Papers

Thermonuclear flame fronts in Type Ia supernovae develop hydrodynamic instabilities that generate turbulent mesoscale flow and substantial local thermodynamic variability. Recent work by \citet{Brooker+25} demonstrated systematic shortening of fuel ignition times near Rayleigh–Taylor unstable deflagration fronts, but the physical origin remained unclear. We investigate the thermodynamic evolution of fuel near the flame front using multidimensional simulations and Lagrangian tracer-particle analysis, focusing on flame-driven expansion and ignition-time variability in partially degenerate carbon–oxygen plasma. Tracer trajectories show that the most strongly preconditioned fuel parcels near the flame front, which form a minority of the fuel layer, undergo approximately pressure-constrained expansion with modest density reductions and temperature increases of $\approx 2\times10^{8}$~K to $\approx7\times10^{8}$~K ($\approx13$ to $63$ per cent above the unperturbed fuel temperature) between the low- and high-density models. Despite moderate thermodynamic perturbations, the strong temperature sensitivity of carbon ignition produces substantial shortening of ignition times. The results indicate a two-step mechanism: flame thermal expansion perturbs the fuel away from hydrostatic equilibrium, while restoration of pressure balance by weak acoustic waves redistributes internal energy from degenerate to thermal components. This raises the fuel temperature and produces localized thermodynamic preconditioning. These results suggest that unsteady thermonuclear flames can shorten ignition times ahead of the flame, influencing fuel over distances larger than the laminar flame thickness. Whether this preconditioning leads to secondary ignition or contributes to deflagration-to-detonation transition remains untested here, as nuclear burning is disabled in the analyzed fuel.

NVMe SSDs are now widely deployed as the storage tier in data centers. As SSDs have evolved over the past decade, the commu- nity has continued to debate the interfaces they expose and how operating systems and storage systems should exploit them. The NVMe Flexible Data Placement (FDP) proposal is the latest point in this design space. FDP introduces an interface based on Reclaim Units that enables explicit data placement to reduce device write amplification without the software engineering costs of sequential- write constraints and host garbage collection. FDP-enabled SSDs are emerging in commercial products and early data center de- ployments. Their compatibility with conventional block I/O allows existing applications to run unchanged, allowing a frictionless adop- tion in industry. This paper presents an experimental evaluation of FDP SSDs to characterize their data placement guarantees over the raw device interface. We then revisit two widely deployed and distinct open- source storage systems, MySQL and RocksDB, and examine whether lifetime-based data separation and distinct write patterns built into their architectures can be mapped onto FDP SSDs without inva- sive changes. Our evaluation shows end-to-end WAF reductions at higher device utilization, along with QoS and throughput improve- ments under synthetic and real-world workloads. These results demonstrate that FDP provides a practical and deployable cross- layer mechanism for data placement with open-source ecosystem support on Linux. They also highlight why FDP SSDs are gaining traction in industry.

Single-photon avalanche diode (SPAD) cameras operate fundamentally differently from conventional cameras due to their photon-counting nature. Each frame produces a binary image: pixels report zero if no photons arrived during exposure, and one if one or more photons arrived. Reconstructing a scene or inferring its properties from a single binary frame is difficult because many different images could produce the same measurement; thus, the inverse problem is fundamentally one-to-many. As we gather more binary measurements, the inherent uncertainty associated with the inverse problem and any associated inference diminishes. With sufficient photon counts, photon noise becomes negligible relative to the signal mean, enabling near-deterministic scene recovery and inference. This work characterizes the transition from stochastic to near-deterministic scene understanding as photon budget increases, analyzing how the stochasticity in photon arrival affects downstream inference tasks. Technically, we develop a conditional generative framework based on a Hypergeometric frame-thinning process for accumulated binary SPAD measurements. Generative models capture the one-to-many nature of photon-starved inverse problems, enabling empirical characterization of how this ambiguity diminishes with increasing measurements and its impact on downstream tasks like character recognition, QR code decoding, and facial analysis.

