Papers

Large language models are increasingly deployed as course-specific tutors, but their usefulness depends on grounding in vetted instructional materials that are often revised mid-semester. Our prior work built a multimodal retrieval-augmented generation (RAG) system over an authentic machine learning course corpus (Foundations of Machine Learning) and found that retrieval improved contextual grounding, but that fixed retrieval strategies were suboptimal. That motivates a different question: whether how a corpus is structured at ingest time matters more than how much is retrieved at query time. We present a controlled head-to-head comparison of two knowledge representations over an identical classroom corpus: (A) vector RAG, replicating the best-performing configuration from our prior study, and (B) an LLM-compiled wiki (Karpathy framework), in which the corpus is synthesized at ingest into linked concept pages with explicit cross-references and citations back to source materials. We evaluate 59 questions spanning single-fact recall, cross-unit concept linking, synthesis and explanation, and currency after a syllabus revision, scored by an LLM judge against a human-authored rubric. Both representations answered single-fact questions about equally well (9.33 vs. 9.96 of 10), but diverged sharply on questions requiring links across course units. The compiled wiki remained accurate and grounded (9.93; 100% grounded in cited sources), while retrieval scored lower and was markedly less grounded (8.14; 64%). The wiki's citations let students and instructors trace any claim back to the lecture that introduced it, adding a layer of dynamic retrieval that machine learning courses require. While further testing is needed, instructors using AI to support learning in ML courses should consider wiki-based structure for its potential to support foundational elements of best practice.

Transmission latency significantly degrades user quality of experience in real-time interactive perception systems. In remote driving, maintaining reliable visual feedback is critical for safe operation under dynamic network variability. Although video prediction offers a promising approach to compensate for short-term transmission delays and approximate near-zero-latency streaming, prediction-only methods remain vulnerable in highly dynamic scenes, especially when newly emerged objects appear during uplink outages. To address these challenges, we propose a multi-agent video prediction framework that combines continuous edge-side video prediction with lightweight mask-guided conditional frame reconditioning. The framework consists of three role-specialized agents: a continuous prediction agent for low-latency visual continuity, a vehicle-side trigger agent for detecting newly appeared objects, and a conditional reconditioning agent that repairs the predictor conditioning state using sparse mask guidance. This design enables semantic recovery of exogenous scene changes without requiring full-frame retransmission. We validate the proposed framework through extensive experiments on benchmark video data under realistic 5G communication traces. Results show that our method improves semantic recovery of novel objects while preserving perceptual quality and practical runtime efficiency under network-induced disruptions.

This paper establishes a mesoscopic central limit theorem for linear statistics of $\beta$-ensembles or log-gas, as the dimension $N\to\infty$, in the temperature regime $1/N\ll\beta(N)\le 1$. For simplicity, we assume that the potential is one-cut regular and analytic. In this regime, the size of the fluctuations depends on $\beta(N)$ and the mesoscopic scale. We show that there is a transition at a critical $\eta\asymp 1/ N\beta(N)$ between a Random Matrix regime, where the limiting variance is given by the $\mathsf{H}^{1/2}$-norm and a Poisson regime where the limiting variance is given by the $L^2$-norm. We also describe the critical regime. The proof of the CLT relies on optimal local laws at intermediate temperatures and Stein's method for $\beta$-ensembles. In particular, in this regime, it is necessary to construct new correction terms to the classical equilibrium measure to obtain a suitable re-centring of linear statistics and describe their fluctuations. We also obtain a free energy expansion.

To demonstrate the astrometric capability of the combined Korean VLBI (Very Long Baseline Interferometry) Network (KVN) and VLBI Exploration of Radio Astrometry (VERA) Array (KaVA), we conducted six-epoch VLBI observations of 22-GHz H$_{2}$O masers associated with the star-forming region W3(OH). Two atmospheric calibration methods, (1) GPS and (2) JMA (Japan Meteorological Agency) mesoscale analysis data, and two phase-reference sources were independently applied to the astrometric analysis. Trigonometric parallaxes of W3(OH) were successfully measured with all calibration strategies, including the first successful parallax measurement using JMA calibration. The combined-fit parallax is 0.497$\pm$0.024 mas, corresponding to a distance of 2.01$^{+0.10}_{-0.09}$ kpc. This value is consistent with the previous Very Long Baseline Array (VLBA) result of 0.489$\pm$0.017 mas. KaVA achieved a 55$\%$ higher signal-to-noise ratio in phase-referenced maps than VERA, in good agreement with theoretical expectations. These results suggest that KaVA will enable trigonometric parallax measurements of 22-GHz H$_2$O masers that are difficult to observe with VERA alone because of low flux densities and/or limited $uv$ coverage. A flux variation from 510\,$\pm$\,50 to 3900\,$\pm$\,400 Jy was detected in W3(OH) over a one-year observing campaign and is attributed to two nearby maser features separated by only $\sim$64 AU at 2.01 kpc. The brightest feature showed a decrease in linewidth with increasing peak flux density, consistent with unsaturated maser amplification, whereas no similar trend was found for the other feature, suggesting different responses to the same amplification conditions, possibly owing to differences in saturation state and internal velocity structure.

