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White dwarfs are often found in close binaries with stellar or even substellar companions. It is generally thought that these compact binaries form via common envelope evolution, triggered by the progenitor of the white dwarf expanding after it evolved off the main-sequence and engulfing its companion. To date, a handful of white dwarfs in compact binaries with substellar companions have been found, typically with masses greater than around 50 M$_\mathrm{Jup}$. Here we report the discovery of two eclipsing white dwarf plus brown dwarf binaries containing very low mass brown dwarfs. ZTF J1828+2308 consists of a hot ($15900\pm75$ K) $0.610\pm0.004$ M$_{\odot}$ white dwarf in a 2.7 hour binary with a $0.0186\pm0.0008$ M$_{\odot}$ ($19.5\pm0.8$ M$_\mathrm{Jup}$) brown dwarf. ZTF J1230$-$2655 contains a cool ($10000\pm110$ K) $0.65\pm0.02$ M$_{\odot}$ white dwarf in a 5.7 hour binary with a companion that has a mass of less than 0.0211 M$_{\odot}$ (22.1 M$_\mathrm{Jup}$). While the brown dwarf in ZTF J1828+2308 has a radius consistent with its mass and age, ZTF J1230$-$2655 contains a roughly 20 per cent overinflated brown dwarf for its age. We are only able to reconstruct the common envelope phase for either system if it occurred after the first thermal pulse, when the white dwarf progenitor had already lost a significant fraction of its original mass. This is true even for very high common envelope ejection efficiencies ($\alpha_\mathrm{CE}\sim 1$), unless both systems have extremely low metallicities. It may be that the lowest mass companions can only survive a common envelope phase if it occurs at this very late stage., Comment: 15 pages, 13 figures. Accepted for publication in MNRAS

We prove a monoidal equivalence between spectral and automorphic realizations of the universal affine Hecke category, thereby proving the tamely ramified local Betti geometric Langlands correspondence, as conjectured by Ben-Zvi--Nadler [BZN07, BZN18]. Specializing to the case of unipotent monodromy, this provides another argument for a fundamental theorem of Bezrukavnikov [B16].

We identify equivariant quasicoherent sheaves on the Grothendieck alteration of a reductive group $\mathsf{G}$ with universal monodromic Iwahori--Whittaker sheaves on the enhanced affine flag variety of the Langlands dual group $G$. This extends a similar result for equivariant quasicoherent sheaves on the Springer resolution due to Arkhipov--Bezrukavnikov. We further give a monoidal identification between adjoint equivariant coherent sheaves on the group $\mathsf{G}$ itself and bi-Iwahori--Whittaker sheaves on the loop group of $G$. These results are used in the sequel to this paper to prove the tame local Betti geometric Langlands conjecture of Ben-Zvi--Nadler. Our proof of fully faithfulness provides an alternative to the argument of Arkhipov--Bezrukavnikov. Namely, while they localize in unipotent directions, we localize in semi-simple directions, thereby reducing fully faithfulness to an order of vanishing calculation in semi-simple rank one.

In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At each time point, the time changing component is the composition of two uniformly distributed independent random variables with support over all the past steps. Several conditional distributional properties including the conditional mean increments and conditional displacement of ERW with random memory are obtained. Using these conditional results, we derive the recursive and explicit expressions for the mean increments and mean displacement of the walk.

Dwarf novae are a crucial astrophysical laboratory for probing the nature of accretion, binary mass transfer, and binary evolution -- yet their diverse observational characteristics continue to challenge our theoretical understanding. We here present the discovery of, and subsequent observing campaign on GOTO065054+593624 (hereafter GOTO0650), a dwarf nova of the WZ Sge type, discovered in real-time by citizen scientists via the Kilonova Seekers citizen science project. An extensive dataset charts the photometric and spectroscopic evolution of this object, covering the first two months of its 2024 superoutburst. GOTO0650 shows a complete absence of visible emission lines during the high state, strong H and barely-detected He~II emission, and high-amplitude echo outbursts with a rapidly decreasing timescale that together do not neatly fit in with our current view of cataclysmic variables. The comprehensive dataset presented here not only underscores the uniqueness of this dwarf nova and marks it as a candidate period bouncer, but also highlights the important contribution that citizen scientists can make to the study of Galactic transients., Comment: 14 pages, 14 figures. Submitted to A&A

Van der Waals heterostructures have promised the realisation of artificial materials with multiple physical phenomena such as giant optical nonlinearities, spin-to-charge interconversion in spintronics and topological carrier protection, in a single layered device through an infinitely diverse set of quantum materials. However, most efforts have only focused on exfoliated material that inherently limits both the dimensions of the materials and the scalability for applications. Here, we show the epitaxial growth of large area heterostructures of topological insulators (Bi2Se3), transition metal dichalcogenides (TMDs, WSe2) and ferromagnets (Co), resulting in the combination of functionalities including tuneable optical nonlinearities, spin-to-charge conversion and magnetic proximity effects. This is demonstrated through coherent phase resolved terahertz currents, bringing novel functionalities beyond those achievable in simple homostructures. In particular, we show the role of different TMD polymorphs, with the simple change of one atomic monolayer of the artificial material stack entirely changing its optical, electrical and magnetic properties. This epitaxial integration of diverse two-dimensional materials offers foundational steps towards diverse perspectives in quantum material engineering, where the material polymorph can be controlled at technological relevant scales for coupling applications in, for example, van der Waals nonlinear optics, optoelectronics, spintronics, multiferroics and coherent current control.

It is generally thought that AGN optical variability is produced, at least in part, by reprocessing of central X-rays by a surrounding accretion disc, resulting in wavelength-dependent lags between bands. Any good model of AGN optical variability should explain not only these lags, but also the overall pattern of variability as quantified by the power spectral density (PSD). Here we present $\sim$daily g'-band monitoring of the low-mass AGN NGC\,4395 over 3 years. Together with previous TESS and GTC/HiPERCAM observations we produce an optical PSD covering an unprecedented frequency range of $\sim7$ decades allowing excellent determination of PSD parameters. The PSD is well fitted by a bending power law with low-frequency slope $\alpha_{L} = 1.0 \pm 0.2$, high-frequency slope $2.1^{+0.2}_{-0.4}$ and bend timescale $3.0^{+6.6}_{-1.7}\,$\,d. This timescale is close to that derived previously from a damped random walk (DRW) model fitted to just the TESS observations, although $\alpha_{L}$ is too steep to be consistent with a DRW. We compare the observed PSD with one made from light curves synthesized assuming reprocessing of X-rays, as observed by \xmm and Swift, in a disc defined by the observed lags. The simulated PSD is also well described by a bending power law but with a bend two decades higher in frequency. We conclude that the large-amplitude optical variations seen on long-timescales are not due to disc reprocessing but require a second source of variability whose origin is unknown but could be propagating disc accretion rate variations.

