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We present the first interferometric imaging of molecular line emission from the Ring Nebula, NGC~6720, in the form of Submillimeter Array (SMA) observations of CO $J=2\rightarrow 1$ emission. The SMA $^{12}$CO(2--1) mapping data, with $\sim$3$''$ spatial resolution and 2 km s$^{-1}$ velocity resolution, provide an unprecedentedly detailed, 3D view of the Ring's clumpy molecular envelope. The morphology of the velocity-integrated SMA $^{12}$CO(2--1) image closely resembles those of near-IR H$_2$ and PAH emission in JWST/NIRCam imaging of NGC~6720, with the molecular gas forming a geometrically thin layer surrounding the ionized gas imaged by HST and JWST. A simple, geometrical model of the $^{12}$CO(2--1) data shows that the intrinsic structure of NGC~6720's molecular envelope closely resembles a truncated, triaxial ellipsoid that is viewed close to pole-on, and that the dynamical age of the molecular envelope is $\sim$6000 yr. The SMA $^{12}$CO(2--1) data furthermore reveal that filamentary features seen projected in the Ring's interior in JWST imaging are in fact fast-moving polar knots or bullets with radial velocities of $\pm$45--50 km s$^{-1}$ relative to systemic, and that the hot progenitor star remnant is positioned at the precise geometric center of the clumpy, ellipsoidal molecular shell. We assert that the Ring's molecular envelope was formed via a relatively sudden, AGB-terminating mass ejection event $\sim$6000 yr ago, and that this ellipsoidal envelope was then punctured by fast, collimated polar outflows resulting from interactions between the progenitor and one or more companion stars. Such an evolutionary scenario may describe most molecule-rich, ``Ring-like'' planetary nebulae., Comment: 17 pages, 10 figures; to appear in The Astrophysical Journal (accepted 20 Jan. 2025)

Contrary to the conventional emphasis on dataset size, we explore the role of data alignment -- an often overlooked aspect of data quality -- in training capable Large Language Models (LLMs). To do so, we use the Task2Vec-based alignment coefficient, a quantitative measure of the similarity between two datasets, to quantify the impact of alignment between training data and evaluation data on downstream performance. In particular, we conduct controlled \textit{interventional} experiments for two settings: 1. the impact of increased alignment coefficients between various pre-training (pt) against evaluation datasets, and 2. the impact of increased alignment coefficients between domain specific fine-tuning (ft) against domain specific evaluation. The domain specific task we explore is Autoformalization -- the machine translation task between natural language and code for formal verification. In both settings, we find a strong, predictable negative correlation between the alignment coefficient of a model's training and evaluation data and the model's loss/perplexity on the respective downstream task. These findings suggest a re-evaluation of LLM training approaches, demonstrating the relevance of data alignment compared to data quantity, especially in specialized downstream tasks such as Autoformalization.

Low- and intermediate-mass stars evolve through the asymptotic giant branch (AGB), when an efficient mass-loss process removes a significant fraction of their initial mass. A substantial increase in the mass-loss rate at the end of the AGB is observed for at least some stars for unknown reasons. This creates post-AGB objects that are completely enshrouded in thick dusty envelopes and might be associated with binary interactions. We observed the $J=2-1$ line of $^{13}$CO, C$^{17}$O, and C$^{18}$O with the Atacama Large Millimeter / submillimeter Array (ALMA) towards six obscured post-AGB stars (four C-rich and two O-rich sources) to constrain the properties of their circumstellar envelopes, recent mass-loss histories, and initial mass of the central stars. Based on the inferred $^{17}$O/$^{18}$O isotopic ratios, we find all stars to have relatively low initial masses ($< 2~M_\odot$) contrary to suggestions in the literature of higher masses for some sources. We infer a mass for HD~187885 $\sim 1.15~M_\odot$, which is relatively low for a carbon star. For all but one source (GLMP~950), we observe kinematic components with velocities $\gtrsim 30$~km~s$^{-1}$, which are faster than typical AGB wind expansion velocities. For most sources, these higher-velocity outflows display point-symmetric morphologies. The case of Hen~3-1475 is particularly spectacular, with the high-velocity molecular outflow interleaved with the high-velocity outflow of ionised gas observed at optical wavelengths. Based on the size of the emission regions of the slow components of the outflows, we derive typical kinematic ages associated with the C$^{18}$O~$J=2-1$ emission $\lesssim 1500$~years and obtain relatively high associated mass-loss rates ($\gtrsim10^{-4}~M_\odot~{\rm yr}^{-1}$). The sources with known spectral types are found to have evolved faster than expected based on stellar evolutionary models., Comment: Accepted for publication in Astronomy & Astrophysics

The field of computational pathology has been transformed with recent advances in foundation models that encode histopathology region-of-interests (ROIs) into versatile and transferable feature representations via self-supervised learning (SSL). However, translating these advancements to address complex clinical challenges at the patient and slide level remains constrained by limited clinical data in disease-specific cohorts, especially for rare clinical conditions. We propose TITAN, a multimodal whole slide foundation model pretrained using 335,645 WSIs via visual self-supervised learning and vision-language alignment with corresponding pathology reports and 423,122 synthetic captions generated from a multimodal generative AI copilot for pathology. Without any finetuning or requiring clinical labels, TITAN can extract general-purpose slide representations and generate pathology reports that generalize to resource-limited clinical scenarios such as rare disease retrieval and cancer prognosis. We evaluate TITAN on diverse clinical tasks and find that TITAN outperforms both ROI and slide foundation models across machine learning settings such as linear probing, few-shot and zero-shot classification, rare cancer retrieval and cross-modal retrieval, and pathology report generation., Comment: The code is accessible at https://github.com/mahmoodlab/TITAN

In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic equations over the finite field $\mathbb{F}_2$ drawn from a specified distribution. In particular, we design a distribution of degree-2 polynomials $\{p_i(x_1,\ldots,x_n)\}_{i\in [m]}$ for $m

The Medium-Resolution Spectrometer on the Mid-Infrared Instrument on JWST obtained spectra of three carbon stars in the Large Magellanic Cloud. Two of the spectra differ significantly from spectra obtained ~16-19 years earlier with the Infrared Spectrograph on the Spitzer Space Telescope. The one semi-regular variable among the three has changed little. The long-period Mira variable in the sample shows changes consistent with its pulsation cycle. The short-period Mira shows dramatic changes in the strength of its molecular absorption bands, with some bands growing weaker and some stronger. Whether these variations result from its pulsation cycle or its evolution is not clear., Comment: 7 pages, 3 figures