On repeated work, agents are inconsistent. We ran 42 tasks three times each and found that, depending on the model, 38% to 74% returned answers that did not agree. Consistency is what a buyer, an auditor, or a regulator requires, and agents do not have it. They are wasteful too: 95.3% to 97.2% of what an agent generates goes to re-deriving a plan the system already knows. We propose skill habit formation. An agent mines its own execution history for candidate skills, deterministic variants that compete against the incumbent rather than replacing it. A candidate declares the region of input space it claims, so the common case runs as a script and the rest falls through to reasoning. Four gates of ascending cost admit candidates; the central one tests a candidate's execution trace against a retained reference, within a tolerance measured from that reference's own run-to-run variability. On text-to-SQL, three of four reasoning arms reproduced their own output on 11 to 13 of 42 repeated questions and the fourth on 26 of 42, while a habit-formed variant reproduced on all 456 dispatches we repeated and was non-inferior to every arm it replaced (p<0.0001). It also used 14% to 56% fewer tokens, turning net positive after 7 to 53 reuses. We measured what this costs in accuracy. The guard admitted work it should have deferred on 2.6% of natural paraphrases and 26% of inputs near its boundary, and 11 of 13 such failures were invisible to the trace-conformance gate at any threshold. Deterministic errors repeat exactly: a bad habit is as reliable as a good one, and that is the price of the property that makes the system auditable. Separating routing from parameter extraction raised end-to-end accuracy from 0.888 to 0.952 at 43% of the cost.

Cultural evaluation coverage and robustness in language models are difficult to diagnose because pretraining corpora and cultural benchmarks are rarely indexed with comparable metadata. Benchmarks increasingly target culturally situated phenomena at the level of languages, regions, and locale-specific practices, while web-scale corpora are usually organized only by language. A shared culture-language-region layer makes these resources comparable, enabling audits of whether a target cultural phenomenon is represented in pretraining data, evaluated by benchmarks or both. To this end, we introduce FineWeb-CLaR, a large-scale annotated dataset derived from FineWeb and FineWeb-2 that places web documents on a shared culture-language-region axis for corpus auditing and benchmark alignment. FineWeb-CLaR annotates the full 30.9B-document collection from FineWeb and FineWeb-2 with URL-derived region labels and cultural-topic provenance. Our region resolver assigns a non-empty region to 25.61% of documents (7.92B). For cultural-topic analysis, we induce locale-specific topics and project them onto the 14 leaves of the Cultural Taxonomy of Liu et al. (2025), producing Locale Topic Distributions (LTDs) for corpus-side comparison. We also annotate 277 cultural NLP benchmarks with the same taxonomy, language coverage, and region coverage. Together, these resources enable direct comparison between corpus-side pretraining evidence and benchmark-side evaluation coverage.

Prioritized experience replay (PER) improves sample efficiency by replaying high-priority transitions, usually according to absolute temporal-difference error. In stochastic environments, PER can distort the distribution of realized outcomes replayed from transitions with the same state-action pair. We call this within-group self-selection. We quantify the resulting changes in within-group outcome frequencies and mean Bellman targets. We decompose PER into between-group allocation and conditional sibling selection, and derive fixed-buffer corrections that preserve current group-level priority mass: SAMPLE selects a group through PER and trains on a uniformly sampled sibling; AVG averages sibling Bellman targets; and MODEL samples from an empirical full-outcome model. In exact state-action environments with rare high-magnitude outcomes, sibling-aware replay improves learning efficiency over PER, although matched parameter sweeps show that tuning can narrow some gaps. In MinAtar, approximate VQ-VAE groups with SAMPLE mitigate degradation under mean-preserving reward tails in four of five games. Sibling-aware replay thus retains the focus on high-priority state-action regions while recovering their empirical outcome frequencies.

