Article
Physics, Fluids & Plasmas
Leonie Neuhaeuser, Renaud Lambiotte, Michael T. Schaub
Summary: The study indicates that in network systems with time-dependent, multiway interactions, the convergence speed of consensus dynamics is slower than systems with only pairwise interactions, and slower than consensus dynamics on corresponding static networks. Additionally, the final consensus value in a temporal system may differ significantly from the consensus value on an aggregated, static hypergraph, with early movers having a greater influence.
Article
Physics, Fluids & Plasmas
Sarika Jalan, Ayushi Suman
Summary: This study discovers that higher-order interactions on globally coupled systems can lead to abrupt first-order transitions to synchronization. Moreover, on multilayer systems, simplicial complexes can result in multiple abrupt first-order transitions to (de)synchronization. By employing the Ott-Antonsen approach, the researchers develop an analytical framework that reduces the high-dimensional evolution equation to a low-dimensional manifold, providing a comprehensive explanation for the origin and stability of all possible dynamic states.
Article
Multidisciplinary Sciences
L. V. Gambuzza, F. Di Patti, L. Gallo, S. Lepri, M. Romance, R. Criado, M. Frasca, V. Latora, S. Boccaletti
Summary: Various systems have been successfully modeled as networks of coupled dynamical systems, with recent studies showing the presence of higher-order many-body interactions in social groups, ecosystems, and the human brain. The proposed analytical approach by Gambuzza et al. provides conditions for stable synchronization in many-body interaction networks.
NATURE COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Leo Torres, Ann S. Blevins, Danielle Bassett, Tina Eliassi-Rad
Summary: The paper proposes a basic, domain-agnostic language to advance towards a more cohesive vocabulary for complex systems. It evaluates each step of the complex systems analysis pipeline and discusses different types of dependencies that can affect the results and the entire analysis process.
Article
Multidisciplinary Sciences
Huan Wang, Chuang Ma, Han-Shuang Chen, Ying-Cheng Lai, Hai-Feng Zhang
Summary: Researchers have developed a general framework that combines statistical inference and expectation maximization to fully reconstruct the topology of 2-simplicial complexes with two- and three-body interactions based on binary time-series data. The framework's effectiveness has been validated, demonstrating its robustness against noisy data or stochastic disturbance.
NATURE COMMUNICATIONS
(2022)
Article
Mathematics
Mohammad Reza-Rahmati, Gerardo Flores
Summary: This paper introduces the concepts of graded linear resolution and graded linear quotients, and compares them with componentwise linearity. The paper also provides specific characterizations for certain modules and rings, and offers analogous results for the Orlik-Terao ideal of hyperplane arrangements.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Riccardo Muolo, Luca Gallo, Vito Latora, Mattia Frasca, Timoteo Carletti
Summary: Turing theory is widely used to explain the spatio-temporal structures observed in Nature. This paper proposes a method to include group interactions in reaction-diffusion systems and examines their effects on Turing pattern formation. Results demonstrate the mechanisms of pattern formation in systems with many-body interactions and provide a basis for further extensions of the Turing framework.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics
Ron Rosenthal, Lior Tenenbaum
Summary: This paper proves a high-dimensional generalization of McKay's result for random d-dimensional, k-regular simplicial complexes on n vertices, showing that the weighted number of simplicial spanning trees is of order (?(d,k) + o(1))(n/d) as n? 8, where ?(d,k) is an explicit constant, provided k > 4d(2) + d + 2.
Article
Mathematics, Applied
Y. Lee, J. Lee, S. M. Oh, D. Lee, B. Kahng
Summary: The simplicial complex representation is a mathematical framework for describing the high-order interaction effects of complex groups in various systems. The homological percolation transitions can be determined by the first and second Betti numbers. A minimal SC model with growth and preferential attachment factors successfully reproduces the HPTs in social coauthorship relationships.
Article
Mathematics, Applied
Xiaomeng Zhu, Yangjiang Wei
Summary: In this paper, quaternary linear codes are constructed using simplicial complexes and their weight distributions are determined. Additionally, an infinite family of minimal quaternary linear codes that meet the Griesmer bound is presented.
