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Purpose: To describe SLOctolyzer: an open-source analysis toolkit for en face retinal vessels appearing in infrared reflectance scanning laser ophthalmoscopy (SLO) images. Methods: SLOctolyzer includes two main modules: segmentation and measurement. The segmentation module use deep learning methods to delineate retinal anatomy, while the measurement module quantifies key retinal vascular features such as vessel complexity, density, tortuosity, and calibre. We evaluate the segmentation module using unseen data and measure its reproducibility. Results: SLOctolyzer's segmentation module performed well against unseen internal test data (Dice for all-vessels, 0.9097; arteries, 0.8376; veins, 0.8525; optic disc, 0.9430; fovea, 0.8837). External validation against severe retinal pathology showed decreased performance (Dice for arteries, 0.7180; veins, 0.7470; optic disc, 0.9032). SLOctolyzer had good reproducibility (mean difference for fractal dimension, -0.0007; vessel density, -0.0003; vessel calibre, -0.3154 $\mu$m; tortuosity density, 0.0013). SLOctolyzer can process a macula-centred SLO image in under 20 seconds and a disc-centred SLO image in under 30 seconds using a standard laptop CPU. Conclusions: To our knowledge, SLOctolyzer is the first open-source tool to convert raw SLO images into reproducible and clinically meaningful retinal vascular parameters. SLO images are captured simultaneous to optical coherence tomography (OCT), and we believe our software will be useful for extracting retinal vascular measurements from large OCT image sets and linking them to ocular or systemic diseases. It requires no specialist knowledge or proprietary software, and allows manual correction of segmentations and re-computing of vascular metrics. SLOctolyzer is freely available at https://github.com/jaburke166/SLOctolyzer., Comment: 10 pages, 5 figures, 6 tables + Supplementary (7 pages, 10 figures, 4 tables). Submitted for peer review at Translational Vision Science and Technology

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA's work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware co-design in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing and describe improved methods for simulating quantum systems of various types on high-performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, as well as insights into fundamental quantum physics that can be harnessed for computational purposes., Comment: 27 pages, 0 figures

Fast radio bursts (FRBs) are brilliant short-duration flashes of radio emission originating at cosmological distances. The vast diversity in the properties of currently known FRBs, and the fleeting nature of these events make it difficult to understand their progenitors and emission mechanism(s). Here we report high time resolution polarization properties of FRB 20210912A, a highly energetic event detected by the Australian Square Kilometre Array Pathfinder (ASKAP) in the Commensal Real-time ASKAP Fast Transients (CRAFT) survey, which show intra-burst PA variation similar to Galactic pulsars and unusual variation of Faraday Rotation Measure (RM) across its two sub-bursts. The observed intra-burst PA variation and apparent RM variation pattern in FRB 20210912A may be explained by a rapidly-spinning neutron star origin, with rest-frame spin periods of ~1.1 ms. This rotation timescale is comparable to the shortest known rotation period of a pulsar, and close to the shortest possible rotation period of a neutron star. Curiously, FRB 20210912A exhibits a remarkable resemblance with the previously reported FRB 20181112A, including similar rest-frame emission timescales and polarization profiles. These observations suggest that these two FRBs may have similar origins., Comment: Accepted for publication in ApJ Letters

Circularly polarized, nearly parallel propagating waves are prevalent in the solar wind at ion-kinetic scales. At these scales, the spectrum of turbulent fluctuations in the solar wind steepens, often called the transition-range, before flattening at sub-ion scales. Circularly polarized waves have been proposed as a mechanism to couple electromagnetic fluctuations to ion gyromotion, enabling ion-scale dissipation that results in observed ion-scale steepening. Here, we study Parker Solar Probe observations of an extended stream of fast solar wind ranging from 15-55 solar radii. We demonstrate that, throughout the stream, transition-range steepening at ion-scales is associated with the presence of significant left handed ion-kinetic scale waves, which are thought to be ion-cyclotron waves. We implement quasilinear theory to compute the rate at which ions are heated via cyclotron resonance with the observed circularly polarized waves given the empirically measured proton velocity distribution functions. We apply the Von Karman decay law to estimate the turbulent decay of the large-scale fluctuations, which is equal to the turbulent energy cascade rate. We find that the ion-cyclotron heating rates are correlated with, and amount to a significant fraction of, the turbulent energy cascade rate, implying that cyclotron heating is an important dissipation mechanism in the solar wind.

Virtual, Mixed, and Augmented Reality (XR) technologies hold immense potential for transforming productivity beyond PC. Therefore there is a critical need for improved text input solutions for XR. However, achieving efficient text input in these environments remains a significant challenge. This paper examines the current landscape of XR text input techniques, focusing on the importance of keyboards (both physical and virtual) as essential tools. We discuss the unique challenges and opportunities presented by XR, synthesizing key trends from existing solutions.