This paper proposes a mathematical model for long-term Generation and Transmission Expansion Planning (GTEP) that integrates a relaxed Virtual Transmission Line (VTL) as a Storage in Place of Transmission Asset (SIPTA) strategy to address challenges posed by transmission capacity shortages and system congestion in deregulated power markets, particularly under the rapid growth of renewable energy resources and integrated data centers. The proposed VTL formulation coordinates the operation of the two battery energy storage systems (BESSs) forming a VTL pair by preventing them from charging or discharging simultaneously, thereby providing additional congestion relief without introducing an explicit congestion cost into the objective function. Base case studies on a revised IEEE 24-bus system demonstrate that VTL reduces system congestion compared with the standalone BESS case, achieving a 12.3% reduction in weighted total congestion and up to approximately 67% reduction in congestion on individual transmission branches, with only a 0.3% increase in total planning cost. Furthermore, improvements across multiple congestion metrics indicate that the benefits of VTL extend beyond reducing congested line-hours to reducing congestion rent and N-1 transmission violations in the base case. These results demonstrate the potential of VTL to provide congestion mitigation that complements standalone BESS applications.

A theory draws many independent observations into one framework with novel hypotheses. A researcher building such a theory must synthesize observations scattered across many papers, each describing related concepts but often in different terms. Which concepts matter most also depends on their preferences and research questions. Recent approaches scale theory synthesis with LLMs, but automate away choices and intuitions from researchers. We present Asterism, which extracts observations from hundreds of papers as concept-relation triples, with concepts unified in a hierarchical ontology. Researchers curate an evidence graph using the ontology and aggregate observations at different levels of granularity to focus theory formation on specific phenomena of interest. In a field deployment (n=10), researchers worked from observations to theories, and kept concepts and hypotheses fitting their preferences. In two case studies, teams of immunology and agriculture researchers discovered mechanisms outside their standard analyses and constructed hypotheses worth follow-up experiments.

Inferring an Allen-Cahn constitutive force from images requires more than an accurate optimizer: nonlinear observation noise alters the mean of force features, shared noise couples instruments to the response, and a temporal balance borrowed from another solver can remain biased even on clean data. We develop observation-aware, noise-adjusted moment equations that address these effects before inversion. The surface-tension-calibrated constitutive transformer (SCCT) couples the resulting moments to a positive Bernstein inverse and can adapt its prior and precision from images and moments. A conditional stability bound separates moment residuals from prior error. Synthetic tests show that correcting the estimating equation matters more than increasing regularizer flexibility; the benefit of learned adaptation is smaller and depends on the training comparison. Forces inferred from planar movies predict unseen planar and three-dimensional evolutions. A ring-cage breakup shows why diffuse-interface accuracy distinguishes forces even when their topological predictions agree, while external surface tension sets the energy scale separately.

Manipulating crystal structures towards targeted geometric properties or symmetry constraints is a longstanding challenge. Existing computational frameworks fall short: LLMs have poor spatial awareness and operate at coarse granularity in the token space, while diffusion- and gradient-based structure generation approaches generally produce complete structures de novo rather allowing for fine-grained editing of a given input under arbitrary constraints. We present LATHE, a geometric toolkit that closes this gap by expressing seven classes of crystallographic properties — bond length, bond angle, dihedral angle, coordination environment, lattice parameters, cell volume, and space group, as differentiable objectives to enable direct geometric editing of crystal structures. To demonstrate its usage in materials design, we further expose LATHE through a Model Context Protocol server and embed it in a closed-loop multi-agent system which translates hypotheses intogeometric modifications in natural language towards a given design objective. Across single-property benchmarks, LATHE attains near-perfect constraint satisfaction on all seven property types while keeping optimized structures close to local energy minima. The LATHE-equipped agent translates over 87.5% of natural-language prompts into valid executable configurations and faithfully completes them. In a band-gap inverse-design case study, the multi-agent loop reaches the target tolerance window in nine of ten independent runs at a typical cost of thirteen hypothesis-evaluation cycles. By bridging natural-language hypothesis generation and physically grounded gradient-based structural editing, this work establishes a paradigm for interpretable, closed-loop computational materials discovery that is immediately applicable to a broad class of functional material design tasks.

LLM agents are known to be slow in rollouts. An agent completes a task one step at a time. At each step, it reasons and then chooses an action to execute. The next step and action cannot start until the previous one has finished. Speculative decoding accelerates the rollouts at the reason phase by drafting and verifying the inference tokens. Recent works have also started to apply similar ideas at the action phase. These works use off-the-shelf models, usually large, to draft action proposals for target model to verify. Large drafters match the target more often but take longer to propose, while small off-the-shelf models are fast but rarely make the same decision as the target. We ask a more general question: what determines the end-to-end speedup of action speculation? To answer it, we develop a latency framework for the speculative round. The framework compares what a round gains with what it costs. The gain depends on how well the drafter predicts the target and on how many steps the task can take before it ends. The cost comes from drafting, from waiting for target verification and from executing tools. Guided by the framework, we introduce LEAP (Learning Efficient Action Proposals) which keeps the drafter small and makes it accurate by training it on the target actions sequences. With a small 0.6B model, LEAP agrees with the target on most decisions and makes agents up to 60% faster in end-to-end wall clock time, with no systematic change in task success. Across various datasets, target models and draft models, the framework accounts for most of the measured speedups. We also show the draft model can be online trained with no prior trace collection and match the performance of offline training, making LEAP practical to deploy in the real world.

