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- Mauricio Barahona, Louis M. Pecora
- Physical review letters
- 2002

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcutsâ€¦ (More)

- Ali Jadbabaie, John C. Doyle, +5 authors Luz E Vela
- 2000

With the advent of faster and cheaper computers, optimization based control methodologies have become a viable candidate for control of nonlinear systems. Over the past twenty years, a group of such control schemes have been successfully used in the process control industry where the processes are either intrinsically stable or have very large timeâ€¦ (More)

- Hannah H. Chang, Martin Hemberg, Mauricio Barahona, Donald E. Ingber, Sui Huang
- Nature
- 2008

Phenotypic cell-to-cell variability within clonal populations may be a manifestation of 'gene expression noise', or it may reflect stable phenotypic variants. Such 'non-genetic cell individuality' can arise from the slow fluctuations of protein levels in mammalian cells. These fluctuations produce persistent cell individuality, thereby rendering a clonalâ€¦ (More)

- Jean-Charles Delvenne, Sophia N. Yaliraki, Mauricio Barahona
- Proceedings of the National Academy of Sciencesâ€¦
- 2010

The complexity of biological, social, and engineering networks makes it desirable to find natural partitions into clusters (or communities) that can provide insight into the structure of the overall system and even act as simplified functional descriptions. Although methods for community detection abound, there is a lack of consensus on how to quantify andâ€¦ (More)

- Chi-Sang Poon, Mauricio Barahona
- Proceedings of the National Academy of Sciencesâ€¦
- 2001

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in manyâ€¦ (More)

- Renaud Lambiotte, J. - C. Delvenne, Mauricio Barahona
- 2009

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The timescale of the process acts as an intrinsic parameter that uncoversâ€¦ (More)

- Natalja Strelkowa, Mauricio Barahona
- Journal of the Royal Society, Interface
- 2010

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable,â€¦ (More)

- Jun Wu, Mauricio Barahona, Yuejin Tan, Hongzhong Deng
- IEEE Transactions on Systems, Man, andâ€¦
- 2011

We introduce the concept of natural connectivity as a measure of structural robustness in complex networks. The natural connectivity characterizes the redundancy of alternative routes in a network by quantifying the weighted number of closed walks of all lengths. This definition leads to a simple mathematical formulation that links the natural connectivityâ€¦ (More)

- Costas A. Anastassiou, Sean M. Montgomery, Mauricio Barahona, GyÃ¶rgy BuzsÃ¡ki, Christof Koch
- The Journal of neuroscience : the officialâ€¦
- 2010

The cooperative action of neurons and glia generates electrical fields, but their effect on individual neurons via ephaptic interactions is mostly unknown. Here, we analyze the impact of spatially inhomogeneous electric fields on the membrane potential, the induced membrane field, and the induced current source density of one-dimensional cables as well asâ€¦ (More)

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, therebyâ€¦ (More)