19,878 research outputs found
Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework
While many existing formal concept analysis algorithms are efficient, they
are typically unsuitable for distributed implementation. Taking the MapReduce
(MR) framework as our inspiration we introduce a distributed approach for
performing formal concept mining. Our method has its novelty in that we use a
light-weight MapReduce runtime called Twister which is better suited to
iterative algorithms than recent distributed approaches. First, we describe the
theoretical foundations underpinning our distributed formal concept analysis
approach. Second, we provide a representative exemplar of how a classic
centralized algorithm can be implemented in a distributed fashion using our
methodology: we modify Ganter's classic algorithm by introducing a family of
MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the
algorithm's lineage. To evaluate the factors that impact distributed algorithm
performance, we compare our MR* algorithms with the state-of-the-art.
Experiments conducted on real datasets demonstrate that MRGanter+ is efficient,
scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201
Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm
In this paper, we study an efficient algorithm for constructing node sets of
high-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh,
and Sobolev spaces. The algorithm presented is a reduced fast successive
coordinate search (SCS) algorithm, which is adapted to situations where the
weights in the function space show a sufficiently fast decay. The new SCS
algorithm is designed to work for the construction of lattice points, and, in a
modified version, for polynomial lattice points, and the corresponding
integration rules can be used to treat functions in different kinds of function
spaces. We show that the integration rules constructed by our algorithms
satisfy error bounds of optimal convergence order. Furthermore, we give details
on efficient implementation such that we obtain a considerable speed-up of
previously known SCS algorithms. This improvement is illustrated by numerical
results. The speed-up obtained by our results may be of particular interest in
the context of QMC for PDEs with random coefficients, where both the dimension
and the required numberof points are usually very large. Furthermore, our main
theorems yield previously unknown generalizations of earlier results.Comment: 33 pages, 2 figure
Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
We report on some recent developments in the search for optimal network
topologies. First we review some basic concepts on spectral graph theory,
including adjacency and Laplacian matrices, and paying special attention to the
topological implications of having large spectral gaps. We also introduce
related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we
discuss two different dynamical feautures of networks: synchronizability and
flow of random walkers and so that they are optimized if the corresponding
Laplacian matrix have a large spectral gap. From this, we show, by developing a
numerical optimization algorithm that maximum synchronizability and fast random
walk spreading are obtained for a particular type of extremely homogeneous
regular networks, with long loops and poor modular structure, that we call
entangled networks. These turn out to be related to Ramanujan and Cage graphs.
We argue also that these graphs are very good finite-size approximations to
Bethe lattices, and provide almost or almost optimal solutions to many other
problems as, for instance, searchability in the presence of congestion or
performance of neural networks. Finally, we study how these results are
modified when studying dynamical processes controlled by a normalized (weighted
and directed) dynamics; much more heterogeneous graphs are optimal in this
case. Finally, a critical discussion of the limitations and possible extensions
of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted
for pub. in JSTA
Quivers, Tilings, Branes and Rhombi
We describe a simple algorithm that computes the recently discovered brane
tilings for a given generic toric singular Calabi-Yau threefold. This therefore
gives AdS/CFT dual quiver gauge theories for D3-branes probing the given
non-compact manifold. The algorithm solves a longstanding problem by computing
superpotentials for these theories directly from the toric diagram of the
singularity. We study the parameter space of a-maximization; this study is made
possible by identifying the R-charges of bifundamental fields as angles in the
brane tiling. We also study Seiberg duality from a new perspective.Comment: 36 pages, 40 figures, JHEP
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