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We develop signal capture and analysis techniques for precisely extracting and characterizing the frame timing of the Starlink constellation's Ku-band downlink transmissions. The aim of this work is to determine whether Starlink frame timing has sufficient short-term stability to support pseudorange-based opportunistic positioning, navigation, and timing (PNT). A second goal is to determine whether frame timing is disciplined to a common time scale such as GPS time. Our analysis reveals several timing characteristics not previously known that carry strong implications for PNT. On the favorable side, periods of ns-level jitter in frame arrival times across all satellite versions indicate that Starlink hardware is fundamentally capable of the short-term stability required to support GPS-like PNT. But there are several unfavorable characteristics that, if not addressed, will make GPS-like PNT impractical: (1) The v1.0 and v1.5 Starlink satellites exhibit once-per-second abrupt frame timing adjustments whose magnitude (as large as 100s of ns) and sign appear unpredictable. Similar discontinuities are also present in the v2.0-Mini frame timing, though smaller and irregularly spaced. (2) Episodic 15-s periods of high frame jitter routinely punctuate the nominal low-jitter frame arrival timing. (3) Starlink frame timing is disciplined to GPS time, but only loosely: to within a few ms by adjustments occurring every 15 s; otherwise exhibiting drift that can exceed 20 ppm. These unfavorable characteristics are essentially incompatible with accurate PNT. Fortunately, they appear to be a consequence of software design choices, not hardware limitations. Moreover, they could be compensated with third-party-provided corrections., Comment: 16 pages, 16 figures

Arp 220 is the prototypical Ultraluminous Infrared Galaxy (ULIRG), and one of the brightest objects in the extragalactic far-infrared sky. It is the result of a merger between two gas rich spiral galaxies which has triggered starbursting activity in the merger nuclear regions. Observations with the Submillimeter Array centred at a frequency of 345 GHz and with a synthesised beamsize of 0.77 x 0.45 arcseconds were used to search for polarized dust emission from the nuclear regions of Arp 220. Polarized dust emission was clearly detected at 6 sigma significance associated with the brighter, western nucleus, with a peak polarization fraction of 2.7 +/- 0.35 per cent somewhat offset from the western nucleus. A suggestive 2.6 sigma signal is seen from the fainter eastern nucleus. The dust emission polarization is oriented roughly perpendicular to the molecular disk in the western nucleus suggesting that the magnetic field responsible is orientated broadly in the plane of the disk, but may be being reordered by the interaction between the two nuclei. Unlike more evolved interacting systems, we see no indication that the magnetic field is being reordered by the outflow from the western nucleus. These observations are the first detection of dust polarization, and thus of magnetic fields, in the core of a ULIRG., Comment: Accepted for publication in MNRAS

Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation. We propose a method to exploit this loop-based structure to more efficiently simulate such systems. Our algorithm exploits a causal-cone argument to decompose the circuit into smaller effective components that can each be simulated sequentially by calling a state vector simulator as a subroutine. To quantify the complexity of our approach, we develop a new lattice path formalism that allows us to efficiently characterize the state space that must be tracked during the simulation. In addition, we develop a heuristic method that allows us to predict the expected average and worst-case memory requirements of running these simulations. We use these methods to compare the simulation complexity of different families of loop-based interferometers, allowing us to quantify the potential for quantum advantage of single-photon Boson Sampling in loop-based architectures., Comment: 27 pages, 15 figures

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing more tailorable light-matter interactions in general. In this paper, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of $2\pi\cdot1.45~ \rm MHz$ we achieve $\langle n \rangle = 1.3 \pm 1.1$ in $500~\mu \rm s$ and cooling rates of ${\sim}0.3 \, \rm quanta/\mu s$. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a simple model. Cooling is fast and power-efficient, with improved performance compared to simulated operation under the corresponding running wave configuration., Comment: 16 pages, 11 figures