The diversity of 2D materials and their van der Waals (vdW) stacking presents a fertile ground for engineering novel multifunctional materials and quantum states of matter. This permits unique opportunities to tailor the electronic properties of vdW heterostructures by the insertion of only a single 2D material layer. However, such vdW materials engineering at the atomic scale has yet to be investigated for spin-charge interconversion phenomena. Here, we report on the control of these effects at the monolayer level, where drastic increase in intensity and change in sign of THz spintronic emission are demonstrated by inserting a single layer of MoSe$_2$ between PtSe$_2$ and graphene in a fully epitaxial, large area stacked structure. By using a combination of spin and angle resolved photoemission and density functional theory to reveal the electronic and spin structures, we illustrate two different mechanisms relying on charge transfer and electronic hybridization for the formation of Rashba states, which are responsible for spin-charge conversion and hence the THz spintronic emission. These findings open new pathways to design, at the atomic scale, efficient THz spintronic emitters made of 2D materials and other spintronic devices based on spin-charge interconversion phenomena., Comment: 16 pages, 4 figures

Spintronic Terahertz emitters, based on optically triggered spin-to-charge interconversion processes, have recently emerged as novel route towards compact and efficient THz sources. Yet, the next challenge for further technologically-relevant devices remains to modulate the emission, with low-energy consumption operation. To this aim, ferroelectric materials coupled to active spin-orbit layers such as two-dimensional transition metal dichalcogenides are suitable candidates. In this work, we present the realization of a large area heterostructure of CoFeB/PtSe2/MoSe2 on a bi-domain LiNbO3 substrate. Using THz time-domain spectroscopy, we show that the ferroelectric polarization direction induces a sizeable modulation of the THz emission. We rationalise these experimental results by using band structure and spin accumulation calculations that are consistent with an interfacial spin-to-charge conversion mediated by inverse Rashba-Edelstein effect at the MoSe2/PtSe2 interface and being tuned by ferroelectricity in the adjacent LiNbO3 surface. This work points out the relevance of field effect spin-orbit architectures for novel THz technologies., Comment: 13 pages, 4 figures, 35 references

Traditional recommender systems based on utility maximization and revealed preferences often fail to capture users' dual-self nature, where consumption choices are driven by both long-term benefits (enrichment) and desire for instant gratification (temptation). Consequently, these systems may generate recommendations that fail to provide long-lasting satisfaction to users. To address this issue, we propose a novel user model that accounts for this dual-self behavior and develop an optimal recommendation strategy to maximize enrichment from consumption. We highlight the limitations of historical consumption data in implementing this strategy and present an estimation framework that makes minimal assumptions and leverages explicit user feedback and implicit choice data to overcome these constraints. We evaluate our approach through both synthetic simulations and simulations based on real-world data from the MovieLens dataset. Results demonstrate that our proposed recommender can deliver superior enrichment compared to several competitive baseline algorithms that assume a single utility type and rely solely on revealed preferences. Our work emphasizes the critical importance of optimizing for enrichment in recommender systems, particularly in temptation-laden consumption contexts. Our findings have significant implications for content platforms, user experience design, and the development of responsible AI systems, paving the way for more nuanced and user-centric recommendation approaches.

Let $X$ be a smooth geometrically connected projective curve of genus at least 2 over a field of characteristic zero. We compute the essential dimension of the moduli stack of symplectic bundles over $X$. Unlike the case of vector bundles, we are able to precisely compute the essential dimension as the generic gerbe of the moduli stack has period 2 over it's moduli space.

Type Ia supernovae, critical for studying cosmic expansion, arise from thermonuclear explosions of white dwarfs, but their precise progenitor pathways remain unclear. Growing evidence supports the ``double-degenerate'' scenario, where two white dwarfs interact. The absence of other companion types capable of explaining the observed Ia rate, along with observations of hyper-velocity white dwarfs interpreted as surviving companions of such systems provide compelling evidence in favor of this scenario. Upcoming millihertz gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) are expected to detect thousands of double-degenerate systems, though the most compact known candidate Ia progenitors produce only marginally detectable gravitational wave signals. Here, we report observations of ATLAS J1138-5139, a binary white dwarf system with an orbital period of 28 minutes. Our analysis reveals a 1 solar mass carbon-oxygen white dwarf accreting from a helium-core white dwarf. Given its mass, the accreting carbon-oxygen white dwarf is poised to trigger a typical-luminosity Type Ia supernova within a few million years, or to evolve into a stably mass-transferring AM CVn system. ATLAS J1138-5139 provides a rare opportunity to calibrate binary evolution models by directly comparing observed orbital parameters and mass transfer rates closer to merger than any previously identified candidate Type Ia progenitor. Its compact orbit ensures detectability by LISA, demonstrating the potential of millihertz gravitational wave observatories to reveal a population of Type Ia progenitors on a Galactic scale, paving the way for multi-messenger studies offering insights into the origins of these cosmologically significant explosions., Comment: 40 pages, 7 figures, 2 tables

