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

Performance of the HAWC Observatory and TeV Gamma-Ray Measurements of the Crab Nebula with Improved Extensive Air Shower Reconstruction Algorithms

The High-Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory, located on the side of the Sierra Negra volcano in Mexico, has been fully operational since 2015. The HAWC collaboration has recently significantly improved their extensive air shower reconstruction algorithms, which has notably advanced the observatory performance. The energy resolution for primary gamma rays with energies below 1 TeV was improved by including a noise-suppression algorithm. Corrections have also been made to systematic errors in direction fitting related to the detector and shower plane inclinations, O ( 0 .° 1 ) biases in highly inclined showers, and enhancements to the core reconstruction. The angular resolution for gamma rays approaching the HAWC array from large zenith angles (\u3e37°) has improved by a factor of 4 at the highest energies (\u3e70 TeV) as compared to previous reconstructions. The inclusion of a lateral distribution function fit to the extensive air shower footprint on the array to separate gamma-ray primaries from cosmic-ray ones based on the resulting χ 2 values improved the background rejection performance at all inclinations. At large zenith angles, the improvement in significance is a factor of 4 compared to previous HAWC publications. These enhancements have been verified by observing the Crab Nebula, which is an overhead source for the HAWC Observatory. We show that the sensitivity to Crab-like point sources (E −2.63) with locations overhead to 30° zenith is comparable to or less than 10% of the Crab Nebula’s flux between 2 and 50 TeV. Thanks to these improvements, HAWC can now detect more sources, including the Galactic center

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

Observation of the Galactic Center PeVatron beyond 100 TeV with HAWC

We report an observation of ultrahigh-energy (UHE) gamma rays from the Galactic center (GC) region, using 7 yr of data collected by the High-Altitude Water Cherenkov (HAWC) Observatory. The HAWC data are best described as a point-like source (HAWC J1746-2856) with a power-law spectrum ( d N / d E = ϕ E / 26 TeV γ ), where γ = −2.88 ± 0.15stat − 0.1sys and ϕ = 1.5 × 10−15 (TeV cm2 s)−1 ± 0.3 stat − 0.13 sys + 0.08 sys extending from 6 to 114 TeV. We find no evidence of a spectral cutoff up to 100 TeV using HAWC data. Two known point-like gamma-ray sources are spatially coincident with the HAWC gamma-ray excess: Sgr A* (HESS J1745-290) and the Arc (HESS J1746-285). We subtract the known flux contribution of these point sources from the measured flux of HAWC J1746-2856 to exclude their contamination and show that the excess observed by HAWC remains significant (\u3e5σ), with the spectrum extending to \u3e100 TeV. Our result supports that these detected UHE gamma rays can originate via hadronic interaction of PeV cosmic-ray protons with the dense ambient gas and confirms the presence of a proton PeVatron at the GC

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

Multiwavelength Investigation of γ-Ray Source MGRO J1908+06 Emission Using Fermi-LAT, VERITAS and HAWC

This paper investigates the origin of the γ-ray emission from MGRO J1908+06 in the GeV-TeV energy band. By analyzing the data collected by the Fermi Large Area Telescope, the Very Energetic Radiation Imaging Telescope Array System, and High Altitude Water Cherenkov, with the addition of spectral data previously reported by LHAASO, a multiwavelength study of the morphological and spectral features of MGRO J1908+06 provides insight into the origin of the γ-ray emission. The mechanism behind the bright TeV emission is studied by constraining the magnetic field strength, the source age, and the distance through detailed broadband modeling. Both spectral shape and energy-dependent morphology support the scenario that inverse Compton emission of an evolved pulsar wind nebula associated with PSR J1907+0602 is responsible for the MGRO J1908+06 γ-ray emission with a best-fit true age of T = 22 ± 9 kyr and a magnetic field of B = 5.4 ± 0.8 μG, assuming the distance to the pulsar dPSR = 3.2 kpc

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

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

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