Trapped ions are a promising modality for quantum systems, with demonstrated utility as the basis for quantum processors and optical clocks. However, traditional trapped-ion systems are implemented using complex free-space optical configurations, whose large size and susceptibility to vibrations and drift inhibit scaling to large numbers of qubits. In recent years, integrated-photonics-based systems have been demonstrated as an avenue to address the challenge of scaling trapped-ion systems while maintaining high fidelities. While these previous demonstrations have implemented both Doppler and resolved-sideband cooling of trapped ions, these cooling techniques are fundamentally limited in efficiency. In contrast, polarization-gradient cooling can enable faster and more power-efficient cooling and, therefore, improved computational efficiencies in trapped-ion systems. While free-space implementations of polarization-gradient cooling have demonstrated advantages over other cooling mechanisms, polarization-gradient cooling has never previously been implemented using integrated photonics. In this paper, we design and experimentally demonstrate key polarization-diverse integrated-photonics devices and utilize them to implement a variety of integrated-photonics-based polarization-gradient-cooling systems, culminating in the first experimental demonstration of polarization-gradient cooling of a trapped ion by an integrated-photonics-based system. By demonstrating polarization-gradient cooling using an integrated-photonics-based system and, in general, opening up the field of polarization-diverse integrated-photonics-based devices and systems for trapped ions, this work facilitates new capabilities for integrated-photonics-based trapped-ion platforms.

This report details exploratory research undertaken by Newcastle University from November 2022 to May 2023. The aim of this exploratory project was to develop, trial and evaluate approaches to providing indications of how outdoor space is being perceived, used and valued by students in four schools -- to ascertain which approach (or approaches) may be best suited for use as part of Building in Use (BiU) reviews. The report details the three digital methods tested, as well as the enablers and barriers encountered while using them. The digital tools developed can be used individually to obtain limited data, but a combination of several methods is most and can be combined with information from the BiU site visit and staff survey in providing an overall BiU assessment. However, there are barriers to this including financial outlay, support from schools, and the time and effort required to create the data collection tools, even with the templates and prototypes that we detail in the report. We recommend initial discussions between the BiU technical adviser (TA) and school about tools, so that these can be chosen to fit with school procedures, especially relating to online access, and also fulfil particular needs of a specific BiU review. This would form part of a developed relationship between TA and school, beyond the existing one of schools accommodating data collection using pre-specified methods, which would also include feedback from the TA to the school.

High-redshift protoclusters consisting of dusty starbursts are thought to play an important role in galaxy evolution. Their dusty nature makes them bright in the FIR/submm but difficult to find in optical/NIR surveys. Radio observations are an excellent way to study these dusty starbursts, as dust is transparent in the radio and there is a tight correlation between the FIR and radio emission of a galaxy. Here, we present MeerKAT 1.28 GHz radio imaging of 3 Herschel candidate protoclusters, with a synthesised beam size of ~$7.5'' \times 6.6''$ and a central thermal noise down to $4.35~\mu$Jy/beam. Our source counts are consistent with other radio counts with no evidence of overdensities. Around 95% of the Herschel sources have 1.28 GHz IDs. Using the Herschel 250 micron primary beam size as the searching radius, we find 54.2% Herschel sources have multiple 1.28 GHz IDs. Our average FIR-radio correlation coefficient $q_{250\mu m}$ is $2.33\pm 0.26$. Adding $q_{250\mu m}$ as a new constraint, the probability of finding chance-aligned sources is reduced by a factor of ~6, but with the risk of discarding true identifications of radio-loud/quiet sources. With accurate MeerKAT positions, we cross-match our Herschel sources to optical/NIR data followed by photometric redshift estimations. By removing $z<1$ sources, the density contrasts of two of the candidate protoclusters increase, suggestive of them being real protoclusters at $z>1$. There is also potentially a $0.9

Though parameter shift rules have drastically improved gradient estimation methods for several types of quantum circuits, leading to improved performance in downstream tasks, so far they have not been transferable to linear optics with single photons. In this work, we derive an analytical formula for the gradients in these circuits with respect to phaseshifters via a generalized parameter shift rule, where the number of parameter shifts depends linearly on the total number of photons. Experimentally, this enables access to derivatives in photonic systems without the need for finite difference approximations. Building on this, we propose two strategies through which one can reduce the number of shifts in the expression, and hence reduce the overall sample complexity. Numerically, we show that this generalized parameter-shift rule can converge to the minimum of a cost function with fewer parameter update steps than alternative techniques. We anticipate that this method will open up new avenues to solving optimization problems with photonic systems, as well as provide new techniques for the experimental characterization and control of linear optical systems., Comment: 13 + 11 pages, 7 figures