The origin(s) of Fast Radio Bursts (FRBs), mysterious radio bursts coming from extragalactic distances, remains unknown. Multi-wavelength observations are arguably the only way to answer this question unambiguously. We attempt to detect hard X-ray/soft gamma-ray counterparts to one of the most active FRB sources, FRB20121102, as well as improve understanding of burst properties in radio through a long-term monitoring campaign using the Nan\c{c}ay Radio Telescope (NRT). Multi-wavelength campaigns involving the International Gamma-ray Astrophysics Laboratory (INTEGRAL) satellite, the Nan\c{c}ay Radio Observatory, the optical telescopes at the Observatoire de Haute Provence as well as Arecibo were conducted between 2017 and 2019. In 2017, the telescopes were scheduled to observe simultaneously between Sept 24-29. We specifically used the Fast Response Enhanced CCDs for the optical observations to ensure a high time resolution. In 2019, we changed the strategy to instead conduct ToO observations on INTEGRAL and other available facilities upon positive detection triggers from the NRT. In the 2017 campaign, FRB20121102 was not in its burst activity window. We obtain a 5-sigma optical flux limit of 12 mJy ms using the GASP and a 3-sigma limit from OHP T120cm R-band image of R=22.2 mag of any potential persistent emission not associated to radio bursts. In the 2019 campaign, we have simultaneous INTEGRAL data with 11 radio bursts from the NRT and Arecibo. We obtain a 5-sigma upper limit of 2.7e-7 erg/cm2 in the 25-400 keV energy range for contemporary radio and high energy bursts, and a 5-sigma upper limit of 3.8e-11 erg/cm2 for permanent emission in the 25-100 keV energy range. In addition, we report on the regular observations from NRT between 2016-2020, which accounts for 119 additional radio bursts from FRB20121102. We present an updated fit of the periodic active window of 154+/-2 days., Comment: Submitted to A&A

We report the discovery of three ultracompact binary white dwarf systems hosting accretion disks, with orbital periods of 7.95, 8.68, and 13.15 minutes. This significantly augments the population of mass-transferring binaries at the shortest periods, and provides the first evidence that accretors in ultracompacts can be dense enough to host accretion disks even below 10 minutes (where previously only direct-impact accretors were known). In the two shortest-period systems, we measured changes in the orbital periods driven by the combined effect of gravitational wave emission and mass transfer; we find $\dot{P}$ is negative in one case, and positive in the other. This is only the second system measured with a positive $\dot{P}$, and it the most compact binary known that has survived a period minimum. Using these systems as examples, we show how the measurement of $\dot{P}$ is a powerful tool in constraining the physical properties of binaries, e.g. the mass and mass-radius relation of the donor stars. We find that the chirp masses of ultracompact binaries at these periods seem to cluster around $\mathcal{M}_c \sim 0.3 M_\odot$, perhaps suggesting a common origin for these systems or a selection bias in electromagnetic discoveries. Our new systems are among the highest-amplitude known gravitational wave sources in the millihertz regime, providing exquisite opportunity for multi-messenger study with future space-based observatories such as \textit{LISA} and TianQin; we discuss how such systems provide fascinating laboratories to study the unique regime where the accretion process is mediated by gravitational waves., Comment: Accepted for publication in ApJ

In this paper, we study the composition of two independent GCPs which we call the iterated generalized counting process (IGCP). Its distributional properties such as the transition probabilities, probability generating function, state probabilities and its corresponding L\'evy measure are obtained. We study some integrals of the IGCP. Also, we study some of its extensions, for example, the compound IGCP, the multivariate IGCP and the $q$-iterated GCP. It is shown that the IGCP and the compound IGCP are identically distributed to a compound GCP which leads to their martingale characterizations. Later, a time-changed version of the IGCP is considered where the time is changed by an inverse stable subordinator. Using its covariance structure, we establish that the time-changed IGCP exhibits long-range dependence property. Moreover, we show that its increment process exhibits short-range dependence property. Also, it is shown that its one-dimensional distributions are not infinitely divisible. Initially, some of its potential real life applications are discussed.

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's performance. We analyze the gradients backpropagated through the softmax operation in the attention mechanism and observe that these gradients can often be small. This poor gradient signal backpropagation can lead to inefficient learning of parameters preceeding the attention operations. To this end, we introduce a new attention mechanism called LASER, which we analytically show to admit a larger gradient signal. We show that LASER Attention can be implemented by making small modifications to existing attention implementations. We conduct experiments on autoregressive large language models (LLMs) with upto 2.2 billion parameters where we show upto 3.38% and an average of ~1% improvement over standard attention on downstream evaluations. Using LASER gives the following relative improvements in generalization performance across a variety of tasks (vision, text and speech): 4.67% accuracy in Vision Transformer (ViT) on Imagenet, 2.25% error rate in Conformer on the Librispeech speech-to-text and 0.93% fraction of incorrect predictions in BERT with 2.2 billion parameters., Comment: 15 pages, under review in ICLR 2025

Large language models (LLMs) have shown remarkable progress in encoding clinical knowledge and responding to complex medical queries with appropriate clinical reasoning. However, their applicability in subspecialist or complex medical settings remains underexplored. In this work, we probe the performance of AMIE, a research conversational diagnostic AI system, in the subspecialist domain of breast oncology care without specific fine-tuning to this challenging domain. To perform this evaluation, we curated a set of 50 synthetic breast cancer vignettes representing a range of treatment-naive and treatment-refractory cases and mirroring the key information available to a multidisciplinary tumor board for decision-making (openly released with this work). We developed a detailed clinical rubric for evaluating management plans, including axes such as the quality of case summarization, safety of the proposed care plan, and recommendations for chemotherapy, radiotherapy, surgery and hormonal therapy. To improve performance, we enhanced AMIE with the inference-time ability to perform web search retrieval to gather relevant and up-to-date clinical knowledge and refine its responses with a multi-stage self-critique pipeline. We compare response quality of AMIE with internal medicine trainees, oncology fellows, and general oncology attendings under both automated and specialist clinician evaluations. In our evaluations, AMIE outperformed trainees and fellows demonstrating the potential of the system in this challenging and important domain. We further demonstrate through qualitative examples, how systems such as AMIE might facilitate conversational interactions to assist clinicians in their decision making. However, AMIE's performance was overall inferior to attending oncologists suggesting that further research is needed prior to consideration of prospective uses.

