15th Anniversary of Axioms: Geometry and Topology

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: 31 March 2027 | Viewed by 467

Editor


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Guest Editor
Department of Applied Mathematics, Braude College, Karmiel 2161002, Israel
Interests: discrete differential geometry; image segmentation; internet; complex networks; computational geometry; feature extraction; image texture; quasi-conformal mappings and applications
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Special Issue Information

Dear Colleagues,

Axioms is celebrating its 15th anniversary from the launch of its inaugural issue. We greatly appreciate the efforts and support of our authors, reviewers, readers and editors over the last fifteen years. We would like to celebrate this significant milestone and commemorate the journal’s achievements throughout the years, by launching a Special Issue entitled "15th Anniversary of Axioms: Geometry and Topology”.

Submissions related to Geometry and Topology, in all aspects and branches, are welcome. However, we especially encourage the submission of articles that illustrate the manifold applications and benefits to a variety of fields, such as Computer Science, Artificial Intelligence, Bioinformatics, Physics, Chemistry, Medicine, and Architecture. We thus hope not only to illustrate past achievements of the journal, but also to spur the interest of future researchers dedicated to Geometry and Topology and their multifaceted uses and embodiments.

Dr. Emil Saucan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topological data analysis
  • persistent homology
  • discrete curvatures
  • curvature flows
  • spectral geometry
  • complex networks and generalizations
  • Regge calculus

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Published Papers (1 paper)

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Research

20 pages, 270 KB  
Article
Decision-Sufficient Feature Sets, Decision Cores, and Decision Complexes: A Topological Approach to Classification
by Sidney A. Morris
Axioms 2026, 15(7), 549; https://doi.org/10.3390/axioms15070549 - 21 Jul 2026
Viewed by 288
Abstract
Statistical classification is traditionally studied using probability, decision theory, information theory, and optimisation. We show that classification problems also possess a natural combinatorial and topological structure. Given a binary classification problem, we introduce the notion of a decision-sufficient feature set, namely a collection [...] Read more.
Statistical classification is traditionally studied using probability, decision theory, information theory, and optimisation. We show that classification problems also possess a natural combinatorial and topological structure. Given a binary classification problem, we introduce the notion of a decision-sufficient feature set, namely a collection of features that preserves the optimal Bayes decision rule. Rather than focusing on a single optimal feature subset, we study the entire family of decision-sufficient feature sets. We prove that this family forms an order filter in the Boolean lattice of feature subsets and that its complement forms an abstract simplicial complex. Consequently, every classification problem canonically determines a topological object, called the decision complex, the faces of whichh correspond to feature subsets that fail to preserve optimal decisions. This viewpoint leads naturally to three invariants: the decision core, the decision dimension, and the decision complex. General structural results are established, and a complete characterisation is obtained for Gaussian-discriminant models. In that setting, the decision core coincides with the support of the discriminant vector, yielding explicit formulae for the decision core and decision dimension. These results establish a new connection between statistical decision theory and combinatorial topology. Full article
(This article belongs to the Special Issue 15th Anniversary of Axioms: Geometry and Topology)
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