Related papers: A Note on Matching in Groups and Field Extensions
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
Schema Matching is a method of finding attributes that are either similar to each other linguistically or represent the same information. In this project, we take a hybrid approach at solving this problem by making use of both the provided…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Matrices over a finite field having fixed rank and restricted support are a natural $q$-analogue of rook placements on a board. We develop this $q$-rook theory by defining a corresponding analogue of the hit numbers. Using tools from coding…
In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
This paper investigates the synchronization problems for general high-dimensional linear networks over finite fields. By using the technique of linear transformations and invariant subspaces for linear spaces over finite fields, several…
The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…
This note, suitable for a lecture in an advanced undergraduate or basic graduate course on the economic theory of networks, exposits basic ideas of linear best-response games and their equilibria.
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
The aim of this note is to describe a geometric relation between simple plane curve singularities classified by simply laced Cartan matrices and cluster varieties of finite type also classified by the simply laced Cartan matrices. We…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
We study a relation between roots of characteristic polynomials and intersection points of line arrangements. Using these results, we obtain a lot of applications for line arrangements. Namely, we give (i) a generalized addition theorem for…
This Note presents the resolution of a differential system on the plane that translates a geometrical problem about isotropic deformations of area and length. The system stems from a probability study on deformed random fields [J.Fournier…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.