1,896 research outputs found
Sparse Fault-Tolerant BFS Trees
This paper addresses the problem of designing a sparse {\em fault-tolerant}
BFS tree, or {\em FT-BFS tree} for short, namely, a sparse subgraph of the
given network such that subsequent to the failure of a single edge or
vertex, the surviving part of still contains a BFS spanning tree for
(the surviving part of) . Our main results are as follows. We present an
algorithm that for every -vertex graph and source node constructs a
(single edge failure) FT-BFS tree rooted at with O(n \cdot
\min\{\Depth(s), \sqrt{n}\}) edges, where \Depth(s) is the depth of the BFS
tree rooted at . This result is complemented by a matching lower bound,
showing that there exist -vertex graphs with a source node for which any
edge (or vertex) FT-BFS tree rooted at has edges. We then
consider {\em fault-tolerant multi-source BFS trees}, or {\em FT-MBFS trees}
for short, aiming to provide (following a failure) a BFS tree rooted at each
source for some subset of sources . Again, tight bounds
are provided, showing that there exists a poly-time algorithm that for every
-vertex graph and source set of size constructs a
(single failure) FT-MBFS tree from each source , with
edges, and on the other hand there exist
-vertex graphs with source sets of cardinality , on
which any FT-MBFS tree from has edges.
Finally, we propose an approximation algorithm for constructing
FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result
stating that there exists no approximation algorithm for these
problems under standard complexity assumptions
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
We develop a method for achieving scalable transmission stabilization and
switching of colliding soliton sequences in optical waveguides with
broadband delayed Raman response and narrowband nonlinear gain-loss. We show
that dynamics of soliton amplitudes in -sequence transmission is described
by a generalized -dimensional predator-prey model. Stability and bifurcation
analysis for the predator-prey model are used to obtain simple conditions on
the physical parameters for robust transmission stabilization as well as on-off
and off-on switching of out of soliton sequences. Numerical simulations
for single-waveguide transmission with a system of coupled nonlinear
Schr\"odinger equations with show excellent agreement with the
predator-prey model's predictions and stable propagation over significantly
larger distances compared with other broadband nonlinear single-waveguide
systems. Moreover, stable on-off and off-on switching of multiple soliton
sequences and stable multiple transmission switching events are demonstrated by
the simulations. We discuss the reasons for the robustness and scalability of
transmission stabilization and switching in waveguides with broadband delayed
Raman response and narrowband nonlinear gain-loss, and explain their advantages
compared with other broadband nonlinear waveguides.Comment: 37 pages, 7 figures, Eur. Phys. J. D (accepted
A Mean-field Approach for an Intercarrier Interference Canceller for OFDM
The similarity of the mathematical description of random-field spin systems
to orthogonal frequency-division multiplexing (OFDM) scheme for wireless
communication is exploited in an intercarrier-interference (ICI) canceller used
in the demodulation of OFDM. The translational symmetry in the Fourier domain
generically concentrates the major contribution of ICI from each subcarrier in
the subcarrier's neighborhood. This observation in conjunction with mean field
approach leads to a development of an ICI canceller whose necessary cost of
computation scales linearly with respect to the number of subcarriers. It is
also shown that the dynamics of the mean-field canceller are well captured by a
discrete map of a single macroscopic variable, without taking the spatial and
time correlations of estimated variables into account.Comment: 7pages, 3figure
Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford
A \emph{metric tree embedding} of expected \emph{stretch~}
maps a weighted -node graph to a weighted tree with such that, for all ,
and
. Such embeddings are highly useful for designing
fast approximation algorithms, as many hard problems are easy to solve on tree
instances. However, to date the best parallel -depth algorithm that achieves an asymptotically optimal expected stretch of
requires
work and a metric as input.
In this paper, we show how to achieve the same guarantees using
depth and
work, where and is an arbitrarily small constant.
Moreover, one may further reduce the work to at the expense of increasing the expected stretch to
.
Our main tool in deriving these parallel algorithms is an algebraic
characterization of a generalization of the classic Moore-Bellman-Ford
algorithm. We consider this framework, which subsumes a variety of previous
"Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss
it in depth. In our tree embedding algorithm, we leverage it for providing
efficient query access to an approximate metric that allows sampling the tree
using depth and work.
We illustrate the generality and versatility of our techniques by various
examples and a number of additional results
Simulations of the Angular Dependence of the Dipole-Dipole Interaction
In our project we ran computations on a supercomputer to simulate experiments performed on highly excited atoms at μK temperatures. At μK temperatures the atoms are moving slowly so there are essentially no collisions of the atoms on the time scales at which we perform our experiments. In the absence of collisions the atoms exchange energy through long range dipole-dipole interactions. This exchange depends on the distances between and relative orientation of the atoms. The angular dependence between two atoms has recently been studied experimentally1 . We simulate experimentally accessible spatial arrangements to see if the effect of the angular dependence can be measured in the many atom case. We present results that show that the angular dependence has a measurable effect on the time evolution of the spatial distribution of the energy in the system.
