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We report the confirmation of TOI-6324 b, an Earth-sized (1.059 $\pm$ 0.041 R$_\oplus$) ultra-short-period (USP) planet orbiting a nearby ($\sim$20 pc) M dwarf. Using the newly commissioned Keck Planet Finder (KPF) spectrograph, we have measured the mass of TOI-6324 b 1.17 $\pm$ 0.22 M$_\oplus$. Because of its extremely short orbit of just $\sim$6.7 hours, TOI-6324 b is intensely irradiated by its M dwarf host, and is expected to be stripped of any thick, H/He envelope. We were able to constrain its interior composition and found an iron core mass fraction (CMF = 27$\pm$37%) consistent with that of Earth ($\sim$33%) and other confirmed USPs. TOI-6324 b is the closest to Earth-sized USP confirmed to date. TOI-6324 b is a promising target for JWST phase curve and secondary eclipse observations (Emission Spectroscopy Metric = 25) which may reveal its surface mineralogy, day-night temperature contrast, and possible tidal deformation. From 7 sectors of TESS data, we report a tentative detection of the optical phase curve variation with an amplitude of 42$\pm$28 ppm., Comment: 16 pages, 5 figures, 2 tables

This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part of the thesis defines the syntactic foundations of sequential circuit morphisms, and then builds three different semantic theories: denotational, operational and algebraic. We characterise the denotational semantics of sequential circuits as certain causal stream functions, as well as providing a link to existing circuit methodologies by mapping between circuit morphisms, stream functions and Mealy machines. The operational semantics is defined as a strategy for applying some global transformations followed by local reductions to demonstrate how a circuit processes a value, leading to a notion of observational equivalence. The algebraic semantics consists of equations for bringing circuits into a pseudo-normal form, and then encoding between different state sets. This part of the thesis concludes with a discussion of some novel applications, such as those for using partial evaluation for digital circuits. While mathematically rigorous, the categorical string diagram formalism is not suited for reasoning computationally. The second part of this thesis details an extension of string diagram rewriting with hypergraphs so that it is compatible with the traced comonoid structure present in the category of digital circuits. We identify the properties that characterise cospans of hypergraphs corresponding to traced comonoid terms, and demonstrate how to identify rewriting contexts valid for rewriting modulo traced comonoid structure. We apply the graph rewriting framework to fixed point operators as well as the operational semantics from the first part, and present a new hardware description language based on these theoretical developments., Comment: PhD thesis, 272 pages

We proceed with the study of the Nehari manifold method for functionals in $C^1(X \setminus \{0\})$, where $X$ is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimiser followed by a maximiser). Under some additional conditions we show that the Nehari manifold method provides us with the ground state level and two sequences of critical values for these functionals. These results are applied to the class of {\it prescribed energy problems} as well as to the concave-convex problem for the {\it affine} $p$-Laplacian operator.

Relativistic secular perturbation theory has ignited significant interest in uncovering intricate cross-term effects, especially the interplay between 1PN and quadrupole terms. While most existing studies rely on the Lagrangian planetary perturbation method for computing cross terms, a comprehensive Hamiltonian framework for the field has been missing. In this work, we introduce a framework based on von Zeipel transformation, utilizing two sequential canonical transformations to systematically compute cross terms to arbitrary orders. Our results reveal secular cross terms up to quadrupole-squared order, showcasing remarkable consistency with both the Lagrangian method [1] and the effective-field-theory approach [2]. We present leading-order periodic cross terms arising from the interactions between 1PN and quadrupole, and present estimates of higher-order cross terms. It is demonstrated that this method not only accurately predicts the long-term evolution of hierarchical systems but also captures fast oscillations observed in N-body simulations. We identify and validate resonances caused by quadrupole-squared effects, highlighting both consistencies and discrepancies when compared to N-body simulations. These discrepancies underscore the importance of mean-motion resonances, a factor overlooked in current secular perturbation frameworks. Finally, we provide a comprehensive review of the subtleties and limitations inherent to secular perturbation theory, paving the way for future research and advancements in this field., Comment: 28 pages, 9 figures, comments welcome

