1
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Lawson S, Donovan D, Lefevre J. An application of node and edge nonlinear hypergraph centrality to a protein complex hypernetwork. PLoS One 2024; 19:e0311433. [PMID: 39361678 PMCID: PMC11449304 DOI: 10.1371/journal.pone.0311433] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2024] [Accepted: 09/12/2024] [Indexed: 10/05/2024] Open
Abstract
The use of graph centrality measures applied to biological networks, such as protein interaction networks, underpins much research into identifying key players within biological processes. This approach however is restricted to dyadic interactions and it is well-known that in many instances interactions are polyadic. In this study we illustrate the merit of using hypergraph centrality applied to a hypernetwork as an alternative. Specifically, we review and propose an extension to a recently introduced node and edge nonlinear hypergraph centrality model which provides mutually dependent node and edge centralities. A Saccharomyces Cerevisiae protein complex hypernetwork is used as an example application with nodes representing proteins and hyperedges representing protein complexes. The resulting rankings of the nodes and edges are considered to see if they provide insight into the essentiality of the proteins and complexes. We find that certain variations of the model predict essentiality more accurately and that the degree-based variation illustrates that the centrality-lethality rule extends to a hypergraph setting. In particular, through exploitation of the models flexibility, we identify small sets of proteins densely populated with essential proteins. One of the key advantages of applying this model to a protein complex hypernetwork is that it also provides a classification method for protein complexes, unlike previous approaches which are only concerned with classifying proteins.
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Affiliation(s)
- Sarah Lawson
- ARC Centre of Excellence, Plant Success in Nature and Agriculture, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, Australia
| | - Diane Donovan
- ARC Centre of Excellence, Plant Success in Nature and Agriculture, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, Australia
| | - James Lefevre
- ARC Centre of Excellence, Plant Success in Nature and Agriculture, School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland, Australia
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2
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Krieger S, Kececioglu J. Robust Optimal Metabolic Factories. J Comput Biol 2024. [PMID: 39328127 DOI: 10.1089/cmb.2024.0748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/28/2024] Open
Abstract
Perhaps the most fundamental model in synthetic and systems biology for inferring pathways in metabolic reaction networks is a metabolic factory: a system of reactions that starts from a set of source compounds and produces a set of target molecules, while conserving or not depleting intermediate metabolites. Finding a shortest factory-that minimizes a sum of real-valued weights on its reactions to infer the most likely pathway-is NP-complete. The current state-of-the-art for shortest factories solves a mixed-integer linear program with a major drawback: it requires the user to set a critical parameter, where too large a value can make optimal solutions infeasible, while too small a value can yield degenerate solutions due to numerical error. We present the first robust algorithm for optimal factories that is both parameter-free (relieving the user from determining a parameter setting) and degeneracy-free (guaranteeing it finds an optimal nondegenerate solution). We also give for the first time a complete characterization of the graph-theoretic structure of shortest factories, that reveals an important class of degenerate solutions which was overlooked and potentially output by the prior state-of-the-art. We show degeneracy is precisely due to invalid stoichiometries in reactions, and provide an efficient algorithm for identifying all such misannotations in a metabolic network. In addition we settle the relationship between the two established pathway models of hyperpaths and factories by proving hyperpaths actually comprise a subclass of factories. Comprehensive experiments over all instances from the standard metabolic reaction databases in the literature demonstrate our parameter-free exact algorithm is fast in practice, quickly finding optimal factories in large real-world networks containing thousands of reactions. A preliminary implementation of our robust algorithm for shortest factories in a new tool called Freeia is available free for research use at http://freeia.cs.arizona.edu.
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Affiliation(s)
- Spencer Krieger
- Ray and Stephanie Lane Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
| | - John Kececioglu
- Department of Computer Science, The University of Arizona, Tucson, Arizona, USA
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3
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Restrepo G. Spaces of mathematical chemistry. Theory Biosci 2024:10.1007/s12064-024-00425-4. [PMID: 39259256 DOI: 10.1007/s12064-024-00425-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2024] [Accepted: 08/22/2024] [Indexed: 09/12/2024]
Abstract
In an effort to expand the domain of mathematical chemistry and inspire research beyond the realms of graph theory and quantum chemistry, we explore five mathematical chemistry spaces and their interconnectedness. These spaces comprise the chemical space, which encompasses substances and reactions; the space of reaction conditions, spanning the physical and chemical aspects involved in chemical reactions; the space of reaction grammars, which encapsulates the rules for creating and breaking chemical bonds; the space of substance properties, covering all documented measurements regarding substances; and the space of substance representations, composed of the various ontologies for characterising substances.
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Affiliation(s)
- Guillermo Restrepo
- Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, Leipzig, 04103, Saxony, Germany.
- Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstr. 16-18, Leipzig, 04107, Saxony, Germany.
- School of Applied Sciences and Engineering, EAFIT University, Carrera 49 No 7 Sur-50, Medellin, 050022, Antioquia, Colombia.
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4
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Huang Y, Ma T, Wan Z, Zhong C, Wang J. AFP: Finding pathways accounting for stoichiometry along with atom group tracking in metabolic network. J Biotechnol 2024; 392:139-151. [PMID: 39009230 DOI: 10.1016/j.jbiotec.2024.07.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Revised: 04/29/2024] [Accepted: 07/08/2024] [Indexed: 07/17/2024]
Abstract
Automatically finding novel pathways plays an important role in the initial designs of metabolic pathways in synthetic biology and metabolic engineering. Although path-finding methods have been successfully applied in identifying valuable synthetic pathways, few efforts have been made in fusing atom group tracking into building stoichiometry model to search metabolic pathways from arbitrary start compound via Mixed Integer Linear Programming (MILP). We propose a novel method called AFP to find metabolic pathways by incorporating atom group tracking into reaction stoichiometry via MILP. AFP tracks the movements of atom groups in the reaction stoichiometry to construct MILP model to search the pathways containing atom groups exchange in the reactions and adapts the MILP model to provide the options of searching pathways from an arbitrary or given compound to the target compound. Combining atom group tracking with reaction stoichiometry to build MILP model for pathfinding may promote the search of well-designed alternative pathways at the stoichiometric modeling level. The experimental comparisons to the known pathways show that our proposed method AFP is more effective to recover the known pathways than other existing methods and is capable of discovering biochemically feasible pathways producing the metabolites of interest.
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Affiliation(s)
- Yiran Huang
- School of Computer and Electronics and Information, Guangxi University, Nanning, China; Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning, China; Key Laboratory of Parallel, Distributed and Intelligent Computing, (Guangxi University), Education Department of Guangxi Zhuang Autonomous Region, Guangxi University, Nanning, China; Guangxi Intelligent Digital Services Research Center of Engineering Technology, Guangxi University, Nanning, China.
| | - Tao Ma
- School of Computer and Electronics and Information, Guangxi University, Nanning, China
| | - Zhiyuan Wan
- School of Computer and Electronics and Information, Guangxi University, Nanning, China
| | - Cheng Zhong
- School of Computer and Electronics and Information, Guangxi University, Nanning, China; Guangxi Key Laboratory of Multimedia Communications and Network Technology, Guangxi University, Nanning, China; Key Laboratory of Parallel, Distributed and Intelligent Computing, (Guangxi University), Education Department of Guangxi Zhuang Autonomous Region, Guangxi University, Nanning, China; Guangxi Intelligent Digital Services Research Center of Engineering Technology, Guangxi University, Nanning, China
| | - Jianyi Wang
- Medical College, Guangxi University, Nanning, China
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5
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Di Gaetano L, Carugno G, Battiston F, Coghi F. Dynamical Fluctuations of Random Walks in Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 133:107401. [PMID: 39303236 DOI: 10.1103/physrevlett.133.107401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 06/04/2024] [Accepted: 07/26/2024] [Indexed: 09/22/2024]
Abstract
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation. Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks.
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Affiliation(s)
| | | | | | - Francesco Coghi
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SEa-106 91 Stockholm, Sweden
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6
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Badalyan A, Ruggeri N, De Bacco C. Structure and inference in hypergraphs with node attributes. Nat Commun 2024; 15:7073. [PMID: 39152121 PMCID: PMC11329712 DOI: 10.1038/s41467-024-51388-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 08/06/2024] [Indexed: 08/19/2024] Open
Abstract
Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes can be used to improve our understanding of the structure resulting from higher-order interactions. We consider the problem of community detection in hypergraphs and develop a principled model that combines higher-order interactions and node attributes to better represent the observed interactions and to detect communities more accurately than using either of these types of information alone. The method learns automatically from the input data the extent to which structure and attributes contribute to explain the data, down weighing or discarding attributes if not informative. Our algorithmic implementation is efficient and scales to large hypergraphs and interactions of large numbers of units. We apply our method to a variety of systems, showing strong performance in hyperedge prediction tasks and in selecting community divisions that correlate with attributes when these are informative, but discarding them otherwise. Our approach illustrates the advantage of using informative node attributes when available with higher-order data.