We present the analysis of optical data of a bright and extremely-rapidly evolving transient, AT2024wpp, whose properties are similar to the enigmatic AT2018cow (aka the Cow). AT2024wpp rose to a peak brightness of c=-21.9mag in 4.3d and remained above the half-maximum brightness for only 6.7d. The blackbody fits to the multi-band photometry show that the event remained persistently hot (T>20000K) with a rapidly receding photosphere (v~11500km/s) until the end of the photometric dataset at +16.1d post-discovery. This behaviour mimics that of AT2018cow, albeit with a several times larger photosphere. The spectra are consistent with blackbody emission throughout our spectral sequence ending at +21.9d, showing a tentative, very broad emission feature at 5500{\AA} -- implying that the optical photosphere is likely within a near-relativistic outflow. Furthermore, reports of strong X-ray and radio emission cement the nature of AT2024wpp as a likely Cow-like transient. AT2024wpp is only the second event of the class with optical polarimetry. Our BVRI observations obtained from +6.1 to +14.4d show a low polarisation of P<0.5% across all bands, similar to AT2018cow that was consistent with P~0% during the same outflow-driven phase. In the absence of evidence for a preferential viewing angle, it is unlikely that both events would have shown low polarisation in the case that their photospheres were aspherical. As such, we conclude that the near-relativistic outflows launched in these events are likely highly spherical, but polarimetric observations of further events are crucial to constrain their ejecta geometry and stratification in detail., Comment: 10 pages, 6 figures. Submitted to MNRAS

JWST, despite not being designed to observe astrophysical phenomena that vary on rapid time scales, can be an unparalleled tool for such studies. If timing systematics can be controlled, JWST will be able to open up the sub-second infrared timescale regime. Rapid time-domain studies, such as lag measurements in accreting compact objects and Solar System stellar occultations, require both precise inter-frame timing and knowing when a time series begins to an absolute accuracy significantly below 1s. In this work we present two long-duration observations of the deeply eclipsing double white dwarf system ZTF J153932.16+502738.8, which we use as a natural timing calibrator to measure the absolute timing accuracy of JWST's clock. From our two epochs, we measure an average clock accuracy of $0.12\pm0.06$s, implying that JWST can be used for sub-second time-resolution studies down to the $\sim100$ms level, a factor $\sim5$ improvement upon the pre-launch clock accuracy requirement. We also find an asymmetric eclipse profile in the F322W2 band, which we suggest has a physical origin., Comment: 16 pages, 13 figures, accepted for publication in AJ

Inverse rendering pipelines are gaining prominence in realizing photo-realistic reconstruction of real-world objects for emulating them in virtual reality scenes. Apart from material reflectances, spectral rendering and in-scene illuminants' spectral power distributions (SPDs) play important roles in producing photo-realistic images. We present a simple, low-cost technique to capture and reconstruct the SPD of uniform illuminants. Instead of requiring a costly spectrometer for such measurements, our method uses a diffractive compact disk (CD-ROM) and a machine learning approach for accurate estimation. We show our method to work well with spotlights under simulations and few real-world examples. Presented results clearly demonstrate the reliability of our approach through quantitative and qualitative evaluations, especially in spectral rendering of iridescent materials., Comment: 3 pages, 3 Figures, Submitted as a Tiny Paper at ICVGIP'24, Bangalore, India

Supervised fine-tuning (SFT) and alignment of large language models (LLMs) are key steps in providing a good user experience. However, the concept of an appropriate alignment is inherently application-dependent, and current methods often rely on heuristic choices to drive the optimization. In this work, we formulate SFT and alignment as a constrained optimization problem, where the LLM is trained on a task while being required to meet application-specific requirements, without resorting to heuristics. To solve this, we propose Lagrange Large Language Models (L3Ms), which employ logarithmic barriers to enforce the constraints. This approach allows for the customization of L3Ms across diverse applications while avoiding heuristic-driven processes. We demonstrate experimentally the versatility and efficacy of L3Ms in achieving tailored alignments for various applications.

Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the actual updates to the weights depends on how the two LoRA factors are scaled or rotated. This deficiency leads to inefficient learning and sub-optimal solutions in practice. This paper introduces LoRA-RITE, a novel adaptive matrix preconditioning method for LoRA optimization, which can achieve transformation invariance and remain computationally efficient. We provide theoretical analysis to demonstrate the benefit of our method and conduct experiments on various LLM tasks with different models including Gemma 2B, 7B, and mT5-XXL. The results demonstrate consistent improvements against existing optimizers. For example, replacing Adam with LoRA-RITE during LoRA fine-tuning of Gemma-2B yielded 4.6\% accuracy gain on Super-Natural Instructions and 3.5\% accuracy gain across other four LLM benchmarks (HellaSwag, ArcChallenge, GSM8K, OpenBookQA).

For a reductive group $G$, we introduce a notion of singular support for cocomplete dualizable DG-categories equipped with a strong $G$-action. This is done by considering the singular support of the sheaves of matrix coefficients arising from the action. We focus particularly on dualizable $G$-categories whose singular support lies in the nilpotent cone of $\mathfrak{g}^*$ and refer to these as nilpotent $G$-categories. For such categories, we give a characterization of the singular support in terms of the vanishing of its generalized Whittaker models. We study parabolic induction and restriction functors of nilpotent $G$-categories and show that they interact with singular support in a desired way. We prove that if an orbit is maximal in the singular support of a nilpotent $G$-category $\mathcal{C}$, the Hochschild homology of the generalized Whittaker model of $\mathcal{C}$ coincides with the microstalk of the character sheaf of $\mathcal{C}$ at that orbit. This should be considered a categorified analogue of a result of Moeglin-Waldspurger that the dimension of the generalized Whittaker model of a smooth admissible representation of a reductive group over a non-Archimedean local field of characteristic zero coincides with the Fourier coefficient in the wave-front set of that orbit. As a consequence, we give another proof of a theorem of Bezrukavnikov-Losev, classifying finite-dimensional modules for $W$-algebras with fixed regular central character. More precisely, we realize the (rationalized) Grothendieck group of this category as a certain subrepresentation of the Springer representation. Along the way, we show that the Springer action of the Weyl group on the twisted Grothendieck--Springer sheaves is the categorical trace of the wall crossing functors, extending an observation of Zhu for integral central characters., Comment: Minor updates to the introduction