In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using Fourier transform methods in conjunction with the known properties of delay functions. It is observed that the solutions do not exhibit infinite speed of propagation for smooth initial conditions that are bounded and positive. Sufficient conditions on the initial condition are also established such that the finite time blowup of the solutions can be explicitly calculated. Examples are provided that highlight the contrasting behaviours of these exact solutions with the known dynamics of solutions to the standard diffusion equation., Comment: Errors were discovered in the analysis, significant revisions are being made to the manuscript

Diamond-like carbon thin films have emerged as durable, chemically stable optical coatings for many optical and optoelectronics applications due to their hardness, chemical inertness, and optical transparency. This paper presents a novel high-energy electron cyclotron resonance ion beam sputter deposition technique to fabricate pure diamond-like carbon coatings at room temperature. The chemical composition of the deposited coatings including ratios of sp2/sp3 bonding in the thin films were determined by X-ray photoelectron spectroscopy. Results indicate that the sp3 percentage ranges from 45% - 85%. The transmission and reflectance spectra of the coatings were measured from UV to IR ({\lambda}= 185 to 2500 nm) by utilizing a spectrophotometer. The measured spectra were analysed by the Tauc method to determine the optical band gap and Urbach energy and an optical fitting software, which utilizes the model modified by OJL, to extract the refractive index and extinction coefficient. By varying the ion energy, the optical properties were found to be n = 2.30 - 2.51, band gap energy = 0.4 - 0.68 eV, and the Urbach energy = 0.33 - 0.49 eV. This study provides a flexible method for tuning the structural, optical, and electronic properties of diamond-like carbon coatings by controlling the ion energy during deposition.

A novel high-energy electron cyclotron resonance (ECR) ion beam deposition (IBD) technique was used to fabricate DLC films at different ion beam energies. The ratios of sp2/sp3 bonding in the DLC coatings were determined by Raman spectroscopy and XPS, with the confirmation of being hydrogen-free due to the lack of photoluminescence (PL) background in the Raman spectra. The results indicate that the sp3 percentage ranges from 45% - 85% for the ECR-IBD fabricated DLC films in this study. Monte-Carlo based SRIM simulation was used to extract the energy and angular distribution of the sputtered particles from the carbon target and correlate it to the highest sp3 fraction in the manufactured ECR-IBD DLCs. This study demonstrates a method of depositing DLC thin films under ambient conditions (room temperature with no post-annealing or additional bias voltage applied) which produces high-sp3 coatings (higher than those traditionally reported for other sputtering methods) suitable for applications where high quality DLC coatings are required.

Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language processing, computer vision, and time-series problems. Neural operators, which map spaces of functions into spaces of functions, are necessarily both nonlinear and nonlocal if they are universal; it is thus natural to ask whether the attention mechanism can be used in the design of neural operators. Motivated by this, we study transformers in the function space setting. We formulate attention as a map between infinite dimensional function spaces and prove that the attention mechanism as implemented in practice is a Monte Carlo or finite difference approximation of this operator. The function space formulation allows for the design of transformer neural operators, a class of architectures designed to learn mappings between function spaces, for which we prove a universal approximation result. The prohibitive cost of applying the attention operator to functions defined on multi-dimensional domains leads to the need for more efficient attention-based architectures. For this reason we also introduce a function space generalization of the patching strategy from computer vision, and introduce a class of associated neural operators. Numerical results, on an array of operator learning problems, demonstrate the promise of our approaches to function space formulations of attention and their use in neural operators.

Control of frictional interactions among liquid-suspended particles has led to tunable, strikingly non-Newtonian rheology via the formation of strong flow constraints as particles come into close proximity under shear. Typically, these frictional interactions have been in the form of physical contact, controllable via particle shape and surface roughness. We investigate a different route, where molecular bridging between nearby particle surfaces generates a controllable "sticky" friction. This is achieved with surface-functionalized colloidal particles capable of forming dynamic covalent bonds with telechelic polymers that comprise the suspending fluid. At low shear stress this results in particles coated with a uniform polymer brush layer. Beyond an onset stress the telechelic polymers become capable of bridging and generate shear thickening. Over the size range investigated, we find that the dynamic brush layer leads to dependence of the onset stress on particle diameter that closely follows a power law with exponent -1.76. In the shear thickening regime, we observe an enhanced dilation in measurements of the first normal stress difference and reduction in the extrapolated volume fraction required for jamming, both consistent with an effective particle friction that increases with decreasing particle diameter. These results are discussed in light of predictions for suspensions of hard spheres and of polymer-grafted particles.