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Affiliation(s)
- Anna Badalyan
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany
| | - Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany.
- Department of Computer Science, ETH, Zürich, Switzerland.
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany.
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7
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Zitnik M, Li MM, Wells A, Glass K, Morselli Gysi D, Krishnan A, Murali TM, Radivojac P, Roy S, Baudot A, Bozdag S, Chen DZ, Cowen L, Devkota K, Gitter A, Gosline SJC, Gu P, Guzzi PH, Huang H, Jiang M, Kesimoglu ZN, Koyuturk M, Ma J, Pico AR, Pržulj N, Przytycka TM, Raphael BJ, Ritz A, Sharan R, Shen Y, Singh M, Slonim DK, Tong H, Yang XH, Yoon BJ, Yu H, Milenković T. Current and future directions in network biology. BIOINFORMATICS ADVANCES 2024; 4:vbae099. [PMID: 39143982 PMCID: PMC11321866 DOI: 10.1093/bioadv/vbae099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 05/31/2024] [Accepted: 07/08/2024] [Indexed: 08/16/2024]
Abstract
Summary Network biology is an interdisciplinary field bridging computational and biological sciences that has proved pivotal in advancing the understanding of cellular functions and diseases across biological systems and scales. Although the field has been around for two decades, it remains nascent. It has witnessed rapid evolution, accompanied by emerging challenges. These stem from various factors, notably the growing complexity and volume of data together with the increased diversity of data types describing different tiers of biological organization. We discuss prevailing research directions in network biology, focusing on molecular/cellular networks but also on other biological network types such as biomedical knowledge graphs, patient similarity networks, brain networks, and social/contact networks relevant to disease spread. In more detail, we highlight areas of inference and comparison of biological networks, multimodal data integration and heterogeneous networks, higher-order network analysis, machine learning on networks, and network-based personalized medicine. Following the overview of recent breakthroughs across these five areas, we offer a perspective on future directions of network biology. Additionally, we discuss scientific communities, educational initiatives, and the importance of fostering diversity within the field. This article establishes a roadmap for an immediate and long-term vision for network biology. Availability and implementation Not applicable.
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Affiliation(s)
- Marinka Zitnik
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA 02115, United States
| | - Michelle M Li
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA 02115, United States
| | - Aydin Wells
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, United States
- Lucy Family Institute for Data and Society, University of Notre Dame, Notre Dame, IN 46556, United States
- Eck Institute for Global Health, University of Notre Dame, Notre Dame, IN 46556, United States
| | - Kimberly Glass
- Channing Division of Network Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA 02115, United States
| | - Deisy Morselli Gysi
- Channing Division of Network Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA 02115, United States
- Department of Statistics, Federal University of Paraná, Curitiba, Paraná 81530-015, Brazil
- Department of Physics, Northeastern University, Boston, MA 02115, United States
| | - Arjun Krishnan
- Department of Biomedical Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States
| | - T M Murali
- Department of Computer Science, Virginia Tech, Blacksburg, VA 24061, United States
| | - Predrag Radivojac
- Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115, United States
| | - Sushmita Roy
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53715, United States
- Wisconsin Institute for Discovery, Madison, WI 53715, United States
| | - Anaïs Baudot
- Aix Marseille Université, INSERM, MMG, Marseille, France
| | - Serdar Bozdag
- Department of Computer Science and Engineering, University of North Texas, Denton, TX 76203, United States
- Department of Mathematics, University of North Texas, Denton, TX 76203, United States
| | - Danny Z Chen
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, United States
| | - Lenore Cowen
- Department of Computer Science, Tufts University, Medford, MA 02155, United States
| | - Kapil Devkota
- Department of Computer Science, Tufts University, Medford, MA 02155, United States
| | - Anthony Gitter
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI 53715, United States
- Morgridge Institute for Research, Madison, WI 53715, United States
| | - Sara J C Gosline
- Biological Sciences Division, Pacific Northwest National Laboratory, Seattle, WA 98109, United States
| | - Pengfei Gu
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, United States
| | - Pietro H Guzzi
- Department of Medical and Surgical Sciences, University Magna Graecia of Catanzaro, Catanzaro, 88100, Italy
| | - Heng Huang
- Department of Computer Science, University of Maryland College Park, College Park, MD 20742, United States
| | - Meng Jiang
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, United States
| | - Ziynet Nesibe Kesimoglu
- Department of Computer Science and Engineering, University of North Texas, Denton, TX 76203, United States
- National Center of Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20814, United States
| | - Mehmet Koyuturk
- Department of Computer and Data Sciences, Case Western Reserve University, Cleveland, OH 44106, United States
| | - Jian Ma
- Ray and Stephanie Lane Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, United States
| | - Alexander R Pico
- Institute of Data Science and Biotechnology, Gladstone Institutes, San Francisco, CA 94158, United States
| | - Nataša Pržulj
- Department of Computer Science, University College London, London, WC1E 6BT, England
- ICREA, Catalan Institution for Research and Advanced Studies, Barcelona, 08010, Spain
- Barcelona Supercomputing Center (BSC), Barcelona, 08034, Spain
| | - Teresa M Przytycka
- National Center of Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20814, United States
| | - Benjamin J Raphael
- Department of Computer Science, Princeton University, Princeton, NJ 08544, United States
| | - Anna Ritz
- Department of Biology, Reed College, Portland, OR 97202, United States
| | - Roded Sharan
- School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel
| | - Yang Shen
- Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, United States
| | - Mona Singh
- Department of Computer Science, Princeton University, Princeton, NJ 08544, United States
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, United States
| | - Donna K Slonim
- Department of Computer Science, Tufts University, Medford, MA 02155, United States
| | - Hanghang Tong
- Department of Computer Science, University of Illinois Urbana-Champaign, Urbana, IL 61801, United States
| | - Xinan Holly Yang
- Department of Pediatrics, University of Chicago, Chicago, IL 60637, United States
| | - Byung-Jun Yoon
- Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, United States
- Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973, United States
| | - Haiyuan Yu
- Department of Computational Biology, Weill Institute for Cell and Molecular Biology, Cornell University, Ithaca, NY 14853, United States
| | - Tijana Milenković
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, United States
- Lucy Family Institute for Data and Society, University of Notre Dame, Notre Dame, IN 46556, United States
- Eck Institute for Global Health, University of Notre Dame, Notre Dame, IN 46556, United States
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8
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Gallo L, Lacasa L, Latora V, Battiston F. Higher-order correlations reveal complex memory in temporal hypergraphs. Nat Commun 2024; 15:4754. [PMID: 38834592 DOI: 10.1038/s41467-024-48578-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 05/02/2024] [Indexed: 06/06/2024] Open
Abstract
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data.
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Affiliation(s)
- Luca Gallo
- Department of Network and Data Science, Central European University, Vienna, Austria.
| | - Lucas Lacasa
- Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB, Palma de Mallorca, Spain
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
- Department of Physics and Astronomy, University of Catania, 95125, Catania, Italy
- INFN Sezione di Catania, Via S. Sofia, 64, 95125, Catania, Italy
- Complexity Science Hub Vienna, A-1080, Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, Vienna, Austria.
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9
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Ruggeri N, Battiston F, De Bacco C. Framework to generate hypergraphs with community structure. Phys Rev E 2024; 109:034309. [PMID: 38632750 DOI: 10.1103/physreve.109.034309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 01/11/2024] [Indexed: 04/19/2024]
Abstract
In recent years hypergraphs have emerged as a powerful tool to study systems with multibody interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the standardized evaluation of algorithms and the statistical study of real-world networked data, these are scarcely available in the context of hypergraphs. Here we propose a flexible and efficient framework for the generation of hypergraphs with many nodes and large hyperedges, which allows specifying general community structures and tune different local statistics. We illustrate how to use our model to sample synthetic data with desired features (assortative or disassortative communities, mixed or hard community assignments, etc.), analyze community detection algorithms, and generate hypergraphs structurally similar to real-world data. Overcoming previous limitations on the generation of synthetic hypergraphs, our work constitutes a substantial advancement in the statistical modeling of higher-order systems.
