Here, we present the outcomes from the second Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry, which engaged participants across global hybrid locations, resulting in 34 team submissions. The submissions spanned seven key application areas and demonstrated the diverse utility of LLMs for applications in (1) molecular and material property prediction; (2) molecular and material design; (3) automation and novel interfaces; (4) scientific communication and education; (5) research data management and automation; (6) hypothesis generation and evaluation; and (7) knowledge extraction and reasoning from scientific literature. Each team submission is presented in a summary table with links to the code and as brief papers in the appendix. Beyond team results, we discuss the hackathon event and its hybrid format, which included physical hubs in Toronto, Montreal, San Francisco, Berlin, Lausanne, and Tokyo, alongside a global online hub to enable local and virtual collaboration. Overall, the event highlighted significant improvements in LLM capabilities since the previous year's hackathon, suggesting continued expansion of LLMs for applications in materials science and chemistry research. These outcomes demonstrate the dual utility of LLMs as both multipurpose models for diverse machine learning tasks and platforms for rapid prototyping custom applications in scientific research.

We study spinning particle/defect geometries in the context of AdS$_3$/CFT$_2$. These solutions lie below the BTZ threshold, and can be obtained from identifications of AdS$_3$. We construct the Feynman propagator by solving the bulk equation of motion in the spinning particle geometry, summing over the modes of the fields and passing to the boundary. The quantization of the scalar fields becomes challenging when confined to the regions that are causally well-behaved. If the region containing closed timelike curves (CTCs) is included, the normalization of the scalar fields enjoys an analytical simplification and the propagator can be expressed as an infinite sum over image geodesics. In the dual CFT$_2$, the propagator can be recast as the HHLL four-point function, where by taking into account the $PSL (2,\mathbb{Z})$ modular images, we recover the bulk computation. We comment on the casual behavior of bulk geometries associated with single-trace operators of spin scaling with the central charge below the BTZ threshold.

The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics -- particularly in stochastic thermodynamics -- enable precise characterizations of work, heat, and entropy production in information-processing systems driven far from equilibrium by time-dependent control protocols. A key open question is then how to design protocols that minimize thermodynamic cost while ensur- ing correct outcomes. To this end, we develop a unified framework to identify optimal protocols using fluctuation response relations (FRR) and machine learning. Unlike previous approaches that optimize either distributions or protocols separately, our method unifies both using FRR-derived gradients. Moreover, our method is based primarily on iteratively learning from sampled noisy trajectories, which is generally much easier than solving for the optimal protocol directly from a set of governing equations. We apply the framework to canonical examples -- bit erasure in a double-well potential and translating harmonic traps -- demonstrating how to construct loss functions that trade-off energy cost against task error. The framework extends trivially to underdamped systems, and we show this by optimizing a bit-flip in an underdamped system. In all computations we test, the framework achieves the theoretically optimal protocol or achieves work costs comparable to relevant finite time bounds. In short, the results provide principled strategies for designing thermodynamically efficient protocols in physical information-processing systems. Applications range from quantum gates robust under noise to energy-efficient control of chemical and synthetic biological networks.

Human epidermal growth factor receptor 2 (HER2) is a critical protein in cancer cell growth that signifies the aggressiveness of breast cancer (BC) and helps predict its prognosis. Accurate assessment of immunohistochemically (IHC) stained tissue slides for HER2 expression levels is essential for both treatment guidance and understanding of cancer mechanisms. Nevertheless, the traditional workflow of manual examination by board-certified pathologists encounters challenges, including inter- and intra-observer inconsistency and extended turnaround times. Here, we introduce a deep learning-based approach utilizing pyramid sampling for the automated classification of HER2 status in IHC-stained BC tissue images. Our approach analyzes morphological features at various spatial scales, efficiently managing the computational load and facilitating a detailed examination of cellular and larger-scale tissue-level details. This method addresses the tissue heterogeneity of HER2 expression by providing a comprehensive view, leading to a blind testing classification accuracy of 84.70%, on a dataset of 523 core images from tissue microarrays. Our automated system, proving reliable as an adjunct pathology tool, has the potential to enhance diagnostic precision and evaluation speed, and might significantly impact cancer treatment planning.

