668 research outputs found
Relative periodic orbits in point vortex systems
We give a method to determine relative periodic orbits in point vortex
systems: it consists mainly into perform a symplectic reduction on a fixed
point submanifold in order to obtain a two-dimensional reduced phase space. The
method is applied to point vortices systems on a sphere and on the plane, but
works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method
permits also to determine some relative equilibria and heteroclinic cycles
connecting these relative equilibria.Comment: 27 pages, 17 figure
Bounds on the Sum Capacity of Synchronous Binary CDMA Channels
In this paper, we obtain a family of lower bounds for the sum capacity of
Code Division Multiple Access (CDMA) channels assuming binary inputs and binary
signature codes in the presence of additive noise with an arbitrary
distribution. The envelope of this family gives a relatively tight lower bound
in terms of the number of users, spreading gain and the noise distribution. The
derivation methods for the noiseless and the noisy channels are different but
when the noise variance goes to zero, the noisy channel bound approaches the
noiseless case. The behavior of the lower bound shows that for small noise
power, the number of users can be much more than the spreading gain without any
significant loss of information (overloaded CDMA). A conjectured upper bound is
also derived under the usual assumption that the users send out equally likely
binary bits in the presence of additive noise with an arbitrary distribution.
As the noise level increases, and/or, the ratio of the number of users and the
spreading gain increases, the conjectured upper bound approaches the lower
bound. We have also derived asymptotic limits of our bounds that can be
compared to a formula that Tanaka obtained using techniques from statistical
physics; his bound is close to that of our conjectured upper bound for large
scale systems.Comment: to be published in IEEE Transactions on Information Theor
Rain, power laws, and advection
Localized rain events have been found to follow power-law size and duration
distributions over several decades, suggesting parallels between precipitation
and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power
laws are generated by treating rain as a passive tracer undergoing advection in
a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure
Enhanced tracer transport by the spiral defect chaos state of a convecting fluid
To understand how spatiotemporal chaos may modify material transport, we use
direct numerical simulations of the three-dimensional Boussinesq equations and
of an advection-diffusion equation to study the transport of a passive tracer
by the spiral defect chaos state of a convecting fluid. The simulations show
that the transport is diffusive and is enhanced by the spatiotemporal chaos.
The enhancement in tracer diffusivity follows two regimes. For large Peclet
numbers (that is, small molecular diffusivities of the tracer), we find that
the enhancement is proportional to the Peclet number. For small Peclet numbers,
the enhancement is proportional to the square root of the Peclet number. We
explain the presence of these two regimes in terms of how the local transport
depends on the local wave numbers of the convection rolls. For large Peclet
numbers, we further find that defects cause the tracer diffusivity to be
enhanced locally in the direction orthogonal to the local wave vector but
suppressed in the direction of the local wave vector.Comment: 11 pages, 12 figure
Measuring Topological Chaos
The orbits of fluid particles in two dimensions effectively act as
topological obstacles to material lines. A spacetime plot of the orbits of such
particles can be regarded as a braid whose properties reflect the underlying
dynamics. For a chaotic flow, the braid generated by the motion of three or
more fluid particles is computed. A ``braiding exponent'' is then defined to
characterize the complexity of the braid. This exponent is proportional to the
usual Lyapunov exponent of the flow, associated with separation of nearby
trajectories. Measuring chaos in this manner has several advantages, especially
from the experimental viewpoint, since neither nearby trajectories nor
derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro
Visualizing Structural Balance in Signed Networks
Network visualization has established as a key complement to network analysis
since the large variety of existing network layouts are able to graphically
highlight different properties of networks. However, signed networks, i.e.,
networks whose edges are labeled as friendly (positive) or antagonistic
(negative), are target of few of such layouts and none, to our knowledge, is
able to show structural balance, i.e., the tendency of cycles towards including
an even number of negative edges, which is a well-known theory for studying
friction and polarization.
In this work we present Structural-balance-viz: a novel visualization method
showing whether a connected signed network is balanced or not and, in the
latter case, how close the network is to be balanced. Structural-balance-viz
exploits spectral computations of the signed Laplacian matrix to place
network's nodes in a Cartesian coordinate system resembling a balance (a
scale). Moreover, it uses edge coloring and bundling to distinguish positive
and negative interactions. The proposed visualization method has
characteristics desirable in a variety of network analysis tasks:
Structural-balance-viz is able to provide indications of balance/polarization
of the whole network and of each node, to identify two factions of nodes on the
basis of their polarization, and to show their cumulative characteristics.
Moreover, the layout is reproducible and easy to compare.
Structural-balance-viz is validated over synthetic-generated networks and
applied to a real-world dataset about political debates confirming that it is
able to provide meaningful interpretations
Detection and tracking of discrete phenomena in sensor-network databases
This paper introduces a framework for Phenomena Detection and Tracking (PDT, for short) in sensor network databases. Examples of detectable phenomena include the propagation over time of a pollution cloud or an oil spill region. We provide a crisp definition of a phenomenon that takes into consideration both the strength and the time span of the phenomenon.We focus on discrete phenomena where sensor readings are drawn from a discrete set of values, e.g., item numbers or pollutant IDs, and we point out how our work can be extended to handle continuous phenomena. The challenge for the proposed PDT framework is to detect as much phenomena as possible, given the large number of sensors, the overall high arrival rates of sensor data, and the limited system resources. Our proposed PDT framework uses continuous SQL queries to detect and track phenomena. Execution of these continuous queries is performed in three phases; the joining phase, the candidate selection phase, and the grouping/output phase. The joining phase employs an in-memory multi-way join algorithm that produces a set of sensor pairs with similar readings. The candidate selection phase filters the output of the joining phase to select candidate join pairs, with enough strength and time span, as specified by the phenomenon definition. The grouping/ output phase constructs the overall phenomenon from the candidate join pairs. We introduce two optimizations to increase the likelihood of phenomena detection while using less system resources. Experimental studies illustrate the performance gains of both the proposed PDT framework and the proposed optimizations
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