We apply the momentous quantum mechanics formalism to the non-perturbative study of superconducting circuits in the transmon regime, deriving effective equations of motion for the bare Josephson junction (JJ), the cavity–JJ system, and a dissipative resonator. A Gaussian closure on the hierarchy of quantum moments resums the full cosine nonlinearity into the closed-form effective Hamiltonian $\tfrac{1}{2}[V(\phi+\phi_s)+V(\phi-\phi_s)]$, which is non-perturbative and preserves the periodicity and boundedness of the Josephson potential at all phase amplitudes; the standard Kerr (Duffing) approximation is recovered as a special case. We derive the quantum-dressed frequency $\omega_{\rm eff}=\Omega_p\sqrt{\cos(\phi_{\rm zpf}/\phi_0)}$, and benchmark the effective dynamics against exact Mathieu-function diagonalization, with the quantum width $G^{2,0}(t)$ providing the most sensitive diagnostic of the closure's validity and marks the boundary of the Gaussian approximation more sharply than $\langle\hat\phi\rangle(t)$ does. We compare the Caldirola–Kanai, Bateman, and Lindblad descriptions: the Bateman dynamics, quantized with a switched symplectic structure, preserves the Heisenberg bound, admits exact closed-form moment solutions, and reproduces the Lindblad benchmark for weak damping, i.e., within the analytic error bound $(\lambda/\omega_1)^2\,\phi_{\rm zpf}^2$.

In this work we analyze correlations of X-ray photoelectron and diffraction spectra, and dielectric properties of hafnia-zirconia nanoparticles (the chemical compositions Hf0.4Zr0.6O2 and Hf0.6Zr0.4O2, and the average size of 7.5 nm) prepared by the solid-state organo-nitrate synthesis and annealed in air. The phase state of the nanoparticles, determined by the X-ray diffraction spectroscopy, is the coexistence of the nonpolar monoclinic (42 - 76 mass %) and orthorhombic (56 - 24 mass %) phases. Concentration of the oxygen vacancies was estimated from the X-ray photoelectron spectroscopy. The increase in the intensity of the dielectric permittivity maximum observed near 350 - 450 K in a PVDF matrix with embedded Hf0.4Zr0.6O2 nanoparticles can be related with an increase in oxygen vacancy concentration. Theoretical calculations, based on Landau-Ginzburg-Devonshire theory, explain the increase of the dielectric permittivity in Hf0.4Zr0.6O2 nanoparticles compared to Hf0.6Zr0.4O2 nanoparticles.

Passive radio frequency (RF) sensing is widely used for counter-unmanned-aerial-vehicle (counter-UAV) detection. Existing studies commonly report high accuracy against background RF or WiFi/Bluetooth interference, but rarely isolate controller-only operation without a linked aircraft. We present a dual-band software-defined radio (SDR) measurement study with ambient, controller-only, and linked states for three commercial UAV platforms (DJI Phantom 3 4K, Hubsan H501S, DJI Mavic Mini). Two USRP B210 receivers simultaneously scan eight 2.4 GHz and twelve 5.8 GHz observation windows across twenty rounds. We first train an energy-based detector using linked and ambient scans only. At four ranked concurrent dwell steps (8 s), it achieves 0.992 linked-versus-ambient balanced accuracy but false-confirms 30 out of 60 controller-only scans (FCRctrl = 0.500). We then include controller-only scans in training and use confirm, reject, and defer outputs under an explicit controller-only false-confirmation-rate (FCR) constraint. For the pooled all-platform analysis, the constraint reduces observed FCRctrl from 0.350 to 0.050, while confirm-linked TPR decreases from 0.900 to 0.400 and 42.1% of scans are deferred. The corresponding compact scan performs substantially better for Hubsan and Mavic than for Phantom. A hardware-in-loop experiment reduces measured wall-clock time from 82.9 s to 28.9 s. These measurements show that linked-versus-background accuracy does not measure controller-only false confirmation and that this error should be reported separately.

