Papers

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with $2\Delta$, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at $t=0$ its oscillations decay algebraically as $1/\sqrt{t}$. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge $2\Delta_g$, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal–Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as $1/\sqrt{t}$.

Characterizing the genetic architecture of phenotypic variation is central to human genetics, yet trait polygenicity—the diversity of genetic variants responsible for a heritable trait's variation in a sample—is rarely quantified formally. O'Connor and Sella (2026) addressed this need by proposing four polygenicity measures that are quasi-arithmetic means and therefore satisfy a set of principles they argue are desirable for polygenicity measures. Here, I show that these four measures are points on a continuum corresponding to the Hill numbers, a family of ecological diversity statistics offering a tunable emphasis on variants with small versus large contributions. I further show that the Hill numbers are the only quasi-arithmetic means suitable for measuring polygenicity because they are the only ones that are "effective numbers" of variants. The connection to the Hill numbers clarifies the relationships among O'Connor and Sella's four polygenicity measures: all four are effective numbers of variants, and those that give greater weight to variants with small contributions yield higher estimates of polygenicity. It also connects polygenicity to results in the ecological diversity literature, including the replication principle, a criterion for how such measures should behave when independent sets of variants are combined. Together, these results offer a unified framework for interpreting, comparing, and selecting measures of trait polygenicity.

Carbon ion radiotherapy (CIRT) provides greater biological effectiveness than conventional photon therapy because of its high linear energy transfer and its ability to induce complex DNA damage. Mayo Clinic Florida is developing the first CIRT facility in the United States, using a synchrotron-based system with dose-driven continuous scanning (DDCS). Although DDCS improves delivery efficiency by keeping the beam on during spot transitions, it also creates the challenge of accurately modeling the dose delivered during beam motion (move dose), which is not fully addressed in current treatment planning systems. In this work, we present a method for accurate simulation of move dose to support Monte Carlo (MC) dose calculations. The method models realistic beam trajectories, including the characteristic hockey stick motion caused by different scanning speeds in the X and Y directions, and accounts for time-dependent beam intensity with linear ramp-up behavior. The beam path is divided into small segments, each represented by a move source with analytically determined position, intensity, and monitor units. Beam intensity fluctuations are also included using a stochastic model based on measurements. Validation using TOPAS simulations for a 430 MeV/u carbon ion beam in a water phantom showed accurate modeling of move dose and the resulting dose distributions. This method provides a practical framework for MC-based dose calculation in clinical CIRT.

Scaling a learned flow-matching velocity field $v_\theta$ by a gain $\gamma(t)$ was recently shown to greatly improve generation quality. Prior work argued that velocity fields trained with mean-squared error (MSE) systematically underestimate velocity magnitude and that scaling corrects this error. We show that MSE training does not create a velocity-magnitude deficit. We find instead that velocity scaling reduces population time lag: sampled states at model time $t$ resemble training states from an earlier time. Velocity scaling and moving model time back are two ways to address this population time lag. Across architectures and model sizes, measuring population time lag and using it to select a gain greatly improves generation quality, reducing FID from 28.0 to 12.2 (estimated by linear interpolation between FID measurements at neighboring gains) on ImageNet-256 at NFE 25 without guidance.

Digital sleep technologies make tracking accessible, yet users often struggle to interpret what changes in their sleep mean. Behavioral sleep medicine addresses this through guided discovery, helping patients develop personal interpretations rather than simply receiving explanations. To bring this to everyday tracking, we present DREAM, an LLM-powered voice assistant that monitors conversational sleep diaries, selectively invites users to interpret meaningful changes, and uses their interpretation to tailor subsequent education. We co-designed DREAM with sleep specialists iteratively and evaluated it in a six-week field study (N=14) against a generic-education control. DREAM participants reported greater personal sleep insight, motivation, and willingness to use the system, and described a clearer rationale for trying strategies. Our findings suggest that guided reflection made participants more active interpreters of their own sleep. Furthermore, we argue that expert involvement is not a single transfer of knowledge but an ongoing process of making tacit judgment explicit and testable.

