Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants to these vector fields and/or their potentials based only on discrete samples. Additionally, it is often necessary that the vector approximants preserve the div-free or curl-free properties of the field to maintain certain physical constraints. Div/curl-free radial basis functions (RBFs) are a particularly good choice for this application as they are meshfree and analytically satisfy the div-free or curl-free property. However, this method can be computationally expensive due to its global nature. In this paper, we develop a technique for bypassing this issue that combines div/curl-free RBFs in a partition of unity framework, where one solves for local approximants over subsets of the global samples and then blends them together to form a div-free or curl-free global approximant. The method is applicable to div/curl-free vector fields in $\R^2$ and tangential fields on two-dimensional surfaces, such as the sphere, and the curl-free method can be generalized to vector fields in $\R^d$. The method also produces an approximant for the scalar potential of the underlying sampled field. We present error estimates and demonstrate the effectiveness of the method on several test problems.

Hot subdwarf B stars are core-helium burning objects that have undergone envelope stripping, likely by a binary companion. Using high-speed photometry from the Transiting Exoplanet Survey Satellite, we have discovered the hot subdwarf BPM 36430 is a hybrid sdBV_rs pulsator exhibiting several low-amplitude g-modes and a strong p-mode pulsation. The latter shows a clear, periodic variation in its pulse arrival times. Fits to this phase oscillation imply BPM 36430 orbits a barycenter approximately 10 light-seconds away once every 3.1 d. Using the CHIRON echelle spectrograph on the CTIO 1.5-m telescope, we confirm the reflex motion by detecting a radial velocity variation with semi-amplitude, period, and phase in agreement with the pulse timings. We conclude that a white dwarf companion with minimum mass of 0.42 Msun orbits BPM 36430. Our study represents only the second time a companion orbiting a pulsating hot subdwarf or white dwarf has been detected from pulse timings and confirmed with radial velocities.

The existence of quasi-long range order is demonstrated in nonequilibrium steady states in isotropic $XY$ spin chains including of two types of additional terms that each generate a gap in the energy spectrum. The system is driven out of equilibrium by initializing a domain-wall magnetization profile through application of an external magnetic field and switching off the magnetic field at the same time the energy gap is activated. An energy gap is produced by either applying a staggered magnetic field in the $z$ direction or introducing a modulation to the $XY$ coupling. The magnetization, spin current, and spin-spin correlation functions are computed analytically in the thermodynamic limit at long times after the quench. For both types of systems, we find the persistence of power-law correlations despite the ground-state correlation functions exhibiting exponential decay.

We present a novel method to detect variable astrophysical objects and transient phenomena using anomalous excess scatter in repeated measurements from public catalogs of Gaia DR2 and Zwicky Transient Facility (ZTF) DR3 photometry. We first provide a generalized, all-sky proxy for variability using only Gaia DR2 photometry, calibrated to white dwarf stars. To ensure more robust candidate detection, we further employ a method combining Gaia with ZTF photometry and alerts. To demonstrate the efficacy, we apply this latter technique to a sample of roughly $12,100$ white dwarfs within 200 pc centered on the ZZ Ceti instability strip, where hydrogen-atmosphere white dwarfs are known to pulsate. Through inspecting the top $1\%$ samples ranked by these methods, we demonstrate that both the Gaia-only and ZTF-informed techniques are highly effective at identifying known and new variable white dwarfs, which we verify using follow-up, high-speed photometry. We confirm variability in all 33 out of 33 ($100\%$) observed white dwarfs within our top $1\%$ highest-ranked candidates, both inside and outside the ZZ Ceti instability strip. In addition to dozens of new pulsating white dwarfs, we also identify five white dwarfs highly likely to show transiting planetary debris; if confirmed, these systems would more than triple the number of white dwarfs known to host transiting debris.