Transforming textile fibres into sensors can facilitate continuous physiological monitoring for improving human healthcare. Coating fibres with electronic conductors can help detect physiological stimuli but their sensitivity scales with thickness and often lowers the fibre mechanical flexibility. Proton conductors are potential alternatives; however, they suffer from fragile physical interfaces, and sluggish kinetics. Here, we report a bio-templated, scalable strategy to create superprotonic interfaces using natural silk fibres. We exploit ordered nanofibrils on silk fibres to selectively grow continuous metal-organic framework (MOF) nanostrips. This patterned, ca. $10\,\mu\mathrm{m}$-diameter fibre-structure provides low-defect interfacial pathways for ultrafast proton transport, yielding conductivities up to 40 $S\,cm^{-1}$ - two orders of magnitude above the state of the art - with millisecond response and high mechanical robustness. The individual micro-thread sensors facilitate respiratory monitoring with a mean bias of 0.01 breaths $min^{-1}$ in volunteer testing, unaffected by human movement and readily capture breathing signature in high-flow oxygen therapy devices. We integrate arrays of micro-thread sensors in textiles and exploit deep learning to demonstrate high-resolution spatiotemporal humidity mapping in dynamic flow-fields and resolve asymmetric respiratory patterns that elude conventional single-point detectors. Our results should have broad-ranging implications, e.g. in wearable health monitoring, bioelectronics, and human-machine interfaces.

In the online metric matching problem, we have $n$ servers with known locations in some metric space. Requests arrive one-by-one at certain locations, and upon arrival a request must be matched to a server that was not matched to a previous request. The goal is to minimize the matching cost. For randomized algorithms with an oblivious adversary, the best known competitive ratio is obtained by embedding the metric space into an HST, and then solving the problem in the setting where the metric space is defined by the HST. Bansal et al. (Algorithmica, 2014) introduced a framework for online metric matching where one develops an algorithm in a restricted reassignment model, and then transforms this into a true online algorithm. Using this framework, they obtained an expected competitive ratio of $O(\log n)$ for HSTs; this also gives the best known competitive ratio of $O(\log^2 n)$ for general metrics. In this paper, we revisit this framework with the aim of developing new algorithms. For HSTs where each node has at most $\Delta$ children, we develop an algorithm via this framework with an expected competitive ratio of $O((\log\log \Delta) \cdot \log \Delta)$. In particular, this ratio is independent of $n$, the number of servers/requests. It is near-optimal, as the expected competitive ratio of any algorithm is $\Omega(\log \Delta)$.

We characterise exacting, rank-Berkeley, Berkeley, and club Berkeley cardinals by compactness properties of logics and, equivalently, by compactness properties of certain topological spaces. This raises the strength known to be obtainable by statements about compactness into the realm of choiceless large cardinal axioms, the strongest known statements in terms of consistency strength. Moreover, it shows that compactness assumptions can directly violate the axiom of choice and the axiom $V=\text{HOD}$.

Teleoperation, such as remote driving, is considered as a key use case of 5G and Next-Generation (NextG) networks. In this context, robots, autonomous vehicles, or other autonomous agents transmit sensor data over mobile networks to edge or cloud servers, where AI systems collaborate with human operators to provide situational awareness and enable remote control. In the case of teleoperated driving, vehicles are equipped with an array of cameras and LiDAR devices, which can generate 100s Mbps (megabits per second) of data. As shown in existing measurement studies, such data volumes far exceed the uplink capacity of currently deployed 5G networks, especially when multiple vehicles compete for radio resources. Data compression is thus imperative. In this paper, we explore the impact of sensor data compression on the performance of downstream AI tasks running in edge/cloud servers, which are crucial to alert human operators for safe teleoperation. Using object recognition and semantic segmentation as two example AI tasks, we study how data compression affects the performance of these two AI tasks using unimodal (video or LiDAR) and multi-modal (video+LiDAR) data. We find that lossy data compression generally decreases the performance of AI tasks. The performances of these AI tasks exhibit differing degrees of sensitivity based on the types of data sources and levels of compression. We also empirically identify an optimal trade-off point for the multi-modal vision tasks.

