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In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this method from a motivic viewpoint through some known hypergeometric well-poised formulae of Whipple and McCarthy. We first use the method to derive a class of special weight three modular forms, labeled as $\mathbb{K}_2$-functions. Then using well-poised hypergeometric formulae we further construct a class of degree four Galois representations of the absolute Galois groups of the corresponding cyclotomic fields. These representations are then shown to be extendable to $G_{\mathbb{Q}}$ and the $L$-function of each extension coincides with the $L$-function of an automorphic form.

According to PBS, nearly one-third of Americans lack access to primary care services, and another forty percent delay going to avoid medical costs. As a result, many diseases are left undiagnosed and untreated, even if the disease shows many physical symptoms on the skin. With the rise of AI, self-diagnosis and improved disease recognition have become more promising than ever; in spite of that, existing methods suffer from a lack of large-scale patient databases and outdated methods of study, resulting in studies being limited to only a few diseases or modalities. This study incorporates readily available and easily accessible patient information via image and text for skin disease classification on a new dataset of 26 skin disease types that includes both skin disease images (37K) and associated patient narratives. Using this dataset, baselines for various image models were established that outperform existing methods. Initially, the Resnet-50 model was only able to achieve an accuracy of 70% but, after various optimization techniques, the accuracy was improved to 80%. In addition, this study proposes a novel fine-tuning strategy for sequence classification Large Language Models (LLMs), Chain of Options, which breaks down a complex reasoning task into intermediate steps at training time instead of inference. With Chain of Options and preliminary disease recommendations from the image model, this method achieves state of the art accuracy 91% in diagnosing patient skin disease given just an image of the afflicted area as well as a patient description of the symptoms (such as itchiness or dizziness). Through this research, an earlier diagnosis of skin diseases can occur, and clinicians can work with deep learning models to give a more accurate diagnosis, improving quality of life and saving lives.

In the hyperreals constructed using a free ultrafilter on R, where [f] is the hyperreal represented by f:R->R, it is tempting to define a derivative operator by [f]'=[f'], but unfortunately this is not generally well-defined. We show that if the ultrafilter in question is idempotent and contains (0,epsilon) for arbitrarily small real epsilon then the desired derivative operator is well-defined for all f such that [f'] exists. We also introduce a hyperreal variation of the derivative from finite calculus, and show that it has surprising relationships to the standard derivative. We give an alternate proof, and strengthened version of, Hindman's theorem., Comment: 17 pages. Accepted to the Journal of Logic and Analysis

A fundamental question is understanding the rate at which random quantum circuits converge to the Haar measure. One quantity which is important in establishing this rate is the spectral gap of a random quantum ensemble. In this work we establish a new bound on the spectral gap of the t-th moment of a one-dimensional brickwork architecture on N qudits. This bound is independent of both t and N, provided t does not exceed the qudit dimension q. We also show that the bound is nearly optimal. The improved spectral gaps gives large improvements to the constant factors in known results on the approximate t-design depths of the 1D brickwork, of generic circuit architectures, and of specially-constructed architectures which scramble in depth O(log N). We moreover show that the spectral gap gives the dominant epsilon-dependence of the t-design depth at small epsilon. Our spectral gap bound is obtained by bounding the N-site 1D brickwork architecture by the spectra of 3-site operators. We then exploit a block-triangular hierarchy and a global symmetry in these operators in order to efficiently bound them. The technical methods used are a qualitatively different approach for bounding spectral gaps and and have little in common with previous techniques., Comment: 53 pages, 6 figures

We investigate observations of circumbinary disks (CBD), to find evidence for an equilibrium eccentricity predicted by current binary accretion theory. Although stellar binary demographics in the Milky Way show no evidence for a preferred eccentricity for binary systems, we show that actively accreting systems lie on a predicted equilibrium eccentricity curve. We constrain our sample to only systems that have well defined orbital parameters (e.g,. eccentricity, mass-ratio, inclination angle). We find observations are consistent with theory for stellar binaries that are aligned with the disk and that are separated enough that tidal circularization is negligible. This suggests that eccentricity in these systems evolves after the dissipation of the CBD, given the flat eccentricity distribution of binary systems in the Milky Way., Comment: 5 pages, 2 figures

Activation functions play a crucial role in introducing non-linearities to deep neural networks. We propose a novel approach to designing activation functions by focusing on their gradients and deriving the corresponding functions through integration. Our work introduces the Expanded Integral of the Exponential Linear Unit (xIELU), a trainable piecewise activation function derived by integrating trainable affine transformations applied on the ELU activation function. xIELU combines two key gradient properties: a trainable and linearly increasing gradient for positive inputs, similar to ReLU$^2$, and a trainable negative gradient flow for negative inputs, akin to xSiLU. Conceptually, xIELU can be viewed as extending ReLU$^2$ to effectively handle negative inputs. In experiments with 1.1B parameter Llama models trained on 126B tokens of FineWeb Edu, xIELU achieves lower perplexity compared to both ReLU$^2$ and SwiGLU when matched for the same compute cost and parameter count.

Capturing fresh information in near real-time and using it to augment existing large language models (LLMs) is essential to generate up-to-date, grounded, and reliable output. This problem becomes particularly challenging when LLMs are used for informational tasks in rapidly evolving fields, such as Web search related to recent or unfolding events involving entities, where generating temporally relevant responses requires access to up-to-the-hour news sources. However, the information modeled by the parametric memory of LLMs is often outdated, and Web results from prototypical retrieval systems may fail to capture the latest relevant information and struggle to handle conflicting reports in evolving news. To address this challenge, we present the NEON framework, designed to extract emerging entity interactions -- such as events or activities -- as described in news articles. NEON constructs an entity-centric timestamped knowledge graph that captures such interactions, thereby facilitating enhanced QA capabilities related to news events. Our framework innovates by integrating open Information Extraction (openIE) style tuples into LLMs to enable in-context retrieval-augmented generation. This integration demonstrates substantial improvements in QA performance when tackling temporal, entity-centric search queries. Through NEON, LLMs can deliver more accurate, reliable, and up-to-date responses.

