17,833 research outputs found
A Consistent Histogram Estimator for Exchangeable Graph Models
Exchangeable graph models (ExGM) subsume a number of popular network models.
The mathematical object that characterizes an ExGM is termed a graphon. Finding
scalable estimators of graphons, provably consistent, remains an open issue. In
this paper, we propose a histogram estimator of a graphon that is provably
consistent and numerically efficient. The proposed estimator is based on a
sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree
of a graph, then smooths the sorted graph using total variation minimization.
The consistency of the SAS algorithm is proved by leveraging sparsity concepts
from compressed sensing.Comment: 28 pages, 5 figure
Hydrogen-Bonded Liquids: Effects of Correlations of Orientational Degrees of Freedom
We improve a lattice model of water introduced by Sastry, Debenedetti,
Sciortino, and Stanley to give insight on experimental thermodynamic anomalies
in supercooled phase, taking into account the correlations between
intra-molecular orientational degrees of freedom. The original Sastry et al.
model including energetic, entropic and volumic effect of the
orientation-dependent hydrogen bonds (HBs), captures qualitatively the
experimental water behavior, but it ignores the geometrical correlation between
HBs. Our mean-field calculation shows that adding these correlations gives a
more water-like phase diagram than previously shown, with the appearance of a
solid phase and first-order liquid-solid and gas-solid phase transitions.
Further investigation is necessary to be able to use this model to characterize
the thermodynamic properties of the supercooled region.Comment: 7 pages latex, 3 figures EP
Novel Six-Quark Hidden-Color Dibaryon States in QCD
The recent observation of a hadronic resonance in the proton-neutron
system with isospin and spin-parity raises the possibility
of producing other novel six-quark dibaryon configurations allowed by QCD. A
dramatic example of an exotic six-quark color-singlet system is the charge
, isospin I=3, state which couples strongly to
+ The width and decay properties of such
six-quark resonances could be regarded as manifestations of "hidden-color"
six-quark configurations, a first-principle prediction of QCD -- SU(3)-color
gauge theory for the deuteron distribution amplitude. Other implications and
possible future experiments are discussed
Scaling behavior in economics: I. Empirical results for company growth
We address the question of the growth of firm size. To this end, we analyze
the Compustat data base comprising all publicly-traded United States
manufacturing firms within the years 1974-1993. We find that the distribution
of firm sizes remains stable for the 20 years we study, i.e., the mean value
and standard deviation remain approximately constant. We study the distribution
of sizes of the ``new'' companies in each year and find it to be well
approximated by a log-normal. We find (i) the distribution of the logarithm of
the growth rates, for a fixed growth period of one year, and for companies with
approximately the same size displays an exponential form, and (ii) the
fluctuations in the growth rates -- measured by the width of this distribution
-- scale as a power law with , . We find
that the exponent takes the same value, within the error bars, for
several measures of the size of a company. In particular, we obtain:
for sales, for number of employees,
for assets, for cost of goods sold, and
for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France
(April 1997
Scaling behavior in economics: II. Modeling of company growth
In the preceding paper we presented empirical results describing the growth
of publicly-traded United States manufacturing firms within the years
1974--1993. Our results suggest that the data can be described by a scaling
approach. Here, we propose models that may lead to some insight into these
phenomena. First, we study a model in which the growth rate of a company is
affected by a tendency to retain an ``optimal'' size. That model leads to an
exponential distribution of the logarithm of the growth rate in agreement with
the empirical results. Then, we study a hierarchical tree-like model of a
company that enables us to relate the two parameters of the model to the
exponent , which describes the dependence of the standard deviation of
the distribution of growth rates on size. We find that , where defines the mean branching ratio of the hierarchical tree and
is the probability that the lower levels follow the policy of higher
levels in the hierarchy. We also study the distribution of growth rates of this
hierarchical model. We find that the distribution is consistent with the
exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France
(April 1997
Stochastic blockmodel approximation of a graphon: Theory and consistent estimation
Non-parametric approaches for analyzing network data based on exchangeable
graph models (ExGM) have recently gained interest. The key object that defines
an ExGM is often referred to as a graphon. This non-parametric perspective on
network modeling poses challenging questions on how to make inference on the
graphon underlying observed network data. In this paper, we propose a
computationally efficient procedure to estimate a graphon from a set of
observed networks generated from it. This procedure is based on a stochastic
blockmodel approximation (SBA) of the graphon. We show that, by approximating
the graphon with a stochastic block model, the graphon can be consistently
estimated, that is, the estimation error vanishes as the size of the graph
approaches infinity.Comment: 20 pages, 4 figures, 2 algorithms. Neural Information Processing
Systems (NIPS), 201
Bigger Bursts From Merging Neutron Stars
GRB 990123 may have radiated more than one solar mass equivalent in just its
gamma emissions. Though this may be within the upper limit of the binding
energy available from neutron stars in the Schwarzschild metric, it is
difficult to imagine a process with the required efficiency of conversion to
gamma rays. Neutron stars of ~10 solar mass are permitted in the Yilmaz metric.
A merger of two neutron stars of maximum mass could release approximately 10
solar mass equivalent binding energy.Comment: 5 pages, 1 figure, submitted to ApJ Letter
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