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Affiliation(s)
- Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
- Department of Computer Science, ETH, 8004 Zürich, Switzerland
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
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10
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Kim JH, Goh KI. Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs. PHYSICAL REVIEW LETTERS 2024; 132:087401. [PMID: 38457718 DOI: 10.1103/physrevlett.132.087401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 11/13/2023] [Accepted: 01/25/2024] [Indexed: 03/10/2024]
Abstract
The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes shared between hyperedges. Although the extensive higher-order component (HOC) could be witnessed ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this Letter, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. Most crucially, the giant HOC is required for the higher-order contagion to invade globally from a single seed. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.
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Affiliation(s)
- Jung-Ho Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - K-I Goh
- Department of Physics, Korea University, Seoul 02841, Korea
- Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
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11
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Burgio G, Gómez S, Arenas A. Triadic Approximation Reveals the Role of Interaction Overlap on the Spread of Complex Contagions on Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 132:077401. [PMID: 38427871 DOI: 10.1103/physrevlett.132.077401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 01/19/2024] [Indexed: 03/03/2024]
Abstract
Contagion processes relying on the exposure to multiple sources are prevalent in social systems, and are effectively represented by hypergraphs. In this Letter, we derive a mean-field model that goes beyond node- and pair-based approximations. We reveal how the stability of the contagion-free state is decided by either two- or three-body interactions, and how this is strictly related to the degree of overlap between these interactions. Our findings demonstrate the dual effect of increased overlap: it lowers the invasion threshold, yet produces smaller outbreaks. Corroborated by numerical simulations, our results emphasize the significance of the chosen representation in describing a higher-order process.
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Affiliation(s)
- Giulio Burgio
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Sergio Gómez
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Alex Arenas
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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12
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Bilbao D, Aimar H, Mateos DM. Filtration evolution of hypergraphs: A novel approach to studying multidimensional datasets. CHAOS (WOODBURY, N.Y.) 2024; 34:023142. [PMID: 38421855 DOI: 10.1063/5.0155459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 02/01/2024] [Indexed: 03/02/2024]
Abstract
The rapid growth of large datasets has led to a demand for novel approaches to extract valuable insights from intricate information. Graph theory provides a natural framework to model these relationships, but standard graphs may not capture the complex interdependence between components. Hypergraphs are a powerful extension of graphs that can represent higher-order relationships in the data. In this paper, we propose a novel approach to studying the structure of a dataset using hypergraph theory and a filtration method. Our method involves building a set of hypergraphs based on a variable distance parameter, enabling us to infer qualitative and quantitative information about the data structure. We apply our method to various sets of points, dynamical systems, signal models, and real electrophysiological data. Our results show that the proposed method can effectively differentiate between varying datasets, demonstrating its potential utility in a range of scientific applications.
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Affiliation(s)
- Dalma Bilbao
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires C1425FQB Argentina
- Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER), Oro Verde, Entre Ríos 3105, Argentina
| | - Hugo Aimar
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires C1425FQB Argentina
- Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER), Oro Verde, Entre Ríos 3105, Argentina
| | - Diego M Mateos
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires C1425FQB Argentina
- Instituto de Matemática Aplicada del Litoral (IMAL-CONICET-UNL), CCT CONICET, Santa Fé 3000, Argentina
- Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos (UADER), Oro Verde, Entre Ríos 3105, Argentina
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13
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Di Gaetano L, Battiston F, Starnini M. Percolation and Topological Properties of Temporal Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 132:037401. [PMID: 38307051 DOI: 10.1103/physrevlett.132.037401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Revised: 10/23/2023] [Accepted: 12/11/2023] [Indexed: 02/04/2024]
Abstract
Many complex systems that exhibit temporal nonpairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variable formalism to analytically characterize a general class of higher-order network models. We apply our framework to a temporal higher-order activity-driven model, providing analytical expressions for the main topological properties of the time-integrated hypergraphs, depending on the integration time and the activity distributions characterizing the model. Furthermore, we provide analytical estimates for the percolation times of general classes of uncorrelated and correlated hypergraphs. Finally, we quantify the extent to which the percolation time of empirical social interactions is underestimated when their higher-order nature is neglected.
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Affiliation(s)
- Leonardo Di Gaetano
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Michele Starnini
- Departament de Fisica, Universitat Politecnica de Catalunya, Campus Nord, 08034 Barcelona, Spain
- CENTAI Institute, 10138 Turin, Italy
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14
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Barton S, Broad Z, Ortiz-Barrientos D, Donovan D, Lefevre J. Hypergraphs and centrality measures identifying key features in gene expression data. Math Biosci 2023; 366:109089. [PMID: 37914024 DOI: 10.1016/j.mbs.2023.109089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Revised: 10/16/2023] [Accepted: 10/18/2023] [Indexed: 11/03/2023]
Abstract
Multidisciplinary approaches can significantly advance our understanding of complex systems. For instance, gene co-expression networks align prior knowledge of biological systems with studies in graph theory, emphasising pairwise gene to gene interactions. In this paper, we extend these ideas, promoting hypergraphs as an investigative tool for studying multi-way interactions in gene expression data. Additional freedoms are achieved by representing individual genes with hyperedges, and simultaneously testing each gene against many features/vertices. Further gene/hyperedge interactions can be captured and explored using the line graph representations, a technique that reduces the complexity of dense hypergraphs. Such an approach provides access to graph centrality measures, which identifies salient features within a data set. For instance dominant or hub-like hyperedges, leading to key knowledge on gene expression. The validity of this approach is established through the study of gene expression data for the plant species Senecio lautus and results will be interpreted within this biological setting.
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Affiliation(s)
- Samuel Barton
- School of Mathematics and Physics, ARC Centre of Excellence, Plant Success in Nature and Agriculture, University of Queensland, Brisbane, 4072, Australia.
| | - Zoe Broad
- School of the Environment, ARC Centre of Excellence, Plant Success in Nature and Agriculture, University of Queensland, Brisbane, 4072, Australia
| | - Daniel Ortiz-Barrientos
- School of the Environment, ARC Centre of Excellence, Plant Success in Nature and Agriculture, University of Queensland, Brisbane, 4072, Australia
| | - Diane Donovan
- School of Mathematics and Physics, ARC Centre of Excellence, Plant Success in Nature and Agriculture, University of Queensland, Brisbane, 4072, Australia
| | - James Lefevre
- School of Mathematics and Physics, ARC Centre of Excellence, Plant Success in Nature and Agriculture, University of Queensland, Brisbane, 4072, Australia
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15
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Meng X, Hu X, Tian Y, Dong G, Lambiotte R, Gao J, Havlin S. Percolation Theories for Quantum Networks. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1564. [PMID: 37998256 PMCID: PMC10670322 DOI: 10.3390/e25111564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Revised: 11/13/2023] [Accepted: 11/17/2023] [Indexed: 11/25/2023]
Abstract
Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.
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Affiliation(s)
- Xiangyi Meng
- Network Science Institute, Northeastern University, Boston, MA 02115, USA;
- Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
| | - Xinqi Hu
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China; (X.H.); (G.D.)
| | - Yu Tian
- Nordita, KTH Royal Institute of Technology and Stockholm University, SE-106 91 Stockholm, Sweden;
| | - Gaogao Dong
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China; (X.H.); (G.D.)
| | - Renaud Lambiotte
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK;
- Turing Institute, London NW1 2DB, UK
| | - Jianxi Gao
- Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;
- Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
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16
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Traversa P, Ferraz de Arruda G, Vazquez A, Moreno Y. Robustness and Complexity of Directed and Weighted Metabolic Hypergraphs. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1537. [PMID: 37998229 PMCID: PMC10670216 DOI: 10.3390/e25111537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Revised: 11/04/2023] [Accepted: 11/09/2023] [Indexed: 11/25/2023]
Abstract
Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here, we propose a directed hypergraph with edge-dependent vertex weight as a novel framework to represent metabolic networks. This hypergraph-based representation captures higher-order interactions among metabolites and reactions, as well as the directionalities of reactions and stoichiometric weights, preserving all essential information. Within this framework, we propose the communicability and the search information as metrics to quantify the robustness and complexity of directed hypergraphs. We explore the implications of network directionality on these measures and illustrate a practical example by applying them to a small-scale E. coli core model. Additionally, we compare the robustness and the complexity of 30 different models of metabolism, connecting structural and biological properties. Our findings show that antibiotic resistance is associated with high structural robustness, while the complexity can distinguish between eukaryotic and prokaryotic organisms.
