We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional $\mathrm{SU}(3)$ Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as $0.045$ fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions.

Large language models (LLMs) are now routinely used to autonomously execute complex tasks, from natural language processing to dynamic workflows like web searches. The usage of tool-calling and Retrieval Augmented Generation (RAG) allows LLMs to process and retrieve sensitive corporate data, amplifying both their functionality and vulnerability to abuse. As LLMs increasingly interact with external data sources, indirect prompt injection emerges as a critical and evolving attack vector, enabling adversaries to exploit models through manipulated inputs. Through a systematic evaluation of indirect prompt injection attacks across diverse models, we analyze how susceptible current LLMs are to such attacks, which parameters, including model size and manufacturer, specific implementations, shape their vulnerability, and which attack methods remain most effective. Our results reveal that even well-known attack patterns continue to succeed, exposing persistent weaknesses in model defenses. To address these vulnerabilities, we emphasize the need for strengthened training procedures to enhance inherent resilience, a centralized database of known attack vectors to enable proactive defense, and a unified testing framework to ensure continuous security validation. These steps are essential to push developers toward integrating security into the core design of LLMs, as our findings show that current models still fail to mitigate long-standing threats.

In networked multi-agent reinforcement learning (Networked-MARL), decentralized agents must act under local observability and constrained communication over fixed physical graphs. Existing methods often assume static neighborhoods, limiting adaptability to dynamic or heterogeneous environments. While centralized frameworks can learn dynamic graphs, their reliance on global state access and centralized infrastructure is impractical in real-world decentralized systems. We propose a stochastic graph-based policy for Networked-MARL, where each agent conditions its decision on a sampled subgraph over its local physical neighborhood. Building on this formulation, we introduce BayesG, a decentralized actor-framework that learns sparse, context-aware interaction structures via Bayesian variational inference. Each agent operates over an ego-graph and samples a latent communication mask to guide message passing and policy computation. The variational distribution is trained end-to-end alongside the policy using an evidence lower bound (ELBO) objective, enabling agents to jointly learn both interaction topology and decision-making strategies. BayesG outperforms strong MARL baselines on large-scale traffic control tasks with up to 167 agents, demonstrating superior scalability, efficiency, and performance.

Introduction: This study presents FetalSleepNet, the first published deep learning approach to classifying sleep states from the ovine electroencephalogram (EEG). Fetal EEG is complex to acquire and difficult and laborious to interpret consistently. However, accurate sleep stage classification may aid in the early detection of abnormal brain maturation associated with pregnancy complications (e.g. hypoxia or intrauterine growth restriction). Methods: EEG electrodes were secured onto the ovine dura over the parietal cortices of 24 late gestation fetal sheep. A lightweight deep neural network originally developed for adult EEG sleep staging was trained on the ovine EEG using transfer learning from adult EEG. A spectral equalisation-based domain adaptation strategy was used to reduce cross-domain mismatch. Results: We demonstrated that while direct transfer performed poorly, full fine tuning combined with spectral equalisation achieved the best overall performance (accuracy: 86.6 percent, macro F1-score: 62.5), outperforming baseline models. Conclusions: To the best of our knowledge, FetalSleepNet is the first deep learning framework specifically developed for automated sleep staging from the fetal EEG. Beyond the laboratory, the EEG-based sleep stage classifier functions as a label engine, enabling large scale weak/semi supervised labeling and distillation to facilitate training on less invasive signals that can be acquired in the clinic, such as Doppler Ultrasound or electrocardiogram data. FetalSleepNet's lightweight design makes it well suited for deployment in low power, real time, and wearable fetal monitoring systems.

Usability evaluation is an essential method to support the design of effective and intuitive user interfaces (UIs). However, it commonly relies on resource-intensive, expert-driven methods, which limit its accessibility, especially for small organizations. Recent multimodal large language models (MLLMs) have the potential to support usability evaluation by analyzing textual instructions together with visual UI context. This paper investigates the use of MLLMs as assistive tools for usability evaluation by framing the task as a prioritization problem. It identifies and explains usability issues and ranks them by severity. We report a study that compares the evaluations generated by multiple MLLMs with assessments from usability experts. The results demonstrate that MLLMs can offer complementary insights and support the efficient prioritization of critical issues. Additionally, we present an interactive visualization tool that enables the transparent review and validation of model-generated findings. Based on this, we outline concepts for integrating MLLM-based usability evaluation into real-world development workflows.