In this article, we construct, for a broad class of one-dimensional stochastic reaction-diffusion equations, a sequence of spatially-structured individual-based models whose rescaled empirical processes converge to the solution of the equation. The purpose of this article is to show that, whenever the rescaled one-step mean and variance of a reasonable individual-based model converge to those of an SDE with drift $b(x)x(1-x)+\theta^+(1-x)-\theta^-x$ and noise coefficient $\sqrt{\sigma(x)x(1-x)}$, under certain moment conditions there also exists a corresponding multi-island model, composed of independent and identically distributed copies of the individual-based model on each island, with selection and mutation scaled to the diffusive time scale, coupled through migration, which converges to an SPDE with a Laplacian plus the same drift and noise coefficients, provided this SPDE is unique in law.

Automated liquid handlers execute digital protocols, but operators must assemble the deck and confirm that the physical setup matches the intended experiment. We present the Labware Setup Checker, a passive vision system that verifies deck preparation on an Opentrons Flex without modifying its hardware or firmware. A consumer webcam mounted outside the robot supplies images to a browser application. The checker segments the deck into slots, corrects slot assignments using the known deck geometry, classifies the labware, and compares the observed setup with a reference protocol library to report missing, misplaced, or unexpected labware. It operates independently of the robot controller and does not interrupt or gate a run. During SwabSeq Respiratory Viral Panel (RVP) pre-PCR deck preparation, the checker tracked a slot from empty to a base and then to the completed plate-and-base assembly, identifying the completed assembly in all 29 frames before robot motion. Across these frames, 95.1% of the 348 labware classifications for slots requiring exact matches agreed with the protocol reference. In 480 frames with partially occluded reservoirs, all 6,720 slot assignments were correct. Across three camera positions and two lighting conditions, slot assignment was 100% correct, and 97.73% of labware classifications matched the protocol reference. Median verification time was 2.10 s on a laptop using only its CPU and 4.24 s from frame capture to receipt of results during AWS deployment in the laboratory. These results show that an external camera and independent software can provide verification of deck setup against protocol requirements within seconds, allowing operators to review the physical setup before starting a run.

Cosmic birefringence, the isotropic rotation of the plane of linear polarization of photons from sources at cosmological distances, can be generated by different parity-violating mechanisms. While the net rotation angle of a single polarized source carries little information about its physical origin, sources at various redshifts $z$ can be used to distinguish between different origins. Parity-sensitive correlations of the $E$- and $B$-mode polarization fields of the cosmic microwave background measured on large and small angular scales probe sources at $z\simeq 10$ and $1100$, respectively. Thus, the detailed shape of the $EB$ power spectrum is sensitive to the redshift evolution of the birefringence source. In this paper, we calculate the $EB$ power spectrum due to a neutrino-asymmetry current, and compare it to axion dark energy and dark matter using a common Chern–Simons framework. We find that the $EB$ power spectrum due to a neutrino asymmetry is suppressed at low multipoles, $\ell\lesssim 20$, similar to the dark matter case. This can be clearly distinguished from the dark energy case, which has no such suppression. Large-scale polarization measurements, including LiteBIRD, can therefore distinguish late-time dark energy birefringence from that generated at higher redshifts by axion dark matter or neutrino asymmetry. We also find that the evolution of the neutrino density during recombination alters the shape of the $EB$ power spectrum at high multipoles. This signature can be used to distinguish between the neutrino and axion dark matter interpretations, using ground-based experiments such as the Simons Observatory.

