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A magnitude-least-squares radiofrequency pulse design algorithm is reported which uses interleaved exact and stochastically-generated inexact updates to escape local minima and find low-cost solutions. Inexact updates are performed using a small randomly selected minibatch of the available B1+ measurements to update RF pulse weights, which perturbs the sequence of alternating projections. Applications to RF shimming, parallel transmit spokes RF pulse design, and spectral-spatial RF pulse design are considered. Numerical and simulation studies characterized the optimal minibatch size, which was found to consistently produce lower power and lower RMSE solutions across subjects, coil geometries, B1+ resolutions and orientations. The method was validated in-vivo at 7 Tesla and produced improvements in image quality in a slice-by-slice RF-shimmed imaging sequence. Compared to conventional methods, the pulse design method can more robustly design RF pulses that correct for B1+ inhomogeneities at ultra-high field strengths, and enable pulse designs to be completed with increased computational efficiency, Comment: 14 pages (including initial blank page), 15 figures (including 2 tables)

We present measurements of X-ray Parametric Down Conversion at the Advanced Photon Source synchrotron facility. Using an incoming pump beam at 22 keV, we observe the simultaneous, elastic emission of down-converted photon pairs generated in a diamond crystal. The pairs are detected using high count rate silicon drift detectors with low noise. Production by down-conversion is confirmed by measuring time-energy correlations in the detector signal, where photon pairs within an energy window ranging from 10 to 12 keV are only observed at short time differences. By systematically varying the crystal misalignment and detector positions, we obtain results that are consistent with the constant total of the down-converted signal. Our maximum rate of observed pairs was 130 /hour, corresponding to a conversion efficiency for the down-conversion process of $5.3 \pm 0.5 \times 10^{-13}$.

Signal to noise ratios (SNR) in magnetic resonance microscopy images are limited by acquisition times and the decreasing number of spins in smaller voxels. Significant SNR gains from cooling of the RF receiver are only realized when the Johnson noise generated within the RF hardware is large compared to the electromagnetic noise produced by the sample. Cryogenic cooling of imaging probes is common in high field systems but proves difficult to insulate the sample from extreme temperatures. We designed a chamber to cool only the tune and match circuitry to show it is possible to achieve much of the available SNR gain available for cooled coils. We designed a microcoil circuit to resonate at 650 MHz for imaging on a 15.2 T scanner. Surface loops and solenoids of varying diameters were tested to determine the largest diameter coil that demonstrated significant SNR gains from cooling. A liquid N2 cryochamber was designed to cool the circuitry while leaving the RF coil in ambient air. As the cryochamber was filled with liquid N2, Q-factors were measured on the bench while monitoring the coil's surface temperature. Improvements of SNR on images of solutions were demonstrated via cooling the tune and match circuit in the magnet bore. At 650 MHz, loops and solenoids < 3 mm in diameter showed significant improvements in quality factor on the bench. The resistance of the variable capacitors and the coaxial cable were measured to be 45% and 32% of room temperature values near the Larmor frequency. Images obtained with a 2 turn, 3 mm diameter loop with the matching circuit at room temperature and then cooled with liquid nitrogen demonstrated SNR improvements of a factor of 2. By cooling the tune and match circuit and leaving the surface loop in ambient air, SNR was improved by a factor of 2. The results are significant because it allows for more space to insulate the sample from extreme temperatures., Comment: 33 pages, 10 figures, 1 table, 4 supplemental figures, 1 supplemental table

Magnetic resonance microscopy images at cellular resolution (< 10 microns) are limited by diffusion. SNR and spatial resolution suffer from the dephasing of transverse magnetization caused by diffusion of spins in strong gradients. Such effects may be reduced by using phase encoding instead of frequency encoding readout gradients. Demonstration of the benefits of phase encoding are lacking, and the conditions in which it is preferred are not clearly established. We quantify when phase encoding outperforms a readout gradient with emphasis on the detrimental effects of diffusion on SNR and resolution. A 15.2T MRI scanner, with 1 T/m gradients, and micro solenoid RF coils < 1 mm in diameter, were used to quantify diffusion effects on resolution and SNR of frequency and phase encoded acquisitions. Frequency and phase encoding resolution and SNR per square root time were calculated and measured for images at the diffusion limited resolution. The point-spread-function was measured for phase and frequency encoding using additional constant time gradients with voxels 3-15 microns. The effect of diffusion during the readout gradient on SNR was experimentally demonstrated. The achieved resolutions of frequency and phase encoded acquisitions were measured via the point-spread-function. SNR per square root time and actual resolution were calculated for a wide range of gradient amplitudes, diffusion coefficients, and relaxation properties. The results provide a practical guide on how to choose between phase and frequency encoding. Images of excised rat spinal cord at 10 x 10 microns in-plane demonstrate benefits of phase encoding in the form of higher measured resolution and SNR vs the same image acquired with a conventional readout. We demonstrate the extent to which phase encoding outperforms readout gradients in SNR and resolution over a wide range of voxel sizes, sample, and hardware properties., Comment: 36 pages, 9 figures, 1 table, and 4 supplemental figures. Submitted to Journal of Magnetic Resonance; cleaned up metadata, fixed heading typo