Statistical learning methods for automated variable selection, such as the Least Absolute Shrinkage and Selection Operator (LASSO), elastic nets, and gradient boosting, have become increasingly popular tools for building powerful prediction models. Yet, in practice, analyses are often complicated by missing data. The most widely used approach to address missingness is multiple imputation, which involves creating several completed datasets. However, there is an ongoing debate about how to perform model selection in the presence of multiple imputed datasets. Simple strategies, such as pooling models across datasets, have been shown to have suboptimal properties. Although more sophisticated methods exist, they are often difficult to implement and therefore not widely applied. In contrast, two recent approaches extend the regularization methods LASSO and elastic nets to multiply imputed datasets by defining a single loss function, resulting in a unified set of coefficients across imputations. Our key contribution is to extend this principle to the framework of component-wise gradient boosting by proposing MIBoost, a novel algorithm that employs a uniform variable-selection mechanism across imputed datasets, together with its corresponding cross-validation routine MIBoostCV. In a simulation study, MIBoost yielded predictive performance comparable to that of other established methods, providing a practical boosting-based approach for variable selection with multiply imputed data. The proposed framework is implemented as the R package booami.

While Large Language Models (LLMs) demonstrate strong performance across domains, their long-context capabilities are limited by transient neural activations causing information decay and unstructured feed-forward network (FFN) weights leading to semantic fragmentation. Inspired by the brain's working memory and cortical modularity, we propose PaceLLM, featuring two innovations: (1) a Persistent Activity (PA) Mechanism that mimics prefrontal cortex (PFC) neurons' persistent firing by introducing an activation-level memory bank to dynamically retrieve, reuse, and update critical FFN states, addressing contextual decay; and (2) Cortical Expert (CE) Clustering that emulates task-adaptive neural specialization to reorganize FFN weights into semantic modules, establishing cross-token dependencies and mitigating fragmentation. Extensive evaluations show that PaceLLM achieves 6% improvement on LongBench's Multi-document QA and 12.5-17.5% performance gains on Infinite-Bench tasks, while extending measurable context length to 200K tokens in Needle-In-A-Haystack (NIAH) tests. This work pioneers brain-inspired LLM optimization and is complementary to other works. Besides, it can be generalized to any model and enhance their long-context performance and interpretability without structural overhauls.

Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We propose a novel objective function for tailoring error correction codes to specific noise structures by maximizing the distinguishability between quantum states after a noise channel, ensuring efficient recovery operations. We formalize this concept with the distinguishability loss function, serving as a machine learning objective to discover resource-efficient encoding circuits optimized for given noise characteristics. We implement this methodology using variational techniques, termed variational quantum error correction (VarQEC). Our approach yields codes with desirable theoretical and practical properties and outperforms standard codes in various scenarios. We also provide proof-of-concept demonstrations on IBM and IQM hardware devices, highlighting the practical relevance of our procedure.

We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the nonlinear inverse link function, which we address with our two-stage approach. We prove a *local minimax lower bound*, showing that our `GL-LowPopArt` enjoys instance-wise optimality up to the condition number of the ground-truth Hessian. Our method immediately achieves an improved Frobenius error guarantee for generalized linear matrix completion. We also introduce a new problem setting called **bilinear dueling bandits**, a contextualized version of dueling bandits with a general preference model. Using an explore-then-commit approach with `GL-LowPopArt', we show an improved Borda regret bound over naïve vectorization (Wu et al., 2024).

