#### Filter Results:

#### Publication Year

2000

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

We propose a method of community detection that is computationally inexpensive and possesses physical significance to a member of a social network. This method is unlike many divisive and agglomerative techniques and is local in the sense that a community can be detected within a network without requiring knowledge of the entire network. A global… (More)

In previous work [J. empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will… (More)

— We consider image denoising as the problem of removing spurious oscillations due to noise while preserving edges in the images. We will suggest here how to directly make infinitesimal adjustment to standard variational methods of image denoising, to enhance desirable target assumption of the noiseless image. The standard regularization method is used to… (More)

— We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted… (More)

We consider systems that are well modelled as networks that evolve in time, which we call Moving Neighborhood Networks. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent interactions arise from ad hoc networks. In a natural way, the time-averaged degree distribution gives rise to a scale-free network.… (More)

- Erik M Bollt, Joseph D Skufca, Stephen J McGregor
- Mathematical biosciences and engineering : MBE
- 2009

We propose an entropy statistic designed to assess the behavior of slowly varying parameters of real systems. Based on correlation entropy, the method uses symbol dynamics and analysis of increments to achieve sufficient recurrence in a short time series to enable entropy measurements on small data sets. We analyze entropy along a moving window of a time… (More)

- Jie Sun, Erik M Bollt, Mason A Porter, Marian S Dawkins
- 2010

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynam-ical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow " oscillators " together to… (More)

This paper is meant to serve as a tutorial describing the link between symbolic dynamics as a description of a chaotic attractor, and how to use control of chaos to manipulate the corresponding symbolic dynamics to transmit an information bearing signal. We use the Lorenz attractor, in the form of the discrete successive maxima map of the z-variable… (More)

an oil well cap explosion below the Deepwater Horizon, an offshore oil rig in the Gulf of Mexico, started the worst human-caused submarine oil spill ever. Though an historic tragedy for the marine ecosystem, the unprecedented monitoring of the spill in real time by satellites and increased modeling of the natural oceanic flows has provided a wealth of data,… (More)