1
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Richard D, Kapteijns G, Lerner E. Detecting low-energy quasilocalized excitations in computer glasses. Phys Rev E 2023; 108:044124. [PMID: 37978582 DOI: 10.1103/physreve.108.044124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 09/15/2023] [Indexed: 11/19/2023]
Abstract
Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow one to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies, and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input and outputs a library of QLEs embedded in that sample. We demonstrate the power of the algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon hybridizations. Future applications are discussed.
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Affiliation(s)
- David Richard
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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2
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Pihlajamaa I, Laudicina CCL, Luo C, Janssen LMC. Emergent structural correlations in dense liquids. PNAS NEXUS 2023; 2:pgad184. [PMID: 37342651 PMCID: PMC10279420 DOI: 10.1093/pnasnexus/pgad184] [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: 02/27/2023] [Accepted: 05/23/2023] [Indexed: 06/23/2023]
Abstract
The complete quantitative description of the structure of dense and supercooled liquids remains a notoriously difficult problem in statistical physics. Most studies to date focus solely on two-body structural correlations, and only a handful of papers have sought to consider additional three-body correlations. Here, we go beyond the state of the art by extracting many-body static structure factors from molecular dynamics simulations and by deriving accurate approximations up to the six-body structure factor via density functional theory. We find that supercooling manifestly increases four-body correlations, akin to the two- and three-body case. However, at small wave numbers, we observe that the four-point structure of a liquid drastically changes upon supercooling, both qualitatively and quantitatively, which is not the case in two-point structural correlations. This indicates that theories of the structure or dynamics of dense liquids should incorporate many-body correlations beyond the two-particle level to fully capture their intricate behavior.
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Affiliation(s)
| | | | - Chengjie Luo
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
- Max Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany
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3
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Shiba H, Hanai M, Suzumura T, Shimokawabe T. BOTAN: BOnd TArgeting Network for prediction of slow glassy dynamics by machine learning relative motion. J Chem Phys 2023; 158:084503. [PMID: 36859106 DOI: 10.1063/5.0129791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/03/2023] Open
Abstract
Recent developments in machine learning have enabled accurate predictions of the dynamics of slow structural relaxation in glass-forming systems. However, existing machine learning models for these tasks are mostly designed such that they learn a single dynamic quantity and relate it to the structural features of glassy liquids. In this study, we propose a graph neural network model, "BOnd TArgeting Network," that learns relative motion between neighboring pairs of particles, in addition to the self-motion of particles. By relating the structural features to these two different dynamical variables, the model autonomously acquires the ability to discern how the self motion of particles undergoing slow relaxation is affected by different dynamical processes, strain fluctuations and particle rearrangements, and thus can predict with high precision how slow structural relaxation develops in space and time.
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Affiliation(s)
- Hayato Shiba
- Information Technology Center, University of Tokyo, Chiba 277-0882, Japan
| | - Masatoshi Hanai
- Information Technology Center, University of Tokyo, Chiba 277-0882, Japan
| | - Toyotaro Suzumura
- Information Technology Center, University of Tokyo, Chiba 277-0882, Japan
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4
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Zhang K, Li X, Jin Y, Jiang Y. Machine learning glass caging order parameters with an artificial nested neural network. SOFT MATTER 2022; 18:6270-6277. [PMID: 35959881 DOI: 10.1039/d2sm00310d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Around a glass transition, the dynamics of a supercooled liquid dramatically slow down, exhibited by caging of particles, while the structural changes remain subtle. Alternative to recent machine learning studies searching for structural predictors of glassy dynamics, here we propose to learn directly particle caging features defined purely according to dynamics. We focus on three transitions in a simulated hard sphere glass model, the melting of ultra-stable glasses, the Gardner transition and the liquid to ordinary glass transition. Implementing the machine learning algorithm based on a two-level nested neural network, we attain not only appropriate caging order parameters for all three transitions, but also a phase classification for input samples. A finite-size scaling analysis of the phase classification results identifies the order of melting (first) and Gardner (second) transitions. A false positive is avoided, as the liquid to glass transition is indicated as a crossover, rather than a phase transition with a well-defined transition point. This study paves the way to a generic approach for learning dynamical features in glassy systems, with a minimum requirement of system-specific knowledge.