Vision-Language-Action (VLA) models map visual observations and language instructions to continuous robot actions, but a diffusion-based action expert (AE) poses a key challenge for low-bit post-training quantization (PTQ). The AE is repeatedly invoked across denoising steps and policy queries, where fixed calibration scales can be mismatched with activation ranges that vary with denoising progress and intended motion. We propose CHASE-VLA, a chunk-aware PTQ method that exploits a VLA-specific signal readily available from the policy: the generated action chunk, including its unexecuted future suffix. Rather than relying only on static scale matching for AE layers, CHASE-VLA combines the previously generated chunk as causal action context with denoising step group information to adapt AE activation scales. This enables W4A4 quantization of both MLP and attention projections in the repeated AE without modifying the pretrained policy. On LIBERO, CHASE-VLA achieves 97.3% average success rate on $\pi_{0.5}$ when both MLP and attention projections in the AE are quantized to W4A4, restoring FP16-level performance. CHASE-VLA also reduces the weight storage of the quantized AE linear layers by 73.4% and their single-chunk memory traffic by 70.9% and 71.2% on $\pi_{0.5}$ and GR00T N1.6, respectively, with a predictor overhead of at most 1.26% of the saved storage.

Despite the success of discrete diffusion language models (dLMs) for fast parallel decoding, their non-smooth, high-dimensional space hinders trajectory steering for reasoning and inference acceleration. To overcome this, we present Sigma, the first large-scale (3B/8B) continuous dLM built on steerable, low-dimensional ODE/SDE latent trajectories. Trained blockwise via likelihood optimization, Sigma jointly denoises Gaussian-corrupted token embeddings while learning an optimal embedding geometry. To accelerate training, Sigma leverages pre-trained weights from autoregressive (AR) models for warm-starting. During inference, we identify classifier-free guidance and score temperature as essential for high-fidelity reasoning and coding. Across comprehensive math reasoning and coding evaluations against state-of-the-art discrete counterparts (masked dLMs and AR baselines), Sigma achieves competitive performance with discrete models on standard benchmarks (e.g., GSM8K, Minerva, HumanEval, MBPP) after pre-training and on challenging reasoning tasks (e.g., MATH-500, AIME) after supervised fine-tuning. Beyond performance parity, we uncover key structural properties unique to continuous dLMs: (i) embedding-space steering effectively governs the quality-diversity trade-off, yielding strong pass@k performance and (ii) continuous trajectories enable graceful degradation for low NFEs and efficient distillation. These establish continuous dLMs as a promising paradigm for efficient language generation.

Long-horizon agents are now playing an increasingly significant role in assisting humans with complex problem-solving. However, it is exactly their extended interaction history that introduces an underexplored execution-safety concern. Under benign interaction conditions, an agent may execute an action that violates a safety constraint specified many turns earlier. We term this failure mode Governance Hazard from Overlooked Safety Constraints across Turns (GHOST), which may cause irreversible damage. Our experiments reveal that GHOST events are not isolated cases: this failure mode, occurring precisely under benign interaction conditions, yields an occurrence rate of 11.5% on GPT-5.5. Furthermore, we theoretically show that if the residual conditional violation hazard along each safe prefix is bounded below by a non-summable sequence, the execution enters the hazard region almost surely. Leveraging this theoretical insight, we further propose STAR-Guard, a two-layer defense coupling historical semantic safety constraint restoration with pre-execution audit. STAR-Guard restores applicable safety constraints to reduce unsafe proposals, while its deterministic audit layer prevents residual violations from reaching the environment. Consistent with this two-layer design, we observe no GHOST events in our experiments under the GPT-5.5 setup.

Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped. Existing analyses often impose restrictive assumptions on the estimated velocity field and yield convergence rates that fail to reflect the intrinsic low-dimensional structure common in real data, such as natural images and molecular geometries. In this work, we study the statistical generalization of flow-matching models for learning an unknown distribution $P_{\mathrm{data}}$ from finitely many samples. We derive finite-sample error bounds on the learned generative distribution, measured in the Wasserstein-$p$ distance, for all $p\geq 1$. Specifically, given $n$ i.i.d. samples from $P_{\mathrm{data}}$, we show that, for every $d>d_p^\ast(P_{\mathrm{data}})$ and appropriately chosen network architectures and hyperparameters, the learned distribution $\widehat{P}^{\mathrm{FM}}$ satisfies $ \mathbb{W}_p(\widehat{P}^{\mathrm{FM}},P_{\mathrm{data}}) \lesssim n^{-1/d}+n^{-1/(2p)}\bigl(\log(1/\xi)\bigr)^{1/(2p)}$ with probability at least $1-\xi$, where $d_p^\ast(P_{\mathrm{data}})$ denotes the Wasserstein-$p$ dimension of the target measure. Our results demonstrate that flow matching naturally adapts to the intrinsic geometry of data and mitigates the curse of dimensionality, as the convergence exponent depends on the intrinsic rather than ambient dimension. These guarantees remain meaningful in high-dimensional regimes and provide a theoretical explanation for the empirical success of flow matching on structured data distributions under substantially more relaxed assumptions than those in existing analyses.