We present the first results from the ongoing, intensive, multi-wavelength monitoring program of the luminous Seyfert 1 galaxy Mrk 817. While this AGN was, in part, selected for its historically unobscured nature, we discovered that the X-ray spectrum is highly absorbed, and there are new blueshifted, broad and narrow UV absorption lines, which suggest that a dust-free, ionized obscurer located at the inner broad line region partially covers the central source. Despite the obscuration, we measure UV and optical continuum reverberation lags consistent with a centrally illuminated Shakura-Sunyaev thin accretion disk, and measure reverberation lags associated with the optical broad line region, as expected. However, in the first 55 days of the campaign, when the obscuration was becoming most extreme, we observe a de-coupling of the UV continuum and the UV broad emission line variability. The correlation recovers in the next 42 days of the campaign, as Mrk 817 enters a less obscured state. The short CIV and Ly alpha lags suggest that the accretion disk extends beyond the UV broad line region., Comment: 28 pages, 14 figures, submitted to ApJ. Comments welcome

We present geometric and dynamical modeling of the broad line region for the multi-wavelength reverberation mapping campaign focused on NGC 5548 in 2014. The dataset includes photometric and spectroscopic monitoring in the optical and ultraviolet, covering the H$\beta$, C IV, and Ly$\alpha$ broad emission lines. We find an extended disk-like H$\beta$ BLR with a mixture of near-circular and outflowing gas trajectories, while the C IV and Ly$\alpha$ BLRs are much less extended and resemble shell-like structures. There is clear radial structure in the BLR, with C IV and Ly$\alpha$ emission arising at smaller radii than the H$\beta$ emission. Using the three lines, we make three independent black hole mass measurements, all of which are consistent. Combining these results gives a joint inference of $\log_{10}(M_{\rm BH}/M_\odot) = 7.64^{+0.21}_{-0.18}$. We examine the effect of using the $V$ band instead of the UV continuum light curve on the results and find a size difference that is consistent with the measured UV-optical time lag, but the other structural and kinematic parameters remain unchanged, suggesting that the $V$ band is a suitable proxy for the ionizing continuum when exploring the BLR structure and kinematics. Finally, we compare the H$\beta$ results to similar models of data obtained in 2008 when the AGN was at a lower luminosity state. We find that the size of the emitting region increased during this time period, but the geometry and black hole mass remain unchanged, which confirms that the BLR kinematics suitably gauge the gravitational field of the central black hole., Comment: 26 pages, 19 figures, 1 table, accepted for publication in ApJ

We report velocity-delay maps for prominent broad emission lines, Ly_alpha, CIV, HeII and H_beta, in the spectrum of NGC5548. The emission-line responses inhabit the interior of a virial envelope. The velocity-delay maps reveal stratified ionization structure. The HeII response inside 5-10 light-days has a broad single-peaked velocity profile. The Ly_alpha, CIV, and H_beta responses peak inside 10 light-days, extend outside 20 light-days, and exhibit a velocity profile with two peaks separated by 5000 km/s in the 10 to 20 light-day delay range. The velocity-delay maps show that the M-shaped lag vs velocity structure found in previous cross-correlation analysis is the signature of a Keplerian disk with a well-defined outer edge at R=20 light-days. The outer wings of the M arise from the virial envelope, and the U-shaped interior of the M is the lower half of an ellipse in the velocity-delay plane. The far-side response is weaker than that from the near side, so that we see clearly the lower half, but only faintly the upper half, of the velocity--delay ellipse. The delay tau=(R/c)(1-sin(i))=5 light-days at line center is from the near edge of the inclined ring, giving the inclination i=45 deg. A black hole mass of M=7x10^7 Msun is consistent with the velocity-delay structure. A barber-pole pattern with stripes moving from red to blue across the CIV and possibly Ly_alpha line profiles suggests the presence of azimuthal structure rotating around the far side of the broad-line region and may be the signature of precession or orbital motion of structures in the inner disk. Further HST observations of NGC 5548 over a multi-year timespan but with a cadence of perhaps 10 days rather than 1 day could help to clarify the nature of this new AGN phenomenon., Comment: 19 pages, 9 figures, ApJ in press

Mounting evidence from both seismology and experiments on core composition suggests the existence of a layer of stably stratified fluid at the top of Earth's outer core. In this work we examine the structure of the geomagnetic field within such a layer, building on the important but little known work of Malkus (1979). We assume (i) an idealised magnetostrophic spherical model of the geodynamo neglecting inertia, viscosity and the solid inner core, and (ii) a strongly stratified layer of constant depth immediately below the outer boundary within which there is no spherically radial flow. Due to the restricted dynamics, Malkus showed that the geomagnetic field must obey a certain condition which is a more restrictive version of the condition of Taylor (1963). The nonlinear nature of these constraints makes finding a magnetic field that obeys them, here termed a Malkus state, a challenging task. Nevertheless, such Malkus states when constrained further by geomagnetic observations have the potential to probe the interior of the core. By focusing on a particular class of magnetic fields for which the Malkus constraints are linear, we describe a constructive method that turns any purely-poloidal field into an exact Malkus state by adding a suitable toroidal field. We consider poloidal fields following a prescribed smooth profile within the core that match observation-derived models of the magnetic field in either epoch 2015 or the 10000-yr time averaged field. Multiple possible solutions for the toroidal field exist, hence we determine the Malkus state of miumum toroidal energy and we find that it has a strong azimuthal toroidal field, larger than the observed poloidal component at the core-mantle boundary. For the 2015 field for a layer of depth 300 km, we estimate a root mean squared azimuthal toroidal field of 3 mT with a pointwise maximum of 8 mT occurring at a depth of about 70 km., Comment: 27 pages, 10 figures

