{
  "abstract": "Environmental systems are characterized by complex spatial interactions that cannot be fully described through pairwise relationships or local uncertainty measures. We propose a unified framework combining higher-order information theory and topological data analysis to characterize the organization and uncertainty of environmental networks. Spatial entities, represented by monitoring stations or municipalities, are embedded into a Delaunay simplicial complex, and O-information is used to quantify redundancy and synergy among neighboring triplets. The resulting field of higher-order interactions is analyzed through persistent homology, enabling the identification of topological structures that remain stable across interaction scales. The methodology is applied to both an air-quality monitoring network based on weekly \\(\\mathrm{NO_2}\\) and \\(\\mathrm{O_3}\\) observations and a multi-hazard territorial assessment. We show that regions exhibiting strong O-information and persistent topological structures correspond to robust environmental patterns, whereas areas characterized by heterogeneous regimes and rapidly varying interactions display increased uncertainty. Building on these results, we introduce a topological uncertainty framework that integrates simplex divergence, higher-order interactions, and topological uncertainty. Our results demonstrate that uncertainty can be interpreted not only as statistical variability but also as the instability of the underlying information topology. By integrating O-information and persistent homology within a common spatial framework, the proposed approach provides a new methodology for detecting robust higher-order structures and topologically uncertain regions in environmental and multi-hazard systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18439",
  "author_total": 19,
  "authors": [
    {
      "name": "Domenico Pomarico"
    },
    {
      "name": "Alessandro Fania"
    },
    {
      "name": "Gabriel Ramirez Sanchez"
    },
    {
      "name": "Loredana Bellantuono"
    },
    {
      "name": "Domenico Capolongo"
    },
    {
      "name": "Roberto Cilli"
    },
    {
      "name": "Alessandra Costantino"
    },
    {
      "name": "Davide D' Alo"
    },
    {
      "name": "Mario Elia"
    },
    {
      "name": "Francesco Giordano"
    },
    {
      "name": "Niloofar Kheirkhahan"
    },
    {
      "name": "Raffaele Lafortezza"
    },
    {
      "name": "Raffaele Nutricato"
    },
    {
      "name": "Ester Pantaleo"
    },
    {
      "name": "Sabina Tangaro"
    },
    {
      "name": "Roberto Bellotti"
    },
    {
      "name": "Sebastiano Stramaglia"
    },
    {
      "name": "Alfonso Monaco"
    },
    {
      "name": "Nicola Amoroso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g3pjmrpfd5vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18439",
  "fulltext_url": null,
  "id": "5g3pjmrpfd5vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18439",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7213502515",
  "pdf_url": "https://arxiv.org/pdf/2609.18439",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g3pjmrpfd5vv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18439",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18439"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Topological Uncertainty and Higher-Order Interactions in Spatial Networks",
  "title_text": "Topological Uncertainty and Higher-Order Interactions in Spatial Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/5g3pjmrpfd5vv",
  "venue": "arXiv",
  "versions": []
}