3,849 research outputs found

### An information theoretic approach to statistical dependence: copula information

We discuss the connection between information and copula theories by showing
that a copula can be employed to decompose the information content of a
multivariate distribution into marginal and dependence components, with the
latter quantified by the mutual information. We define the information excess
as a measure of deviation from a maximum entropy distribution. The idea of
marginal invariant dependence measures is also discussed and used to show that
empirical linear correlation underestimates the amplitude of the actual
correlation in the case of non-Gaussian marginals. The mutual information is
shown to provide an upper bound for the asymptotic empirical log-likelihood of
a copula. An analytical expression for the information excess of T-copulas is
provided, allowing for simple model identification within this family. We
illustrate the framework in a financial data set.Comment: to appear in Europhysics Letter

### Faint K Selected Galaxy Correlations and Clustering Evolution

Angular and spatial correlations are measured for K-band--selected galaxies,
248 having redshifts, 54 with z>1, in two patches of combined area 27 arcmin^2.
The angular correlation for K<=21.5 mag is (theta/1.4+/-0.19 arcsec
e^{+/-0.1})^{-0.8}. From the redshift sample we find that the real-space
correlation, calculated with q_0=0.1, of M_K<=-23.5 mag galaxies (k-corrected)
is \xi(r) = (r/2.9e^{+/-0.12}1/h Mpc)^{-1.8} at a mean z= 0.34,
(r/2.0e^{+/-0.15}1/h Mpc)^{-1.8} at z= 0.62, (r/1.4e^{+/-0.15}1/h Mpc)^{-1.8}
at z= 0.97, and (r/1.0e^{+/-0.2}1/h Mpc)^{-1.8} at z= 1.39, the last being a
formal upper limit for a blue-biased sample. In general, these are more
correlated than optically selected samples in the same redshift ranges. Over
the interval 0.32 AB
mag, have \xi(r)=(r/2.4e^{+/-0.14}1/h Mpc)^{-1.8} whereas bluer galaxies, which
have a mean B of 23.7 mag and mean [OII] equivalent width W_{eq} = 41=\AA, are
very weakly correlated, with \xi(r)=(r/0.9e^{+/-0.22}1/h Mpc)^{-1.8}. For our
measured growth rate of clustering, this blue population, if non-merging, can
grow only into a low-redshift population less luminous than 0.4L_\ast. The
cross-correlation of low- and high-luminosity galaxies at z=0.6 appears to have
an excess in the correlation amplitude within 100/h kpc. The slow redshift
evolution is consistent with these galaxies tracing the mass clustering in low
density, Omega= 0.2, relatively unbiased, sigma_8=0.8, universe, but cannot yet
exclude other possibilities.Comment: to be published in the Aug 1 ApJ, 20 pages as a uuencoded postscript
file Postscript with all figures is available at
http://manaslu.astro.utoronto.ca/~carlberg/paper

### Landslide Risk: Economic Valuation in the North-Eastern Zone of Medellin City

Natural disasters of a geodynamic nature can cause enormous economic and human losses. The economic costs of a landslide disaster include relocation of communities and physical repair of urban infrastructure. However, when performing a quantitative risk analysis, generally, the indirect economic consequences of such an event are not taken into account. A probabilistic approach methodology that considers several scenarios of hazard and vulnerability to measure the magnitude of the landslide and to quantify the economic costs is proposed. With this approach, it is possible to carry out a quantitative evaluation of the risk by landslides, allowing the calculation of the economic losses before a potential disaster in an objective, standardized and reproducible way, taking into account the uncertainty of the building costs in the study zone. The possibility of comparing different scenarios facilitates the urban planning process, the optimization of interventions to reduce risk to acceptable levels and an assessment of economic losses according to the magnitude of the damage. For the development and explanation of the proposed methodology, a simple case study is presented, located in north-eastern zone of the city of MedellĂn. This area has particular geomorphological characteristics, and it is also characterized by the presence of several buildings in bad structural conditions. The proposed methodology permits to obtain an estimative of the probable economic losses by earthquake-induced landslides, taking into account the uncertainty of the building costs in the study zone. The obtained estimative shows that the structural intervention of the buildings produces a reduction the order of 21 % in the total landslide risk. Â© Published under licence by IOP Publishing Ltd

### Universality of rain event size distributions

We compare rain event size distributions derived from measurements in
climatically different regions, which we find to be well approximated by power
laws of similar exponents over broad ranges. Differences can be seen in the
large-scale cutoffs of the distributions. Event duration distributions suggest
that the scale-free aspects are related to the absence of characteristic scales
in the meteorological mesoscale.Comment: 16 pages, 10 figure