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Affiliation(s)
- Pietro Traversa
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
- Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain
- CENTAI Institute, 10138 Turin, Italy
| | | | - Alexei Vazquez
- Nodes & Links Ltd., Salisbury House, Station Road, Cambridge CB1 2LA, UK
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
- Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain
- CENTAI Institute, 10138 Turin, Italy
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17
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Krieger S, Kececioglu J. Shortest Hyperpaths in Directed Hypergraphs for Reaction Pathway Inference. J Comput Biol 2023; 30:1198-1225. [PMID: 37906100 DOI: 10.1089/cmb.2023.0242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023] Open
Abstract
Signaling and metabolic pathways, which consist of chains of reactions that produce target molecules from source compounds, are cornerstones of cellular biology. Properly modeling the reaction networks that represent such pathways requires directed hypergraphs, where each molecule or compound maps to a vertex, and each reaction maps to a hyperedge directed from its set of input reactants to its set of output products. Inferring the most likely series of reactions that produces a given set of targets from a given set of sources, where for each reaction its reactants are produced by prior reactions in the series, corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. We give the first exact algorithm for general shortest hyperpaths that can find provably optimal solutions for large, real-world, reaction networks. In particular, we derive a novel graph-theoretic characterization of hyperpaths, which we leverage in a new integer linear programming formulation of shortest hyperpaths that for the first time handles cycles, and develop a cutting-plane algorithm that can solve this integer linear program to optimality in practice. Through comprehensive experiments over all of the thousands of instances from the standard Reactome and NCI-PID reaction databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath-inferring the most likely pathway-with a median running time of under 10 seconds, and a maximum time of less than 30 minutes, even on instances with thousands of reactions. We also explore for the first time how well hyperpaths infer true pathways, and show that shortest hyperpaths accurately recover known pathways, typically with very high precision and recall. Source code implementing our cutting-plane algorithm for shortest hyperpaths is available free for research use in a new tool called Mmunin.
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Affiliation(s)
- Spencer Krieger
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
| | - John Kececioglu
- Department of Computer Science, The University of Arizona, Tucson, Arizona, USA
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18
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Liu Z, Peach RL, Laumann F, Vallejo Mengod S, Barahona M. Kernel-based joint independence tests for multivariate stationary and non-stationary time series. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230857. [PMID: 38034126 PMCID: PMC10685129 DOI: 10.1098/rsos.230857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 11/03/2023] [Indexed: 12/02/2023]
Abstract
Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d-variable Hilbert-Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.
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Affiliation(s)
- Zhaolu Liu
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | - Robert L. Peach
- Department of Brain Sciences, Imperial College London, London W12 0NN, UK
- Department of Neurology, University Hospital Würzburg, Würzburg 97070, Germany
| | - Felix Laumann
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | | | - Mauricio Barahona
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
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19
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Kim J, Lee DS, Goh KI. Contagion dynamics on hypergraphs with nested hyperedges. Phys Rev E 2023; 108:034313. [PMID: 37849153 DOI: 10.1103/physreve.108.034313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Accepted: 09/11/2023] [Indexed: 10/19/2023]
Abstract
In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is the nestedness: Some hyperedges can be entirely contained (that is, nested) within another larger hyperedge, which itself can also be nested further in a hierarchical manner. Yet the effect of such hierarchical structure of hyperedges on the dynamics has remained unexplored. In this context, here we propose a random nested-hypergraph model with a tunable level of nestedness and investigate the effects of nestedness on a higher-order susceptible-infected-susceptible process. By developing an analytic framework called the facet approximation, we obtain the steady-state fraction of infected nodes on the random nested-hypergraph model more accurately than existing methods. Our results show that the hyperedge-nestedness affects the phase diagram significantly. Monte Carlo simulations support the analytical results.
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Affiliation(s)
- Jihye Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - Deok-Sun Lee
- School of Computational Sciences and Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - K-I Goh
- Department of Physics, Korea University, Seoul 02841, Korea
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20
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Ruggeri N, Contisciani M, Battiston F, De Bacco C. Community detection in large hypergraphs. SCIENCE ADVANCES 2023; 9:eadg9159. [PMID: 37436987 PMCID: PMC10337898 DOI: 10.1126/sciadv.adg9159] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 06/12/2023] [Indexed: 07/14/2023]
Abstract
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. Here, we propose a principled framework to model the organization of higher-order data. Our approach recovers community structure with accuracy exceeding that of currently available state-of-the-art algorithms, as tested in synthetic benchmarks with both hard and overlapping ground-truth partitions. Our model is flexible and allows capturing both assortative and disassortative community structures. Moreover, our method scales orders of magnitude faster than competing algorithms, making it suitable for the analysis of very large hypergraphs, containing millions of nodes and interactions among thousands of nodes. Our work constitutes a practical and general tool for hypergraph analysis, broadening our understanding of the organization of real-world higher-order systems.
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Affiliation(s)
- Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
- Department of Computer Science, ETH, 8004 Zürich, Switzerland
| | - Martina Contisciani
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
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21
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Nie Y, Zhong M, Li R, Zhao D, Peng H, Zhong X, Lin T, Wang W. Digital contact tracing on hypergraphs. CHAOS (WOODBURY, N.Y.) 2023; 33:063146. [PMID: 37347642 DOI: 10.1063/5.0149384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/05/2023] [Indexed: 06/24/2023]
Abstract
The higher-order interactions emerging in the network topology affect the effectiveness of digital contact tracing (DCT). In this paper, we propose a mathematical model in which we use the hypergraph to describe the gathering events. In our model, the role of DCT is modeled as individuals carrying the app. When the individuals in the hyperedge all carry the app, epidemics cannot spread through this hyperedge. We develop a generalized percolation theory to investigate the epidemic outbreak size and threshold. We find that DCT can effectively suppress the epidemic spreading, i.e., decreasing the outbreak size and enlarging the threshold. DCT limits the spread of the epidemic to larger cardinality of hyperedges. On real-world networks, the inhibitory effect of DCT on the spread of epidemics is evident when the spread of epidemics is small.
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Affiliation(s)
- Yanyi Nie
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Ming Zhong
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Runchao Li
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Dandan Zhao
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Hao Peng
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
| | - Xiaoni Zhong
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
| | - Tao Lin
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Wei Wang
- School of Public Health, Chongqing Medical University, Chongqing 400016, China
- Research Center of Public Health Security, Chongqing Medical University, Chongqing 400016, China
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22
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Chen C, Liao C, Liu YY. Teasing out missing reactions in genome-scale metabolic networks through hypergraph learning. Nat Commun 2023; 14:2375. [PMID: 37185345 PMCID: PMC10130184 DOI: 10.1038/s41467-023-38110-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 04/14/2023] [Indexed: 05/17/2023] Open
Abstract
GEnome-scale Metabolic models (GEMs) are powerful tools to predict cellular metabolism and physiological states in living organisms. However, due to our imperfect knowledge of metabolic processes, even highly curated GEMs have knowledge gaps (e.g., missing reactions). Existing gap-filling methods typically require phenotypic data as input to tease out missing reactions. We still lack a computational method for rapid and accurate gap-filling of metabolic networks before experimental data is available. Here we present a deep learning-based method - CHEbyshev Spectral HyperlInk pREdictor (CHESHIRE) - to predict missing reactions in GEMs purely from metabolic network topology. We demonstrate that CHESHIRE outperforms other topology-based methods in predicting artificially removed reactions over 926 high- and intermediate-quality GEMs. Furthermore, CHESHIRE is able to improve the phenotypic predictions of 49 draft GEMs for fermentation products and amino acids secretions. Both types of validation suggest that CHESHIRE is a powerful tool for GEM curation to reveal unknown links between reactions and observed metabolic phenotypes.
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Affiliation(s)
- Can Chen
- Channing Division of Network Medicine, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, 02115, USA
| | - Chen Liao
- Program for Computational and Systems Biology, Memorial Sloan Kettering Cancer Center, New York, NY, 10065, USA
| | - Yang-Yu Liu
- Channing Division of Network Medicine, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, 02115, USA.
- Center for Artificial Intelligence and Modeling, The Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Champaign, IL, 61801, USA.
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23
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Mishra A, Jalan S. Eigenvector localization in hypergraphs: Pairwise versus higher-order links. Phys Rev E 2023; 107:034311. [PMID: 37072980 DOI: 10.1103/physreve.107.034311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 03/02/2023] [Indexed: 04/20/2023]
Abstract
Localization behaviors of Laplacian eigenvectors of complex networks furnish an explanation to various dynamical phenomena of the corresponding complex systems. We numerically examine roles of higher-order and pairwise links in driving eigenvector localization of hypergraphs Laplacians. We find that pairwise interactions can engender localization of eigenvectors corresponding to small eigenvalues for some cases, whereas higher-order interactions, even being much much less than the pairwise links, keep steering localization of the eigenvectors corresponding to larger eigenvalues for all the cases considered here. These results will be advantageous to comprehend dynamical phenomena, such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions in better manner.