The James Webb Space Telescope (JWST) is opening new frontiers of transient discovery and follow-up at high-redshift. Here we present the discovery of a spectroscopically confirmed Type Ia supernova (SN Ia; SN 2023aeax) at z=2.15 with JWST, with cadenced NIRCam observations that enable multi-band light curve fitting. SN 2023aeax lands at the edge of traditional low-z cosmology color cuts because of its blue color (peak rest-frame B-V~-0.3), but we still apply a fiducial standardization approach with the BayeSN model and find that the SN 2023aeax luminosity distance measurement is in agreement (~0.1sigma) with LambdaCDM. SN 2023aeax is only the second spectroscopically confirmed SN Ia in the dark matter-dominated Universe at z>2 (the other is SN 2023adsy), giving it rare leverage to constrain any potential evolution in SN Ia standardized luminosities. Similar to SN 2023adsy (B-V~0.8), SN 2023aeax has a fairly extreme (but opposite) color, which may be due to the small sample size or a secondary factor, such as host galaxy properties. Nevertheless, the SN 2023aeax spectrum is well-represented by normal low-z SN Ia spectra and we find no definitive evolution in SN Ia standardization with redshift. Still, the first two spectroscopically confirmed z>2 SNe Ia have peculiar colors and combine for a ~1sigma distance slope relative to LambdaCDM, the implications of which require a larger sample and dedicated host galaxy observations to investigate., Comment: Submitted to ApJL. arXiv admin note: text overlap with arXiv:2406.05089

The unique connectivity of kagome lattices gives rise to topological properties, such as flat bands and Dirac cones. When combined with ferromagnetism and a chemical potential near the 2D Dirac points, this structure offers the potential to realize the highly sought-after topological Chern magnetotransport. Recently, there was considerable excitement surrounding this possibility in the ferrimagnetic kagome metal TbMn$_\mathbf{6}$Sn$_\mathbf{6}$. However, density functional theory (DFT) calculations reveal that the 2D Chern gap lies well above the Fermi energy, challenging its relevance in the observed anomalous Hall conductivity. Here, we investigate YMn$_\mathbf{6}$Sn$_\mathbf{5.45}$Ga$_\mathbf{0.55}$, a compound with similar crystallographic, magnetic, and electronic properties to TbMn$_\mathbf{6}$Sn$_\mathbf{6}$. Our findings show that the intrinsic anomalous Hall conductivity in this material, while comparable in magnitude to that in TbMn$_\mathbf{6}$Sn$_\mathbf{6}$, is fully three-dimensional, thus providing experimental evidence that Hall conductivity in this class of materials does not originate from 2D Chern gaps. Additionally, we confirm that the newly proposed empirical scaling relation for extrinsic Hall conductivity is universally governed by spin fluctuations.

In Radio Super Novae (RSNe) a magnetic field of $(B \, \times \, r) \, = \, 10^{16.0 \pm 0.12} \, {\rm Gauss \, \times \, cm}$ is observed; these are the same numbers for Blue Super Giant (BSG) star explosions as for Red Super Giant (RSG) star explosions, despite their very different wind properties. The EHT data for M87 as well for low power radio galaxies all show consistency with just this value of the quantity $(B \, \times \, r )$, key for angular momentum and energy transport, and can be derived from the radio jet data. We interpret this as a property of the near surroundings of a black hole (BH) at near maximal rotation, independent of BH mass. In the commonly used green onion model, in which a $2 \, \pi$ flow changes over to a jet flow we interpret this as a wind emanating from the BH/accretion disk system and its surroundings. Near the BH collisions in the wind can produce a large fraction of anti-protons. In this scenario the cosmic Ray (CR) population from the wind/jet is proposed to be visible as EeV protons and anti-protons in the CR data to EeV energy, with a $E^{-7/3}$ spectrum. This can be connected to a concept of inner and outer Penrose zones in the ergo-region. The observed numbers for the magnetic field imply the Planck time as the governing time scale: A BH rotating near maximum can accept a proton per log bin of energy in an extended spectrum with the associated pions every Planck time., Comment: 81 pages, 5 figures, invited paper (in press), Frontiers in Astronomy and Space Sciences

We recall the lower-upper varieties from [Knutson '05] and give a formula for their equivariant cohomology classes, as a sum over generic pipe dreams. We recover as limits the classic and bumpless pipe dream formulae for double Schubert polynomials. As a byproduct, we obtain a formula for the degree of the $n$th commuting variety as a sum of powers of 2. Generic pipe dreams also appear in the Segre-Schwarz-MacPherson analogue of the AJS/Billey formula, and when computing the Chern-Schwarz-MacPherson class of the orbit $B_- w B_+ \subseteq Mat_{k\times n}$ or of a double Bruhat cell $B_-u B_+ \cap B_+ v B_-$.

Terwilliger algebras are finite-dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance-regular graphs. The Terwilliger algebras of the conjugacy class association schemes of the symmetric groups $\operatorname {sym}(n)$, for $3\leq n \leq 6$, have been studied and completely determined. The case for $\operatorname {sym}(7)$ is computationally much more difficult and has a potential application to find the size of the largest permutation codes of $\operatorname {sym}(7)$ with a minimal distance of at least $4$. In this paper, the dimension, the Wedderburn decomposition, and the block dimension decomposition of the Terwilliger algebra of the conjugacy class scheme of the group $\operatorname {sym}(7)$ are determined.