High-level robot actions such as goto(region) can hide intermediate traversal, allowing a monitor of the listed actions to accept a plan whose graph-level execution violates a safety rule. We present Graph-Aware Refinement and Verification (GARV), which composes graph-grounded action contracts with a safety monitor to produce a model-relative certificate or counterexample and, when route choice is enforceable, a minimum-cost safe refinement. In a 28-case controlled audit, refinement exposed all 12 targeted hidden hazards and produced the expected verdicts on 16 controls; a separate 14-case SPINE-RoboGuard instantiation yielded two false-safe cases and five action-interface errors. In standalone finite-graph simulation, all 16 designed cases met their expected outcomes, and product verification agreed with exhaustive enumeration on classification, minimum safe hop count, and witness safety in 160 comparisons across 40 graphs. Across 90 graph-contract evaluations on 30 graphs with a hazard deliberately placed on the selected shortest route, GARV found a safe refinement in 72 evaluations and no safe route within the permitted hop bound in 18. For the static forbidden-region rule, synthesis matched a simple hazard-deletion baseline in all 90 evaluations; GARV's guarantees remain conditional on the semantic graph, action contract, safety specification, and enforceability of any selected route.

Real-time data streams in Web of Things (WoT) and edge computing environments often evolve through latent regime changes. For online representation learning under strict computational constraints, the central problem is resolving the stability-plasticity dilemma: keeping useful historical knowledge while rapidly reacting to concept drift. Existing methods employ fixed update schedules or rolling windows. However, they suffer from parameter ossification during sudden shifts and waste computational resources when the stream remains stable. This paper proposes the Adaptive Incremental Gating System (AIGS), a lightweight closed-loop state-aware adaptation framework. AIGS introduces the Shock Ratio, an endogenous residual feedback mechanism that normalizes current reconstruction error against recent variation. This signal drives a Continuous Plasticity Controller that smoothly interpolates between learning plasticity and memory retention. By treating representation learning as a closed-loop control mechanism, AIGS avoids catastrophic forgetting and maintains a strictly linear $\mathcal{O}\left(k\cdot d\right)$ per-step complexity suitable for latency-sensitive edge devices. Experiments on real-world smart city dynamic streams-spanning traffic networks, meteorological systems, and industrial infrastructure-demonstrate distinct domain-dependent advantages. On Electricity Transformer Temperature datasets, AIGS achieves preventative early-warning lead times of 8.31 (ETTm1) and 9.88 (ETTm2) steps under gradual degradation. On Performance Measurement System traffic datasets, it shows significantly faster post-shift recovery after abrupt mutations. On the highly noisy Weather dataset, it improves anomaly recall while resisting stochastic noise overfitting. These findings establish AIGS as a practical, plug-and-play adapter for resource-constrained edge monitoring systems.

Diffusion-based world models enable high-quality interactive environment generation but suffer from substantial inference overhead due to repeated Transformer evaluations during denoising. Existing caching methods mainly exploit temporal redundancy at the feature or token level, leaving the underlying mathematical structure of diffusion features largely unexplored. In this work, we reveal that world-model features exhibit highly stable singular subspaces across nearby denoising steps, while their singular values follow predictable evolution patterns. Building on this observation, we propose SpectralCache, a training-free spectral caching framework that reuses stable singular subspaces and estimates only low-dimensional singular values through linear extrapolation. We further exploit the spectral consistency between neighboring full-computation features to skip selected expensive backbone evaluations via singular value scaling. Extensive experiments on representative world models demonstrate that SpectralCache consistently improves inference efficiency while preserving generation quality. On HunyuanWorld-Voyager-13B, SpectralCache achieves 5.22x acceleration while maintaining a WorldScore of 65.90 for static scenes, substantially outperforming existing training-free caching methods in inference efficiency.