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Affiliation(s)
- Ankit Mishra
- Department of Physics, Complex systems Lab, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
| | - Sarika Jalan
- Department of Physics, Complex systems Lab, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore-453552, India
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24
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Hypergraph geometry reflects higher-order dynamics in protein interaction networks. Sci Rep 2022; 12:20879. [PMID: 36463292 PMCID: PMC9719542 DOI: 10.1038/s41598-022-24584-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 11/17/2022] [Indexed: 12/05/2022] Open
Abstract
Protein interactions form a complex dynamic molecular system that shapes cell phenotype and function; in this regard, network analysis is a powerful tool for studying the dynamics of cellular processes. Current models of protein interaction networks are limited in that the standard graph model can only represent pairwise relationships. Higher-order interactions are well-characterized in biology, including protein complex formation and feedback or feedforward loops. These higher-order relationships are better represented by a hypergraph as a generalized network model. Here, we present an approach to analyzing dynamic gene expression data using a hypergraph model and quantify network heterogeneity via Forman-Ricci curvature. We observe, on a global level, increased network curvature in pluripotent stem cells and cancer cells. Further, we use local curvature to conduct pathway analysis in a melanoma dataset, finding increased curvature in several oncogenic pathways and decreased curvature in tumor suppressor pathways. We compare this approach to a graph-based model and a differential gene expression approach.
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25
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Saito S, Herbster M. Generalizing p-Laplacian: spectral hypergraph theory and a partitioning algorithm. Mach Learn 2022. [DOI: 10.1007/s10994-022-06264-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
AbstractFor hypergraph clustering, various methods have been proposed to define hypergraph p-Laplacians in the literature. This work proposes a general framework for an abstract class of hypergraph p-Laplacians from a differential-geometric view. This class includes previously proposed hypergraph p-Laplacians and also includes previously unstudied novel generalizations. For this abstract class, we extend current spectral theory by providing an extension of nodal domain theory for the eigenvectors of our hypergraph p-Laplacian. We use this nodal domain theory to provide bounds on the eigenvalues via a higher-order Cheeger inequality. Following our extension of spectral theory, we propose a novel hypergraph partitioning algorithm for our generalized p-Laplacian. Our empirical study shows that our algorithm outperforms spectral methods based on existing p-Laplacians.
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26
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Inference of hyperedges and overlapping communities in hypergraphs. Nat Commun 2022; 13:7229. [PMID: 36433942 PMCID: PMC9700742 DOI: 10.1038/s41467-022-34714-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 11/02/2022] [Indexed: 11/27/2022] Open
Abstract
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.
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27
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Müller S, Flamm C, Stadler PF. What makes a reaction network "chemical"? J Cheminform 2022; 14:63. [PMID: 36123755 PMCID: PMC9484159 DOI: 10.1186/s13321-022-00621-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 06/04/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Reaction networks (RNs) comprise a set X of species and a set [Formula: see text] of reactions [Formula: see text], each converting a multiset of educts [Formula: see text] into a multiset [Formula: see text] of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix [Formula: see text] have been discussed extensively in the chemical literature. Here, we provide sufficient conditions for [Formula: see text] that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively. RESULTS Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. For finite RNs, both conditions can be expressed equivalently as properties of the stoichiometric matrix [Formula: see text]. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and-in a stricter sense-futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. It is also sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless [Formula: see text] implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved. In particular, for every conservative RN, there exists a Lewis realization, in which any two compounds are realized by pairwisely distinct multigraphs. Finally, we show that, in general, there are infinitely many realizations for a given conservative RN. CONCLUSIONS "Chemical" RNs are directed hypergraphs with a stoichiometric matrix [Formula: see text] whose left kernel contains a strictly positive vector and whose right kernel does not contain a futile cycle involving an irreversible reaction. This simple characterization also provides a concise specification of random models for chemical RNs that additionally constrain [Formula: see text] by rank, sparsity, or distribution of the non-zero entries. Furthermore, it suggests several interesting avenues for future research, in particular, concerning alternative representations of reaction networks and infinite chemical universes.
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Affiliation(s)
- Stefan Müller
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
| | - Christoph Flamm
- Department of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Peter F. Stadler
- Department of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16–18, 04107 Leipzig, Germany
- German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig & Competence Center for Scalable Data Services and Solutions Dresden-Leipzig & Leipzig Research Center for Civilization Diseases University Leipzig, 04107 Leipzig, Germany
- Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
- Faculdad de Ciencias, Universidad Nacional de Colombia, Sede Bogotá, Ciudad Universitaria, Bogotá, 111321 Colombia
- Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM87501 USA
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28
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Nijholt E, DeVille L. Dynamical systems defined on simplicial complexes: Symmetries, conjugacies, and invariant subspaces. CHAOS (WOODBURY, N.Y.) 2022; 32:093131. [PMID: 36182350 DOI: 10.1063/5.0093842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon, especially with regard to invariant subspaces in the dynamics.
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Affiliation(s)
- Eddie Nijholt
- ICMC São Carlos, Universidade de São Paulo, Av. Trab. São Carlense 400, São Carlos SP 13566-590, Brasil
| | - Lee DeVille
- Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801, USA
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A seizure detection method based on hypergraph features and machine learning. Biomed Signal Process Control 2022. [DOI: 10.1016/j.bspc.2022.103769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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30
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Evolutionary timeline of a modeled cell. J Theor Biol 2022; 551-552:111233. [DOI: 10.1016/j.jtbi.2022.111233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Revised: 06/23/2022] [Accepted: 07/21/2022] [Indexed: 11/22/2022]
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31
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Klimm F. Topological data analysis of truncated contagion maps. CHAOS (WOODBURY, N.Y.) 2022; 32:073108. [PMID: 35907735 DOI: 10.1063/5.0090114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space. Specifically, one can use the activation times of threshold contagions to construct contagion maps as a manifold-learning approach. One drawback of contagion maps is their high computational cost. Here, we demonstrate that a truncation of the threshold contagions may considerably speed up the construction of contagion maps. Finally, we show that contagion maps may be used to find an insightful low-dimensional embedding for single-cell RNA-sequencing data in the form of cell-similarity networks and so reveal biological manifolds. Overall, our work makes the use of contagion maps as manifold-learning approaches on empirical network data more viable.
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Affiliation(s)
- Florian Klimm
- Department of Computational Molecular Biology, Max Planck Institute for Molecular Genetics, Ihnestraße 63-73, D-14195 Berlin, Germany
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32
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Diaz LPM, Stumpf MPH. HyperGraphs.jl - representing high-order relationships in Julia. Bioinformatics 2022; 38:3660-3661. [PMID: 35674360 PMCID: PMC9326852 DOI: 10.1093/bioinformatics/btac347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 05/10/2022] [Accepted: 06/01/2022] [Indexed: 11/14/2022] Open
Abstract
Summary HyperGraphs.jl is a Julia package that implements hypergraphs. These are a generalization of graphs that allow us to represent n-ary relationships and not just binary, pairwise relationships. High-order interactions are commonplace in biological systems and are of critical importance to their dynamics; hypergraphs thus offer a natural way to accurately describe and model these systems. Availability and implementation HyperGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/lpmdiaz/HyperGraphs.jl. Supplementary information Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Léo P M Diaz
- Melbourne Integrative Genomics and School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia
| | - Michael P H Stumpf
- Melbourne Integrative Genomics and School of Mathematics and Statistics, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia.,School of BioSciences, University of Melbourne, Melbourne, Parkville, 3010, VIC, Australia
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33
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Monroy Kuhn JM, Miok V, Lutter D. Correlation-guided Network Integration (CoNI), an R package for integrating numerical omics data that allows multiform graph representations to study molecular interaction networks. BIOINFORMATICS ADVANCES 2022; 2:vbac042. [PMID: 36699352 PMCID: PMC9710706 DOI: 10.1093/bioadv/vbac042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Revised: 05/09/2022] [Accepted: 06/01/2022] [Indexed: 02/01/2023]
Abstract
Summary Today's immense growth in complex biological data demands effective and flexible tools for integration, analysis and extraction of valuable insights. Here, we present CoNI, a practical R package for the unsupervised integration of numerical omics datasets. Our tool is based on partial correlations to identify putative confounding variables for a set of paired dependent variables. CoNI combines two omics datasets in an integrated, complex hypergraph-like network, represented as a weighted undirected graph, a bipartite graph, or a hypergraph structure. These network representations form a basis for multiple further analyses, such as identifying priority candidates of biological importance or comparing network structures dependent on different conditions. Availability and implementation The R package CoNI is available on the Comprehensive R Archive Network (https://cran.r-project.org/web/packages/CoNI/) and GitLab (https://gitlab.com/computational-discovery-research/coni). It is distributed under the GNU General Public License (version 3). Supplementary information Supplementary data are available at Bioinformatics Advances online.
