31 research outputs found
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
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<sub>B</sub>) were analyzed to determine whether sufficient biomechanical information was available to support a subject's psychophysical selection (R<sub>Ψ</sub>) of interval 1 or 2 as the stimulus interval. A time-series-bitmap approach was used to identify anomalies in interval 1 (a<sub>1</sub>) and interval 2 (a<sub>2</sub>) that were present in the resultant APCoP signal. If a<sub>1 </sub>> a<sub>2 </sub>then R<sub>B </sub>= Interval 1. If a<sub>1 </sub>< a<sub>2</sub>, then R<sub>B</sub>= Interval 2. If a<sub>2 </sub>- a<sub>1 </sub>< 0.1, R<sub>B </sub>was 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<sub>B</sub>) and psychophysical (R<sub>Ψ</sub>) responses, each trial run could be classified as a: 1) HIT (and True Negative), if R<sub>B </sub>and R<sub>Ψ </sub>both matched the stimulus interval (SI); 2) MISS, if R<sub>B </sub>matched SI but the subject's reported response did not; 3) PSUEDO HIT, if the subject signalled the correct SI, but R<sub>B </sub>was linked to the non-SI; 4) FALSE POSITIVE, if R<sub>B </sub>= R<sub>Ψ</sub>, and both associated to non-SI; and 5) GUESS, if R<sub>B </sub>= 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
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
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