The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based block sparse Bayesian learning methods, and introduces a novel space power prior based on undirected graph models to adaptively capture the unknown patterns of block-sparse signals. By combining the EM algorithm with high-order equation root-solving, we develop a new structured sparse Bayesian learning method, SPP-SBL, which effectively addresses the open problem of space coupling parameter estimation in pattern-based methods. We further demonstrate that learning the relative values of space coupling parameters is key to capturing unknown block-sparse patterns and improving recovery accuracy. Experiments validate that SPP-SBL successfully recovers various challenging structured sparse signals (e.g., chain-structured signals and multi-pattern sparse signals) and real-world multi-modal structured sparse signals (images, audio), showing significant advantages in recovery accuracy across multiple metrics.

In this paper, we show that an eXtremely Large (XL) Multiple-Input Multiple-Output (MIMO) wireless system with appropriate analog combining components exhibits the properties of a universal function approximator, similar to a feedforward neural network. By treating the channel coefficients as the random nodes of a hidden layer and the receiver's analog combiner as a trainable output layer, we cast the XL MIMO system to the Extreme Learning Machine (ELM) framework, leading to a novel formulation for Over-The-Air (OTA) edge inference without requiring traditional digital processing nor pre-processing at the transmitter. Through theoretical analysis and numerical evaluation, we showcase that XL-MIMO-ELM enables near-instantaneous training and efficient classification, even in varying fading conditions, suggesting the paradigm shift of beyond massive MIMO systems as OTA artificial neural networks alongside their profound communications role. Compared to conventional ELMs and deep learning approaches, whose training takes seconds to minutes, the proposed framework achieves on par performance (above $90\%$ classification accuracy across multiple data sets) with optimization latency of few milliseconds under the same number of trainable parameters, considering rich fading, low noise channels with XL receive antennas, making it highly attractive for inference tasks with ultra-low-power devices.

We propose a fully decentralized multi-agent world model that enables both symbol emergence for communication and coordinated behavior through temporal extension of collective predictive coding. Unlike previous research that focuses on either communication or coordination separately, our approach achieves both simultaneously. Our method integrates world models with communication channels, enabling agents to predict environmental dynamics, estimate states from partial observations, and share critical information through bidirectional message exchange with contrastive learning for message alignment. Using a two-agent trajectory drawing task, we demonstrate that our communication-based approach outperforms non-communicative models when agents have divergent perceptual capabilities, achieving the second-best coordination after centralized models. Importantly, our decentralized approach with constraints preventing direct access to other agents' internal states facilitates the emergence of more meaningful symbol systems that accurately reflect environmental states. These findings demonstrate the effectiveness of decentralized communication for supporting coordination while developing shared representations of the environment.

In recent years, researchers have leveraged social relations to enhance recommendation performance. However, most existing social recommendation methods require carefully designed auxiliary social tasks tailored to specific scenarios, which depend heavily on domain knowledge and expertise. To address this limitation, we propose Automatic Self-supervised Learning for Social Recommendations (AusRec), which integrates multiple self-supervised auxiliary tasks with an automatic weighting mechanism to adaptively balance their contributions through a meta-learning optimization framework. This design enables the model to automatically learn the optimal importance of each auxiliary task, thereby enhancing representation learning in social recommendations. Extensive experiments on several real-world datasets demonstrate that AusRec consistently outperforms state-of-the-art baselines, validating its effectiveness and robustness across different recommendation scenarios.

Social recommendation models weave social interactions into their design to provide uniquely personalized recommendation results for users. However, social networks not only amplify the popularity bias in recommendation models, resulting in more frequent recommendation of hot items and fewer long-tail items, but also include a substantial amount of redundant information that is essentially meaningless for the model's performance. Existing social recommendation models often integrate the entire social network directly, with little effort to filter or adjust social information to mitigate popularity bias introduced by the social network. In this paper, we propose a Condition-Guided Social Recommendation Model (named CGSoRec) to mitigate the model's popularity bias by denoising the social network and adjusting the weights of user's social preferences. More specifically, CGSoRec first includes a Condition-Guided Social Denoising Model (CSD) to remove redundant social relations in the social network for capturing users' social preferences with items more precisely. Then, CGSoRec calculates users' social preferences based on denoised social network and adjusts the weights in users' social preferences to make them can counteract the popularity bias present in the recommendation model. At last, CGSoRec includes a Condition-Guided Diffusion Recommendation Model (CGD) to introduce the adjusted social preferences as conditions to control the recommendation results for a debiased direction. Comprehensive experiments on three real-world datasets demonstrate the effectiveness of our proposed method.

