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Falk MJ, Wu J, Matthews A, Sachdeva V, Pashine N, Gardel ML, Nagel SR, Murugan A. Learning to learn by using nonequilibrium training protocols for adaptable materials. Proc Natl Acad Sci U S A 2023; 120:e2219558120. [PMID: 37364104 PMCID: PMC10319023 DOI: 10.1073/pnas.2219558120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2022] [Accepted: 05/25/2023] [Indexed: 06/28/2023] Open
Abstract
Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.
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Affiliation(s)
- Martin J. Falk
- Department of Physics, The University of Chicago, Chicago, IL60637
| | - Jiayi Wu
- Department of Physics, The University of Chicago, Chicago, IL60637
| | - Ayanna Matthews
- Graduate Program in Biophysical Sciences, The University of Chicago, Chicago, IL60637
| | - Vedant Sachdeva
- Graduate Program in Biophysical Sciences, The University of Chicago, Chicago, IL60637
| | - Nidhi Pashine
- School of Engineering and Applied Science, Yale University, New Haven, CT06511
| | - Margaret L. Gardel
- Department of Physics, The University of Chicago, Chicago, IL60637
- James Franck Institute, The University of Chicago, Chicago, IL60637
- Institute for Biophysical Dynamics, The University of Chicago, Chicago, IL60637
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL60637
| | - Sidney R. Nagel
- Department of Physics, The University of Chicago, Chicago, IL60637
- James Franck Institute, The University of Chicago, Chicago, IL60637
| | - Arvind Murugan
- Department of Physics, The University of Chicago, Chicago, IL60637
- James Franck Institute, The University of Chicago, Chicago, IL60637
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Calmon L, Krishnagopal S, Bianconi G. Local Dirac Synchronization on networks. CHAOS (WOODBURY, N.Y.) 2023; 33:033117. [PMID: 37003807 DOI: 10.1063/5.0132468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 02/13/2023] [Indexed: 06/19/2023]
Abstract
We propose Local Dirac Synchronization that uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely while the other modes are interacting non-linearly, leading to a collectively synchronized state when the coupling constant of the model is increased. Local Dirac Synchronization is characterized by discontinuous transitions and the emergence of a rhythmic coherent phase. In this rhythmic phase, one of the two complex order parameters oscillates in the complex plane at a slow frequency (called emergent frequency) in the frame in which the intrinsic frequencies have zero average. Our theoretical results obtained within the annealed approximation are validated by extensive numerical results on fully connected networks and sparse Poisson and scale-free networks. Local Dirac Synchronization on both random and real networks, such as the connectome of Caenorhabditis Elegans, reveals the interplay between topology (Betti numbers and harmonic modes) and non-linear dynamics. This unveils how topology might play a role in the onset of brain rhythms.
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Affiliation(s)
- Lucille Calmon
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Sanjukta Krishnagopal
- Department of Electrical Engineering and Computer Science, University of California Berkeley, California 94720, USA
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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A new and potential application for network science in the field of life sciences: Comment on "Networks behind the morphology and structural design of living systems" by Gosak et al. Phys Life Rev 2023; 44:105-107. [PMID: 36603331 DOI: 10.1016/j.plrev.2022.12.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Accepted: 12/20/2022] [Indexed: 12/29/2022]
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Giambagli L, Calmon L, Muolo R, Carletti T, Bianconi G. Diffusion-driven instability of topological signals coupled by the Dirac operator. Phys Rev E 2022; 106:064314. [PMID: 36671168 DOI: 10.1103/physreve.106.064314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 11/30/2022] [Indexed: 12/24/2022]
Abstract
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now, reaction-diffusion systems have been studied only when species are defined on the nodes of a network. However, in a number of real systems including, e.g., the brain and the climate, dynamical variables are not only defined on nodes but also on links, faces, and higher-dimensional cells of simplicial or cell complexes, leading to topological signals. In this work, we study reaction-diffusion processes of topological signals coupled through the Dirac operator. The Dirac operator allows topological signals of different dimension to interact or cross-diffuse as it projects the topological signals defined on simplices or cells of a given dimension to simplices or cells of one dimension up or one dimension down. By focusing on the framework involving nodes and links, we establish the conditions for the emergence of Turing patterns and we show that the latter are never localized only on nodes or only on links of the network. Moreover, when the topological signals display a Turing pattern their projection does as well. We validate the theory hereby developed on a benchmark network model and on square lattices with periodic boundary conditions.
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Affiliation(s)
- Lorenzo Giambagli
- Department of Physics and Astronomy, University of Florence, INFN & CSDC, Sesto Fiorentino, Italy.,Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
| | - Lucille Calmon
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Riccardo Muolo
- Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium.,Department of Applied Mathematics, Mathematical Institute Federal University of Rio de Janeiro, Avenida Athos da Silveira Ramos, 149, Rio de Janeiro 21941-909, Brazil
| | - Timoteo Carletti
- Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.,The Alan Turing Institute, 96 Euston Road, London NW1 2DB, United Kingdom
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Guyard G, Restagno F, McGraw JD. Elastohydrodynamic Relaxation of Soft and Deformable Microchannels. PHYSICAL REVIEW LETTERS 2022; 129:204501. [PMID: 36462008 DOI: 10.1103/physrevlett.129.204501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 10/12/2022] [Indexed: 06/17/2023]
Abstract
Hydrodynamic flows in compliant channels are of great interest in physiology and microfluidics. In these situations, elastohydrodynamic coupling leads to (i) a nonlinear pressure-vs-flow-rate relation, strongly affecting the hydraulic resistance; and (ii), because of the compliance-enabled volume storage, a finite relaxation time under a stepwise change in pressure. This latter effect remains relatively unexplored, even while the timescale can vary over a decade in typical situations. In this study we provide time-resolved measurements of the relaxation dynamics for thin and soft, rectangular microfluidic channels. We describe our data using a perturbative lubrication approximation of the Stokes equation coupled to linear elasticity, while taking into account the effect of compliance and resistance of the entrance. The modeling allows us to completely describe all of the experimental results. Our Letter is relevant for any microfluidic scenario wherein a time-dependent driving is applied and provides a first step in the dynamical description of compliant channel networks.