Though multiple instance learning (MIL) has been a foundational strategy in computational pathology for processing whole slide images (WSIs), current approaches are designed for traditional hematoxylin and eosin (H&E) slides rather than emerging multiplexed technologies. Here, we present an MIL strategy, the Fluoroformer module, that is specifically tailored to multiplexed WSIs by leveraging scaled dot-product attention (SDPA) to interpretably fuse information across disparate channels. On a cohort of 434 non-small cell lung cancer (NSCLC) samples, we show that the Fluoroformer both obtains strong prognostic performance and recapitulates immuno-oncological hallmarks of NSCLC. Our technique thereby provides a path for adapting state-of-the-art AI techniques to emerging spatial biology assays., Comment: Findings paper presented at Machine Learning for Health (ML4H) symposium 2024, December 15-16, 2024, Vancouver, Canada, 14 pages

Model stealing, where a learner tries to recover an unknown model via carefully chosen queries, is a critical problem in machine learning, as it threatens the security of proprietary models and the privacy of data they are trained on. In recent years, there has been particular interest in stealing large language models (LLMs). In this paper, we aim to build a theoretical understanding of stealing language models by studying a simple and mathematically tractable setting. We study model stealing for Hidden Markov Models (HMMs), and more generally low-rank language models. We assume that the learner works in the conditional query model, introduced by Kakade, Krishnamurthy, Mahajan and Zhang. Our main result is an efficient algorithm in the conditional query model, for learning any low-rank distribution. In other words, our algorithm succeeds at stealing any language model whose output distribution is low-rank. This improves upon the previous result by Kakade, Krishnamurthy, Mahajan and Zhang, which also requires the unknown distribution to have high "fidelity", a property that holds only in restricted cases. There are two key insights behind our algorithm: First, we represent the conditional distributions at each timestep by constructing barycentric spanners among a collection of vectors of exponentially large dimension. Second, for sampling from our representation, we iteratively solve a sequence of convex optimization problems that involve projection in relative entropy to prevent compounding of errors over the length of the sequence. This is an interesting example where, at least theoretically, allowing a machine learning model to solve more complex problems at inference time can lead to drastic improvements in its performance.

We introduce Concept Bottleneck Protein Language Models (CB-pLM), a generative masked language model with a layer where each neuron corresponds to an interpretable concept. Our architecture offers three key benefits: i) Control: We can intervene on concept values to precisely control the properties of generated proteins, achieving a 3 times larger change in desired concept values compared to baselines. ii) Interpretability: A linear mapping between concept values and predicted tokens allows transparent analysis of the model's decision-making process. iii) Debugging: This transparency facilitates easy debugging of trained models. Our models achieve pre-training perplexity and downstream task performance comparable to traditional masked protein language models, demonstrating that interpretability does not compromise performance. While adaptable to any language model, we focus on masked protein language models due to their importance in drug discovery and the ability to validate our model's capabilities through real-world experiments and expert knowledge. We scale our CB-pLM from 24 million to 3 billion parameters, making them the largest Concept Bottleneck Models trained and the first capable of generative language modeling.

We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a certain theta function in terms of eta quotients. We also analyze certain shifted convolution $L$-series involving mock modular forms and bound certain shifted convolution sums., Comment: 19 pages, comments welcome!

Advances in Autonomous Underwater Vehicles (AUVs) have evolved vastly in short period of time. While advancements in sonar and camera technology with deep learning aid the obstacle detection and path planning to a great extent, achieving the right balance between computational resources , precision and safety maintained remains a challenge. Finding optimal solutions for real-time navigation in cluttered environments becomes pivotal as systems have to process large amounts of data efficiently. In this work, we propose a novel obstacle avoidance method for navigating 3D underwater environments. This approach utilizes a standard multibeam forward-looking sonar to detect and map obstacle in 3D environment. Instead of using computationally expensive 3D sensors, we pivot the 2D sonar to get 3D heuristic data effectively transforming the sensor into a 2.5D sonar for real-time 3D navigation decisions. This approach enhances obstacle detection and navigation by leveraging the simplicity of 2D sonar with the depth perception typically associated with 3D systems. We have further incorporated Control Barrier Function (CBF) as a filter to ensure safety of the AUV. The effectiveness of this algorithm was tested on a six degrees of freedom (DOF) rover in various simulation scenarios. The results demonstrate that the system successfully avoids obstacles and navigates toward predefined goals, showcasing its capability to manage complex underwater environments with precision. This paper highlights the potential of 2.5D sonar for improving AUV navigation and offers insights into future enhancements and applications of this technology in underwater autonomous systems. \url{https://github.com/AIRLabIISc/EROAS}, Comment: Submitted to ICRA 2025

We study the problem of finding a product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to efficiently learn a simple approximation to an arbitrary state? We give an algorithm which finds a product state with fidelity $\varepsilon$-close to optimal, using $N = n^{\text{poly}(1/\varepsilon)}$ copies of $\rho$ and $\text{poly}(N)$ classical overhead. We further show that estimating the optimal fidelity is NP-hard for error $\varepsilon = 1/\text{poly}(n)$, showing that the error dependence cannot be significantly improved. For our algorithm, we build a carefully-defined cover over candidate product states, qubit by qubit, and then demonstrate that extending the cover can be reduced to approximate constrained polynomial optimization. For our proof of hardness, we give a formal reduction from polynomial optimization to finding the closest product state. Together, these results demonstrate a fundamental connection between these two seemingly unrelated questions. Building on our general approach, we also develop more efficient algorithms in three simpler settings: when the optimal fidelity exceeds $5/6$; when we restrict ourselves to a discrete class of product states; and when we are allowed to output a matrix product state., Comment: 74 pages

