Papers

Entangled few-photon states, such as Bell and Greenberger-Horne-Zeilinger (GHZ) states, are central resources for discrete-variable photonic quantum information processing. In many architectures, these states are generated probabilistically by first heralding single photons from biphoton sources and then interfering them in linear-optical circuits. In this work, we show that the entanglement structure of said biphoton sources can be directly exploited for noise-engineering to deliver higher quality resource states. Using the transpose identity of multi-mode squeezed vacuum states, we introduce "ghost-unitary" implementations in which the target resource-generation interferometer is applied to the heralding modes rather than to the delivered resource modes. When the dominant imperfection is interferometric loss, this relocation converts direct amplitude damping of the output into false-positive heralding events that require both higher-pair emission and photon loss. In the low-squeezing regime, these events are parametrically suppressed, yielding higher-fidelity conditional resource states. We analyze this mechanism for single-qubit states, two-photon NOON states, Bell states, and a family of $n$-qubit GHZ states, as well as for single-qubit teleportation and type-I-fusion-based resource growth. Across these examples, we delineate finite parameter regimes in which ghost-unitary implementations outperform direct implementations, with particular relevance to frequency-bin photonics where active linear-optical transformations can be relatively lossy. We also prove that, in the setting considered here, the direct implementation of the $n$-GHZ family delivers identically damped outputs: equivalent to the ideal state followed by uniform amplitude damping. This extends the known $n=2,3$ cases and provides a structural result of independent interest for photonic quantum information processing.

Quantum skyrmions in frustrated spin-$1/2$ magnets are bound states of a few flipped spins in a ferromagnetic background. Using exact diagonalization and density-matrix renormalization group calculations for the $J_1$–$J_2$ triangular-lattice model with easy-axis anisotropy $K$, we ask what happens when two such objects are brought together. The binding energy per flipped spin of a single skyrmion has a minimum at $\Nf^{*}=7$ for $K=0.02$–$0.04$, and skyrmions smaller than $\Nf^{*}$ do not exist as pairs: at any distance they coalesce into a single larger object, and pinning wells cannot prevent it. Two skyrmions of natural size, by contrast, form a bound molecule without pinning or external field, with binding energy $U\simeq-0.007J_1$ at $K=0.03$–$0.04$ and an equilibrium separation of $5.5$ lattice spacings that does not depend on $K$ or on the size of the simulation domain; at $K=0.02$, where the single skyrmion is itself marginally bound, the pair is unbound within our resolution. The two constituents keep their identity ($7+7$ flipped spins) and are coupled by a coherent exchange of magnons, visible as number fluctuations between the two halves of the domain in excess of those of two independent skyrmions and as in-plane spin correlations between the two skyrmion walls that reach $0.16$ across the gap. These correlations follow the vortex pattern of the two textures and lock their relative helicity, the quantum counterpart of the helicity-dependent interaction of classical skyrmions. We discuss the molecule as a self-assembled two-qubit element for skyrmion helicity qubits in a single layer.

In this work, we explore the idea of expert intervention delays in human-supervised robotic systems for imitation learning system. Previous works in imitation learning have primarily examined the impact of suboptimal experts, where the expert policy makes mistakes, but assumed expert interventions occur immediately after errors are made. Although delayed expert intervention can be viewed as a form of noise that might improve policy robustness, our results show that learning from delayed expert interventions is overall less effective than learning from non-delayed expert interventions; delayed expert interventions are less effective at demonstrating error avoidance behaviors. To address this, we propose Learning from Delayed Intervention (LfDI), which learns a cost function based on where and when the expert intervenes, combined with limited information about the extent of intervention delays provided by the expert. This cost function is then used to infer additional supervision for states without expert data, guiding the policy to avoid states that would likely trigger interventions. We evaluate our method, Learning from Delayed Intervention (LfDI), on simulated environments and show that it outperforms other methods that do not account for intervention delays.

Analytic time-domain expressions for the elution-time density and its parameter derivatives were recently derived from a stochastic model of linear isocratic chromatography incorporating advective-diffusive transport, injection dispersion, and fast and slow retention mechanisms. A Gaussian approximation, justified asymptotically at high column-scale Péclet numbers, was adopted for the distribution of the combined mobile-phase and fast-retention time, while slow retention was incorporated through a series of Gaussian-Gamma convolutions. Here, the underlying normal-inverse-Gaussian density is approximated by a finite Gaussian mixture using an existing quadrature rule. The elution-time PDF is a weighted sum of series of the previously derived Gaussian-Gamma form. Its parameter derivatives are also obtained. Newly derived recurrences reduce the cost of evaluating the coefficients of that series and their derivatives from quadratic to linear in truncation order for a fixed number of mechanisms. Through a probabilistic analysis of the series coefficients, the required number of terms is found to be small enough for rapid evaluation under usual chromatographic conditions. A relative roundoff-error estimator is derived to quantify finite-precision loss in the inherited forward recurrence for Gaussian-Gamma convolutions. For the cancellation-prone regime, a backward reconstruction is developed, initialized from an exact ratio of consecutive Gaussian-Gamma terms expressed through parabolic-cylinder functions. A highly accurate approximation is derived for rapid evaluation of this ratio. Independent high-precision calculations confirm the high accuracy of the resulting double-precision evaluation in the tested numerical case.

