Papers

Legged robots offer a variety of automation applications in real-world scenarios. But areas that are difficult to traverse, like slopes, caves, or scaffolding, still pose a great challenge for traversal. To tackle this problem, we propose an optimized algorithm for evaluating the full actuatable wrench polytope for arbitrary contact scenarios. With our improved analysis algorithm, the torques for each joint of the robot can be calculated within a control frequency of 49 Hz. The achieved speedup allows for deployment within a regular control loop for actuating robot poses for different contact scenarios. We evaluated our stability controller extensively in simulation scenarios and validated its applicability by deploying it on actual walking robot hardware. The proposed controller achieved stability in very complex scenarios that are currently not achievable by any other controller.

Dexterous in-hand manipulation requires coordinated control of multiple actuated joints, and a runtime joint fault can abruptly disrupt the contact configuration required for successful manipulation. In this work, we propose residual fault adaptation (RFA), a teacher-anchored framework for compensating for hidden command-channel faults. RFA retains a frozen healthy teacher to provide nominal behavior and trains a recurrent residual policy to infer corrective actions from proprioceptive and command-response history. During training, fault-injection domain randomization (FIDR) varies the fault mode, affected joint, severity, and onset time, while adaptive sampling increases the frequency of fault modes associated with lower recent performance. A frozen Direct FIDR policy provides a distributional reference only on fault-active training samples and is absent from deployment. The deployed controller receives neither fault labels nor controller-switching signals. Simulation experiments on the dexterous hand indicate that RFA can improve manipulation performance relative to the healthy policy under a fixed mixed-fault protocol. Real-robot experiments with software-injected faults further demonstrate zero-shot deployment of the learned adaptation policy.

We study pseudometric-weighted correlation clustering, in which pairs have arbitrary positive or negative labels and nonnegative disagreement weights satisfying the triangle inequality. For every fixed $\varepsilon>0$, we give a randomized polynomial-time $(2+\varepsilon)$-approximation, improving the previous factor of $10/3$. The algorithm constructs an explicit feasible solution to the cluster LP with polynomial support and value at most $(1+\varepsilon)\mathrm{OPT}$, where $\mathrm{OPT}$ is the minimum integral clustering cost. Our main contribution is a weighted preclustering construction that witnesses a near-optimal clustering while bounding the total weight of admissible edges by $\operatorname{poly}(1/\varepsilon)\mathrm{OPT}$. We obtain admissibility certificates from random walks, where the factor-two Ptolemy's inequality for pseudometrics reduces the required length of walks from $O(\log n)$ to a constant. We then bound the rounding error separately at each vertex and use the triangle inequality to control its weighted cost. Sampling and coverage corrections produce an exactly feasible solution, and the factor-two rounding completes the approximation algorithm.

It is shown how evaporative cooling in hot plasma is essentially different from evaporative cooling in other media, such as neutral gases or Bose-Einstein condensates. The fundamental difference in plasmas arises both from the large mass ratio between electrons and ions in fully ionized plasma and the unusually sensitive dependence of plasma collisionality on speed. Thus, a hot ion mode plasma ($T_e < T_i$) is shown to support a distinctive evaporative cooling regime, where a strong reduction in the ion evaporation rate appears. This new regime may have application to approaches to economical nuclear fusion, where the ion tail plays an outsized role in the fusion reaction rate.

We prove that there is a function $f:\mathbb N\to\mathbb N$ such that $\chi(\Gamma(R))\leq f(\omega(\Gamma(R)))$ for the zero-divisor graph of any ring $R$, if the clique number is finite. On the one hand, this consolidates a disproved conjecture of Beck from 1988, claiming $\chi(\Gamma(R))=\omega(\Gamma(R))$ for unital commutative rings. While previous counterexamples satisfy $\chi(\Gamma(R))\leq \omega(\Gamma(R))+2$, we obtain the lower bound $f\geq k^{\Omega(\log k)}$ among finite commutative rings. Finally, we show that neither zero-divisor graphs of finite commutative semirings nor those of finite commutative nonassociative rings are $\chi$-bounded.