Direct-current resistivity is a key probe for the physical properties of materials. In metals, Fermi-liquid (FL) theory serves as the basis for understanding transport. A $T^2$ behavior of the resistivity is often taken as a signature of FL electron-electron scattering. However, the presence of impurity and phonon scattering as well as material-specific aspects such as Fermi surface geometry can complicate this interpretation. We demonstrate how density-functional theory combined with dynamical mean-field theory can be used to elucidate the FL regime. We take as examples SrVO$_{3}$ and SrMoO$_{3}$, two moderately correlated perovskite oxides, and establish a precise framework to analyze the FL behavior of the self-energy at low energy and temperature. Reviewing published low-temperature resistivity measurements, we find agreement between our calculations and experiments performed on samples with exceptionally low residual resistivity. This comparison emphasizes the need for further theoretical, synthesis, and characterization developments in these and other FL materials., Comment: 9 pages, 4 figures

X-ray attenuation, phase, and dark-field images provide complementary information. Different experimental techniques can capture these contrast mechanisms, and the corresponding images can be retrieved using various theoretical algorithms. Our previous works developed the Multimodal Intrinsic Speckle-Tracking (MIST) algorithm, which is suitable for multimodal image retrieval from speckle-based X-ray imaging (SBXI) data. MIST is based on the X-ray Fokker-Planck equation, requiring the inversion of derivative operators that are often numerically unstable. These instabilities can be addressed by employing regularization techniques, such as Tikhonov regularization. The regularization output is highly sensitive to the choice of the Tikhonov regularization parameter, making it crucial to select this value carefully and optimally. Here, we present an automated iterative algorithm to optimize the regularization of the inverse Laplacian operator in our most recently published MIST variant, addressing the operator's instability near the Fourier-space origin. Our algorithm leverages the inherent stability of the phase solution obtained from the transport-of-intensity equation for SBXI, using it as a reliable ground truth for the more complex Fokker-Planck-based algorithms that incorporate the dark-field signal. We applied the algorithm to an SBXI dataset collected using synchrotron light of a four-rod sample. The four-rod sample's phase and dark-field images were optimally retrieved using our developed algorithm, eliminating the tedious and subjective task of selecting a suitable Tikhonov regularization parameter. The developed regularization-optimization algorithm makes MIST more user-friendly by eliminating the need for manual parameter selection. We anticipate that our optimization algorithm can also be applied to other image retrieval approaches derived from the Fokker-Planck equation.

X-ray dark-field imaging visualises scattering from sample microstructure, and has found application in medical and security contexts. While most X-ray dark-field imaging techniques rely on masks, gratings, or crystals, recent work on the Fokker--Planck model of diffusive imaging has enabled dark-field imaging in the propagation-based geometry. Images captured at multiple propagation distances or X-ray energies can be used to reconstruct dark-field from propagation-based images but have previously required multiple exposures. Here, we show single-exposure dark-field imaging by exploiting the harmonic content in a monochromatised synchrotron beam and utilising an energy-discriminating photon-counting detector to capture dual-energy propagation-based images. The method is validated by filming time-varying samples, showing the advantage of the dark-field contrast in analysing dynamic evolution. We measure and adjust for the impact of detector charge-sharing on the images. This work opens the way for low-dose and dynamic dark-field X-ray imaging without the need for a high-stability set-up and precision optics., Comment: 9 pages, 7 figures

The global food system provides the energy that supports human metabolism, with complex spatial interdependencies between food production, transformation, and consumption. Empirical food system data for these global processes are often fragmented and inconsistent, with only certain components captured in spatially resolved formats. Here we propose a flexible approach to allocating country-level food system data subnationally. We estimate the spatial patterns of food energy production and supply, which we compare to estimates of human metabolism based on average body size. We downscale these rates onto a one-degree resolution grid with 95 corresponding food types to derive an internally consistent, energy-conserving, and spatially resolved dataset. We show that national food supply varies linearly with metabolism per capita, with about half the variation in food supply explained by metabolic rates. Our data processing pipeline is openly available and can readily incorporate new inputs in order to advance trans-disciplinary food system modeling efforts., Comment: 19 pages, 4 figures