Let $(M^n,g)$ be a complete, connected, noncompact Riemannian manifold, and let $f\ge0$ be a proper $C^2$ weight. We assume polynomial bounds on $f$, $|\nabla f|$, and $\Delta f$ (Assumptions H1-H3), with growth exponent $\alpha>0$. We study the drift Laplacian $L_f=\Delta-\langle\nabla f,\nabla\cdot\rangle$ on $L^2(M,e^{-f}dV)$. We assume that its eigenfunctions have finite polynomial growth orders $\gamma_k$, measured on the level sets of $f^{1/\alpha}$. We also assume that $\gamma_k\to\infty$ in spectral order (Assumption H4). We compare this growth filtration with the filtration by eigenvalue $\lambda_k$. For $\alpha>1$, we study the relation $\lambda_k\asymp\gamma_k^{(2\alpha-2)/\alpha}$, called compatibility. An explicit rotationally symmetric example shows that this relation can fail for the full spectrum, even when $\alpha=2$. We prove discreteness and weighted Agmon estimates for $\alpha>1$. A moment estimate bounds the concentration radius in terms of the growth order and a finite-scale prefactor. A lower localization condition gives one direction of the spectral comparison. For exact warped products with a one-dimensional base, we impose the radial growth condition and a regularity assumption on the radial drift. These give $\alpha=2$ and $\lambda_k\asymp\gamma_k$ in the radial sector. For general $(M,g)$, we assume a transitive isometric symmetry of the level sets instead of a warped-product structure. The invariant-sector growth condition and radial-drift regularity then give $\alpha=2$ and $\lambda_k\asymp\gamma_k\asymp k$. Finally, exact polynomiality of the invariant eigenfunctions implies $\alpha=2$ without the drift regularity assumptions. The reduced equation is then Hermite or generalized Laguerre after normalization. The arguments use neither curvature bounds nor soliton equations.

Let $B^d$ denote the $d$-dimensional Euclidean ball of unit radius. What is the largest constant $f(B^d) \in [0,1]$ with the property that every finite collection $\mathcal{C}$ of unit balls in $\mathbb{R}^d$ admits a disjoint sub-collection $\mathcal{S}$ occupying at least a fraction $f(B^d)$ of the volume of $\mathcal{C}$? This problem was first raised by T. Radó in 1928, for axis-parallel squares in the plane; the author was motivated by a classical covering lemma in real analysis due to Vitali. The case of Euclidean balls was first considered by R. Rado in 1949. Until last year the best known estimates on $f(B^d)$ for unit balls where very far apart: \[ (1+\epsilon_d) 3^{-d} \leq f(B^d) \leq 2^{-d}, \] where $0<\epsilon_d=o_{d\rightarrow \infty}(1)$. Recently, the authors of this note observed that an exponential improvement on the upper bound follows from the Kabatiansky–Levenshtein spherical code bound, while the lower bound was improved by a linear factor by C.~Xie and G.~Ge (see arxiv:2608.09744). The current best estimates for large $d$ are \[ c \cdot d \cdot 3^{-d} \leq f(B^d) \leq 2.447^{-d}, \] where $c>0$ is an absolute constant. Here we offer the first exponential improvement of the lower bound in almost 80 years, which narrows the gap to: \[ 2.910^{-d} \leq f(B^d) \leq 2.447^{-d}. \] Our method is constructive and yields a polynomial time algorithm for finding a disjoint sub-collection realizing the estimate. Moreover the same technique gives similar exponentially improved lower bounds for all symmetric convex bodies satisfying a uniform convexity assumption, e.g., $\ell^p$-balls for all $p\in (1,\infty)$.

Ruptures represent common albeit critical moments in interaction where relational alignment breaks down, making them essential for evaluating AI where trust and engagement matter most. In a scenario-driven empirical study, we examined the performance of three LLMs at identifying and resolving ruptures across 21 mental health conversations and 22 experts' evaluation of the strategies. For identification, LLMs relied on explicit linguistic cues within single turns whereas experts integrated implicit, relational, and contextual information across the conversation. For resolution, LLMs tended to produce more directive and scripted responses whereas experts adopted process-oriented strategies such as validation, open-ended exploration, and psychoeducation. Overall, LLMs showed higher agreement with predefined labels in identification, but not in resolution where experts rated their responses only moderately effective, with consistent limitations in timing, depth, and contextual sensitivity. We discuss implications for the design of mental health conversational agents emphasizing relational awareness, pacing, and human-in-the-loop support.

