arXiv subjects

Soheil Anbouhi

Publications and source records attributed to Soheil Anbouhi.

3 recordsLinked to original sources

arXiv2026

Improving Topological Detection of Weather Regimes in climate dynamical systems

Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather regimes. Recent work has shown that weather regimes can be interpreted geometrically as topological structures in the phase space of the atmospheric system. In this approach, regimes are identified using a density--radius bifiltration combined with persistent homology, a well-established tool from Topological Data Analysis (TDA). This topological perspective provides a unifying view of regimes and, unlike traditional methods, does not require the number of regimes to be specified in advance. However, the method relies on density estimation techniques (typically Gaussian kernel density estimation), which can over--smooth weakly populated but dynamically important regions of the phase space.

math.AT↗

arXiv2024

On Metrics for Analysis of Functional Data on Geometric Domains

This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as fields. Formally, fields are viewed as 1-Lipschitz mappings between Polish metric spaces with the domain possibly equipped with a Borel probability measure. We introduce field analogues of the Gromov-Hausdorff, Gromov-Prokhorov, and Gromov-Wasserstein distances, investigate their main properties and provide a characterization of the Gromov-Hausdorff distance in terms of isometric embeddings in a Urysohn universal field. Adapting the notion of distance matrices to fields, we formulate a discrete model, obtain an empirical estimation result that provides a theoretical basis for its use in functional data analysis, and prove a field analogue of Gromov's Reconstruction Theorem. We also investigate field versions of the Vietoris-Rips and neighborhood (or offset) filtrations and prove that they are stable with respect to appropriate metrics.

math.MG↗

arXiv2022

Universal Mappings and Analysis of Functional Data on Geometric Domains

This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of scientific and practical interest. For example, $f$ could represent a functional magnetic resonance image, or the nodes of a social network labeled with attributes or preferences, where the underlying metric structure is given by the shortest path distance, commute distance, or diffusion distance. Formally, these may be viewed as functions defined on metric spaces, sometimes equipped with additional structure such as a probability measure, in which case the domain is referred to as a metric-measure space, or simply $mm$-space. Our primary goal is threefold: (i) to develop metrics that allow us to model and quantify variation in functional data, possibly with distinct domains; (ii) to investigate principled empirical estimations of these metrics; (iii) to construct a universal function that ``contains'' all functions whose domains and ranges are Polish (separable and complete metric) spaces, assuming Lipschitz regularity. The latter is much in the spirit of constructing universal spaces for structural data (metric spaces) whose investigation dates back to the early 20th century and are of classical interest in metric geometry.

math.MG↗