Binaries are known to play a key role in the mass loss and dynamical environments of evolved stars. Stellar and sub-stellar companion interactions produce complex wind morphologies including rotating/expanding disks, bipolar outflows, and spiral wind patterns; however, the connection between these many structures and the gas phase chemistry they harbor is not well-constrained. To expand the sample of chemical inventories in interacting systems, we present a detailed spectroscopic case study of the binary C-rich Asymptotic Giant Branch (AGB) star V Hya. Using spatially resolved ALMA observations at Bands 3, 6 and 7, we characterize the rotational emission lines and distributions of molecules in its surrounding disk undergoing dynamical expansion (DUDE). We detect emission from over 15 molecules and isotopologues toward this source, and present resolved maps for the brightest tracers of carbonaceous chemistry (e.g. CCH, C4H, HC5N, HNC, CH3CN). Employing LTE and non-LTE models of emission from the DUDE, we estimate the abundance distributions for optically thin species, and compare them with prototypical carbon-rich AGB envelopes. We find that the average abundances of detected species are within a factor of ${\sim}5$ from sources with similar mass-loss rates; however, the distribution of daughter species in V Hya is much more compact, with carbon chain species (CCH, C4H, HC3N) appearing with abundances $>$10$^{-7}$ even in the innermost sampled regions (200 au) of the disk., Comment: 40 pages, 27 figures, 2 appendices. Accepted for publication in ApJ

A set of polar rod-shaped liquid crystalline molecules with large dipole moments (mu > 10.4-14.8 D), their molecular structures based on the ferroelectric nematic prototype DIO, are designed, synthesized, and investigated. When the penultimate fluoro-phenyl ring is replaced by phenylpyrimidine moiety, the molecular dipole moment increases from 9.4 D for DIO to 10.4 D for the new molecule and when the terminal fluoro-group is additionally replaced by the nitrile group, the dipole moment rises to 14.8 D. Such a replacement enhances not only the net dipole moment of the molecule, but it also reduces the steric hindrance to rotations of the moieties within the molecule. The superparaelectric nematic (N) and smectic A (SmA) phases of these compounds are found to exhibit colossal dielectric permittivity, obtained both from dielectric spectroscopy, and capacitance measurements using a simple capacitor divider circuit. The electric polarization is measured vs. the field (E). However, no hysteresis in P vs. E is found in the nematic and smectic A phases. The colossal dielectric permittivity persists over the entire fluidic range. The experimental results lead us to conclude that these materials belong to the class of superparaelectrics (SPE) rather than to ferroelectrics due to the absence hysteresis and linear P vs E dependence. The synthesized organic materials are the first fluids for which superparaelectricity is discovered and furthermore these show great potential for the applications in supercapacitors used in storing energy., Comment: 24 pages, 7 figures, 1 table. Submited to JMC C

In-Context Learning (ICL) is a phenomenon where task learning occurs through a prompt sequence without the necessity of parameter updates. ICL in Multi-Headed Attention (MHA) with absolute positional embedding has been the focus of more study than other sequence model varieties. We examine implications of architectural differences between GPT-2 and LLaMa as well as LlaMa and Mamba. We extend work done by Garg et al. (2022) and Park et al. (2024) to GPT-2/LLaMa hybrid and LLaMa/Mamba hybrid models - examining the interplay between sequence transformation blocks and regressive performance in-context. We note that certain architectural changes cause degraded training efficiency/ICL accuracy by converging to suboptimal predictors or converging slower. We also find certain hybrids showing optimistic performance improvements, informing potential future ICL-focused architecture modifications. Additionally, we propose the "ICL regression score", a scalar metric describing a model's whole performance on a specific task. Compute limitations impose restrictions on our architecture-space, training duration, number of training runs, function class complexity, and benchmark complexity. To foster reproducible and extensible research, we provide a typed, modular, and extensible Python package on which we run all experiments., Comment: 18 pages, 16 figures

GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

The hydrogen recombination lines H30$\alpha$, H40$\alpha$, H42$\alpha$, H50$\beta$ and H57$\gamma$ and the underlying bremsstrahlung continuum emission were detected with ALMA in the bipolar nebula Mz3. The source was not spatially resolved, but the velocity profile of the H30$\alpha$ line shows clear indication of maser amplification, confirming previous reports of laser amplification in the far infrared H recombination lines observed with Herschel Space Observatory. Comparison between the flux densities of the H50$\beta$, H40$\alpha$ and H42$\alpha$ lines show overcooling, or darkness amplification by stimulated absorption (dasar effect) at the LSR velocity of about $-25$ km s$^{-1}$, which constrains the density of the absorbing region to about 10$^3$ cm$^{-3}$. The H30$\alpha$ line, on the other hand, presents maser lines at LSR velocities of $-69$ and $-98$ km s$^{-1}$, which indicates ionized gas with densities close to 10$^7$ cm$^{-3}$. Although the source of emission was not resolved, it was possible to find the central position of the images for each velocity interval, which resulted in a well defined position-velocity distribution., Comment: Accepted for publication in The Astrophysical Journal

The classic teacher-student model in machine learning posits that a strong teacher supervises a weak student to improve the student's capabilities. We instead consider the inverted situation, where a weak teacher supervises a strong student with imperfect pseudolabels. This paradigm was recently brought forth by Burns et al.'23 and termed \emph{weak-to-strong generalization}. We theoretically investigate weak-to-strong generalization for binary and multilabel classification in a stylized overparameterized spiked covariance model with Gaussian covariates where the weak teacher's pseudolabels are asymptotically like random guessing. Under these assumptions, we provably identify two asymptotic phases of the strong student's generalization after weak supervision: (1) successful generalization and (2) random guessing. Our techniques should eventually extend to weak-to-strong multiclass classification. Towards doing so, we prove a tight lower tail inequality for the maximum of correlated Gaussians, which may be of independent interest. Understanding the multilabel setting reinforces the value of using logits for weak supervision when they are available., Comment: 40 pages, 5 figures