Assembly Theory (AT) was developed to help distinguish living from non-living systems. The theory is simple as it posits that the amount of selection or Assembly is a function of the number of complex objects where their complexity can be objectively determined using assembly indices. The assembly index of a given object relates to the number of recursive joining operations required to build that object and can be not only rigorously defined mathematically but can be experimentally measured. In pervious work we outlined the theoretical basis, but also extensive experimental measurements that demonstrated the predictive power of AT. These measurements showed that is a threshold in assembly indices for organic molecules whereby abiotic chemical systems could not randomly produce molecules with an assembly index greater or equal than 15. In a recent paper by Hazen et al [1] the authors not only confused the concept of AT with the algorithms used to calculate assembly indices, but also attempted to falsify AT by calculating theoretical assembly indices for objects made from inorganic building blocks. A fundamental misunderstanding made by the authors is that the threshold is a requirement of the theory, rather than experimental observation. This means that exploration of inorganic assembly indices similarly requires an experimental observation, correlated with the theoretical calculations. Then and only then can the exploration of complex inorganic molecules be done using AT and the threshold for living systems, as expressed with such building blocks, be determined. Since Hazen et al.[1] present no experimental measurements of assembly theory, their analysis is not falsifiable., Comment: 6 pages, 11 references

Magnetic skyrmion crystals are traditionally associated with non-centrosymmetric crystal structures; however, it has been demonstrated that skyrmion crystals can be stabilized by competing interactions in centrosymmetric crystals. To understand and optimize the physical responses associated with topologically-nontrivial skyrmion textures, it is important to quantify their magnetic interactions by comparing theoretical predictions with spectroscopic data. Here, we present neutron diffraction and spectroscopy data on the centrosymmetric skyrmion material GdRu$_2$Si$_2$, and show that the key spectroscopic features can be explained by the magnetic interactions calculated using density-functional theory calculations. We further show that the recently-proposed 2-$\mathbf{q}$ "topological spin stripe" structure yields better agreement with our data than a 1-$\mathbf{q}$ helical structure, and identify how the magnetic structure evolves with temperature., Comment: 6 pages, 3 figures

Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a separation of variables approach. Examples are provided showing oscillatory and translatory behaviours that are fundamentally different to standard propagating wave solutions., Comment: Letter

Do neural networks learn to implement algorithms such as look-ahead or search "in the wild"? Or do they rely purely on collections of simple heuristics? We present evidence of learned look-ahead in the policy network of Leela Chess Zero, the currently strongest neural chess engine. We find that Leela internally represents future optimal moves and that these representations are crucial for its final output in certain board states. Concretely, we exploit the fact that Leela is a transformer that treats every chessboard square like a token in language models, and give three lines of evidence (1) activations on certain squares of future moves are unusually important causally; (2) we find attention heads that move important information "forward and backward in time," e.g., from squares of future moves to squares of earlier ones; and (3) we train a simple probe that can predict the optimal move 2 turns ahead with 92% accuracy (in board states where Leela finds a single best line). These findings are an existence proof of learned look-ahead in neural networks and might be a step towards a better understanding of their capabilities., Comment: Project page: https://leela-interp.github.io/

Large language models generate code one token at a time. Their autoregressive generation process lacks the feedback of observing the program's output. Training LLMs to suggest edits directly can be challenging due to the scarcity of rich edit data. To address these problems, we propose neural diffusion models that operate on syntax trees of any context-free grammar. Similar to image diffusion models, our method also inverts ``noise'' applied to syntax trees. Rather than generating code sequentially, we iteratively edit it while preserving syntactic validity, which makes it easy to combine this neural model with search. We apply our approach to inverse graphics tasks, where our model learns to convert images into programs that produce those images. Combined with search, our model is able to write graphics programs, see the execution result, and debug them to meet the required specifications. We additionally show how our system can write graphics programs for hand-drawn sketches., Comment: https://tree-diffusion.github.io

Since volcanic activity was first discovered on Io from Voyager images in 1979, changes on Io's surface have been monitored from both spacecraft and ground-based telescopes. Here, we present the highest spatial resolution images of Io ever obtained from a ground-based telescope. These images, acquired by the SHARK-VIS instrument on the Large Binocular Telescope, show evidence of a major resurfacing event on Io's trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images show that a plume deposit from a powerful eruption at Pillan Patera has covered part of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io's surface using adaptive optics at visible wavelengths., Comment: 15 pages, 4 figures

Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown parameter to an element of a solution space, often the solution space for a differential equation; an observation operator mapping an element of the solution space to the data space; a noise model describing how noise pollutes the observations; and a prior model describing knowledge about the unknown parameter before the data is acquired. This paper is concerned with learning the prior model from data; in particular, learning the prior from multiple realizations of indirect data obtained through the noisy observation process. The prior is represented, using a generative model, as the pushforward of a Gaussian in a latent space; the pushforward map is learned by minimizing an appropriate loss function. A metric that is well-defined under empirical approximation is used to define the loss function for the pushforward map to make an implementable methodology. Furthermore, an efficient residual-based neural operator approximation of the forward model is proposed and it is shown that this may be learned concurrently with the pushforward map, using a bilevel optimization formulation of the problem; this use of neural operator approximation has the potential to make prior learning from indirect data more computationally efficient, especially when the observation process is expensive, non-smooth or not known. The ideas are illustrated with the Darcy flow inverse problem of finding permeability from piezometric head measurements.