We determine the equal-mass two-dimensional three- and four-loop sunset Feynman integrals $I^{(3)}_\circleddash$ and $I^{(4)}_\circleddash$ at large Euclidean momentum in terms of the genus-zero Gromov–Witten theory of the local Calabi–Yau fourfold and fivefold $X_L=\operatorname{Tot}(K_{F_L})$, where $F_L\subset(\mathbb P^1)^{L+1}$, $L=3,4$, is a smooth hypersurface of multidegree $(1,\ldots,1)$. At two loops the sunset integral is governed by the prepotential of a local Calabi–Yau threefold. For $L\geq3$ the moduli spaces of unmarked stable maps have positive virtual dimension and there is no prepotential, therefore the Feynman integral is governed instead by the one-point potential $\mathcal F_{\gamma_L}$ with insertion $\gamma_L=H^{L-1}/(L-1)!$, by its gravitational descendants, and by $\zeta(3)$ boundary terms coming from the Gamma class. At both loop orders the coefficient of $R^{L-1}$ in the Frobenius expansion in the mirror coordinate $R$ is $-\theta_Q\mathcal F_{\gamma_L}$ with the Novikov variable $Q=\exp(R)$. At three loops the whole Feynman integral is an explicit expression in $\mathcal F_{\gamma_3}$ alone, because genus-zero recursion determines all descendant series from it; at four loops two diagonal series suffice, and the $\zeta(3)$ term is itself corrected by $\theta_Q\mathcal F_{\gamma_4}$. At three loops we also derive the analytic normalization independently, from the Picard–Fuchs equation and the polar part of a Mellin transform, prove integrality of the multiple-cover transforms for arbitrary integral insertions together with an explicit quantum-$K$ formula, and compute the exact period connection polynomials. Finally we give endpoint values along the Euclidean axis, bounds on the Taylor radii in the Novikov variable $Q$, a computer-assisted proof of the four-loop endpoint nonanalyticity, and a comparison of the normalizations at two, three and four loops.

One aspect of complexity for quantum many-body systems resides in their ability to exhibit entanglement, uniquely quantum correlations central to quantum computation. To quantitatively explore the diminishing effect that quantum noise has on entanglement resources, we focus on the negativity witness, an entanglement measure based on local time reversal transformations that provides a perfect witness in simple physical contexts. Beyond calculation of the negativity, we analyze the associated eigenvalue spectra of partially transposed density matrices for qudit-qudit bipartitions, finding that higher negativity rank provides greater(reduced) robustness to targeted(depolarizing) noise. In particular, we extend the maximum number of separable states that can be arbitrarily mixed into an entangled pure ensemble while retaining negativity to be exactly equal to the original negativity rank. Furthermore, we report how understanding the role of the negativity rank with respect to the completely depolarizing channel allows direct calculation of (1) certain noise boundaries for the Absolutely Positive Partial Transpose (APPT) subspace beyond which no unitary operator is capable of generating negativity and (2) the maximum qutrit-qutrit APPT purity. Beyond proving tight bounds and contributing to the ongoing search for APPT entanglement, these results expand our understanding of the nuanced relationship between computation with entanglement and practical environments for operating quantum devices.

Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. Here we define different types of stagnation - commonly referred to as swamping or absorption, where one operand in an addition is nearly or completely rounded off—in floating-point summation, and propose algorithms for detecting it in numerical code that uses floating-point arithmetic. Whilst cancellation in floating-point arithmetic has been studied, for example by Lam et al. in `Dynamic floating point cancellation detection', stagnation has not been exploited as a property for detecting and reporting accuracy loss in floating-point operations. We have built prototype dynamic stagnation detection tools in two languages, MATLAB and Julia, and applied them to applications ranging from basic summation of a vector, to matrix multiplication, to a fluid flow simulation model. With this tool, users are able to identify areas of their floating-point code where stagnation occurs - in those areas of the code one may need to switch to a higher precision number format, apply stochastic rounding, or use different summation algorithms such as compensated summation. To the best of our knowledge we provide a first rigorous definition of stagnation in floating-point summation.