We define and construct a conformally invariant energy for closed smoothly immersed submanifolds of even dimension, but of arbitrary codimension, in conformally flat Riemannian manifolds. This is a higher dimensional analogue of the Willmore energy for immersed surfaces and is given directly via a coupling of the tractor connection to the (submanifold critical) GJMS operators. In the case where the submanifold is of dimension 4 we compare this to other energies, including one found using a second simple construction that uses $Q$-operators., Comment: 29 pages

Chemical vapour deposition enables large-domain growth of ideal graphene, yet many applications of graphene require the controlled inclusion of specific defects. We present a one-step chemical vapour deposition procedure aimed at retaining the precursor topology when incorporated into the grown carbonaceous film. When azupyrene, the molecular analogue of the Stone-Wales defect in graphene, is used as a precursor, carbonaceous monolayers with a range of morphologies are produced as a function of the copper substrate growth temperature. The higher the substrate temperature during deposition, the closer the resulting monolayer is to ideal graphene. Analysis, with a set of complementary materials characterisation techniques, reveals morphological changes closely correlated with changes in the atomic adsorption heights, network topology, and concentration of 5-/7-membered carbon rings. The engineered defective carbon monolayers can be transferred to different substrates, potentially enabling applications in nanoelectronics, sensorics, and catalysis., Comment: manuscript and SI provided

A wide variety of reactions are reported to be dramatically accelerated in aqueous microdroplets, making them a promising platform for environmentally clean chemical synthesis. However to fully utilize the microdroplets for accelerating chemical reactions requires a fundamental understanding of how microdroplet chemistry differs from that of a homogeneous phase. Here we provide our perspective on recent progress to this end both experimentally and theoretically. We begin by reviewing the many ways in which microdroplets can be prepared, creating water/hydrophobic interfaces which have been frequently implicated in microdroplet reactivity due to preferential surface adsorption of solutes, persistent electric fields, and their acidity or basicity. These features of the interface interplay with specific mechanisms proposed for microdroplet reactivity, including partial solvation and possible gas phase channels. We especially highlight the role of droplet charge, which appears key to understanding how certain reactions, like the formation of hydrogen peroxide and reduced transition metal complexes, are thermodynamically possible in microdroplets. Lastly, we emphasize opportunities for theoretical advances in the microdroplet field generally, and to suggest experiments which would greatly enhance our understanding of this fascinating and emerging subject.

Large language models (LLMs) have exhibited remarkable reasoning and planning capabilities. Most prior work in this area has used LLMs to reason through steps from an initial to a goal state or criterion, thereby effectively reasoning in a forward direction. Nonetheless, many planning problems exhibit an inherent asymmetry such that planning backward from the goal is significantly easier -- for example, if there are bottlenecks close to the goal. We take inspiration from this observation and demonstrate that this bias holds for LLM planning as well: planning performance in one direction correlates with the planning complexity of the problem in that direction. However, our experiments also reveal systematic biases which lead to poor planning in the backward direction. With this knowledge, we propose a backward planning algorithm for LLMs that first flips the problem and then plans forward in the flipped problem. This helps avoid the backward bias, generate more diverse candidate plans, and exploit asymmetries between the forward and backward directions in planning problems -- we find that combining planning in both directions with self-verification improves the overall planning success rates by 4-24% in three planning domains., Comment: Under review

We study the minimum number of distinct eigenvalues over a collection of matrices associated with a graph. Lower bounds are derived based on the existence or non-existence of certain cycle(s) in a graph. A key result proves that every Johnson graph has a signed variant with exactly two distinct eigenvalues. We also explore applications to weighing matrices, linear ternary codes, tight frames, and compute the minimum rank of Johnson graphs. Further results involve the minimum number of distinct eigenvalues for graphs in association schemes, distance-regular graphs, and Hamming graphs. We also draw some connections with simplicial complexes and higher-order Laplacians., Comment: 33 pages, 2 figures, and 2 tables. This version includes new results added in Section 6. Additionally, Section 7, which discusses the summary and further questions, has been introduced

In this work, the recently introduced fluid-like treatment of the phase-space has been further extended and some interesting outcomes have been presented. A modified form of the Vlasov equation has been presented which describes the diffusion of the phase-space density. This anisotropic diffusion is analysed and the flow of the phase-space probability field is shown. Growth of phase-space vortices is then shown due to increased turbulent-like flow, which is marked by the dominating inertial flow above the diffusive flow. The nature of this flow is judged by using a parameter for the phase-space. It is then shown that the formation of phase-space vortices is due to growth of turbulent-like flow in the phase-space. On the bases of the diffusion parameters, the vorticity field transport of the hydrodynamic phase-space is studied and a Schamel-KdV form of the vorticity transport equation is derived, suggesting solitary modes of the phase-space vorticity waves.

Disentanglement, or identifying salient statistically independent factors of the data, is of interest in many areas of machine learning and statistics, with relevance to synthetic data generation with controlled properties, robust classification of features, parsimonious encoding, and a greater understanding of the generative process underlying the data. Disentanglement arises in several generative paradigms, including Variational Autoencoders (VAEs), Generative Adversarial Networks and diffusion models. Particular progress has recently been made in understanding disentanglement in VAEs, where the choice of diagonal posterior covariance matrices is suggested to promote mutual orthogonality between columns of the decoder's Jacobian. We continue this thread to show how this linear independence translates to statistical independence, completing the chain in understanding how the VAE's objective identifies independent components of, or disentangles, the data.

