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Collective dynamics of ‘small-world’ networks
TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. Expand
Random graphs with arbitrary degree distributions and their applications.
TLDR
It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph. Expand
Exploring complex networks
TLDR
This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture. Expand
Nonlinear Dynamics And Chaos
TLDR
The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered. Expand
Synchronization of pulse-coupled biological oscillators
A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker (Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences,Expand
From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certainExpand
Random graph models of social networks
TLDR
It is found that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph. Expand
Network robustness and fragility: percolation on random graphs.
TLDR
This paper studies percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolators, bond percolations, and models in which occupation probabilities depend on vertex degree. Expand
Quantifying the benefits of vehicle pooling with shareability networks
TLDR
The notion of shareability network is introduced, which allows to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets, and demonstrates the feasibility of a shareable taxi service in New York City. Expand
Linguistics: Modelling the dynamics of language death
TLDR
A simple model of language competition is developed that explains historical data on the decline of Welsh, Scottish Gaelic, Quechua, and other endangered languages and a linguistic parameter that quantifies the threat of language extinction can be derived. Expand
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