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Affiliation(s)
- Kaihua Zhang
- School of Chemistry, Beihang University, Beijing 100191, China.
| | - Xinyang Li
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yuliang Jin
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
| | - Ying Jiang
- School of Chemistry, Beihang University, Beijing 100191, China.
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China
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5
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Baggioli M, Kriuchevskyi I, Sirk TW, Zaccone A. Plasticity in Amorphous Solids Is Mediated by Topological Defects in the Displacement Field. PHYSICAL REVIEW LETTERS 2021; 127:015501. [PMID: 34270321 DOI: 10.1103/physrevlett.127.015501] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Revised: 03/31/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatiotemporal correlations in the undeformed glass that may trigger plastic instability. In contrast, in this Letter we show that the topological defects that correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) that are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular nonlocal peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between antiparallel DTDs; and (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45° for uniaxial deformations, as widely observed in experiments and simulations.
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Affiliation(s)
- Matteo Baggioli
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ivan Kriuchevskyi
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Timothy W Sirk
- Polymers Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, USA
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
- Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, CB30HE Cambridge, United Kingdom
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6
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Fang C, Barzeger A, Katzgraber HG. Machine learning in physics: the pitfalls of poisoned training sets. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/aba821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
Known for their ability to identify hidden patterns in data, artificial neural networks are among the most powerful machine learning tools. Most notably, neural networks have played a central role in identifying states of matter and phase transitions across condensed matter physics. To date, most studies have focused on systems where different phases of matter and their phase transitions are known, and thus the performance of neural networks is well controlled. While neural networks present an exciting new tool to detect new phases of matter, here we demonstrate that when the training sets are poisoned (i.e. poor training data or mislabeled data) it is easy for neural networks to make misleading predictions.
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7
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Ariel G, Diamant H. Inferring entropy from structure. Phys Rev E 2020; 102:022110. [PMID: 32942515 DOI: 10.1103/physreve.102.022110] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 07/13/2020] [Indexed: 11/07/2022]
Abstract
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively inefficient to sample or difficult to obtain experimentally. It is beneficial, therefore, to relate the entropy to other integrated properties which are accessible out of equilibrium. We focus on the structure factor, which describes the spatial correlations of density fluctuations and can be directly measured by scattering. The information gained by a given structure factor regarding an otherwise unknown system provides an upper bound for the system's entropy. We find that the maximum-entropy model corresponds to an equilibrium system with an effective pair interaction. Approximate closed-form relations for the effective pair potential and the resulting entropy in terms of the structure factor are obtained. As examples, the relations are used to estimate the entropy of an exactly solvable model and two simulated systems out of equilibrium. The focus is on low-dimensional examples, where our method, as well as a recently proposed compression-based one, can be tested against a rigorous direct-sampling technique. The entropy inferred from the structure factor is found to be consistent with the other methods, superior for larger system sizes, and accurate in identifying global transitions. Our approach allows for extensions of the theory to more complex systems and to higher-order correlations.
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Affiliation(s)
- Gil Ariel
- Department of Mathematics, Bar-Ilan University, 52000 Ramat Gan, Israel
| | - Haim Diamant
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
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8
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Paret J, Jack RL, Coslovich D. Assessing the structural heterogeneity of supercooled liquids through community inference. J Chem Phys 2020; 152:144502. [DOI: 10.1063/5.0004732] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joris Paret
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, Montpellier, France
| | - Robert L. Jack
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Daniele Coslovich
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, Montpellier, France
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9
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Kishore R, Gogineni AK, Nussinov Z, Sahu KK. A nature inspired modularity function for unsupervised learning involving spatially embedded networks. Sci Rep 2019; 9:2631. [PMID: 30796343 PMCID: PMC6385190 DOI: 10.1038/s41598-019-39180-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Accepted: 01/18/2019] [Indexed: 11/09/2022] Open
Abstract
The quality of network clustering is often measured in terms of a commonly used metric known as "modularity". Modularity compares the clusters found in a network to those present in a random graph (a "null model"). Unfortunately, modularity is somewhat ill suited for studying spatially embedded networks, since a random graph contains no basic geometrical notions. Regardless of their distance, the null model assigns a nonzero probability for an edge to appear between any pair of nodes. Here, we propose a variant of modularity that does not rely on the use of a null model. To demonstrate the essentials of our method, we analyze networks generated from granular ensemble. We show that our method performs better than the most commonly used Newman-Girvan (NG) modularity in detecting the best (physically transparent) partitions in those systems. Our measure further properly detects hierarchical structures, whenever these are present.