Emerging healthcare services, such as real-time diagnostics, remote health monitoring and computer-assisted surgery, require stringent Quality of Service (QoS) guarantees while operating under limited and heterogeneous edge resources. Existing Internet of Medical Things (IoMT) orchestration methods primarily focus on communication metrics such as latency and bandwidth, while overlooking edge resource constraints and dynamic adaptation to workload and user mobility. This paper presents a novel resource-slicing-based adaptive orchestration framework that integrates 5G network slicing (NS), resource-aware orchestration, and mobility-aware task offloading into a single adaptive system. IoMT services are assigned to distinct 5G network slices while jointly considering CPU capacity, memory availability and amount of storage, enabling more efficient service placement and execution. In addition, the system supports user mobility and dynamic task offloading to maintain service continuity under changing network conditions. SimPy-based simulation demonstrates that the proposed method enhances service deployment efficiency, reduces request blocking, and improves user acceptance while maintaining reliable performance across diverse IoMT scenarios.

Continuum soft robots are highly nonlinear and underactuated systems, which makes stabilizing them around unstable equilibrium points difficult. This challenge becomes even greater in low stiffness regimes, where gravitational forces dominate elastic forces. In this letter, we explore whether optimal control can address these challenges using a computa- tionally efficient method suitable for real time use. We propose a nonlinear model predictive control (NMPC) approach based on Differential Dynamic Programming (DDP), combined with an accurate reduced order Variable Strain model with analytical derivatives. This results in an efficient control framework for addressing the stabilization problem. Tested on a soft inverted pendulum and other hybrid soft rigid systems, the method outperforms traditional controllers, stabilizes more challenging configurations, and operates reliably at real time speeds (50 150 Hz), demonstrating both effectiveness and practical feasibility in experimental settings.

We consider the Neumann Laplacian on a three-dimensional periodic network of thin rods with edge thickness of order $h$ and vertex diameter of order $h^{2/3}$. We extend the fixed-graph resonant reduction to obtain a finite-$h$ periodic graph approximation with generalised norm-resolvent error $O(h)$, uniformly in the Floquet quasi-momentum. An exact gauge transformation identifies the phase-corrected graph fibres with the canonical lattice Floquet fibres, giving the same rate for the global operators. Collapsing the contact points while retaining the ambient edge tangents gives an approximation with error $O(h^{2/3})$. The proof uses a Ryzhov boundary triple and a Schur–Feshbach reduction. The estimates yield quantitative approximation of Bloch bands and stability of open gaps on bounded energy intervals. For the simple-cubic lattice, we refine the known resonant dispersion calculation to obtain a complete band-gap decomposition and $O(h)$ control of the persistence of each fixed finite collection of gaps in the thin structure.

Higher Order Modes (HOMs) in accelerating structures are resonant electromagnetic fields excited and left behind by charged particle bunches. They can severely degrade the beam quality in accelerators, such as the multi-bunch energy spread and transverse emittance, and therefore one must carefully study and mitigate them. In this lecture, various methods of HOM mitigation are reviewed. On one hand, one tries to avoid their existence, for example by careful design of the accelerating structures and damping systems. On the other hand, one can reduce the effect of the excited HOM fields, for example by means of fast feedbacks or beam alignment. Additionally, a few ways to make HOM signals useful are referred to, such as diagnostics of the beam or of accelerating structures.

Spin-driven multiferroics owe their electric polarization to lattice distortions that follow the magnetic order, yet in incommensurate magnets symmetry normally forbids such a distortion at the fundamental magnetic wavevector, and the distortions themselves are rarely observed. Here we use half-polarized neutron scattering to show that the Y-type hexaferrite Ba$_{0.4}$Sr$_{1.6}$Mg$_2$Fe$_{12}$O$_{22}$ hosts, in its saturated high-field state, a magnetic modulation and a longitudinal lattice modulation at one and the same wavevector, locked in phase. The signature is a large nuclear-magnetic interference asymmetry, $r$ ~ 0.8, of the same sign at the two conjugate satellites and persisting to 275 K. The zone contrast and the field dependence of the satellite indicate an internal, field-induced longitudinal distortion. The modulated state coexists with the transverse-conical magnetoelectric phase and outlives it, revealing a fundamental-wavevector spin-lattice coupling in a magnetic field regime previously regarded as a simple ferrimagnet.

