Theoretical mechanics: Crowd synchrony on the Millennium Bridge

Strogatz, Steven H.; Abrams, Daniel M.; McRobie, Allan; Eckhardt, Bruno; Ott, Edward

doi:10.1038/43843a

Cited by 143 publications

(131 citation statements)

References 3 publications

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“…This evolving nature of genomic order prompted us to use a mathematical framework to model the interrelated behaviors of gene regulation and chromosome association as a dynamical system. The cooperative phenomenon of mutual entrainment is well described by the classical Kuramoto model (4,(19)(20)(21), in which a collection of globally coupled phase oscillators exhibit a transition from incoherence to a coherent state as the coupling strength increases past a critical threshold. Therefore, the Kuramoto framework is an ideal mathematical model with which to demonstrate the organized behavior of the complex dynamical reorganization of the genome during differentiation.…”

Section: Resultsmentioning

confidence: 99%

The emergence of lineage-specific chromosomal topologies from coordinate gene regulation

Rajapakse

Perlman

Scalzo

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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Although the importance of chromosome organization during mitosis is clear, it remains to be determined whether the nucleus assumes other functionally relevant chromosomal topologies. We have previously shown that homologous chromosomes have a tendency to associate during hematopoiesis according to their distribution of coregulated genes, suggesting cell-specific nuclear organization. Here, using the mathematical approaches of distance matrices and coupled oscillators, we model the dynamic relationship between gene expression and chromosomal associations during the differentiation of a multipotential hematopoietic progenitor. Our analysis reveals dramatic changes in total genomic order: Commitment of the progenitor results in an initial increase in entropy at both the level of gene coregulation and chromosomal organization, which we suggest represents a phase transition, followed by a progressive decline in entropy during differentiation. The stabilization of a highly ordered state in the differentiated cell types results in lineage-specific chromosomal topologies and is related to the emergence of coherence-or self-organization-between chromosomal associations and coordinate gene regulation. We discuss how these observations may be generally relevant to cell fate decisions encountered by progenitor/stem cells. cellular differentiation ͉ chromosomal organization ͉ coregulated gene expression ͉ distance matrices ͉ networks

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Section: Resultsmentioning

confidence: 99%

The emergence of lineage-specific chromosomal topologies from coordinate gene regulation

Rajapakse

Perlman

Scalzo

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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“…1 and the previously listed applications (Bergen and Hill, 1981;Ermentrout, 1991;Chiang et al, 1995;Sauer and Pai, 1998;Wiesenfeld et al, 1998;Hoppensteadt and Izhikevich, 2000;Bennett et al, 2002;Pantaleone, 2002;Strogatz et al, 2005;Righetti and Ijspeert, 2006;Shim et al, 2007;Ha et al, 2010bKapitaniak et al, 2012;Zhang et al, 2012) the coupled oscillator dynamics are not exactly given by the first-order phase model (1). In many cases, the dynamics are of second order as in (9).…”

Section: Conclusion and Open Research Directionsmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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“…Various authors have proposed models of the pedestrian loading mechanism, based on the assumption that synchronization is the cause (Nakamura 2004;Newland 2004;Roberts 2005a,b;Strogatz et al 2005;Eckhardt et al 2007). Often these models have free parameters that are chosen to fit the data.…”

Section: K2mentioning

confidence: 99%

Lateral excitation of bridges by balancing pedestrians

2008

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On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian-structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to 'pedestrian synchronous lateral excitation' or 'pedestrian lock-in'. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field-the inverted pendulum model-for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.

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Theoretical mechanics: Crowd synchrony on the Millennium Bridge

Cited by 143 publications

References 3 publications

The emergence of lineage-specific chromosomal topologies from coordinate gene regulation

The emergence of lineage-specific chromosomal topologies from coordinate gene regulation

Synchronization in complex networks of phase oscillators: A survey

Lateral excitation of bridges by balancing pedestrians

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