Hybrid quantum-classical computing algorithms offer significant potential for accelerating the calculation of the electronic structure of strongly correlated molecules. In this work, we present the first quantum simulation of conical intersections (CIs) in a biomolecule, cytosine, using a superconducting quantum computer. We apply the Contracted Quantum Eigensolver (CQE) -- with comparisons to conventional Variational Quantum Deflation (VQD) -- to compute the near-degenerate ground and excited states associated with the conical intersection, a key feature governing the photostability of DNA and RNA. The CQE is based on an exact ansatz for many-electron molecules in the absence of noise -- a critically important property for resolving strongly correlated states at CIs. Both methods demonstrate promising accuracy when compared with exact diagonalization, even on noisy intermediate-scale quantum computers, highlighting their potential for advancing the understanding of photochemical and photobiological processes. The ability to simulate these intersections is critical for advancing our knowledge of biological processes like DNA repair and mutation, with potential implications for molecular biology and medical research.

The dielectric layers surrounding a metasurface have a large impact on its frequency and angular response. The notion of effective permittivity captures this dependence by suggesting that a layered dielectric environment will perturb metasurface resonances in the same manner as an infinite environment of that effective permittivity. A model for effective permittivity is presented in this work. In contrast to previous empirically derived models, this multi-term model is a robust approximation based on the modal expansion of fields at the metasurface. A simple dipole metasurface array is simulated to demonstrate the accuracy of the model, which is shown to be improved over other models. Finally, we show that it is possible for dielectric layers to produce an effective permeability different than unity, which must be considered in conjunction with higher-order equivalent circuit modeling to effectively predict metasurface impedance variation., Comment: 15 pages, 18 figures. This work has been submitted to the IEEE for possible publication

The synthesis of binary nanocrystal superlattices (BNSLs) enables the targeted integration of orthogonal physical properties, like photoluminescence and magnetism, into a single superstructure, unlocking a vast design space for multifunctional materials. Yet, the formation mechanism of BNSLs remains poorly understood, restricting the use of simulation to predict the structure and properties of the superlattices. Here, we use a combination of in situ scattering and molecular simulation to elucidate the self-assembly of two common BNSLs through emulsion templating. Our self-assembly experiments reveal that no intermediate structures precede the formation of the final binary phases, indicating that their formation proceeds through classical nucleation. Using simulations, we find that, despite the formation of AlB2 and NaZn13 typically being attributed to entropy, their self-assembly is most consistent with the nanocrystals possessing short-range interparticle attraction, which we find can dramatically accelerate nucleation kinetics in BNSLs. We also find homogenous, classical nucleation in simulation, corroborating our experiments. These results establish a robust correspondence between experiment and theory, paving the way towards a priori prediction of BNSLs.

Renewable energy is becoming an increasingly important component of energy systems. However, renewable energy production is heavily dependent on the prevailing weather conditions, which are changing as a result of climate change. It is therefore necessary to build energy systems that are robust to energy shortages caused by weather-dependent changes to energy demand and renewable energy production. To design such systems, we must monitor how changes in the climate are expected to influence future energy production and demand; this is important for policymakers to decide when, where, and by how much renewable energy installed capacities should be increased, for example. In this paper, we study the behaviour of standardised energy indices in future European climate projections, and use this to monitor how characteristics of energy production droughts in Europe are expected to change in the future. We use these results to make suggestions regarding how the energy mix should be adapted in the future to decrease the risk of energy production droughts., Comment: Main body: 14 pages, 7 Figures. Under review at Environmental Research Letters

Observational constraints on classical novae are heavily biased to phases near optical peak and later because of the simple fact that novae are not typically discovered until they become bright. The earliest phases of brightening, coming before discovery, are typically missed, but this is changing with the proliferation of wide-field optical monitoring systems including ZTF, ASAS-SN, and Evryscope. Here, we report on unprecedented observations of the fast nova V1674 Her beginning >10 mag below its optical peak and including high-cadence (2 min.) observations that chart a rise of ~8 mag in just 5 hours. Two clear breaks are identified as the light curve transitions first from rising slowly to rising rapidly, followed by a transition to an even faster, nearly linear rate of increasing flux with time. The depths of the observations allow us to place tight constraints on the size of the photosphere under the assumption of blackbody emission from a white dwarf emitting at its Eddington luminosity. We find that the white dwarf was unlikely to have overflowed its Roche lobe prior to the launch of a fast wind, which poses a challenge for explaining the Fermi $\gamma$-ray detections as the interaction of a fast wind with a slow-torus of gas stripped from the inflated white dwarf envelope by the companion. High-cadence observations of novae from Evryscope and the planned Argus Array can record the diversity of rising nova light curves and help resolve how the interplay between thermonuclear fusion, binary interaction, and shocks power their earliest light., Comment: 20 pages, 6 figures, 2 tables, accepted for publication in ApJ

Task and motion planning (TAMP) frameworks address long and complex planning problems by integrating high-level task planners with low-level motion planners. However, existing TAMP methods rely heavily on the manual design of planning domains that specify the preconditions and postconditions of all high-level actions. This paper proposes a method to automate planning domain inference from a handful of test-time trajectory demonstrations, reducing the reliance on human design. Our approach incorporates a deep learning-based estimator that predicts the appropriate components of a domain for a new task and a search algorithm that refines this prediction, reducing the size and ensuring the utility of the inferred domain. Our method is able to generate new domains from minimal demonstrations at test time, enabling robots to handle complex tasks more efficiently. We demonstrate that our approach outperforms behavior cloning baselines, which directly imitate planner behavior, in terms of planning performance and generalization across a variety of tasks. Additionally, our method reduces computational costs and data amount requirements at test time for inferring new planning domains., Comment: 8 pages, 7 figures

