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In addressing the Department of Energy's April, 2022 announcement of a Bold Decadal Vision for delivering a Fusion Pilot Plant by 2035, associated software tools need to be developed for the integration of real world engineering and supply chain data with advanced science models that are accelerated with Machine Learning. An associated research and development effort has been introduced here with promising early progress on the delivery of a realistic Digital Twin Tokamak that has benefited from accelerated advances by the Princeton University AI Deep Learning innovative near-real-time simulators accompanied by technological capabilities from the NVIDIA Omniverse, an open computing platform for building and operating applications that connect with leading scientific computing visualization software. Working with the CAD files for the GA/DIII-D tokamak including equilibrium evolution as an exemplar tokamak application using Omniverse, the Princeton-NVIDIA collaboration has integrated modern AI/HPC-enabled near-real-time kinetic dynamics to connect and accelerate state-of-the-art, synthetic, HPC simulators to model fusion devices and control systems. The overarching goal is to deliver an interactive scientific digital twin of an advanced MFE tokamak that enables near-real-time simulation workflows built with Omniverse to eventually help open doors to new capabilities for generating clean power for a better future.

In this article, we develop nonparametric inference methods for comparing survival data across two samples, which are beneficial for clinical trials of novel cancer therapies where long-term survival is a critical outcome. These therapies, including immunotherapies or other advanced treatments, aim to establish durable effects. They often exhibit distinct survival patterns such as crossing or delayed separation and potentially leveling-off at the tails of survival curves, clearly violating the proportional hazards assumption and rendering the hazard ratio inappropriate for measuring treatment effects. The proposed methodology utilizes the mixture cure framework to separately analyze the cure rates of long-term survivors and the survival functions of susceptible individuals. We evaluate a nonparametric estimator for the susceptible survival function in the one-sample setting. Under sufficient follow-up, it is expressed as a location-scale-shift variant of the Kaplan-Meier (KM) estimator. It retains several desirable features of the KM estimator, including inverse-probability-censoring weighting, product-limit estimation, self-consistency, and nonparametric efficiency. In scenarios of insufficient follow-up, it can easily be adapted by incorporating a suitable cure rate estimator. In the two-sample setting, besides using the difference in cure rates to measure the long-term effect, we propose a graphical estimand to compare the relative treatment effects on susceptible subgroups. This process, inspired by Kendall's tau, compares the order of survival times among susceptible individuals. The proposed methods' large-sample properties are derived for further inference, and the finite-sample properties are examined through extensive simulation studies. The proposed methodology is applied to analyze the digitized data from the CheckMate 067 immunotherapy clinical trial.

Breast cancer is one of the two cancers responsible for the most deaths in women, with about 42,000 deaths each year in the US. That there are over 300,000 breast cancers newly diagnosed each year suggests that only a fraction of the cancers result in mortality. Thus, most of the women undergo seemingly curative treatment for localized cancers, but a significant later succumb to metastatic disease for which current treatments are only temporizing for the vast majority. The current prognostic metrics are of little actionable value for 4 of the 5 women seemingly cured after local treatment, and many women are exposed to morbid and even mortal adjuvant therapies unnecessarily, with these adjuvant therapies reducing metastatic recurrence by only a third. Thus, there is a need for better prognostics to target aggressive treatment at those who are likely to relapse and spare those who were actually cured. While there is a plethora of molecular and tumor-marker assays in use and under-development to detect recurrence early, these are time consuming, expensive and still often un-validated as to actionable prognostic utility. A different approach would use large data techniques to determine clinical and histopathological parameters that would provide accurate prognostics using existing data. Herein, we report on machine learning, together with grid search and Bayesian Networks to develop algorithms that present a AUC of up to 0.9 in ROC analyses, using only extant data. Such algorithms could be rapidly translated to clinical management as they do not require testing beyond routine tumor evaluations.

