Radar backscattering data for surfaces of geological interest

Radar backscattering data for surfaces of geological interes

Magnetic Fields in Dark Cloud Cores: Arecibo OH Zeeman Observations

We have carried out an extensive survey of magnetic field strengths toward dark cloud cores in order to test models of star formation: ambipolar-diffusion driven or turbulence driven. The survey involved $\sim500$ hours of observing with the Arecibo telescope in order to make sensitive OH Zeeman observations toward 34 dark cloud cores. Nine new probable detections were achieved at the 2.5-sigma level; the certainty of the detections varies from solid to marginal, so we discuss each probable detection separately. However, our analysis includes all the measurements and does not depend on whether each position has a detection or just a sensitive measurement. Rather, the analysis establishes mean (or median) values over the set of observed cores for relevant astrophysical quantities. The results are that the mass-to-flux ratio is supercritical by $\sim 2$, and that the ratio of turbulent to magnetic energies is also $\sim 2$. These results are compatible with both models of star formation. However, these OH Zeeman observations do establish for the first time on a statistically sound basis the energetic importance of magnetic fields in dark cloud cores at densities of order $10^{3-4}$ cm$^{-3}$, and they lay the foundation for further observations that could provide a more definitive test.Comment: 22 pages, 2 figures, 2 table

Machine learning invariants of arithmetic curves

We show that standard machine learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around 105, we demonstrate the utility of machine learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998

Machine-learning the Sato-Tate conjecture

We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato–Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato–Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato–Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato–Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato–Tate distributions and may be able to classify curves efficiently

Character expansion of Kac–Moody correction factors

A correction factor naturally arises in the theory of p-adic Kac–Moody groups. We expand the correction factor into a sum of irreducible characters of the underlying Kac–Moody algebra. We derive a formula for the coefficients which lie in the ring of power series with integral coefficients. In the case that the Weyl group is a universal Coxeter group, we show that the coefficients are actually polynomials

Real-time Assessment of Right and Left Ventricular Volumes and Function in Children Using High Spatiotemporal Resolution Spiral bSSFP with Compressed Sensing

Background: Real-time (RT) assessment of ventricular volumes and function enables data acquisition during free-breathing. However, in children the requirement for high spatiotemporal resolution requires accelerated imaging techniques. In this study, we implemented a novel RT bSSFP spiral sequence reconstructed using Compressed Sensing (CS) and validated it against the breath-hold (BH) reference standard for assessment of ventricular volumes in children with heart disease. Methods: Data was acquired in 60 children. Qualitative image scoring and evaluation of ventricular volumes was performed by 3 clinical cardiac MR specialists. 30 cases were reassessed for intra-observer variability, and the other 30 cases for inter-observer variability. Results: Spiral RT images were of good quality, however qualitative scores reflected more residual artefact than standard BH images and slightly lower edge definition. Quantification of Left Ventricular (LV) and Right Ventricular (RV) metrics showed excellent correlation between the techniques with narrow limits of agreement. However, we observed small but statistically significant overestimation of LV end-diastolic volume, underestimation of LV end-systolic volume, as well as a small overestimation of RV stroke volume and ejection fraction using the RT imaging technique. No difference in inter-observer or intra-observer variability were observed between the BH and RT sequences. Conclusions: Real-time bSSFP imaging using spiral trajectories combined with a compressed sensing reconstruction is feasible. The main benefit is that it can be acquired during free breathing. However, another important secondary benefit is that a whole ventricular stack can be acquired in ~20 seconds, as opposed to ~6 minutes for standard BH imaging. Thus, this technique holds the potential to significantly shorten MR scan times in children

Explicit solution of the linearized Einstein equations in TT gauge for all multipoles

We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to appear in Class. Quantum Gra

Radar and microwave radiometric techniques for geoscience experiments

Radar backscattering data for farm crop

Nonlinear resonant behavior of the dispersive readout scheme for a superconducting flux qubit

A nonlinear resonant circuit comprising a SQUID magnetometer and a parallel capacitor is studied as a readout scheme for a persistent-current (PC) qubit. The flux state of the qubit is detected as a change in the Josephson inductance of the SQUID magnetometer, which in turn mediates a shift in the resonance frequency of the readout circuit. The nonlinearity and resulting hysteresis in the resonant behavior are characterized as a function of the power of both the input drive and the associated resonance peak response. Numerical simulations based on a phenomenological circuit model are presented which display the features of the observed nonlinearity.Comment: 9 pages, 9 figure

Forster-induced energy transfer in functionalized graphene

Carbon nanostructures are ideal substrates for functionalization with molecules since they consist of a single atomic layer giving rise to an extraordinary sensitivity to changes in their surrounding. The functionalization opens a new research field of hybrid nanostructures with tailored properties. Here, we present a microscopic view on the substrate–molecule interaction in the exemplary hybrid material consisting of graphene functionalized with perylene molecules. First experiments on similar systems have been recently realized illustrating an extremely efficient transfer of excitation energy from adsorbed molecules to the carbon substrate, a process with a large application potential for high-efficiency photovoltaic devices and biomedical imaging and sensing. So far, there has been no microscopically founded explanation for the observed energy transfer. Based on first-principle calculations, we have explicitly investigated the different transfer mechanisms revealing the crucial importance of Förster coupling. Due to the efficient Coulomb interaction in graphene, we obtain strong Förster rates in the range of 1/fs. We investigate its dependence on the substrate–molecule distance R and describe the impact of the momentum transfer q for an efficient energy transfer. Furthermore, we find that the Dexter transfer mechanism is negligibly small due to the vanishing overlap between the involved strongly localized orbital functions. The gained insights are applicable to a variety of carbon-based hybrid nanostructures.We thank the Einstein Foundation Berlin and the Deutsche Forschungsgemeinschaft (within the collaborative research center SFB 658) for financial support. O.T.H. acknowledges the support from FWF (Project: J 3285-N20). A.R. acknowledges financial support from the European Research Council (ERC-2010-AdG-267374), Spanish Grant (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and the EU Project (280879-2 CRONOS CP-FP7).Peer Reviewe