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-$p_t$ 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

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

Crumbling Reefs and Cold-Water Coral Habitat Loss in a Future Ocean: Evidence of “Coralporosis” as an Indicator of Habitat Integrity

Ocean acidification is a threat to the net growth of tropical and deep-sea coral reefs, due to gradual changes in the balance between reef growth and loss processes. Here we go beyond identification of coral dissolution induced by ocean acidification and identify a mechanism that will lead to a loss of habitat in cold-water coral reef habitats on an ecosystem-scale. To quantify this, we present in situ and year-long laboratory evidence detailing the type of habitat shift that can be expected (in situ evidence), the mechanisms underlying this (in situ and laboratory evidence), and the timescale within which the process begins (laboratory evidence). Through application of engineering principals, we detail how increased porosity in structurally critical sections of coral framework will lead to crumbling of load-bearing material, and a potential collapse and loss of complexity of the larger habitat. Importantly, in situ evidence highlights that cold-water corals can survive beneath the aragonite saturation horizon, but in a fundamentally different way to what is currently considered a biogenic cold-water coral reef, with a loss of the majority of reef habitat. The shift from a habitat with high 3-dimensional complexity provided by both live and dead coral framework, to a habitat restricted primarily to live coral colonies with lower 3-dimensional complexity represents the main threat to cold-water coral reefs of the future and the biodiversity they support. Ocean acidification can cause ecosystem-scale habitat loss for the majority of cold-water coral reefs.BN/Marie-Eve Aubin-Tam La

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

CLT in Functional Linear Regression Models

International audienceWe propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

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

Invariance of the essential spectra of operator pencils

The essential spectrum of operator pencils with bounded coefficients in a Hilbert space is studied. Sufficient conditions in terms of the operator coefficients of two pencils are derived which guarantee the same essential spectrum. This is done by exploiting a strong relation between an operator pencil and a specific linear subspace (linear relation)