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R has recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction, and showing that one can reduce all the key problems in the 3D reconstruction of static scenes to predicting such point maps. In this paper, we develop an analogous concept for a very different problem, namely, the reconstruction of the 3D shape and pose of deformable objects. To this end, we introduce the Dual Point Maps (DualPM), where a pair of point maps is extracted from the same image, one associating pixels to their 3D locations on the object, and the other to a canonical version of the object at rest pose. We also extend point maps to amodal reconstruction, seeing through self-occlusions to obtain the complete shape of the object. We show that 3D reconstruction and 3D pose estimation reduce to the prediction of the DualPMs. We demonstrate empirically that this representation is a good target for a deep network to predict; specifically, we consider modeling horses, showing that DualPMs can be trained purely on 3D synthetic data, consisting of a single model of a horse, while generalizing very well to real images. With this, we improve by a large margin previous methods for the 3D analysis and reconstruction of this type of objects., Comment: First two authors contributed equally. Project page: https://dualpm.github.io

X-ray dark-field imaging is well-suited to visualizing the health of the lungs because the alveoli create a strong dark-field signal. However, time-resolved and tomographic (i.e., 4D) dark-field imaging is challenging, since most x-ray dark-field techniques require multiple sample exposures, captured while scanning the position of crystals or gratings. Here, we present the first in vivo 4D x-ray dark-field lung imaging in mice. This was achieved by synchronizing the data acquisition process of a single-exposure grid-based imaging approach with the breath cycle. The short data acquisition time per dark-field projection made this approach feasible for 4D x-ray dark-field imaging by minimizing the motion-blurring effect, the total time required and the radiation dose imposed on the sample. Images were captured from a control mouse and from mouse models of muco-obstructive disease and lung cancer, where a change in the size of the alveoli was expected. This work demonstrates that the 4D dark-field signal provides complementary information that is inaccessible from conventional attenuation-based CT images, in particular, how the size of the alveoli from different parts of the lungs changes throughout a breath cycle, with examples shown across the different models. By quantifying the dark-field signal and relating it to other physical properties of the alveoli, this technique could be used to perform functional lung imaging that allows the assessment of both global and regional lung conditions where the size or expansion of the alveoli is affected., Comment: 11 pages, 5 figures, supplementary information available

A key contribution to X-ray dark-field (XDF) is X-ray diffusion by sample structures smaller than the imaging system's spatial resolution. However, some XDF techniques report that resolvable sample edges also generate XDF. Speckle-based X-ray imaging (SBXI) extracts XDF by analyzing sample-imposed changes to a reference speckle pattern's visibility. We present an algorithm for SBXI (a variant of our Multimodal Intrinsic Speckle-Tracking (MIST) algorithm) capable of separating these two distinct XDF contrast mechanisms. The algorithm uses the 'devolving' X-ray Imaging Fokker-Planck equation as its forward model and then solves the associated multimodal inverse problem, to retrieve sample attenuation, phase, and XDF. Previous MIST variants were based on the evolving Fokker-Planck equation, which considers how a reference-speckle image is modified by introducing a sample. The devolving perspective instead considers how the image collected in the presence of the sample and speckle membrane optically flows in reverse, to generate the reference-speckle image when the sample is removed from the system. We compare single- and multiple-exposure multimodal retrieval algorithms from the two Fokker-Planck perspectives. We demonstrate that the devolving perspective can distinguish between two physically different XDF contrast mechanisms; unresolved microstructure- and sharp-edge-induced XDF. This was verified by applying the retrieval algorithms to two experimental data sets. We anticipate that this work will be useful in: Yielding a pair of complementary XDF images that separate sharp-edge diffuse scatter from unresolved microstructure diffuse scatter. XDF computed tomography, where the strong edge XDF can lead to tainting streaking artefacts. Sample preparation, as samples will not need to be embedded since the strong XDF edge signal seen between the sample and air can be separated out., Comment: 21 pages and 7 figures

Hundreds of exoplanets between 1-1.8 times the size of the Earth have been discovered on close in orbits. However, these planets show such a diversity in densities that some appear to be made entirely of iron, while others appear to host gaseous envelopes. To test this diversity in composition, we update the masses of 5 rocky exoplanets (HD 93963 A b, Kepler-10 b, Kepler-100 b, Kepler-407 b, and TOI-1444 b) and present the confirmation of a new planet (TOI-1011) using 187 high precision RVs from Gemini/MAROON-X and Keck/KPF. Our updated planet masses suggest compositions closer to that of the Earth than previous literature values for all planets in our sample. In particular, we report that two previously identified ``super-Mercuries'' (Kepler-100 b and HD 93963 A b) have lower masses that suggest less iron-rich compositions. We then compare the ratio of iron to rock-building species to the abundance ratios of those elements in their host stars. These updated planet compositions do not suggest a steep relationship between planet and host star compositions, contradictory to previous results, and suggest that planets and host stars have similar abundance ratios., Comment: Submitted to AJ 09/30/2024

Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the {\it prescribed energy problem} for a family of functionals depending on a parameter, problems involving the {\it affine} $p$-Laplacian operator, and degenerate Kirchhoff type problems.