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Affiliation(s)
- Raj Kishore
- School of Minerals, Metallurgical and Materials Engineering, Indian Institute of Technology Bhubaneswar-, Bhubaneswar, 752050, India
| | - Ajay K Gogineni
- School of Electrical Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, 752050, India
| | - Zohar Nussinov
- Department of Physics, Washington University in Saint Louis, Saint Louis, MO, 63130-4899, USA
| | - Kisor K Sahu
- School of Minerals, Metallurgical and Materials Engineering, Indian Institute of Technology Bhubaneswar-, Bhubaneswar, 752050, India.
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10
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Kelton KF. Kinetic and structural fragility-a correlation between structures and dynamics in metallic liquids and glasses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:023002. [PMID: 27841996 DOI: 10.1088/0953-8984/29/2/023002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
The liquid phase remains poorly understood. In many cases, the densities of liquids and their crystallized solid phases are similar, but since they are amorphous they lack the spatial order of the solid. Their dynamical properties change remarkably over a very small temperature range. At high temperatures, near their melting temperature, liquids flow easily under shear. However, only a few hundred degrees lower flow effectively ceases, as the liquid transforms into a solid-like glass. This temperature-dependent dynamical behavior is frequently characterized by the concept of kinetic fragility (or, generally, simply fragility). Fragility is believed to be an important quantity in glass formation, making it of significant practical interest. The microscopic origin of fragility remains unclear, however, making it also of fundamental interest. It is widely (although not uniformly) believed that the dynamical behavior is linked to the atomic structure of the liquid, yet experimental studies show that although the viscosity changes by orders of magnitude with temperature, the structural change is barely perceptible. In this article the concept of fragility is discussed, building to a discussion of recent results in metallic glass-forming liquids that demonstrate the presumed connection between structural and dynamical changes. In particular, it becomes possible to define a structural fragility parameter that can be linked with the kinetic fragility.
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Affiliation(s)
- K F Kelton
- Department of Physics and the Institute of Materials Science and Engineering, Washington University, St. Louis, MO 63130, USA
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11
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Peixoto TP. Inferring the mesoscale structure of layered, edge-valued, and time-varying networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042807. [PMID: 26565289 DOI: 10.1103/physreve.92.042807] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Indexed: 05/24/2023]
Abstract
Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges, or as a time dependence of the network structure. Although they are crucial for a more comprehensive scientific understanding, these representations offer substantial challenges. Namely, it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects. Furthermore, the direct incorporation of these features invariably increases the effective dimension of the network description, and hence aggravates the problem of overfitting, i.e., the use of overly complex characterizations that mistake purely random fluctuations for actual structure. In this work, we propose a robust and principled method to tackle these problems, by constructing generative models of modular network structure, incorporating layered, attributed and time-varying properties, as well as a nonparametric Bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence. We show that the method is capable of revealing hidden structure in layered, edge-valued, and time-varying networks, and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified. We illustrate our approach on a variety of empirical systems, including a social network of physicians, the voting correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.
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Affiliation(s)
- Tiago P Peixoto
- Institut für Theoretische Physik, Universität Bremen, Hochschulring 18, D-28359 Bremen, Germany
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12
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Dong X, Mavroeidis D, Calabrese F, Frossard P. Multiscale event detection in social media. Data Min Knowl Discov 2015. [DOI: 10.1007/s10618-015-0421-2] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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13
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Bassett DS, Owens ET, Porter MA, Manning ML, Daniels KE. Extraction of force-chain network architecture in granular materials using community detection. SOFT MATTER 2015; 11:2731-2744. [PMID: 25703651 DOI: 10.1039/c4sm01821d] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no agreement on a quantitative description of force chains. Consequently, it is difficult to compare the force-chain structures in different materials or experimental conditions. To address this challenge, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges that represent contact forces. We use techniques from community detection, which is a type of clustering, to find sets of closely connected particles. By using a geographical null model that is constrained by the particles' contact network, we extract chain-like structures that are reminiscent of force chains. We propose three diagnostics to measure these chain-like structures, and we demonstrate the utility of these diagnostics for identifying and characterizing classes of force-chain network architectures in various materials. To illustrate our methods, we describe how force-chain architecture depends on pressure for two very different types of packings: (1) ones derived from laboratory experiments and (2) ones derived from idealized, numerically-generated frictionless packings. By resolving individual force chains, we quantify statistical properties of force-chain shape and strength, which are potentially crucial diagnostics of bulk properties (including material stability). These methods facilitate quantitative comparisons between different particulate systems, regardless of whether they are measured experimentally or numerically.
