58,828 research outputs found
DG Affinity of DQ-modules
In this paper, we prove the dg affinity of formal deformation algebroid
stacks over complex smooth algebraic varieties. For that purpose, we introduce
the triangulated category of formal deformation modules which are
cohomologically complete and whose associated graded module is quasi-coherent.Comment: 21 pages, references adde
Tempered subanalytic topology on algebraic varieties
On a smooth algebraic variety over , we build the tempered
subanalytic and Stein tempered subanalytic sites. We construct the sheaf of
holomorphic functions tempered at infinity over these sites and study their
relations with the sheaf of regular functions, proving in particular that these
sheaves are isomorphic on Zariski open subsets. We show that these data allow
to define the functors of tempered and Stein tempered analytifications. We
study the relations between these two functors and the usual analytification
functor. We also obtain algebraization results in the non-proper case and
flatness results.Comment: 24 pages. Preliminary version. Comments are welcom
The Codimension-Three conjecture for holonomic DQ-modules
We prove an analogue for holonomic DQ-modules of the codimension-three
conjecture for microdifferential modules recently proved by Kashiwara and
Vilonen. Our result states that any holonomic DQ-module having a lattice
extends uniquely beyond an analytic subset of codimension equal to or larger
than three in a Lagrangian subvariety containing the support of the DQ-module.Comment: 37 pages, several minor correction
Harmonic functions on hyperbolic graphs
We consider admissible random walks on hyperbolic graphs. For a given
harmonic function on such a graph, we prove that asymptotic properties of
non-tangential boundedness and non-tangential convergence are almost everywhere
equivalent. The proof is inspired by the works of F. Mouton in the cases of
Riemannian manifolds of pinched negative curvature and infinite trees. It
involves geometric and probabilitistic methods.Comment: 14 page
A Riemann-Roch Theorem for dg Algebras
Given a smooth proper dg-algebra , a perfect dg -module , and an
endomorphism of , we define the Hochschild class of the pair
with values in the Hochschild homology of . Our main result is a
Riemann-Roch type formula involving the convolution of two such Hochschild
classes.Comment: 26 pages. Many change
Hamiltonian cycles in faulty random geometric networks
In this paper we analyze the Hamiltonian properties of
faulty random networks.
This consideration is of interest when considering wireless
broadcast networks.
A random geometric network is a graph whose vertices
correspond to points
uniformly and independently distributed in the unit square,
and whose edges
connect any pair of vertices if their distance is below some
specified bound.
A faulty random geometric network is a random geometric
network whose vertices
or edges fail at random. Algorithms to find Hamiltonian
cycles in faulty random
geometric networks are presented.Postprint (published version
Combining spectral sequencing and parallel simulated annealing for the MinLA problem
In this paper we present and analyze new sequential and parallel
heuristics to approximate the Minimum Linear Arrangement problem
(MinLA). The heuristics consist in obtaining a first global solution
using Spectral Sequencing and improving it locally through Simulated
Annealing. In order to accelerate the annealing process, we present a
special neighborhood distribution that tends to favor moves with high
probability to be accepted. We show how to make use of this
neighborhood to parallelize the Metropolis stage on distributed memory
machines by mapping partitions of the input graph to processors and
performing moves concurrently. The paper reports the results obtained
with this new heuristic when applied to a set of large graphs,
including graphs arising from finite elements methods and graphs
arising from VLSI applications. Compared to other heuristics, the
measurements obtained show that the new heuristic improves the
solution quality, decreases the running time and offers an excellent
speedup when ran on a commodity network made of nine personal
computers.Postprint (published version
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