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Topological Data Analysis Meets Information Theory. New Perspectives for the Analysis of Higher-Order Interactions in Complex Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 1285

Special Issue Editors

IMT School for Advanced Studies, Piazza San Francesco 19, 55100 Lucca, Italy
Interests: complexity; graph theory; information theory; statistical mechanics of networks; pattern detection; network reconstruction; graph combinatorics; systemic risk estimation; (mis)information spreading on social networks; functional brain network analysis; higher-order interactions
1. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
2. Institute for Advanced Studies (IAS), University of Amsterdam, 1105 AZ Amsterdam, The Netherlands
Interests: statistical mechanics; applied topology and geometry; network science; information theory; neuroscience
Networks Unit, IMT School for Advanced Studies, Piazza San Francesco 19, 55100 Lucca, Italy
Interests: complex networks; graph theory; statistical physics; randomization techniques for graphs; higher-order interactions; social networks; economics; neuroscience
Special Issues, Collections and Topics in MDPI journals
Computer Science Division, School of Science and Technology, University of Camerino, 62032 Camerino, Italy
Interests: complexity; topological data analysis; higher-order interactions; self-adaptive systems; deep learning; information theory; pattern recognition; interpretable machine learning; artificial intelligence; intelligent manufacturing; computer vision; signal processing; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complexity lies in the rich variety of interactions taking place among the constituents of a given system. While research has mostly focused on pairwise relationships, recent work has shown that neglecting higher-order interactions can lead to a poor representation of the same systems. Examples of these "group-wise" interactions can be found in many fields, including neuroscience, biology, finance and sociology. Researchers have developed various approaches to quantify and investigate these interactions, including Topological Data Analysis and Information Theory. While the former focuses on defining the structures to be considered and their topological invariants, the latter deals with inferring higher-order interdependencies among the system constituents using, for instance, multivariate information theory. This Special Issue aims to bridge the perspectives of Complex Systems, Topological Data Analysis and Information Theory to better understand higher-order structures. Researchers are encouraged to explore commonalities between these approaches, their integration and the challenges they bring to application domains.

Both theoretical and applied contributions about the following topics fall within the scope of this Special Issue (though well-motivated systematic literature reviews on the same topics may be considered):

- Higher-order representations of interacting systems (e.g., hypergraphs, simplicial complexes);

- Topological data analysis and algebraic topology (e.g., persistent homology, dimension reduction);

- Multivariate information theory for higher-order inference (e.g., higher-order pattern detection);

- Generative models for higher-order interactions;

- Dynamical models of higher-order interactions;

- Entropy (e.g. persistent, Renyi, Shannon, transfer, Tsallis);

- Applications in economics and finance (e.g., cryptocurrencies), neurosciences (e.g., structural and functional brain networks, epilepsy, Alzheimer's disease and dementia), chemistry and biology (protein interactions), cybersecurity, artificial intelligence, machine/deep learning and robotics.

Dr. Tiziano Squartini
Dr. Fernando Antônio Nóbrega Santos
Dr. Rossana Mastrandrea
Dr. Marco Piangerelli
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy 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 2600 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

  • complexity
  • information theory
  • topological data analysis
  • higher-order interactions
  • simplicial complexes
  • hypergraphs

Published Papers (1 paper)

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Research

28 pages, 6348 KiB  
Article
A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
Entropy 2023, 25(8), 1150; https://doi.org/10.3390/e25081150 - 31 Jul 2023
Cited by 1 | Viewed by 621
Abstract
In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and [...] Read more.
In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and to increase the stability of TDA in the presence of noisy data. In particular, we prove that GENEOs can control the expected value of the perturbation of persistence diagrams caused by uniformly distributed impulsive noise, when data are represented by L-Lipschitz functions from R to R. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Tentative title: Patterns in temporal networks with higher-order egocentric structures
Authors: Beatriz Arregui Garcia1, Quintino Francesco Lotito2, Antonio Longa2, Alain Barrat3, Sandro Meloni1 and Giulia Cencetti3
Affiliations:
1. Instituto de Física Interdisciplinar y Sistemas Complejos IFISC, 07122 Palma de Mallorca, Spain
2. Department of Information Engineering and Computer Science, University of Trento, 38122 Trento, Italy.
3. Aix Marseille Univ, Université de Toulon, CNRS, CPT, 13009 Marseille, France
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