Designing seamless, frictionless user experiences has long been a dominant trend in both applied behavioral science and artificial intelligence (AI), in which the goal of making desirable actions easy and efficient informs efforts to minimize friction in user experiences. However, in some settings, friction can be genuinely beneficial, such as the insertion of deliberate delays to increase reflection, preventing individuals from resorting to automatic or biased behaviors, and enhancing opportunities for unexpected discoveries. More recently, the popularization and availability of AI on a widespread scale has only increased the need to examine how friction can help or hinder users of AI; it also suggests a need to consider how positive friction can benefit AI practitioners, both during development processes (e.g., working with diverse teams) and to inform how AI is designed into offerings. This paper first proposes a "positive friction" model that can help characterize how friction is currently beneficial in user and developer experiences with AI, diagnose the potential need for friction where it may not yet exist in these contexts, and inform how positive friction can be used to generate solutions, especially as advances in AI continue to be progress and new opportunities emerge. It then explores this model in the context of AI users and developers by proposing the value of taking a hybrid "AI+human" lens, and concludes by suggesting questions for further exploration.

We consider the three-dimensional incompressible Euler equations for helical flows without swirl. By adapting gluing techniques, we construct the first smooth multi-vortex solution in the whole space $\mathbb{R}^3$ exhibiting a cluster of collapsing helical filaments, with the associated cross-sectional vorticity remaining compactly supported in $\mathbb{R}^2$ for all times. Our result generalises previous collapsing configurations in $\mathbb{R}^3$ with rapidly decaying vorticity cores, and extends related variational solutions obtained in infinite cylindrical domains.

We construct effective $\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau theories for Abelian and non-Abelian fractional quantum Hall hierarchies for those which had previously been described only through categorical data or trial wavefunctions. Our framework captures both Abelian hierarchy states built on half-filled Pfaffian-type parents and non-Abelian hierarchies emerging from Abelian states. It reproduces all filling fractions obtained from wavefunction and categorical constructions and, moreover, uniquely determines the corresponding topological orders. We also identify an intriguing particle-hole symmetry relating two hierarchy sequences, one built on a trivial insulator and the other on the $ν=1$ integer quantum Hall state, which respectively generate the Read-Rezayi sequences and their particle-hole conjugates under the same hierarchy construction.

Retrieval Augmented Generation (RAG) systems deployed across organizational boundaries face fundamental tensions between security, accuracy, and efficiency. Current encryption methods expose plaintext during decryption, while federated architectures prevent resource integration and incur substantial overhead. We introduce Trans-RAG, implementing a novel vector space language paradigm where each organization's knowledge exists in a mathematically isolated semantic space. At the core lies vector2Trans, a multi-stage transformation technique that enables queries to dynamically "speak" each organization's vector space "language" through query-centric transformations, eliminating decryption overhead while maintaining native retrieval efficiency. Security evaluations demonstrate near-orthogonal vector spaces with 89.90° angular separation and 99.81% isolation rates. Experiments across 8 retrievers, 3 datasets, and 3 LLMs show minimal accuracy degradation (3.5% decrease in nDCG@10) and significant efficiency improvements over homomorphic encryption.

Molecular docking is a crucial step in the development of new drugs as it guides the positioning of a small molecule (ligand) within the pocket of a target protein. In the literature, a feasibility study explored the potential of D-Wave quantum annealers for purely geometric molecular docking, neglecting physicochemical interactions between the protein and the ligand and focusing solely on their simplified geometries. To achieve this, the ligands were represented as graphs incorporating their geometric properties and then mapped onto a grid that discretized the three-dimensional space of the protein pocket. The quality of the ligand pose on the protein pocket was evaluated through the isomorphism between the ligand graph and the spatial grid. This paper builds on the previous study by introducing physicochemical interactions between the protein-ligand pair into the QUBO problem to improve the accuracy of the docking results. This paper presents a novel QUBO formulation that includes Coulomb and van der Waals forces, together with components representing H-bond and hydrophobic interactions. We integrate these physical interactions as corrective terms to the previous purely geometric QUBO formulation, and provide experimental results using the D-Wave quantum annealers to demonstrate their impact on the accuracy of the docking results.

