Network Structure Revealed by Short Cycles (2006)
Bagrow, James, Bollt, Erik, Costa, Luciano Da F.
This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked...
Basis Markov Partitions and Transition Matrices for Stochastic Systems (2006)
Bollt, Erik, Gora, Pawel, Ostruszka, Andrzej, Zyczkowski, Karol
We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition...
A Fast and Accurate Nonlinear Spectral Method for Image Recognition and Registration (2006)
Costa, Luciano Da Fontoura, Bollt, Erik
This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration....
Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies (2005)
Stilwell, Daniel, Bollt, Erik, Roberson, D. Gray
In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an...
A gradient descent solution to the Monge-Kantorovich problem (2005)
R. Chartr, K. Vixie, B. Wohlberg, Erik Bollt
We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem...
A Local Method for Detecting Communities (2004)
We propose a novel 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...