International Journal of Topology

32 pages, 6068 KB

Open AccessFeature PaperArticle

Curved Geometries in Persistent Homology: From Euclidean to AdS Metrics in Bow Echo Dynamics

by Hélène Canot, Philippe Durand and Emmanuel Frenod

Int. J. Topol. 2025, 2(4), 19; https://doi.org/10.3390/ijt2040019 - 4 Nov 2025

We propose a geometry topological framework to analyze storm dynamics by coupling persistent homology with Anti-de Sitter (AdS)-inspired metrics. On radar images of a bow echo event, we compare Euclidean distance with three compressive AdS metrics (

α

= 0.01, 0.1, 0.3) via [...] Read more.

α

= 0.01, 0.1, 0.3) via time-resolved

H_{1}

persistence diagrams for the arc and its internal cells. The moderate curvature setting (

α = 0.1

) offers the best trade-off: it suppresses spurious cycles, preserves salient features, and stabilizes lifetime distributions. Consistently, the arc exhibits longer, more dispersed cycles (large-scale organizer), while cells show shorter, localized patterns (confined convection). Cross-correlations of

H_{1}

lifetimes reveal a temporal asymmetry: arc activation precedes cell activation. A differential indicator

Δ (t)

based on Wasserstein distances quantifies this divergence and aligns with the visual onset in radar, suggesting early warning potential. Results are demonstrated on a rapid Corsica bow echo; broader validation remains future work. Full article

(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)

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15 pages, 1238 KB

Open AccessFeature PaperArticle

Topological Modelling in Public Procurement and Platform Economies: An Interdisciplinary Legal–Economic Framework

by Jitka Matějková

Int. J. Topol. 2025, 2(4), 18; https://doi.org/10.3390/ijt2040018 - 3 Nov 2025

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Abstract

This article develops an interdisciplinary framework that applies topological and graph-theoretical methods to public procurement markets and digital platform economies. Conceptualizing legal–economic interactions as dynamic networks of nodes and edges, we show how structural properties—centrality, clustering, connectivity, and boundary formation—shape contestability, resilience, and compliance. Using EU-relevant contexts (public procurement directives and the Digital Markets Act), we formalize network representations for buyers, suppliers, platforms, and regulators; define operational indicators; and illustrate an empirical, value-weighted buyer → supplier network to reveal a sparse but highly modular architecture with a high-value backbone. We then map these structural signatures to concrete legal levers (lotting and framework design, modification scrutiny, interoperability and data-access duties) and propose dashboard-style diagnostics for proactive oversight. The findings demonstrate how topological modelling complements doctrinal analysis by making hidden architectures visible and by linking measurable structure to regulatory outcomes. We conclude with implications for evidence-informed regulatory design and a research agenda integrating graph analytics, comparative evaluation across jurisdictions, and machine-learning-assisted anomaly detection. Full article

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26 pages, 1118 KB

Open AccessArticle

Nested Ensemble Learning with Topological Data Analysis for Graph Classification and Regression

by Innocent Abaa and Umar Islambekov

Int. J. Topol. 2025, 2(4), 17; https://doi.org/10.3390/ijt2040017 - 14 Oct 2025

Viewed by 339

Abstract

We propose a nested ensemble learning framework that utilizes Topological Data Analysis (TDA) to extract and integrate topological features from graph data, with the goal of improving performance on classification and regression tasks. Our approach computes persistence diagrams (PDs) using lower-star filtrations induced by three filter functions: closeness, betweenness, and degree 2 centrality. To overcome the limitation of relying on a single filter, these PDs are integrated through a data-driven, three-level architecture. At Level-0, diverse base models are independently trained on the topological features extracted for each filter function. At Level-1, a meta-learner combines the predictions of these base models for each filter to form filter-specific ensembles. Finally, at Level-2, a meta-learner integrates the outputs of these filter-specific ensembles to produce the final prediction. We evaluate our method on both simulated and real-world graph datasets. Experimental results demonstrate that our framework consistently outperforms base models and standard stacking methods, achieving higher classification accuracy and lower regression error. It also surpasses existing state-of-the-art approaches, ranking among the top three models across all benchmarks. Full article

(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)

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9 pages, 407 KB

Open AccessArticle

Rigid and Shaky Hard Link Diagrams

by Michał Jabłonowski

Int. J. Topol. 2025, 2(4), 16; https://doi.org/10.3390/ijt2040016 - 11 Oct 2025

Viewed by 307

Abstract

In this study of the Reidemeister moves within the classical knot theory, we focus on hard diagrams of knots and links, categorizing them as either rigid or shaky based on their adaptability to certain moves. We establish that every link possesses a diagram that is a rigid hard diagram, and we provide an upper limit for the number of crossings in such diagrams. Furthermore, we investigate rigid hard diagrams for specific knots or links to determine their rigid hard index. In the topic of shaky hard diagrams, we demonstrate the existence of such diagrams for the unknot and unlink of any number of components and present examples of shaky hard diagrams. Full article

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Int. J. Topol., Volume 2, Issue 4 (December 2025) – 4 articles

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