We study the properties of matrix coupled oscillators in ring networks and show that the system supports several families of synchronized clustered solutions. One of these families is characterized by consecutive oscillators belonging to distinct clusters, called alternate ordering, with two classes of solutions. The first consists of one or two static clusters, that lock on phases that depend on the coupling parameters, despite the non-zero natural oscillation frequency. The second one is comprised of clusters that rotate rigidly. The number of clusters depends on the neighbor connectivity. We also investigated sequential ordered clusters and showed that the constraints imposed by the interface oscillators imposes additional restrictions to equilibrium configurations. Although some of these solutions are stable, their basins of attraction depend on model parameters: when the system is initialized with random phases, the oscillators tend to organize themselves into dynamical clusters whose interfaces move along the ring. The oscillators within each cluster remain close to one of the stable phase configurations, while particles are exchanged at the interfaces. When interfaces moving in opposite directions collide, the corresponding clusters annihilate, until a state with interfaces moving in a common direction is reached.

Supermoire lattices in large-angle twisted bilayers have recently been shown to emerge from periodic arrangements of commensurate stacking motifs, yet the microscopic structural mechanism governing their formation has remained unresolved. Here, we uncover the microscopic origin of supermoire order as a hierarchical lattice relaxation process. Combining force-field simulations with experimental validation via super-resolution, layer-resolved multislice electron ptychography, our results identify interlayer Se-Se repulsion at the picometer scale as the driving force, giving rise to coupled short-range (about 1 nm) moire relaxation and coexisting long-range (about 10 nm) supermoire modulation. These findings demonstrate that even picometer-scale lattice relaxation remains critical in large-angle moire systems and must be explicitly considered in understanding their emergent electronic and quantum phenomena.

Social media have expanded opportunities for communication and political participation, but today's dominant platforms are optimized primarily for engagement and advertising revenue, contributing to concerns about polarization, misinformation, social isolation, and loss of civility. We explore how social media might instead be deliberately designed to support democratic discourse, collective deliberation, and collective intelligence. Drawing on literature across computer science, psychology, political science, and related fields, we present a modular collection of mechanisms that could be implemented individually or in combination. These include user-controlled and open recommender systems, tools for exposure to diverse perspectives, new forms of cognitive and epistemic feedback, collaborative and AI-assisted fact-checking, privacy and visibility controls, mechanisms for improving civility and evidentiary integrity, and reputation systems that reward high-quality participation. The proposals are intended both as a practical menu of design possibilities and as a starting point for broader interdisciplinary discussion about digital public spaces designed around democratic values rather than engagement alone.

An explorative study of Type Ia Supernovae (SNe Ia) light curves is presented. $\Delta m_{t}(X)$ decline-rate metrics are used to evaluate alternative characterisations of light curve diversity and the Luminosity-Width Relation (LWR). Using a sample of 362 SNe Ia from the Carnegie Supernova Project (CSP-I and CSP-II), Gaussian Process regression is used to fit $B$- and $g$-band light curves and measure decline-rates across multiple post-maximum timescales. The LWR is calibrated using a clean subsample of SNe Ia with host-independent distance moduli and Fitzpatrick (1999) reddening corrections. Decline-rates $\Delta m_{10}(B)$ and $\Delta m_{10}(g)$ are found to capture the LWR effectively, while mitigating the severe degeneracy that affects longer timescales for fast-declining ($\Delta m_{15}(B) \geq 1.6$ mag) events. Continuous, piecewise linear models are presented that seamlessly anchor the transition between normal and fast-declining regimes. The decline-rate $\Delta m_{10}(X)$ closely approximates the results of the more complex colour-stretch parameters, requiring less post-maximum temporal coverage than $\Delta m_{15}(B)$ or $s_{BV}$, and offers an even greater sensitivity for slow decliners. $\Delta m_{10}(B)$ provides a precise and practical tool for large-scale photometric surveys and real-time observer classification.photometric surveys and real-time observer classification.

