Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

The clinical profile of moderate amblyopia in children younger than 7 years

Objective To describe the demographic and clinical characteristics of a cohort of children with moderate amblyopia participating in the Amblyopia Treatment Study 1, a randomized trial comparing atropine and patching. Methods The children enrolled were younger than 7 years and had strabismic, anisometropic, or combined strabismic and anisometropic amblyopia. Visual acuity, measured with a standardized testing protocol using single-surround HOTV optotypes, was 20/40 to 20/100 in the amblyopic eye, with an intereye acuity difference of 3 or more logMAR lines. There were 419 children enrolled, 409 of whom met these criteria and were included in the analyses. Results The mean age of the 409 children was 5.3 years. The cause of the amblyopia was strabismus in 38%, anisometropia in 37%, and both strabismus and anisometropia in 24%. The mean visual acuity of the amblyopic eyes (approximately 20/60) was similar among the strabismic, anisometropic, and combined groups (P = .24), but visual acuity of the sound eyes was worse in the strabismic group compared with the anisometropic group (P<.001). For the patients randomized into the patching group, 43% were initially treated for 6 hours per day, whereas 17% underwent full-time patching. Patients with poorer visual acuity in the amblyopic eye were prescribed more hours of patching than patients with better acuity (P = .003). Conclusions In the Amblyopia Treatment Study 1, there were nearly equal proportions of patients with strabismic and anisometropic amblyopia. A similar level of visual impairment was found irrespective of the cause of amblyopia. There was considerable variation in treatment practices with regard to the number of hours of initial patching prescribed

Impact of Patching and Atropine Treatment on the Child and Family in the Amblyopia Treatment Study

Objective To assess the psychosocial impact on the child and family of patching and atropine as treatments for moderate amblyopia in children younger than 7 years. Methods In a randomized, controlled clinical trial, 419 children younger than 7 years with amblyopic eye visual acuity in the range of 20/40 to 20/100 were assigned to receive treatment with either patching or atropine at 47 clinical sites. After 5 weeks of treatment, a parental quality-of-life questionnaire was completed for 364 (87%) of the 419 patients. Main Outcome Measure Overall and subscale scores on the Amblyopia Treatment Index. Results High internal validity and reliability were demonstrated for the Amblyopia Treatment Index questionnaire. The overall Amblyopia Treatment Index scores and the 3 subscale scores were consistently higher (worse) in the patching group compared with the atropine-treated group (overall mean, 2.52 vs 2.02, P<.001; adverse effects of treatment: mean, 2.35 vs 2.11, P = .002; difficulty with compliance: mean, 2.46 vs 1.99, P<.001; and social stigma: mean, 3.09 vs 1.84, P<.001, respectively). Conclusion Although the Amblyopia Treatment Index questionnaire results indicated that both atropine and patching treatments were well tolerated by the child and family, atropine received more favorable scores overall and on all 3 questionnaire subscales

Photospheric and Subphotospheric Dynamics of Emerging Magnetic Flux

Magnetic fields emerging from the Sun's interior carry information about physical processes of magnetic field generation and transport in the convection zone. Soon after appearance on the solar surface the magnetic flux gets concentrated in sunspot regions and causes numerous active phenomena on the Sun. This paper discusses some properties of the emerging magnetic flux observed on the solar surface and in the interior. A statistical analysis of variations of the tilt angle of bipolar magnetic regions during the emergence shows that the systematic tilt with respect to the equator (the Joy's law) is most likely established below the surface. However, no evidence of the dependence of the tilt angle on the amount of emerging magnetic flux, predicted by the rising magnetic flux rope theories, is found. Analysis of surface plasma flows in a large emerging active region reveals strong localized upflows and downflows at the initial phase of emergence but finds no evidence for large-scale flows indicating future appearance a large-scale magnetic structure. Local helioseismology provides important tools for mapping perturbations of the wave speed and mass flows below the surface. Initial results from SOHO/MDI and GONG reveal strong diverging flows during the flux emergence, and also localized converging flows around stable sunspots. The wave speed images obtained during the process of formation of a large active region, NOAA 10488, indicate that the magnetic flux gets concentrated in strong field structures just below the surface. Further studies of magnetic flux emergence require systematic helioseismic observations from the ground and space, and realistic MHD simulations of the subsurface dynamics.Comment: 21 pages, 15 figures, to appear in Space Science Review

Advances in Global and Local Helioseismology: an Introductory Review

Helioseismology studies the structure and dynamics of the Sun's interior by observing oscillations on the surface. These studies provide information about the physical processes that control the evolution and magnetic activity of the Sun. In recent years, helioseismology has made substantial progress towards the understanding of the physics of solar oscillations and the physical processes inside the Sun, thanks to observational, theoretical and modeling efforts. In addition to the global seismology of the Sun based on measurements of global oscillation modes, a new field of local helioseismology, which studies oscillation travel times and local frequency shifts, has been developed. It is capable of providing 3D images of the subsurface structures and flows. The basic principles, recent advances and perspectives of global and local helioseismology are reviewed in this article.Comment: 86 pages, 46 figures; "Pulsation of the Sun and Stars", Lecture Notes in Physics, Vol. 832, Rozelot, Jean-Pierre; Neiner, Coralie (Eds.), 201

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58×10-8, Ω0V<6.35×10-8, and Ω0S<1.08×10-7 at a reference frequency f0=25 Hz. © 2018 American Physical Society

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society

On the progenitor of binary neutron star merger GW170817

On 2017 August 17 the merger of two compact objects with masses consistent with two neutron stars was discovered through gravitational-wave (GW170817), gamma-ray (GRB 170817A), and optical (SSS17a/AT 2017gfo) observations. The optical source was associated with the early-type galaxy NGC 4993 at a distance of just ∼40 Mpc, consistent with the gravitational-wave measurement, and the merger was localized to be at a projected distance of ∼2 kpc away from the galaxy's center. We use this minimal set of facts and the mass posteriors of the two neutron stars to derive the first constraints on the progenitor of GW170817 at the time of the second supernova (SN). We generate simulated progenitor populations and follow the three-dimensional kinematic evolution from binary neutron star (BNS) birth to the merger time, accounting for pre-SN galactic motion, for considerably different input distributions of the progenitor mass, pre-SN semimajor axis, and SN-kick velocity. Though not considerably tight, we find these constraints to be comparable to those for Galactic BNS progenitors. The derived constraints are very strongly influenced by the requirement of keeping the binary bound after the second SN and having the merger occur relatively close to the center of the galaxy. These constraints are insensitive to the galaxy's star formation history, provided the stellar populations are older than 1 Gyr