Related papers: The Distribution Relation and Inverse Function The…
When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is…
Angle halving, or alternatively the reverse operation of angle doubling, is a useful tool when studying directional distributions. It is especially useful on the circle where, in particular, it yields an identification between the wrapped…
The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
We survey recent applications of topology and singularity theory in the study of the algebraic complexity of concrete optimization problems in applied algebraic geometry and algebraic statistics.
Hadamard's global inverse theorem provides conditions for a function to be globally invertible on Rn. In this note we show that the conditions are robust enough for the conclusion to hold even if we relax the conditions by removing the…
An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form…
We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory,…