Analyzing images of the Cygnus Loop, a core-collapse supernova (CCSN) remnant, in different emission bands, we identify a point-symmetrical morphology composed of three symmetry axes that we attribute to shaping by three pairs of jets. The main jet axis has an elongated S shape, appearing as a faint narrow zone in visible and UV. We term it the S-shaped hose, and the structure of three symmetry lines, the point-symmetric wind rose. The two other lines connect a protrusion (an ear or a bulge) with a hole on the opposite side of the center (a nozzle or a cavity), structures that we identify in the X-ray, UV, visible, IR, and/or radio images. There is a well-known blowout at the southern end of the S-shaped hose, and we identify a possible opposite blowout at the northern end of the S-shaped hose. The point-symmetrical morphology of the Cygnus Loop is according to the expectation of the jittering jets explosion mechanism (JJEM) of CCSNe, where several to few tens of pairs of jets with stochastically varying directions explode the star. The three pairs of jets that shaped the wind-rose structure of the Cygnus Loop are the last energetic pairs of this series of jets. Our study further supports the JJEM as the main explosion mechanism of CCSNe., Comment: 11 pages, 5 figures. Published in the Astrophysical Journal

The cadmium zinc TElluride Radiation Imager, or TERI, is an instrument to space qualify large-volume $4 \times 4 \times 1.5 \ \mathrm{cm}^3$ pixelated CdZnTe (CZT) detector technology. The CZT's anode is composed of a $22 \times 22$ array of pixels while the cathode is planar. TERI will contain four of those crystals with each pixel having an energy range of $40 \ \mathrm{keV}$ up to $3 \ \mathrm{MeV}$ with a resolution of $1.3 \%$ full-width-at-half maximum at $662 \ \mathrm{keV}$ all while operating in room temperature. As the detectors are 3D position sensitive, TERI can Compton image events. TERI is fitted with a coded-aperture mask which permits imaging low energy photons in the photoelectric regime. TERI's primary mission is to space-qualify large-volume CZT and measure its degradation due to radiation damage in a space environment. Its secondary mission includes detecting and localizing astrophysical gamma-ray transients. TERI is manifested on DoD's STP-H10 mission for launch to the International Space Station in early 2025.

Characterizing outer companions to hot Jupiters plays a crucial role in deciphering their origins. We present the discovery of a long-period giant planet, HD 118203 c ($m_{c}=11.79^{+0.69}_{-0.63}\ \mathrm{M_{J}}$, $a_{c}=6.28^{+0.10}_{-0.11}$ AU) exterior to a close-in eccentric hot Jupiter HD 118203 b ($P_{b}=6.135\ \mathrm{days}$, $m_{b}=2.14\pm{0.12}\ \mathrm{M_{J}}$, $r_{b}=1.14\pm{0.029}\ \mathrm{R_{J}}$, $e_{b}=0.31\pm{0.007}$) based on twenty-year radial velocities. Using Rossiter-McLaughlin (RM) observations from the Keck Planet Finder (KPF), we measured a low sky-projected spin-orbit angle $\lambda_{b}=-11^{\circ}.7^{+7.6}_{-10.0}$ for HD 118203 b and detected stellar oscillations in the host star, confirming its evolved status. Combining the RM observation with the stellar inclination measurement, we constrained the true spin-orbit angle of HD 118203 b as $\Psi_{b}<33^{\circ}.5\ (2\sigma)$, indicating the orbit normal of the hot Jupiter nearly aligned with the stellar spin axis. Furthermore, by combining radial velocities and Hipparcos-Gaia astrometric acceleration, we constrained the line-of-sight mutual inclination between the hot Jupiter and the outer planet to be $9^{\circ}.8^{+16.2}_{-9.3}$ at $2\sigma$ level. HD 118203 is one of first hot Jupiter systems where both the true spin-orbit angle of the hot Jupiter and the mutual inclination between inner and outer planets have been determined. Our results are consistent with a system-wide alignment, with low mutual inclinations between the outer giant planet, the inner hot Jupiter, and the host star. This alignment, along with the moderate eccentricity of HD 118203 c, implies that the system may have undergone coplanar high-eccentricity tidal migration. Under this framework, our dynamical analysis suggests an initial semi-major axis of 0.3 to 3.2 AU for the proto-hot Jupiter., Comment: 30 pages, 12 figures, accepted by AJ

