On the spectral properties of L_{+-} in three dimensions

This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators which arise in this setting, traditionally denoted by L_{+-}, satisfy the gap property, at least over the radial functions. This means that the interval (0,1] does not contain any eigenvalues of L_{+-} and that the threshold 1 is neither an eigenvalue nor a resonance. The gap property is required in order to prove scattering to the ground states for solutions starting on the center-stable manifold associated with these states. This paper therefore provides the final installment in the proof of this scattering property for the cubic Klein-Gordon and Schrodinger equations in the radial case, see the recent theory of Nakanishi and the third author, as well as the earlier work of the third author and Beceanu on NLS. The method developed here is quite general, and applicable to other spectral problems which arise in the theory of nonlinear equations

Finite N Fluctuation Formulas for Random Matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - )$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the circular random matrix ensemble the p.d.f.'s for the linear statistics ${1 \over 2} \sum_{j=1}^N (\theta_j - \pi)$ and $- \sum_{j=1}^N \log 2|\sin \theta_j/2|$ are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem as $N \to \infty$.Comment: LaTeX 2.09, 11 pages + 3 eps figs (needs epsf.sty

Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process

Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d. complex Gaussian coefficients a_n. We show that these zeros form a determinantal process: more precisely, their joint intensity can be written as a minor of the Bergman kernel. We show that the number of zeros of f in a disk of radius r about the origin has the same distribution as the sum of independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover, the set of absolute values of the zeros of f has the same distribution as the set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in [0,1]. The repulsion between zeros can be studied via a dynamic version where the coefficients perform Brownian motion; we show that this dynamics is conformally invariant.Comment: 37 pages, 2 figures, updated proof

The Legacy of Hope Summit: A Consensus-Based Initiative and Report on Eating Disorders in the U.S. and Recommendations for the Path Forward

Background: Several unsuccessful attempts have been made to reach a cross-disciplinary consensus on issues fundamental to the field of eating disorders in the United States (U.S.). In January 2020, 25 prominent clinicians, academicians, researchers, persons with lived experience, and thought leaders in the U.S. eating disorders community gathered at the Legacy of Hope Summit to try again. This paper articulates the points on which they reached a consensus. It also: (1) outlines strategies for implementing those recommendations; (2) identifies likely obstacles to their implementation; and (3) charts a course for successfully navigating and overcoming those challenges. Methods: Iterative and consensual processes were employed throughout the Summit and the development of this manuscript. Results: The conclusion of the Summit culminated in several consensus points, including: (1) Eating disorder outcomes and prevention efforts can be improved by implementing creative health education initiatives that focus on societal perceptions, early detection, and timely, effective intervention; (2) Such initiatives should be geared toward parents/guardians, families, other caretakers, and frontline healthcare providers in order to maximize impact; (3) Those afflicted with eating disorders, their loved ones, and the eating disorders community as a whole would benefit from greater accessibility to affordable, quality care, as well as greater transparency and accountability on the part of in-hospital, residential, and outpatient health care providers with respect to their qualifications, methodologies, and standardized outcomes; (4) Those with lived experience with eating disorders, their loved ones, health care providers, and the eating disorders community as a whole, also would benefit from the establishment and maintenance of treatment program accreditation, professional credentialing, and treatment type and levels of care guidelines; and (5) The establishment and implementation of effective, empirically/evidence-based standards of care requires research across a diverse range of populations, adequate private and government funding, and the free exchange of ideas and information among all who share a commitment to understanding, treating, and, ultimately, markedly diminishing the negative impact of eating disorders. Conclusions: Widespread uptake and implementation of these recommendations has the potential to unify and advance the eating disorders field and ultimately improve the lives of those affected. A cross-disciplinary group of eating disorder professionals, thought leaders, and persons with lived experience have come together and reached a consensus on issues that are fundamental to the battle against the life-threatening and life-altering illnesses that are eating spectrum disorders. Those issues include: (1) the need for early detection, intervention, prevention, and evidenced-based standards of care; (2) the critical need to make specialized care more accessible and affordable to all those in need; (3) the importance of developing uniform, evidenced-based standards of care; (4) the need for funding and conducting eating spectrum disorder research; and (5) the indispensability of advocacy, education, and legislation where these illnesses are concerned. During the consensus process, the authors also arrived at strategies for implementing their recommendations, identified likely obstacles to their implementation, and charted a course for successfully navigating and overcoming those challenges. Above all else, the authors demonstrated that consensus in the field of eating spectrum disorders is possible and achievable and, in doing so, lit a torch of hope that is certain to light the path forward for years to come