We combine the highest resolution N-body simulation of a $\sim 10^{12}\, M_\odot$ $Λ$CDM halo (Aquarius-A) with the {\sc GALFORM} galaxy formation semianalytic model to study the full satellite population expected in a MW-like galaxy. The model assumes that galaxies only form in subhalos whose peak circular velocity exceeds the H-cooling threshold, all of which are well resolved in the simulation. The number of luminous subhalos ever accreted into the main halo is thus well defined, and implies that the total number of MW satellites, down to arbitrarily low luminosity, should not exceed a few hundred. The model tracks satellites even after their halos cease to be resolved ("orphan" galaxies), and includes a novel treatment of dark matter and stellar tidal stripping which takes into account that all $Λ$CDM subhalos survive until the present because of their cuspy inner density profiles. After accounting for tides, our results match well the massive end of the observed MW satellite mass function and predict that a large number of ultra-faint dwarfs are missing from the current MW satellite census. The missing UFDs are predicted to avoid the innermost regions of the host, and to have properties that overlap with those of the many ultra-faint compact MW satellites (UFCSs) discovered recently, with properties intermediate between globular clusters and dwarf galaxies. Our results suggest that many UFCS systems are dark matter-dominated dwarfs with velocity dispersions between $1-3$km/s, which have survived disruption because they reside in the dense cusp of $Λ$CDM subhalos. UFCSs should have mean densities of order $10^{10}$-$10^{11}\,M_\odot/$kpc$^3$, higher than those of more extended ultra-faint systems. If confirmed, our results would provide support for the cuspy nature of $Λ$CDM dark matter halos and for the hydrogen-cooling threshold for galaxy formation.

The Difference-of-Gaussian (DoG) is a widely used operator across applications, including image processing (feature and edge detection), quantum machine learning, and finite-difference methods (approximations of the Laplacian-of-Gaussian). In this paper, we construct an explicit quantum block encoding of the DoG operator on a periodic grid, exploiting its natural probabilistic structure. The central observation is that the DoG admits a natural decomposition to two normalized Gaussian distributions, each preparable by explicit and efficient circuits, with the negation encoded using a single Pauli-$Z$ gate on a branch-indicator qubit. This enables the operator's block encoding to be directly mapped to the Linear Combination of Unitaries framework without requiring signed amplitude loading, quantum random-access memory, or any other black-box oracles. The proposed method achieves a constant subnormalization factor $λ= 2$ independent of the grid size $N$, the spatial dimension $D$, and the stencil width. Additionally, we show that the DoG operator is diagonalized by the discrete Fourier basis, which allows us to derive an exact closed-form expression for the block-encoding success probability in terms of the input signal's power spectrum, weighted by the operator's transfer function. Finally, we prove that the expression reduces to $O(h^4)$ scaling with respect to grid spacing $h$ as the periodic grid becomes finer. This implementation provides an explicit construction method for a tunable, wide-stencil bandpass filter whose frequency response is controlled by two Gaussian scale parameters.

We prove results that imply, under various hypotheses, that every elliptic curve over a number field $k$ corresponding to a point on a modular curve has bad reduction at a certain prime $p$ of $\mathcal{O}_k$. For example, every elliptic curve with a cyclic torsion subgroup of order 20 defined over $\mathbb{Q}(\sqrt{-11})$ or $\mathbb{Q}(\sqrt{17})$ has bad reduction at all primes lying over $3$. The proofs of these statements are quite different, since $3$ is split in $\mathbb{Q}(\sqrt{-11})$ and inert in $\mathbb{Q}(\sqrt{17})$.