Large language models demonstrate impressive reasoning abilities but struggle to provide personalized content due to their lack of individual user preference information. Existing methods, such as in-context learning and parameter-efficient fine-tuning, fall short in capturing the complexity of human preferences, especially given the small, personal datasets individuals possess. In this paper, we propose a novel approach utilizing small parameter models as preference agents to generate natural language rules that guide a larger, pre-trained model, enabling efficient personalization. Our method involves a small, local "steering wheel" model that directs the outputs of a much larger foundation model, producing content tailored to an individual's preferences while leveraging the extensive knowledge and capabilities of the large model. Importantly, this personalization is achieved without the need to fine-tune the large model. Experimental results on email and article datasets, demonstrate that our technique significantly outperforms baseline personalization methods. By allowing foundation models to adapt to individual preferences in a data and compute-efficient manner, our approach paves the way for highly personalized language model applications., Comment: EMNLP 2024 Main Conference

Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies to two-term complexes of this type. We apply this to give a new proof of Poincar\'e duality for relative algebraic de Rham cohomology., Comment: 26 pages

As mass-losing asymptotic giant branch (AGB) stars evolve to planetary nebulae (PNe), the mass outflow geometries transform from nearly spherical to extreme aspherical. The physical mechanisms governing this transformation are widely believed to be linked to binarity and the associated production of disks and fast jets during transitional (post-AGB) evolutionary stages. We are carrying out a systematic ALMA survey ($P$re-planet$A$ry $N$ebulae high-angular-res$O$lution su$R$vey with $A$L$MA$ or PANORAMA) of a representative sample of bipolar and multipolar post-AGB objects. We have obtained high angular-resolution (0".1-0".4) observations of the CO(3--2) and/or 6--5 emission in order to probe the spatio-kinematic structure of the collimated outflows and the central disk/torii. The results are remarkable, generally showing the presence of bipolar or multipolar high-velocity outflows, dense toroidal waists, and in one case, a geometrically-thin circular ring around the central bipolar nebula. A high degree of point-symmetry characterizes the morphology of the mass ejecta. In this contribution, we present these and other highlights from our survey. We aim to use 2D/3D radiative transfer modeling in order to derive accurate outflow momenta, masses and mass-loss rates for our sample, and build hydrodynamical models that can explain the observed spatio-kinematic structures. These results will then be used to distinguish between different classes of PN-shaping binary interaction models.

We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of algorithms that combine emerging quantum and analog platforms to accelerate computations. Our hybrid algorithm is equivalent to spectral clustering and has a computational complexity of $O(N)$, where $N$ is the number of nodes in the graph, compared to $O(N^3)$ scaling on classical computing platforms. The proposed method employs the dynamic mode decomposition (DMD) framework on the data generated by Schr\"{o}dinger dynamics that evolves on the manifold induced by the graph Laplacian. In particular, we prove and demonstrate that one can extract the eigenvalues and scaled eigenvectors of the normalized graph Laplacian by evolving Schr\"{o}dinger dynamics on quantum computers followed by DMD computations on analog devices.

Preplanetary nebulae (PPNe) are formed from mass-ejecting late-stage AGB stars. Much of the light from the star gets scattered or absorbed by dust particles, giving rise to the observed reflection nebula seen at visible and near-IR wavelengths. Precursors to planetary nebulae (PNe), PPNe generally have not yet undergone any ionization by UV radiation from the still-buried stellar core. Bipolar PPNe are a common form of observed PPNe. This study lays the groundwork for future dynamical studies by reconstructing the dust density distribution of a particularly symmetric bipolar PPN, M1-92 (Minkowski's Footprint, IRAS 19343$+$2926). For this purpose, we develop an efficient single-scattering radiative transfer model with corrections for double-scattering. Using a V-band image from the Hubble Space Telescope (HST), we infer the dust density profile and orientation of M1-92. These results indicate that M1-92's slowly expanding equatorial torus exhibits an outer radial cutoff in its density, which implicates the influence of a binary companion during the formation of the nebula., Comment: 21 pages, 8 figures, accepted for publications in Galaxies

Developing self-supervised learning (SSL) models that can learn universal and transferable representations of H&E gigapixel whole-slide images (WSIs) is becoming increasingly valuable in computational pathology. These models hold the potential to advance critical tasks such as few-shot classification, slide retrieval, and patient stratification. Existing approaches for slide representation learning extend the principles of SSL from small images (e.g., 224 x 224 patches) to entire slides, usually by aligning two different augmentations (or views) of the slide. Yet the resulting representation remains constrained by the limited clinical and biological diversity of the views. Instead, we postulate that slides stained with multiple markers, such as immunohistochemistry, can be used as different views to form a rich task-agnostic training signal. To this end, we introduce Madeleine, a multimodal pretraining strategy for slide representation learning. Madeleine is trained with a dual global-local cross-stain alignment objective on large cohorts of breast cancer samples (N=4,211 WSIs across five stains) and kidney transplant samples (N=12,070 WSIs across four stains). We demonstrate the quality of slide representations learned by Madeleine on various downstream evaluations, ranging from morphological and molecular classification to prognostic prediction, comprising 21 tasks using 7,299 WSIs from multiple medical centers. Code is available at https://github.com/mahmoodlab/MADELEINE., Comment: ECCV'24

Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or multi-layer-perceptrons lack the structure required to explore things like prompting and alignment within models capable of in-context-learning. We propose univariate polynomial regression as a function class that is just rich enough to study prompting and alignment, while allowing us to visualize and understand what is going on clearly., Comment: ICML Workshop on In-Context Learning

Binary interactions have been proposed to explain a variety of circumstellar structures seen around evolved stars, including asymptotic giant branch (AGB) stars and planetary nebulae. Studies resolving the circumstellar envelopes of AGB stars have revealed spirals, discs and bipolar outflows, with shaping attributed to interactions with a companion. For the first time, we have used a combined chemical and dynamical analysis to reveal a highly eccentric and long-period orbit for W Aquilae, a binary system containing an AGB star and a main sequence companion. Our results are based on anisotropic SiN emission, the first detections of NS and SiC towards an S-type star, and density structures observed in the CO emission. These features are all interpreted as having formed during periastron interactions. Our astrochemistry-based method can yield stringent constraints on the orbital parameters of long-period binaries containing AGB stars, and will be applicable to other systems., Comment: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1038/s41550-023-02154-y

