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From October 2021, the government introduced a pilot in 30 local authorities to support 16 to 18-year-old children looked-after (CLA) and care leavers (CLs) in general further education (FE) colleges through the extension of Pupil Premium Plus funding to post-16 (PP+ Post-16). The 6-month pilot was completed between autumn 2021 and spring 20221 , before funding was extended to a further 28 local authorities in autumn 2022 and subsequently extended to all local authorities in England in autumn 2023. The purpose of PP+ Post-16 was also extended in 2023/24 to provide funding to support all CLA and CLs at post-16, rather than focusing on support for CLA and CLs in general FE colleges. This mixed methods evaluation is formative in intention and involves an exploratory study of the use of the funding by virtual schools (VS). It also considers early evidence about progress towards the outcomes in the Theory of Change (ToC), developed during the pilot evaluation and updated at the start of this evaluation through a series of ToC workshops with VSHs. The outcomes are arranged in the ToC under 3 headings, which are outcomes relating to young people, post-16 settings and joint working. This interim report presents findings from year 1 of the evaluation (2023/24) based on a national online survey of VSHs, case study interviews in 6 local authorities involving interviews with a range of stakeholders, and documentary analysis. [This report was produced with support from the Cordis Bright and the Rees Centre, University of Oxford.]

We analyze the dynamics of BPS 3-vortex solutions. First, for unexcited vortices, we study the 2-dimensional moduli space of centred vortices with $y \to -y$ symmetry, and its metric. We identify the 1-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in $90^\circ$ and 60^\circ$ scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multi-bounce collisions., Comment: 27 pages, 9 figures

Ischaemic stroke, a leading cause of death and disability, critically relies on neuroimaging for characterising the anatomical pattern of injury. Diffusion-weighted imaging (DWI) provides the highest expressivity in ischemic stroke but poses substantial challenges for automated lesion segmentation: susceptibility artefacts, morphological heterogeneity, age-related comorbidities, time-dependent signal dynamics, instrumental variability, and limited labelled data. Current U-Net-based models therefore underperform, a problem accentuated by inadequate evaluation metrics that focus on mean performance, neglecting anatomical, subpopulation, and acquisition-dependent variability. Here, we present a high-performance DWI lesion segmentation tool addressing these challenges through optimized vision transformer-based architectures, integration of 3563 annotated lesions from multi-site data, and algorithmic enhancements, achieving state-of-the-art results. We further propose a novel evaluative framework assessing model fidelity, equity (across demographics and lesion subtypes), anatomical precision, and robustness to instrumental variability, promoting clinical and research utility. This work advances stroke imaging by reconciling model expressivity with domain-specific challenges and redefining performance benchmarks to prioritize equity and generalizability, critical for personalized medicine and mechanistic research., Comment: 29 pages, 7 figures, 2 tables, 1 supplementary table, 2 supplementary figures

We prove that the word problem in an Artin group G based on a diagram without A_3 or B_3 subdiagrams can be solved using a system of length preserving rewrite rules which, together with free reduction, can be used to reduce any word over the standard generators of G to a geodesic word in G in quadratic time. This result builds on work of Holt and Rees, and of Blasco-Garc\'ia, Cumplido and Morris-Wright. Those articles prove the same result for all Artin groups that are either sufficiently large or 3-free, respectively., Comment: 53 pages. arXiv admin note: substantial text overlap with arXiv:2310.14632

Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE coefficients at large spin and fixed twist always become that of a generalized free field theory., Comment: 3+5 pages

Electrons trapped on the surface of cryogenic substrates (liquid helium, solid neon or hydrogen) are an emerging platform for quantum information processing made attractive by the inherent purity of the electron environment, the scalability of trapping devices and the predicted long lifetime of electron spin states. Here we demonstrate the spatial control and detection of single electrons above the surface of liquid helium at temperatures above 1 K. A superconducting coplanar waveguide resonator is used to read out the charge state of an electron trap defined by gate electrodes beneath the helium surface. Dispersive frequency shifts are observed as the trap is loaded with electrons, from several tens down to single electrons. These frequency shifts are in good agreement with our theoretical model that treats each electron as a classical oscillator coupled to the cavity field. This sensitive charge readout scheme can aid efforts to develop large-scale quantum processors that require the high cooling powers available in cryostats operating above 1 K., Comment: 12 pages, 6 figures