Thermodynamic uncertainty relations (TURs) express a fundamental tradeoff between the precision (inverse scaled variance) of any thermodynamic current by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend these inequalities by incorporating and analyzing the impact of higher statistical cumulants of entropy production within a general framework of time-symmetrically controlled computation. This allows us to derive an exact expression for the current that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name Thermodynamic Uncertainty Theorem (TUT). Importantly, both the minimum scaled variance current and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any current's precision. This is made explicit via a thorough numerical analysis of swap and reset computations that quantitatively compares the TUT against previous generalized TURs. Our results demonstrate how to interpolate between previously-established bounds and how to identify the most relevant TUR bounds in different nonequilibrium regimes.

The tsNET algorithm utilizes t-SNE to compute high-quality graph drawings, preserving the neighborhood and clustering structure. We present three fast algorithms for reducing the time complexity of tsNET algorithm from O(nm) time to O(n log n) time and O(n) time. To reduce the runtime of tsNET, there are three components that need to be reduced: (C0) computation of high-dimensional probabilities, (C1) computation of KL divergence gradient, and (C2) entropy computation. Specifically, we reduce the overall runtime of tsNET, integrating our new fast approaches for C0 and C2 with fast t-SNE algorithms for C1. We first present O(n log n)-time BH-tsNET, based on (C0) new O(n)-time partial BFS-based high-dimensional probability computation and (C2) new O(n log n)-time quadtree-based entropy computation, integrated with (C1) O(n log n)-time quadtree-based KL divergence computation of BH-SNE. We next present faster O(n log n)-time FIt-tsNET, using (C0) O(n)-time partial BFS-based high-dimensional probability computation and (C2) quadtree-based O(n log n)-time entropy computation, integrated with (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Finally, we present the O(n)-time L-tsNET, integrating (C2) new O(n)-time FFT-accelerated interpolation-based entropy computation with (C0) O(n)-time partial BFS-based high-dimensional probability computation, and (C1) O(n)-time interpolation-based KL divergence computation of FIt-SNE. Extensive experiments using benchmark data sets confirm that BH-tsNET, FIt-tsNET, and L-tsNET outperform tsNET, running 93.5%, 96%, and 98.6% faster while computing similar quality drawings in terms of quality metrics (neighborhood preservation, stress, edge crossing, and shape-based metrics) and visual comparison. We also present a comparison between our algorithms and DRGraph, another dimension reduction-based graph drawing algorithm.

We develop information theory for the temporal behavior of memoryful agents moving through complex -- structured, stochastic -- environments. We introduce and explore information processes -- stochastic processes produced by cognitive agents in real-time as they interact with and interpret incoming stimuli. We provide basic results on the ergodicity and semantics of the resulting time series of Shannon information measures that monitor an agent's adapting view of uncertainty and structural correlation in its environment.

Accurate downlink channel state information (CSI) is vital to achieving high spectrum efficiency in massive MIMO systems. Existing works on the deep learning (DL) model for CSI feedback have shown efficient compression and recovery in frequency division duplex (FDD) systems. However, practical DL networks require sizeable wireless CSI datasets during training to achieve high model accuracy. To address this labor-intensive problem, this work develops an efficient training enhancement solution of DL-based feedback architecture based on a modest dataset by exploiting the complex CSI features, and augmenting CSI dataset based on domain knowledge. We first propose a spherical CSI feedback network, SPTM2-ISTANet+, which employs the spherical normalization framework to mitigate the effect of path loss variation. We exploit the trainable measurement matrix and residual recovery structure to improve the encoding efficiency and recovery accuracy. For limited CSI measurements, we propose a model-driven lightweight and universal augmentation strategy based on decoupling CSI magnitude and phase information, applying the circular shift in angular-delay domain, and randomizing the CSI phase to approximate phase distribution. Test results demonstrate the efficacy and efficiency of the proposed training strategy and feedback architecture for accurate CSI feedback under limited measurements.