Resolved molecular line observations are essential for gaining insight into the physical and chemical structure of protoplanetary disks, particularly in cold, dense regions where planets form and acquire their chemical compositions. However, tracing these regions is challenging because most molecules freeze onto grain surfaces and are not observable in the gas phase. We investigated cold molecular chemistry in the triple stellar T Tauri disk GG Tau A, which harbours a massive gas and dust ring and an outer disk, using ALMA Band 7 observations. We present high angular resolution maps of N2H+ and DCO+ emission, with upper limits reported for H2D+, 13CS, and SO2. The radial intensity profile of N2H+ shows most emission near the ring outer edge, while DCO+ exhibits double peaks, one near the ring inner edge and the other in the outer disk. With complementary observations of lower-lying transitions, we constrained the molecular surface densities and rotation temperatures. We compared the derived quantities with model predictions across different cosmic ray ionization (CRI) rates, carbon-to-oxygen (C/O) ratios, and stellar UV fluxes. Cold molecular chemistry, affecting N2H+, DCO+, and H2D+ abundances, is most sensitive to CRI rates, while stellar UV flux and C/O ratios have minimal impact on these three ions. Our best model requires a low cosmic ray ionization rate of 1e-18 s-1. However, it fails to match the low temperatures derived from N2H+ and DCO+, 12 to 16 K, which are much lower than the CO freezing temperature., Comment: Accepted for publication in the Astrophysical Journal; 26 Pages (15 figures and 8 tables)

Evaluations of creative stories generated by large language models (LLMs) often focus on objective properties of the text, such as its style, coherence, and diversity. While these metrics are indispensable, they do not speak to a story's subjective, psychological impact from a reader's perspective. We introduce the Psychological Depth Scale (PDS), a novel framework rooted in literary theory that measures an LLM's ability to produce authentic and narratively complex stories that provoke emotion, empathy, and engagement. We empirically validate our framework by showing that humans can consistently evaluate stories based on PDS (0.72 Krippendorff's alpha). We also explore techniques for automating the PDS to easily scale future analyses. GPT-4o, combined with a novel Mixture-of-Personas (MoP) prompting strategy, achieves an average Spearman correlation of 0.51 with human judgment while Llama-3-70B with constrained decoding scores as high as 0.68 for empathy. Finally, we compared the depth of stories authored by both humans and LLMs. Surprisingly, GPT-4 stories either surpassed or were statistically indistinguishable from highly-rated human-written stories sourced from Reddit. By shifting the focus from text to reader, the Psychological Depth Scale is a validated, automated, and systematic means of measuring the capacity of LLMs to connect with humans through the stories they tell., Comment: EMNLP 2024

Large language models have been proven to be capable of handling complex linguistic and cognitive tasks. Therefore their usage has been extended to tasks requiring logical reasoning ability such as Mathematics. In this paper, we propose a prompting technique called MathDivide that breaks down the mathematical problem into simpler subproblems. Each of the subproblems is formulated as an algebraic expression whose value is evaluated by the Python code generated by the LLM for the corresponding algebraic expression. The values fed to the Python code are the numerical values provided in the problem statement. The solutions for the subproblems are composed together to obtain the final answer for the problem statement. Finally, the final answer is compared to the correct answer. If the final answer matches the correct answer, it is produced as output else a refinement prompt is fed to the LLM. We experiment with this prompting technique on both closed-source LLM models and open-source LLM models using GSM8K dataset. The results obtained demonstrate that MathDivide was able to significantly outperform the leading prompting technique called Math-prompter., Comment: 10 pages, 3 figures

We present a method to estimate distances to Asymptotic Giant Branch (AGB) stars in the Galaxy, using spectral energy distributions (SEDs) in the near- and mid-infrared. By assuming that a given set of source properties (initial mass, stellar temperature, composition, and evolutionary stage) will provide a typical SED shape and brightness, sources are color-matched to a distance-calibrated template and thereafter scaled to extract the distance. The method is tested by comparing the distances obtained to those estimated from Very Long Baseline Interferometry or Gaia parallax measurements, yielding a strong correlation in both cases. Additional templates are formed by constructing a source sample likely to be close to the Galactic center, and thus with a common, typical distance for calibration of the templates. These first results provide statistical distance estimates to a set of almost 15,000 Milky Way AGB stars belonging to the Bulge Asymmetries and Dynamical Evolution (BAaDE) survey, with typical distance errors of $\pm 35$%. With these statistical distances a map of the intermediate-age population of stars traced by AGBs is formed, and a clear bar structure can be discerned, consistent with the previously reported inclination angle of 30$^\circ$ to the GC-Sun direction vector. These results motivate deeper studies of the AGB population to tease out the intermediate-age stellar distribution throughout the Galaxy, as well as determining statistical properties of the AGB population luminosity and mass-loss rate distributions., Comment: Accepted to APJ

The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite multiple insightful results in the past few years, a proof for the conjecture remains elusive. In this work, we construct a novel dynamical systems-based approach for studying unique games and, more generally, the field of computational complexity. We propose a family of dynamical systems whose equilibria correspond to solutions of unique games and prove that unsatisfiable instances lead to ergodic dynamics. Moreover, as the instance hardness increases, the weight of the invariant measure in the vicinity of the optimal assignments scales polynomially, sub-exponentially, or exponentially depending on the value gap. We numerically reproduce a previously hypothesized hardness plot associated with the UGC. Our results indicate that the UGC is likely true, subject to our proposed conjectures that link dynamical systems theory with computational complexity.

Nanosciences largely rely on plasmons which are quasiparticles constituted by collective oscillations of quantum electron gas composed of conduction band electrons that occupy discrete quantum states. Our work has introduced non-perturbative plasmons with oscillation amplitudes that approach the extreme limit set by breakdown in characteristic coherence. In contrast, conventional plasmons are small-amplitude oscillations. Controlled excitation of extreme plasmons modeled in our work unleashes unprecedented Petavolts per meter fields. In this work, an analytical model of this new class of plasmons is developed based on quantum kinetic framework. A controllable extreme plasmon, the surface "crunch-in" plasmon, is modeled here using a modified independent electron approximation which takes into account the quantum oscillation frequency. Key characteristics of such realizable extreme plasmons that unlock unparalleled possibilities, are obtained.