Article
Physics, Multidisciplinary
P. L. Krapivsky
Summary: Random recursive hypergraphs (RRHs) grow by adding a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge at each step. The model is parameter-free, and several characteristics of emerging hypergraphs can be expressed neatly through harmonic numbers, Bernoulli numbers, Eulerian numbers, and Stirling numbers of the first kind. Natural deformations of RRHs lead to fascinating models of growing random hypergraphs.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Hao Peng, Yifan Zhao, Dandan Zhao, Ming Zhong, Zhaolong Hu, Jianming Han, Runchao Li, Wei Wang
Summary: In recent years, the research of multilayer interdependent networks with higher-order interactions has become a hotspot in complex networks. This paper introduces the concept of simplicial complexes to better reflect real-world complex networks. A theoretical model of a two-layer network with simplicial complexes is constructed, and percolation theory is applied to study the network's robustness and properties. The density of the triangle and the dependent strength between the two networks are found to affect the network's percolation behaviors.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Dandan Zhao, Runchao Li, Hao Peng, Ming Zhong, Wei Wang
Summary: In this study, a framework for investigating the percolation of simplicial complexes with arbitrary dimensions is developed, taking into account the effects of higher-order and pairwise interactions. The robustness of simplicial complexes is assessed and properties of the model are calculated, revealing the double transition characteristics of the system.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Dandan Zhao, Runchao Li, Hao Peng, Ming Zhong, Wei Wang
Summary: This article introduces a generalized theoretical model for describing higher order networks with simplicial complexes, considering the synergistic effects of pairwise and higher-order interactions. The research finds that when the number of triangles exceeds a certain value, simplicial complexes become highly vulnerable and undergo a double phase transition.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Fluids & Plasmas
Lorenzo Giambagli, Lucille Calmon, Riccardo Muolo, Timoteo Carletti, Ginestra Bianconi
Summary: This study focuses on reaction-diffusion processes of topological signals, revealing that the projection of topological signals also exhibit Turing patterns, which holds significant theoretical and experimental value.
Article
Mathematics
Alexander Lubotzky, Jason Fox Manning, Henry Wilton
COMMENTARII MATHEMATICI HELVETICI
(2019)
Article
Mathematics
Nir Avni, Alexander Lubotzky, Chen Meiri
INVENTIONES MATHEMATICAE
(2019)
Article
Mathematics
Mikhail Belolipetsky, Alexander Lubotzky
ISRAEL JOURNAL OF MATHEMATICS
(2019)
Article
Mathematics
Gady Kozma, Alexander Lubotzky
BULLETIN OF MATHEMATICAL SCIENCES
(2019)
Article
Mathematics
Alexander Lubotzky, Tyakal Nanjundiah Venkataramana
ALGEBRA & NUMBER THEORY
(2019)
Article
Mathematics
Oren Becker, Alexander Lubotzky, Andreas Thom
DUKE MATHEMATICAL JOURNAL
(2019)
Article
Mathematics
Oren Becker, Alexander Lubotzky
JOURNAL OF FUNCTIONAL ANALYSIS
(2020)
Article
Mathematics
Montserrat Alsina, Dimitrios Chatzakos
JOURNAL OF NUMBER THEORY
(2020)
Review
Multidisciplinary Sciences
Alexander Lubotzky, Ori Parzanchevski
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2020)
Article
Mathematics, Applied
E. Lubetzky, A. Lubotzky, O. Parzanchevski
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2020)
Article
Mathematics, Applied
Arie Levit, Alexander Lubotzky
Summary: In this study, it is proven that all invariant random subgroups of the Lamplighter group L are co-sofic. This leads to the conclusion that L is permutation stable, serving as an example of an infinitely presented group. The proof presented here can be generally applied to all permutational wreath products of finitely generated abelian groups, relying on the pointwise ergodic theorem for amenable groups.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Marston Conder, Alexander Lubotzky, Jeroen Schillewaert, Francois Thilmany
Summary: This paper introduces the concept of highly regular graphs and uses the theory of Coxeter groups and abstract regular polytopes to construct such graphs. By constructing highly regular quotients of the 1-skeleton of the associated Wythoffian polytope with finite vertex links, an infinite family of expander graphs is obtained. This method solves the problem proposed by Chapman, Linial and Peled.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Alexander Lubotzky, Izhar Oppenheim
JOURNAL D ANALYSE MATHEMATIQUE
(2020)
Article
Mathematics, Applied
Marcus De Chiffre, Lev Glebsky, Alexander Lubotzky, Andreas Thom
FORUM OF MATHEMATICS SIGMA
(2020)