We extend DiBenedetto's intrinsic parabolic Harnack estimates to a class of integro-differential equations with measurable kernels modeled on the fractional $p$-Laplacian. More remarkably, we establish intrinsic, representation type nonlocal estimates and reveal that nonnegative local solutions abide by a strong maximum principle even for $p>2$, a property unique to nonlocal problems. Analogous results hold true for nonlocal equations of porous medium type.

Capability-based architectures such as CHERI provide strong support for the architectural isolation of software components. To additionally protect against microarchitectural leakage, software can be written in a constant-time fashion. Modern processors, however, rely heavily on speculative execution, which can invalidate the constant-time guarantees and leak isolated secrets transiently. In this work, we show that providing secure speculation for CHERI is non-trivial, and that existing proposals fail to preserve the confidentiality guarantees. We develop a formal framework for reasoning jointly about capability safety, speculative execution, and information-flow security, and use it to demonstrate potential leaks. We then present SCHERI, a new processor design within this framework, and formally prove that it provides end-to-end secure speculation guarantees for the constant-time policy. Our results provide formal foundations and practical guidance for building future capability-based processors, which are resilient to Spectre attacks for constant-time programs.

This paper addresses the challenge of making complex healthcare information more accessible through automated Plain Language Adaptation (PLA). PLA aims to simplify technical medical language, bridging a critical gap between the complexity of healthcare texts and patients' reading comprehension. Recent advances in Large Language Models (LLMs), such as GPT and BART, have opened new possibilities for PLA, especially in zero-shot and few-shot learning contexts where task-specific data is limited. In this work, we leverage the capabilities of LLMs such as GPT-4o-mini, Gemini-1.5-pro, and LLaMA for text simplification. Additionally, we incorporate Mixture-of-Agents (MoA) techniques to enhance adaptability and robustness in PLA tasks. Key contributions include a comparative analysis of prompting strategies, finetuning with QLoRA on different LLMs, and the integration of MoA technique. Our findings demonstrate the effectiveness of LLM-driven PLA, showcasing its potential in making healthcare information more comprehensible while preserving essential content.

Fully encrypted protocols (FEPs) provide encrypted channels that make all protocol-generated bytes computationally indistinguishable from uniform random strings. Several previous works have explored security definitions and constructions of unidirectional FEPs: protocols in which one party acts only as a sender, and the other acts only as a receiver. However, most applications require two-way information exchange, and a network adversary can observe communication in both directions and their shared lifetime. Because the semantics of bidirectional channels involve more complex shared state, it is possible that the “naïve” composition of two unidirectional channels can result in a two-way protocol that can be detected based on dependencies between the two directions, such as traffic imbalance, channel closure, failures, or connection tear-down. To address this issue, we introduce new formal security definitions for bidirectional FEPs that capture exact shaping, delivery, protocol-state integrity, private half-close, and cross-direction isolation, while revealing a public “sending schedule” and “closing epoch” that may be randomized. We show that the trivial composition fails to meet these definitions, leading to practical detection attacks. We then construct provably secure bidirectional FEPs (BiFEPs) for both the datastream and datagram settings. For datastream, we combine two direction-separated FEPs with a “wrapper” layer that prevents detection based on the mismatch between uni- and bi-directional connection states. For datagram, we add encrypted DATA/FIN/ACK with replay protection and loss-tolerant close. We validate the design through a Rust implementation and show that none of the surveyed deployed protocols provides the full set of BiFEP security properties.