Context: Fault localization (FL) is the key activity while debugging a program. Any improvement to this activity leads to significant improvement in total software development cost. There is an internal linkage between the program spectrum and test execution result. Conditional probability in statistics captures the probability of occurring one event in relationship to one or more other events. Objectives: The aim of this paper is to use the conception of conditional probability to design an effective fault localization technique. Methods: In the paper, we present a fault localization technique that derives the association between statement coverage information and test case execution result using condition probability statistics. This association with the failed test case result shows the fault containing the probability of that specific statement. Subsequently, we use a grouping method to refine the obtained statement ranking sequence for better fault localization. Results: We evaluated the effectiveness of proposed method over eleven open-source data sets. Our obtained results show that on average, the proposed CGFL method is 24.56% more effective than other contemporary fault localization methods such as D*, Tarantula, Ochiai, Crosstab, BPNN, RBFNN, DNN, and CNN. Conclusion: We devised an effective fault localization technique by combining the conditional probabilistic method with failed test case execution-based approach. Our experimental evaluation shows our proposed method outperforms the existing fault localization techniques.

In this paper, we study the Appell function $F_4$ from discrete point of view. In particular, we obtain regions of convergence, difference-differential equations, finite and infinite summation formulas and a list of recursion relations satisfied by the discrete analogues of Appell function $F_4$.

We present Submillimeter Array (SMA) mapping of $^{12}$CO $J=2\rightarrow 1$, $^{13}$CO $J=2\rightarrow 1$, and CN $N=2\rightarrow 1$ emission from the Ring-like planetary nebula (PN) NGC 3132, one of the subjects of JWST Early Release Observation (ERO) near-infrared imaging. The $\sim$5$''$ resolution SMA data demonstrate that the Southern Ring's main, bright, molecule-rich ring is indeed an expanding ring, as opposed to a limb-brightened shell, in terms of its intrinsic (physical) structure. This suggests that NGC 3132 is a bipolar nebula viewed more or less pole-on (inclination $\sim$15--30$^\circ$). The SMA data furthermore reveal that the nebula harbors a second expanding molecular ring that is aligned almost orthogonally to the main, bright molecular ring. We propose that this two-ring structure is the remnant of an ellipsoidal molecular envelope of ejecta that terminated the progenitor star's asymptotic giant branch evolution and was subsequently disrupted by a series of misaligned fast, collimated outflows or jets resulting from interactions between the progenitor and one or more companions., Comment: 20 pages, 12 figures; accepted by The Astrophysical Journal

Reinforcement Learning (RL) techniques have been increasingly applied in optimizing control systems. However, their application in quantum systems is hampered by the challenge of performing closed-loop control due to the difficulty in measuring these systems. This often leads to reliance on assumed models, introducing model bias, a problem that is exacerbated in open quantum dynamics where Markovian approximations are not valid. To address these challenges, we propose a novel approach that incorporates the non-Markovian nature of the environment into a low-dimensional effective reservoir. By initially employing a series of measurements as a 'dataset', we utilize machine learning techniques to learn the effective quantum dynamics more efficiently than traditional tomographic methods. Our methodology aims to demonstrates that by integrating reinforcement learning with model learning, it is possible to devise control policies and models that can counteract decoherence in a spin-boson system. This approach may not only mitigates the issues of model bias but also provides a more accurate representation of quantum dynamics, paving the way for more effective quantum control strategies., Comment: 9 pages, 3 figures

The dusty winds of cool evolved stars are a major contributor of the newly synthesised material enriching the Galaxy and future generations of stars. However, the details of the physics and chemistry behind dust formation and wind launching have yet to be pinpointed. Recent spatially resolved observations show the importance of gaining a more comprehensive view of the circumstellar chemistry, but a comparative study of the intricate interplay between chemistry and physics is still difficult because observational details such as frequencies and angular resolutions are rarely comparable. Aiming to overcome these deficiencies, ATOMIUM is an ALMA Large Programme to study the physics and chemistry of the circumstellar envelopes of a diverse set of oxygen-rich evolved stars under homogeneous observing conditions at three angular resolutions between ~0.02"-1.4". Here we summarize the molecular inventory of these sources, and the correlations between stellar parameters and molecular content. Seventeen oxygen-rich or S-type asymptotic giant branch (AGB) and red supergiant (RSG) stars have been observed in several tunings with ALMA Band 6, targeting a range of molecules to probe the circumstellar envelope and especially the chemistry of dust formation close to the star. We systematically assigned the molecular carriers of the spectral lines and measured their spectroscopic parameters and the angular extent of the emission of each line from integrated intensity maps. Across the ATOMIUM sample, we detect 291 transitions of 24 different molecules and their isotopologues. This includes several first detections in oxygen-rich AGB/RSG stars: PO v=1, SO2 v1=1 and v2=2, and several high energy H2O transitions. We also find several first detections in S-type AGB stars: vibrationally excited HCN v2=2,3 and SiS v=4,5,6, as well as first detections of the molecules SiC, AlCl, and AlF in W Aql..., Comment: 19 pages plus appendices, forthcoming publication in Astronomy & Astrophysics

The X-ray spectrum of the Coma galaxy cluster was studied using the data from the XMM-Newton observatory. We combined 7 observations performed with the MOS camera of XMM-Newton in the 40'x 40' region centered at the Coma cluster. The analyzed observations were performed in 2000-2005 and have a total duration of 196 ksec. We focus on the analysis of the MOS camera spectra due to their lower affection by strong instrumental line-like background. The obtained spectrum was fitted with a model including contributions from the Solar system/Milky Way hot plasma and a power law X-ray background. The contribution of the instrumental background was modeled as a power law (not convolved with the effective area) and a number of Gaussian lines. The contribution from the Coma cluster was modeled with a single-temperature hot plasma emission. In addition, we searched for possible non-thermal radiation present in the vicinity of the center of the Coma cluster, originating e.g. from synchrotron emission of relativistic electrons on a turbulent magnetic field. We compared the results with previous works by other authors and spectra obtained from other instruments that operate in the similar energy range of 1-10 keV. Careful and detailed spectrum analysis shall be a necessary contribution to our future work - searching for axion-like particles' manifestations in the Coma cluster., Comment: 6 pages, 2 figures, 2 tables

As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in formalizing mathematics, and discovering connections between different mathematical areas, to name a few. While prior work has leveraged computers for exhaustive mathematical proof search, recent efforts based on large language models (LLMs) aspire to position computing platforms as co-contributors in the mathematical research process. Despite their current limitations in logic and mathematical tasks, there is growing interest in melding theorem proving systems with foundation models. This work investigates the applicability of LLMs in formalizing advanced mathematical concepts and proposes a framework that can critically review and check mathematical reasoning in research papers. Given the noted reasoning shortcomings of LLMs, our approach synergizes the capabilities of proof assistants, specifically PVS, with LLMs, enabling a bridge between textual descriptions in academic papers and formal specifications in PVS. By harnessing the PVS environment, coupled with data ingestion and conversion mechanisms, we envision an automated process, called \emph{math-PVS}, to extract and formalize mathematical theorems from research papers, offering an innovative tool for academic review and discovery.