Modern state space models (SSMs), such as Mamba2, provide a compelling alternative to transformers by combining linear-time sequence modeling with recurrent state-space dynamics. However, the behavior of SSMs in distributed learning settings remains poorly understood. In particular, the existing standard federated learning methods are largely architecture-agnostic, and do not account for the stability, selectivity, and state-space parameterization that characterize modern selective SSMs. To address this, we derive architecture-aware gradient and smoothness bounds for single- and multi-layer selective SSMs, and convergence bounds for FedAvg and FedProx, characterizing how recurrent stability, input-dependent discretization, and state projection norms affect federated optimization. We then numerically validate the single-layer bounds on sequences generated by a teacher SSM, using a learner that follows the analyzed recurrence. We use this analysis to formulate expectations about the effects of local training and client heterogeneity, and examine these expectations by comparing nine federated learning algorithms on Mamba2 language modeling across six text domains. These experiments illustrate how SSM-specific bounds can provide a basis for interpreting the behavior of practical federated learning algorithms.

Tenstorrent Blackhole combines distributed local memories, explicit inter-core communication, and Tensix cores decoupling data movement from computation. CUDA offers a substantial HPC software base but leaves physical data placement and scheduling largely implicit. Migrating CUDA HPC kernels to Blackhole requires spatial mapping across cores and per-core coordination of compute and data-movement kernels. We present an MLIR-based compiler deriving data placement, inter-core communication, and tile computation from a statically shaped affine CUDA subset. Declarative annotations express choices not fixed by the source, including compute/DM operation placement and streaming granularity. We evaluate it on Gaussian elimination, five-point stencil, and symmetric rank-k update. Relative to our compiler's default realizations, the best measured configurations achieve a 4.2x speedup for BF16 Gaussian and 2.1-2.2x for FP32 Gaussian and Jacobi. A choice's performance impact can reverse with surrounding policies, precision, and loop schedule, motivating comparison of alternative per-core realizations rather than independent policy selection.

Converting a pretrained autoregressive (AR) model to a diffusion language model (dLLM) enables parallel generation without pretraining a new model. Published conversion methods differ by roughly three orders of magnitude in training data and have not been compared under a common protocol. We compare two conversions of the same 30B Mixture-of-Experts (MoE) parent, holding the corpus, supervised-token budget, trainable parameter set and evaluation harness fixed, each under its own training recipe. The in-place model updates a subset of the parent's weights using denoising and representation-alignment losses; the frozen-tower model instead conditions through cross-attention on a frozen causal copy of the parent. With 1B training tokens, the frozen-tower model scores 71.60 on HumanEval pass@10 against 6.19 for the in-place model, an 11.6x improvement. At the same budget it also keeps 95% of the parent's GSM8K score and 99% of its MMLU-Pro score. A dense-parent experiment reproduces the HumanEval separation. Within the two-tower design at about 500M tokens, freezing the context tower retains substantially more MMLU-Pro performance than training it, while both give similar observed HumanEval scores. Our theoretical analysis establishes that both conversion classes contain an exact sampler for the AR parent under a hard attention mask and left-to-right commitment of one position per round. Under a shared loss, freezing removes the gradient contribution through the context states. Furthermore, evaluation protocol substantially affects a published 500B-token conversion's scores in both directions across tasks, while its AR parent's scores vary by less than three points, so comparing dLLMs needs a common protocol. These results show that, in the tested low-budget regime, the frozen-tower configuration retains substantially more of the parent's generation performance than in-place conversion.

We construct the quantized electromagnetic field and the corresponding photon propagators in a rigidly rotating cylindrical reference frame. Starting from covariant Maxwell theory, we formulate the gauge-fixed field equations and solve them in cylindrical coordinates. The vector nature of the electromagnetic field requires distinguishing orbital and intrinsic angular momentum, with the total angular momentum as the natural quantum number. We construct the two independent physical photon modes in terms of Bessel functions by solving the coupled differential equations, and provide an alternative construction based on a covariant basis of vector eigenfunctions generated by a covariantly constant tetrad. After normalizing the modes with the Maxwell inner product, we quantize the electromagnetic field and define the corresponding photon states and greater and lesser two-point functions. The physical time-ordered propagator is obtained directly from the quantized modes, with its transverse dependence encoded in polarization kernels that retain the cylindrical spatial structure and its spectral poles exhibiting the rotational energy shift. The full gauge-fixed photon propagator is constructed in two complementary ways: from the scalar Green function combined with the tensor transformation of the inertial Feynman-gauge propagator, and from the covariant vector eigensystem through its spectral decomposition and the Fock–Schwinger proper-time representation. We verify that both constructions satisfy the Green-function equation for the complete gauge-fixed Maxwell operator, providing the propagator required for covariant perturbative calculations with internal photon lines.