Structured-data agents in enterprise settings must reason over complex data environments whose relevant evidence is distributed across schemas, relationships, policies, and recurring business roles. Modern agentic systems often address this burden through reusable markdown-style memory or skill files that preserve previously discovered information for later queries, reducing the need to rediscover the same structure repeatedly. This is useful, but it obscures a natural division of labor: agents are well suited to semantic reasoning, while learned systems are well suited to predicting and organizing recurring structure. We introduce latent equivalence learning to bridge this gap. The framework separates persistent task-relevant identities from their dataset-relative realizations. In our realization, supporting and opposing evidence shape support-realized Gaussian prototypes that learn how those identities are expressed in a particular data environment, while soft-membership profiles retain distinctions lost under a hard assignment. A separate learned query-prototype system represents recurring evidential requirements and maps them through a learned compatibility function into the same persistent identity structure. This identity-factorized, query-conditioned routing materializes the relevant dataset-specific evidence for downstream reasoning, allowing the agent to operate over an already organized evidential state rather than reconstructing cross-schema structure at every query. On the Data Agent Benchmark, spanning 54 queries across 12 heterogeneous datasets, our full implementation achieves 94.67% dataset-macro stratified Pass@1 over five complete trials and 258/270 successful raw query attempts, compared with 55.51% for the benchmark's Claude Opus 4.6 reference agent, ranking first among 40 leaderboard entries at submission.

Finding circuits in language models usually means running many careful interventions. We try something simpler: treat attention as a routing map from one forward pass, keep a small set of routes that point toward the answer, and ask whether those routes actually matter. They often do. On induction and IOI (tasks where the "right" circuit is already known), ablating our extracted edges hurts the model much more than ablating a random set of the same size. We evaluate n=100 prompts per cell on GPT-2 Small, GPT-2 Medium, and Pythia-410M, with paired gap tests and bootstrap confidence intervals. The extract step costs one forward; a head-by-head patch sweep costs about two orders of magnitude more. We are not claiming a complete circuit atlas. We are claiming a cheap sketch that carries real causal signal on known tasks, with clear failure modes when it does not. Code and evaluation artifacts are at https://github.com/Aquinf03/live-circuit-routing.

A social agent's most basic decisions (should I react to this post? who should I reach out to?) are not purely content problems. The right action often hinges on the latent relationship between people – tie strength, reciprocity, mutual connections – rather than on which content is most salient. Standard LLM agent loops do not explicitly represent how new relational evidence should revise the agent's current social hypothesis, leaving them prone to surface-obvious choices when relational and content cues diverge. We formalize this failure mode with a relationship-reasoning benchmark: 500 synthetic social worlds with friendships, follows, reaction histories, and feeds, yielding 1,000 queries over two tasks, reaction selection and warm introduction (finding the best bridge to a target person). By construction, the surface-obvious candidate differs from the relationship-grounded oracle in about 53% of queries, forming an overturn subset where the agent must use relational evidence to revise an initially plausible choice. We propose ReAdapt (Relationship-Adaptive Agent with Policy-driven sTate), which augments the ReAct loop with an explicit structured social state z = (G, B, R, N, D) capturing goal, belief, relationship, norm, and disclosure. After each tool observation, ReAdapt runs a typed Adapt step that updates this state and emits a policy operation (continue, switch, abandon, or clarify) before choosing the next action. With Gemini-3-Flash on a stratified subset of n = 150 queries per task, ReAdapt improves warm-introduction accuracy from 37% to 51% (+14 points) and reaction-selection accuracy from 69% to 77% (+8 points). Oracle regret drops from 0.260 to 0.152 and from 0.095 to 0.053, respectively. Holding the model, tools, and environments fixed, these results suggest that explicit relational-state adaptation helps LLM agents turn retrieved social evidence into revised decisions.

Spin-orbit-coupled $d^1$ double perovskites exhibit a rich interplay of spin, orbital, and quadrupolar degrees of freedom (DOF), giving rise to competing magnetic and multipolar phases. Although quantum mean-field theories predict many exotic phases, their stability against thermal fluctuations and reproducibility within a classical framework remain an open question. Here, we surpass the mean-field limitations by deploying large-scale classical Monte Carlo simulations on the projected $j=3/2$ manifold of the FCC lattice, allowing complex ordering patterns to emerge spontaneously without preassigned magnetic symmetries. Our thermodynamic mapping reveals that thermal fluctuations melt the intermediate-temperature quadrupolar phase over part of the phase diagram, while it survives intact elsewhere. Crucially, by systematically isolating the boundary between classical and quantum stability, we demonstrate that while the four-sublattice antiferromagnetic and ferromagnetic (FM) phases are robustly classical, the coplanar canted FM[110] state completely destabilizes. This identifies the FM[110] phase as an intrinsically quantum state born out of quantum fluctuations. Our results demonstrate that the dominant magnetic phases are robust within a classical description, where the essential physics of the system is captured by weakly entangled, short-range correlated DOF and highlight the role of thermal fluctuations in determining the stability of different types of magnetic and quadrupolar order.