Artificial Intelligence (AI) has paved the way for revolutionary decision-making processes, which if harnessed appropriately, can contribute to advancements in various sectors, from healthcare to economics. However, its black box nature presents significant ethical challenges related to bias and transparency. AI applications are hugely impacted by biases, presenting inconsistent and unreliable findings, leading to significant costs and consequences, highlighting and perpetuating inequalities and unequal access to resources. Hence, developing safe, reliable, ethical, and Trustworthy AI systems is essential. Our team of researchers working with Trustworthy and Responsible AI, part of the Transdisciplinary Scholarship Initiative within the University of Calgary, conducts research on Trustworthy and Responsible AI, including fairness, bias mitigation, reproducibility, generalization, interpretability, and authenticity. In this paper, we review and discuss the intricacies of AI biases, definitions, methods of detection and mitigation, and metrics for evaluating bias. We also discuss open challenges with regard to the trustworthiness and widespread application of AI across diverse domains of human-centric decision making, as well as guidelines to foster Responsible and Trustworthy AI models., Comment: 44 pages, 2 figures

We use data from the ALMA Evolutionary Study of High Mass Protocluster Formation in the Galaxy (ALMAGAL) survey to study 100 ALMAGAL regions at $\sim$ 1 arsecond resolution located between $\sim$ 2 and 6 kpc distance. Using ALMAGAL $\sim$ 1.3mm line and continuum data we estimate flow rates onto individual cores. We focus specifically on flow rates along filamentary structures associated with these cores. Our primary analysis is centered around position velocity cuts in H$_2$CO (3$_{0,3}$ - 2$_{0,2}$) which allow us to measure the velocity fields, surrounding these cores. Combining this work with column density estimates we derive the flow rates along the extended filamentary structures associated with cores in these regions. We select a sample of 100 ALMAGAL regions covering four evolutionary stages from quiescent to protostellar, Young Stellar Objects (YSOs), and HII regions (25 each). Using dendrogram and line analysis, we identify a final sample of 182 cores in 87 regions. In this paper, we present 728 flow rates for our sample (4 per core), analysed in the context of evolutionary stage, distance from the core, and core mass. On average, for the whole sample, we derive flow rates on the order of $\sim$10$^{-4}$ M$_{sun}$yr$^{-1}$ with estimated uncertainties of $\pm$50%. We see increasing differences in the values among evolutionary stages, most notably between the less evolved (quiescent/protostellar) and more evolved (YSO/HII region) sources. We also see an increasing trend as we move further away from the centre of these cores. We also find a clear relationship between the flow rates and core masses $\sim$M$^{2/3}$ which is in line with the result expected from the tidal-lobe accretion mechanism. Overall, we see increasing trends in the relationships between the flow rate and the three investigated parameters; evolutionary stage, distance from the core, and core mass., Comment: 11 pages, 11 figures, accepted for publication in A&A

A grid search, at the cost of training and testing a large number of models, is an effective way to optimize the prediction performance of deep learning models. A challenging task concerning grid search is the time management. Without a good time management scheme, a grid search can easily be set off as a mission that will not finish in our lifetime. In this study, we introduce a heuristic three-stage mechanism for managing the running time of low-budget grid searches, and the sweet-spot grid search (SSGS) and randomized grid search (RGS) strategies for improving model prediction performance, in predicting the 5-year, 10-year, and 15-year risk of breast cancer metastasis. We develop deep feedforward neural network (DFNN) models and optimize them through grid searches. We conduct eight cycles of grid searches by applying our three-stage mechanism and SSGS and RGS strategies. We conduct various SHAP analyses including unique ones that interpret the importance of the DFNN-model hyperparameters. Our results show that grid search can greatly improve model prediction. The grid searches we conducted improved the risk prediction of 5-year, 10-year, and 15-year breast cancer metastasis by 18.6%, 16.3%, and 17.3% respectively, over the average performance of all corresponding models we trained using the RGS strategy. We not only demonstrate best model performance but also characterize grid searches from various aspects such as their capabilities of discovering decent models and the unit grid search time. The three-stage mechanism worked effectively. It made our low-budget grid searches feasible and manageable, and in the meantime helped improve model prediction performance. Our SHAP analyses identified both clinical risk factors important for the prediction of future risk of breast cancer metastasis, and DFNN-model hyperparameters important to the prediction of performance scores.

Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof systems, and increased accessibility. However, semantic markup is more involved than "regular" typesetting and presents a challenge for authors of mathematical documents. We aim to smooth out the transition from plain LaTeX to semantic markup by developing semi-automatic tools for authors. In this paper we present an approach to semantic markup of formulas by (semi-)automatically generating grammars from existing sTeX macro definitions and parsing mathematical formulas with them. We also present a GUI-based tool for the disambiguation of parse results and showcase its functionality and potential using a grammar for parsing untyped $\lambda$-terms., Comment: Submitted to the CICM 2024 conference, due to be published in Volume 14960 of Springer's Lecture Notes in Computer Science

In this paper, we investigate the facets of the Vietoris--Rips complex $\mathcal{VR}(Q_n; r)$ where $Q_n$ denotes the $n$-dimensional hypercube. We are particularly interested in those facets which are somehow independent of the dimension $n$. Using Hadamard matrices, we prove that the number of different dimensions of such facets is a super-polynomial function of the scale $r$, assuming that $n$ is sufficiently large. We show also that the $(2r-1)$-th dimensional homology of the complex $\mathcal{VR}(Q_n; r)$ is non-trivial when $n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.