Existing AI alignment approaches assume that preferences are static, which is unrealistic: our preferences change, and may even be influenced by our interactions with AI systems themselves. To clarify the consequences of incorrectly assuming static preferences, we introduce Dynamic Reward Markov Decision Processes (DR-MDPs), which explicitly model preference changes and the AI's influence on them. We show that despite its convenience, the static-preference assumption may undermine the soundness of existing alignment techniques, leading them to implicitly reward AI systems for influencing user preferences in ways users may not truly want. We then explore potential solutions. First, we offer a unifying perspective on how an agent's optimization horizon may partially help reduce undesirable AI influence. Then, we formalize different notions of AI alignment that account for preference change from the outset. Comparing the strengths and limitations of 8 such notions of alignment, we find that they all either err towards causing undesirable AI influence, or are overly risk-averse, suggesting that a straightforward solution to the problems of changing preferences may not exist. As there is no avoiding grappling with changing preferences in real-world settings, this makes it all the more important to handle these issues with care, balancing risks and capabilities. We hope our work can provide conceptual clarity and constitute a first step towards AI alignment practices which explicitly account for (and contend with) the changing and influenceable nature of human preferences., Comment: Accepted to ICML 2024

We present an event observed by Parker Solar Probe at $\sim$0.2 au on March 2, 2022 in which imaging and \emph{in situ} measurements coincide. During this event, PSP passed through structures on the flank of a streamer blowout CME including an isolated flux tube in front of the CME, a turbulent sheath, and the CME itself. Imaging observations and \emph{in situ} helicity and principal variance signatures consistently show the presence of flux ropes internal to the CME. In both the sheath, and the CME interval, the distributions are more isotropic, the spectra are softer, and the abundance ratios of Fe/O and He/H are lower than those in the isolated flux tube, and yet elevated relative to typical plasma and SEP abundances. These signatures in the sheath and the CME indicate that both flare populations and those from the plasma are accelerated to form the observed energetic particle enhancements. In contrast, the isolated flux tube shows large streaming, hard spectra and large Fe/O and He/H ratios, indicating flare sources. Energetic particle fluxes are most enhanced within the CME interval from suprathermal through energetic particle energies ($\sim$ keV to $>10$ MeV), indicating particle acceleration, and confinement local to the closed magnetic structure. The flux-rope morphology of the CME helps to enable local modulation and trapping of energetic particles, particularly along helicity channels and other plasma boundaries. Thus, the CME acts to build-up energetic particle populations, allowing them to be fed into subsequent higher energy particle acceleration throughout the inner heliosphere where a compression or shock forms on the CME front., Comment: 41 pages, 19 figures, In Press

During Parker Solar Probe (Parker) Encounter 15 (E15), we observe an 18-hour period of near subsonic ($\mathrm{M_S \sim}$ 1) and sub-Alfv\'enic (SA), $\mathrm{M_A}$ <<< 1, slow speed solar wind from 22 to 15.6 R$_\odot$. As the most extreme SA interval measured to date and skirting the solar wind sonic point, it is the deepest Parker has probed into the formation and acceleration region of the solar wind in the corona. The stream is also measured by Wind and MMS near 1AU at times consistent with ballistic propagation of this slow stream. We investigate the stream source, properties and potential coronal heating consequences via combining these observations with coronal modeling and turbulence analysis. Through source mapping, in situ evidence and multi-point arrival time considerations of a candidate CME, we determine the stream is a steady (non-transient), long-lived and approximately Parker spiral aligned and arises from overexpanded field lines mapping back to an active region. Turbulence analysis of the Els\"{a}sser variables shows the inertial range scaling of the $\mathrm{\mathbf{z}^{+}}$ mode ($\mathrm{f \sim ^{-3/2}}$) to be dominated by the slab component. We discuss the spectral flattening and difficulties associated with measuring the $\mathrm{\mathbf{z}^{-}}$ spectra, cautioning against making definitive conclusions from the $\mathrm{\mathbf{z}^{-}}$ mode. Despite being more extreme than prior sub-Alfv\'enic intervals, its turbulent nature does not appear to be qualitatively different from previously observed streams. We conclude that this extreme low dynamic pressure solar wind interval (which has the potential for extreme space weather conditions) is a large, steady structure spanning at least to 1AU., Comment: 14 figures

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

The choroid is a key vascular layer of the eye, supplying oxygen to the retinal photoreceptors. Non-invasive enhanced depth imaging optical coherence tomography (EDI-OCT) has recently improved access and visualisation of the choroid, making it an exciting frontier for discovering novel vascular biomarkers in ophthalmology and wider systemic health. However, current methods to measure the choroid often require use of multiple, independent semi-automatic and deep learning-based algorithms which are not made open-source. Previously, Choroidalyzer -- an open-source, fully automatic deep learning method trained on 5,600 OCT B-scans from 385 eyes -- was developed to fully segment and quantify the choroid in EDI-OCT images, thus addressing these issues. Using the same dataset, we propose a Robust, Resolution-agnostic and Efficient Attention-based network for CHoroid segmentation (REACH). REACHNet leverages multi-resolution training with domain-specific data augmentation to promote generalisation, and uses a lightweight architecture with resolution-agnostic self-attention which is not only faster than Choroidalyzer's previous network (4 images/s vs. 2.75 images/s on a standard laptop CPU), but has greater performance for segmenting the choroid region, vessels and fovea (Dice coefficient for region 0.9769 vs. 0.9749, vessels 0.8612 vs. 0.8192 and fovea 0.8243 vs. 0.3783) due to its improved hyperparameter configuration and model training pipeline. REACHNet can be used with Choroidalyzer as a drop-in replacement for the original model and will be made available upon publication., Comment: 13 pages, 2 figures, 8 tables (including supplementary material)