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation

Modal Series Expansions for Plane Gravitational Waves

[EN] Propagation of gravitational disturbances at the speed of light is one of the key predictions of the General Theory of Relativity. This result is now backed indirectly by the observations of the behavior of the ephemeris of binary pulsar systems. These new results have increased the interest in the mathematical theory of gravitational waves in the last decades, and severalmathematical approaches have been developed for a better understanding of the solutions. In this paper we develop a modal series expansion technique in which solutions can be built for plane waves from a seed integrable function. The convergence of these series is proven by the Raabe-Duhamel criteria, and we show that these solutions are characterized by a well-defined and finite curvature tensor and also a finite energy content.Acedo Rodríguez, L. (2016). Modal Series Expansions for Plane Gravitational Waves. Gravitation and Cosmology. 22(3):251-257. doi:10.1134/S0202289316030026S251257223A. Einstein and N. Rosen, Journal of the Franklin Institute 223, 43–54 (1937).N. Rosen, Gen. Rel. Grav. 10, 351–364 (1979).C. Sivaram, Bull. Astr. Soc. India 23, 77–83 (1995).J. M. Weisberg, D. J. Nice, and J. H. Taylor, Astroph. J. 722, 1030–1034(2010); arXiv: 1011.0718.B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016).J. B. Griffiths, Colliding waves in general relativity (Clarendon, Oxford, 1991).S. Chandrasekhar, The mathematical theory of black holes (Clarendon, Oxford, 1983).D. Bini, V. Ferrari and J. Ibañez, Nuovo Cim. B 103, 29–44 (1989).L. Acedo, G. González-Parra, and A. J. Arenas, Nonlinear Analysis: Real World Applications 11, 1819–1825 (2010).L. Acedo, G. González-Parra, and A. J. Arenas, Physica A 389, 1151–1157 (2010).G. González-Parra, L. Acedo, and A. J. Arenas, Numerical Algorithms, published online 2013. doi 10.1007/s11075-013-9776-xW. Rindler, Relativity: Special, General and Cosmological, 2nd ed. (Oxford Univ., New York, 2006).G. Arfken, Mathematical Methods for Physicists, 3rd. ed. (Academic, Orlando, Florida, 1985).L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 3rd ed. (Pergamon, New York, 1971).O. Costin, “Topological construction of transseries and introduction to generalized Borel summability,” in Analyzable Functions and Applications, Ed. by O. Costin, M. D. Kruskal, and A. Macintyre, Contemp. Math. 373 (Providence, RI, USA: Am. Math. Soc., 2005); arXiv: math/0608309.S. R. Coleman, Phys. Lett. B 70, 59–60 (1977).W. B. Campbell and T. A. Morgan, Phys. Lett. B 84, 87–88 (1979).A. S. Rabinowitch, Int. J. Adv. Math. Sciences 1 (3), 109–121 (2013).A. Feinstein and J. Ibañez, Phys. Rev. D 39 (2), 470–473 (1989)

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011

Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC

Measurements are presented of production properties and couplings of the recently discovered Higgs boson using the decays into boson pairs, H →γ γ, H → Z Z∗ →4l and H →W W∗ →lνlν. The results are based on the complete pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at centre-of-mass energies of √s = 7 TeV and √s = 8 TeV, corresponding to an integrated luminosity of about 25 fb−1. Evidence for Higgs boson production through vector-boson fusion is reported. Results of combined fits probing Higgs boson couplings to fermions and bosons, as well as anomalous contributions to loop-induced production and decay modes, are presented. All measurements are consistent with expectations for the Standard Model Higgs boson