1. arXiv:1504.00301[physics.atom-ph
Simulations of the Angular Dependence of the Dipole-Dipole Interaction
In our project we ran computations on a supercomputer to simulate experiments performed on highly excited atoms at μK temperatures. At μK temperatures the atoms are moving slowly so there are essentially no collisions of the atoms on the time scales at which we perform our experiments. In the absence of collisions the atoms exchange energy through long range dipole-dipole interactions. This exchange depends on the distances between and relative orientation of the atoms. The angular dependence between two atoms has recently been studied experimentally1 . We simulate experimentally accessible spatial arrangements to see if the effect of the angular dependence can be measured in the many atom case. We present results that show that the angular dependence has a measurable effect on the time evolution of the spatial distribution of the energy in the system.
1. arXiv:1504.00301[physics.atom-ph
Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss
We investigate fast collisions between pulsed optical beams in a linear
medium with weak cubic loss that arises due to nondegenerate two-photon
absorption. We introduce a perturbation method with two small parameters and
use it to obtain general formulas for the collision-induced changes in the
pulsed-beam's shape and amplitude. Moreover, we use the method to design and
characterize collision setups that lead to strong localized and nonlocalized
intensity reduction effects. The values of the collision-induced changes in the
pulsed-beam's shape in both setups are larger by one to two orders of magnitude
compared with the values obtained in previous studies of fast two-pulse
collisions. Furthermore, we show that for nonlocalized setups, the graph of the
collision-induced amplitude shift vs the difference between the first-order
dispersion coefficients for the two pulsed-beams has two local minima. This
finding represents the first observation of a deviation of the graph from the
common funnel shape that was obtained in all previous studies of fast two-pulse
collisions in the presence of weak nonlinear loss. The predictions of our
perturbation theory are in good agreement with results of numerical simulations
with the perturbed linear propagation model, despite the strong
collision-induced effects. Our results can be useful for multisequence optical
communication links and for reshaping of pulsed optical beams.Comment: 44 pages, 12 figures. The paper contains a brief description of a
generalization of the perturbation approach that was introduced in
arXiv:2102.07438 for fast collisions between time independent optical beams.
The paper is devoted to an investigation of strong effects in fast collisions
between pulsed optical beams, whereas in arXiv:2102.07438, only weak
collision-induced effects for time-independent beams were considered
Simulations of the Angular Dependence of the Dipole-Dipole Interaction
We conducted simulations of Rydberg atoms in a magneto-optical trap using the supercomputer available on campus and the COMET supercomputer provided by the NSF. Our research focused on the angular dependence of the long range interaction between Rydberg atoms. We simulated randomly distributed atoms alligned with a magnetic and electric field. We compared the simulated interaction rates for different electric field directions
Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2
We investigate the dynamics of fast two-pulse collisions in linear
diffusion-advection systems with weak quadratic loss in spatial dimension 2. We
introduce a two-dimensional perturbation method, which generalizes the
perturbation method used for studying two-pulse collisions in spatial dimension
1. We then use the generalized perturbation method to show that a fast
collision in spatial dimension 2 leads to a change in the pulse shape in the
direction transverse to the advection velocity vector. Moreover, we show that
in the important case of a separable initial condition, the longitudinal part
in the expression for the amplitude shift has a simple universal form, while
the transverse part does not. Additionally, we show that anisotropy in the
initial condition leads to a complex dependence of the amplitude shift on the
orientation angle between the pulses. Our perturbation theory predictions are
in very good agreement with results of extensive numerical simulations with the
weakly perturbed diffusion-advection model. Thus, our study significantly
enhances and generalizes the results of previous works on fast collisions in
diffusion-advection systems, which were limited to spatial dimension 1.Comment: The paper presents a perturbation method for fast two-pulse
collisions in diffusion-advection systems with weak nonlinear loss in
dimension higher than 1. It generalizes the method that was used in
arXiv:1702.05583 and arXiv:1808.04323 for the 1-dimensional problem. It
complements the method that was presented in arXiv:2102.07438 for the
high-dimensional problem in weakly nonlinear optical medi
Prefect Klein tunneling in anisotropic graphene-like photonic lattices
We study the scattering of waves off a potential step in deformed honeycomb
lattices. For small deformations below a critical value, perfect Klein
tunneling is obtained. This means that a potential step in any direction
transmits waves at normal incidence with unit transmission probability,
irrespective of the details of the potential. Beyond the critical deformation,
a gap in the spectrum is formed, and a potential step in the deformation
direction reflects all normal-incidence waves, exhibiting a dramatic transition
form unit transmission to total reflection. These phenomena are generic to
honeycomb lattice systems, and apply to electromagnetic waves in photonic
lattices, quasi-particles in graphene, cold atoms in optical lattices
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