Let $E/F$ be a CM extension and let $m\geq2$ be an even integer. Starting from the odd-degree Hermitian Ikeda lift of degree $m+1$ constructed by Yamana, we construct a Hermitian Ikeda lift of degree $m$ from the theta components of its first Fourier-Jacobi coefficient. We determine its global Arthur parameter and its local constituents at every finite place. Using the global multiplicity formula for unitary groups, we obtain an explicit multiplicity-free decomposition of the resulting representation of $\mathrm{U}_{m.m}(\mathbb{A}_{F,\mathbf{h}})$ and show that its isomorphism class is independent of the Fourier-Jacobi index. When $F=\mathbb{Q}$, we compare Fourier coefficients and identify the construction with Ikeda's even-degree Hermitian lift.

At edge price $\alpha=1$, we construct an infinite family of pure Nash equilibria of the unilateral max-distance network creation game with $\PoA\ge2^{\sqrt{\log_2 n}-O(\log\log n)}$. Together with the known upper bound, this gives $2^{\Theta(\sqrt{\log n})}$ along the constructed sequence of population sizes. We subdivide every edge of the bipartite double cover of a distance-uniform graph with large diameter constructed by Lavrov, Loh and Messegué, and let each subdivision vertex buy its two incident edges. A distance calculation rules out every profitable unilateral deviation. The equilibria are not strict. We also give a short proof that the price of anarchy is constant for every polynomially vanishing edge price.

Small differences on coding-agent leaderboards are often read as an ordering of systems. We audit whether the published verdicts support this reading, using 254 SWE-bench submissions across four splits without running models. On Verified, the leading two entries each resolve 396 of 500 instances. The top ten share 285 successes and 51 failures, leaving 164 instances that distinguish their outcomes. Frontier solution sets have median nesting 0.935 against a score-implied baseline of 0.774, indicating strongly shared successes. Scores also depend on the evaluated model-scaffold pair: observed within-model scaffold ranges reach 29.8 percentage points, compared with the 8.8-point spread of the top thirty. Six of nine cell-mean interaction tests remain significant after Holm correction, although this observational design does not identify causal scaffold effects. Exact paired McNemar tests separate none of the 29 adjacent Verified top-thirty pairs at alpha=0.05, while the larger Test split separates 14 of 23. A stated leader-based rule yields three descriptive tiers, or two after Holm correction; non-rejection does not establish equivalence. We release the partition and a five-step audit protocol that profiles shared outcomes, tests paired differences, reports grouping sensitivity, and estimates the instance budget needed for resolution. The results motivate reporting comparison-set-specific resolution and model-scaffold provenance instead of interpreting small aggregate gaps as established rank differences.

We discuss the interpretation of an observed running Hubble constant with the redshift, in terms of the possible underlying physical scenario. Assuming, like in the $\Lambda$CDM model, that the matter and dark energy components do not directly interact, we arrive at the conclusion that the physical content of the cosmological dynamics can always be represented with an evolutionary dark energy paradigm. We discuss both the case of the power-law running Hubble constant, and that of an optimized fitting model, both studied with the binned Pantheon Sample of the Type Ia Supernovae data. These two cases turn out to be associated with a phantom-like evolutionary dark energy.

Software-Defined Vehicles (SDVs) rely on middleware-based communication and hardware abstraction mechanisms that introduce temporal uncertainty affecting end-to-end timing guarantees. Previous work proposed probabilistic architectural models for early timing analysis, but the representativeness of these abstractions with respect to SDV implementations remained unclear. This paper presents an experimental framework combining probabilistic design-time timing analysis with a monitored Kuksa-based implementation. The same reaction-time analysis is applied both to simulation and implementation traces, enabling direct comparison between predicted and observed timing behaviour. We additionally introduce a comparison methodology separating conservative coverage from predictive fidelity of timing distributions. The results show that the proposed abstractions remain representative under different middleware load conditions while preserving conservative timing guarantees, supporting incremental timing verification approaches for SDV platforms.

