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

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

Composition and micromechanical properties of the femoral neck compact bone in relation to patient age, sex and hip fracture occurrence

Current clinical methods of bone health assessment depend to a great extent on bone mineral density (BMD) measurements. However, these methods only act as a proxy for bone strength and are often only carried out after the fracture occurs. Besides BMD, composition and tissue-level mechanical properties are expected to affect the whole bone's strength and toughness. While the elastic properties of the bone extracellular matrix (ECM) have been extensively investigated over the past two decades, there is still limited knowledge of the yield properties and their relationship to composition and architecture. In the present study, morphological, compositional and micropillar compression bone data was collected from patients who underwent hip arthroplasty. Femoral neck samples from 42 patients were collected together with anonymous clinical information about age, sex and primary diagnosis (coxarthrosis or hip fracture). The femoral neck cortex from the inferomedial region was analyzed in a site-matched manner using a combination of micromechanical testing (nanoindentation, micropillar compression) together with micro-CT and quantitative polarized Raman spectroscopy for both morphological and compositional characterization. Mechanical properties, as well as the sample-level mineral density, were constant over age. Only compositional properties demonstrate weak dependence on patient age: decreasing mineral to matrix ratio (p = 0.02, R2 = 0.13, 2.6 % per decade) and increasing amide I sub-peak ratio I~1660/I~1683 (p = 0.04, R2 = 0.11, 1.5 % per decade). The patient's sex and diagnosis did not seem to influence investigated bone properties. A clear zonal dependence between interstitial and osteonal cortical zones was observed for compositional and elastic bone properties (p  200). The proposed classification algorithm together with the output database of bone tissue properties can be used for the future comparison of existing methods to evaluate bone quality as well as to form a better understanding of the mechanisms through which bone tissue is affected by aging or disease

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

HAWC Study of the Very-high-energy γ-Ray Spectrum of HAWC J1844−034

Recently, the region surrounding eHWC J1842−035 has been studied extensively by γ-ray observatories due to its extended emission reaching up to a few hundred TeV and potential as a hadronic accelerator. In this work, we use 1910 days of cumulative data from the High Altitude Water Cherenkov (HAWC) observatory to carry out a dedicated systematic source search of the eHWC J1842−035 region. During the search, we found three sources in the region, namely, HAWC J1844−034, HAWC J1843−032, and HAWC J1846−025. We have identified HAWC J1844−034 as the extended source that emits photons with energies up to 175 TeV. We compute the spectrum for HAWC J1844−034, and by comparing with the observational results from other experiments, we have identified HESS J1843−033, LHAASO J1843−0338, and TASG J1844−038 as very-high-energy γ-ray sources with a matching origin. Also, we present and use the multiwavelength data to fit the hadronic and leptonic particle spectra. We have identified four pulsar candidates in the nearby region in which PSR J1844−0346 is found to be the most likely candidate due to its proximity to HAWC J1844−034 and the computed energy budget. We have also found SNR G28.6−0.1 as a potential counterpart source of HAWC J1844−034 for which both leptonic and hadronic scenarios are feasible

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

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