Automated soft moderation systems are unable to ascertain if a post supports or refutes a false claim, resulting in a large number of contextual false positives. This limits their effectiveness, for example undermining trust in health experts by adding warnings to their posts or resorting to vague warnings instead of granular fact-checks, which result in desensitizing users. In this paper, we propose to incorporate stance detection into existing automated soft-moderation pipelines, with the goal of ruling out contextual false positives and providing more precise recommendations for social media content that should receive warnings. We develop a textual deviation task called Contrastive Textual Deviation (CTD) and show that it outperforms existing stance detection approaches when applied to soft moderation.We then integrate CTD into the stateof-the-art system for automated soft moderation Lambretta, showing that our approach can reduce contextual false positives from 20% to 2.1%, providing another important building block towards deploying reliable automated soft moderation tools on social media.

Recent observations made using the James Webb Space Telescope have identified a number of high-redshift galaxies that are unexpectedly luminous. In light of this, it is clear that a more detailed understanding of the high redshift, pre-reionization universe is required for us to obtain the complete story of galaxy formation. This study is the first in a series that seeks to tell the story of galaxy formation at $z \gtrsim 10$ using a suite of large-scale adaptive mesh refinement cosmological simulations. Our machine-learning-accelerated surrogate model for Population III star formation and feedback, StarNet, gives us an unprecedented ability to obtain physically accurate, inhomogeneous chemical initial conditions for a statistically significant number of galaxies. We find that of the 12,423 halos in the mass range of $10^6\,\,M_\odot < M_\mathrm{vir} < 10^9\,\, M_\odot$ that form in our fiducial simulation, $16\%$ are chemically enriched by Population III supernovae by $z\sim12$. We then profile and compare various cooling processes at the centers of halos, and find a complete absence of atomic cooling halos. All of our halos with central cooling gas are dominated by H$_2$ cooling, metal cooling, or a mixture of the two, even in the presence of a strong H$_2$-photodissociating Lyman-Werner background. We also find that gas accretion through the virial radius is not driven by cooling. We find that gas virialization in halos with $M_\mathrm{vir}\gtrsim10^7\,\,M_\odot$ is supported by bulk turbulent flows, and that thermal energy accounts for only a small fraction of the total kinetic energy. Because of this, the mean gas temperature is well below the virial temperature for these halos. We then compute the mass of gas that is available for Population II star formation, and infer star formation rates for each potential star-forming halo., Comment: 36 pages, 27 figures

We argue that a measurement of the Higgs boson self-coupling becomes particularly meaningful when its sensitivity is within 40\% of its Standard Model value. This constitutes a target for a future impactful experimental achievement. It is derived from recently obtained results of how extreme the differences can be between effective field theory operator coefficients when their origins are from reasonable theories beyond the Standard Model., Comment: 10 pages, 2 figures

Electron backscatter diffraction (EBSD) has developed over the last few decades into a valuable crystallographic characterisation method for a wide range of sample types. Despite these advances, issues such as the complexity of sample preparation, relatively slow acquisition, and damage in beam-sensitive samples, still limit the quantity and quality of interpretable data that can be obtained. To mitigate these issues, here we propose a method based on the subsampling of probe positions and subsequent reconstruction of an incomplete dataset. The missing probe locations (or pixels in the image) are recovered via an inpainting process using a dictionary-learning based method called beta-process factor analysis (BPFA). To investigate the robustness of both our inpainting method and Hough-based indexing, we simulate subsampled and noisy EBSD datasets from a real fully sampled Ni-superalloy dataset for different subsampling ratios of probe positions using both Gaussian and Poisson noise models. We find that zero solution pixel detection (inpainting un-indexed pixels) enables higher quality reconstructions to be obtained. Numerical tests confirm high quality reconstruction of band contrast and inverse pole figure maps from only 10% of the probe positions, with the potential to reduce this to 5% if only inverse pole figure maps are needed. These results show the potential application of this method in EBSD, allowing for faster analysis and extending the use of this technique to beam sensitive materials.