Model serving is one of the largest cost drivers in production recommender systems. Maximizing its throughput requires navigating a deeply layered hierarchy: GPU kernels, the ML framework computation graph, the model server, and on-demand feature processing – each demanding specialized domain expertise. Such cross-layer expertise is inherently difficult to acquire, and does not scale with a workload that continuously grows and evolves, leaving significant cost efficiency gains unrealized. While recent AI agents have demonstrated human expert level efficiency in standalone GPU kernel optimization, automated tuning and optimization for the rest of the serving stack remain largely unexplored. We present FlashVector, an agentic system that optimizes performance across all layers of the model serving stack. The key contribution is an extensible framework to generalize the single kernel optimization agent paradigm to heterogeneous technical stacks, and to deliver performance improvements holistically. After deployment in Unity's Vector advertising platform, FlashVector achieved up to 2x throughput increase and up to 1.98x latency speedup on model server, and up to 1.6x throughput increase on feature store. These optimizations were discovered not only at the GPU kernel and computation graph levels, but also across the other components of the model serving stack, such as the model server (NVIDIA Triton's C++ codebase) and the on-demand feature transformation service (Python codebase), demonstrating the extensibility of the framework to more complex system architectures.

In the direction of Szpiro's conjecture for all elliptic curves $E$ over $\mathbb{Q}$, the current best bound is $\log \Delta \ll N \log N$ where $\Delta$ is the absolute value of the minimal discriminant of $E$ and $N$ is the conductor of $E$ (the implicit constant is absolute). This bound dates back to 2013. We obtain the stronger bound $\log \Delta \ll N\log \log N$ which was previously known only under GRH. In addition, for semistable elliptic curves we prove $\log \Delta \ll N$. Our methods build on the theory developed by the author for approaching the $abc$ conjecture via Shimura curves.

We prove two conjectures regarding partition perimeter inequalities. It was conjectured by Gray, Payne, and Watson that Franklin's partition identity becomes an eventual inequality if one replaces the size of the partition with its perimeter. We prove this conjecture by asymptotic analysis of the corresponding generating functions. Gray, Payne, Swisher, and Watson also conjectured that there is a bias for partitions with fixed perimeter to have more odd parts than even parts. We prove this conjecture by deriving the corresponding generating functions and give a positive recurrence for the coefficients. In the case that there are an equal number of odd parts and even parts we provide a connection to peakless Motzkin paths.

Real-time and cyber-physical systems are developed through successive refinements from abstract requirements to platform deployments. While timing knowledge evolves throughout this process, existing stochastic real-time formalisms typically require uncertainty to be embedded from the outset or necessitate model reconstruction when new timing information becomes available, hindering iterative timing engineering. This paper presents a refinement-oriented timing specification framework built upon the Clock Constraint Specification Language (CCSL). It supports the progressive introduction of timing knowledge across three levels: logical timing relations, quantitative real-time constraints, and stochastic timing models. Instead of altering behavioural semantics, stochastic information is attached directly to timing quantities as a refinement. This enables implementation measurements and operational observations to be incorporated incrementally within a unified declarative framework. We implement our approach in an OCaml-based simulation tool and evaluate it on a simplified but representative Software-Defined Vehicle use case.

Real-time dense SLAM is a core capability for robotics applications that require robust localization and high- quality mapping in dynamic or fast-changing environments. Recent 3D Gaussian Splatting (3DGS)-based SLAM methods have shown promising performance, but most are designed for narrow-FoV pinhole cameras, where limited angular coverage weakens pose observability and often leads to unstable photo- metric optimization under rapid motion and large viewpoint changes. We present PanoGS-SLAM, the first panoramic dense SLAM system built on 3D Gaussian Splatting. Our method per- forms differentiable rendering and pose optimization directly in the spherical domain, enabling omnidirectional photometric constraints for more stable tracking. To improve geometric consistency and robustness, we introduce (1) a sphere-consistent photometric loss that compensates for the area distortion of equirectangular projection, and (2) a depth-guided Gaussian initialization strategy that stabilizes incremental mapping in newly observed regions. Extensive experiments on both real and synthetic panoramic benchmarks (PALVIO and SynPano) show that PanoGS-SLAM consistently outperforms geometric and GS-based baselines in tracking accuracy and rendering quality, while achieving fast front-end convergence and real-time perfor- mance. In addition, controlled field-of-view experiments reveal a clear monotonic improvement in optimization conditioning and convergence stability as angular coverage increases, high- lighting the fundamental role of sensing geometry in shaping the optimization landscape of differentiable Gaussian-based SLAM. The source code will be made publicly available.

