31,057 research outputs found
Upper Tail Estimates with Combinatorial Proofs
We study generalisations of a simple, combinatorial proof of a Chernoff bound
similar to the one by Impagliazzo and Kabanets (RANDOM, 2010).
In particular, we prove a randomized version of the hitting property of
expander random walks and apply it to obtain a concentration bound for expander
random walks which is essentially optimal for small deviations and a large
number of steps. At the same time, we present a simpler proof that still yields
a "right" bound settling a question asked by Impagliazzo and Kabanets.
Next, we obtain a simple upper tail bound for polynomials with input
variables in which are not necessarily independent, but obey a certain
condition inspired by Impagliazzo and Kabanets. The resulting bound is used by
Holenstein and Sinha (FOCS, 2012) in the proof of a lower bound for the number
of calls in a black-box construction of a pseudorandom generator from a one-way
function.
We then show that the same technique yields the upper tail bound for the
number of copies of a fixed graph in an Erd\H{o}s-R\'enyi random graph,
matching the one given by Janson, Oleszkiewicz and Ruci\'nski (Israel J. Math,
2002).Comment: Full version of the paper from STACS 201
Geometric Error of Finite Volume Schemes for Conservation Laws on Evolving Surfaces
This paper studies finite volume schemes for scalar hyperbolic conservation
laws on evolving hypersurfaces of . We compare theoretical
schemes assuming knowledge of all geometric quantities to (practical) schemes
defined on moving polyhedra approximating the surface. For the former schemes
error estimates have already been proven, but the implementation of such
schemes is not feasible for complex geometries. The latter schemes, in
contrast, only require (easily) computable geometric quantities and are thus
more useful for actual computations. We prove that the difference between
approximate solutions defined by the respective families of schemes is of the
order of the mesh width. In particular, the practical scheme converges to the
entropy solution with the same rate as the theoretical one. Numerical
experiments show that the proven order of convergence is optimal.Comment: 23 pages, 5 figures, to appear in Numerische Mathemati
What might the Soviet Union learn from the OECD countries in economics and politics ? An article from 1991 with some comments from 2005
When cleaning up my archives I came across a short article of April 1991 co-authored with Jan Tinbergen, on what the Soviet Union might learn from OECD countries in economics and politics. The article apparently never got published, partly since the Soviet Union collapsed in December 1991. Jan Tinbergen died in 1994. Reading the article again in 2005 shows that some arguments still have value. In 2005, an advice, purely my own now, would be that Russia and the other republics of the former Soviet Union apply for membership of the European Union.
Antiblockade in Rydberg excitation of an ultracold lattice gas
It is shown that the two-step excitation scheme typically used to create an
ultracold Rydberg gas can be described with an effective two-level rate
equation, greatly reducing the complexity of the optical Bloch equations. This
allows us to solve the many-body problem of interacting cold atoms with a Monte
Carlo technique. Our results reproduce the Rydberg blockade effect. However, we
demonstrate that an Autler-Townes double peak structure in the two-step
excitation scheme, which occurs for moderate pulse lengths as used in the
experiment, can give rise to an antiblockade effect. It is observable in a
lattice gas with regularly spaced atoms. Since the antiblockade effect is
robust against a large number of lattice defects it should be experimentally
realizable with an optical lattice created by CO lasers.Comment: 4 pages, 6 figure
Solving equations in the relational algebra
Enumerating all solutions of a relational algebra equation is a natural and
powerful operation which, when added as a query language primitive to the
nested relational algebra, yields a query language for nested relational
databases, equivalent to the well-known powerset algebra. We study
\emph{sparse} equations, which are equations with at most polynomially many
solutions. We look at their complexity, and compare their expressive power with
that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin
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