Many recent studies have expounded the benefits of active learning in tertiary education. It can be challenging to implement these techniques at large scale (for example in first year mathematics courses). A common method for actively engaging students in large classes is through online quizzes, which may include peer instruction. In this paper, we investigate the effect of having students answer quiz-style questions during class both with and without discussion in a first year mathematics course. We also investigate the short- and long-term effects of each protocol. We find that peer instruction improves student learning in mathematics in the following ways: First, when the responses to questions was measured before and after peer instruction the proportion of questions answered correctly increased by 0.2; second, when correct responses were compared to similar questions the following week the proportion correct increased by 0.34 (compared to 0.07 for the control); finally, when measured at the end of the semester the proportion of questions answered correctly increased by 0.42 (compared to 0.2 for the control)., Comment: 13 pages, 8 figures

Most stripped envelope supernova progenitors are formed through binary interaction, losing hydrogen and/or helium from their outer layers. An emerging class of supernovae with the highest degree of envelope-stripping are thought to be the product of stripping by a NS companion. However, relatively few examples are known and the outcomes of such systems can be diverse and are poorly understood at present. Here, we present spectroscopic observations and high cadence multi-band photometry of SN 2023zaw, a low ejecta mass and rapidly evolving supernova. SN 2023zaw was discovered in a nearby spiral galaxy at D = 39.7 Mpc, with significant Milky Way extinction, $E(B-V) = 0.21$, and significant (but uncertain) host extinction. Bayesian evidence comparison reveals that nickel is not the only power source and an additional energy source is required to explain our observations. Our models suggest an ejecta mass of $M_{\rm ej} \sim 0.07\,\rm M_\odot$ and a synthesised nickel mass of $M_{\rm ej} \sim 0.007\,\rm M_\odot$ is required to explain the explosion. However an additional heating from a magnetar or interaction with circumstellar material is required to power the early light curve.

The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and $F$ is nonlinear. Such problems arise in the context of Bayesian inference and recent machine learning-inspired PDE solvers. We give a representer theorem for the conditioned random variable $\xi \mid F\circ \phi(\xi)$, stating that it decomposes as the sum of an infinite-dimensional Gaussian (which is identified analytically) as well as a finite-dimensional non-Gaussian measure. We also introduce a novel notion of the mode of a conditional measure by taking the limit of the natural relaxation of the problem, to which we can apply the existing notion of maximum a posteriori estimators of posterior measures. Finally, we introduce a variant of the Laplace approximation for the efficient simulation of the aforementioned conditioned Gaussian random variables towards uncertainty quantification.

Phase-coherent pulsed driving of passive optical fiber resonators enable the generation of ultrashort dissipative Raman solitons with durations well below 100~fs. The existence and characteristics of such solitons critically depends on the desynchronisation between the pulsed driving source and the resonator roundtrip time, yet the full mechanism through which these dependencies arise remains unclear. Here, we numerically demonstrate that Raman solitons can exist even under conditions of continuous wave driving, and by numerically examining the existence and characteristics of Raman solitons under such conditions, we elucidate the role of desynchronisation in pulse-driven systems. In addition to providing new insights on the existence and characteristics of ultrashort Raman solitons, our analysis yields a qualitative explanation for the range of desynchronisations over which the solitons can exist.

Multi-wavelength polarimetry and radio observations of Swift J1727.8-1613 at the beginning of its recent 2023 outburst suggested the presence of a bright compact jet aligned in the north-south direction, which could not be confirmed without high angular resolution images. Using the Very Long Baseline Array and the Long Baseline Array, we imaged Swift J1727.8-1613, during the hard/hard-intermediate state, revealing a bright core and a large, two-sided, asymmetrical, resolved jet. The jet extends in the north-south direction, at a position angle of $-0.60\pm0.07\deg$ East of North. At 8.4 GHz, the entire resolved jet structure is $\sim110 (d/2.7\,\text{kpc})/\sin i$ AU long, with the southern approaching jet extending $\sim80 (d/2.7\,\text{kpc})/\sin i$ AU from the core, where $d$ is the distance to the source and $i$ is the inclination of the jet axis to the line of sight. These images reveal the most resolved continuous X-ray binary jet, and possibly the most physically extended continuous X-ray binary jet ever observed. Based on the brightness ratio of the approaching and receding jets, we put a lower limit on the intrinsic jet speed of $\beta\geq0.27$ and an upper limit on the jet inclination of $i\leq74\deg$. In our first observation we also detected a rapidly fading discrete jet knot $66.89\pm0.04$ mas south of the core, with a proper motion of $0.66\pm0.05$ mas hour$^{-1}$, which we interpret as the result of a downstream internal shock or a jet-ISM interaction, as opposed to a transient relativistic jet launched at the beginning of the outburst., Comment: Accepted in ApJL