Test-time prompt tuning (TPT) enables adaptation on a single test instance, achieving improved accuracy but often sacrificing calibration performance. Most existing calibration methods introduce additional regularization terms to promote dispersion across text embeddings and reduce calibration error, yet these methods often suffer from a drop in accuracy. Motivated by the well-calibrated nature of zero-shot predictions, we propose CoTS, a simple yet effective post-hoc calibration method that preserves accuracy. Specifically, CoTS applies temperature scaling to minimize the confidence gap between adapted and zero-shot predictions. To fully exploit the potential of multiple augmentations during adaptation, we introduce a weak-strong ensemble strategy that further boosts accuracy. We then apply CoTS to this ensemble, termed E-CoTS, to maintain its well-calibrated property. Extensive experiments on diverse datasets and backbones show that our approaches effectively mitigate miscalibration without compromising primary accuracy. For instance, E-CoTS reduces the average expected calibration error of TPT from 11.90% to 5.38% on ImageNet variants, while even increasing accuracy from 60.74% to 62.95%. Moreover, when integrated with existing calibration methods, E-CoTS usually enhances both accuracy and calibration simultaneously.

Quantifying the magnetic properties of open-shell molecules is a common task in chemistry and is increasingly performed in silico using Kohn-Sham density functional theory (KS-DFT). Previous work demonstrates that the predictive accuracy of a few functionals for one such property - hyperfine coupling constants (HFCCs) - is possible, implying that such approximations must yield accurate spin-densities at the nucleus. However, the ability of such functionals to globally predict accurate spin-densities of comparable quality to rigorous ab initio coupled cluster theory, for example, is dubious, despite this being a fundamental quantity for KS-DFT. This work intends to explore the matter by evaluating moments of the spin-density, $\langle r^n \rangle = \int \rho(r)r^n d\tau$, $n=-2,\cdots,2,3$, for second-, third-, and fourth-row atoms to compare various KS-DFT functionals against CCSD. Our results broadly indicate that the tested functionals experience significant deviations with respect to CCSD spin-densities in regions up to 1 Bohr away from the nuclei, with most errors occurring in the immediate vicinity of the nucleus. We find evidence of extreme errors by some functionals for individual $\alpha$/$\beta$ spin-densities, although several ultimately end up benefiting from significant error cancellation once the corresponding global spin-density is formed. Nevertheless, a comparison between CAM-B3LYP and the Quantum Theory Project (QTP)-family of DFT functionals based on Correlated Orbital Theory conditions across all error metrics demonstrates that QTP00 more accurately reproduces the global spin-density as well as HFCCs, generally offering results in better agreement with CCSD. In line with previous work, we also corroborate the success of PBE0 and the TPSS-family of functionals for HFCCs, further finding that both approximations generally yield spin-densities that are amongst the best.

Robot teams that learn a common environment model exchange belief summaries and plan by the expected information gain of their actions. Under conjugate exponential-family beliefs the shared belief is counted once per robot at two points: at fusion, the product of local posteriors counts the common prior $n$ times, and at planning, every robot scores its plan under the same belief and the team converges on the same unknown. Both errors are removed by adding evidence increments to the shared natural parameter, realized increments at fusion and expected increments at planning. The expected increment of a committed teammate gives the next robot its conditional gain; corrected gains sum to the joint gain, the redundancy removed equals the total correlation of the planned observation streams, and sequential commitment keeps the $1/2$ greedy guarantee. The expected increment is exact for Gaussian beliefs with fixed sampling paths and for Dirichlet beliefs under the novelty approximation of discrete active inference, whose team objective has a closed concave form within an explicit bound of the exact mutual information, and fails for finite hypothesis classes, where a short exact enumeration replaces it. Experiments on cooperative RockSample, foraging, and field monitoring show that fusion correction leaves exploration redundancy unchanged, anticipated evidence removes it, and sequential commitment recovers most of the value of centralized joint planning at cost linear in the team size.

