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Using spatial patterns of English folk speech to infer the universality class of linguistic copying

Physical Review Research 2020年第4期2卷 043053-043053页

作者： James Burridge Tamsin Blaxter School of Mathematics and Physics University of Portsmouth Portsmouth PO1 3HF United Kingdom Gonville and Caius College Cambridge CB2 1TA United Kingdom

Both linguistic and genetic evolution involve copying and mutation of variants. The simplest copying process assumes that variants are reproduced at a rate equal to their current frequency, exemplified by Kimura's stepping stone model of neutral evolution, and the voter model. In this case, spatial patterns are driven by noise. In the linguistic context, an alternative possibility is that speakers preferentially select variants which are already popular, yielding patterns driven by surface tension, exemplified by the Ising model. In this paper, we model language change using a spatial network of speakers, inspired by the Hopfield neural network. The model's universality class—Voter or Ising—is determined by speakers' learning function. We view maps generated by the Survey of English Dialects as samples from our network. Maximum likelihood analysis, and comparison of spatial auto-correlations between real and simulated maps, indicates that the underlying copying processes is more likely to belong to the conformity-driven Ising class.

关键词： patterns in complex systems Phase separation Social systems

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Erosion patterns on dissolving and melting bodies

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Physical Review Fluids 2016年第5期1卷 050508-050508页

作者： Caroline Cohen Michael Berhanu Julien Derr Sylvain Courrech du Pont Univ Paris Diderot CNRS UMR 7057 Lab Mat & Syst Complexes F-75205 Paris 13 France

This paper is associated with a poster winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original poster is available from the Gallery of Fluid Motion, http://***/10.1103/***.P0051

关键词： Convection Geophysical fluid dynamics patterns in complex systems

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Multiscale dynamical embeddings of complex networks

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Physical Review E 2019年第6期99卷 062308-062308页

作者： Michael T. Schaub Jean-Charles Delvenne Renaud Lambiotte Mauricio Barahona Institute for Data Systems and Society Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Engineering Science University of Oxford Oxford United Kingdom ICTEAM Université catholique de Louvain B-1348 Louvain-la-Neuve Belgium CORE Université catholique de Louvain B-1348 Louvain-la-Neuve Belgium Mathematical Institute University of Oxford Oxford United Kingdom Department of Mathematics Imperial College London London SW7 2AZ United Kingdom

complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.

关键词： complex systems Network structure patterns in complex systems Deterministic networks Directed networks Networks & random structures Neuronal network activity Neuronal networks Real world networks Weighted networks Coarse graining Data analysis

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One-dimensional theoretical analysis of coupling and confinement effects on the cybotactic clusters of bent-core nematic liquid crystals

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Physical Review E 2019年第1期99卷 012703-012703页

作者： Sourav Patranabish Yiwei Wang Aloka Sinha Apala Majumdar Department of Physics Indian Institute of Technology Delhi Hauz Khas New Delhi 110016 India School of Mathematical Sciences Peking University Beijing 100871 China Department of Mathematical Sciences University of Bath Bath BA2 7AY England United Kingdom

The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smecticlike cybotactic clusters which are promising for electro-optic applications. We have studied a one-dimensional Landau–de Gennes model of spatially inhomogeneous order parameters for the N phase of bent-core LCs. We investigate the effects of spatial confinement and coupling (between these clusters and the surrounding LC molecules modeled by a coupling parameter γ) on the order parameters. The coupling is found to increase the cluster order parameter significantly, suggesting enhancement in cluster formation, and also predicts a transition to a phase with weak nematiclike ordering above the nematic supercooling temperature.

关键词： patterns in complex systems

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Simultaneous unpinning of multiple vortices in two-dimensional excitable media

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Physical Review E 2019年第4期99卷 042216-042216页

作者： Henrik tom Wörden Ulrich Parlitz Stefan Luther Max Planck Institute for Dynamics and Self-Organization Göttingen Germany DZHK (German Center for Cardiovascular Research) partner site Göttingen Göttingen Germany Institute for the Dynamics of Complex Systems University of Göttingen Göttingen Germany Institute of Pharmacology University Medical Center Göttingen Göttingen Germany

There are many examples of excitable media, such as the heart, that can show complex dynamics and where control is a challenging task. Heavy means like a strong electric shock are nowadays still necessary to control and terminate ventricular fibrillation (VF). It is known that heterogeneities in an excitable medium can stabilize the activity, e.g., spiral waves can pin to such obstacles. This might also be a reason for the persistence of VF and the difficulty to control it. Previous studies investigated systems with a single pinned spiral wave and demonstrated how the spiral can be unpinned. In this article, we extend this case and investigate a generic excitable system with multiple pinned spiral waves. We describe a control technique that allows the simultaneous unpinning of pinned spiral waves. Apart from theoretical considerations, we provide numerical evidence that the proposed technique is superior to the underdrive pacing method that has reportedly high success rates when applied to a single pinned spiral.