### Chiral Corrections to Lattice Calculations of Charge Radii

Logarithmic divergences in pion and proton charge radii associated with
chiral loops are investigated to assess systematic uncertainties in current
lattice determinations of charge radii. The chiral corrections offer a possible
solution to the long standing problem of why present lattice calculations yield
proton and pion radii which are similar in size.Comment: PostScript file only. Ten pages. Figures included. U. of MD Preprint
#92-19

### Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B,
and Bs mesons from the two-point correlator of heavy-light pseudoscalar
currents. We use the operator product expansion for this correlator expressed
in terms of the MSbar heavy-quark mass, for which the perturbative expansion
exhibits a reasonable convergence. Our main emphasis is laid on the control
over the uncertainties in the decay constants, related both to the input QCD
parameters and to the limited accuracy of the method of sum-rules. This becomes
possible due to the application of our procedure of extracting hadron
observables that involves as novel feature dual thresholds depending on the
Borel parameter. For charmed mesons, we find the decay constants f_D=206.2\pm
7.3(OPE)\pm 5.1(syst) MeV and f_Ds=245.3\pm 15.7(OPE)\pm 4.5(syst) MeV. For
beauty mesons, the decay constants turn out to be extremely sensitive to the
precise value of mb(mb). By requiring our sum-rule estimate to match the
average of the lattice results for f_B, a very accurate value mb(mb)=4.245\pm
0.025 GeV is extracted, leading to f_B=193.4\pm 12.3(OPE)\pm 4.3(syst) MeV and
f_Bs=232.5\pm 18.6(OPE)\pm 2.4(syst) MeV.Comment: 12 page

### A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality
constraints. Although there are variety of methods for solving such problems,
most statisticians find constrained estimation challenging. The current paper
proposes a new path following algorithm for quadratic programming based on
exact penalization. Similar penalties arise in $l_1$ regularization in model
selection. Classical penalty methods solve a sequence of unconstrained problems
that put greater and greater stress on meeting the constraints. In the limit as
the penalty constant tends to $\infty$, one recovers the constrained solution.
In the exact penalty method, squared penalties are replaced by absolute value
penalties, and the solution is recovered for a finite value of the penalty
constant. The exact path following method starts at the unconstrained solution
and follows the solution path as the penalty constant increases. In the
process, the solution path hits, slides along, and exits from the various
constraints. Path following in lasso penalized regression, in contrast, starts
with a large value of the penalty constant and works its way downward. In both
settings, inspection of the entire solution path is revealing. Just as with the
lasso and generalized lasso, it is possible to plot the effective degrees of
freedom along the solution path. For a strictly convex quadratic program, the
exact penalty algorithm can be framed entirely in terms of the sweep operator
of regression analysis. A few well chosen examples illustrate the mechanics and
potential of path following.Comment: 26 pages, 5 figure

### Validation of nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA
by using artificial neural networks. But the benefit of curved components
requires a careful control of the model complexity. Moreover, standard
techniques for model selection, including cross-validation and more generally
the use of an independent test set, fail when applied to nonlinear PCA because
of its inherent unsupervised characteristics. This paper presents a new
approach for validating the complexity of nonlinear PCA models by using the
error in missing data estimation as a criterion for model selection. It is
motivated by the idea that only the model of optimal complexity is able to
predict missing values with the highest accuracy. While standard test set
validation usually favours over-fitted nonlinear PCA models, the proposed model
validation approach correctly selects the optimal model complexity.Comment: 12 pages, 5 figure

### Decuplet Baryon Structure from Lattice QCD

The electromagnetic properties of the SU(3)-flavor baryon decuplet are
examined within a lattice simulation of quenched QCD. Electric charge radii,
magnetic moments, and magnetic radii are extracted from the E0 and M1 form
factors. Preliminary results for the E2 and M3 moments are presented giving the
first model independent insight to the shape of the quark distribution in the
baryon ground state. As in our octet baryon analysis, the lattice results give
evidence of spin-dependent forces and mass effects in the electromagnetic
properties. The quark charge distribution radii indicate these effects act in
opposing directions. Some baryon dependence of the effective quark magnetic
moments is seen. However, this dependence in decuplet baryons is more subtle
than that for octet baryons. Of particular interest are the lattice predictions
for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent
experimental measurements are available. The lattice prediction of the
$\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the
lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good
agreement with the experimental ratio.Comment: RevTeX manuscript, 34 pages plus 21 figures (available upon request

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