The evolution of galaxy sizes in different wavelengths provides unique insights on galaxy build-up across cosmic epochs. Such measurements can now finally be done at $z>3$ thanks to the exquisite spatial resolution and multi-wavelength capability of the JWST. With the public data from the CEERS, PRIMER-UDS, and PRIMER-COSMOS surveys, we measure the sizes of $\sim 3500$ star-forming galaxies at $3 \leqslant z<9$, in 7 NIRCam bands using the multi-wavelength model fitting code GalfitM. The size-mass relation is measured in four redshift bins, across all NIRCam bands. We find that, the slope and intrinsic scatter of the rest-optical size-mass relation are constant across this redshift range and consistent with previous HST-based studies at low-z. When comparing the relations across different wavelengths, the average rest-optical and rest-UV relations are consistent with each other up to $z=6$, but the intrinsic scatter is largest in rest-UV wavelengths compared to rest-optical and redder bands. This behaviour is independent of redshift and we speculate that it is driven by bursty star-formation in $z>4$ galaxies. Additionally, for $3\leqslant z<4$ star-forming galaxies at $\rm M_* > 10^{10} M_{\odot}$, we find smaller rest-$\rm 1\rm\,\mu m$ sizes in comparison to rest-optical (and rest-UV) sizes, suggestive of colour gradients. When comparing to simulations, we find agreement over $\rm M_* \approx 10^{9} - 10^{10} M_{\odot}$ but beyond this mass, the observed size-mass relation is significantly steeper. Our results show the power of JWST/NIRCam to provide new constraints on galaxy formation models., Comment: 14 pages, 9 figures, submitted to A&A

Mapping computations to processors and assigning data to memory are critical for maximizing performance in parallel programming. These mapping decisions are managed through the development of specialized low-level system code, called mappers, crafted by performance engineers. Each mapper is tailored to a specific application and optimized for the underlying machine architecture, a process that requires days of refinement and tuning from an expert. Despite advances in system research, automating mapper generation remains a challenge due to the complexity of making millions of decisions to find the optimal solution and generate the solution as code. We introduce an approach that leverages recent advances in LLM-based optimizers for mapper design. In under ten minutes, our method automatically discovers mappers that surpass human expert designs in scientific applications by up to 1.34X speedup. For parallel matrix multiplication algorithms, our mapper achieves up to 1.31X of the expert-designed solution. To achieve this, we simplify the complexity of low-level code generation by introducing a domain-specific language (DSL) that abstracts the low-level system programming details and defines a structured search space for LLMs to explore. To maximize the application performance, we use an LLM optimizer to improve an agentic system that generates the mapper code. As a result, this approach significantly reduces the workload for performance engineers while achieving substantial performance gains across diverse applications. Finally, our results demonstrate the effectiveness of LLM-based optimization in system design and suggest its potential for addressing other complex system challenges., Comment: 26 pages, 8 figures

Event-keyed summarization (EKS) requires generating a summary about a specific event described in a document, given the document and an event representation extracted from it. In this work, we extend EKS to the cross-document setting (CDEKS), in which summaries must synthesize information from accounts of the same event given by multiple sources. We introduce SEAMUS (Summaries of Events Across Multiple Sources), a high-quality dataset for CDEKS based on an expert reannotation of the FAMUS dataset for cross-document argument extraction. We present a suite of baselines on SEAMUS, covering both smaller, fine-tuned models, as well as zero- and few-shot prompted LLMs, along with detailed ablations, and a human evaluation study, showing SEAMUS to be a valuable benchmark for this new task.

Li-ion battery performance is strongly influenced by their cathodes' properties and consequently by the 3D microstructure of the particles the cathodes are comprised of. During calendaring and cycling, cracks develop within cathode particles, which may affect performance in multiple ways. On the one hand, cracks reduce internal connectivity such that electron transport within cathode particles is hindered. On the other hand, intra-particle cracks can increase the cathode reactive surface. Due to these contradictory effects, it is necessary to quantitatively investigate how battery cycling effects cracking and how cracking in-turn influences battery performance. Thus, it is necessary to characterize the 3D particle morphology with structural descriptors and quantitatively correlate them with effective battery properties. Typically, 3D structural characterization is performed using image data. However, informative 3D imaging techniques are time-consuming, costly and rarely available, such that analyses often have to rely on 2D image data. This paper presents a novel stereological approach for generating virtual 3D cathode particles that exhibit crack networks that are statistically equivalent to those observed in 2D sections of experimentally measured particles. Consequently, more easily available 2D image data suffices for deriving a full 3D characterization of cracked cathodes particles. In future research, the virtually generated 3D particles will be used as geometry input for spatially resolved electro-chemo-mechanical simulations, to enhance our understanding of structure-property relationships of cathodes in Li-ion batteries.

