93 research outputs found
Plastic-scintillator based PET detector for proton beam therapy range monitoring : preliminary study
Near-optimum universal graphs for graphs with bounded degrees (Extended abstract)
Let H be a family of graphs. We say that G is H-universal if, for each H ∈H, the graph G contains a subgraph isomorphic to H. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For each fixed k and each n sufficiently large, we explicitly construct an H(k, n)-universal graph Γ(k, n) with O(n2−2/k(log n)1+8/k) edges. This is optimal up to a small polylogarithmic factor, as Ω(n2−2/k) is a lower bound for the number of edges in any such graph. En route, we use the probabilistic method in a rather unusual way. After presenting a deterministic construction of the graph Γ(k, n), we prove, using a probabilistic argument, that Γ(k, n) is H(k, n)-universal. So we use the probabilistic method to prove that an explicit construction satisfies certain properties, rather than showing the existence of a construction that satisfies these properties. © Springer-Verlag Berlin Heidelberg 200
The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization
Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to (Formula presented.) islands optimizing the so-called Maze fitness function (Kötzing and Molter in Proceedings of parallel problem solving from nature (PPSN XII), Springer, Berlin, pp 113–122, 2012). Previous work has shown that when a complete migration topology is used, migration must not occur too frequently, nor too soon before the optimum changes, to track the optimum of the Maze function. We show that using a sparse migration topology alleviates these restrictions. More specifically, we prove that there exist choices of model parameters for which using a unidirectional ring of logarithmic diameter as the migration topology allows the model to track the oscillating optimum through nMaze-like phases with high probability, while using any graph of diameter less than (Formula presented.) for some sufficiently small constant (Formula presented.) results in the island model losing track of the optimum with overwhelming probability. Experimentally, we show that very frequent migration on a ring topology is not an effective diversity mechanism, while a lower migration rate allows the ring topology to track the optimum for a wider range of oscillation patterns. When migration occurs only rarely, we prove that dense migration topologies of small diameter may be advantageous. Combined, our results show that the sparse migration topology is able to track the optimum through a wider range of oscillation patterns, and cope with a wider range of migration frequencies
Neutral H density at the termination shock: a consolidation of recent results
We discuss a consolidation of determinations of the density of neutral
interstellar H at the nose of the termination shock carried out with the use of
various data sets, techniques, and modeling approaches. In particular, we focus
on the determination of this density based on observations of H pickup ions on
Ulysses during its aphelion passage through the ecliptic plane. We discuss in
greater detail a novel method of determination of the density from these
measurements and review the results from its application to actual data. The H
density at TS derived from this analysis is equal to 0.087 \pm 0.022 cm-3, and
when all relevant determinations are taken into account, the consolidated
density is obtained at 0.09 \pm 0.022 cm-3. The density of H in CHISM based on
literature values of filtration factor is then calculated at 0.16 \pm 0.04
cm-3.Comment: Submitted to Space Science Review
Ring Migration Topology Helps Bypassing Local Optima
Running several evolutionary algorithms in parallel and occasionally
exchanging good solutions is referred to as island models. The idea is that the
independence of the different islands leads to diversity, thus possibly
exploring the search space better. Many theoretical analyses so far have found
a complete (or sufficiently quickly expanding) topology as underlying migration
graph most efficient for optimization, even though a quick dissemination of
individuals leads to a loss of diversity. We suggest a simple fitness function
FORK with two local optima parametrized by and a scheme for
composite fitness functions. We show that, while the (1+1) EA gets stuck in a
bad local optimum and incurs a run time of fitness evaluations
on FORK, island models with a complete topology can achieve a run time of
by making use of rare migrations in order to explore the
search space more effectively. Finally, the ring topology, making use of rare
migrations and a large diameter, can achieve a run time of
, the black box complexity of FORK. This shows that the
ring topology can be preferable over the complete topology in order to maintain
diversity.Comment: 12 page
The early evolution of the H-free process
The H-free process, for some fixed graph H, is the random graph process
defined by starting with an empty graph on n vertices and then adding edges one
at a time, chosen uniformly at random subject to the constraint that no H
subgraph is formed. Let G be the random maximal H-free graph obtained at the
end of the process. When H is strictly 2-balanced, we show that for some c>0,
with high probability as , the minimum degree in G is at least
. This gives new lower bounds for
the Tur\'an numbers of certain bipartite graphs, such as the complete bipartite
graphs with . When H is a complete graph with we show that for some C>0, with high probability the independence number of
G is at most . This gives new lower bounds
for Ramsey numbers R(s,t) for fixed and t large. We also obtain new
bounds for the independence number of G for other graphs H, including the case
when H is a cycle. Our proofs use the differential equations method for random
graph processes to analyse the evolution of the process, and give further
information about the structure of the graphs obtained, including asymptotic
formulae for a broad class of subgraph extension variables.Comment: 36 page
Moderate deviations via cumulants
The purpose of the present paper is to establish moderate deviation
principles for a rather general class of random variables fulfilling certain
bounds of the cumulants. We apply a celebrated lemma of the theory of large
deviations probabilities due to Rudzkis, Saulis and Statulevicius. The examples
of random objects we treat include dependency graphs, subgraph-counting
statistics in Erd\H{o}s-R\'enyi random graphs and -statistics. Moreover, we
prove moderate deviation principles for certain statistics appearing in random
matrix theory, namely characteristic polynomials of random unitary matrices as
well as the number of particles in a growing box of random determinantal point
processes like the number of eigenvalues in the GUE or the number of points in
Airy, Bessel, and random point fields.Comment: 24 page
A model of AW UMa
The contact binary AW UMa has an extreme mass ratio, with the more massive
component (the current primary) close to the main sequence, while the low mass
star at q ~ 0.1 (the current secondary) has a much larger radius than a main
sequence star of a comparable mass. We propose that the current secondary has
almost exhausted hydrogen in its center and is much more advanced in its
evolution, as suggested by Stepien. Presumably the current secondary lost most
of its mass during its evolution with part of it transferred to the current
primary. After losing a large fraction of its angular momentum, the binary may
evolve into a system of FK Com type.Comment: 5 pages, 6 figures, Accepted to MNRAS, content change
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