2,399 research outputs found
Network Structure, Topology and Dynamics in Generalized Models of Synchronization
We explore the interplay of network structure, topology, and dynamic
interactions between nodes using the paradigm of distributed synchronization in
a network of coupled oscillators. As the network evolves to a global steady
state, interconnected oscillators synchronize in stages, revealing network's
underlying community structure. Traditional models of synchronization assume
that interactions between nodes are mediated by a conservative process, such as
diffusion. However, social and biological processes are often non-conservative.
We propose a new model of synchronization in a network of oscillators coupled
via non-conservative processes. We study dynamics of synchronization of a
synthetic and real-world networks and show that different synchronization
models reveal different structures within the same network
The Lie-Poisson structure of the reduced n-body problem
The classical n-body problem in d-dimensional space is invariant under the
Galilean symmetry group. We reduce by this symmetry group using the method of
polynomial invariants. As a result we obtain a reduced system with a
Lie-Poisson structure which is isomorphic to sp(2n-2), independently of d. The
reduction preserves the natural form of the Hamiltonian as a sum of kinetic
energy that depends on velocities only and a potential that depends on
positions only. Hence we proceed to construct a Poisson integrator for the
reduced n-body problem using a splitting method.Comment: 26 pages, 2 figure
A Parameterized Centrality Metric for Network Analysis
A variety of metrics have been proposed to measure the relative importance of
nodes in a network. One of these, alpha-centrality [Bonacich, 2001], measures
the number of attenuated paths that exist between nodes. We introduce a
normalized version of this metric and use it to study network structure,
specifically, to rank nodes and find community structure of the network.
Specifically, we extend the modularity-maximization method [Newman and Girvan,
2004] for community detection to use this metric as the measure of node
connectivity. Normalized alpha-centrality is a powerful tool for network
analysis, since it contains a tunable parameter that sets the length scale of
interactions. By studying how rankings and discovered communities change when
this parameter is varied allows us to identify locally and globally important
nodes and structures. We apply the proposed method to several benchmark
networks and show that it leads to better insight into network structure than
alternative methods.Comment: 11 pages, submitted to Physical Review
Towards a Formal Verification Methodology for Collective Robotic Systems
We introduce a UML-based notation for graphically modeling
systemsā security aspects in a simple and intuitive
way and a model-driven process that transforms graphical
specifications of access control policies in XACML. These
XACML policies are then translated in FACPL, a policy
language with a formal semantics, and the resulting policies
are evaluated by means of a Java-based software tool
Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures
Results of numerical simulations of a recently derived most general
dissipative-dispersive PDE describing evolution of a film flowing down an
inclined plane are presented. They indicate that a novel complex type of
spatiotemporal patterns can exist for strange attractors of nonequilibrium
systems. It is suggested that real-life experiments satisfying the validity
conditions of the theory are possible: the required sufficiently viscous
liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations
available upon or reques
Point vortices on the sphere: a case with opposite vorticities
We study systems formed of 2N point vortices on a sphere with N vortices of
strength +1 and N vortices of strength -1. In this case, the Hamiltonian is
conserved by the symmetry which exchanges the positive vortices with the
negative vortices. We prove the existence of some fixed and relative
equilibria, and then study their stability with the ``Energy Momentum Method''.
Most of the results obtained are nonlinear stability results. To end, some
bifurcations are described.Comment: 35 pages, 9 figure
Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows
When an integrable two-degrees-of-freedom Hamiltonian system possessing a
circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It
is proved that its occurrence is generic for one parameter families
(co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical
experiments indicate that the motion near a parabolic resonance exhibits new
type of chaotic behavior which includes instabilities in some directions and
long trapping times in others. Moreover, in a degenerate case, near a {\it flat
parabolic resonance}, large scale instabilities appear. A model arising from an
atmospherical study is shown to exhibit flat parabolic resonance. This supplies
a simple mechanism for the transport of particles with {\it small} (i.e.
atmospherically relevant) initial velocities from the vicinity of the equator
to high latitudes. A modification of the model which allows the development of
atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities
are clearly observed
A new method for tracking of motor skill learning through practical application of Fittsā law
This article is made available through the Brunel Open Access Publishing Fund.A novel upper limb motor skill measure, task productivity rate (TPR) was developed integrating speed and spatial error, delivered by a practical motor skill rehabilitation task (MSRT). This prototype task involved placement of 5 short pegs horizontally on a spatially configured rail array. The stability of TPR was tested on 18 healthy right-handed adults (10 women, 8 men, median age 29 years) in a prospective single-session quantitative within-subjects study design. Manipulations of movement rate 10% faster and slower relative to normative states did not significantly affect TPR, F(1.387, 25.009) = 2.465, p = .121. A significant linear association between completion time and error was highest during the normative state condition (Pearson's r = .455, p < .05). Findings provided evidence that improvements in TPR over time reflected motor learning with possible changes in coregulation behavior underlying practice under different conditions. These findings extend Fittsā law theory to tracking of practical motor skill using a dexterity task, which could have potential clinical applications in rehabilitation
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