The Optimal Polynomial Intersection (OPI) problem is the following: Given sets $S_1, \ldots, S_m \subseteq \mathbb{F}$ and evaluation points $a_1, \ldots, a_m \in \mathbb{F}$, find a polynomial $Q \in \mathbb{F}[x]$ of degree less than $n$ so that $Q(a_i) \in S_i$ for as many $i \in \{1, 2, \ldots, m\}$ as possible. Decoded Quantum Interferometry (DQI) is a quantum algorithm that efficiently returns good solutions to the problem, even on worst-case instances (Jordan et. al., 2025). The quality of the solutions returned follows a semicircle law, which outperforms known efficient classical algorithms. But does DQI obtain the best possible solutions? That is, are there solutions better than the semicircle law for worst-case OPI instances? Surprisingly, before this work, the best existential results coincide with (and follow from) the best algorithmic results. In this work, we show that there are better solutions for worst-case OPI instances over prime fields. In particular, DQI and the semicircle law are not optimal. For example, when the lists $S_i$ have size $ρp$ for $ρ\sim 1/2$, our results imply the existence of a solution that asymptotically beats the semicircle law whenever $n/m \geq 0.6225$, and we show that an asymptotically perfect solution exists whenever $n/m \geq 0.7496$. Our results generalize to Max-LINSAT problems derived from any Maximum Distance Separable (MDS) code, and to any $ρ\in (0,1)$. The key insight to our improvement is a connection to local leakage resilience of secret sharing schemes. Along the way, we recover several re-proofs of the existence of solutions achieving the semicircle law.

We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the invasion of stripe and hexagonal patterns into the spatially homogeneous state and model a possible mechanism for pattern formation, as observed in a wide range of real-world applications. For this, we develop a rigorous framework to establish the existence of such solutions using spatial dynamics and non-standard centre manifold theory. Our approach exploits geometric and algebraic structures generic to $\mathrm{O}(2)$-symmetric pattern-forming systems near a Turing instability, and addresses fundamental technical challenges due to a non-uniform spectral gap around the imaginary axis, quadratic resonances induced by the hexagonal structure, and the high-dimensional phase space of the reduced equations.

A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators that are not diagonal in the measurement basis. In this paper we take a step towards addressing this issue in the context of Boson superfluids, where standard in-situ imaging yields only the spatially resolved density, leaving the phase field - crucial for identifying topological defects such as vortices and confirming superfluidity - indirectly encoded. Previous work has shown that the location of vortices in the phase field may be detected, but has not solved the problems of fully reconstructing the phase or identifying the charge (vortex vs. antivortex). This paper shows that a combination of a deep machine learning (ML) model and classical computer vision post-processing steps can address this gap. We use realistic snapshots of the thermal state of a two-dimensional BEC in a harmonic trap using synthetic data obtained from projected Gross-Pitaevskii equation simulations to train a U-Net-based architecture to infer the absolute values of the phase field gradients from an observed density field, and then employ a separate ML model to locate the positions of the vortex cores and a post-processing graphical analysis to determine with high accuracy the phase field, including the quantized charge of each vortex.

Planet formation remains a fundamentally important yet poorly understood process. Protoplanetary disks, the birthplaces of planetary systems, exhibit a wide range of substructures that are increasingly interpreted as signatures of interactions with forming planets. However, the direct detection rate of protoplanets within these disks remains low, leaving critical gaps in our understanding of the physical mechanisms driving their formation and early evolution. In this chapter, we review recent efforts by the high-contrast imaging community to directly observe forming protoplanets and their immediate environments. These observations aim to provide key constraints on thermal and accretion processes, planetary growth, and the formation of circumplanetary disks and satellite systems. We also propose a path forward for deriving observational estimates of the planet mass-to-radius ratio ($M_p/R_p$), a crucial parameter for distinguishing between competing formation models and understanding the thermal evolution of young planets. Finally, we highlight how upcoming instruments on the Extremely Large Telescope (ELT), with their unprecedented combination of high spatial and spectral resolution, will transform our ability to probe planet formation at the smallest and most critical scales.