Distinguishing trivial from topological superconducting phase remains a central and contested experimental challenge, since most existing probes infer the bulk phase transition indirectly, from boundary signatures that can be sensitive to local physics. Here, we propose an alternative that probes the bulk topological phase and is based on supercurrent response. We study a one-dimensional Rashba spin-orbit-coupled superconducting nanowire with an applied magnetic field that opens a topological gap. We show that for strong spin-orbit coupling, the superfluid stiffness, and consequently the supercurrent, is suppressed by a factor of two inside the topological phase, producing a non-monotonic signature of the bulk phase transition as a function of chemical potential. We further use a low-energy helical model to understand this suppression analytically. Our results show that the bulk topological phase transition can be detected through kinetic inductance measurements.

We study strictly abnormal sub-Riemannian extremals satisfying the Goh condition and a strong (i.e., coercive) generalized Legendre condition, imposed only at the Lebesgue points of the reference control. We prove that such a control is smooth, that the projected extended Hessian of the end-point map is uniformly coercive on the admissible set of variations for short times, and that the abnormal covector gives a quantitative separation of the end-point of the reference arc from the image of the admissible set under the nonlinear end-point map. As a consequence the reference arc is rigid and, for short times, it is a length minimizer: every admissible curve with the same end-points and no greater length is a reparametrization of the reference arc. In particular, among controls of constant speed the reference control is the unique length minimizer. All the estimates are uniform on the admissible set, and no assumption is made on the dimension of the manifold, on the growth vector of the distribution, or on the corank of the differential of the end-point map.

Small language models (SLMs) have been increasingly adopted for onboard robot operation because they enable intelligent decision-making. However, existing approaches are mainly distillation-oriented and rely on enumerating representative task-solution pairs. This makes dataset construction difficult and limits generalization to diverse robot tasks whose possible forms grow rapidly. This paper proposes Skill-SLM, a framework that reformulates SLM-driven robot operation as a task-decomposition and skill-composition problem. Given a natural language task instruction, Skill-SLM decomposes the task into subtasks, selects appropriate skills from the skill library, and orchestrates the selected skills into executable robot operations. First, to support the skill-driven workflow, we propose a novel robot operational skill aware context-free grammar (CFG) to extract the skills required to accomplish tasks and build the skill library accordingly. Then, we configure LLM teachers to induce and synthesize training datasets for the SLMs, enabling SLMs to decompose tasks and orchestrate skills reliably. Additionally, we employ a progressive skill orchestration strategy to improve the reliability of skill implementation and overall robot operation. Experiments on UAV operation tasks indicate that Skill-SLM substantially outperforms distillation-oriented baselines, especially on unseen tasks that require generalization of capabilities. Additional experiments on ground vehicle tasks further demonstrate that Skill-SLM can be applied to different robot platforms.

Low framerates during rendering arise when frame time exceeds the rendering budget, or can be introduced deliberately to save computation, for example in foveated rendering, where the periphery can be rendered at a reduced spatial and temporal resolution. However, low frame rates also cause non-smooth motion, or judder, degrading perceived image quality. Judder manifests as aliasing in the spatiotemporal frequency domain; temporal filtering, such as blurring, can suppress it, but at an additional computational cost and incur a larger loss of detail. Prior work has shown that inexpensive synthesized noise can compensate for the loss of spatial detail and velocity perception caused by foveation, but its potential for restoring motion cues lost to reduced temporal resolution has not yet been explored. We show that such noise can itself restore these cues: translating a Gabor kernel reduces to a phase shift, and modulating a kernel phase creates a perception of smooth motion without having to fully rerender the noise. We derive a method that, given the on-screen angular velocity and the temporal rendering rate, selects a spatial frequency noise band such that phase shifts perceptually mask judder without introducing motion aliasing of their own. User experiments show that our technique substantially expands the range of angular velocities over which motion at reduced temporal resolution remains smooth, without objectionable degradation of image quality.