The degree of alignment between a star's spin axis and the orbital plane of its planets (the stellar obliquity) is related to interesting and poorly understood processes that occur during planet formation and evolution. Hot Jupiters orbiting hot stars ($\gtrsim$6250 K) display a wide range of obliquities, while similar planets orbiting cool stars are preferentially aligned. Tidal dissipation is expected to be more rapid in stars with thick convective envelopes, potentially explaining this trend. Evolved stars provide an opportunity to test the damping hypothesis, particularly stars that were hot on the main sequence and have since cooled and developed deep convective envelopes. We present the first systematic study of the obliquities of hot Jupiters orbiting subgiants that recently developed convective envelopes using Rossiter-McLaughlin observations. Our sample includes two newly discovered systems in the Giants Transiting Giants Survey (TOI-6029 b, TOI-4379 b). We find that the orbits of hot Jupiters orbiting subgiants that have cooled below $\sim$6250 K are aligned or nearly aligned with the spin-axis of their host stars, indicating rapid tidal realignment after the emergence of a stellar convective envelope. We place an upper limit for the timescale of realignment for hot Jupiters orbiting subgiants at $\sim$500 Myr. Comparison with a simplified tidal evolution model shows that obliquity damping needs to be $\sim$4 orders of magnitude more efficient than orbital period decay to damp the obliquity without destroying the planet, which is consistent with recent predictions for tidal dissipation from inertial waves excited by hot Jupiters on misaligned orbits., Comment: 22 pages, 14 figures, 3 tables

We introduce the OATMEAL survey, an effort to measure the obliquities of stars with transiting brown dwarf companions. We observed a transit of the close-in ($P_{\rm orb} = 1.74 \,$ days) brown dwarf GPX-1 b using the Keck Planet Finder (KPF) spectrograph to measure the sky-projected angle between its orbital axis and the spin axis of its early F-type host star ($\lambda$). We measured $\lambda = 6.88 \pm 1.72 ^\circ$ (with additional unquantified systematic uncertainty), suggesting an orbit that is prograde and well aligned with the stellar equator. Hot Jupiters around early F stars are frequently found to have highly misaligned orbits, with polar and retrograde orbits being commonplace. It has been theorized that these misalignments stem from dynamical interactions, such as von Zeipel-Kozai-Lidov cycles, and are retained over long timescales due to weak tidal dissipation in stars with radiative envelopes. By comparing GPX-1 to similar systems under the frameworks of different tidal evolution theories, we argued that the rate of tidal dissipation is too slow to have re-aligned the system. This suggests that GPX-1 may have arrived at its close-in orbit via coplanar high-eccentricity migration or migration through an aligned protoplanetary disk. Our result for GPX-1 is one of few measurements of the obliquity of a star with a transiting brown dwarf. By enlarging the number of such measurements and comparing them with hot Jupiter systems, we will more clearly discern the differences between the mechanisms that dictate the formation and evolution of both classes of objects., Comment: 8 pages, 4 figures