The Shear TEsting Programme, STEP, is a collaborative project to improve the accuracy and reliability of all weak lensing measurements in preparation for the next generation of wide-field surveys. In this first STEP paper we present the results of a blind analysis of simulated ground-based observations of relatively simple galaxy morphologies. The most successful methods are shown to achieve percent level accuracy. From the cosmic shear pipelines that have been used to constrain cosmology, we find weak lensing shear measured to an accuracy that is within the statistical errors of current weak lensing analyses, with shear measurements accurate to better than 7%. The dominant source of measurement error is shown to arise from calibration uncertainties where the measured shear is over or under-estimated by a constant multiplicative factor. This is of concern as calibration errors cannot be detected through standard diagnostic tests. The measured calibration errors appear to result from stellar contamination, false object detection, the shear measurement method itself, selection bias and/or the use of biased weights. Additive systematics (false detections of shear) resulting from residual point-spread function anisotropy are, in most cases, reduced to below an equivalent shear of 0.001, an order of magnitude below cosmic shear distortions on the scales probed by current surveys. Our results provide a snapshot view of the accuracy of current ground-based weak lensing methods and a benchmark upon which we can improve. To this end we provide descriptions of each method tested and include details of the eight different implementations of the commonly used Kaiser, Squires and Broadhurst (1995) method (KSB+) to aid the improvement of future KSB+ analyses.

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, combined with an ensemble aggregation and a distance-based threshold for classification. It imposes no requirement on the training sample size, and is shown to achieve zero misclassification error rate asymptotically when the underlying time series differ only mildly in their second-order characteristics. The new method is demonstrated to outperform a variety of state-of-the-art solutions, including wavelet-based, tree-based, convolution-based methods, as well as modern deep learning methods, through intensive numerical simulations and a real EEG data analysis for epilepsy classification.

Every day, 34 million Chicken McNuggets are sold worldwide. At most McDonalds locations in the United States today, Chicken McNuggets are sold in packs of 4, 6, 10, 20, 40, and 50 pieces. However, shortly after their introduction in 1979 they were sold in packs of 6, 9, and 20. The use of these latter three numbers spawned the so-called Chicken McNugget problem, which asks: "what numbers of Chicken McNuggets can be ordered using only packs with 6, 9, or 20 pieces?" In this paper, we present an accessible introduction to this problem, as well as several related questions whose motivation comes from the theory of non-unique factorization.

Channel state information (CSI) reporting is important for multiple-input multiple-output (MIMO) transmitters to achieve high capacity and energy efficiency in frequency division duplex (FDD) mode. CSI reporting for massive MIMO systems could consume excessive bandwidth and degrade spectrum efficiency. Deep learning (DL)-based compression integrated with channel correlations have demonstrated success in improving CSI recovery. However, existing works focusing on CSI compression have shown little on the efficient encoding of CSI report. In this paper, we propose an efficient DL-based compression framework (called CQNet) to jointly tackle CSI compression, report encoding, and recovery under bandwidth constraint. CQNet can be directly integrated within other DL-based CSI feedback works for further enhancement. CQNet significantly outperforms solutions using uniform CSI quantization and $\mu$-law non-uniform quantization. Compared with traditional CSI reporting, much fewer bits are required to achieve comparable CSI reconstruction accuracy.

Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many scenarios where this is not possible and one must instead use another ensemble, such as the diagonal, microcanonical or generalized Gibbs ensembles. However, these all require detailed information about the energy or other conserved quantities to be constructed. Here we propose a general and computationally easy approach to determine the stationary probability distribution of observables with few outcomes. Interpreting coarse measurements at equilibrium as noisy communication channels, we provide general analytical arguments in favor of the applicability of a maximum entropy principle for this class of observables. We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 non-weakly interacting spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework in both quantum integrable and chaotic models.

Semantic communication marks a new paradigm shift from bit-wise data transmission to semantic information delivery for the purpose of bandwidth reduction. To more effectively carry out specialized downstream tasks at the receiver end, it is crucial to define the most critical semantic message in the data based on the task or goal-oriented features. In this work, we propose a novel goal-oriented communication (GO-COM) framework, namely Goal-Oriented Semantic Variational Autoencoder (GOS-VAE), by focusing on the extraction of the semantics vital to the downstream tasks. Specifically, we adopt a Vector Quantized Variational Autoencoder (VQ-VAE) to compress media data at the transmitter side. Instead of targeting the pixel-wise image data reconstruction, we measure the quality-of-service at the receiver end based on a pre-defined task-incentivized model. Moreover, to capture the relevant semantic features in the data reconstruction, imitation learning is adopted to measure the data regeneration quality in terms of goal-oriented semantics. Our experimental results demonstrate the power of imitation learning in characterizing goal-oriented semantics and bandwidth efficiency of our proposed GOS-VAE.

Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such cases, one compromises and instead seeks nearly maximally predictive features. Here, we derive upper-bounds on the rates at which the number and the coding cost of nearly maximally predictive features scales with desired predictive power. The rates are determined by the fractal dimensions of a process' mixed-state distribution. These results, in turn, show how widely-used finite-order Markov models can fail as predictors and that mixed-state predictive features offer a substantial improvement.

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two $L \times L$ images using the sliced 2-Wasserstein distance in $O(L^2 \log L)$ operations. We show that our method is robust to translations, rotations and deformations in the images.

High mobility environment leads to severe Doppler effects and poses serious challenges to the conventional physical layer based on the widely popular orthogonal frequency division multiplexing (OFDM). The recent emergence of orthogonal time frequency space (OTFS) modulation, along with its many related variants, presents a promising solution to overcome such channel Doppler effects. This paper aims to clearly establish the relationships among the various manifestations of OTFS. Among these related modulations, we identify their connections, common features, and distinctions. Building on existing works, this work provides a general overview of various OTFS-related detection schemes and performance comparisons. We first provide an overview of OFDM and filter bank multi-carrier (FBMC) by demonstrating OTFS as a precoded FBMC through the introduction of inverse symplectic finite Fourier transform (ISFFT). We explore the relationship between OTFS and related modulation schemes with similar characteristics. We provide an effective channel model for high-mobility channels and offer a unified detection representation. We provide numerical comparisons of power spectrum density (PSD) and bit error rate (BER) to underscore the benefit of these modulation schemes in high-mobility scenarios. We also evaluate various detection schemes, revealing insights into their efficacies. We discuss opportunities and challenges for OTFS in high mobility, setting the stage for future research and development in this field.

Semantic communications represent a new paradigm of next-generation networking that shifts bit-wise data delivery to conveying the semantic meanings for bandwidth efficiency. To effectively accommodate various potential downstream tasks at the receiver side, one should adaptively convey the most critical semantic information. This work presents a novel task-adaptive semantic communication framework based on diffusion models that is capable of dynamically adjusting the semantic message delivery according to various downstream tasks. Specifically, we initialize the transmission of a deep-compressed general semantic representation from the transmitter to enable diffusion-based coarse data reconstruction at the receiver. The receiver identifies the task-specific demands and generates textual prompts as feedback. Integrated with the attention mechanism, the transmitter updates the semantic transmission with more details to better align with the objectives of the intended receivers. Our test results demonstrate the efficacy of the proposed method in adaptively preserving critical task-relevant information for semantic communications while preserving high compression efficiency.