The integration of non-terrestrial networks (NTN) into 5G new radio (NR) has opened up the possibility of developing a new positioning infrastructure using NR signals from Low-Earth Orbit (LEO) satellites. LEO-based cellular positioning offers several advantages, such as a superior link budget, higher operating bandwidth, and large forthcoming constellations. Due to these factors, LEO-based positioning, navigation, and timing (PNT) is a potential enhancement for NTN in 6G cellular networks. However, extending the existing terrestrial cellular positioning methods to LEO-based NTN positioning requires considering key fundamental enhancements. These include creating broad positioning beams orthogonal to conventional communication beams, time-domain processing at the user equipment (UE) to resolve large delay and Doppler uncertainties, and efficiently accommodating positioning reference signals (PRS) from multiple satellites within the communication resource grid. In this paper, we present the first set of design insights by incorporating these enhancements and thoroughly evaluating LEO-based positioning, considering the constraints and capabilities of the NR-NTN physical layer. To evaluate the performance of LEO-based NTN positioning, we develop a comprehensive NR-compliant simulation framework, including LEO orbit simulation, transmission (Tx) and receiver (Rx) architectures, and a positioning engine incorporating the necessary enhancements. Our findings suggest that LEO-based NTN positioning could serve as a complementary infrastructure to existing Global Navigation Satellite Systems (GNSS) and, with appropriate enhancements, may also offer a viable alternative., Comment: 7 pages, 6 figures, submitted to IEEE Communications Magazine

Interband Cascade Lasers (ICLs) are semiconductor lasers emitting in the mid-wave infrared (MWIR 3-6 {\mu}m) and can operate as frequency combs (FCs). These demonstrations are based on double section cavities that can reduce dispersion and/or are adapted for radio-frequency operation. Here we show that ICLs FCs at long wavelengths, where the refractive index dispersion reduces, can be realized in a single long section cavity. We show FC generation for ICLs operating at {\lambda} ~ 4.2 {\mu}m, demonstrating narrow electrical beatnotes over a large current range. We also reconstruct the ultrafast temporal response through a modified SWIFT spectroscopy setup with two fast MWIR detectors, which shows a frequency modulated response in free-running operation. Further, we show that, through active modelocking, the ICL can be forced to generate short pulses on the order of 3 ps. This temporal response is in agreement with Maxwell Bloch simulations, highlighting that these devices possess long dynamics (~100ps) and potentially makes them appropriate for the generation of large peak powers in the MWIR., Comment: 11 pages, 6 figures

SN 2023tsz is a Type Ibn supernova (SNe Ibn) discovered in an extremely low-mass host. SNe Ibn are an uncommon subtype of stripped-envelope core-collapse SNe. They are characterised by narrow helium emission lines in their spectra and are believed to originate from the collapse of massive Wolf-Rayet (WR) stars, though their progenitor systems still remain poorly understood. In terms of energetics and spectrophotometric evolution, SN 2023tsz is largely a typical example of the class, although line profile asymmetries in the nebular phase are seen, which may indicate the presence of dust formation or unshocked circumstellar material. Intriguingly, SN 2023tsz is located in an extraordinarily low-mass host galaxy that is in the 2nd percentile for SESN host masses and star formation rates (SFR). The host has a radius of 1.0 kpc, a $g$-band absolute magnitude of $-12.73$, and an estimated metallicity of $\log(Z_{*}/Z_{\odot}$) = $-1.56$. The SFR and metallicity of the host galaxy raise questions about the progenitor of SN 2023tsz. The low SFR suggests that a star with sufficient mass to evolve into a WR would be uncommon in this galaxy. Further, the very low-metallicity is a challenge for single stellar evolution to enable H and He stripping of the progenitor and produce a SN Ibn explosion. The host galaxy of SN 2023tsz adds another piece to the ongoing puzzle of SNe Ibn progenitors, and demonstrates that they can occur in hosts too faint to be observed in contemporary sky surveys at a more typical SN Ibn redshift., Comment: 14 pages, 10 figures, submitted to MNRAS

CXOU J110926.4-650224 is a candidate transitional millisecond pulsar (tMSP) with X-ray and radio emission properties reminiscent of those observed in confirmed tMSPs in their X-ray 'subluminous' disc state. We present the results of observing campaigns that, for the first time, characterise the optical and near-infrared variability of this source and establish a connection with the mode-switching phenomenon observed in X-rays. The optical emission exhibited flickering activity, frequent dipping episodes where it appeared redder, and a multi-peaked flare where it was bluer. The variability pattern was strongly correlated with that of the X-ray emission. Each dip matched an X-ray low-mode episode, indicating that a significant portion of the optical emission originates from nearly the same region as the X-ray emission. The near-infrared emission also displayed remarkable variability, including a dip of 20 min in length during which it nearly vanished. Time-resolved optical spectroscopic observations reveal significant changes in the properties of emission lines from the disc and help infer the spectral type of the companion star to be between K0 and K5. We compare the properties of CXOU J110926.4-650224 with those of other tMSPs in the X-ray subluminous disc state and discuss our findings within the context of a recently proposed scenario that explains the phenomenology exhibited by the prototypical tMSP PSR J1023+0038., Comment: 12 pages, 7 figures, 2 tables. Accepted for publication on Astronomy & Astrophysics

Despite significant algorithmic advances in vision-based positioning, a comprehensive probabilistic framework to study its performance has remained unexplored. The main objective of this paper is to develop such a framework using ideas from stochastic geometry. Due to limitations in sensor resolution, the level of detail in prior information, and computational resources, we may not be able to differentiate between landmarks with similar appearances in the vision data, such as trees, lampposts, and bus stops. While one cannot accurately determine the absolute target position using a single indistinguishable landmark, obtaining an approximate position fix is possible if the target can see multiple landmarks whose geometric placement on the map is unique. Modeling the locations of these indistinguishable landmarks as a Poisson point process (PPP) $\Phi$ on $\mathbb{R}^2$, we develop a new approach to analyze the localizability in this setting. From the target location $\mathbb{x}$, the measurements are obtained from landmarks within the visibility region. These measurements, including ranges and angles to the landmarks, denoted as $f(\mathbb{x})$, can be treated as mappings from the target location. We are interested in understanding the probability that the measurements $f(\mathbb{x})$ are sufficiently distinct from the measurement $f(\mathbb{x}_0)$ at the given location, which we term localizability. Expressions of localizability probability are derived for specific vision-inspired measurements, such as ranges to landmarks and snapshots of their locations. Our analysis reveals that the localizability probability approaches one when the landmark intensity tends to infinity, which means that error-free localization is achievable in this limiting regime., Comment: 23 pages, 7 figures