In the French pedagogic tradition of Gaspard Monge, geometry was learned by drawing and handling models: drawing was knowing. The formalism of the early twentieth century placed illustration on the side of intuition, perhaps useful for discovery but kept apart from proof. Yet illustration stayed active in mathematics and provides a model for mathematical knowledge as proofs can be generated by automated systems and the Leiden Declaration asks again what mathematical knowledge is. We trace a persistent tradition of illustration through Hadamard, Coxeter, Conway, Thurston and the Geometry Center, and draw on the philosophy of mathematical practice, including Manders' distinction between exact and coexact claims, De Toffoli's account of diagrams with justificatory force, and Giardino's representational affordances. Using examples from Schwartz's minimal flat torus, early images of the Mandelbrot set, and shader renderings of algebraic starscapes, we argue for the development of rigorous illustration, to help inspire and certify the insights it affords. We close by asking the mathematical community to recognise the role illustration plays in helping develop mathematical research and understanding.

Models of social contagion usually assume how individuals adopt beliefs and derive population behavior from it. We instead empirically measure belief adoption in language model agents, quantifying the probability an agent adopts a claim given how many peers endorse it. We find this adoption kernel to be sigmoid, a characteristic of complex contagion, with a threshold that is sensitive to three sources: the claim's plausibility, the source's reliability, and the agent's disposition. These three dimensions are well approximated by a single effective dimension which we propose can be understood as the coherence of the incoming belief with the LLM agent's prior beliefs. Further, we observe a characteristic of complex contagion in the collective dynamics of belief adoption in a system of AI agents: further spread on clustered than random networks. These systems also exhibit a bifurcating cascade window, and self-sustaining hysteretic consensus which lead to consensus being far harder to remove than to establish.

Thermal X-ray pulse profiles constrain neutron-star masses and radii through the effects of gravitational light bending and rotation on surface emission. The precision anticipated from the enhanced X-ray Timing and Polarimetry (eXTP) mission motivates more accurate analytic light-bending formulae that retain the efficiency needed for repeated model evaluations. We derive a refined analytic flux expression within the oblate–Schwarzschild (OS) approximation that combines bending, propagation-delay, and lensing approximations with a spheroidal surface. We compare its profiles with numerical Schwarzschild and second-order Hartle–Thorne ray tracing on the same spheroidal surfaces. The comparisons use a selected two-spot configuration at 300 Hz with isotropic blackbody emission and three choices for surface eccentricity: a freely specified value, the Maclaurin relation for a uniformly rotating Newtonian fluid, and a fit to rotating-neutron-star surfaces. Across these cases, the refined OS profiles have RMS flux differences of $1.76-1.98\%$ relative to the Hartle–Thorne reference, compared with $6.50-21.39\%$ for the spherical Schwarzschild-plus-Doppler (S+D) model. All differences are normalized to the phase-averaged reference flux. The corresponding differences between Schwarzschild and Hartle–Thorne ray tracing remain below $1.1\%$. These comparisons separate errors in analytic photon transfer from the effects of surface deformation and the rotating exterior spacetime. For the configurations examined, accounting for oblateness substantially improves agreement with ray tracing. The model retains the speed of an analytic calculation while making the physical origin of profile changes explicit.

SSD-resident approximate nearest-neighbor search is essential when vector collections exceed DRAM capacity. The challenge is to reduce SSD reads and hide I/O latency through concurrent reads and overlap with computation. However, for graph-based search, progressive candidate discovery limits advance I/O planning while IVF search reads inverted lists in full, incurring unnecessary SSD reads. In this paper, we present RaBitQ-SSD, an extension of IVF-RaBitQ for SSD-resident vector search. Specifically, we propose Split-RaBitQ, which retains a configurable prefix of each binary code in DRAM, allowing in-memory code storage below one bit per dimension. Using this partial representation, it provides an unbiased distance estimator with a probabilistic error bound. Once the in-memory coarse quantizer identifies candidate lists, this bound supports pruning individual candidates within them, enabling finer-grained SSD access. We also design an asynchronous search pipeline that coordinates candidate pruning with SSD read scheduling to reduce unnecessary reads while overlapping I/O with computation. On datasets ranging from $5$ million to $1$ billion vectors, RaBitQ-SSD delivers up to $1.74\times$ the throughput of graph-based baselines at $90\%$ recall, while reducing SSD page reads by up to $3.8\times$. Its on-SSD indexes are up to $7.0\times$ smaller and $10.0\times$ faster to build than DiskANN. We also build and search an index of $10$ billion vectors on a single machine with one SSD, achieving over $3{,}000$ queries per second at $90\%$ recall.