The dominance of proprietary LLMs has led to restricted access and raised information privacy concerns. High-performing open-source alternatives are crucial for information-sensitive and high-volume applications but often lag behind in performance. To address this gap, we propose (1) A untargeted variant of iterative self-critique and self-refinement devoid of external influence. (2) A novel ranking metric - Performance, Refinement, and Inference Cost Score (PeRFICS) - to find the optimal model for a given task considering refined performance and cost. Our experiments show that SoTA open source models of varying sizes from 7B - 65B, on average, improve 8.2% from their baseline performance. Strikingly, even models with extremely small memory footprints, such as Vicuna-7B, show a 11.74% improvement overall and up to a 25.39% improvement in high-creativity, open ended tasks on the Vicuna benchmark. Vicuna-13B takes it a step further and outperforms ChatGPT post-refinement. This work has profound implications for resource-constrained and information-sensitive environments seeking to leverage LLMs without incurring prohibitive costs, compromising on performance and privacy. The domain-agnostic self-refinement process coupled with our novel ranking metric facilitates informed decision-making in model selection, thereby reducing costs and democratizing access to high-performing language models, as evidenced by case studies., Comment: Accepted to Findings of EMNLP 2023

In this paper, we introduce a variant of Francis Su's "Game of Cycles," that we call "Cycles with Sources." The only change to the rules is permitting nodes to be sources, while sinks are still prohibited. Despite this minor change in the rules, we show that even on simple games, like line graphs, there is a great change in the outcome of optimal play, which we fully analyze using Sprague-Grundy Theory.

Tissue phenotyping is a fundamental computational pathology (CPath) task in learning objective characterizations of histopathologic biomarkers in anatomic pathology. However, whole-slide imaging (WSI) poses a complex computer vision problem in which the large-scale image resolutions of WSIs and the enormous diversity of morphological phenotypes preclude large-scale data annotation. Current efforts have proposed using pretrained image encoders with either transfer learning from natural image datasets or self-supervised pretraining on publicly-available histopathology datasets, but have not been extensively developed and evaluated across diverse tissue types at scale. We introduce UNI, a general-purpose self-supervised model for pathology, pretrained using over 100 million tissue patches from over 100,000 diagnostic haematoxylin and eosin-stained WSIs across 20 major tissue types, and evaluated on 33 representative CPath clinical tasks in CPath of varying diagnostic difficulties. In addition to outperforming previous state-of-the-art models, we demonstrate new modeling capabilities in CPath such as resolution-agnostic tissue classification, slide classification using few-shot class prototypes, and disease subtyping generalization in classifying up to 108 cancer types in the OncoTree code classification system. UNI advances unsupervised representation learning at scale in CPath in terms of both pretraining data and downstream evaluation, enabling data-efficient AI models that can generalize and transfer to a gamut of diagnostically-challenging tasks and clinical workflows in anatomic pathology.

We present JWST images of the well-known planetary nebula NGC 6720 (the Ring Nebula), covering wavelengths from 1.6$\mu$m to 25 $\mu$m. The bright shell is strongly fragmented with some 20 000 dense globules, bright in H$_2$, with a characteristic diameter of 0.2 arcsec and density $n_{\rm H} \sim 10^5$-$10^6$ cm$^{-3}$. The shell contains a thin ring of polycyclic aromatic hydrocarbon (PAH) emission. H$_2$ is found throughout the shell and in the halo. H$_2$ in the halo may be located on the swept-up walls of a biconal polar flow. The central cavity is shown to be filled with high ionization gas and shows two linear structures. The central star is located 2 arcsec from the emission centroid of the cavity and shell. Linear features (`spikes') extend outward from the ring, pointing away from the central star. Hydrodynamical simulations are shown which reproduce the clumping and possibly the spikes. Around ten low-contrast, regularly spaced concentric arc-like features are present; they suggest orbital modulation by a low-mass companion with a period of about 280 yr. A previously known much wider companion is located at a projected separation of about 15 000 au; we show that it is an M2-M4 dwarf. The system is therefore a triple star. These features, including the multiplicity, are similar to those seen in the Southern Ring Nebula (NGC 3132) and may be a common aspect of such nebulae., Comment: 25 pages, 23 figures. Submitted to Monthly Notices of the Royal Astronomical Society. Corrected typos in metadata

The Alexa Prize program has empowered numerous university students to explore, experiment, and showcase their talents in building conversational agents through challenges like the SocialBot Grand Challenge and the TaskBot Challenge. As conversational agents increasingly appear in multimodal and embodied contexts, it is important to explore the affordances of conversational interaction augmented with computer vision and physical embodiment. This paper describes the SimBot Challenge, a new challenge in which university teams compete to build robot assistants that complete tasks in a simulated physical environment. This paper provides an overview of the SimBot Challenge, which included both online and offline challenge phases. We describe the infrastructure and support provided to the teams including Alexa Arena, the simulated environment, and the ML toolkit provided to teams to accelerate their building of vision and language models. We summarize the approaches the participating teams took to overcome research challenges and extract key lessons learned. Finally, we provide analysis of the performance of the competing SimBots during the competition.