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Affiliation(s)
| | - Viktorian Miok
- Computational Discovery Unit, Institute for Diabetes & Obesity, Helmholtz Zentrum München, Neuherberg, Germany
- German Center for Diabetes Research (DZD), Neuherberg, Germany
- Astrocyte-Neuron Networks, Institute for Diabetes & Obesity, Helmholtz Zentrum München, Neuherberg, Germany
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34
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Krieger S, Kececioglu J. Heuristic shortest hyperpaths in cell signaling hypergraphs. Algorithms Mol Biol 2022; 17:12. [PMID: 35619179 PMCID: PMC9134692 DOI: 10.1186/s13015-022-00217-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 02/01/2022] [Indexed: 01/04/2023] Open
Abstract
BACKGROUND Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs, where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The current state-of-the-art for shortest hyperpaths in cell signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. RESULTS We present, for the first time, a heuristic for general shortest hyperpaths that properly handles cycles, and is guaranteed to be efficient. We show the heuristic finds provably optimal hyperpaths for the class of singleton-tail hypergraphs, and also give a practical algorithm for tractably generating all source-sink hyperpaths. The accuracy of the heuristic is demonstrated through comprehensive experiments on all source-sink instances from the standard NCI-PID and Reactome pathway databases, which show it finds a hyperpath that matches the state-of-the-art mixed-integer linear program on over 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all source-sink hyperpaths shows the solution found by the heuristic was in fact optimal. CONCLUSIONS The new shortest hyperpath heuristic is both fast and accurate. This makes finding source-sink hyperpaths, which in general may contain cycles, now practical for real cell signaling networks. AVAILABILITY Source code for the hyperpath heuristic in a new tool we call Hhugin (as well as for hyperpath enumeration, and all dataset instances) is available free for non-commercial use at http://hhugin.cs.arizona.edu.
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Affiliation(s)
- Spencer Krieger
- grid.134563.60000 0001 2168 186XDepartment of Computer Science, The University of Arizona, Tucson, Arizona 85721 USA
| | - John Kececioglu
- grid.134563.60000 0001 2168 186XDepartment of Computer Science, The University of Arizona, Tucson, Arizona 85721 USA
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35
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Gao Y, Zhang Z, Lin H, Zhao X, Du S, Zou C. Hypergraph Learning: Methods and Practices. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2022; 44:2548-2566. [PMID: 33211654 DOI: 10.1109/tpami.2020.3039374] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Hypergraph learning is a technique for conducting learning on a hypergraph structure. In recent years, hypergraph learning has attracted increasing attention due to its flexibility and capability in modeling complex data correlation. In this paper, we first systematically review existing literature regarding hypergraph generation, including distance-based, representation-based, attribute-based, and network-based approaches. Then, we introduce the existing learning methods on a hypergraph, including transductive hypergraph learning, inductive hypergraph learning, hypergraph structure updating, and multi-modal hypergraph learning. After that, we present a tensor-based dynamic hypergraph representation and learning framework that can effectively describe high-order correlation in a hypergraph. To study the effectiveness and efficiency of hypergraph generation and learning methods, we conduct comprehensive evaluations on several typical applications, including object and action recognition, Microblog sentiment prediction, and clustering. In addition, we contribute a hypergraph learning development toolkit called THU-HyperG.
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36
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A graph model of combination therapies. Drug Discov Today 2022; 27:1210-1217. [PMID: 35143962 DOI: 10.1016/j.drudis.2022.02.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Revised: 12/31/2021] [Accepted: 02/02/2022] [Indexed: 11/24/2022]
Abstract
The simultaneous use of multiple medications causes drug-drug interactions (DDI) that impact therapeutic efficacy. Here, we argue that graph theory, in conjunction with game theory and ecosystem theory, can address this issue. We treat the coexistence of multiple drugs as a system in which DDI is modeled by game theory. We develop an ordinary differential equation model to characterize how the concentration of a drug changes as a result of its independent capacity and the dependent influence of other drugs through the metabolic response of the host. We coalesce all drugs into personalized and context-specific networks, which can reveal key DDI determinants of therapeutical efficacy. Our model can quantify drug synergy and antagonism and test the translational success of combination therapies to the clinic.
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37
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Knots and Knot-Hyperpaths in Hypergraphs. MATHEMATICS 2022. [DOI: 10.3390/math10030424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
This paper deals with some theoretical aspects of hypergraphs related to hyperpaths and hypertrees. In ordinary graph theory, the intersecting or adjacent edges contain exactly one vertex; however, in the case of hypergraph theory, the adjacent or intersecting hyperedges may contain more than one vertex. This fact leads to the intuitive notion of knots, i.e., a collection of explicit vertices. The key idea of this manuscript lies in the introduction of the concept of the knot, which is a subset of the intersection of some intersecting hyperedges. We define knot-hyperpaths and equivalent knot-hyperpaths and study their relationships with the algebraic space continuity and the pseudo-open character of maps. Moreover, we establish a sufficient condition under which a hypergraph is a hypertree, without using the concept of the host graph.
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38
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Arora V, Sanguinetti G. Challenges for machine learning in RNA-protein interaction prediction. Stat Appl Genet Mol Biol 2022; 21:sagmb-2021-0087. [PMID: 35073469 DOI: 10.1515/sagmb-2021-0087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Accepted: 01/02/2022] [Indexed: 11/15/2022]
Abstract
RNA-protein interactions have long being recognised as crucial regulators of gene expression. Recently, the development of scalable experimental techniques to measure these interactions has revolutionised the field, leading to the production of large-scale datasets which offer both opportunities and challenges for machine learning techniques. In this brief note, we will discuss some of the major stumbling blocks towards the use of machine learning in computational RNA biology, focusing specifically on the problem of predicting RNA-protein interactions from next-generation sequencing data.
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Affiliation(s)
- Viplove Arora
- Data Science, Department of Physics, International School for Advanced Studies (SISSA), Trieste 34136, Italy
| | - Guido Sanguinetti
- Data Science, Department of Physics, International School for Advanced Studies (SISSA), Trieste 34136, Italy
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39
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Yuan Y, Qu A. High-Order Joint Embedding for Multi-Level Link Prediction. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2021.2005608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Yubai Yuan
- Department of Statistics, University of California, Irvine, Irvine, CA
| | - Annie Qu
- Department of Statistics, University of California, Irvine, Irvine, CA
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40
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Krieger S, Kececioglu J. OUP accepted manuscript. Bioinformatics 2022; 38:i369-i377. [PMID: 35758789 PMCID: PMC9235471 DOI: 10.1093/bioinformatics/btac231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Motivation A factory in a metabolic network specifies how to produce target molecules from source compounds through biochemical reactions, properly accounting for reaction stoichiometry to conserve or not deplete intermediate metabolites. While finding factories is a fundamental problem in systems biology, available methods do not consider the number of reactions used, nor address negative regulation. Methods We introduce the new problem of finding optimal factories that use the fewest reactions, for the first time incorporating both first- and second-order negative regulation. We model this problem with directed hypergraphs, prove it is NP-complete, solve it via mixed-integer linear programming, and accommodate second-order negative regulation by an iterative approach that generates next-best factories. Results This optimization-based approach is remarkably fast in practice, typically finding optimal factories in a few seconds, even for metabolic networks involving tens of thousands of reactions and metabolites, as demonstrated through comprehensive experiments across all instances from standard reaction databases. Availability and implementation Source code for an implementation of our new method for optimal factories with negative regulation in a new tool called Odinn, together with all datasets, is available free for non-commercial use at http://odinn.cs.arizona.edu.