Asteroseismology of dwarf stars cooler than the Sun is very challenging due to the low amplitudes and rapid timescales of oscillations. Here, we present the asteroseismic detection of solar-like oscillations at 4-minute timescales ($\nu_{\mathrm{max}}\sim4300\mu$Hz) in the nearby K-dwarf $\sigma$ Draconis using extreme precision Doppler velocity observations from the Keck Planet Finder and 20-second cadence photometry from NASA's Transiting Exoplanet Survey Satellite. The star is the coolest dwarf star to date with both velocity and luminosity observations of solar-like oscillations, having amplitudes of $5.9\pm0.8\,$cm$\,\text{s}^{-1}$ and $0.8\pm0.2$ ppm, respectively. These measured values are in excellent agreement with established luminosity-velocity amplitude relations for oscillations and provide further evidence that mode amplitudes for stars with $T_{\mathrm{eff}}<\,5500\,$K diminish in scale following a $(L/M)^{1.5}$ relation. By modeling the star's oscillation frequencies from photometric data, we measure an asteroseismic age of $4.5\pm0.9\,\rm{(ran)} \pm 1.2\,\rm{(sys)}$ Gyr. The observations demonstrate the capability of next-generation spectrographs and precise space-based photometry to extend observational asteroseismology to nearby cool dwarfs, which are benchmarks for stellar astrophysics and prime targets for directly imaging planets using future space-based telescopes., Comment: Accepted for publication in The Astrophysical Journal

Several scenario-based frameworks exist to aid in vehicle system development and safety assurance. However, there is a need for approaches that combine different types of datasets that offer varying levels of case severity, data richness, and representativeness. This study presents an integrated scenario-based analysis approach that encompasses scenario definition, fusion, parametrization, and test case generation. For this process, ten years of fatal and non-fatal national crash data from the United States are combined with over 34 million miles of naturalistic driving data. An illustrative example scenario, "turns at intersection", is chosen to demonstrate this approach. First, scenario definitions are established from both record-based and continuous time series data. Second, a frequency analysis is performed to understand how often events from the same scenario occur at different severities across datasets. Third, an analysis is performed to show the key factors relevant to the scenario and the distribution of various parameters. Finally, a method to combine both types of data into representative test case scenarios is presented. These techniques improve scenario representativeness in two major ways: first, they populate an entire spectrum of cases ranging from routine events to fatal crashes; and second, they provide context-rich, multi-year data by combining large-scale national and naturalistic datasets., Comment: 8 pages, 5 figures, 27th IEEE International Conference on Intelligent Transportation Systems

Many lung diseases require detailed visualisation for accurate diagnosis and treatment. High-resolution computed tomography (CT) is the gold-standard technique for non-invasive lung disease detection, but it presents a risk to the patient through the relatively high ionising radiation dose required. Utilising the X-ray phase information may allow improvements in image resolution at equal or lower radiation levels than current clinical imaging. Propagation-based phase-contrast imaging requires minimal adaption of existing medical systems, and is well suited to lung imaging due to the strong phase gradients introduced by the lung-air material interfaces. Herein, propagation-based phase contrast CT is demonstrated for large animals, namely lambs, as a model for paediatric patients, using monochromatic radiation and a photon-counting detector at the Imaging and Medical Beamline of the Australian Synchrotron. Image quality, normalised against radiation dose, was optimised as a function of the beam energy and propagation distance, with the optimal conditions used to test the available image quality at very low radiation dose. The resulting CT images demonstrate superior resolution to existing high-resolution CT systems, pushing dose to the quantum limit to comply with current Australian guidelines for infant chest CT exposure of $<2.5\:\text{mSv}$ effective dose. Constituent raw projections are shown to have significant proportions of pixels with zero photon counts that would create severe information loss in conventional CT. Phase retrieval enabled clear visualisation of minor lung airways at doses up to 1,225$\pm$31\% times lower than conventional CT reconstruction, at a voxel size of just 75$\mathrm{\mu}$m.

We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity with a non-zero but small broadening factor $\eta$, focusing on the case in which a Hamiltonian in a downfolded model can be evaluated efficiently using Wannier interpolation. The algorithm uses iterated adaptive integration to exploit the localization of the transport distribution near energy and energy-difference iso-surfaces, yielding polylogarithmic computational complexity with respect to $\eta$. To demonstrate the method, we compute the AC optical conductivity of a three-band tight-binding model, and are able to resolve the Drude and interband peaks with broadening in the sub-meV regime to several digits of accuracy. Our algorithm automates convergence testing to a user-specified error tolerance, providing an important tool in black-box first-principles calculations of electrical transport phenomena and other response functions., Comment: 12 pages, 5 figures

