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of…

Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well-known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when…

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…

We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials…

For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical…

A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.

This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of…

Nearest neighbor classifier is arguably the most simple and popular nonparametric classifier available in the literature. However, due to the concentration of pairwise distances and the violation of the neighborhood structure, this…

Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…

The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…

Nonparametric estimation of mutual information is used in a wide range of scientific problems to quantify dependence between variables. The k-nearest neighbor (knn) methods are consistent, and therefore expected to work well for large…

We introduce a graphical presentation for the false nearest neighbors (FNN) method. In the original method only the percentage of false neighbors is computed without regard to the distribution of neighboring points in the time-delay…

We prove, in ZFC, that there is an infinite strictly descending chain of classes of theories in Keisler's order. Thus Keisler's order is infinite and not a well order. Moreover, this chain occurs within the simple unstable theories,…