The discovery of phosphine in Venus' atmosphere provides lessons for the search for life. The detection has survived all challenges and has acquired independent support from archival data from PVP. The presence of phosphine in Venus' oxidising environment is perplexing, and comprehensive studies rule out all known abiotic sources. More data is needed to understand the origin of phosphine, leading to JCMT-Venus, a long term atmospheric monitoring programme. This can find how phosphine varies in relation to other species providing clues to its origin. We present the latest JCMT-Venus results. The discovery and subsequent papers were explicit that they did not constitute evidence for life, only of phosphine. Media and public reaction to the discovery and its implications provide lessons for future life searches, as does the reaction of the scientific community. How this was handled by the team, media, and general public will be reviewed., Comment: Accepted for publication in Proceedings of the KAVLI-IAU SYMPOSIUM (IAUS 387): (Toward) Discovery of Life Beyond Earth and its Impact

Given the rapidly expanding capabilities of generative AI models for radiology, there is a need for robust metrics that can accurately measure the quality of AI-generated radiology reports across diverse hospitals. We develop ReXamine-Global, a LLM-powered, multi-site framework that tests metrics across different writing styles and patient populations, exposing gaps in their generalization. First, our method tests whether a metric is undesirably sensitive to reporting style, providing different scores depending on whether AI-generated reports are stylistically similar to ground-truth reports or not. Second, our method measures whether a metric reliably agrees with experts, or whether metric and expert scores of AI-generated report quality diverge for some sites. Using 240 reports from 6 hospitals around the world, we apply ReXamine-Global to 7 established report evaluation metrics and uncover serious gaps in their generalizability. Developers can apply ReXamine-Global when designing new report evaluation metrics, ensuring their robustness across sites. Additionally, our analysis of existing metrics can guide users of those metrics towards evaluation procedures that work reliably at their sites of interest.

One of the greatest challenges in galaxy evolution over the last decade has been constraining the prevalence of heavily dust-obscured galaxies in the early Universe. At $z>3$, these galaxies are increasingly rare, and difficult to identify as they are interspersed among the more numerous dust-obscured galaxy population at $z=1-3$, making efforts to secure confident spectroscopic redshifts expensive, and sometimes unsuccessful. In this work, we present the Extended Mapping Obscuration to Reionization with ALMA (Ex-MORA) Survey -- a 2mm blank-field survey in the COSMOS-Web field, and the largest ever ALMA blank-field survey to-date covering 577 arcmin$^2$. Ex-MORA is an expansion of the MORA survey designed to identify primarily $z>3$ dusty, star-forming galaxies while simultaneously filtering out the more numerous $z<3$ population by leveraging the very negative $K$-correction at observed-frame 2mm. We identify 37 significant ($>$5$\sigma$) sources, 33 of which are robust thermal dust emitters. We measure a median redshift of $\langle z \rangle = 3.6^{+0.1}_{-0.2}$, with two-thirds of the sample at $z>3$, and just under half at $z>4$, demonstrating the overall success of the 2mm-selection technique. The integrated $z>3$ volume density of Ex-MORA sources is $\sim1-3\times10^{-5}$ Mpc$^{-3}$, consistent with other surveys of infrared luminous galaxies at similar epochs. We also find that techniques using rest-frame optical emission (or lack thereof) to identify $z>3$ heavily dust-obscured galaxies miss at least half of Ex-MORA galaxies. This supports the idea that the dusty galaxy population is heterogeneous, and that synergies across observatories spanning multiple energy regimes are critical to understanding their formation and evolution at $z>3$., Comment: 13 pages, 5 figures, submitted to ApJ; fully reduced mosaic will be shared upon publication

