相关论文: Foundations of iterated star maps and their use in…

By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers.

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

In literature, many important combinatorial properties of subsets of N have been studied both with nonstandard techniques and from the point of view of N. In this thesis we mix these two different approaches in a technique that, at the same…

This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…

In [9], [15] it has been introduced a technique, based on nonstandard analysis, to study some problems in combinatorial number theory. In this paper we present three applications of this technique: the first one is a new proof of a known…

A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.

We review in brief the development and implementation of the Star integral, a tool yielding measurements of correlations much superior to conventional methods. A version for use in pion interferometry is explained. We also show how effects…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…

We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as…

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…

We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…

The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…

The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…

Using standard techniques from combinatorics, model theory, and algebraic geometry, we prove generalized versions of several basic results in the theory of spectrally arbitrary matrix patterns. Also, we point out a counterexample to a…

We lay the combinatorial foundations for [ShSt:340] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.

This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).