We present an end-to-end statistical framework for personalized, accurate, and minimally invasive modeling of female reproductive hormonal patterns. Reconstructing and forecasting the evolution of hormonal dynamics is a challenging task, but a critical one to improve general understanding of the menstrual cycle and personalized detection of potential health issues. Our goal is to infer and forecast individual hormone daily levels over time, while accommodating pragmatic and minimally invasive measurement settings. To that end, our approach combines the power of probabilistic generative models (i.e., multi-task Gaussian processes) with the flexibility of neural networks (i.e., a dilated convolutional architecture) to learn complex temporal mappings. To attain accurate hormone level reconstruction with as little data as possible, we propose a sampling mechanism for optimal reconstruction accuracy with limited sampling budget. Our results show the validity of our proposed hormonal dynamic modeling framework, as it provides accurate predictive performance across different realistic sampling budgets and outperforms baselines methods., Comment: Accepted and presented in Machine Learning for Healthcare 2019

Purpose: Cell size is a fundamental characteristic of all tissues, and changes in cell size in cancer reflect tumor status and response to treatments, such as apoptosis and cell cycle arrest. Unfortunately, cell size can only be obtained by pathologic evaluation of the tumor in the current standard of care. Previous imaging approaches can be implemented on only animal MRI scanners or require relatively long acquisition times that are undesirable for clinical imaging. There is a need to develop cell size imaging for clinics. Experimental Design: We propose a new method, IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) that can characterize mean cell sizes in solid tumors. We report the use of combined sequences with different gradient waveforms on human MRI and analytical equations that link DWI signals of real gradient waveforms and specific microstructural parameters such as cell size. We also describe comprehensive validations using computer simulations, cell experiments in vitro, and animal experiments in vivo and finally demonstrate applications in pre-operative breast cancer patients. Results: With fast acquisitions (~ 7 mins), IMPULSED can provide high-resolution (1.3 mm in-plane) mapping of mean cell size of human tumors in vivo on currently-available 3T MRI scanners. All validations suggest IMPULSED provide accurate and reliable measurements of mean cell size. Conclusion: The proposed IMPULSED method can assess cell size variations in the tumor of breast cancer patients, which may have the potential to assess early response to neoadjuvant therapy.

The flux variations in the emission lines in active galactic nuclei (AGNs) are driven by variations in the ionizing continuum flux --which are usually reflected in the observable UV-optical continuum. The "Reverberation mapping" technique measures the delay between line and continuum variations to determine the size of the line emitting region, this is the basis for measurements of the central black hole mass in AGNs. The Space Telescope and Optical Reverberation Mapping Project (AGN STORM) on NGC 5548 in 2014 is the most intensive multi-wavelength AGN monitoring campaign ever. For most of the campaign, the emission-line variations followed changes in the continuum with a time lag, as expected. However, the lines varied independently of the observed UV-optical continuum during a 60 -- 70 day "holiday." To understand this remarkable phenomenon, we study the intrinsic absorption lines present in NGC 5548. We identify a novel cycle that reproduces the absorption line variability and thus identify the physics that allows the holiday to occur. In our model, variations in this obscurer's line-of-sight covering factor modify the soft X-ray continuum. This leads to changes in the ionization of helium gas in the broad-line region. Ionizing radiation produced by recombining helium then affects the ionization of other species as observed during the AGN STORM holiday. It is likely that any other model which selectively changes the soft X-ray part of the continuum during the holiday can also explain the anomalous emission line behavior observed., Comment: This is the version accepted by ApJ. Will be published shortly

In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically-averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalisation of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any 3D Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully 3D case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular., Comment: 29 Pages, 8 figures

Using the variational Monte-Carlo method we find that a relatively weak long-range electron-phonon interaction induces a d-wave superconducting state of doped Mott-Hubbard insulators and/or strongly-correlated metals with a condensation energy significantly larger than can be obtained with Coulomb repulsion only. Moreover, the superconductivity is shown to exist for infinite on-site Coulomb repulsion, removing the requirement for additional mechanisms such as spin fluctuations to mediate d-wave superconductivity. We argue that the superconducting state is robust with respect to a more intricate choice of the trial function and that the true origin of high-temperature superconductivity lies in a proper combination of strong electron-electron correlations with poorly screened Froehlich electron-phonon interaction., Comment: 4 pages, 4 figures