21,482 research outputs found
Generating and Analyzing Constrained Dark Energy Equations of State and Systematics Functions
Some functions entering cosmological analysis, such as the dark energy
equation of state or systematic uncertainties, are unknown functions of
redshift. To include them without assuming a particular form we derive an
efficient method for generating realizations of all possible functions subject
to certain bounds or physical conditions, e.g. w\in[-1,+1] as for quintessence.
The method is optimal in the sense that it is both pure and complete in filling
the allowed space of principal components. The technique is applied to
propagation of systematic uncertainties in supernova population drift and dust
corrections and calibration through to cosmology parameter estimation and bias
in the magnitude-redshift Hubble diagram. We identify specific ranges of
redshift and wavelength bands where the greatest improvements in supernova
systematics due to population evolution and dust correction can be achieved.Comment: 12 pages, 11 figures; v2 minor revisions, higher resolution figures,
matches PRD versio
Quantum Spacetime and Algebraic Quantum Field Theory
We review the investigations on the quantum structure of spactime, to be
found at the Planck scale if one takes into account the operational limitations
to localization of events which result from the concurrence of Quantum
Mechanics and General Relativity. We also discuss the different approaches to
(perturbative) Quantum Field Theory on Quantum Spacetime, and some of the
possible cosmological consequences.Comment: 49 pages, 2 figure
Approximating the Distribution of the Median and other Robust Estimators on Uncertain Data
Robust estimators, like the median of a point set, are important for data
analysis in the presence of outliers. We study robust estimators for
locationally uncertain points with discrete distributions. That is, each point
in a data set has a discrete probability distribution describing its location.
The probabilistic nature of uncertain data makes it challenging to compute such
estimators, since the true value of the estimator is now described by a
distribution rather than a single point. We show how to construct and estimate
the distribution of the median of a point set. Building the approximate support
of the distribution takes near-linear time, and assigning probability to that
support takes quadratic time. We also develop a general approximation technique
for distributions of robust estimators with respect to ranges with bounded VC
dimension. This includes the geometric median for high dimensions and the
Siegel estimator for linear regression.Comment: Full version of a paper to appear at SoCG 201
Regression analysis of MCS Intensity and ground motion parameters in Italy and its application in ShakeMap
In Italy, the Mercalli-Cancani-Sieberg, MCS, is the intensity scale in use to describe the level of earthquake ground shaking, and its subsequent effects on communities and on the built environment. This scale differs to some extent from the Mercalli Modified scale in use in other countries and adopted as standard within the USGS-ShakeMap procedure to predict intensities from observed instrumental data. We have assembled a new PGM/MCS-intensity data set from the Italian database of macroseismic information, DBMI04, and the Italian accelerometric database, ITACA. We have determined new regression relations between intensities and PGM parameters (acceleration and velocity). Since both PGM parameters and intensities suffer of consistent uncertainties we have used the orthogonal distance regression technique. The new relations are IMCS = 1.68 ± 0.22 + 2.58 ± 0.14 log P GA, σ = 0.35 and IMCS = 5.11 ± 0.07 + 2.35 ± 0.09 log P GV , σ = 0.26. Tests designed to assess the robustness of the estimated coefficients have shown that single-line parameterizations for the regression are sufficient to model the data within the model uncertainties. The relations have been inserted in the Italian implementation of the USGS-ShakeMap to determine intensity maps from instrumental data and to determine PGM maps from the sole intensity values. Comparisons carried out for earthquakes where both kinds of data are available have shown the general effectiveness of the relations
Parametric Regression on the Grassmannian
We address the problem of fitting parametric curves on the Grassmann manifold
for the purpose of intrinsic parametric regression. As customary in the
literature, we start from the energy minimization formulation of linear
least-squares in Euclidean spaces and generalize this concept to general
nonflat Riemannian manifolds, following an optimal-control point of view. We
then specialize this idea to the Grassmann manifold and demonstrate that it
yields a simple, extensible and easy-to-implement solution to the parametric
regression problem. In fact, it allows us to extend the basic geodesic model to
(1) a time-warped variant and (2) cubic splines. We demonstrate the utility of
the proposed solution on different vision problems, such as shape regression as
a function of age, traffic-speed estimation and crowd-counting from
surveillance video clips. Most notably, these problems can be conveniently
solved within the same framework without any specifically-tailored steps along
the processing pipeline.Comment: 14 pages, 11 figure
Dynamical system analysis and forecasting of deformation produced by an earthquake fault
We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.Comment: 30 pages, 12 figure
- …