Long-horizon robotic manipulation is often built by chaining independently trained skills. Although each skill can be reliable in isolation, performance degrades sharply when skills are chained: each downstream skill must start from the state its predecessor leaves behind rather than from its training distribution. We study this failure mode, Observation-Space Shift (OSS), and ask what causes these skill-seam failures. Using privileged simulator resets, we find that the dominant shift comes from displaced scene state (e.g., an open drawer or secondary objects left behind by earlier skills), not from the robot's joint configuration or the object the downstream skill manipulates. To test this diagnosis, we build a fully learned detect-restore-resume system: a task-progress monitor detects the stall, a learned policy restores the displaced scene components, and seam-robust fine-tuning lets the skill resume. It recovers the seam where every tested alternative fails, which we treat as evidence for the diagnosis rather than as a general-purpose method. On the BOSS-44 benchmark, the system improves full-chain success from 7.6% to 26.5%, a 3.5x improvement over the base policy and 51% of a privileged restoration oracle, whereas best-of-K resampling, a Diffusion Policy, and world-model baselines fail to recover from the evaluated seam states. On a real Franka arm running a fine-tuned $\pi_{0.5}$ policy, the same monitor is limited by exterior-camera observability, yet closing the loop still recovers some otherwise-terminal failures, motivating wrist and gripper sensing. These results suggest that some long-horizon composition failures are better addressed by restoring the scene before resuming the policy than by retrying from an off-support state.

Instance-specific rubrics are common in AI benchmarks where reliable evaluation requires specific expert knowledge. This approach is difficult to scale, prompting research into the generation of rubrics with large language models (LLMs). However, even when expert rubrics are available as references, it is unclear how to productively evaluate the quality of generated rubrics at scale. In this paper, we introduce a method for the evaluation of rubric generation, which we call Interventional Transfer (IT), based on the idea that two rubrics are similar if they move together when a response is perturbed to pass/fail one of them. In contrast to existing approaches for evaluation of rubric generation, we argue that different forms of interventional transfer can be used to evaluate the utility of generated rubrics for different tasks. For instance, we apply this approach in a case study on HealthBench, where we demonstrate an asymmetry in rubrics generated by Qwen3.8-27B, Deepseek-V4-Flash, and Opus-5, used to evaluate responses from GPT-5.6-Terra. Perturbations that degrade responses according to the generated/expert rubric transfer into lower scores on the corresponding expert/generated rubric, but perturbations that improve on one rubric do not reliably transfer into higher scores on the other. We argue that this finding has implications for the usage of LLM-generated rubrics for performance monitoring and hill-climbing. We contrast our approach with existing approaches for rubric evaluation, which do not surface the same asymmetry that we observe.

When audio, video, and text disagree, accuracy alone does not show whether to acquire another source or abstain. We study these choices in a controlled three-score benchmark: a policy observes two signed scores, may request the third at a cost, and can abstain. The primary reward is mechanism-specific: abstention is correct only for one designated ambiguity mechanism and is penalized under mixed corruption. Matched controls show that a threshold policy matches always-request decisions with fewer requests; its advantage over always-answer fusion depends on the reward assigned to that ambiguity. On a partially held-out synthetic split, the threshold policy reaches 0.789 +/- 0.006 targeted decision accuracy and 0.481 +/- 0.014 utility across 83 seeds. A three-score majority reference reaches 0.626 +/- 0.008 and 0.252 +/- 0.016, but uses more information. In a matched-budget test, a train-only value selector improves utility over no-query and matched-random policies at 10% and 25% budgets, while pair uncertainty has higher utility at every budget. At 50% and 63.7% budgets, the selector lowers utility despite slightly higher non-ambiguous accuracy. If all abstentions are scored incorrect, majority outranks the threshold policy in utility. At a central temporal setting, full-trace controls match the neural models while position perturbations separate them. On held-out-actor emotion clips, eight-frame fusion has opposite-signed accuracy differences for two encoder pairs, with both actor intervals containing zero; matched-request routing gains are small and uncertain. These results separate full-modality accuracy from pre-request selection value and show that selection value depends on budget and the observed-pair ranking.

Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical for deriving interpretable and generalizable relationships characterizing the underlying phenomenon. Traditionally, this estimation depends strongly on domain expertise and prior field-specific knowledge, with experts selecting appropriate functional forms or parametric families based on empirical evidence and theoretical understanding. The coefficients of these forms are then typically determined through parameter estimation. In this paper, we develop a framework for estimating symbolic expressions of unnormalized distributions from observed samples using domain-specific prior knowledge, such as the range of interactions and a predefined set of primitive functions. We integrate deep generative models with symbolic regression (SR), incorporating inductive biases, such as factorizing large distributions, to keep the problem tractable. The deep generative models we examine include likelihood-based models, viz., flow models, and score-based models. Experiments show the effectiveness of the proposed framework for estimating density functions for multivariate toy distributions as well as lattices from computational physics, namely, XY model and $\phi^4$ theory. When applied to the renormalization problem in $\phi^4$ theory, the proposed framework estimates compact symbolic approximations of the hamiltonian function at different scales directly from samples, yielding expressions that may be challenging to derive using traditional perturbative or analytic approaches in nonperturbative settings.

We study stochastic Hamilton–Jacobi–Bellman equations arising from stochastic optimal control problems with random coefficients and possible degenerateness. The viscosity solution is reformulated by using adapted smooth random test fields that touch on stopped space–time neighborhoods almost surely. The state coefficients are predictable, with no continuity assumption on their dependence on the underlying Brownian path. Under linear growth of locally Lipschitz drift and diffusion coefficients, polynomial growth of the running and terminal cost coefficients, and a nonempty separable metric space-valued control set, we show that the value function is the unique viscosity solution in this formulation among adapted continuous fields with square-integrable random polynomial growth bounds. The comparison proof constructs adapted fields from controlled trajectories and spatially shaken conditional values, using a weak semimartingale decomposition and regularization of its positive finite-variation part. In particular, the uniqueness allows for diffusion coefficients being random, degenerate, and depending on time, state, and control, whereas earlier uniqueness results of Qiu [SIAM J. Control Optim. 56 (2018), pp. 3708–3730] and Qiu and Zhang [Ann. Appl. Probab. 33 (2023), pp. 889–930] were obtained under additional structural restrictions on the diffusion coefficient, such as determinism combined with either superparabolicity or independence of the state and controls.

As AI systems increasingly interact with people and make decisions about them, understanding human interpretations becomes an important part of developing human-centered AI. Conventional machine learning and AI systems are largely developed under the assumption that a single definitive ground truth exists, with variability in human annotations often resolved through aggregation or treated as noise. However, for many human-centered tasks, human interpretation is inherently ambiguous, and multiple interpretations of the same input may be simultaneously reasonable and valid. Reducing such ambiguity to a single target risks overlooking meaningful information about the diversity of human perception, judgment, and experience. In this position paper, we call for a shift towards modeling the interpretation space of plausible human judgments, while distinguishing meaningful ambiguity from annotation noise. We argue that this perspective should guide how AI systems are represented, learned, evaluated, deployed, and governed, supporting more human-centered AI that better reflects the diversity of human interpretation.

We introduce, for an embedded Legendrian link~$L$ in a contact 3-manifold~$(M,\xi)$, the group of its Legendrian motions. Analogously with the smooth case, we prove that this Legendrian motion group is isomorphic to the fundamental group of the space of unparametrised Legendrian embeddings. For all Legendrian knots in the standard contact 3-sphere, we characterise Legendrian motions in terms of contact mapping classes of the knot exterior. In an appendix, we give a short exposition of our techniques applied to the smooth case, comparing to the classical Dahm homomorphism.

