8,807 research outputs found
Projections of determinantal point processes
Let be a space filling-design of
points defined in . In computer experiments, an important property
seeked for is a nice coverage of . This property could
be desirable as well as for any projection of onto
for . Thus we expect that , which represents the design
with coordinates associated to any index set , remains
regular in where is the cardinality of . This paper
examines the conservation of nice coverage by projection using spatial point
processes, and more specifically using the class of determinantal point
processes. We provide necessary conditions on the kernel defining these
processes, ensuring that the projected point process is
repulsive, in the sense that its pair correlation function is uniformly bounded
by 1, for all . We present a few examples, compare
them using a new normalized version of Ripley's function. Finally, we
illustrate the interest of this research for Monte-Carlo integration
Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems
We propose a novel decomposition framework for the distributed optimization
of general nonconvex sum-utility functions arising naturally in the system
design of wireless multiuser interfering systems. Our main contributions are:
i) the development of the first class of (inexact) Jacobi best-response
algorithms with provable convergence, where all the users simultaneously and
iteratively solve a suitably convexified version of the original sum-utility
optimization problem; ii) the derivation of a general dynamic pricing mechanism
that provides a unified view of existing pricing schemes that are based,
instead, on heuristics; and iii) a framework that can be easily particularized
to well-known applications, giving rise to very efficient practical (Jacobi or
Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for
very specific problems. Interestingly, our framework contains as special cases
well-known gradient algorithms for nonconvex sum-utility problems, and many
blockcoordinate descent schemes for convex functions.Comment: submitted to IEEE Transactions on Signal Processin
Fast Distributed Approximation for Max-Cut
Finding a maximum cut is a fundamental task in many computational settings.
Surprisingly, it has been insufficiently studied in the classic distributed
settings, where vertices communicate by synchronously sending messages to their
neighbors according to the underlying graph, known as the or
models. We amend this by obtaining almost optimal
algorithms for Max-Cut on a wide class of graphs in these models. In
particular, for any , we develop randomized approximation
algorithms achieving a ratio of to the optimum for Max-Cut on
bipartite graphs in the model, and on general graphs in the
model.
We further present efficient deterministic algorithms, including a
-approximation for Max-Dicut in our models, thus improving the best known
(randomized) ratio of . Our algorithms make non-trivial use of the greedy
approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing
an unconstrained (non-monotone) submodular function, which may be of
independent interest
Application of The Method of Elastic Maps In Analysis of Genetic Texts
Abstract - Method of elastic maps ( http://cogprints.ecs.soton.ac.uk/archive/00003088/ and
http://cogprints.ecs.soton.ac.uk/archive/00003919/ )
allows us to construct efficiently 1D, 2D and 3D non-linear approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. We describe the idea of the method and demonstrate its applications in analysis of genetic sequences. The animated 3D-scatters are available on our web-site: http://www.ihes.fr/~zinovyev/7clusters/
We found the universal cluster structure of genetic sequences, and demonstrated the thin structure of these clusters for coding regions. This thin structure is related to different translational efficiency
Normal cycles and curvature measures of sets with d.c. boundary
We show that for every compact domain in a Euclidean space with d.c.
(delta-convex) boundary there exists a unique Legendrian cycle such that the
associated curvature measures fulfil a local version of the Gauss-Bonnet
formula. This was known in dimensions two and three and was open in higher
dimensions. In fact, we show this property for a larger class of sets including
also lower-dimensional sets. We also describe the local index function of the
Legendrian cycles and we show that the associated curvature measures fulfill
the Crofton formula.Comment: 22 pp, corrected versio
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