We present a comprehensive evaluation of proprietary and open-weights large language models using the first astronomy-specific benchmarking dataset. This dataset comprises 4,425 multiple-choice questions curated from the Annual Review of Astronomy and Astrophysics, covering a broad range of astrophysical topics. Our analysis examines model performance across various astronomical subfields and assesses response calibration, crucial for potential deployment in research environments. Claude-3.5-Sonnet outperforms competitors by up to 4.6 percentage points, achieving 85.0% accuracy. For proprietary models, we observed a universal reduction in cost every 3-to-12 months to achieve similar score in this particular astronomy benchmark. Open-source models have rapidly improved, with LLaMA-3-70b (80.6%) and Qwen-2-72b (77.7%) now competing with some of the best proprietary models. We identify performance variations across topics, with non-English-focused models generally struggling more in exoplanet-related fields, stellar astrophysics, and instrumentation related questions. These challenges likely stem from less abundant training data, limited historical context, and rapid recent developments in these areas. This pattern is observed across both open-weights and proprietary models, with regional dependencies evident, highlighting the impact of training data diversity on model performance in specialized scientific domains. Top-performing models demonstrate well-calibrated confidence, with correlations above 0.9 between confidence and correctness, though they tend to be slightly underconfident. The development for fast, low-cost inference of open-weights models presents new opportunities for affordable deployment in astronomy. The rapid progress observed suggests that LLM-driven research in astronomy may become feasible in the near future., Comment: 45 pages, 12 figures, 7 tables. Submitted to ApJ. Comments welcome. AstroMLab homepage: https://astromlab.org/

With the development of Human-AI Collaboration in Classification (HAI-CC), integrating users and AI predictions becomes challenging due to the complex decision-making process. This process has three options: 1) AI autonomously classifies, 2) learning to complement, where AI collaborates with users, and 3) learning to defer, where AI defers to users. Despite their interconnected nature, these options have been studied in isolation rather than as components of a unified system. In this paper, we address this weakness with the novel HAI-CC methodology, called Learning to Complement and to Defer to Multiple Users (LECODU). LECODU not only combines learning to complement and learning to defer strategies, but it also incorporates an estimation of the optimal number of users to engage in the decision process. The training of LECODU maximises classification accuracy and minimises collaboration costs associated with user involvement. Comprehensive evaluations across real-world and synthesized datasets demonstrate LECODU's superior performance compared to state-of-the-art HAI-CC methods. Remarkably, even when relying on unreliable users with high rates of label noise, LECODU exhibits significant improvement over both human decision-makers alone and AI alone., Comment: ECCV 2024

Mediation analyses allow researchers to quantify the effect of an exposure variable on an outcome variable through a mediator variable. If a binary mediator variable is misclassified, the resulting analysis can be severely biased. Misclassification is especially difficult to deal with when it is differential and when there are no gold standard labels available. Previous work has addressed this problem using a sensitivity analysis framework or by assuming that misclassification rates are known. We leverage a variable related to the misclassification mechanism to recover unbiased parameter estimates without using gold standard labels. The proposed methods require the reasonable assumption that the sum of the sensitivity and specificity is greater than 1. Three correction methods are presented: (1) an ordinary least squares correction for Normal outcome models, (2) a multi-step predictive value weighting method, and (3) a seamless expectation-maximization algorithm. We apply our misclassification correction strategies to investigate the mediating role of gestational hypertension on the association between maternal age and pre-term birth., Comment: 44 pages, 5 figures, 6 tables

This paper presents verification-guided development (VGD), a software engineering process we used to build Cedar, a new policy language for expressive, fast, safe, and analyzable authorization. Developing a system with VGD involves writing an executable model of the system and mechanically proving properties about the model; writing production code for the system and using differential random testing (DRT) to check that the production code matches the model; and using property-based testing (PBT) to check properties of unmodeled parts of the production code. Using VGD for Cedar, we can build fast, idiomatic production code, prove our model correct, and find and fix subtle implementation bugs that evade code reviews and unit testing. While carrying out proofs, we found and fixed 4 bugs in Cedar's policy validator, and DRT and PBT helped us find and fix 21 additional bugs in various parts of Cedar.