Lattice compression has emerged as a fundamental tuning parameter for nickelate superconductivity. Pressure acts as a trigger to induce superconductivity in bulk Ruddlesden-Popper nickelates. For infinite-layer nickelate thin films, compressive epitaxial strain and rare-earth ion chemical pressure have been used to substantially enhance the superconducting transition temperature ($T_c$). Efforts to go further have been constrained by the limits of epitaxial stability or the challenges of measuring thin films in high-pressure environments. Here, we overcome this limitation by developing a technique to incorporate freestanding infinite-layer $\mathrm{Nd_{0.85}Sr_{0.15}NiO_2}$ membranes into a diamond anvil cell. Using this platform, we observe a strong increase in $T_c$ up to our highest measurement pressure of $\sim$90 GPa, where a superconducting downturn can be observed near liquid nitrogen temperatures. Strikingly, we find a simple linear enhancement of $T_c$ at a rate of 0.65 K GPa$^{-1}$, with no signs of saturation. This suggests that the pairing strength in infinite-layer nickelates can be raised to a surprisingly high scale, using an approach that can be broadly applied to many two-dimensional materials.

The vertical redistribution of materials in the lunar regolith - ranging from continuously produced space-weathering products to sporadic pulses of supernova- or kilonova-derived isotopes - remains a fundamental problem in planetary science. We present a unified stochastic model of regolith gardening induced by the impact flux. Treating gardening as a competition between impact-driven advection and diffusion predicts the maturity profiles of Apollo cores over more than two orders of magnitude in time ($1.4 \times 10^7$ to $4.5 \times 10^8$ years). This model describes well the depth profiles of live Fe60 in Apollo regolith samples, suggesting that supernova dust capture is independent of native iron abundance, and is consistent with a uniform influx at the latitudes of the Apollo landing sites. We extend our model to predict lunar signals for live r-process species that might originate from supernovae or kilonovae: Pu244 tied to terrestrial detections, and I129, Hf182, and Cm247 based on r-process calculations. The Pu244/Fe60 depth profile can probe the origin of Pu244, motivating searches in Artemis regolith samples down to depths O(100) cm.

Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and that satisfy additional composition requirements, such as a minimum population/weight threshold or balanced weight types (e.g., political affiliations). We aim to maximize coverage by disjoint districts that meet these requirements. In this work, we present new results that substantially improve the previously known bounds on balanced star districts for planar and minor-free graphs (Dharangutte et al. 2025). In particular, we improve the approximation factor from $O(\log n)$ to $O(1)$ for packing balanced star districts using the exact same algorithm, but with a refined analysis. We also extend the results beyond planar graphs to minor-free graphs and an even broader family of graphs of bounded expansion. Additionally, we obtain an $O(1)$ approximation for packing radius-$k$ districts (with a constant $k$) in planar and apex-minor-free graphs. In order to get a $(1+\varepsilon)$ approximation on the max coverage, we show that this can be achieved if we allow a slight relaxation of the balancedness parameters (by a factor that can be made arbitrarily close to $1$), for bounded radius-$k$ districts on planar and apex-minor-free graphs. We show that all of these results can also be obtained if we enforce a minimum weight threshold for each district as the composition requirement, rather than balancedness. We present various results on hardness and hardness of approximation for this variant, by graph and district types.

A 0/1-polytope is the convex hull of a subset $V\subseteq \{0,1\}^n$. A celebrated conjecture of Mihail and Vazirani asserts that the graph of every 0/1-polytope has edge-expansion at least 1. In this paper, we show that typical 0/1-polytopes have significantly stronger expansion. Specifically, if $V$ is formed by sampling each vertex of $\{0,1\}^n$ independently with constant probability $p$, then with high probability the edge-expansion is $Θ(n)$ for $p \in (1/2, 1)$, and $n^{Θ(\log \log n)}$ for $p \in (0, 1/2)$. This improves the previously best known bound $Ω(1)$ due to Ferber, Krivelevich, Sales and Samotij.