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Affiliation(s)
- Danielle S Bassett
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
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14
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Jeub LGS, Balachandran P, Porter MA, Mucha PJ, Mahoney MW. Think locally, act locally: detection of small, medium-sized, and large communities in large networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012821. [PMID: 25679670 PMCID: PMC5125638 DOI: 10.1103/physreve.91.012821] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2014] [Indexed: 06/04/2023]
Abstract
It is common in the study of networks to investigate intermediate-sized (or "meso-scale") features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are typically construed as sets of nodes with denser connections internally than with the remainder of a network. In this paper, we adopt a complementary perspective that communities are associated with bottlenecks of locally biased dynamical processes that begin at seed sets of nodes, and we employ several different community-identification procedures (using diffusion-based and geodesic-based dynamics) to investigate community quality as a function of community size. Using several empirical and synthetic networks, we identify several distinct scenarios for "size-resolved community structure" that can arise in real (and realistic) networks: (1) the best small groups of nodes can be better than the best large groups (for a given formulation of the idea of a good community); (2) the best small groups can have a quality that is comparable to the best medium-sized and large groups; and (3) the best small groups of nodes can be worse than the best large groups. As we discuss in detail, which of these three cases holds for a given network can make an enormous difference when investigating and making claims about network community structure, and it is important to take this into account to obtain reliable downstream conclusions. Depending on which scenario holds, one may or may not be able to successfully identify "good" communities in a given network (and good communities might not even exist for a given community quality measure), the manner in which different small communities fit together to form meso-scale network structures can be very different, and processes such as viral propagation and information diffusion can exhibit very different dynamics. In addition, our results suggest that, for many large realistic networks, the output of locally biased methods that focus on communities that are centered around a given seed node (or set of seed nodes) might have better conceptual grounding and greater practical utility than the output of global community-detection methods. They also illustrate structural properties that are important to consider in the development of better benchmark networks to test methods for community detection.
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Affiliation(s)
- Lucas G S Jeub
- Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Prakash Balachandran
- Morgan Stanley, Montreal, Quebec, H3C 3S4, Canada and Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Mason A Porter
- Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, United Kingdom
| | - Peter J Mucha
- Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA
| | - Michael W Mahoney
- International Computer Science Institute, Berkeley, California 94704, USA and Department of Statistics, University of California at Berkeley, Berkeley, California 94720, USA
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15
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Hocky GM, Coslovich D, Ikeda A, Reichman DR. Correlation of local order with particle mobility in supercooled liquids is highly system dependent. PHYSICAL REVIEW LETTERS 2014; 113:157801. [PMID: 25375744 DOI: 10.1103/physrevlett.113.157801] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2014] [Indexed: 06/04/2023]
Abstract
We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models, we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.
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Affiliation(s)
- Glen M Hocky
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Daniele Coslovich
- CNRS, Laboratoire Charles Coulomb UMR 5221, Montpellier 34095, France and Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, Montpellier 34095, France
| | - Atsushi Ikeda
- CNRS, Laboratoire Charles Coulomb UMR 5221, Montpellier 34095, France and Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, Montpellier 34095, France
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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16
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Jack RL, Dunleavy AJ, Royall CP. Information-theoretic measurements of coupling between structure and dynamics in glass formers. PHYSICAL REVIEW LETTERS 2014; 113:095703. [PMID: 25215994 DOI: 10.1103/physrevlett.113.095703] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2014] [Indexed: 06/03/2023]
Abstract
We analyze connections between structure and dynamics in two model glass formers, using the mutual information between an initial configuration and the ensuing dynamics to compare the predictive value of different structural observables. We consider the predictive power of normal modes, locally favored structures, and coarse-grained measurements of local energy and density. The mutual information allows the influence of the liquid structure on the dynamics to be analyzed quantitatively as a function of time, showing that normal modes give the most useful predictions on short time scales while local energy and density are most strongly predictive at long times.