Wireless positioning in Non-Line-of-Sight (NLoS) scenarios presents significant challenges due to multipath effects that lead to biased measurements and reduced positioning accuracy. This paper revisits electromagnetic field theory related to diffraction and in the context of wireless positioning and proposes a novel positioning technique that greatly improves accuracy in NLoS environments dominated by diffraction. The method is applied to a critical public safety use case: precisely locating at-risk individuals within buildings, with a particular focus on improving 3D positioning and z-axis accuracy. By leveraging the Geometrical Theory of Diffraction (GTD), the approach introduces an innovative NLoS path length model and a new NLOS positioning technique. Using Fisher information analysis, we establish the conditions required for 3D positioning and derive lower bounds on positioning performance for both 3D and z-axis estimates for the proposed NLOS positioning technique. Additionally, we propose an algorithmic implementation of the proposed NLoS positioning method using non-linear least squares estimation, which we term D-NLS. The positioning performance of our proposed NLOs positioning technique is validated using an extensive ray-tracing simulation. The numerical results highlight the superiority of our approach in outdoor-to-indoor environments, which directly estimates NLoS path lengths and delivers significant performance enhancements over existing methods for both 3D and z-axis positioning scenarios.

We present the first X-ray observation of the energetic millisecond pulsar binary PSR J1431-4715, performed with XMM-Newton and complemented with fast optical multi-band photometry acquired with the ULTRACAM instrument at ESO-NTT. It is found as a faint X-ray source without a significant orbital modulation. This contrasts with the majority of systems that instead display substantial X- ray orbital variability. The X-ray spectrum is dominated by non-thermal emission and, due to the lack of orbital modulation, does not favour an origin in an intrabinary shock between the pulsar and companion star wind. While thermal emission from the neutron star polar cap cannot be excluded in the soft X-rays, the dominance of synchrotron emission favours an origin in the pulsar magnetosphere that we describe at both X-ray and gamma-ray energies with a synchro-curvature model. The optical multi-colour light curve folded at the 10.8h orbital period is double-humped, dominated by ellipsoidal effects, but also affected by irradiation. The ULTRACAM light curves are fit with several models encompassing direct heating and a cold spot, or heat redistribution after irradiation either through convection or convection plus diffusion. Despite the inability to constrain the best irradiation models, the fits provide consistent system parameters, giving an orbital inclination of 59$\pm$6deg and a distance of 3.1$\pm$0.3 kpc. The companion is found to be an F-type star, underfilling its Roche lobe ( f_RL = 73$\pm$4%), with a mass of 0.20$\pm$0.04 M_sun, confirming the redback status, although hotter than the majority of redbacks. The stellar dayside and nightside temperatures of 7500K and 7400K, respectively, indicate a weak irradiation effect on the companion, likely due to its high intrinsic luminosity. Although the pulsar mass cannot be precisely derived, a heavy (1.8-2.2 M_sun) neutron star is favoured, Comment: 16 pages, 11 figures, Accepted for publication in A&A

Quasi-periodic Eruptions (QPEs) are luminous bursts of soft X-rays from the nuclei of galaxies, repeating on timescales of hours to weeks. The mechanism behind these rare systems is uncertain, but most theories involve accretion disks around supermassive black holes (SMBHs), undergoing instabilities or interacting with a stellar object in a close orbit. It has been suggested that this disk could be created when the SMBH disrupts a passing star, implying that many QPEs should be preceded by observable tidal disruption events (TDEs). Two known QPE sources show long-term decays in quiescent luminosity consistent with TDEs, and two observed TDEs have exhibited X-ray flares consistent with individual eruptions. TDEs and QPEs also occur preferentially in similar galaxies. However, no confirmed repeating QPEs have been associated with a spectroscopically confirmed TDE or an optical TDE observed at peak brightness. Here we report the detection of nine X-ray QPEs with a mean recurrence time of approximately 48 hours from AT2019qiz, a nearby and extensively studied optically-selected TDE. We detect and model the X-ray, ultraviolet and optical emission from the accretion disk, and show that an orbiting body colliding with this disk provides a plausible explanation for the QPEs.

Colloidal Solids (COLIS) is a state-of-the-art light scattering setup developed for experiments onboard the International Space Station (ISS). COLIS allows for probing the structure and dynamics of soft matter systems on a wide range of length scales, from a few nm to tens of microns, and on time scales from 100 ns to tens of hours. In addition to conventional static and dynamic light scattering, COLIS includes depolarized dynamic light scattering, a small-angle camera, photon correlation imaging, and optical manipulation of thermosensitive samples through an auxiliary near-infrared laser beam, thereby providing a unique platform for probing soft matter systems. We demonstrate COLIS through ground tests on standard Brownian suspensions, and on protein, colloidal glasses, and gel systems similar to those to be used in future ISS experiments.

In this paper, we use the Fisher information matrix (FIM) to analyze the interaction between low-earth orbit (LEO) satellites and $5$G base stations in providing $9$D receiver localization and correcting LEO ephemeris. First, we give a channel model that captures all the information in the LEO-receiver, LEO-BS, and BS-receiver links. Subsequently, we use FIM to capture the amount of information about the channel parameters in these links. Then, we transform these FIM for channel parameters to the FIM for the $9$D ($3$D position, $3$D orientation, and $3$D velocity estimation) receiver localization parameters and the LEO position and velocity offset. Closed-form expressions for the entries in the FIM for these location parameters are presented. Our results on identifiability utilizing the FIM for the location parameters indicate: i) with one LEO, we need three BSs and three time slots to both estimate the $9$D location parameters and correct the LEO position and velocity, ii) with two LEO, we need three BSs and three time slots to both estimate the $9$D location parameters and correct the LEO position and velocity, and iii) with three LEO, we need three BSs and four-time slots to both estimate the $9$D location parameters and correct the LEO position and velocity. Another key insight is that through the Cramer Rao lower bound we show that with a single LEO, three time slots, and three BSs, the receiver positioning error, velocity estimation error, orientation error, LEO position offset estimation error, and LEO velocity offset estimation error are $0.1 \text{ cm}$, $1 \text{ mm/s}$, $10^{-3} \text{ rad}$, $0.01 \text{ m}$, and $1 \text{ m/s}$, respectively., Comment: arXiv admin note: text overlap with arXiv:2408.16710

