195,365 research outputs found
Smoothed Analysis of Dynamic Networks
We generalize the technique of smoothed analysis to distributed algorithms in
dynamic network models. Whereas standard smoothed analysis studies the impact
of small random perturbations of input values on algorithm performance metrics,
dynamic graph smoothed analysis studies the impact of random perturbations of
the underlying changing network graph topologies. Similar to the original
application of smoothed analysis, our goal is to study whether known strong
lower bounds in dynamic network models are robust or fragile: do they withstand
small (random) perturbations, or do such deviations push the graphs far enough
from a precise pathological instance to enable much better performance? Fragile
lower bounds are likely not relevant for real-world deployment, while robust
lower bounds represent a true difficulty caused by dynamic behavior. We apply
this technique to three standard dynamic network problems with known strong
worst-case lower bounds: random walks, flooding, and aggregation. We prove that
these bounds provide a spectrum of robustness when subjected to
smoothing---some are extremely fragile (random walks), some are moderately
fragile / robust (flooding), and some are extremely robust (aggregation).Comment: 20 page
Soft supersymmetry breaking in the nonlinear sigma model
In this work we discuss the dynamical generation of mass in a deformed supersymmetric nonlinear sigma model in a two-dimensional ()
space-time. We introduce the deformation by imposing a constraint that softly
breaks supersymmetry. Through the tadpole method, we compute the effective
potential at leading order in expansion showing that the model exhibit a
dynamical generation of mass to the matter fields. Supersymmetry is recovered
in the limit of the deformation parameter going to zero.Comment: 9 pages, 2 figures. Revised version. arXiv admin note: text overlap
with arXiv:1308.471
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