We construct an infinite family of directed strongly regular graphs (DSRGs) with intransitive full automorphism groups whose Weisfeiler–Leman closure are association schemes of rank 6. This is the smallest possible rank for an association scheme admitting a proper DSRG merging. We also exhibit rigid sporadic DSRGs with the same closure property, showing that combinatorial regularity, group-theoretic symmetry, and Weisfeiler–Leman regularity capture fundamentally different aspects of graph structure.

The Teukolsky and SpinWeightedSpheroidalHarmonics packages of the black hole perturbation toolkit (BHPT) are one of the main public libraries to compute numerical solutions to the Teukolsky equation and related quantities. This work is a companion paper presenting their new and improved weak-field analytic functionality focusing on post-Newtonian expansions. The Teukolsky package now allows users to independently extract multiple useful quantities, such as the so called MST coefficients, renormalized angular momentum, amplitudes of the radial functions or the phase shift as a low frequency/PM expansion. It also provides PN expansions of the homogeneous radial functions or - for circular orbits in Kerr - inhomogeneous amplitudes, as well as energy and angular momentum fluxes at infinity and the horizon. All quantities can be computed to state of the art precision on regular laptops. It also provides a suite of tools for post-Newtonian self force computations and updates the analytic functionality of the SpinWeightedSpheroidalHarmonics package. Computations are possible both for specific and generic spin weight $s$ and harmonic mode numbers $\ell$ and $m$. This package paves the way for intensive high-order post-Newtonian self-force calculations at the forefront of waveform modelling of small mass ratio black hole binaries, as well as giving widely useful low-frequency expansions for black hole perturbation theory. All functions described in this paper are available in BHPT versions Teukolsky v.1.2 and SpinWeightedSpheroidalHarmonics v.1.1.

The classical circumstellar habitable zone restricts the search for life to planetary surfaces where stellar irradiation sustains liquid water, overlooking vast subsurface environments. Here, we present a geophysical model integrating internal radial structure, mineralogy, radiogenic heat, and pressure-dependent porosity to quantify the three-dimensional habitable volume-the eirenesphere-of rocky exoplanets. We distinguish between aquability (thermodynamic water stability) and habitability, which requires temperatures and pressures within extremophile biological limits, plus sufficient porosity for fluid circulation. To compare planetary capacities, we introduce the Eirenesphere Volumetric Index (EVI), measuring average subsurface biosphere volume. Applying this framework, we find that Earth's current state (EVI$\approx 0.06$ terrestrial oceans) represents only a moderate regime. Instead, mature super-Earths with high geothermal activity provide the most extensive environments for deep biospheres. Crustal mineralogy exerts a first-order control: thermally insulating felsic crusts sustain significantly larger eirenespheres than primary mafic lithologies. Tracking secular cooling reveals internal habitability is an evolutionary property; young planets host confined biospheres due to steep thermal gradients, whereas mature worlds maximize habitable volumes over billions of years. Finally, we demonstrate that around solar-like stars, subsurface habitability persists out to $5-7$ au, effectively decoupling life's potential from surface radiative balance. Extrapolating to the Milky Way reveals a staggering galactic capacity for subsurface life, on the order of billions of terrestrial oceans. Ultimately, this framework shifts the astrobiological paradigm from a surface-dependent phenomenon to an intrinsic planetary property, offering a metric to prioritize targets.

Links between blast exposure and mild traumatic brain injury (mTBI), as well as other negative physical and mental effects are well established. However, the effects of low-level blast exposure, which does not rise to the level of a mTBI diagnosis, are less well-documented. Low-level blast exposure may initiate or accelerate neurodegenerative changes, leading to accelerated age-related cognitive decline or overt neuropathological diagnoses such as Chronic Traumatic Encephalopathy (CTE), in addition to other non-neurodegenerative long-term harmful effects, such as clinical depression. This study analyzed the effect of low-level blast exposure through a survey of military veterans who served in the U.S. military as mortarmen (n = 42). Survey participants responded to screening assessments measuring depression, PTSD, anxiety, and alcohol use disorder. Through a matched pair study design, surveyed mortarmen were compared to two control groups consisting of veterans without a history of mTBI exposure (n = 283) and veterans who had suffered at least one mTBI exposure (n = 1264). We found that surveyed mortarmen reported statistically significant higher depression (as measured by PHQ-9) than both groups of controls. Even after accounting for Post-Traumatic Stress disorder (PTSD) and unhealthy alcohol use, mortarmen still reported higher depression, suggesting that PTSD was not the sole factor responsible for worse mental health symptoms. These results highlight the importance of more comprehensive study of cumulative blast overpressure and its relationship with mental health.