As both Parker Solar Probe (PSP) and Solar Orbiter (SolO) reach heliocentric distances closer to the Sun, they present an exciting opportunity to study the structure of CMEs in the inner heliosphere. We present an analysis of the global flux rope structure of the 2022 September 5 CME event that impacted PSP at a heliocentric distance of only 0.07 au and SolO at 0.69 au. We compare in situ measurements at PSP and SolO to determine global and local expansion measures, finding a good agreement between magnetic field relationships with heliocentric distance, but significant differences with respect to flux rope size. We use PSP/WISPR images as input to the ELEvoHI model, providing a direct link between remote and in situ observations; we find a large discrepancy between the resulting modeled arrival times, suggesting that the underlying model assumptions may not be suitable when using data obtained close to the Sun, where the drag regime is markedly different in comparison to larger heliocentric distances. Finally, we fit the SolO/MAG and PSP/FIELDS data independently with the 3DCORE model and find that many parameters are consistent between spacecraft, however, challenges are apparent when reconstructing a global 3D structure that aligns with arrival times at PSP and Solar Orbiter, likely due to the large radial and longitudinal separations between spacecraft. From our model results, it is clear the solar wind background speed and drag regime strongly affect the modeled expansion and propagation of CMEs and need to be taken into consideration.

We present self-consistent numerical simulations in general relativity of putative primordial black holes inside neutron stars. Complementing a companion paper in which we assumed the black hole mass $m$ to be much smaller than the mass $M_*$ of the neutron star, thereby justifying a point-mass treatment, we here consider black holes with masses large enough so that their effect on the neutron star cannot be neglected. We develop and employ several new numerical techniques, including initial data describing boosted black holes in neutron-star spacetimes, a relativistic determination of the escape speed, and a gauge condition that keeps the black hole hole at a fixed coordinate location. We then perform numerical simulations that highlight different aspects of the capture of primordial black holes by neutron stars. In particular, we simulate the initial passage of the black hole through the star, demonstrating that the neutron star remains dynamically stable provided the black-hole mass is sufficiently small, $m \lesssim 0.05 M_*$. We also model the late evolution of a black hole oscillating about the center of an initially stable neutron star while accreting stellar mass and ultimately triggering gravitational collapse., Comment: 16 pages, 9 figures, animations at https://www.youtube.com/playlist?list=PLe7W1aFCp-Ocfs00Q3Z0fvkuULlznLi1u

A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0, 2{\pi}] x [0, 2{\pi}] x [0, 1] to a toroidal domain in R3. This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier-Zernike basis via action minimization. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of 3D MHD equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed., Comment: 18 pages and 10 figures submitted to the Journal of Plasma Physics

Virtual humans (i.e., embodied conversational agents) have the potential to support college students' mental health, particularly in Science, Technology, Engineering, and Mathematics (STEM) fields where students are at a heightened risk of mental disorders such as anxiety and depression. A comprehensive understanding of students, considering their cultural characteristics, experiences, and expectations, is crucial for creating timely and effective virtual human interventions. To this end, we conducted a user study with 481 computer science students from a major university in North America, exploring how they co-designed virtual humans to support mental health conversations for students similar to them. Our findings suggest that computer science students who engage in co-design processes of virtual humans tend to create agents that closely resemble them demographically--agent-designer demographic similarity. Key factors influencing virtual human design included age, gender, ethnicity, and the matching between appearance and voice. We also observed that the demographic characteristics of virtual human designers, especially ethnicity and gender, tend to be associated with those of the virtual humans they designed. Finally, we provide insights concerning the impact of user-designer demographic similarity in virtual humans' effectiveness in promoting mental health conversations when designers' characteristics are shared explicitly or implicitly. Understanding how virtual humans' characteristics serve users' experiences in mental wellness conversations and the similarity-attraction effects between agents, users, and designers may help tailor virtual humans' design to enhance their acceptance and increase their counseling effectiveness., Comment: 43 pages, 12 figures, revision after acceptance with minor revisions at ACM Transactions on Applied Perception