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Affiliation(s)
| | - John Kececioglu
- Department of Computer Science, The University of Arizona, Tucson, AZ 85721, USA
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41
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The Genomic Physics of COVID-19 Pathogenesis and Spread. Cells 2021; 11:cells11010080. [PMID: 35011641 PMCID: PMC8750765 DOI: 10.3390/cells11010080] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/19/2021] [Accepted: 12/23/2021] [Indexed: 12/11/2022] Open
Abstract
Coronavirus disease (COVID-19) spreads mainly through close contact of infected persons, but the molecular mechanisms underlying its pathogenesis and transmission remain unknown. Here, we propose a statistical physics model to coalesce all molecular entities into a cohesive network in which the roadmap of how each entity mediates the disease can be characterized. We argue that the process of how a transmitter transforms the virus into a recipient constitutes a triad unit that propagates COVID-19 along reticulate paths. Intrinsically, person-to-person transmissibility may be mediated by how genes interact transversely across transmitter, recipient, and viral genomes. We integrate quantitative genetic theory into hypergraph theory to code the main effects of the three genomes as nodes, pairwise cross-genome epistasis as edges, and high-order cross-genome epistasis as hyperedges in a series of mobile hypergraphs. Charting a genome-wide atlas of horizontally epistatic hypergraphs can facilitate the systematic characterization of the community genetic mechanisms underlying COVID-19 spread. This atlas can typically help design effective containment and mitigation strategies and screen and triage those more susceptible persons and those asymptomatic carriers who are incubation virus transmitters.
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42
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Abstract
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that includes all possible measures of path length for weighted graphs. The result, without breaking the graph into smaller components, is a distance backbone subgraph sufficient to compute all shortest paths. This is important for understanding the dynamics of spread and communication phenomena in real-world networks. The general methodology we formally derive yields a principled graph reduction technique and provides a finer characterization of the triangular geometry of all edges-those that contribute to shortest paths and those that do not but are involved in other network phenomena. We demonstrate that the distance backbone is very small in large networks across domains ranging from air traffic to the human brain connectome, revealing that network robustness to attacks and failures seems to stem from surprisingly vast amounts of redundancy.
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Affiliation(s)
- Tiago Simas
- Departamento de Engenharia Informtáica e Sistemas de Informação, Universidade Lusófona, Lisboa, Portugal
| | - Rion Brattig Correia
- Center for Social and Biomedical Complexity, Luddy School of Informatics, Computing & Engineering, Indiana University, Bloomington IN, USA, Instituto Gulbenkian de Ciência, Oeiras, Portugal and CAPES Foundation, Ministry of Education of Brazil, Brasília, DF, Brazil
| | - Luis M. Rocha
- Center for Social and Biomedical Complexity, Luddy School of Informatics, Computing & Engineering, Indiana University, Bloomington IN, USA, Instituto Gulbenkian de Ciência, Oeiras, Portugal and Department of Systems Science and Industrial Engineering, Binghamton University, Binghamton, NY 13902, USA
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43
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Voutsa V, Battaglia D, Bracken LJ, Brovelli A, Costescu J, Díaz Muñoz M, Fath BD, Funk A, Guirro M, Hein T, Kerschner C, Kimmich C, Lima V, Messé A, Parsons AJ, Perez J, Pöppl R, Prell C, Recinos S, Shi Y, Tiwari S, Turnbull L, Wainwright J, Waxenecker H, Hütt MT. Two classes of functional connectivity in dynamical processes in networks. J R Soc Interface 2021; 18:20210486. [PMID: 34665977 PMCID: PMC8526174 DOI: 10.1098/rsif.2021.0486] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Accepted: 09/13/2021] [Indexed: 12/12/2022] Open
Abstract
The relationship between network structure and dynamics is one of the most extensively investigated problems in the theory of complex systems of recent years. Understanding this relationship is of relevance to a range of disciplines-from neuroscience to geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity, SC) with a (network) representation of the dynamics (functional connectivity, FC). Here, we show that one can distinguish two classes of functional connectivity-one based on simultaneous activity (co-activity) of nodes, the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes-excitations, regular and chaotic oscillators-and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in geomorphology, ecology, systems biology, neuroscience and socio-ecological systems. Seeing the organisation of dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks.
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Affiliation(s)
- Venetia Voutsa
- Department of Life Sciences and Chemistry, Jacobs University Bremen, 28759 Bremen, Germany
| | - Demian Battaglia
- Aix-Marseille Université, Inserm, Institut de Neurosciences des Systèmes (UMR 1106), Marseille, France
- University of Strasbourg Institute for Advanced Studies (USIAS), Strasbourg 67083, France
| | | | - Andrea Brovelli
- Aix-Marseille Université, CNRS, Institut de Neurosciences de la Timone (UMR 7289), Marseille, France
| | - Julia Costescu
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - Mario Díaz Muñoz
- Department of Sustainability, Governance and Methods, Modul University Vienna, 1190 Vienna, Austria
| | - Brian D. Fath
- Department of Biological Sciences, Towson University, Towson, Maryland 21252, USA
- Advancing Systems Analysis Program, International Institute for Applied Systems Analysis, Laxenburg 2361, Austria
- Department of Environmental Studies, Masaryk University, 60200 Brno, Czech Republic
| | - Andrea Funk
- Institute of Hydrobiology and Aquatic Ecosystem Management (IHG), University of Natural Resources and Life Sciences Vienna (BOKU), 1180 Vienna, Austria
- WasserCluster Lunz - Biologische Station GmbH, Dr. Carl Kupelwieser Promenade 5, 3293 Lunz am See, Austria
| | - Mel Guirro
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - Thomas Hein
- Institute of Hydrobiology and Aquatic Ecosystem Management (IHG), University of Natural Resources and Life Sciences Vienna (BOKU), 1180 Vienna, Austria
- WasserCluster Lunz - Biologische Station GmbH, Dr. Carl Kupelwieser Promenade 5, 3293 Lunz am See, Austria
| | - Christian Kerschner
- Department of Sustainability, Governance and Methods, Modul University Vienna, 1190 Vienna, Austria
- Department of Environmental Studies, Masaryk University, 60200 Brno, Czech Republic
| | - Christian Kimmich
- Department of Environmental Studies, Masaryk University, 60200 Brno, Czech Republic
- Regional Science and Environmental Research, Institute for Advanced Studies, 1080 Vienna, Austria
| | - Vinicius Lima
- Aix-Marseille Université, Inserm, Institut de Neurosciences des Systèmes (UMR 1106), Marseille, France
- Aix-Marseille Université, CNRS, Institut de Neurosciences de la Timone (UMR 7289), Marseille, France
| | - Arnaud Messé
- Department of Computational Neuroscience, University Medical Center Eppendorf, Hamburg University, Germany
| | | | - John Perez
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - Ronald Pöppl
- Department of Geography and Regional Research, University of Vienna, Universitätsstr. 7, 1010 Vienna, Austria
| | - Christina Prell
- Department of Cultural Geography, University of Groningen, 9747 AD, Groningen, The Netherlands
| | - Sonia Recinos
- Institute of Hydrobiology and Aquatic Ecosystem Management (IHG), University of Natural Resources and Life Sciences Vienna (BOKU), 1180 Vienna, Austria
| | - Yanhua Shi
- Department of Environmental Studies, Masaryk University, 60200 Brno, Czech Republic
| | - Shubham Tiwari
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - Laura Turnbull
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - John Wainwright
- Department of Geography, Durham University, Durham DH1 3LE, UK
| | - Harald Waxenecker
- Department of Environmental Studies, Masaryk University, 60200 Brno, Czech Republic
| | - Marc-Thorsten Hütt
- Department of Life Sciences and Chemistry, Jacobs University Bremen, 28759 Bremen, Germany
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Mulas R, Sánchez-García RJ, MacArthur BD. Geometry and symmetry in biochemical reaction systems. Theory Biosci 2021; 140:265-277. [PMID: 34268705 PMCID: PMC8568762 DOI: 10.1007/s12064-021-00353-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 07/06/2021] [Indexed: 12/02/2022]
Abstract
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products. Here, we make use of a recently developed hypergraph theory of chemical reactions that naturally allows for higher-order interactions to explore the geometry and quantify functional redundancy in biochemical reactions systems. Our results constitute a general theory of automorphisms for oriented hypergraphs and describe the effect of automorphism group structure on hypergraph Laplacian spectra.
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Affiliation(s)
- Raffaella Mulas
- Mathematical Sciences, University of Southampton, Southampton, UK.
- Institute of Life Sciences, University of Southampton, Southampton, UK.