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Affiliation(s)
- Gabriel Guyard
- Gulliver CNRS UMR 7083, PSL Research University, ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France
- IPGG, 6 rue Jean-Calvin, 75005 Paris, France
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - Frédéric Restagno
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - Joshua D McGraw
- Gulliver CNRS UMR 7083, PSL Research University, ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France
- IPGG, 6 rue Jean-Calvin, 75005 Paris, France
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Baccini F, Geraci F, Bianconi G. Weighted simplicial complexes and their representation power of higher-order network data and topology. Phys Rev E 2022; 106:034319. [PMID: 36266916 DOI: 10.1103/physreve.106.034319] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 09/08/2022] [Indexed: 06/16/2023]
Abstract
Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the adopted mathematical framework to describe higher-order networks starting from data of higher-order interactions. Unweighted simplicial complexes typically involve a loss of information of the data, though having the benefit to capture the higher-order topology of the data. In this work we show that weighted simplicial complexes allow one to circumvent all the limitations of unweighted simplicial complexes to represent higher-order interactions. In particular, weighted simplicial complexes can represent higher-order networks without loss of information, allowing one at the same time to capture the weighted topology of the data. The higher-order topology is probed by studying the spectral properties of suitably defined weighted Hodge Laplacians displaying a normalized spectrum. The higher-order spectrum of (weighted) normalized Hodge Laplacians is studied combining cohomology theory with information theory. In the proposed framework we quantify and compare the information content of higher-order spectra of different dimension using higher-order spectral entropies and spectral relative entropies. The proposed methodology is tested on real higher-order collaboration networks and on the weighted version of the simplicial complex model "Network Geometry with Flavor."
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Affiliation(s)
- Federica Baccini
- Department of Computer Science, University of Pisa, 56127 Pisa, Italy
- Institute for Informatics and Telematics, CNR, 56124 Pisa, Italy
| | - Filippo Geraci
- Institute for Informatics and Telematics, CNR, 56124 Pisa, Italy
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom
- The Alan Turing Institute, The British Library, London NW1 2DB, United Kingdom
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Leykam D, Rondón I, Angelakis DG. Dark soliton detection using persistent homology. CHAOS (WOODBURY, N.Y.) 2022; 32:073133. [PMID: 35907713 DOI: 10.1063/5.0097053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 07/01/2022] [Indexed: 06/15/2023]
Abstract
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models, such as logistic regression models, which are easier to train. As an example, we consider the identification of dark solitons using a dataset of 6257 labeled atomic Bose-Einstein condensate density images.
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Affiliation(s)
- Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Irving Rondón
- School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegi-ro, Seoul 02455, Republic of Korea
| | - Dimitris G Angelakis
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
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Networks behind the morphology and structural design of living systems. Phys Life Rev 2022; 41:1-21. [DOI: 10.1016/j.plrev.2022.03.001] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 03/04/2022] [Indexed: 01/06/2023]
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Deng N, Wautier A, Tordesillas A, Thiery Y, Yin ZY, Hicher PY, Nicot F. Lifespan dynamics of cluster conformations in stationary regimes in granular materials. Phys Rev E 2022; 105:014902. [PMID: 35193243 DOI: 10.1103/physreve.105.014902] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 12/17/2021] [Indexed: 11/07/2022]
Abstract
We examine stationary regimes in granular materials from a dynamical systems theory perspective. The aim is to enrich the classical view of the critical state regime in granular materials, and more broadly, to improve the fundamental understanding of the underlying mesoscale mechanisms responsible for macroscopic stationary states in complex systems. This study is based on a series of discrete element method simulations, in which two-dimensional assemblies of nonuniformly sized circular particles are subjected to biaxial compression under constant lateral confining pressure. The lifespan and life expectancy of specific cluster conformations, comprising particles in force chains and grain loops, are tracked and quantified. Results suggest that these conformational clusters reorganize at similar rates in the critical state regime, depending on strain magnitudes and confining pressure levels. We quantified this rate of reorganization and found that the material memory rapidly fades, with an entirely new generation of force chains and grain loops replacing the old within a few percent strain.
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Affiliation(s)
- Na Deng
- Grenoble Alps University, INRAE, UR ETNA, 2 rue de la Papeterie-BP 76, 38402 St-Martin-d'Hères, France
| | - Antoine Wautier
- Aix-Marseille University, INRAE, UMR RECOVER, 3275 Rte Cézanne, CS 40061, 13182 Aix-en-Provence Cedex 5, France
| | - Antoinette Tordesillas
- School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, 3010, Australia
| | - Yannick Thiery
- BRGM (French Geological Survey), Risk and Prevention Division, 3 Av. Claude Guillemin, 45100, Orléans, France
| | - Zhen-Yu Yin
- Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China
| | - Pierre-Yves Hicher
- Research Institute in Civil Engineering and Mechanics (GeM), UMR CNRS 6183, Ecole Centrale de Nantes, 1 Rue de la Noë, 44300, Nantes, France
| | - François Nicot
- Grenoble Alps University, INRAE, UR ETNA, 2 rue de la Papeterie-BP 76, 38402 St-Martin-d'Hères, France and Université Savoie Mont Blanc, Laboratoire EDYTEM, UMR 5204, 5 bd. de la Mer Caspienne, 73376 Le Bourget-du-Lac, France
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