Machine learning surrogates for density functional theory (DFT) have been increasingly used to reduce the cost of first-principles calculations. In this arena, predicting real-space electron densities offers a scalable and transferable initialization for self-consistent field (SCF) procedures. However, current methods face a clear dilemma. That is, grid-based architectures incur a high computational cost, while basis-set methods fail to capture the structural correlations inherent in the coefficient space. Here, we develop OrbFlow, an $\mathrm{SE}(3)$-equivariant generative model that predicts Gaussian-type orbital (GTO) coefficients via flow matching. OrbFlow retains the efficiency of a compact atom-centered basis while replacing pointwise regression with a learned probability path over the full coefficient space. It is trained through a two-phase trajectory curriculum that mitigates discretization drift during numerical integration. OrbFlow achieves state-of-the-art accuracy on QM9, reducing density error by 13.6% relative to the previous best model, and reduces error by 51% to 63% on every molecule of the MD benchmark relative to the strongest prior method sharing its basis. The predicted density also cuts SCF iterations by up to 68% with zero-shot transfer to unseen exchange-correlation functionals and recovers dipole and quadrupole moments to within a few percent of DFT references without any SCF calculation.

We study a family of aperiodic metric graphs generated by one-dimensional tilings. We prove that, generically, the spectrum of the associated Kirchhoff Laplacian has Lebesgue measure zero and, apart from a discrete set of isolated eigenvalues, is a generalized Cantor set. For a large subclass of these graphs, we further show that isolated eigenvalues are generically absent. This extends several well-known results from the setting of discrete ergodic Schrödinger operators on $\mathbb{Z}$ to a large family of metric graphs. Earlier results of this kind for metric graphs typically assume equilateral edges and exploit symmetries that reduce the analysis to a Sturm-Liouville operator on the real line. By contrast, the graph families considered here need not have equilateral edges or the symmetries needed for such a reduction and therefore require a different analytical approach.

We study compactness of the product of two weighted Hardy primitives into $L^q(u)$, $0<q<\infty$, on the input boundary $1\le p_1,p_2\le\infty$, where at least one input exponent is $1$ or $\infty$. For $L^1\times L^p$, $1<p<\infty$, boundedness implies compactness when $q<p/(p+1)$. For $L^1\times L^1$, the corresponding range is $q<1/2$. At and above these boundaries compactness is characterized by additional active-tail decay, and critical power weights give bounded noncompact examples. The endpoint reductions use cumulative Stieltjes measures with their initial atoms and strict Hardy-Copson brackets. An output-mass allocation argument proves local finite-rank density, including quasi-Banach targets. Applying the localization principles developed for the interior-input regime identifies the essential distance, finite-rank distance and Hausdorff noncompactness radius with the coupled active tail, with the appropriate metric power when $q<1$. For a finite left endpoint, ordinary $L^\infty$ inputs admit an exact scalar transfer completed by linear nodal approximation.

We show that for any $R,\epsilon >0$ and any prime $p\geq 2$, there exists an infinite family of $p$-ary quantum low-density parity-check (QLDPC) codes, rate $R$, checks of weight $O_\epsilon(1)$, and normalized distance at least $\delta_{\mathrm{GV}}(p,R)-\epsilon$. Here, $\delta_{\mathrm{GV}}(p,R)$ denotes the quantum Gilbert-Varshamov (GV) bound for $p$-ary stabilizer codes. In fact, we construct an ensemble of such QLDPC codes, such that a random code from this ensemble is close to the GV bound with high probability. Moreover, this ensemble matches the performance of random stabilizer codes on several quantum channels. Specifically, it approaches the quantum capacity of the erasure channel and the hashing bound for memoryless Pauli channels, including the depolarizing channel. A significant challenge in working with QLDPC codes is that they are necessarily degenerate, i.e., contain many low-weight stabilizers. A key contribution of our work is a construction of QLDPC codes with quantitative control on their degeneracy. These codes are obtained by combining known constructions of asymptotically good QLDPC codes with the expander-based distance amplification procedure of Alon, Edmonds, and Luby [FOCS'95]. Our random ensemble is constructed by starting with these low-degeneracy QLDPC codes near the quantum Singleton bound and concatenating each coordinate with a random inner code. This can be viewed as a quantum analogue of Thommesen's construction, and as an LDPC version of a result of Ouyang, with an appropriately designed outer code.