The in-plane motion of an electron on helium can couple to superconducting microwave resonators via electrical dipole coupling, offering a robust and rapid readout scheme. In previous efforts, microwave resonator designs for electrons on helium have lacked the coupling strength to reach the strong coupling regime, where coherent quantum effects outlast both electron and resonator decoherence rates. High-impedance superconducting microwave resonators offer a path to strong coupling, but integrating such resonators with electrons on helium remains an outstanding challenge. Here, we introduce a high-impedance resonator design compatible with strong coupling to electrons on helium. We fabricate and measure titanium nitride resonators with median internal quality factors of $3.9\times 10^5$ and average impedance of 2.5 k$\Omega$, promising a seven-fold increase in coupling strength compared with standard 50$\Omega$ resonators. Additionally, we develop a simplified resonator model from the capacitance matrix and sheet inductance that accurately predicts the mode frequencies, significantly simplifying the design process of future resonators for investigating quantum effects with electrons on helium., Comment: 15 pages, 7 figures, 2 tables

Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the interfaces with the atmosphere and ocean. The salinity of sea ice has a large effect on its thermal properties so might naively be expected to have a large effect on its growth rate. However, previous studies observed a low sensitivity throughout the winter growth season. The goal of this study is to identify the controlling physical mechanisms that explain this observation. We develop a simplified quasi-static framework by applying a similarity transformation to the underlying heat equation and neglecting the explicit time dependence. We find three key processes controlling the sensitivity of growth rate to salinity. First, the trade-off between thermal conductivity and (latent) heat capacity leads to low sensitivity to salinity even at moderately high salinity and brine volume fraction. Second, the feedback on the temperature profile reduces the sensitivity relative to models that assume a linear profile, such as zero-layer Semtner models. Third, thicker ice has the opposite sensitivity of growth rate to salinity compared to thinner ice, sensitivities that counteract each other as the ice grows. Beyond its use in diagnosing these sensitivities, we show that the quasi-static approach offers a valuable sea-ice model of intermediate complexity between zero-layer Semtner models and full partial-differential-equation-based models such as Maykut-Untersteiner/Bitz-Lipscomb and mushy-layer models., Comment: Revised manuscript, accepted for publication in J. Fluid Mech., 30 pages, 12 figures

Mode-locked lasers are of interest for applications such as biological imaging, non-linear frequency conversion, and single-photon generation. In the infrared, chip-integrated mode-locked lasers have been demonstrated through integration of laser diodes with low-loss photonic circuits. However additional challenges, such as a higher propagation loss and smaller alignment tolerances have prevented the realization of such lasers in the visible range. Here, we demonstrate the first chip-integrated mode-locked diode laser in the visible using an integrated photonic circuit for cavity extension. Based on a gallium arsenide gain chip and a low-loss silicon nitride feedback circuit, the laser is passively mode-locked using a saturable absorber implemented by focused ion beam milling. At a center wavelength of 642 nm, the laser shows an average output power of 3.4 mW, with a spectral bandwidth of 1.5 nm at a repetition rate of 7.84 GHz., Comment: 7 pages, 4 figures

We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex non-Hermitian and, due to the pollution effect, either very large or else still large but under-resolved in terms of the physics. These factors make finding general purpose, efficient and scalable solvers difficult and no one approach has become the clear method of choice. In this work we take inspiration from domain decomposition strategies known as sweeping methods, which have gained notable interest for their ability to yield nearly-linear asymptotic complexity and which can also be favourable for high-frequency problems. While successful approaches exist, such as those based on higher-order interface conditions, perfectly matched layers (PMLs), or complex tracking of wave fronts, they can often be quite involved or tedious to implement. We investigate here the use of simple sweeping techniques applied in different directions which can then be incorporated in parallel into a multipreconditioned GMRES strategy. Preliminary numerical results on a two-dimensional benchmark problem will demonstrate the potential of this approach.

An ensemble of electrons trapped above the surface of superfluid helium is a paradigm system for investigating, and controlling, the collective charge dynamics of low-dimensional electronic matter. Of particular interest is the ability to engineer the spatial and spectral structure of surface plasmon modes in this system for integration into hybrid quantum systems or circuit quantum electrodynamic device architectures. Here we present experiments on a hybrid electron-on-helium microchannel device designed to host microwave-frequency plasmon modes having a spatial structure dictated by the geometry of the microchannel confinement. The plasma oscillations are generated via local microwave frequency excitation of the electrons in the microchannel. When this excitation is resonant with a particular surface plasmon-mode it produces a non-equilibrium decrease in the electron conductance, which we detect via simultaneous transport measurements. We find that the spatial structure of the surface plasmons is in excellent agreement with our device design parameters and modeling, and their frequency can be tuned over a broad range (several GHz) by precisely varying the areal density of electrons in the channel. By measuring the plasma resonance spectrum lineshape, and its power dependence, we can quantify the level of spatial homogeneity associated with each plasmon mode. The results highlight the versatility of electrons on helium as a model system for investigating, and engineering, the collective mode structure of low-dimensional Coulomb liquid and solid states and demonstrate a viable path for integrating precisely engineered surface plasmons in electrons on helium with future hybrid circuit quantum electrodynamic systems., Comment: 10 pages, 5 figures, 1 Appendix