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Affiliation(s)
- Robert L Jack
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Andrew J Dunleavy
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom and School of Chemistry, University of Bristol, Cantock Close, Bristol BS8 1TS, United Kingdom and Bristol Centre for Complexity Sciences, Bristol BS8 1TW, United Kingdom
| | - C Patrick Royall
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom and School of Chemistry, University of Bristol, Cantock Close, Bristol BS8 1TS, United Kingdom and Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
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17
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Petri G, Expert P. Temporal stability of network partitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022813. [PMID: 25215787 DOI: 10.1103/physreve.90.022813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2013] [Indexed: 06/03/2023]
Abstract
We present a method to find the best temporal partition at any time scale and rank the relevance of partitions found at different time scales. This method is based on random walkers coevolving with the network and as such constitutes a generalization of partition stability to the case of temporal networks. We show that, when applied to a toy model and real data sets, temporal stability uncovers structures that are persistent over meaningful time scales as well as important isolated events, making it an effective tool to study both abrupt changes and gradual evolution of a network mesoscopic structures.
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Affiliation(s)
| | - Paul Expert
- Centre for Neuroimaging Sciences, Institute of Psychiatry, De Crespigny Park, King's College London, London SE5 8AF, United Kingdom
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18
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Charbonneau P, Tarjus G. Decorrelation of the static and dynamic length scales in hard-sphere glass formers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042305. [PMID: 23679412 DOI: 10.1103/physreve.87.042305] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Revised: 03/13/2013] [Indexed: 06/02/2023]
Abstract
We show that, in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in the dynamics unambiguously decorrelate. The former grow at a much slower rate than the latter when density increases. This observation is valid for the dynamical range that is accessible to computer simulations, which roughly corresponds to that accessible in colloidal experiments. We also find that, in this same range, no one-to-one correspondence between relaxation time and point-to-set correlation length exists. These results point to the coexistence of several relaxation mechanisms in the dynamically accessible regime of three-dimensional hard-sphere glass formers.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
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Charbonneau B, Charbonneau P, Tarjus G. Geometrical frustration and static correlations in hard-sphere glass formers. J Chem Phys 2013; 138:12A515. [DOI: 10.1063/1.4770498] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Melchert O, Hartmann AK. Information-theoretic approach to ground-state phase transitions for two- and three-dimensional frustrated spin systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022107. [PMID: 23496460 DOI: 10.1103/physreve.87.022107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/01/2023]
Abstract
The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.
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Affiliation(s)
- O Melchert
- Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky Strasse, 26111 Oldenburg, Germany.
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Cardillo A, Gómez-Gardeñes J, Zanin M, Romance M, Papo D, Pozo FD, Boccaletti S. Emergence of network features from multiplexity. Sci Rep 2013; 3:1344. [PMID: 23446838 PMCID: PMC3583169 DOI: 10.1038/srep01344] [Citation(s) in RCA: 331] [Impact Index Per Article: 30.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2012] [Accepted: 02/14/2013] [Indexed: 11/30/2022] Open
Abstract
Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years theoretical studies have examined a variety of structural features of complex networks, the outstanding question is whether such features are characterizing all single layers, or rather emerge as a result of coarse-graining, i.e. when going from the multilayered to the aggregate network representation. Here we address this issue with the help of real data. We analyze the structural properties of an intrinsically multilayered real network, the European Air Transportation Multiplex Network in which each commercial airline defines a network layer. We examine how several structural measures evolve as layers are progressively merged together. In particular, we discuss how the topology of each layer affects the emergence of structural properties in the aggregate network.