The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations., Comment: 8 pages, 3 figures

Self-supervised learning (SSL) representations from massively multilingual models offer a promising solution for low-resource language speech tasks. Despite advancements, language adaptation in TTS systems remains an open problem. This paper explores the language adaptation capability of ZMM-TTS, a recent SSL-based multilingual TTS system proposed in our previous work. We conducted experiments on 12 languages using limited data with various fine-tuning configurations. We demonstrate that the similarity in phonetics between the pre-training and target languages, as well as the language category, affects the target language's adaptation performance. Additionally, we find that the fine-tuning dataset size and number of speakers influence adaptability. Surprisingly, we also observed that using paired data for fine-tuning is not always optimal compared to audio-only data. Beyond speech intelligibility, our analysis covers speaker similarity, language identification, and predicted MOS., Comment: Accepted to Interspeech 2024

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant ($H_{0}$). The TDCOSMO collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038-4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtain $D_{\Delta t} = 1.68^{+0.40}_{-0.38}$ Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat $\Lambda$CDM cosmology, we constrain the Hubble constant to be $H_{0} = 65^{+23}_{-14}\, \rm km\ s^{-1}\,Mpc^{-1}$. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of the Vera C. Rubin Observatory's Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future., Comment: 8 pages, 5 figures, 3 tables; accepted for publication in Astronomy & Astrophysics

CHEOPS is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission and remains in excellent operational conditions. The mission has been extended until the end of 2026. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission's performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation programme. It consists of dedicated observations that allow us to characterise the instrument's response. In addition to the standard collection of nominal science and housekeeping data, these observations provide input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument's actual performance with expectations. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission's performance., Comment: Accepted for publication in Astronomy and Astrophysics

The existence of high-$z$ over-massive supermassive black holes represents a major conundrum in our understanding of black hole evolution. In this paper, we probe from the observational point of view how early Universe environmental conditions could have acted as an evolutionary mechanism for the accelerated growth of the first black holes. Under the assumption that the early Universe is dominated by dwarf galaxies, we investigate the hypothesis that dwarf-dwarf galaxy interactions trigger black hole accretion. We present the discovery of 82 dwarf-dwarf galaxy pairs and 11 dwarf galaxy groups using the Hubble Space Telescope, doubling existing samples. The dwarf systems span a redshift range of 0.13$<$z$<$1.5, and a stellar mass range of 7.24$<$log(M$_*$/\(M_\odot\))$<$9.73. We performed an X-ray study of a subset of these dwarf systems with Chandra and detected six new AGN, increasing the number of known dwarf-dwarf-merger-related AGN from one to seven. We then compared the frequency of these AGN in grouped/paired dwarfs to that of isolated dwarfs and found a statistically significant enhancement (4$\sigma$-6$\sigma$) in the interacting sample. This study, the first of its kind at the lowest mass scales, implies that the presence of a nearby dwarf neighbor is efficient in triggering black hole accretion. These results open new avenues for indirect studies of the emergence of the first supermassive black holes., Comment: 19 pages, 5 figures, 4 tables. Accepted for publication in the Astrophysical Journal Letters

Intraoperative ultrasound (iUS) imaging has the potential to improve surgical outcomes in brain surgery. However, its interpretation is challenging, even for expert neurosurgeons. In this work, we designed the first patient-specific framework that performs brain tumor segmentation in trackerless iUS. To disambiguate ultrasound imaging and adapt to the neurosurgeon's surgical objective, a patient-specific real-time network is trained using synthetic ultrasound data generated by simulating virtual iUS sweep acquisitions in pre-operative MR data. Extensive experiments performed in real ultrasound data demonstrate the effectiveness of the proposed approach, allowing for adapting to the surgeon's definition of surgical targets and outperforming non-patient-specific models, neurosurgeon experts, and high-end tracking systems. Our code is available at: \url{https://github.com/ReubenDo/MHVAE-Seg}., Comment: Early accept at MICCAI 2024 - code available at: https://github.com/ReubenDo/MHVAE-Seg

Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have random runtime, limiting their applicability when a consistent encoding time is desirable. Thus, this paper considers approximate schemes with a fixed runtime instead. First, we strengthen a result of Agustsson and Theis and show that there is a class of pairs of target distribution $Q$ and coding distribution $P$, for which the runtime of any approximate scheme scales at least super-polynomially in $D_\infty[Q \Vert P]$. We then show, by contrast, that if we have access to an unnormalised Radon-Nikodym derivative $r \propto dQ/dP$ and knowledge of $D_{KL}[Q \Vert P]$, we can exploit global-bound, depth-limited A* coding to ensure $\mathrm{TV}[Q \Vert P] \leq \epsilon$ and maintain optimal coding performance with a sample complexity of only $\exp_2\big((D_{KL}[Q \Vert P] + o(1)) \big/ \epsilon\big)$., Comment: Accepted as a spotlight paper at the first 'Learn to Compress' Workshop@ ISIT 2024. V2: corrected some typos and simplified Appendix C

