82,725 research outputs found
Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs
We show that superreflexivity can be characterized in terms of bilipschitz
embeddability of word hyperbolic groups. We compare characterizations of
superreflexivity in terms of diamond graphs and binary trees. We show that
there exist sequences of series-parallel graphs of increasing topological
complexity which admit uniformly bilipschitz embeddings into a Hilbert space,
and thus do not characterize superreflexivity
Uniform random sampling of planar graphs in linear time
This article introduces new algorithms for the uniform random generation of
labelled planar graphs. Its principles rely on Boltzmann samplers, as recently
developed by Duchon, Flajolet, Louchard, and Schaeffer. It combines the
Boltzmann framework, a suitable use of rejection, a new combinatorial bijection
found by Fusy, Poulalhon and Schaeffer, as well as a precise analytic
description of the generating functions counting planar graphs, which was
recently obtained by Gim\'enez and Noy. This gives rise to an extremely
efficient algorithm for the random generation of planar graphs. There is a
preprocessing step of some fixed small cost. Then, the expected time complexity
of generation is quadratic for exact-size uniform sampling and linear for
approximate-size sampling. This greatly improves on the best previously known
time complexity for exact-size uniform sampling of planar graphs with
vertices, which was a little over .Comment: 55 page
Exploiting parallelism in coalgebraic logic programming
We present a parallel implementation of Coalgebraic Logic Programming (CoALP)
in the programming language Go. CoALP was initially introduced to reflect
coalgebraic semantics of logic programming, with coalgebraic derivation
algorithm featuring both corecursion and parallelism. Here, we discuss how the
coalgebraic semantics influenced our parallel implementation of logic
programming
Hardware-based Security for Virtual Trusted Platform Modules
Virtual Trusted Platform modules (TPMs) were proposed as a software-based
alternative to the hardware-based TPMs to allow the use of their cryptographic
functionalities in scenarios where multiple TPMs are required in a single
platform, such as in virtualized environments. However, virtualizing TPMs,
especially virutalizing the Platform Configuration Registers (PCRs), strikes
against one of the core principles of Trusted Computing, namely the need for a
hardware-based root of trust. In this paper we show how strength of
hardware-based security can be gained in virtual PCRs by binding them to their
corresponding hardware PCRs. We propose two approaches for such a binding. For
this purpose, the first variant uses binary hash trees, whereas the other
variant uses incremental hashing. In addition, we present an FPGA-based
implementation of both variants and evaluate their performance
Dynamic load balancing in parallel KD-tree k-means
One among the most influential and popular data mining methods is the k-Means algorithm for cluster analysis.
Techniques for improving the efficiency of k-Means have been
largely explored in two main directions. The amount of computation can be significantly reduced by adopting geometrical constraints and an efficient data structure, notably a multidimensional binary search tree (KD-Tree). These techniques allow to reduce the number of distance computations the algorithm performs at each iteration. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient k-Means variants in parallel computing environments. In this work, we provide a parallel formulation of the KD-Tree based k-Means algorithm for distributed memory systems and address its load balancing
issue. Three solutions have been developed and tested. Two
approaches are based on a static partitioning of the data set and a third solution incorporates a dynamic load balancing policy
Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model
Given a 3D binary digital image I, we define and compute
an edge-weighted tree, called Homological Region Tree (or Hom-Tree,
for short). It coincides, as unweighted graph, with the classical Region
Adjacency Tree of black 6-connected components (CCs) and white 26-
connected components of I. In addition, we define the weight of an edge
(R, S) as the number of tunnels that the CCs R and S “share”. The
Hom-Tree structure is still an isotopic invariant of I. Thus, it provides
information about how the different homology groups interact between
them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different
shapes and different complexity of connected component nesting is performed
for numerically validating the method.Ministerio de Economía y Competitividad MTM2016-81030-
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