We present a component-resolved analysis of the IR–X-ray connection in a sample of 104 spectroscopically confirmed Type~1 AGN. By combining \xmm, \swift/UVOT, and new high–angular resolution \jwst/NIRCam imaging for a subset of the sources, we constructed detailed SEDs in which the IR emission was explicitly decomposed into accretion-disk, torus, and polar-dust components. This approach enables us to isolate the intrinsic AGN-IR luminosities with minimal host-galaxy contamination, providing a clean assessment of the physical relationship between the accretion flow, circumnuclear dust, and the X-ray corona. By incorporating JWST/NIRCam observations into our SED decomposition, we significantly reduce host-galaxy contamination and isolate the nuclear infrared emission with greater fidelity, particularly at near-infrared (NIR) wavelengths. This improvement is most apparent at 1 $\mu\mathrm{m}$, where sources with JWST coverage exhibit a markedly steeper relation between $\nu$L$_{\nu}$ (2 keV) and the NIR luminosity than those without JWST data. This behavior is naturally explained by starlight dilution, whereby host-galaxy emission dominates lower-resolution measurements.

The terrestrial ionosphere is a major limitation for high angular resolution imaging at decametre wavelengths. Its rapidly varying and direction-dependent phase errors can defocus sources, reduce recovered flux densities, and produce strong field-to-field variations in image quality. We investigate these effects using three overlapping pointings from the LOFAR Decametre Sky Survey (LoDeSS), observed under different ionospheric conditions. Using phase-calibration solutions on a bright source, we derive the spatial diffractive scale, the temporal decorrelation time, and the angular scale over which direction-dependent calibration solutions can be transferred before residual phase errors become significant. These metrics are reflected in the final image quality. The field with the weakest ionospheric phase structure has the sharpest compact sources and the most reliable flux-density scale, while the field with the strongest phase structure shows substantial source broadening and flux-density loss. The comparison indicates that spatial ionospheric structure is the dominant limitation in these observations. Calibration-derived ionospheric metrics, therefore, provide a practical way to diagnose and predict image-quality variations in decametre survey data.

The linear complexity and the error linear complexity of multi-sequences are measures for security in stream ciphers. In this manuscript, we present a general framework for constructing periodic multi-sequences via function fields. We prove that the constructed multi-sequences possess both large linear complexity and large error linear complexity. We apply this framework of constructing multi-sequences to various maximal function fields and we obtain many new multi-sequences with various lengths and dimensions. As a byproduct, we adopt this idea and produce many new quasi-cyclic algebraic geometric codes as well.

Open-source language models have a reproducibility problem. Despite releasing weights, training data, and recipes, none of them are provably reproducible due to the non-associativity of floating-point arithmetic. Deep learning frameworks often offer a deterministic execution mode, allowing reproducible operations on the same machines. Unfortunately, this determinism does not carry across hardware such that a user can verify that a released checkpoint was actually produced using the declared training recipe. This leaves room for undisclosed data, injected biases, or backdoors that existing techniques such as proof-of-learning or proof-of-training-data cannot rule out. We introduce a new tier of model transparency, fully auditable, in which every operation on every data sample during training is independently reproducible on heterogeneous commodity hardware with bitwise certainty. By imposing a definite order on the sources of training nondeterminism, GPU kernel reductions, data batch ordering across a data-parallel cluster, and inter/intra-node collective communication, we make it possible to replay any individual step of a large, distributed training run on a single piece of commodity hardware and check it against the published trajectory. Because replaying an entire run on one machine is infeasible, we support this with a collective verification scheme in which many independent auditors each certify individual steps, together covering the whole run. We release Open-1B, a model trained under this regime, together with its full pretraining dataset, every intermediate checkpoint, the training codebase, and the audit harness needed to reproduce and verify any step of its training.