Collisionless shock waves, ubiquitous in the universe, are crucial for particle acceleration in various astrophysical systems. Currently, the heliosphere is the only natural environment available for their in situ study. In this work, we showcase the collective acceleration of electrons and ions by one of the fastest in situ shocks ever recorded, observed by the pioneering Parker Solar Probe at only 34.5 million kilometers from the Sun. Our analysis of this unprecedented, near-parallel shock shows electron acceleration up to 6 MeV amidst intense multi-scale electromagnetic wave emissions. We also present evidence of a variable shock structure capable of injecting and accelerating ions from the solar wind to high energies through a self-consistent process. The exceptional capability of the probe's instruments to measure electromagnetic fields in a shock traveling at 1% the speed of light has enabled us, for the first time, to confirm that the structure of a strong heliospheric shock aligns with theoretical models of strong shocks observed in astrophysical environments. This alignment offers viable avenues for understanding astrophysical shock processes and the acceleration of charged particles., Comment: Main text: 9 pages, 4 figures, 1 table; Supplementary text: 9 pages, 6 figures

Ensuring that AI systems reliably and robustly avoid harmful or dangerous behaviours is a crucial challenge, especially for AI systems with a high degree of autonomy and general intelligence, or systems used in safety-critical contexts. In this paper, we will introduce and define a family of approaches to AI safety, which we will refer to as guaranteed safe (GS) AI. The core feature of these approaches is that they aim to produce AI systems which are equipped with high-assurance quantitative safety guarantees. This is achieved by the interplay of three core components: a world model (which provides a mathematical description of how the AI system affects the outside world), a safety specification (which is a mathematical description of what effects are acceptable), and a verifier (which provides an auditable proof certificate that the AI satisfies the safety specification relative to the world model). We outline a number of approaches for creating each of these three core components, describe the main technical challenges, and suggest a number of potential solutions to them. We also argue for the necessity of this approach to AI safety, and for the inadequacy of the main alternative approaches.

Auto-regressive large language models (LLMs) show impressive capacities to solve many complex reasoning tasks while struggling with some simple logical reasoning tasks such as inverse search: when trained on ''A is B'', LLM fails to directly conclude ''B is A'' during inference, which is known as the ''reversal curse'' (Berglund et al., 2023). In this paper, we theoretically analyze the reversal curse via the training dynamics of (stochastic) gradient descent for two auto-regressive models: (1) a bilinear model that can be viewed as a simplification of a one-layer transformer; (2) one-layer transformers using the framework of Tian et al. (2023a). Our analysis reveals a core reason why the reversal curse happens: the (effective) weights of both auto-regressive models show asymmetry, i.e., the increase of weights from a token $A$ to token $B$ during training does not necessarily cause the increase of the weights from $B$ to $A$. Moreover, our analysis can be naturally applied to other logical reasoning tasks such as chain-of-thought (COT) (Wei et al., 2022b). We show the necessity of COT, i.e., a model trained on ''$A \to B$'' and ''$B \to C$'' fails to directly conclude ''$A \to C$'' without COT (also empirically observed by Allen-Zhu and Li (2023)), for one-layer transformers via training dynamics, which provides a new perspective different from previous work (Feng et al., 2024) that focuses on expressivity. Finally, we also conduct experiments to validate our theory on multi-layer transformers under different settings., Comment: 40 pages, 15 figures

Anomalous Microwave Emission (AME) is a major component of Galactic emission in the frequency band 10 to 60 GHz and is commonly modelled as rapidly rotating spinning dust grains. The photodissociation region (PDR) at the boundary of the $\lambda$-Orionis Hii region has been identified by several recent analyses as one of the brightest spinning dust emitting sources in the sky. We investigate the Barnard 30 dark cloud, a dark cloud embedded within the $\lambda$-Orionis PDR. We use total-power observations of Barnard 30 from the CO Mapping Array Project (COMAP) pathfinder instrument at 26 to 34GHz with a resolution of 4.5 arcminutes alongside existing data from Planck, WISE, IRAS, ACT, and the 1.447GHz GALFACTS survey. We use aperture photometry and template fitting to measure the spectral energy distribution of Barnard 30. We find that the spinning dust is the dominant emission component in the 26 to 34GHz range at the $7 \sigma$ level ($S_{30GHz} = 2.85\pm0.43$Jy). We find no evidence that polycyclic aromatic hydrocarbons are the preferred carrier for the spinning dust emission, suggesting that the spinning dust carriers are due to a mixed population of very small grains. Finally, we find evidence for variations in spinning dust emissivity and peak frequency within Barnard 30, and that these variations are possibly driven by changes in dust grain population and the total radiation field. Confirming the origin of the variations in the spinning dust spectrum will require both future COMAP observations at 15GHz combined with spectroscopic mid-infrared data of Barnard 30., Comment: 21 pages, 13 figures. Submitted to MNRAS