We establish a sample of 370 Mira variables that are likely near the Galactic center (GC). The sources have been selected from the OGLE and BAaDE surveys based on their sky coordinates, OGLE classifications, and BAaDE maser-derived line-of-sight velocities. As the distance to the GC is known to a high accuracy, this sample is a test bed for reddening and extinction studies toward the GC and in Mira envelopes. We calculated separate interstellar- and circumstellar-extinction values for individual sources, showing that there is a wide range of circumstellar extinction values (up to four magnitudes in the K$_s$ band) in the sample, and that circumstellar reddening is statistically different from interstellar reddening laws. Further, the reddening laws in the circumstellar environments of our sample and the circumstellar environments of Large Magellanic Cloud (LMC) Miras are strikingly similar despite the different metallicities of the samples. Period-magnitude relations for the mid-infrared (MIR) WISE and MSX bands are also explored, and in the WISE bands we compare these to period-magnitude relationships derived from Miras in the LMC as it is important to compare these LMC relations to those in a higher metallicity environment. Emission from the envelope itself may contaminate MIR magnitudes altering the relations, especially for sources with thick envelopes., Comment: 14 pages, 10 figures; accepted to A&A

Let $C_{k}$ (resp. $P_{k}$) denote the cycle (resp. path) of length $k$. In this paper, we examine the necessary and sufficient conditions for the existence of a $(8; p, q)$-decomposition of tensor product and wreath product of complete graphs.

We study the asymptotic generalization of an overparameterized linear model for multiclass classification under the Gaussian covariates bi-level model introduced in Subramanian et al.~'22, where the number of data points, features, and classes all grow together. We fully resolve the conjecture posed in Subramanian et al.~'22, matching the predicted regimes for generalization. Furthermore, our new lower bounds are akin to an information-theoretic strong converse: they establish that the misclassification rate goes to 0 or 1 asymptotically. One surprising consequence of our tight results is that the min-norm interpolating classifier can be asymptotically suboptimal relative to noninterpolating classifiers in the regime where the min-norm interpolating regressor is known to be optimal. The key to our tight analysis is a new variant of the Hanson-Wright inequality which is broadly useful for multiclass problems with sparse labels. As an application, we show that the same type of analysis can be used to analyze the related multilabel classification problem under the same bi-level ensemble., Comment: NeurIPS 2023, 56 pages

Using the GALEX archive, we have discovered extended structures around ten asymptotic giant branch (AGB) stars (out of a total 92 searched) emitting in the far-ultraviolet (FUV) band. In all but one, we find the typical morphology expected for a spherical wind moving relative to, and interacting with the ISM to produce an astrosphere. The exception is V\,Hya whose mass-ejection is known to be highly aspherical, where we find evidence of its large parabolic outflows interacting with the ISM, and its collimated, extreme velocity outflows interacting with the circumstellar medium. For 8 objects with relatively large proper motions, we find (as expected) that the termination-shock region lies in a hemisphere that contains the proper motion vector. Radial intensity cuts for each source have been used to locate the termination shock and the astropause's outer edge. In a few objects, the cuts also reveal faint emission just outside the astropause that likely arises in shocked ISM material. We have used these data, together with published mass-loss rates and wind expansion velocities, to determine the total mass lost and duration for each source -- we find that the duration of and total mass in the shocked wind are significantly larger than their corresponding values for the unshocked wind. The combination of FUV and far-IR data on AGB astrospheres, provides a unique database for theoretical studies (numerical simulations) of wind-ISM interactions. We show that a Cyclical Spatial Heterodyne Spectrometer on a small space-based telescope, can provide high-resolution spectra of astrospheres to confirm the emission mechanism.

We present dual-attention neural biasing, an architecture designed to boost Wake Words (WW) recognition and improve inference time latency on speech recognition tasks. This architecture enables a dynamic switch for its runtime compute paths by exploiting WW spotting to select which branch of its attention networks to execute for an input audio frame. With this approach, we effectively improve WW spotting accuracy while saving runtime compute cost as defined by floating point operations (FLOPs). Using an in-house de-identified dataset, we demonstrate that the proposed dual-attention network can reduce the compute cost by $90\%$ for WW audio frames, with only $1\%$ increase in the number of parameters. This architecture improves WW F1 score by $16\%$ relative and improves generic rare word error rate by $3\%$ relative compared to the baselines., Comment: Accepted to Proc. IEEE ICASSP 2023

What is the role of soil moisture in maintaining the land ITCZ during the active phase of the monsoon? This question has been addressed in this study by using ERA5 reanalysis datasets, and then we evaluate the question in the CFS model-free run. Like rainfall, soil moisture also show intraseasonal oscillation. Furthermore, the sub-seasonal and seasonal features of soil moisture are different from each other. During the summer monsoon season, the maximum soil moisture is found over western coastal regions, central parts of India, and the northeastern Indian subcontinent. However, during active phases of the monsoon, the maximum positive soil moisture anomaly was found in North West parts of India. soil moisture also play a pre-conditioning role during active phases of the monsoon over the monsoon core zone of India. When it is further divided into two boxes, the north monsoon core zone, and the south monsoon core zone, it is found that the preconditioning depends on that region's soil type and climate classification. Also, we calculate the moist static energy (MSE) budget during the monsoon phases to show how soil moisture feedback affects the boundary layer MSE and rainfall. A similar analysis is applied to the model run, but it cannot show the realistic preconditioning role of soil moisture and its feedback on the rainfall as in observations. We conclude that to get proper feedback between soil moisture and precipitation during the active phase of the monsoon in the model, the pre-conditioning of soil moisture should be realistic.

Gas Electron Multiplier (GEM) detector, one of the advanced members of the Micro Pattern Gas Detector (MPGD) group, is widely used in High Energy Physics (HEP) experiments. The high rate handling capability and spatial resolution make it a desired tracking detector for high rate HEP experiments. Investigation of the long-term stability is an essential criterion for any tracking device used in HEP experiments. To investigate the long-term stability of a Single Mask~(SM) triple GEM detector prototype, it is irradiated continuously using a $^{55}$Fe X-ray source of energy 5.9 keV. The chamber is operated with Ar/CO$_2$ gas mixture in continuous flow mode. The gain and energy resolution of the chamber are calculated from the 5.9 keV X-ray peak and studied as a function of time. The applied voltage, divider current and also the environmental parameters (ambient temperature, pressure and relative humidity) are recorded continuously. It is observed that at a fixed applied voltage, the divider current of the detector is changing with time and as a result, the gain of the detector also changes. A systematic investigation is carried out to understand the probable reasons behind the observed variation in divider current and also to find its possible remedies. The details of the experimental setup, methodology and results are discussed in this article.