A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is specified on the boundary, and one where the tangential component of the curl-free part of the field specified. These two decompositions can then be combined to obtain a full Helmholtz-Hodge decomposition of the field, i.e. the sum of divergence-free, curl-free, and harmonic fields. All decompositions are computed from samples of the field at (possibly scattered) nodes over the domain, and all boundary conditions are imposed on the vector fields, not their potentials, distinguishing this technique from many current methods. Sobolev-type error estimates for the various decompositions are provided and demonstrated with numerical examples.

A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser-Horne-Shimony-Holt (CHSH) inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely-available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics.

The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims at finding hot subdwarf stars with massive compact companions like massive white dwarfs (M>1.0 M$_\odot$), neutron stars, or stellar-mass black holes. We present orbital and atmospheric parameters and put constraints on the nature of the companions of 12 close hot subdwarf B star (sdB) binaries found in the course of the MUCHFUSS project. The systems show periods between 0.14 and 7.4 days. Three systems most likely have white dwarf companions. SDSS J083006.17+475150.3 is likely to be a rare example of a low-mass helium-core white dwarf. SDSS J095101.28+034757.0 shows an excess in the infrared that probably originates from a third companion in a wide orbit. SDSS J113241.58-063652.8 is the first helium deficient sdO star with a confirmed close companion. This study brings to 142 the number of sdB binaries with orbital periods of less than 30 days and with measured mass functions. We present an analysis of the minimum companion mass distribution and show that it is bimodal. One peak around 0.1 M$_\odot$ corresponds to the low-mass main sequence and substellar companions. The other peak around 0.4 M$_\odot$ corresponds to the white dwarf companions. The derived masses for the white dwarf companions are significantly lower than the average mass for single carbon-oxygen white dwarfs. In a T$_{\rm eff}$-log(g) diagram of sdB+dM companions, we find signs that the sdB components are more massive than the rest of the sample. The full sample was compared to the known population of extremely low-mass white dwarf binaries as well as short-period white dwarfs with main sequence companions. Both samples show a significantly different companion mass distribution. We calculate merger timescales and timescales when the companion will fill its Roche Lobe and the system evolves into a cataclysmic variable.

Hot subdwarfs (sdO/B) are the stripped helium cores of red giants formed by binary interactions. Close hot subdwarf binaries with massive white dwarf companions have been proposed as possible progenitors of thermonuclear supernovae type Ia (SN Ia). If the supernova is triggered by stable mass transfer from the helium star, the companion should survive the explosion and should be accelerated to high velocities. The hypervelocity star US 708 is regarded as the prototype for such an ejected companion. To find more of those objects we conducted an extensive spectroscopic survey. Candidates for such fast stars have been selected from the spectroscopic database of the Sloan Digital Sky Survey (SDSS) and several ground-based proper motion surveys. Follow-up spectroscopy has been obtained with several 4m- to 10m-class telescopes. Combining the results from quantitative spectroscopic analyses with space-based astrometry from \textit{Gaia} Early Data Release 3 (EDR3) we determined the atmospheric and kinematic parameters of 53 fast hot subdwarf stars. None of these stars is unbound to the Galaxy, although some have Galactic restframe velocities close to the Galactic escape velocity. 21 stars are apparently single objects, which crossed the Galactic disc within their lifetimes in the sdO/B stage and could be regarded as potential candidates for the SN Ia ejection scenario. However, the properties of the full sample are more consistent with a pure old Galactic halo population. We therefore conclude that the fast sdO/B stars we found are likely to be extreme halo stars.

Modern machine learning algorithms are capable of providing remarkably accurate point-predictions; however, questions remain about their statistical reliability. Unlike conventional machine learning methods, conformal prediction algorithms return confidence sets (i.e., set-valued predictions) that correspond to a given significance level. Moreover, these confidence sets are valid in the sense that they guarantee finite sample control over type 1 error probabilities, allowing the practitioner to choose an acceptable error rate. In our paper, we propose inductive conformal prediction (ICP) algorithms for the tasks of text infilling and part-of-speech (POS) prediction for natural language data. We construct new conformal prediction-enhanced bidirectional encoder representations from transformers (BERT) and bidirectional long short-term memory (BiLSTM) algorithms for POS tagging and a new conformal prediction-enhanced BERT algorithm for text infilling. We analyze the performance of the algorithms in simulations using the Brown Corpus, which contains over 57,000 sentences. Our results demonstrate that the ICP algorithms are able to produce valid set-valued predictions that are small enough to be applicable in real-world applications. We also provide a real data example for how our proposed set-valued predictions can improve machine generated audio transcriptions.

