25,478 research outputs found
Parallel algorithms for two processors precedence constraint scheduling
The final publication is available at link.springer.comPeer ReviewedPostprint (author's final draft
Heterotic non-linear sigma models with anti-de Sitter target spaces
We calculate the beta function of non-linear sigma models with S^{D+1} and
AdS_{D+1} target spaces in a 1/D expansion up to order 1/D^2 and to all orders
in \alpha'. This beta function encodes partial information about the spacetime
effective action for the heterotic string to all orders in \alpha'. We argue
that a zero of the beta function, corresponding to a worldsheet CFT with
AdS_{D+1} target space, arises from competition between the one-loop and
higher-loop terms, similarly to the bosonic and supersymmetric cases studied
previously in hep-th/0512355. Various critical exponents of the non-linear
sigma model are calculated, and checks of the calculation are presented.Comment: 36 pages, 7 figure
Generalized Score Matching for Non-Negative Data
A common challenge in estimating parameters of probability density functions
is the intractability of the normalizing constant. While in such cases maximum
likelihood estimation may be implemented using numerical integration, the
approach becomes computationally intensive. The score matching method of
Hyv\"arinen [2005] avoids direct calculation of the normalizing constant and
yields closed-form estimates for exponential families of continuous
distributions over . Hyv\"arinen [2007] extended the approach to
distributions supported on the non-negative orthant, . In this
paper, we give a generalized form of score matching for non-negative data that
improves estimation efficiency. As an example, we consider a general class of
pairwise interaction models. Addressing an overlooked inexistence problem, we
generalize the regularized score matching method of Lin et al. [2016] and
improve its theoretical guarantees for non-negative Gaussian graphical models.Comment: 70 pages, 76 figure
Core percolation on complex networks
As a fundamental structural transition in complex networks, core percolation
is related to a wide range of important problems. Yet, previous theoretical
studies of core percolation have been focusing on the classical
Erd\H{o}s-R\'enyi random networks with Poisson degree distribution, which are
quite unlike many real-world networks with scale-free or fat-tailed degree
distributions. Here we show that core percolation can be analytically studied
for complex networks with arbitrary degree distributions. We derive the
condition for core percolation and find that purely scale-free networks have no
core for any degree exponents. We show that for undirected networks if core
percolation occurs then it is always continuous while for directed networks it
becomes discontinuous when the in- and out-degree distributions are different.
We also apply our theory to real-world directed networks and find,
surprisingly, that they often have much larger core sizes as compared to random
models. These findings would help us better understand the interesting
interplay between the structural and dynamical properties of complex networks.Comment: 17 pages, 6 figure
Cliques in rank-1 random graphs: the role of inhomogeneity
We study the asymptotic behavior of the clique number in rank-1 inhomogeneous
random graphs, where edge probabilities between vertices are roughly
proportional to the product of their vertex weights. We show that the clique
number is concentrated on at most two consecutive integers, for which we
provide an expression. Interestingly, the order of the clique number is
primarily determined by the overall edge density, with the inhomogeneity only
affecting multiplicative constants or adding at most a
multiplicative factor. For sparse enough graphs the clique number is always
bounded and the effect of inhomogeneity completely vanishes.Comment: 29 page
How good are MatLab, Octave and Scilab for Computational Modelling?
In this article we test the accuracy of three platforms used in computational
modelling: MatLab, Octave and Scilab, running on i386 architecture and three
operating systems (Windows, Ubuntu and Mac OS). We submitted them to numerical
tests using standard data sets and using the functions provided by each
platform. A Monte Carlo study was conducted in some of the datasets in order to
verify the stability of the results with respect to small departures from the
original input. We propose a set of operations which include the computation of
matrix determinants and eigenvalues, whose results are known. We also used data
provided by NIST (National Institute of Standards and Technology), a protocol
which includes the computation of basic univariate statistics (mean, standard
deviation and first-lag correlation), linear regression and extremes of
probability distributions. The assessment was made comparing the results
computed by the platforms with certified values, that is, known results,
computing the number of correct significant digits.Comment: Accepted for publication in the Computational and Applied Mathematics
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