In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical schemes, namely Chang-Cooper and implicit finite difference. We then compute the solution of the resulting system of linear equations using the quantum linear systems algorithm. We present detailed error and complexity analyses for both these schemes and demonstrate that our proposed algorithms, under certain conditions, provably compute the solution to the FPE within prescribed $\epsilon$ error bounds with polynomial dependence on state dimension $d$. Classical numerical methods scale exponentially with dimension, thus, our approach, under the aforementioned conditions, provides an \emph{exponential speed-up} over traditional approaches., Comment: IEEE International Conference on Quantum Computing and Engineering (QCE23)

Planetary nebulae (PNe), the ejected envelopes of red giant stars, provide us with a history of the last, mass-losing phases of 90 percent of stars initially more massive than the Sun. Here, we analyse James Webb Space Telescope (JWST) Early Release Observation (ERO) images of the PN NGC3132. A structured, extended H2 halo surrounding an ionised central bubble is imprinted with spiral structures, likely shaped by a low-mass companion orbiting the central star at 40-60 AU. The images also reveal a mid-IR excess at the central star interpreted as a dusty disk, indicative of an interaction with another, closer companion. Including the previously known, A-type visual companion, the progenitor of the NGC3132 PN must have been at least a stellar quartet. The JWST images allow us to generate a model of the illumination, ionisation and hydrodynamics of the molecular halo, demonstrating the power of JWST to investigate complex stellar outflows. Further, new measurements of the A-type visual companion allow us to derive the value for the mass of the progenitor of a central star to date with excellent precision: 2.86+/-0.06 Mo. These results serve as path finders for future JWST observations of PNe providing unique insight into fundamental astrophysical processes including colliding winds, and binary star interactions, with implications for supernovae and gravitational wave systems., Comment: 32 pages, 5 figures for the main article. 12 pages 8 figures for the supplementary material

Aims. Through the ATOMIUM project, based on an ALMA large program, we aim to present a consistent view of a sample of 17 nearby cool evolved stars (Aymptotic Giant Branch and red supergiant stars). Methods. Here we present VLT/SPHERE-ZIMPOL polarimetric maps obtained in the visible of 14 out of the 17 ATOMIUM sources. They were obtained contemporaneously with the ALMA high spatial resolution data. To help interpret the polarized signal, we produced synthetic maps of light scattering by dust, through 3D radiative transfer simulations with the RADMC3D code. Results. The degree of linear polarization (DoLP) observed by ZIMPOL spreads across several optical filters. We infer that it primarily probes dust located just outside of the point spread function, and in or near the plane of the sky, with a total optical depth close to unity in the line of sight, representing only a fraction of the total circumstellar dust. The maximum DoLP ranges from 0.03-0.38 depending on the source, fractions that can be reproduced by our 3D pilot models for grains composed of common dust species. The spatial structure of the DoLP shows a diverse set of shapes. Only for three sources do we note a correlation between the ALMA CO and SiO lines, which trace the gas density, and the DoLP, which traces the dust. Conclusion. The clumpiness of the DoLP and the lack of a consistent correlation between the gas and the dust location show that, in the inner circumstellar environment (CSE), dust formation occurs at very specific sites. This has potential consequences for the derived mass-loss rates and dust-to-gas ratio in the inner region of the CSE. Except for $\pi^1$~Gru and perhaps GY Aql, we do not detect interactions between the circumstellar wind and the hypothesized companions that shape the wind at larger scales. This suggests that the orbits of any other companions are tilted out of the plane of the sky., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages, 15 figures, 5 tables

We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations (ODEs) or partial differential equation (PDEs) can be challenging to solve on classical computers due to high dimensionality, stiffness, nonlinearities, and sensitive dependence to initial conditions. For sparse $n$-dimensional linear ODEs, quantum algorithms have been developed which can produce a quantum state proportional to the solution in poly(log(nx)) time using the quantum linear systems algorithm (QLSA). Recently, this framework was extended to systems of nonlinear ODEs with quadratic polynomial vector fields by applying Carleman linearization that enables the embedding of the quadratic system into an approximate linear form. A detailed complexity analysis was conducted which showed significant computational advantage under certain conditions. We present an extension of this algorithm to deal with systems of nonlinear ODEs with $k$-th degree polynomial vector fields for arbitrary (finite) values of $k$. The steps involve: 1) mapping the $k$-th degree polynomial ODE to a higher dimensional quadratic polynomial ODE; 2) applying Carleman linearization to transform the quadratic ODE to an infinite-dimensional system of linear ODEs; 3) truncating and discretizing the linear ODE and solving using the forward Euler method and QLSA. Alternatively, one could apply Carleman linearization directly to the $k$-th degree polynomial ODE, resulting in a system of infinite-dimensional linear ODEs, and then apply step 3. This solution route can be computationally more efficient. We present detailed complexity analysis of the proposed algorithms, prove polynomial scaling of runtime on $k$ and demonstrate the framework on an example.

The planetary nebula (PN) NGC3132 is a striking example of the dramatic but poorly understood, mass-loss phenomena that (1-8) Msun stars undergo during their death throes as they evolve into white dwarfs (WDs). From an analysis of JWST multiwavelength (0.9-18 micron) imaging of NGC3132, we report the discovery of an asymmetrical dust cloud around the WD central star (CS) of NGC3132, seen most prominently in the 18 micron~image, with a surface-brightness limited radial extent of >~2 arcsec. We show that the A2V star located 1.7 arcsec to CS's North-East (and 0.75 kpc from Earth) is gravitationally-bound to the latter, by the detection of relative orbital angular motion of (0.24+/-0.045) deg between these stars over ~20 yr. Using aperture photometry of the CS extracted from the JWST images, together with published optical photometry and an archival UV spectrum, we have constructed the spectral-energy distribution (SED) of the CS and its extended emission over the UV to mid-IR (0.091-18 micron) range. We find that fitting the SED of the CS and the radial intensity distributions at 7.7, 12.8 and 18 micron with thermal emission from dust requires a cloud that extends to a radius of >~1785 au, with a dust mass of ~1.3 x 10^(-2) M(Earth) and grains that are 70% silicate and 30% amorphous carbon. We propose plausible origins of the dust cloud and an evolutionary scenario in which a system of three stars -- the CS, a close low-mass companion, and a more distant A2V star -- forms a stable hierarchical triple system on the main-sequence but becomes dynamically unstable later, resulting in the spectacular mass-ejections that form the current, multipolar PN., Comment: 23 pages, 5 tables, 8 figures (ApJ, in press) references added, minor revision of Fig 5 caption, minor typos corrected