- The Alan Turing Institute, London, UK.
| | - Rubén J Sánchez-García
- Mathematical Sciences, University of Southampton, Southampton, UK
- Institute of Life Sciences, University of Southampton, Southampton, UK
- The Alan Turing Institute, London, UK
| | - Ben D MacArthur
- Mathematical Sciences, University of Southampton, Southampton, UK
- Institute of Life Sciences, University of Southampton, Southampton, UK
- The Alan Turing Institute, London, UK
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45
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Mulas R, Casey MJ. Estimating cellular redundancy in networks of genetic expression. Math Biosci 2021; 341:108713. [PMID: 34560090 DOI: 10.1016/j.mbs.2021.108713] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Revised: 07/22/2021] [Accepted: 09/06/2021] [Indexed: 11/26/2022]
Abstract
Networks of genetic expression can be modeled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to encode structural information of the data. We show how these spectra can be used, in particular, in order to give an estimation of cellular redundancy, a novel measure of gene expression heterogeneity, of the network. We analyze some simulated and real data sets of gene expression for illustrating the new method proposed here.
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Affiliation(s)
- Raffaella Mulas
- The Alan Turing Institute, London, UK; Mathematical Sciences, University of Southampton, UK; Institute of Life Sciences, University of Southampton, UK.
| | - Michael J Casey
- Mathematical Sciences, University of Southampton, UK; Institute of Life Sciences, University of Southampton, UK
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46
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Yen PTW, Xia K, Cheong SA. Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1211. [PMID: 34573837 PMCID: PMC8467365 DOI: 10.3390/e23091211] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Revised: 09/05/2021] [Accepted: 09/06/2021] [Indexed: 12/24/2022]
Abstract
In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.
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Affiliation(s)
- Peter Tsung-Wen Yen
- Center for Crystal Researches, National Sun Yet-Sen University, No. 70, Lien-hai Rd., Kaohsiung 80424, Taiwan;
| | - Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore;
| | - Siew Ann Cheong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
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Lugo-Martinez J, Zeiberg D, Gaudelet T, Malod-Dognin N, Przulj N, Radivojac P. Classification in biological networks with hypergraphlet kernels. Bioinformatics 2021; 37:1000-1007. [PMID: 32886115 DOI: 10.1093/bioinformatics/btaa768] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Revised: 06/13/2020] [Accepted: 08/26/2020] [Indexed: 11/15/2022] Open
Abstract
MOTIVATION Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins and drugs) and edges represent relational ties between these objects (binds-to, interacts-with and regulates). This approach has been highly successful owing to the theory, methodology and software that support analysis and learning on graphs. Graphs, however, suffer from information loss when modeling physical systems due to their inability to accurately represent multiobject relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. RESULTS We present a hypergraph-based approach for modeling biological systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs. We then introduce a novel kernel method on vertex- and edge-labeled (colored) hypergraphs for analysis and learning. The method is based on exact and inexact (via hypergraph edit distances) enumeration of hypergraphlets; i.e. small hypergraphs rooted at a vertex of interest. We empirically evaluate this method on fifteen biological networks and show its potential use in a positive-unlabeled setting to estimate the interactome sizes in various species. AVAILABILITY AND IMPLEMENTATION https://github.com/jlugomar/hypergraphlet-kernels. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Jose Lugo-Martinez
- Computational Biology Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Daniel Zeiberg
- Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115, USA
| | - Thomas Gaudelet
- Department of Computer Science, University College London, London WC1E 6BT, UK
| | | | - Natasa Przulj
- Barcelona Supercomputing Center (BSC), Barcelona 08034, Spain.,ICREA, Pg. Lluis Companys 23, Barcelona 08010, Spain
| | - Predrag Radivojac
- Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115, USA
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Jernigan R, Jia K, Ren Z, Zhou W. Large-scale multiple inference of collective dependence with applications to protein function. Ann Appl Stat 2021; 15:902-924. [DOI: 10.1214/20-aoas1431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Robert Jernigan
- Department of Biochemistry, Biophysics, and Molecular Biology, Program of Bioinformatics and Computational Biology, Iowa State University
| | - Kejue Jia
- Department of Biochemistry, Biophysics, and Molecular Biology, Program of Bioinformatics and Computational Biology, Iowa State University
| | - Zhao Ren
- Department of Statistics, University of Pittsburgh
| | - Wen Zhou
- Department of Statistics, Colorado State University
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49
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Lee J, Lee Y, Oh SM, Kahng B. Betweenness centrality of teams in social networks. CHAOS (WOODBURY, N.Y.) 2021; 31:061108. [PMID: 34241328 DOI: 10.1063/5.0056683] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 06/01/2021] [Indexed: 06/13/2023]
Abstract
Betweenness centrality (BC) was proposed as an indicator of the extent of an individual's influence in a social network. It is measured by counting how many times a vertex (i.e., an individual) appears on all the shortest paths between pairs of vertices. A question naturally arises as to how the influence of a team or group in a social network can be measured. Here, we propose a method of measuring this influence on a bipartite graph comprising vertices (individuals) and hyperedges (teams). When the hyperedge size varies, the number of shortest paths between two vertices in a hypergraph can be larger than that in a binary graph. Thus, the power-law behavior of the team BC distribution breaks down in scale-free hypergraphs. However, when the weight of each hyperedge, for example, the performance per team member, is counted, the team BC distribution is found to exhibit power-law behavior. We find that a team with a widely connected member is highly influential.
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Affiliation(s)
- Jongshin Lee
- CCSS, CTP, Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
| | - Yongsun Lee
- CCSS, CTP, Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
| | - Soo Min Oh
- CCSS, CTP, Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
| | - B Kahng
- CCSS, CTP, Department of Physics and Astronomy, Seoul National University, Seoul 08826, South Korea
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50
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Feng S, Heath E, Jefferson B, Joslyn C, Kvinge H, Mitchell HD, Praggastis B, Eisfeld AJ, Sims AC, Thackray LB, Fan S, Walters KB, Halfmann PJ, Westhoff-Smith D, Tan Q, Menachery VD, Sheahan TP, Cockrell AS, Kocher JF, Stratton KG, Heller NC, Bramer LM, Diamond MS, Baric RS, Waters KM, Kawaoka Y, McDermott JE, Purvine E. Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC Bioinformatics 2021; 22:287. [PMID: 34051754 PMCID: PMC8164482 DOI: 10.1186/s12859-021-04197-2] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Accepted: 05/13/2021] [Indexed: 12/25/2022] Open
Abstract
Background Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets. Results We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Conclusions Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-021-04197-2.
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Affiliation(s)
- Song Feng
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Emily Heath
- Department of Mathematics, University of Illinois, Urbana-Champaign, IL, USA
| | - Brett Jefferson
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA
| | - Cliff Joslyn
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA.,Systems Science Program, Portland State University, Portland, OR, USA
| | - Henry Kvinge
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA
| | - Hugh D Mitchell
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Brenda Praggastis
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA
| | - Amie J Eisfeld
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA
| | - Amy C Sims
- Signature Science and Technology Division, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Larissa B Thackray
- Department of Medicine, Washington University School of Medicine, 63110, Saint Louis, MO, USA
| | - Shufang Fan
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA
| | - Kevin B Walters
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA
| | - Peter J Halfmann
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA
| | - Danielle Westhoff-Smith
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA
| | - Qing Tan
- Department of Medicine, Washington University School of Medicine, 63110, Saint Louis, MO, USA
| | - Vineet D Menachery
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA.,Department of Microbiology and Immunology, University of Texas Medical Branch, Galveston, TX, USA
| | - Timothy P Sheahan
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | | | - Jacob F Kocher
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Kelly G Stratton
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Natalie C Heller
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA
| | - Lisa M Bramer
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Michael S Diamond
- Department of Medicine, Washington University School of Medicine, 63110, Saint Louis, MO, USA.,Department of Pathology and Immunology, Washington University School of Medicine, St. Louis, MO, USA.,Department of Molecular Microbiology, Washington University School of Medicine, St. Louis, MO, USA
| | - Ralph S Baric
- Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
| | - Katrina M Waters
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA.,Department of Comparative Medicine, University of Washington, Seattle, WA, USA
| | - Yoshihiro Kawaoka
- Department of Pathobiological Sciences, School of Veterinary Medicine, Influenza Research Institute, University of Wisconsin-Madison, 575 Science Drive, 53711, Madison, WI, USA.,Division of Virology, Department of Microbiology and Immunology, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan.,ERATO Infection-Induced Host Responses Project, Saitama, 332-0012, Japan.,Department of Special Pathogens, International Research Center for Infectious Diseases, Institute of Medical Science, University of Tokyo, Tokyo, 108-8639, Japan
| | - Jason E McDermott
- Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA.,Department of Molecular Microbiology and Immunology, Oregon Health and Science University, Portland, OR, USA
| | - Emilie Purvine
- Computing and Analytics Division, Pacific Northwest National Laboratory, Seattle, WA, USA.
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