Background: The established GADGET detection system, designed for measuring weak, low-energy $\beta$-delayed proton decays, features a gaseous Proton Detector with MICROMEGAS readout for calorimetric particle detection, surrounded by a Segmented Germanium Array for high-resolution prompt $\gamma$-ray detection. Purpose: To upgrade GADGET's Proton Detector to operate as a compact Time Projection Chamber (TPC) for the detection, 3D imaging and identification of low-energy $\beta$-delayed single- and multi-particle emissions mainly of interest to astrophysical studies. Method: A new high granularity MM board with 1024 pads has been designed, fabricated, installed and tested. A high-density data acquisition system based on Generic Electronics for TPCs has been installed and optimized to record and process the gas avalanche signals collected on the readout pads. The TPC's performance has been tested using a $^{220}$Rn $\alpha$-particle source and cosmic-ray muons. In addition, decay events in the TPC have been simulated by adapting the ATTPCROOT data analysis framework. Further, a novel application of 2D convolutional neural networks for GADGET II event classification is introduced. Results: The GADGET II TPC is capable of detecting and identifying $\alpha$-particles, as well as measuring their track direction, range, and energy. It has also been demonstrated that the GADGET II TPC is capable of tracking cosmic-ray muons. In addition to being one of the first generation of micro pattern gaseous detectors to utilize a resistive anode applied to low-energy nuclear physics, the GADGET II TPC will also be the first TPC surrounded by a high-efficiency array of high-purity germanium $\gamma$-ray detectors. \textbf{Conclusions:} The TPC of GADGET II has been designed, fabricated, tested, and is ready for operation at the FRIB for radioactive beam-line experiments.

Detailed studies of hot subdwarf B stars with red dwarf or brown dwarf companions can shed light on the effects of binarity on late stellar evolution. Such systems exhibit a strong, quasi-sinusoidal reflection effect due to irradiation of the cool companion, and some even show primary and secondary eclipses. Here we compute Fourier transforms of TESS light curves of sdB+dM/BD binaries and investigate correlations between the relative amplitudes and phases of their harmonics and system parameters. We show that the reflection effect shape strongly depends on the orbital inclination, with nearly face-on systems having much more sinusoidal shapes than nearly edge-on systems. This information is encoded by the relative strength of the first harmonic in the Fourier transform. By comparing observations of solved systems to synthetic light curves generated by LCURVE, we find that the inclination of non-eclipsing systems with high S/N light curves can be determined to within ~10 degrees simply by measuring their orbital periods and first harmonic strengths. We also discover a slight asymmetry in the reflection effect shape of sdB+dM/BD binaries using the relative phase of the first harmonic. From our analysis of synthetic light curves, we conclude the asymmetry results from relativistic beaming of both stellar components. This marks the first time Doppler beaming has been detected in sdB+dM/BD systems. Although advanced modeling is necessary to quantify the effects of secondary parameters like limb darkening, the temperature ratio, and the radius ratio on the reflection effect shape, our pilot study demonstrates that it might be possible to extract both the inclination angle and cool companion velocity from the light curves of non-eclipsing systems.