We apply a finite-state geometric formulation based on Bargmann invariants to a two-band Weyl Hamiltonian and the one-dimensional Kitaev model of a p-wave superconductor. For the Weyl system, a symmetry-antisymmetrized third-order Bargmann combination selects the chirality-sensitive component of the local pseudospin geometry and extends to a two-band lattice Weyl model. For the Kitaev chain, a normalized ratio involving a third-order Bargmann invariant and a second-order overlap factor removes the dependence on an intermediate state and reproduces the $Z_2$ distinction between its two gapped phases. We further construct a fourth-order loop connecting localized Majorana edge-mode profiles with finite-energy BdG states and an alternating fourth-order loop involving opposite Weyl pseudospin sectors. These constructions illustrate how suitable Bargmann combinations can probe chirality-sensitive, topological, and higher-order geometric information directly through quantum-state overlaps, providing an alternative state-based route without requiring a continuous description of the underlying state-space geometry.

The Unruh effect predicts that a uniformly linearly accelerated observer with proper acceleration $a$ reacts to the Minkowski vacuum through excitations and de-excitations with the characteristics of a thermal state at temperature $T_U=a/(2\pi)$. An observer in uniform circular motion will experience similar excitations and de-excitations that we may use to operationally define an effective temperature, which however depends not only on the acceleration but also on the orbital speed and excitation energy. Motivated by the experimental interest in the circular motion Unruh effect, we investigate how spatial confinement modifies the response of an Unruh-DeWitt detector in $2+1$ Minkowski spacetime. We consider a massless scalar field confined within a circular boundary prepared in either the vacuum or a thermal state, probed by an Unruh-DeWitt detector on a circular orbit, a setting that describes proposed analogue spacetime systems for testing the effect, and in which both a boundary and an ambient temperature will necessarily be present. We establish analytic results for the detector response in the large-boundary regime and identify resonance peaks, which are more prominent when the field has an ambient temperature.

Inspired by the recent progress in the simulation of tight-binding Hamiltonians on large lattices using tensor networks, we introduce a systematic matrix product operator (MPO) construction for single-particle Hamiltonians on recursively structured lattices. Taking advantage of this recursive structure, we encode the lattice geometry in a finite-state automaton and, adapting ideas from Abelian-symmetric tensor networks, obtain an exact and analytical MPO representation of the Hamiltonian, where the number of tensors grows logarithmically with the system size and the bond dimension is set by the number of automaton states. Several examples demonstrate the generality of the framework: regular lattices, fractals, Cayley trees, hyperbolic lattices, and one- and two-dimensional Fibonacci quasicrystals. Combined with the kernel polynomial method, these MPO representations enable large-scale calculations of spectral properties without explicitly constructing the full Hamiltonian. This provides a unified route to the exploration of electronic properties across a broad class of lattices at exponentially large system sizes.

In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of "block-diagonal" inductive limits of semidirect products $\mathbb{T}^N\rtimes\mathfrak{S}_{N}$ of the compact $N$-dimensional torus $\mathbb{T}^{N}$ with the symmetric group $\mathfrak{S}_{N}$. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.

Robot assistants for older adults and people with disabilities need to perform collaborative tasks with users effectively. The core component of these systems is an interaction manager whose job is to observe and assess the task and infer the state of the human and their intent for the robot to choose the best course of action. Due to the sparseness of the data in this domain, the policy for such multimodal systems is often crafted by hand; as the complexity of interactions grows, this process is not scalable. This paper proposes a reinforcement learning (RL) approach to automatically generate the multimodal policy of the robot. Our system focuses on a realistic scenario where a robot assists a user in locating objects within a home environment, managing multimodal signals, including language and physical actions, to select the best action. In contrast to traditional dialog systems, our agent is trained with a simulator that uses human data and can deal with multiple modalities. We use a simple high-level reward function that needs no fine-tuning and enforce some preconditions to speed up the training process. A human study evaluating the system in a real-world setting demonstrates promising results, indicating high usability and effective task completion. This RL-based approach offers a scalable and interpretable alternative for designing interaction managers in multimodal human-robot collaborations.