Zobrazeno 1 - 10
of 155
pro vyhledávání: '"Patrick Erik"'
Autor:
Bradley, Patrick Erik
The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gau{\ss} hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an
Externí odkaz:
http://arxiv.org/abs/2412.20591
Autor:
Bradley, Patrick Erik
The transcendent part of the Drinfeld p-adic upper half plane is shown to be a Polish space. Using Radon measures associated with regular differential 1-forms invariant under Schottky groups allows to construct self-adjoint diffusion operators as Lap
Externí odkaz:
http://arxiv.org/abs/2412.14292
Motivated by multi-topology building and city model data, first a lossless representation of multiple $T_0$-topologies on a given finite set by a vertex-edge-weighted graph is given, and the subdominant ultrametric of the associated weighted graph di
Externí odkaz:
http://arxiv.org/abs/2411.00806
Autor:
Bradley, Patrick Erik
New local ultrametricity measures for finite metric data are proposed through the viewpoint that their Vietoris-Rips corners are samples from p-adic Mumford curves endowed with a Radon measure coming from a regular differential 1-form. This is experi
Externí odkaz:
http://arxiv.org/abs/2408.07174
Publikováno v:
ISPRS International Journal of Geo-Information, Vol 11, Iss 10, p 533 (2022)
In order to perform topological queries on geographic data, it is necessary to first develop a topological access method (TOAM). Using the fact that any (incidence or other binary) relation produces a topology which includes the common usage of topol
Externí odkaz:
https://doaj.org/article/c3b79a393f5c4fa39bcbd37b93a4ca8c
Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spaces, first non-autonomous diffusion operators on such spaces, where fin
Externí odkaz:
http://arxiv.org/abs/2407.21555
Autor:
Bradley, Patrick Erik
$p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Z\'u\~niga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the Euler cha
Externí odkaz:
http://arxiv.org/abs/2406.06439
Autor:
Bradley, Patrick Erik
A parametrised diffusion operator on the regular domain $\Omega$ of a $p$-adic Schottky group is constructed. It is defined as an integral operator on the complex-valued functions on $\Omega$ which are invariant under the Schottky group $\Gamma$, whe
Externí odkaz:
http://arxiv.org/abs/2405.17586
Publikováno v:
ISPRS International Journal of Geo-Information, Vol 11, Iss 4, p 224 (2022)
Geometrically induced topology plays a major role in applications such as simulations, navigation, spatial or spatio-temporal analysis and many more. This article computes geometrically induced topology useful for such applications and extends previo
Externí odkaz:
https://doaj.org/article/3968c52d31e342c0a54f585889b6628f
Autor:
Bradley, Patrick Erik
A self-adjoint operator is constructed on the $L_2$-functions on the $K$-rational points $X(K)$ of a Mumford curve $X$ defined over a non-archimedean local field $K$. It generates a Feller semi-group, and the corresponding heat equation describes a M
Externí odkaz:
http://arxiv.org/abs/2402.02869