Earth-Moon vertical orbits are periodic solutions of the circular restricted three-body problem (CR3BP) with substantial out-of-plane motion, considered for high-latitude lunar observation and cislunar navigation. This work develops an end-to-end framework for high-fidelity reference generation under rotating-frame geometry constraints and receding-horizon model predictive control. A representative $L_2$ vertical orbit yields a 5.5-year reference with negligible deterministic correction and remains maintainable in five-year Monte Carlo simulations under realistic uncertainties. The workflow produces locally optimal solutions across 90 consecutive daily start epochs and 200 catalog cases. Finite-Time Lyapunov Exponent along the reference and stable/unstable CR3BP directions interpret station-keeping behavior.

We construct high-accuracy semi-analytic mode functions for scalar cosmological perturbations in mLQC-I within the hybrid approach to study ultraviolet regularity and gravitational particle creation. The evolution comprises an asymptotic pre-de Sitter branch, a pre-inflationary region containing the quantum bounce, and inflation. In the intermediate region, we construct the complete third-order uniform asymptotic solution and introduce adaptive defect correction. The third-order approximation achieves sub-percent complex-mode accuracy for representative higher-wavenumber modes; defect-corrected solutions agree with numerical evolution at the 0.00001% level over the tested low-wavenumber range. Retaining amplitudes and phases provides a controlled basis for future precision calculations of primordial power spectra and non-Gaussian correlations. We compare the de Sitter vacuum selected in the remote contracting branch with a fourth-order adiabatic state imposed at the bounce. Finite-wavenumber matching and the strict ultraviolet limit require different asymptotic treatments: extrapolating the leading connection to infinite wavenumber yields a spurious constant negative-frequency coefficient and an apparent ultraviolet divergence. Instead, the large-wavenumber de Sitter mode agrees with the fourth-order adiabatic expansion through the order required for energy-momentum tensor renormalization, and smooth exact evolution preserves this ultraviolet structure. Finite and intermediate modes can nevertheless undergo nonadiabatic Bogoliubov mixing and particle creation. Finite-mode particle production thus coexists with ultraviolet regularity. The ultraviolet argument also extends to the dressed-metric approach in its corresponding large-wavenumber regime, while quantitative mode functions must be recalculated using its effective mass.

Although cloth is known to exhibit different outcomes under repeated fast dynamic motions, even when the same trajectory is applied, this variability has not yet been systematically characterized. Quantifying it is essential to assess the reliability of learned manipulation policies and the extent to which simulation can reproduce real-world behavior. To study this, we execute the same trajectory ten times across four dynamic tasks, two of which are novel, each tested with three cloths of very different properties and at up to three execution speeds, with a total of 269 recorded rollouts. For all of them, we record small marker positions on the cloth and synchronized stereo camera. We then formalize different metrics to quantify variability, and our results show how it is significant in every test condition, in most cases one to three orders of magnitude above the repeatability inherent to the robot and sensing noise. Our results also show variability is driven mainly by the cloth physical properties but also grows with speed. By replaying all the rollouts in four calibrated modern cloth simulators, we show that none of them can reproduce the variability magnitude we observed in real cloth, nor its ordering. Together with our analysis, we publish the dataset with synchronized OptiTrack, vision and robot logs and their corresponding simulator twins.

