142 research outputs found
The equivalence of fluctuation scale dependence and autocorrelations
We define optimal per-particle fluctuation and correlation measures, relate
fluctuations and correlations through an integral equation and show how to
invert that equation to obtain precise autocorrelations from fluctuation scale
dependence. We test the precision of the inversion with Monte Carlo data and
compare autocorrelations to conditional distributions conventionally used to
study high- jet structure.Comment: 10 pages, 9 figures, proceedings, MIT workshop on correlations and
fluctuations in relativistic nuclear collision
Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities
We study the application of the Augmented Lagrangian Method to the solution
of linear ill-posed problems. Previously, linear convergence rates with respect
to the Bregman distance have been derived under the classical assumption of a
standard source condition. Using the method of variational inequalities, we
extend these results in this paper to convergence rates of lower order, both
for the case of an a priori parameter choice and an a posteriori choice based
on Morozov's discrepancy principle. In addition, our approach allows the
derivation of convergence rates with respect to distance measures different
from the Bregman distance. As a particular application, we consider sparsity
promoting regularization, where we derive a range of convergence rates with
respect to the norm under the assumption of restricted injectivity in
conjunction with generalized source conditions of H\"older type
Regularization of statistical inverse problems and the Bakushinskii veto
In the deterministic context Bakushinskii's theorem excludes the existence of
purely data driven convergent regularization for ill-posed problems. We will
prove in the present work that in the statistical setting we can either
construct a counter example or develop an equivalent formulation depending on
the considered class of probability distributions. Hence, Bakushinskii's
theorem does not generalize to the statistical context, although this has often
been assumed in the past. To arrive at this conclusion, we will deduce from the
classic theory new concepts for a general study of statistical inverse problems
and perform a systematic clarification of the key ideas of statistical
regularization.Comment: 20 page
Regularized energy-dependent solar flare hard x-ray spectral index
The deduction from solar flare X-ray photon spectroscopic data of the energy
dependent model-independent spectral index is considered as an inverse problem.
Using the well developed regularization approach we analyze the energy
dependency of spectral index for a high resolution energy spectrum provided by
Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The regularization
technique produces much smoother derivatives while avoiding additional errors
typical of finite differences. It is shown that observations imply a spectral
index varying significantly with energy, in a way that also varies with time as
the flare progresses. The implications of these findings are discussed in the
solar flare context.Comment: 13 pages; 5 figures, Solar Physics in pres
The polarizability model for ferroelectricity in perovskite oxides
This article reviews the polarizability model and its applications to
ferroelectric perovskite oxides. The motivation for the introduction of the
model is discussed and nonlinear oxygen ion polarizability effects and their
lattice dynamical implementation outlined. While a large part of this work is
dedicated to results obtained within the self-consistent-phonon approximation
(SPA), also nonlinear solutions of the model are handled which are of interest
to the physics of relaxor ferroelectrics, domain wall motions, incommensurate
phase transitions. The main emphasis is to compare the results of the model
with experimental data and to predict novel phenomena.Comment: 55 pages, 35 figure
Generalized Regularization Techniques With Constraints For The Analysis Of Solar Bremsstrahlung X-Ray Spectra
Hard X-ray spectra in solar flares provide knowledge of the electron spectrum
that results from acceleration and propagation in the solar atmosphere.
However, the inference of the electron spectra from solar X-ray spectra is an
ill-posed inverse problem. Here we develop and apply an enhanced regularization
algorithm for this process making use of physical constraints on the form of
the electron spectrum. The algorithm incorporates various features not
heretofore employed in the solar flare context: Generalized Singular Value
Decomposition (GSVD) to deal with different orders of constraints; rectangular
form of the cross-section matrix to extend the solution energy range;
regularization with various forms of the smoothing operator; and
"preconditioning" of the problem. We show by simulations that this technique
yields electron spectra with considerably more information and higher quality
than previous algorithms.Comment: 21 pages, 8 fugures, accepted to Solar Physic
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