5,735 research outputs found
Preconditioning of Improved and ``Perfect'' Fermion Actions
We construct a locally-lexicographic SSOR preconditioner to accelerate the
parallel iterative solution of linear systems of equations for two improved
discretizations of lattice fermions: the Sheikholeslami-Wohlert scheme where a
non-constant block-diagonal term is added to the Wilson fermion matrix and
renormalization group improved actions which incorporate couplings beyond
nearest neighbors of the lattice fermion fields. In case (i) we find the block
llssor-scheme to be more effective by a factor about 2 than odd-even
preconditioned solvers in terms of convergence rates, at beta=6.0. For type
(ii) actions, we show that our preconditioner accelerates the iterative
solution of a linear system of hypercube fermions by a factor of 3 to 4.Comment: 27 pages, Latex, 17 Figures include
Clustering student skill set profiles in a unit hypercube using mixtures of multivariate betas
<br>This paper presents a finite mixture of multivariate betas as a new model-based clustering method tailored to applications where the feature space is constrained to the unit hypercube. The mixture component densities are taken to be conditionally independent, univariate unimodal beta densities (from the subclass of reparameterized beta densities given by Bagnato and Punzo 2013). The EM algorithm used to fit this mixture is discussed in detail, and results from both this beta mixture model and the more standard Gaussian model-based clustering are presented for simulated skill mastery data from a common cognitive diagnosis model and for real data from the Assistment System online mathematics tutor (Feng et al 2009). The multivariate beta mixture appears to outperform the standard Gaussian model-based clustering approach, as would be expected on the constrained space. Fewer components are selected (by BIC-ICL) in the beta mixture than in the Gaussian mixture, and the resulting clusters seem more reasonable and interpretable.</br>
<br>This article is in technical report form, the final publication is available at http://www.springerlink.com/openurl.asp?genre=article &id=doi:10.1007/s11634-013-0149-z</br>
Distance-Dependent Kronecker Graphs for Modeling Social Networks
This paper focuses on a generalization of stochastic
Kronecker graphs, introducing a Kronecker-like operator and
defining a family of generator matrices H dependent on distances
between nodes in a specified graph embedding. We prove
that any lattice-based network model with sufficiently small
distance-dependent connection probability will have a Poisson
degree distribution and provide a general framework to prove
searchability for such a network. Using this framework, we focus
on a specific example of an expanding hypercube and discuss
the similarities and differences of such a model with recently
proposed network models based on a hidden metric space. We
also prove that a greedy forwarding algorithm can find very short
paths of length O((log log n)^2) on the hypercube with n nodes,
demonstrating that distance-dependent Kronecker graphs can
generate searchable network models
SSOR Preconditioning of Improved Actions
We generalize local lexicographic SSOR preconditioning for the
Sheikholeslami-Wohlert improved Wilson fermion action and the truncated perfect
free fermion action. In our test implementation we achieve performance gains as
known from SSOR preconditioning of the standard Wilson fermion action.Comment: 3 pages, Latex, 3 figures, Talk presented at Lattice'9
Construction of nested space-filling designs
New types of designs called nested space-filling designs have been proposed
for conducting multiple computer experiments with different levels of accuracy.
In this article, we develop several approaches to constructing such designs.
The development of these methods also leads to the introduction of several new
discrete mathematics concepts, including nested orthogonal arrays and nested
difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Generalizing Kronecker graphs in order to model searchable networks
This paper describes an extension to stochastic
Kronecker graphs that provides the special structure required
for searchability, by defining a “distance”-dependent Kronecker
operator. We show how this extension of Kronecker graphs
can generate several existing social network models, such as
the Watts-Strogatz small-world model and Kleinberg’s latticebased
model. We focus on a specific example of an expanding
hypercube, reminiscent of recently proposed social network
models based on a hidden hyperbolic metric space, and prove
that a greedy forwarding algorithm can find very short paths
of length O((log log n)^2) for graphs with n nodes
The A-like matrices for a hypercube
Let denote a positive integer and let denote the graph of the
-dimensional hypercube. Let denote the vertex set of and let A
\in \MX denote the adjacency matrix of . A matrix B \in \MX is called
-{\em like} whenever both (i) ; (ii) for all that are
not equal or adjacent, the -entry of is zero. Let \Al denote the
subspace of \MX consisting of the -like elements. We decompose \Al into
the direct sum of its symmetric part and antisymmetric part. We give a basis
for each part. The dimensions of the symmetric part and antisymmetric part are
and , respectively
Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes
Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First we prove that the folded hypercube is optimal in the sense that only a single wildcard dimension can be added to the hypercube. We then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes we construct d-dimensional meshes and tori with wildcard dimensions. Finally, we show how these constructions can be used to tolerate edge and node faults in mesh and torus networks
Application of Permutation Group Theory in Reversible Logic Synthesis
The paper discusses various applications of permutation group theory in the
synthesis of reversible logic circuits consisting of Toffoli gates with
negative control lines. An asymptotically optimal synthesis algorithm for
circuits consisting of gates from the NCT library is described. An algorithm
for gate complexity reduction, based on equivalent replacements of gates
compositions, is introduced. A new approach for combining a group-theory-based
synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is
described. Experimental results are presented to show that the proposed
synthesis techniques allow a reduction in input lines count, gate complexity or
quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016
conferenc
Quantum switching networks for perfect qubit routing
We develop the work of Christandl et al. [M. Christandl, N. Datta, T. C.
Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Phys. Rev. A 71, 032312 (2005)],
to show how a d-hypercube homogenous network can be dressed by additional links
to perfectly route quantum information between any given input and output nodes
in a duration which is independent of the routing chosen and, surprisingly,
size of the network
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