关键词： Cardiac dynamics Coupled oscillators Electromagnetic therapy Heart diseases patterns in complex systems Spiral & scroll waves

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Catastrophic Thinning of Dielectric Elastomers

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Physical Review Letters 2017年第7期118卷 078001-078001页

作者： G. Zurlo M. Destrade D. DeTommasi G. Puglisi Dipartimento di Scienze dell’ Ingegneria Civile e dell’ Architettura Politecnico di Bari Via Re David 200 70125 Bari Italy

We provide an energetic insight into the catastrophic nature of thinning instability in soft electroactive elastomers. This phenomenon is a major obstacle to the development of giant actuators, yet it is neither completely understood nor modeled accurately. In excellent agreement with experiments, we give a simple formula to predict the critical voltages for instability patterns; we model their shape and show that reversible (elastic) equilibrium is impossible beyond their onset. Our derivation is fully analytical, does not require finite element simulations, and can be extended to include prestretch and various material models.

关键词： Actuating materials Creasing Dielectric properties Dielectrics Elasticity Electric field effects Flexible electronics patterns in complex systems

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Traveling phase waves in asymmetric networks of noisy chaotic attractors

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Physical Review E 2016年第4期94卷 042210-042210页

作者： Thomas K. DM. Peron Jürgen Kurths Francisco A. Rodrigues Lutz Schimansky-Geier Bernard Sonnenschein Instituto de Física de São Carlos Universidade de São Paulo CP 369 13560-970 São Carlos São Paulo Brazil Potsdam Institute for Climate Impact Research (PIK) 14473 Potsdam Germany Department of Physics Humboldt-Universität zu Berlin Newtonstrasse 15 12489 Berlin Germany Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo CP 668 13560-970 São Carlos São Paulo Brazil

We explore identical Rössler systems organized into two equally sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. With this asymmetric coupling, we analyze patterns in the phase dynamics that coexist with chaotic amplitudes. We specifically investigate traveling phase waves where the oscillators settle on a new rhythm different from their own. We show that these waves are possible even without coherence in the phase angles. It is further demonstrated that the emergence of these incoherent traveling waves depends on the type of coupling, not on the individual dynamics of the Rössler systems. Together with the study of noise effects, our results suggest a promising new avenue toward the interplay of chaotic, noisy, coherent, and incoherent collective dynamics.

关键词： patterns in complex systems Synchronization Coupled oscillators

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Super-Resolution Community Detection for Layer-Aggregated Multilayer Networks

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Physical Review X 2017年第3期7卷 031056-031056页

作者： Dane Taylor Rajmonda S. Caceres Peter J. Mucha Carolina Center for Interdisciplinary Applied Mathematics Department of Mathematics University of North Carolina Chapel Hill North Carolina 27599 USA Department of Mathematics University at Buffalo State University of New York Buffalo New York 14260 USA Lincoln Laboratory Massachusetts Institute of Technology Lexington Massachusetts 02420 USA

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the trade-offs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with N nodes and L layers, which are drawn from an ensemble of Erdős–Rényi networks with communities planted in subsets of layers. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit K*. When layers are aggregated via a summation, we obtain K*∝O(NL/T), where T is the number of layers across which the community persists. Interestingly, if T is allowed to vary with L, then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that T/L decays more slowly than O(L−1/2). Moreover, we find that thresholding the summation can, in some cases, cause K* to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. In other words, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.

关键词： Community structure Information & communication theory Network phase transitions patterns in complex systems Scaling laws of complex systems

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Meander pattern of spiral wave and the spatial distribution of its cycle length

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Physical Review E 2023年第1期107卷 014215-014215页

作者： Sergei F. Pravdin Mikhail A. Patrakeev Alexander V. Panfilov Ural Federal University Research Laboratory “Mathematical Modeling in Physiology and Medicine Based on Supercomputers” 620002 Ekaterinburg Russia and World-Class Research Center “Digital biodesign and personalized healthcare” Sechenov University 119146 Moscow Russia

One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside Tout and inside Tin the meandering trajectory with a ratio of Tin/Tout=(n+1)/n for the inward and (n−1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.

关键词： Cardiac dynamics Heart diseases patterns in complex systems Spiral & scroll waves Dynamical systems Heart Muscle Reaction diffusion systems

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Permutation entropy of finite-length white-noise time series

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Physical Review E 2016年第2期94卷 022118-022118页

作者： Douglas J. Little Deb M. Kane MQ Photonics Research Centre Department of Physics and Astronomy Macquarie University North Ryde NSW 2109 Australia

Permutation entropy (PE) is commonly used to discriminate complex structure from white noise in a time series. While the PE of white noise is well understood in the long time-series limit, analysis in the general case is currently lacking. Here the expectation value and variance of white-noise PE are derived as functions of the number of ordinal pattern trials, N, and the embedding dimension, D. It is demonstrated that the probability distribution of the white-noise PE converges to a χ2 distribution with D!−1 degrees of freedom as N becomes large. It is further demonstrated that the PE variance for an arbitrary time series can be estimated as the variance of a related metric, the Kullback-Leibler entropy (KLE), allowing the qualitative N≫D! condition to be recast as a quantitative estimate of the N required to achieve a desired PE calculation precision. Application of this theory to statistical inference is demonstrated in the case of an experimentally obtained noise series, where the probability of obtaining the observed PE value was calculated assuming a white-noise time series. Standard statistical inference can be used to draw conclusions whether the white-noise null hypothesis can be accepted or rejected. This methodology can be applied to other null hypotheses, such as discriminating whether two time series are generated from different complex system states.

关键词： Noise patterns in complex systems Stochastic analysis Time series analysis

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