Synchronization is optimal in non-diagonalizable networks

We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks of maximum synchronizability are necessarily non-diagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The extension makes the formalism applicable to all possible network structures, while the maximization results provide insights into hierarchical structures observed in complex networks in which synchronization plays a significant role.Comment: 4 pages, 1 figure; minor revisio

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.Comment: Four pages, four figures. Submitted to PR

Dynamic Computation of Network Statistics via Updating Schema

In this paper we derive an updating scheme for calculating some important network statistics such as degree, clustering coefficient, etc., aiming at reduce the amount of computation needed to track the evolving behavior of large networks; and more importantly, to provide efficient methods for potential use of modeling the evolution of networks. Using the updating scheme, the network statistics can be computed and updated easily and much faster than re-calculating each time for large evolving networks. The update formula can also be used to determine which edge/node will lead to the extremal change of network statistics, providing a way of predicting or designing evolution rule of networks.Comment: 17 pages, 6 figure

Mobility induces global synchronization of oscillators in periodic extended systems

We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which display local order. We use a statistical description valid for a large number of oscillators to show that for any finite system there is a critical spatial diffusion above which all wave-like solutions become unstable. Through Langevin simulations, we show that the transition to global synchronization is mediated by the relative size of attractor basins associated to wave-like states. Spatial diffusion disrupts these states and paves the way for the system to attain global synchronization

Portraits of Complex Networks

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure

Categorizing and comparing psychophysical detection strategies based on biomechanical responses to short postural perturbations

<p>Abstract</p> <p>Background</p> <p>A fundamental unsolved problem in psychophysical detection experiments is in discriminating guesses from the correct responses. This paper proposes a coherent solution to this problem by presenting a novel classification method that compares biomechanical and psychological responses.</p> <p>Methods</p> <p>Subjects (13) stood on a platform that was translated anteriorly 16 mm to find psychophysical detection thresholds through a Adaptive 2-Alternative-Forced-Choice (2AFC) task repeated over 30 separate sequential trials. Anterior-posterior center-of-pressure (APCoP) changes (i.e., the biomechanical response R_B) were analyzed to determine whether sufficient biomechanical information was available to support a subject's psychophysical selection (R_Ψ) of interval 1 or 2 as the stimulus interval. A time-series-bitmap approach was used to identify anomalies in interval 1 (a₁) and interval 2 (a₂) that were present in the resultant APCoP signal. If a₁> a₂then R_B= Interval 1. If a₁< a₂, then R_B= Interval 2. If a₂- a₁< 0.1, R_Bwas set to 0 (no significant difference present in the anomaly scores of interval 1 and 2).</p> <p>Results</p> <p>By considering both biomechanical (R_B) and psychophysical (R_Ψ) responses, each trial run could be classified as a: 1) HIT (and True Negative), if R_Band R_Ψboth matched the stimulus interval (SI); 2) MISS, if R_Bmatched SI but the subject's reported response did not; 3) PSUEDO HIT, if the subject signalled the correct SI, but R_Bwas linked to the non-SI; 4) FALSE POSITIVE, if R_B= R_Ψ, and both associated to non-SI; and 5) GUESS, if R_B= 0, if insufficient APCoP differences existed to distinguish SI. Ensemble averaging the data for each of the above categories amplified the anomalous behavior of the APCoP response.</p> <p>Conclusions</p> <p>The major contributions of this novel classification scheme were to define and verify by logistic models a 'GUESS' category in these psychophysical threshold detection experiments, and to add an additional descriptor, "PSEUDO HIT". This improved classification methodology potentially could be applied to psychophysical detection experiments of other sensory modalities.</p

Multi-agent Coordination in Directed Moving Neighborhood Random Networks

In this paper, we consider the consensus problem of dynamical multiple agents that communicate via a directed moving neighborhood random network. Each agent performs random walk on a weighted directed network. Agents interact with each other through random unidirectional information flow when they coincide in the underlying network at a given instant. For such a framework, we present sufficient conditions for almost sure asymptotic consensus. Some existed consensus schemes are shown to be reduced versions of the current model.Comment: 9 page