The lambda-cube is a famous pure type system (PTS) cube of eight powerful explicit type systems that include the simple, polymorphic and dependent type theories. The lambda-cube only types Strongly Normalising (SN) terms but not all of them. It is well known that even the most powerful system of the lambda-cube can only type the same pure untyped lambda-terms that are typable by the higher-order polymorphic implicitly typed lambda-calculus Fomega, and that there is an untyped {\lambda}-term U' that is SN but is not typable in Fomega or the lambda-cube. Hence, neither system can type all the SN terms it expresses. In this paper, we present the f-cube, an extension of the lambda-cube with finite-set declarations (FSDs) like y\in{C1,...,Cn} : B which means that y is of type B and can only be one of C1,..., Cn. The novelty of our FSDs is that they allow to represent intersection types as Pi-types. We show how to translate and type the term U' in the f-cube using an encoding of intersection types based on FSDs. Notably, our translation works without needing anything like the usual troublesome intersection-introduction rule that proves a pure untyped lambda-term M has an intersection of k types using k independent sub-derivations. As such, our approach is useful for language implementers who want the power of intersection types without the pain of the intersection-introduction rule., Comment: To appear in Wollic 2024

A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved edged polygonal meshes. The proposed method is validated with numerical experiments in which optimal $H^1$ and $L^2$ convergence are observed. This method is then successfully applied to an existing moving mesh algorithm for implicit moving boundary problems in which higher-order convergence is achieved.

We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem transformed onto a computational reference domain. The second method computes a virtual domain and uses bespoke polynomial approximation operators to construct a computable method. Both methods are shown to converge optimally, a behaviour confirmed in practice for the solution of problems posed on curved domains.

The binary star NY Hya is a bright, detached, double-lined eclipsing system with an orbital period of just under five days with two components each nearly identical to the Sun and located in the solar neighbourhood. The objective of this study is to test and confront various stellar evolution models for solar-type stars based on accurate measurements of stellar mass and radius. We present new ground-based spectroscopic and photometric as well as high-precision space-based photometric and astrometric data from which we derive orbital as well as physical properties of the components via the method of least-squares minimisation based on a standard binary model valid for two detached components. Classic statistical techniques were invoked to test the significance of model parameters. Additional empirical evidence was compiled from the public domain; the derived system properties were compared with archival broad-band photometry data enabling a measurement of the system's spectral energy distribution that allowed an independent estimate of stellar properties. We also utilised semi-empirical calibration methods to derive atmospheric properties from Str\"{o}mgren photometry and related colour indices. Data was used to confront the observed physical properties with classic and magnetic stellar evolution models., Comment: 34 pages, 19 figures, 13 tables, (accepted for publication in A&A)

Write $W^{(n)}$ to mean the $n$-letter word obtained by repeating a fixed word $W$ and let $R_n$ denote a uniformly random $n$-letter word sampled from the same alphabet as $W$. We are interested in the average length of the longest common subsequence between $W^{(n)}$ and $R_n$, which is known to be $\gamma(W)\cdot n+o(n)$ for some constant $\gamma(W)$. Bukh and Cox recently developed an interacting particle system, dubbed the frog dynamics, which can be used to compute the constant $\gamma(W)$ for any fixed word $W$. They successfully analyzed the simplest case of the frog dynamics to find an explicit formula for the constants $\gamma(12\cdots k)$. We continue this study by using the frog dynamics to find an explicit formula for the constants $\gamma(12\cdots kk\cdots 21)$. The frog dynamics in this case is a variation of the PushTASEP on the ring where some clocks are identical. Interestingly, exclusion processes with correlated clocks of this type appear to have not been analyzed before. Our analysis leads to a seemingly new combinatorial object which could be of independent interest: frogs with hats!, Comment: 29 pages, 7 figures

Neutral atom arrays have emerged as a versatile platform towards scalable quantum computation and optimization. In this paper we present first demonstrations of weighted graph optimization on a Rydberg atom array using annealing with local light-shifts. We verify the ability to prepare weighted graphs in 1D and 2D arrays, including embedding a five vertex non-unit disk graph using nine physical qubits and demonstration of a simple crossing gadget. We find common annealing ramps leading to preparation of the target ground state robustly over a substantial range of different graph weightings. This work provides a route to exploring large-scale optimization of non-planar weighted graphs relevant for solving relevant real-world problems., Comment: 7 pages, 5 figures. Methods: 3 pages, 2 figures