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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.