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Affiliation(s)
- Alessio Cardillo
- Institute for Biocomputation and Physics of Complex Systems (BIFI), Universidad de Zaragoza, E-50018 Zaragoza, Spain
- Departamento de Física de Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain
| | - Jesús Gómez-Gardeñes
- Institute for Biocomputation and Physics of Complex Systems (BIFI), Universidad de Zaragoza, E-50018 Zaragoza, Spain
- Departamento de Física de Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain
| | - Massimiliano Zanin
- Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain
- Innaxis Foundation & Research Institute, José Ortega y Gasset 20, 28006, Madrid, Spain
- Faculdade de Ciências e Tecnologia, Departamento de Engenharia Electrotécnica, Universidade Nova de Lisboa, Portugal
| | - Miguel Romance
- Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain
- Departmento de Matemática Aplicada, Universidad Rey Juan Carlos, E-28933 Móstoles, Madrid, Spain
| | - David Papo
- Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain
| | - Francisco del Pozo
- Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain
| | - Stefano Boccaletti
- Center for Biomedical Technology, Universidad Politécnica de Madrid, E-28223 Pozuelo de Alarcón, Madrid, Spain
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Bassett DS, Owens ET, Daniels KE, Porter MA. Influence of network topology on sound propagation in granular materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041306. [PMID: 23214579 DOI: 10.1103/physreve.86.041306] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Revised: 07/04/2012] [Indexed: 05/12/2023]
Abstract
Granular media, whose features range from the particle scale to the force-chain scale and the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with each of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures to determine their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of mesoscale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by mesoscale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.
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Affiliation(s)
- Danielle S Bassett
- Department of Physics, University of California, Santa Barbara, California 93106, USA.
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Ronhovde P, Chakrabarty S, Hu D, Sahu M, Sahu KK, Kelton KF, Mauro NA, Nussinov Z. Detection of hidden structures for arbitrary scales in complex physical systems. Sci Rep 2012; 2:329. [PMID: 22461970 PMCID: PMC3314987 DOI: 10.1038/srep00329] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Accepted: 02/29/2012] [Indexed: 11/14/2022] Open
Abstract
Recent decades have experienced the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of contending atomic- and largerscale configurations. In order to obtain a more detailed understanding of such systems, we need tools that enable the detection of pertinent structures on all spatial and temporal scales. Towards this end, we suggest a new method that applies to both static and dynamic systems which invokes ideas from network analysis and information theory. Our approach efficiently identifies basic unit cells, topological defects, and candidate natural structures. The method is particularly useful where a clear definition of order is lacking, and the identified features may constitute a natural point of departure for further analysis.
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Jack RL, Berthier L. Random pinning in glassy spin models with plaquette interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021120. [PMID: 22463166 DOI: 10.1103/physreve.85.021120] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2011] [Indexed: 05/31/2023]
Abstract
We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localization in a single state. At low temperatures, both models exhibit scaling behavior. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group treatments.
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Affiliation(s)
- Robert L Jack
- Department of Physics, University of Bath, Bath, BA2 7AY, United Kingdom
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Charbonneau B, Charbonneau P, Tarjus G. Geometrical frustration and static correlations in a simple glass former. PHYSICAL REVIEW LETTERS 2012; 108:035701. [PMID: 22400759 DOI: 10.1103/physrevlett.108.035701] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2011] [Indexed: 05/31/2023]
Abstract
We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing down of relaxation, because of the strong frustration characterizing these systems. The possibility of a growing static length is furthermore found to be physically irrelevant in the regime that is accessible to computer simulations.
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Affiliation(s)
- Benoit Charbonneau
- Mathematics Department, St. Jerome's University in the University of Waterloo, Waterloo, Ontario, Canada
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Hu D, Ronhovde P, Nussinov Z. Replica inference approach to unsupervised multiscale image segmentation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:016101. [PMID: 22400619 DOI: 10.1103/physreve.85.016101] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2011] [Indexed: 05/31/2023]
Abstract
We apply a replica-inference-based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the problem is cast as identifying tightly bound clusters ("communities" or "solutes") against a background or "solvent." Within our multiresolution approach, we compute information-theory-based correlations among multiple solutions ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by replica correlations manifest by information theory overlaps. We further employ such information theory measures (such as normalized mutual information and variation of information), thermodynamic quantities such as the system entropy and energy, and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases. Within the solvable phase, transitions between contending solutions (such as those corresponding to segmentations on different scales) may also appear. With the aid of these correlations as well as thermodynamic measures, the phase diagram of the corresponding Potts model is analyzed at both zero and finite temperatures. Optimal parameters corresponding to a sensible unsupervised segmentations appear within the "easy phase" of the Potts model. Our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images.
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Affiliation(s)
- Dandan Hu
- Department of Physics, Washington University, Campus Box 1105, 1 Brookings Drive, St. Louis, Missouri 63130, USA
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