In this paper, we derive the fundamental limits of low earth orbit (LEO) enabled localization by analyzing the available information in signals from multiple LEOs during different transmission time slots received on a multiple antennas and evaluate the utility of these signals for $9$D localization ($3$D position, $3$D orientation, and $3$D velocity estimation). We start by deriving the Fisher Information Matrix (FIM) for the channel parameters that are present in the signals received from LEOs in the same or multiple constellations during multiple transmission time slots. To accomplish this, we define a system model that captures i) time offset between LEOs caused by having relatively cheap clocks, ii) frequency offset between LEOs, iii) the unknown Doppler rate caused by high mobility LEOs, and iv) multiple transmission time slots from a particular LEO. We transform the FIM for the channel parameters to the FIM for the location parameters and determine the required conditions for localization. To do this, we start with the $3$D localization cases: i) $3$D positioning with known velocity and orientation, ii) $3$D orientation estimation with known position and velocity, and iii) $3$D velocity estimation with known position and orientation. Subsequently, we derive the FIM for the full $9$D localization case ($3$D position, $3$D orientation, and $3$D velocity estimation) in terms of the FIM for the $3$D localization. Using these results, we determine the number of LEOs, the operating frequency, the number of transmission time slots, and the number of receive antennas that allow for different levels of location estimation.

In this paper we address the question of non-vanishing of $L'(0,f)$ where $f$ is an algebraic valued periodic function. In 2011, Gun, Murty and Rath studied the nature of special values of the derivatives of even Dirichlet-type functions and proved that it can be either zero or transcendental. Here for some special cases we characterize the set of functions for which $L'(0,f)$ is zero or transcendental. Using a theorem of Ramachandra about multiplicative independence of cyclotomic units we also provide some non-trivial examples of functions where $L'(0,f)$ is zero. Finally, assuming Schanuel's conjecture we derive the algebraic independence of special values of derivatives of $L$-functions., Comment: 12 pages

UW Coronae Borealis (UW CrB) is a low mass X-ray binary that shows both Type 1 X-ray and optical bursts, which typically last for 20 s. The system has a binary period of close to 2 hours and is thought to have a relatively high inclination due to the presence of an eclipse in the optical light curve. There is also evidence that an asymmetric disc is present in the system, which precesses every 5.5 days based on changes in the depth of the eclipse. In this paper, we present optical photometry and spectroscopy of UW CrB taken over 2 years. We update the orbital ephemeris using observed optical eclipses and refine the orbital period to 110.97680(1) min. A total of 17 new optical bursts are presented, with 10 of these bursts being resolved temporally. The average $e$-folding time of $19\pm3$s for the bursts is consistent with the previously found value. Optical bursts are observed during a previously identified gap in orbital phase centred on $\phi=0.967$, meaning the reprocessing site is not eclipsed as previously thought. Finally, we find that the apparent P-Cygni profiles present in some of the atomic lines in the optical spectra are due to transient absorption., Comment: 14 pages, 17 figures, submitted to OJAp

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

This paper investigates the frequency of transiting planetary systems around metal-polluted white dwarfs using high-cadence photometry from ULTRACAM and ULTRASPEC on the ground, and space-based observations with TESS. Within a sample of 313 metal-polluted white dwarfs with available TESS light curves, two systems known to have irregular transits are blindly recovered by box-least-squares and Lomb-Scargle analyses, with no new detections, yielding a transit fraction of 0.8 (-0.4, +0.6) per cent. Planet detection sensitivities are determined using simulated transit injection and recovery for all light curves, producing upper limit occurrences over radii from dwarf to Kronian planets, with periods from 1 h to 27 d. The dearth of short-period, transiting planets orbiting polluted white dwarfs is consistent with engulfment during the giant phases of stellar evolution, and modestly constrains dynamical re-injection of planets to the shortest orbital periods. Based on simple predictions of transit probability, where (R + Rp)/a ~ 0.01, the findings here are nominally consistent with a model where 100 per cent of polluted white dwarfs have circumstellar debris near the Roche limit; however, the small sample size precludes statistical confidence in this result. Single transits are also ruled out in all light curves using a search for correlated outliers, providing weak constraints on the role of Oort-like comet clouds in white dwarf pollution., Comment: 10 pages, 5 figures and 1 table. Accepted for publication in MNRAS

The search for the electromagnetic counterparts to gravitational wave (GW) events has been rapidly gathering pace in recent years thanks to the increasing number and capabilities of both gravitational wave detectors and wide field survey telescopes. Difficulties remain, however, in detecting these counterparts due to their inherent scarcity, faintness and rapidly evolving nature. To find these counterparts, it is important that one optimises the observing strategy for their recovery. This can be difficult due to the large number of potential variables at play. Such follow-up campaigns are also capable of detecting hundreds or potentially thousands of unrelated transients, particularly for GW events with poor localisation. Even if the observations are capable of detecting a counterpart, finding it among the numerous contaminants can prove challenging. Here we present the Gravitational wave Electromagnetic RecovRY code (GERry) to perform detailed analysis and survey-agnostic quantification of observing campaigns attempting to recover electromagnetic counterparts. GERry considers the campaign's spatial, temporal and wavelength coverage, in addition to Galactic extinction and the expected counterpart light curve evolution from the GW 3D localisation volume. It returns quantified statistics that can be used to: determine the probability of having detected the counterpart, identify the most promising sources, and assess and refine strategy. Here we demonstrate the code to look at the performance and parameter space probed by current and upcoming wide-field surveys such as GOTO & VRO., Comment: 19 pages, 11 figures, submitted to SPIE Astronomical Telescopes + Instrumentation 2024