In this Roadmap, we present a vision for the future of submillimetre and millimetre astronomy in the United Kingdom over the next decade and beyond. This Roadmap has been developed in response to the recommendation of the Astronomy Advisory Panel (AAP) of the STFC in the AAP Astronomy Roadmap 2022. In order to develop our stragetic priorities and recommendations, we surveyed the UK submillimetre and millimetre community to determine their key priorities for both the near-term and long-term future of the field. We further performed detailed reviews of UK leadership in submillimetre/millimetre science and instrumentation. Our key strategic priorities are as follows: 1. The UK must be a key partner in the forthcoming AtLAST telescope, for which it is essential that the UK remains a key partner in the JCMT in the intermediate term. 2. The UK must maintain, and if possible enhance, access to ALMA and aim to lead parts of instrument development for ALMA2040. Our strategic priorities complement one another: AtLAST (a 50m single-dish telescope) and an upgraded ALMA (a large configurable interferometric array) would be in synergy, not competition, with one another. Both have identified and are working towards the same overarching science goals, and both are required in order to fully address these goals., Comment: 91 pages plus cover, 38 figures. Submitted to the Science and Technology Facilities Council, August 2024. One figure corrected (v2); new appendix with STFC Q&A; corrected SMA access statement; updated references, acronyms & author list (v3)

Herschel surveys have found large numbers of sources with red far-IR colours, and spectral energy distributions (SEDs) rising from 250 to 500$\mu$m: 500 risers. The nature and role of these sources is not fully understood. We here present Submillimeter Array (SMA) interferometric imaging at 200 GHz of a complete sample of five 500 risers with F500 $>$ 44 mJy selected within a 4.5 square degree region of the XMMLSS field. These observations can resolve the separate components of multiple sources and allow cross identification at other wavelengths using the extensive optical-to-IR data in this field. Of our five targets we find that two are likely gravitationally lensed, two are multiple sources, and one an isolated single source. Photometric redshifts, using optical-to-IR data and far-IR/submm data, suggest they lie at redshifts $z \sim 2.5 - 3.5$. Star formation rates and stellar masses estimated from the SEDs show that the majority of our sources lie on the star-formation rate-stellar mass `main sequence', though with outliers both above and below this relation. Of particular interest is our most multiple source which consists of three submm emitters and one submm-undetected optical companion within a 7 arcsecond region, all with photometric redshifts $\sim$ 3. One of the submm emitters in this group lies above the `main sequence', while the optical companion lies well below the relation, and has an estimated stellar mass of 3.3$\pm 1.3 \times$10$^{11}$ M$_{\odot}$. We suggest this object is a forming brightest cluster galaxy (BCG) in the process of accreting actively star forming companions., Comment: Accepted for publication in MNRAS

The finite momentum superconducting pairing states (FMPs), where Cooper pairs carry non-zero momentum, are believed to give rise to exotic physical phenomena including the pseudogap phase of cuprate high-Tc superconductors and Majorana fermions in topological superconductivity. FMPs can emerge in intertwined electronic liquids with strong spin-spin interactions or be induced by lifting the spin degeneracy under magnetic field as originally proposed by Fulde-Ferrell and Larkin-Ovchinnikov. In quantum materials with strong Ising-type spin-orbit coupling, such as the 2D transition metal dichalcogenides (TMDs), the spin degree of freedom is frozen enabling novel orbital driven FMPs via magnetoelectric effect. While evidence of orbital driven FMPs has been revealed in bilayer TMDs, its realization in 3D bulk materials remains an unresolved challenge. Here we report experimental signatures of FMP in a locally noncentrosymmetric bulk superconductor 4Hb-TaS2. Using hard X-ray diffraction and angle-resolved photoemission spectroscopy, we reveal unusual 2D chiral charge density wave (CDW) and weak interlayer hopping in 4Hb-TaS2. Below the superconducting transition temperature, the upper critical field, Hc2, linearly increases via decreasing temperature, and well exceeds the Pauli limit, thus establishing the dominant orbital pair-breaking mechanism. Remarkably, we discover a field-induced superconductivity-to-superconductivity transition that breaks continuous rotational symmetry of the s-wave uniform pairing in the Bardeen-Cooper-Schrieffer theory down to the six-fold rotation symmetry. Combining with a Ginzburg-Landau free energy analysis that incorporates magnetoelectric effect, our observations provide strong evidence of orbital driven FMP in the 3D quantum heterostructure 4Hb-TaS2.