Quantum computers theoretically promise computational advantage in many tasks, but it is much less clear how such advantage can be maintained when using existing and near-term hardware that has limitations in the number and quality of its qubits. One promising application was proposed in Layden et al [Nature 619, 282-287 (2023)] where a method to reduce the thermalisation time required when sampling from hard probability distribution was introduced as a Quantum-enhanced Markov Chain Monte Carlo (QeMCMC) approach. In [Nature 619, 282-287 (2023)] the size of the required quantum computer scales linearly with the problem, putting limitations on the sizes of systems that one can consider. In this work we introduce a framework to coarse grain the algorithm in such a way that the quantum computation can be performed using, multiple times, smaller quantum computers and we term the method the Coarse Grained Quantum-enhanced Markov Chain Monte Carlo (CGQeMCMC). Example strategies within this framework are put to the test, with the quantum speedup of [Nature 619, 282-287 (2023)] persisting while using only $\sqrt{n}$ simulated qubits where $n$ is the number of qubits required in the original QeMCMC -- a quadratic reduction in resources. The coarse graining framework has the potential to be practically applicable in the near term as it requires very few qubits to approach classically intractable problem instances, here only 6 simulated qubits suffice to gain advantage compared to standard classical approaches when investigating the magnetisation of a 36 spin system. Our method is also adjustable to quantum hardware specifications, and it appears that it can be easily combined with other techniques both classical and quantum., Comment: 13 pages, 8 figures

GW170817 and GRB 170817A provided direct evidence that binary neutron star (NSNS) mergers can produce short gamma-ray bursts (sGRBs). However, questions remain about the nature of the central engine. Depending on the mass, the remnant from a NSNS merger may promptly collapse to a black hole (BH), form a hypermassive neutron star (HMNS) which undergoes a delayed collapse to a BH, a supramassive neutron star (SMNS) with a much longer lifetime, or an indefinitely stable NS. There is strong evidence that a BH with an accretion disk can launch a sGRB-compatible jet via the Blandford-Znajek mechanism, but whether a supramassive star can do the same is less clear. We have performed general relativistic magnetohydrodynamics simulations of the merger of both irrotational and spinning, equal-mass NSNSs constructed from a piecewise polytropic representation of the SLy equation of state, with a range of gravitational masses that yield remnants with mass above and below the supramassive limit. Each NS is endowed with a dipolar magnetic field extending from the interior into the exterior, as in a radio pulsar. We examine cases with different initial binary masses, including a case which produces a HMNS which collapses to a BH, and lower mass binaries that produce SMNS remnants. We find similar jetlike structures for both the SMNS and HMNS remnants that meet our basic critera for an incipient jet. The outflow for the HMNS case is consistent with a Blandford-Znajek (BZ) jet. There is sufficient evidence that such BZ-powered outflows can break out and produce ulrarelativistic jets so that we can describe the HMNS system as a sGRB progenitor. However, the incipient jets from the SMNS remnants have much more baryon pollution and we see indications of inefficient acceleration and mixing with the surrounding debris. Therefore, we cannot conclude that SMNS outflows are the progenitors of sGRBs., Comment: 25 pages, 15 figures

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is a common model architecture used for operator learning. The FNO combines pointwise linear and nonlinear operations in physical space with pointwise linear operations in Fourier space, leading to a parameterized map acting between function spaces. Although FNOs formally involve convolutions of functions on a continuum, in practice the computations are performed on a discretized grid, allowing efficient implementation via the FFT. In this paper, the aliasing error that results from such a discretization is quantified and algebraic rates of convergence in terms of the grid resolution are obtained as a function of the regularity of the input. Numerical experiments that validate the theory and describe model stability are performed.

At Diamond Light Source, the UK's national synchrotron facility, electron beam disturbances are attenuated by the fast orbit feedback (FOFB), which controls a cross-directional (CD) system with hundreds of inputs and outputs. Due to the inability to measure the disturbance spectrum in real-time, the closed-loop sensitivity of the FOFB cannot be evaluated, making it difficult to compare FOFB algorithms and detect faults. Existing methods rely on comparing open-loop with closed-loop measurements, but they are prone to instabilities and actuator saturation because of the system's strong directionality. Here, we introduce a reference signal to estimate the complementary sensitivity in closed loop. By decoupling the system into sets of single-input, single-output (SISO) systems, we design the reference mode-by-mode to accommodate the system's strong directionality. This allows SISO system identification to be used, making our approach suitable for large-scale systems. Additionally, we derive lower bounds on reference amplitudes to achieve a predefined estimation error bound in the presence of disturbances and measurement noise. Our approach not only enables performance estimation of ill-conditioned CD systems in closed-loop but also provides a signal for fault detection. Its potential applications extend to other CD systems, such as papermaking, steel rolling, or battery manufacturing processes.

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree (MCTDH) method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton (RPI) methods, and classical mechanics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunnelling-dominated regime is identified at low friction. At low temperatures, incoherent tunnelling dominates most of Kramer's curve, except at very low friction when coherent tunnelling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviours. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

We demonstrate an atom interferometer measurement protocol compatible with operation on a dynamic platform. Our method employs two open interferometers, derived from the same atomic source, with different interrogation times to eliminate initial velocity dependence while retaining precision, accuracy, and long term stability. We validate the protocol by measuring gravitational tides, achieving a precision of 4.5 {\mu}Gal in 2000 runs, marking the first demonstration of inertial quantity measurement with open atom interferometry that achieves long-term phase stability.