The Weisfeiler-Leman (WL) algorithm tests graph isomorphism by assigning colours to $d$-tuples of vertices and iteratively refining the colouring according to neighbourhood configurations until it stabilizes. Increasing $d$ allows the test to detect finer structural differences between graphs, but the computational cost grows exponentially with $d$. The central question is which dimension allows us to distinguish nonisomorphic graphs. We relate a sufficient such dimension to the structure of a graph $G$ through a rank decomposition over $\mathbb F_2$. The two parameters governing the bound are the maximum cut rank $w$ and the fork load $\ell$, which is the largest sum of the parent and two child cut ranks at a fork in the decomposition tree. We prove that WL in dimension $\max\{\ell+1,2w+2\}$ distinguishes every finite nonempty vertex-coloured graph $G$ with such a decomposition from every graph not isomorphic to $G$. Consequently, for $k\geq1$, graphs of rank width at most $k$ can be distinguished from every nonisomorphic graph in dimension $3k+1$, graphs of linear rank width at most $k$ in dimension $2k+2$, and edgeless graphs in dimension one. Uncoloured Cai-Fürer-Immerman (CFI) constructions give linear lower bounds for both width parameters, so the upper bounds are tight up to constant factors.

Motivated by applications in Diophantine approximation, we develop a new fibering mechanism for non-degenerate manifolds in $\mathbb{R}^n$, showing that they admit local decompositions into families of non-degenerate curves with uniform quantitative non-degeneracy properties. The manifolds are required to be $C^N$ with the essentially optimal bound $N\geq \max\lbrace n,l+1\rbrace$, where the manifold is $l$ non-degenerate. Furthermore, we show that this uniform quantitative local control can be globalised into a qualitative statement, so that almost every point of a non-degenerate manifold lies on a non-degenerate curve contained in the manifold. Our approach is perturbative and shows that the fibering structure arising in the analytic setting is stable under sufficiently small $C^N$ perturbations. The method provides a framework for extending fibering based results in Diophantine approximation from curves to manifolds. Such applications are considered in the paper.

A compressible fluid column between two thin elastic plates carrying plane Poiseuille flow supports discrete structural-acoustic wall modes. This paper analyses their coupled dispersion and reports a flow-induced instability. Because a no-slip profile has zero velocity at the wall, the convective (Ingard-Myers) term in the compliant-wall boundary condition vanishes identically, so the plate-admittance conditions stay Mach-independent and a Fredholm solvability argument yields a closed-form $O(M)$ correction to every coupled wavenumber, valid for any smooth no-slip shear profile. Above the critical Mach number $M_c=\Omega/\xi$ at which an interior critical layer first appears, the two structural branches behave oppositely. The antisymmetric mode is not absorbed by the critical layer, a null protected by an exact mid-plane pressure node rather than by weak coupling. The symmetric mode, which carries no such node, is convectively unstable. Its growth rate, fixed both by a spatial calculation anchored to the dissipative wall-Stokes term and by a convention-independent temporal one, strengthens towards the inviscid limit, identifying an inviscid critical-layer instability rather than a viscous artefact. A Briggs-Bers analysis classifies it as convective. Its neutral curve follows $M_c(\Omega)$, and its growth rate is proportional to the wall compliance, vanishing for rigid walls, so it is distinct from the Tollmien-Schlichting and Kelvin-Helmholtz mechanisms. Three independent numerical schemes agree to one part in $10^9$, and the closed-form correction matches numerical differentiation across three shear profiles.

Safety filters that rely on control barrier function (CBF) quadratic programs (QPs) are typically analyzed under the assumption that the QP is solved instantaneously, although nonzero computation time can render a computed input unsafe by the time it is applied. This paper develops a dual leaky integrate-and-fire (LIF) event-triggered safety filter for linear systems that accounts for this delay. Two LIF states monitor a shifted CBF residual and the deviation of the held input from the nominal feedback law. A computation is initiated when either LIF state reaches its threshold; the previous input remains applied until the prescribed application time, and any solution returned earlier is stored until then. A closed-form charging profile relates the safety-LIF threshold to residual-growth bounds, ensuring sufficient residual margin over the application delay. Under the stated assumptions, the resulting hybrid system guarantees forward invariance, completeness, and non-Zeno execution, with positive lower bounds on computation-initiation and input-application times. A spacecraft terminal-approach simulation demonstrates safety with fewer optimizer calls than a delay-tightened periodic filter.