We study groups whose co-word problems are ET0L languages, which we call coET0L groups, using an automaton based model due to van Leeuwen, and recently studied by Bishop and Elder. In particular we prove a number of closure results for the class of groups with co-word problems in a subclass of `special' ET0L languages; that class of groups contains all groups that we know at the time of writing to be co-ET0L, including all groups that were proved by Holt and R\"over to be stack groups, and hence co-indexed. It includes virtually free groups, bounded automata groups, and the Higman-Thompson groups, together with groups constructed from those using finitely generated subgroups, finite extension, free and direct products, and by taking the restricted standard wreath product of a co-\E group by a finitely generated virtually free top group.

Molecular cloud collisions are a prominent theory for the formation of stars. Observational studies into cloud collisions identify the collision via a bridging feature: a continuous strip of line emission that connects two intensity peaks that are related in position space and separated in velocity space. Currently, most observations of collisions and these bridging features take place in the Milky Way disc. They are also theorized to take place in the Central Molecular Zone (CMZ), where temperatures and densities are both significantly higher than in the disc. For studies in the Milky Way Disc, the most commonly-used tracer tends to be CO. However, for studies in the CMZ, where the density and temperature are significantly higher, low-J CO lines lose their ability to adequately highlight the bridging feature of cloud collisions. As a result, studies have begun using other tracers, whose physical and chemical behavior has not been studied under CMZ conditions. We perform combined hydrodynamical, chemical and radiative transfer simulations of cloud collisions under both disc- and CMZ-like conditions, and investigate collision signatures in a number of commonly-observed molecular lines. Under the Milky Way disc conditions CO has the standard bridging feature; however, the other tracers, CS, HCO$^+$, N$_2$H$^+$ only emit in the intermediate-velocity bridge region, making the feature itself challenging to detect. In the CMZ, the higher density and temperature make the bridging feature far more indistinct for CO, but the other tracers have morphologically similar bridging features to the CO disc model, validating their use as tracers of cloud collisions under these conditions., Comment: 6 pages, 4 figures, for submission to Open Journal of Astrophysics

Finding proper collective variables for complex systems and processes is one of the most challenging tasks in simulations, which limits the interpretation of experimental and simulated data and the application of enhanced sampling techniques. Here, we propose a machine learning approach able to distill few, physically relevant variables by associating instantaneous configurations of the system to their corresponding inherent structures as defined in liquids theory. We apply this approach to the challenging case of structural transitions in nanoclusters, managing to characterize and explore the structural complexity of an experimentally relevant system constituted by 147 gold atoms. Our inherent-structure variables are shown to be effective at computing complex free-energy landscapes, transition rates, and at describing non-equilibrium melting and freezing processes. The effectiveness of this machine learning strategy guided by the generally-applicable concept of inherent structures shows promise to devise collective variables for a vast range of systems, including liquids, glasses, and proteins.

We present here RadioSED, a Bayesian inference framework tailored to modelling and classifying broadband radio spectral energy distributions (SEDs) using only data from publicly-released, large-area surveys. We outline the functionality of RadioSED, with its focus on broadband radio emissions which can trace kiloparsec-scale absorption within both the radio jets and the circumgalactic medium of Active Galactic Nuclei (AGN). In particular, we discuss the capability of RadioSED to advance our understanding of AGN physics and composition within youngest and most compact sources, for which high resolution imaging is often unavailable. These young radio AGN typically manifest as peaked spectrum (PS) sources which, before RadioSED, were difficult to identify owing to the large, broadband frequency coverage typically required, and yet they provide an invaluable environment for understanding AGN evolution and feedback. We discuss the implementation details of RadioSED, and we validate our approach against both synthetic and observational data. Since the surveys used are drawn from multiple epochs of observation, we also consider the output from RadioSED in the context of AGN variability. Finally, we show that RadioSED recovers the expected SED shapes for a selection of well-characterised radio sources from the literature, and we discuss avenues for further study of these and other sources using radio SED fitting as a starting point. The scalability and modularity of this framework make it an exciting tool for multiwavelength astronomers as next-generation telescopes begin several all-sky surveys. Accordingly, we make the code for RadioSED, which is written in Python, available on Github., Comment: 20 pages, 2 tables, 15 figures. Accepted for publication in MNRAS

Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a straightforward rescaling of the radial coordinate. However, when applied to oblate- or prolate-shaped particles the SH analysis quality degenerates with significant oscillations appearing after the reconstruction. Here, we propose a spheroidal harmonics (SOH) approach for the expansion and reconstruction of prolate and oblate particles. This generalizes the SH approach by providing additional parameters that can be adjusted per particle to minimize geometric distortion, thus increasing the analysis quality. We propose three mapping techniques for handling both star-shaped and non-star-shaped particles onto spheroidal domains. The results demonstrate the ability of the SOH to overcome the shortcomings of SH without requiring computationally expensive solutions or drastic changes to existing codes and processing pipelines., Comment: 42 pages, 24 figures, submitted preprint

We find a spectral wall in collisions of two vortices in the Abelian Higgs model at the critical coupling. It occurs if the out-of-phase mode of initially separated vortices is excited., Comment: 6 pages, 4 figures and ancillary files (5 videos)

We consider head-on collisions at critical coupling of vortices modelled by the Abelian-Higgs model. We investigate the 2-vortex scattering, whereby the vortices are excited by the shape mode causing fluctuations in the gauge-invariant quantities. When the vortices are excited with a sufficiently large amplitude the moduli space approximation fails, and we observe an interesting behaviour in which the vortices can become trapped in a quasi-bound state with multiple bounces. We perform a detailed investigation on the behaviour of these excited vortices and sample a phase space of solutions. Interestingly, we find a fractal structure dependent on the initial phase of the mode and velocity of the vortices., Comment: 27 pages, 13 figures

We demonstrate absorber-free passive and hybrid mode-locking at sub-GHz repetition rates using a hybrid integrated extended cavity diode laser around 1550 nm. The laser is based on InP as gain medium and a long Si$_3$N$_4$ feedback circuit, with three highly frequency selective microring resonators. The feedback resonators not only increases the cavity length up to 0.6 m to achieve sub-GHz repetition rates but also serve as a dispersive narrowband mirror for sharp spectral filtering, which enables Fourier domain mode-locking. We observe passive mode-locking with repetition rates below 500 MHz, with $\approx$ 15 comb lines at around 0.2 mW total power. To stabilize the repetition rate, hybrid mode-locking is demonstrated by weak RF modulation of the diode current at frequencies around 500 MHz. The RF injection reduces the Lorentzian linewidth component from 8.9 kHz to a detection limited value around 300 mHz. To measure the locking range of the repetition rate, the injected RF frequency is tuned with regard to the passive mode-locking frequency and the injected RF power is varied. The locking range increases approximately as a square-root function of the injected RF power. At 1 mW injection a wide locking range of about 80 MHz is obtained. We observe the laser maintaining stable mode-locking also when the DC diode pump current is increased from 40 mA to 190 mA, provided that the cavity length is maintained constant with thermo-refractive tuning., Comment: This manuscript is under review for publication with optics express

We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 \leq d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms., Comment: 48 pages, 15 figures ; Added references

Astrometry from {\it Gaia} DR3 has enabled the discovery of a sample of 3000+ binaries containing white dwarfs (WD) and main-sequence (MS) stars in relatively wide orbits, with orbital periods $P_{\rm orb} = (100-1000)$ d. This population was not predicted by binary population synthesis models before {\it Gaia} and -- if the {\it Gaia} orbits are robust -- likely requires very efficient envelope ejection during common envelope evolution (CEE). To assess the reliability of the {\it Gaia} solutions, we measured multi-epoch radial velocities (RVs) of 31 WD+MS binary candidates with $P_{\rm orb} = (40-300)$ d and \texttt{AstroSpectroSB1} orbital solutions. We jointly fit the RVs and astrometry, allowing us to validate the {\it Gaia} solutions and tighten constraints on component masses. We find a high success rate for the {\it Gaia} solutions, with only 2 out of the 31 systems showing significant discrepancies between their {\it Gaia} orbital solutions and our RVs. Joint fitting of RVs and astrometry allows us to directly constrain the secondary-to-primary flux ratio $S$, and we find $S\lesssim 0.02$ for most objects, confirming the companions are indeed WDs. We tighten constraints on the binaries' eccentricities, finding a median $e\approx 0.1$. These eccentricities are much lower than those of normal MS+MS binaries at similar periods, but much higher than predicted for binaries formed via stable mass transfer. We present MESA single and binary evolution models to explore how the binaries may have formed. The orbits of most binaries in the sample can be produced through CEE that begins when the WD progenitor is an AGB star, corresponding to initial separations of $2-5$ au. Roughly 50\% of all post-common envelope binaries are predicted to have first interacted on the AGB, ending up in wide orbits like these systems., Comment: 37 pages, 22 figures, Published in PASP