It is important to locate water-ice in the lunar regolith to build futuristic, sustainable bases there. But communication delays from Earth, limited bandwidth, and power constraints demand an onboard, autonomous, time-efficient decision-making framework for locating volatiles such as water-ice in the lunar regolith. In this work, we present a framework, DewTwin-Coin, that can locate potential water-ice sites in real time without drilling. Its decision-making principle is based on a find-S learning algorithm that uses surface temperature and the Hydrogen-to-Oxygen intensity ratio at a location. The core idea is a physics-based rule $-$ water-ice is stable only if the temperature is below 110 K and the Hydrogen-to-Oxygen intensity ratio is between 1.7 and 2.3. We validate DewTwin-Coin on Chandrayaan-3's 3165 laser-induced breakdown spectroscopy (LIBS) elemental data with 387 Chandra's surface thermophysical experiment (ChaSTE) data. On a 16 GB RAM system, it classified all 3165 locations within 615 seconds, yielding no strong signatures of water-ice, which matches the Chandrayaan-3 in-situ analysis. This framework is very important for future lunar and other planetary missions in which an onboard rover can autonomously determine feasible drilling locations for water-ice without issuing false drilling commands in warm terrains. Thus, the mission's onboard setup can stretch its technical limits in both power and memory capacity.

We investigate domain-wall physics in a non-Hermitian Su-Schrieffer-Heeger model featuring the non-Hermitian skin effect and its higher-dimensional extensions, focusing on analytical eigenstate solutions under open boundary conditions. By gluing two Su-Schrieffer-Heeger chains with inverted coupling ratios together, we identify two distinct interface geometries, and derive closed-form quantization conditions for the complex wave number and wave functions using symmetry-based ansatzes. Besides conventional skin modes and topological zero modes, the domain walls generate additional localized states at finite energy that detach from the bulk open-boundary-condition continuum. We validate the analytical results by exact diagonalization, and further generalize the interface construction to a two-dimensional Lieb lattice, where competing nonreciprocities produce tunable funneling regimes towards codimension-one and codimension-two interfaces.

We derive an explicit description of the asymptotic singular behavior of 2D Laplace and Stokes solutions as the distance between a Lipschitz sharp tip and a smooth boundary vanishes. While classical lubrication theory for smoother boundaries relies on the anisotropy of the gap to perform dimensional reduction, the isotropic scaling imposed by a corner singularity requires a different approach. We introduce a stability-based method that allows us to construct the leading-order asymptotics of these solutions in the gap. As an application, we determine the asymptotic behavior of the Stokes resistance matrix and the pressure field.

Large language models (LLMs) trained on next-token prediction exhibit remarkable in-context learning (ICL) abilities, yet the representations that support ICL remain poorly understood. We consider such representations in a controlled setting: prompting LLMs with data emitted from hidden Markov models (HMMs) and probing for the corresponding belief state – the posterior distribution over the HMM's hidden states given the observed token history. Across six open-source LLMs prompted with data from 40 HMMs selected for non-trivial belief structure, we find that belief states are linearly decodable from residual stream activations, with peak probe $R^2$-values from 0.83-0.99 across HMM and LLM combinations, ranging from early to late layers. To establish functional relevance, we intervene directly on the probe-identified subspace via patching and steering, resulting in downstream prediction quality on the order of the untampered model, while controls degrade performance substantially. Together, these results provide representation-level evidence that ICL in open-source LLMs approximates optimal Bayesian prediction over a context-inferred generative model. More broadly, our findings extend prior results linking input-distribution structure to activation geometry: from toy networks trained explicitly on HMM data to production-scale LLMs.