In the pursuit of identifying rare two-particle events within the GADGET II Time Projection Chamber (TPC), this paper presents a comprehensive approach for leveraging Convolutional Neural Networks (CNNs) and various data processing methods. To address the inherent complexities of 3D TPC track reconstructions, the data is expressed in 2D projections and 1D quantities. This approach capitalizes on the diverse data modalities of the TPC, allowing for the efficient representation of the distinct features of the 3D events, with no loss in topology uniqueness. Additionally, it leverages the computational efficiency of 2D CNNs and benefits from the extensive availability of pre-trained models. Given the scarcity of real training data for the rare events of interest, simulated events are used to train the models to detect real events. To account for potential distribution shifts when predominantly depending on simulations, significant perturbations are embedded within the simulations. This produces a broad parameter space that works to account for potential physics parameter and detector response variations and uncertainties. These parameter-varied simulations are used to train sensitive 2D CNN object detectors. When combined with 1D histogram peak detection algorithms, this multi-modal detection framework is highly adept at identifying rare, two-particle events in data taken during experiment 21072 at the Facility for Rare Isotope Beams (FRIB), demonstrating a 100% recall for events of interest. We present the methods and outcomes of our investigation and discuss the potential future applications of these techniques.

Modeling detector response is a key challenge in time projection chambers. We cast this problem as an unpaired point cloud translation task, between data collected from simulations and from experimental runs. Effective translation can assist with both noise rejection and the construction of high-fidelity simulators. Building on recent work in diffusion probabilistic models, we present a novel framework for performing this mapping. We demonstrate the success of our approach in both synthetic domains and in data sourced from the Active-Target Time Projection Chamber.

In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a smooth, compact embedded submanifold $\M\subset \R^d$. For restricted kernels having finite smoothness, we provide a complete characterization of the native space on $\M$. After this and some preliminary setup, we present Sobolev-type error estimates for the interpolation problem. Numerical results verifying the theory are also presented for a one-dimensional curve embedded in $\R^3$ and a two-dimensional torus.

Based on five years of observations with the 40-foot telescope at Green Bank Observatory (GBO), Reichart & Stephens (2000) found that the radio source Cassiopeia A had either faded more slowly between the mid-1970s and late 1990s than Baars et al. (1977) had found it to be fading between the late 1940s and mid-1970s, or that it had rebrightened and then resumed fading sometime between the mid-1970s and mid-1990s, in L band (1.4 GHz). Here, we present 15 additional years of observations of Cas A and Cyg A with the 40-foot in L band, and three and a half additional years of observations of Cas A, Cyg A, Tau A, and Vir A with GBO's recently refurbished 20-meter telescope in L and X (9 GHz) bands. We also present a more sophisticated analysis of the 40-foot data, and a reanalysis of the Baars et al. (1977) data, which reveals small, but non-negligible differences. We find that overall, between the late 1950s and late 2010s, Cas A faded at an average rate of $0.670 \pm 0.019$ %/yr in L band, consistent with Reichart & Stephens (2000). However, we also find, at the 6.3$\sigma$ credible level, that it did not fade at a constant rate. Rather, Cas A faded at a faster rate through at least the late 1960s, rebrightened (or at least faded at a much slower rate), and then resumed fading at a similarly fast rate by, at most, the late 1990s. Given these differences from the original Baars et al. (1977) analysis, and given the importance of their fitted spectral and temporal models for flux-density calibration in radio astronomy, we update and improve on these models for all four of these radio sources. In doing so, we additionally find that Tau A is fading at a rate of $0.102^{+0.042}_{-0.043}$ %/yr in L band.

Honeypots are computing systems used to capture unauthorized, often malicious, activity. While honeypots can take on a variety of forms, researchers agree the technology is useful for studying adversary behavior, tools, and techniques. Unfortunately, researchers also agree honeypots are difficult to implement and maintain. A lack of measures of effectiveness compounds the implementation issues specifically. In other words, existing research does not provide a set of measures to determine if a honeypot is effective in its implementation. This is problematic because an ineffective implementation may lead to poor performance, inadequate emulation of legitimate services, or even premature discovery by an adversary. Accordingly, we have developed a taxonomy for measures of effectiveness in dynamic honeypot implementations. Our aim is for these measures to be used to quantify a dynamic honeypot's effectiveness in fingerprinting its environment, capturing valid data from adversaries, deceiving adversaries, and intelligently monitoring itself and its surroundings.

Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using a curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free RBFs based on polyharmonic splines for this task, since they are free of any shape or support parameters. Furthermore, to make this technique efficient and able to better represent local sharp features, we combine it with a partition of unity (PU) method. The result is the curl-free partition of unity (CFPU) method. We show how CFPU can be adapted to enforce exact interpolation of a point cloud and can be regularized to handle noise in both the normal vectors and the point positions. Numerical results are presented that demonstrate how the method converges for a known surface as the sampling density increases, how regularization handles noisy data, and how the method performs on various problems found in the literature.

Supernova Ia are bright explosive events that can be used to estimate cosmological distances, allowing us to study the expansion of the Universe. They are understood to result from a thermonuclear detonation in a white dwarf that formed from the exhausted core of a star more massive than the Sun. However, the possible progenitor channels leading to an explosion are a long-standing debate, limiting the precision and accuracy of supernova Ia as distance indicators. Here we present HD265435, a binary system with an orbital period of less than a hundred minutes, consisting of a white dwarf and a hot subdwarf -- a stripped core-helium burning star. The total mass of the system is 1.65+/-0.25 solar-masses, exceeding the Chandrasekhar limit (the maximum mass of a stable white dwarf). The system will merge due to gravitational wave emission in 70 million years, likely triggering a supernova Ia event. We use this detection to place constraints on the contribution of hot subdwarf-white dwarf binaries to supernova Ia progenitors.

Hot subdwarf stars are mostly stripped red giants that can exhibit photometric variations due to stellar pulsations, eclipses, the reflection effect, ellipsoidal modulation, and Doppler beaming. Detailed studies of their light curves help constrain stellar parameters through asteroseismological analyses or binary light curve modeling and generally improve our capacity to draw a statistically meaningful picture of this enigmatic stage of stellar evolution. From an analysis of Gaia DR2 flux errors, we have identified around 1200 candidate hot subdwarfs with inflated flux errors for their magnitudes - a strong indicator of photometric variability. As a pilot study, we obtained 2-min cadence TESS Cycle 2 observations of 187 candidate hot subdwarfs with anomalous Gaia flux errors. More than 90% of our targets show significant photometric variations in their TESS light curves. Many of the new systems found are cataclysmic variables, but we report the discovery of several new variable hot subdwarfs, including HW Vir binaries, reflection effect systems, pulsating sdBVs stars, and ellipsoidally modulated systems. We determine atmospheric parameters for select systems using follow-up spectroscopy from the 3-m Shane telescope. Finally, we present a Fourier diagnostic plot for classifying binary light curves using the relative amplitudes and phases of their fundamental and harmonic signals in their periodograms. This plot makes it possible to identify certain types of variables efficiently, without directly investigating their light curves, and may assist in the rapid classification of systems observed in large photometric surveys.

We conduct a systematic search for periodic variables in the hot subdwarf catalogue using data from the Zwicky Transient Facility. We present the classification of 67 HW Vir binaries, 496 reflection effect, pulsation or rotation sinusoids, 11 eclipsing signals, and 4 ellipsoidally modulated binaries. Of these, 486 are new discoveries that have not been previously published including a new mass-transferring hot subdwarf binary candidate. These sources were determined by applying the Lomb-Scargle and Box Least Squares periodograms along with manual inspection. We calculated variability statistics on all periodic sources, and compared our results to traditional methods of determining astrophysical variability. We find that $\approx60$\% percent of variable targets, mostly sinusoidal variability, would have been missed using a traditional $varindex$ cut. Most HW Virs, eclipsing systems and all ellipsoidal variables were recovered with a varindex\,>0.02. We also find a significant reddening effect, with some variable hot subdwarfs meshing with the main sequence stripe in the Hertzprung-Russell Diagram. Examining the positions of the variable stars in Galactic coordinates, we discover a higher proportion of variable stars within |b|<25^\circ of the Galactic Plane, suggesting that the Galactic Plane may be fertile grounds for future discoveries if photometric surveys can effectively process the clustered field.