Cleavable metallic antiferromagnets may be of use for low-dissipation spintronic devices; however, few are currently known. Here we present orthorhombic MnRhBi3 as one such compound and present a thorough study of its physical properties. Exfoliation is demonstrated experimentally, and the cleavage energy and electronic structure are examined by density functional theory calculations. It is concluded that MnRhBi3 is a van der Waals layered material that cleaves easily between neighboring Bi layers, and that the Bi atoms have lone pairs extending into the van der Waals gaps. A series of four phase transitions are observed below room temperature, and neutron diffraction shows that at least two of the transitions involve the formation of antiferromagnetic order. Anomalous thermal expansion points to a crystallographic phase transition and/or strong magnetoelastic coupling. This work reveals a complex phase evolution in MnRhBi3 and establishes this cleavable antiferromagnetic metal as an interesting material for studying the interplay of structure, magnetism, and transport in the bulk and ultrathin limits as well as the role of lone pair electrons in interface chemistry and proximity effects in van der Waals heterostructures.

Segmentation is an integral module in many visual computing applications such as virtual try-on, medical imaging, autonomous driving, and agricultural automation. These applications often involve either widespread consumer use or highly variable environments, both of which can degrade the quality of visual sensor data, whether from a common mobile phone or an expensive satellite imaging camera. In addition to external noises like user difference or weather conditions, internal noises such as variations in camera quality or lens distortion can affect the performance of segmentation models during both development and deployment. In this work, we present an efficient, adaptable, and gradient-free method to enhance the robustness of learning-based segmentation models across training. First, we introduce a novel adaptive sensitivity analysis (ASA) using Kernel Inception Distance (KID) on basis perturbations to benchmark perturbation sensitivity of pre-trained segmentation models. Then, we model the sensitivity curve using the adaptive SA and sample perturbation hyperparameter values accordingly. Finally, we conduct adversarial training with the selected perturbation values and dynamically re-evaluate robustness during online training. Our method, implemented end-to-end with minimal fine-tuning required, consistently outperforms state-of-the-art data augmentation techniques for segmentation. It shows significant improvement in both clean data evaluation and real-world adverse scenario evaluation across various segmentation datasets used in visual computing and computer graphics applications., Comment: 10 pages

We present confusion-limited SCUBA-2 450-$\mu$m observations in the COSMOS-CANDELS region as part of the JCMT Large Program, SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES). Our maps at 450 and 850 $\mu$m cover an area of 450 arcmin$^2$. We achieved instrumental noise levels of $\sigma_{\mathrm{450}}=$ 0.59 mJy beam$^{-1}$ and $\sigma_{\mathrm{850}}=$ 0.09 mJy beam$^{-1}$ in the deepest area of each map. The corresponding confusion noise levels are estimated to be 0.65 and 0.36 mJy beam$^{-1}$. Above the 4 (3.5) $\sigma$ threshold, we detected 360 (479) sources at 450 $\mu$m and 237 (314) sources at 850 $\mu$m. We derive the deepest blank-field number counts at 450 $\mu$m, covering the flux-density range of 2 to 43 mJy. These are in agreement with other SCUBA-2 blank-field and lensing-cluster observations, but are lower than various model counts. We compare the counts with those in other fields and find that the field-to-field variance observed at 450 $\mu$m at the $R=6^\prime$ scale is consistent with Poisson noise, so there is no evidence of strong 2-D clustering at this scale. Additionally, we derive the integrated surface brightness at 450 $\mu$m down to 2.1 mJy to be $57.3^{+1.0}_{-6.2}$~Jy deg$^{-2}$, contributing to (41$\pm$4)\% of the 450-$\mu$m extragalactic background light (EBL) measured by COBE and Planck. Our results suggest that the 450-$\mu$m EBL may be fully resolved at $0.08^{+0.09}_{-0.08}$~mJy, which extremely deep lensing-cluster observations and next-generation submillimeter instruments with large aperture sizes may be able to achieve., Comment: 29 pages, 14 figures, accepted for publication in ApJ