Two conjectures are presented. The first, Conjecture 1, is that the pushforward of a geometric distribution on the integers under $n$ Collatz iterates, modulo $2^p$, is usefully close to uniform distribution on the integers modulo $2^p$, if $p/n$ is small enough. Conjecture 2 is that the density is bounded from zero for the incidence of both $0$ and $1$ for the coefficients in the dyadic expansions of $-3^{-\ell }$ on all but an exponentially small set of paths of a geometrically distributed random walk on the two-dimensional array of these coefficients. It is shown that Conjecture 2 implies Conjecture 1. At present, Conjecture 2 is unresolved., Comment: 28 pages. Version 2 posted within 24 hours of version 1 because of an error around the speculative remarks concerning Question 4.3

We present hybrid-integrated extended cavity diode lasers tunable around 637 nm, with a gain-wide spectral coverage of 8 nm. This tuning range allows addressing the zero-phonon line of nitrogen vacancy centers and includes the wavelength of HeNe lasers (633 nm). The lasers provide wide mode-hop free tuning up to 97 GHz and a narrow intrinsic linewidth down to 10 kHz. The maximum output power is 2.5 mW in a single-mode fiber, corresponding to an on-chip power of 4.0 mW. Full integration and packaging in a standard housing with fiber pigtails provide high intrinsic stability and will enable integration into complex optical systems., Comment: 11 pages, 7 figures

Graph neural networks have been shown successful in recent years. While different GNN architectures and training systems have been developed, GNN training on large-scale real-world graphs still remains challenging. Existing distributed systems load the entire graph in memory for graph partitioning, requiring a huge memory space to process large graphs and thus hindering GNN training on such large graphs using commodity workstations. In this paper, we propose CATGNN, a cost-efficient and scalable distributed GNN training system which focuses on scaling GNN training to billion-scale or larger graphs under limited computational resources. Among other features, it takes a stream of edges as input, instead of loading the entire graph in memory, for partitioning. We also propose a novel streaming partitioning algorithm named SPRING for distributed GNN training. We verify the correctness and effectiveness of CATGNN with SPRING on 16 open datasets. In particular, we demonstrate that CATGNN can handle the largest publicly available dataset with limited memory, which would have been infeasible without increasing the memory space. SPRING also outperforms state-of-the-art partitioning algorithms significantly, with a 50% reduction in replication factor on average.

Researchers urge technology practitioners such as data scientists to consider the impacts and ethical implications of algorithmic decisions. However, unlike programming, statistics, and data management, discussion of ethical implications is rarely included in standard data science training. To begin to address this gap, we designed and tested a toolbox called the data ethics emergency drill (DEED) to help data science teams discuss and reflect on the ethical implications of their work. The DEED is a roleplay of a fictional ethical emergency scenario that is contextually situated in the team's specific workplace and applications. This paper outlines the DEED toolbox and describes three studies carried out with two different data science teams that iteratively shaped its design. Our findings show that practitioners can apply lessons learnt from the roleplay to real-life situations, and how the DEED opened up conversations around ethics and values., Comment: accepted to CHI 2024

While chain-of-thought prompting (CoT) has the potential to improve the explainability of language model reasoning, it can systematically misrepresent the factors influencing models' behavior--for example, rationalizing answers in line with a user's opinion without mentioning this bias. To mitigate this biased reasoning problem, we introduce bias-augmented consistency training (BCT), an unsupervised fine-tuning scheme that trains models to give consistent reasoning across prompts with and without biasing features. We construct a suite testing nine forms of biased reasoning on seven question-answering tasks, and find that applying BCT to GPT-3.5-Turbo with one bias reduces the rate of biased reasoning by 86% on held-out tasks. Moreover, this model generalizes to other forms of bias, reducing biased reasoning on held-out biases by an average of 37%. As BCT generalizes to held-out biases and does not require gold labels, this method may hold promise for reducing biased reasoning from as-of-yet unknown biases and on tasks where supervision for ground truth reasoning is unavailable.