Which rocky exoplanets have atmospheres, and which do not? This presumably simply question is the first that must be answered in the pathway toward understanding the prevalence of nearby habitable planets. A mere 6.9 pc from Earth, the LTT 1445A system is the closest transiting M-dwarf system, and its largest known planet, at $\rm 1.31\; R_{\oplus}$ and 424 K, is one of the best rocky targets in which to search for an atmosphere. We use HST/WFC3 transmission spectroscopy with the G280 and G141 grisms to study the spectrum of LTT 1445Ab between $\rm 0.2-1.65\;\mu m$. In doing so, we uncover a flare on the neighboring star LTT 1445C, and report one of the first simultaneous near-UV/optical spectra of an M dwarf flare. The planet spectrum is consistent with a flat line, though the infrared portion displays potential features that could be explained by known opacity sources such as HCN. Some atmospheric retrievals weakly favor ($\sim2\sigma$) an atmosphere over a flat line, but it remains challenging to discern between stellar contamination, an atmosphere, and a featureless spectrum at this time. We do, however, confidently rule out $\leq100\times$ solar metallicity atmospheres. Although stellar contamination retrievals cannot fit the infrared features well, the overall spectrum is consistent with stellar contamination from hot spots, cold spots, or both. Based on the UV/optical data, we place limits on the extent of stellar variability expected in the near-infrared ($30-40$ ppm), which will be critical for upcoming JWST observations of this highly optimal target., Comment: In Review at AJ. Submitted on 08/06/2024

M dwarf systems offer a unique opportunity to study terrestrial exoplanetary atmospheres due to their smaller size and cooler temperatures. However, due to the extreme conditions these host stars impose, it is unclear whether their small, close-in rocky planets are able to retain any atmosphere at all. The Hot Rocks Survey aims to answer this question by targeting nine different M dwarf rocky planets spanning a range of planetary and stellar properties. LHS 1478 b orbits an M3-type star, has an equilibrium temperature of Teq = 585 K and experiences an instellation 21 times greater than that of Earth. We observe two secondary eclipses using photometric imaging at 15 um using the Mid-Infrared Instrument on the James Webb Space Telescope (JWST MIRI) to measure thermal emission from the dayside of the planet. We then compare these values to different atmospheric scenarios to evaluate potential heat transport and CO2 absorption signatures. We find a secondary eclipse depth of 146 +/- 56 ppm based on the first observation, while the second observation results in a non-detection due to significantly larger unexplained systematics. Based on the first observation alone, we can reject the null hypothesis of the dark (zero Bond albedo) no atmosphere bare rock model with a confidence level of 3.4 sigma. For an airless body with a Bond albedo of A=0.2, the significance decreases to 2.9 sigma. The secondary eclipse depth is consistent with the majority of atmospheric scenarios we considered, which all involve atmospheres which include different concentrations of CO2, and surface pressures from 0.1 to 10 bar. However, we stress that the two observations from our program do not yield consistent results, and more observations are needed to verify our findings. The Hot Rocks Survey serves as a relevant primer for future endeavors such as the Director's Discretionary Time (DDT) Rocky Worlds program., Comment: Submitted to A&A

We present the first emission spectrum of the hot Jupiter WASP-17 b using one eclipse observation from the JWST Near Infrared Imager and Slitless Spectrograph (NIRISS) Single Object Slitless Spectroscopy (SOSS) mode. Covering a wavelength range of 0.6 to 2.8 microns, our retrieval analysis reveals a strong detection of H2O in WASP-17b dayside atmosphere (6.4sigma). Our retrievals consistently favor a super-solar dayside H2O abundance and a non-inverted temperature-pressure profile over a large pressure range. Additionally, our examination of the brightness temperature reveals excess emission below 1 microns, suggesting the possibility of a high internal temperature (600 to 700 K) and/or contributions from reflected light. We highlight that JWST emission spectroscopy retrieval results can be sensitive to whether negative eclipse depths are allowed at optical wavelengths during light curve fitting. Our findings deepen our understanding of WASP-17b atmospheric composition while also highlighting the sensitivity of our results to pressure-temperature profile parameterizations. This work is part of a series of studies by our JWST Telescope Scientist Team (JWST-TST), in which we will use Guaranteed Time Observations to perform Deep Reconnaissance of Exoplanet Atmospheres through Multi-instrument Spectroscopy (DREAMS)., Comment: Accepted for Publication in the Astronomical Journal (AJ) October 4, 2024

We present the first spectroscopic characterisation of the dayside atmosphere of WASP-17b in the mid-infrared using a single JWST MIRI/LRS eclipse observation. From forward-model fits to the 5-12 $\mu$m emission spectrum, we tightly constrain the heat redistribution factor of WASP-17b to be 0.92$\pm$0.02 at the pressures probed by this data, indicative of inefficient global heat redistribution. We also marginally detect a supersolar abundance of water, consistent with previous findings for WASP-17b, but note our weak constraints on this parameter. These results reflect the thermodynamically rich but chemically poor information content of MIRI/LRS emission data for high-temperature hot Jupiters. Using the eclipse mapping method, which utilises the signals that the spatial emission profile of an exoplanet imprints on the eclipse light curve during ingress/egress due to its partial occultation by the host star, we also construct the first eclipse map of WASP-17b, allowing us to diagnose its multidimensional atmospheric dynamics for the first time. We find a day-night temperature contrast of order 1000 K at the pressures probed by this data, consistent with our derived heat redistribution factor, along with an eastward longitudinal hotspot offset of $18.7^{+11.1\deg}_{-3.8}$, indicative of the presence of an equatorial jet induced by day-night thermal forcing being the dominant redistributor of heat from the substellar point. These dynamics are consistent with general circulation model predictions for WASP-17b. This work is part of a series of studies by the JWST Telescope Scientist Team (JWST-TST), in which we use Guaranteed Time Observations to perform Deep Reconnaissance of Exoplanet Atmospheres through Multi-instrument Spectroscopy (DREAMS)., Comment: 28 pages, 8 figures. Published in The Astronomical Journal