We seek to identify genes involved in Parkinson's Disease (PD) by combining information across different experiment types. Each experiment, taken individually, may contain too little information to distinguish some important genes from incidental ones. However, when experiments are combined using the proposed statistical framework, additional power emerges. The fundamental building block of the family of statistical models that we propose is a hierarchical three-group mixture of distributions. Each gene is modeled probabilistically as belonging to either a null group that is unassociated with PD, a deleterious group, or a beneficial group. This three-group formalism has two key features. By apportioning prior probability of group assignments with a Dirichlet distribution, the resultant posterior group probabilities automatically account for the multiplicity inherent in analyzing many genes simultaneously. By building models for experimental outcomes conditionally on the group labels, any number of data modalities may be combined in a single coherent probability model, allowing information sharing across experiment types. These two features result in parsimonious inference with few false positives, while simultaneously enhancing power to detect signals. Simulations show that our three-groups approach performs at least as well as commonly-used tools for GWAS and RNA-seq, and in some cases it performs better. We apply our proposed approach to publicly-available GWAS and RNA-seq datasets, discovering novel genes that are potential therapeutic targets., Comment: 26 pages, 6 figures, 4 tables

We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint.

In recent years, a novel x-ray imaging modality has emerged that reveals unresolved sample microstructure via a "dark-field image", which provides complementary information to conventional "bright-field" images, such as attenuation and phase-contrast modalities. This x-ray dark-field signal is produced by unresolved microstructures scattering the x-ray beam resulting in localised image blur. Dark-field retrieval techniques extract this blur to reconstruct a dark-field image. Unfortunately, the presence of non-dark-field blur such as source-size blur or the detector point-spread-function can affect the dark-field retrieval as they also blur the experimental image. In addition, dark-field images can be degraded by the artefacts induced by large intensity gradients from attenuation and propagation-based phase contrast, particularly around sample edges. By measuring any non-dark-field blurring across the image plane and removing it from experimental images, as well as removing attenuation and propagation-based phase contrast, we show that a directional dark-field image can be retrieved with fewer artefacts and more consistent quantitative measures. We present the details of these corrections and provide "before and after" directional dark-field images of samples imaged at a synchrotron source. This paper utilises single-grid directional dark-field imaging, but these corrections have the potential to be broadly applied to other x-ray imaging techniques.

Combining archival photometric observations from multiple large-area surveys spanning the past 17 years, we detect long-term variability in the light curves of ZTFJ032833.52-121945.27 (ZTFJ0328-1219), ZTFJ092311.41+423634.16 (ZTFJ0923+4236) and WD1145+017, all known to exhibit transits from planetary debris. ZTFJ0328-1219 showed an overall fading in brightness from 2011 through to 2015, with a maximum dimming of ~0.3 mag, and still remains ~0.1 mag fainter compared to 2006. We complement the analysis of the long-term behaviour of these systems with high-speed photometry. In the case of ZTFJ0923+4236 and WD1145+017, the time-series photometry exhibits vast variations in the level of transit activity, both in terms of numbers of transits, as well as their shapes and depths, and these variations correlate with the overall brightness of the systems. Inspecting the current known sample of white dwarfs with transiting debris, we estimate that similar photometric signatures may be detectable in one in a few hundred of all white dwarfs. Accounting for the highly aligned geometry required to detect transits, our estimates imply that a substantial fraction of all white dwarfs exhibiting photospheric metal pollution from accreted debris host close-in planetesimals that are currently undergoing disintegration., Comment: MNRAS in press

A technique, volumetric power optimization, is presented for enhancing the power output of magnetic confinement fusion devices. Applied to a tokamak, this approach involves shifting the burning plasma region to a larger plasma volume while introducing minimal perturbations to the plasma boundary shape. This edge perturbation -- squareness -- is analogous to pinching and stretching the edge boundary. Stability calculations confirm that this edge alteration is compatible with maintaining plasma stability. This optimization method for optimizing fusion power output could improve the performance of magnetic confinement fusion power plants., Comment: 8 pages, 7 figures

We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's functions and self-energies. The DLR is based on a low-rank approximation of the analytic continuation kernel, and yields a compact and explicit basis consisting of exponentials in imaginary time and simple poles in Matsubara frequency. cppdlr constructs the DLR basis and associated interpolation grids, and implements standard operations. It provides a flexible yet high-level interface, facilitating the incorporation of the DLR into both small-scale applications and existing large-scale software projects.