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Frequent disruptions like highway constructions are common now-a-days, often impacting environmental justice communities (communities with low socio-economic status with disproportionately high and adverse human health and environmental effects) that live nearby. Based on our interactions via focus groups with the members of four environmental justice communities impacted by a major highway construction, a common concern is a sense of uncertainty about project activities and loss of social connectedness, leading to increased stress, depression, anxiety and diminished well-being. This paper addresses this concern by developing a localized social media system called PureConnect with a goal to raise the level of awareness about the project and increase social connectedness among the community members. PureConnect has been designed using active engagement with four environmental justice communities affected by a major highway construction. It has been deployed in the real world among the members of the four environmental justice communities, and a detailed analysis of the data collected from this deployment as well as surveys show that PureConnect is potentially useful in improving community members' well-being and the members appreciate the functionalities it provides., Comment: Submitted in COMPSAC 2024

In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach that we previously introduced in previous work. We focus on understanding the impact of re-sampling cost on the algorithm performance and provide algorithm refinements, which allow to obtain unbiased estimators for the variance, estimate the PC variability due to limited samples, and adapt the expansion. An attenuation-only test case is provided to illustrate and discuss the results.

We consider Global Sensitivity Analysis for Monte Carlo radiation transport applications. GSA is usually combined with Uncertainty Quantification, where the latter quantifies the variability of a model output in the presence of uncertain inputs and the former attributes this variability to the inputs. The additional noise inherent to MC RT solvers due to the finite number of particle histories presents an additional challenge to GSA and UQ, which are well-established for deterministic solvers. In this contribution, we apply variance deconvolution to the Saltelli method to address MC RT solver noise without having to over-resolve the MC RT simulation., Comment: Presented at The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, 2023

Planned disruptions such as highway constructions are commonplace nowadays and the communities living near these disruptions generally tend to be environmental justice communities -- low socioeconomic status with disproportionately high and adverse human health and environmental effects. A major concern is that such activities negatively impact people's well-being by disrupting their daily commutes via frequent road closures and increased dust and air pollution. This paper addresses this concern by developing a personalized navigation service called PureNav to mitigate the negative impacts of disruptions in daily commutes on people's well-being. PureNav has been designed using active engagement with four environmental justice communities affected by major highway construction. It has been deployed in the real world among the members of the four communities, and a detailed analysis of the data collected from this deployment as well as surveys show that PureNav is potentially useful in improving people's well-being. The paper describes the design, implementation, and evaluation of PureNav, and offers suggestions for further improving its efficacy., Comment: Accepted for publication in the proceedings of the 2023 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM)

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new Bayesian mixture approach that analyzes ordinal responses with undetectable/uncodable behaviors in two stages: (1) estimate a likelihood of response detection and (2) estimate an Explanatory Item Response Model for the ordinal variable conditional on detection. We present an independent random effects and correlated random effects variant of the new model and demonstrate evidence of model functionality using two simulation studies. To illustrate the utility of our proposed approach, we describe an extended application to data collected during a length measurement teaching experiment (N = 186, 56% girls, 5-6 years at preassessment). Results indicate that students assigned to a learning trajectories instructional condition were more likely to use detectable, mathematically relevant problem-solving strategies than their peers in two comparison conditions and that their problem-solving strategies were also more sophisticated. [This is the online first version of an article published in "Journal of Research on Educational Effectiveness."]

Online credit recovery will likely expand in the coming years as school districts try to address increased course failure rates brought on by the coronavirus pandemic. Some researchers and policymakers, however, raise concerns over how much students learn in online courses, and there is limited evidence about the effectiveness of online credit recovery. This article presents findings from a multisite randomized study, conducted prior to the pandemic, to expand the field's understanding of online credit recovery's effectiveness. Within 24 high schools from a large urban district, the study randomly assigned 1,683 students who failed Algebra 1 or ninth grade English to a summer credit recovery class that either used an online curriculum with in-class teacher support or the school's business-as-usual teacher-directed class. The results suggest that online credit recovery had relatively insignificant effects on student course experiences and content knowledge, but significantly lower credit recovery rates for English. There was limited heterogeneity in effects across students and schools. Non-response on the study-administered student survey and test limit our confidence in the student experience and content knowledge results, but the findings are robust to different approaches to handling the missing data (multiple imputation or listwise deletion). We discuss how the findings add to the evidence base about online credit recovery and the implications for future research. [This paper will be published in "Journal of Research on Educational Effectiveness."]