The Gravitational-wave Optical Transient Observer (GOTO) is a project dedicated to identifying optical counter-parts to gravitational-wave detections using a network of dedicated, wide-field telescopes. After almost a decade of design, construction, and commissioning work, the GOTO network is now fully operational with two antipodal sites: La Palma in the Canary Islands and Siding Spring in Australia. Both sites host two independent robotic mounts, each with a field-of-view of 44 square degrees formed by an array of eight 40 cm telescopes, resulting in an instantaneous 88 square degree field-of-view per site. All four telescopes operate as a single integrated network, with the ultimate aim of surveying the entire sky every 2-3 days and allowing near-24-hour response to transient events within a minute of their detection. In the modern era of transient astronomy, automated telescopes like GOTO form a vital link between multi-messenger discovery facilities and in-depth follow-up by larger telescopes. GOTO is already producing a wide range of scientific results, assisted by an efficient discovery pipeline and a successful citizen science project: Kilonova Seekers., Comment: 8 pages, 5 figures, submitted to SPIE Astronomical Telescopes + Instrumentation 2024

The companion to PSR J1622-0315, one of the most compact known redback millisecond pulsars, shows extremely low irradiation despite its short orbital period. We model this system to determine the binary parameters, combining optical observations from NTT in 2017 and NOT in 2022 with the binary modeling code ICARUS. We find a best-fit neutron star mass of $2.3 \pm 0.4\,\text{M}_\odot $, and a companion mass of $0.15 \pm 0.02\,\text{M}_\odot$. We detect for the first time low-level irradiation from asymmetry in the minima as well as a change in the asymmetry of the maxima of its light curves over five years. Using star spot models, we find better fits than those from symmetric direct heating models, with consistent orbital parameters. We discuss an alternative scenario where the changing asymmetry is produced by a variable intrabinary shock. In summary, we find that PSR J1622-0315 combines low irradiation with variable light curve asymmetry, and a relatively high neutron star mass., Comment: 18 pages, 11 figures

In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator, and their composition, tempered stable subordinator, gamma subordinator $etc.$ Several distributional properties that include the probability generating function, probability mass function and their governing differential equations are obtained for these variants. It is shown that some of these time-changed processes are L\'evy and for such processes we have derived the associated L\'evy measure. The explicit expressions for the covariance and codifference of the component processes for some of these time-changed variants are obtained. An application of the multivariate generalized space fractional counting process to shock models is discussed.

Model predictive control of residential air conditioning could reduce energy costs and greenhouse gas emissions while maintaining or improving occupants' thermal comfort. However, most approaches to predictive air conditioning control either do not model indoor humidity or treat it as constant. This simplification stems from challenges with modeling indoor humidity dynamics, particularly the high-order, nonlinear equations that govern heat and mass transfer between the air conditioner's evaporator coil and the indoor air. This paper develops a machine-learning approach to modeling indoor humidity dynamics that is suitable for real-world deployment at scale. This study then investigates the value of humidity modeling in four field tests of predictive control in an occupied house. The four field tests evaluate two different building models: One with constant humidity and one with time-varying humidity. Each modeling approach is tested in two different predictive controllers: One that focuses on reducing energy costs and one that focuses on constraining electric power below a utility-specified threshold. The two models lead to similar performance for reducing energy costs. Combining the results of this study and a prior heating study of the same house, the estimated year-round energy cost savings were $340-497 or 22-31% (95% confidence intervals); these savings were consistent across both humidity models. However, in the demand response tests, the simplifying assumption of constant humidity led to far more frequent and severe violations of the power constraint. These results suggest that accurate building models are important for nonlinear objectives, such as reducing or constraining peak demand, while for linear objectives such as reducing energy costs or emissions, model accuracy is less important.

We present mid-infrared (MIR) spectral-timing measurements of the prototypical Galactic microquasar GRS 1915+105. The source was observed with the Mid-Infrared Instrument (MIRI) onboard JWST in June 2023 at a MIR luminosity L(MIR)~10^{36} erg/s exceeding past IR levels by about a factor of 10. By contrast, the X-ray flux is much fainter than the historical average, in the source's now-persistent 'obscured' state. The MIRI low-resolution spectrum shows a plethora of emission lines, the strongest of which are consistent with recombination in the hydrogen Pfund (Pf) series and higher. Low amplitude (~1%) but highly significant peak-to-peak photometric variability is found on timescales of ~1,000 s. The brightest Pf(6-5) emission line lags the continuum. Though difficult to constrain accurately, this lag is commensurate with light-travel timescales across the outer accretion disc or with expected recombination timescales inferred from emission line diagnostics. Using the emission line as a bolometric indicator suggests a moderate (~5-30% Eddington) intrinsic accretion rate. Multiwavelength monitoring shows that JWST caught the source close in-time to unprecedentedly bright MIR and radio long-term flaring. Assuming a thermal bremsstrahlung origin for the MIRI continuum suggests an unsustainably high mass-loss rate during this time unless the wind remains bound, though other possible origins cannot be ruled out. PAH features previously detected with Spitzer are now less clear in the MIRI data, arguing for possible destruction of dust in the interim. These results provide a preview of new parameter space for exploring MIR spectral-timing in XRBs and other variable cosmic sources on rapid timescales., Comment: Dedicated to the memory of our colleague, Tomaso Belloni. Submitted 2024 June 21; Comments welcome

The trade-off between expressiveness and interpretability remains a core challenge when building human-centric predictive models for classification and decision-making. While symbolic rules offer interpretability, they often lack expressiveness, whereas neural networks excel in performance but are known for being black boxes. In this paper, we show a combination of Large Language Models (LLMs) and symbolic programs can bridge this gap. In the proposed LLM-based Symbolic Programs (LSPs), the pretrained LLM with natural language prompts provides a massive set of interpretable modules that can transform raw input into natural language concepts. Symbolic programs then integrate these modules into an interpretable decision rule. To train LSPs, we develop a divide-and-conquer approach to incrementally build the program from scratch, where the learning process of each step is guided by LLMs. To evaluate the effectiveness of LSPs in extracting interpretable and accurate knowledge from data, we introduce IL-Bench, a collection of diverse tasks, including both synthetic and real-world scenarios across different modalities. Empirical results demonstrate LSP's superior performance compared to traditional neurosymbolic programs and vanilla automatic prompt tuning methods. Moreover, as the knowledge learned by LSP is a combination of natural language descriptions and symbolic rules, it is easily transferable to humans (interpretable), and other LLMs, and generalizes well to out-of-distribution samples., Comment: Preliminary Version, Code at [this url](https://github.com/ruocwang/llm-symbolic-program)