We report the recent discovery of two new eruptions of the recurrent nova M31N 2017-01e in the Andromeda galaxy. The latest eruption, M31N 2024-08c, reached $R=17.8$ on 2024 August 06.85 UT, $\sim2$ months earlier than predicted. In addition to this recent eruption, a search of archival PTF data has revealed a previously unreported eruption on 2014 June 18.46 UT that reached a peak brightness of $R\sim17.9$ approximately a day later. The addition of these two eruption timings has allowed us to update the mean recurrence time of the nova. We find $\langle T_\mathrm{rec} \rangle = 924.0\pm7.0$ days ($2.53\pm0.02$ yr), which is slightly shorter than our previous determination. Thus, M31N 2017-01e remains the nova with the second shortest recurrence time known, with only M31N 2008-12a being shorter. We also present a low-resolution spectrum of the likely quiescent counterpart of the nova, a $\sim20.5$ mag evolved B star displaying an $\sim14.3$ d photometric modulation., Comment: 6 pages; 1 multi-panel figure; 1 table; expanded references; accepted for publication in the Research Notes of the AAS

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm., Comment: 28 pages

Magnetic kagome materials provide a fascinating playground for exploring the interplay of magnetism, correlation and topology. Many magnetic kagome systems have been reported including the binary FemXn (X=Sn, Ge; m:n = 3:1, 3:2, 1:1) family and the rare earth RMn6Sn6 (R = rare earth) family, where their kagome flat bands are calculated to be near the Fermi level in the paramagnetic phase. While partially filling a kagome flat band is predicted to give rise to a Stoner-type ferromagnetism, experimental visualization of the magnetic splitting across the ordering temperature has not been reported for any of these systems due to the high ordering temperatures, hence leaving the nature of magnetism in kagome magnets an open question. Here, we probe the electronic structure with angle-resolved photoemission spectroscopy in a kagome magnet thin film FeSn synthesized using molecular beam epitaxy. We identify the exchange-split kagome flat bands, whose splitting persists above the magnetic ordering temperature, indicative of a local moment picture. Such local moments in the presence of the topological flat band are consistent with the compact molecular orbitals predicted in theory. We further observe a large spin-orbital selective band renormalization in the Fe d_xy+d_(x^2-y^2 ) spin majority channel reminiscent of the orbital selective correlation effects in the iron-based superconductors. Our discovery of the coexistence of local moments with topological flat bands in a kagome system echoes similar findings in magic-angle twisted bilayer graphene, and provides a basis for theoretical effort towards modeling correlation effects in magnetic flat band systems.

The stellar mass-star formation rate (M$_\star$ - SFR) plane is essential for distinguishing galaxy populations, but how galaxies move within this plane over cosmic time remains unclear. This study aims to describe galaxy migrations in the M$_\star$ - SFR plane by reconstructing star formation histories (SFHs) for a sample of galaxies out to redshift $z < 4$. This provides insights into the physical processes driving star formation. We use data from the COSMOS field, selecting 299131 galaxies at $z < 4$ with COSMOS-Web NIRCam data (m$_\mathrm{F444W} < 27$) over 0.54 deg$^2$. Using the SED modeling code CIGALE with non-parametric SFHs, we derive physical properties and migration vectors for these galaxies. These vectors describe the direction and velocity of evolutionary paths across the M$_\star$ - SFR plane. To assess the accuracy of these vectors, we compare them to results from the Horizon-AGN simulation. Galaxies within the main sequence show low migration amplitudes and dispersed movement directions, indicating oscillation within the main sequence. Most progenitors were already on the main sequence a billion years earlier. Starburst galaxies assembled half their mass in the last 350 Myr and originated from the main sequence. Passive galaxies show uniformly declining SFHs and include massive galaxies already in the passive region at $z = 3.5-4$, with increasing density over time. Using reconstructed SFHs up to $z < 4$, we propose a coherent picture of how galaxies migrate over cosmic time in the M$_\star$ - SFR plane, highlighting the connection between major phases in the star-formation history.

The focused helium ion beam microscope is a versatile imaging and nanofabrication instrument enabling direct-write lithography with sub-10-nm resolution. Subsurface damage and swelling of substrates due to helium ion implantation is generally unwanted. However, these effects can also be leveraged for specific nanofabrication tasks. To explore this, we investigate focused helium ion beam induced swelling of bulk crystalline silicon and free-standing amorphous silicon nitride membranes using various irradiation strategies. We show that the creation of near-surface voids due to helium ion implantation can be used to induce surface nanostructure and create subsurface nanochannels. By tailoring the ion dose and beam energy, the size and depth of the swollen features can be controlled. Swelling heights of several hundred nanometers are demonstrated and for the embedded nanochannels, void internal diameters down to 30nm are shown. Potential applications include the engineering of texturized substrates and the prototyping of on-chip nanofluidic transport devices.

The development of tools and techniques to analyze and extract organizations data habits from privacy policies are critical for scalable regulatory compliance audits. Unfortunately, these tools are becoming increasingly limited in their ability to identify compliance issues and fixes. After all, most were developed using regulation-agnostic datasets of annotated privacy policies obtained from a time before the introduction of landmark privacy regulations such as EUs GDPR and Californias CCPA. In this paper, we describe the first open regulation-aware dataset of expert-annotated privacy policies, C3PA (CCPA Privacy Policy Provision Annotations), aimed to address this challenge. C3PA contains over 48K expert-labeled privacy policy text segments associated with responses to CCPA-specific disclosure mandates from 411 unique organizations. We demonstrate that the C3PA dataset is uniquely suited for aiding automated audits of compliance with CCPA-related disclosure mandates., Comment: 9 pages, EMNLP 2024