Solar filaments are prominent features in H$\alpha$ observations. During their evolution, they often exhibit complex morphological and topological changes, which, due to line-of-sight projection effects, appear as fragmentation and merging. These phenomena make it difficult to reliably track solar filaments using automated methods, as the same structure may appear different over time. To address this issue, we formulate filament fragment association as a graph-based learning problem, where individual fragments are represented as nodes and candidate pairwise relationships are modeled as edges to infer whether fragments belong to the same filament. Furthermore, we propose a novel graph neural network (GNN) that incorporates multiplicative aggregation layers to enhance feature aggregation in the graph, replacing conventional additive aggregation with a multiplicative mechanism to better capture information between fragments. Experimental results demonstrate that the proposed method achieves reliable performance in filament fragment association, validating the effectiveness of the graph-based formulation and the proposed multiplicative aggregation mechanism.

Many optimization problems that arise in signal processing applications are based around optimizing vectors/matrices of numeric sequences. These problems are often inherently non-convex due to non-linear constraints. Such problems are frequently solved through convex relaxations of the original problem to allow for computationally simple algorithms to be leveraged, albeit with the potential for appreciable performance costs in the solution space. When the constraints of a problem can be implicitly satisfied through the structure of a Riemannian manifold, optimizing directly on said manifold affords the opportunity to solve the problem in an unconstrained fashion. Therefore, when feasible, recasting the constrained optimization problem in Euclidean space as an unconstrained optimization over a Riemannian manifold offers greater flexibility and improved efficiency over convex relaxation based approaches. This paper introduces the minimal smooth optimization theory required and adapts the notation to a radar signal design context. In addition, we apply our approach to two different problems in direct parallel to contemporary convex relaxation-based signal design literature.

Using continuum Schwinger function methods, we deliver parameter-free pointwise predictions for the complete set of twelve Standard Model (SM) $\bar B_{(s)} \to D_{(s)}^{(\ast)}$, i.e., $b\to c$, semileptonic transition form factors on the entire kinematically accessible domain. Therewith, we calculate SM theory values for the decay-rate ratios of $\tau$ and $\mu$ final states: $\{ R(D) \, , \, R(D)^\ast \} = \{ 0.290(11) \, , \, 0.267(5) \}$, $\{ R(D_{s}) \, , \, R(D_{s}^{\ast}) \} = \{ 0.283(11) \, , \, 0.251(5) \}$. The former is consistent with an existing average of SM estimates, but disagrees with the experimental average by $2.8\sigma$. Comparing transitions with light quark and strange quark spectators, we find a $2.3\sigma$ signal for violation of SU$(3)$ flavour symmetry, expressed at the 5% level in $D_{(s)}^\ast$ final states. It is induced by Higgs boson couplings into the strong interaction and modulated by phenomena deriving from emergent features of the strong interaction.

Building physical simulations from video requires coding agents to translate observations into executable models and refine them through tool use. We introduce PhysCodeGym, a benchmark for physically verifiable 4D reconstruction with $156$ tasks covering rigid-body, liquid, deformable, and wind-driven motion. Agents autonomously inspect videos, write and run Blender programs, and revise their scenes using simulation feedback. Six metrics combine rule-based measurements with rubric-based judgments to assess visual and physical reconstruction quality. Program inspection, scene measurements, and counterfactual interventions test physical consistency under original and modified conditions. Experiments with frontier coding agents reveal a tradeoff between artifact quality and completion across reasoning-effort settings, while harness comparisons and agent traces link verification behavior with reconstruction performance. Case studies show that matching visible objects and events can coexist with physical defects. Counterfactual tests further expose latent contact and support failures in reconstructions that pass ordinary physical checks, highlighting the gap between reproducing observations and building reliable physical models. Code is available at https://github.com/ShaoShuai0605/PhysCodeGym.

Active noise cancellation (ANC) is common in headphones but rare in hearing aids, and its value for understanding speech in noise is not established. Algorithms that improve signal-to-noise ratio (SNR) act only on the hearing aid's amplified path, while unprocessed sound also reaches the eardrum directly through the vent, limiting the SNR improvement that is realized. Our earlier simulations predicted that attenuating this direct path with ANC would substantially increase the benefit of such processing. We tested that prediction in three hardware conditions: a standard receiver-in-canal (RIC) hearing aid, and an ANC-capable RIC with ANC off and on. Each was fit to NAL-NL2 targets for an N3 hearing loss and recorded on KEMAR with an AI speech-enhancement algorithm (AI-SE) off and on, in seven realistic scenes above 70 dB SPL. Speech and noise spectra were estimated from each recording with a binary time-frequency mask derived from the clean speech. AI-SE produced a similar peak benefit of about 4 dB in the high frequencies in all three conditions, but that benefit stayed at or above 1 dB only above 1500, 600, and 130 Hz for the standard RIC, ANC RIC (ANC off), and ANC RIC (ANC on), respectively, closely tracking the measured attenuation of the direct path. With AI-SE on, ANC RIC (ANC on) improved SII-weighted SNR by 5.1 dB relative to the open ear, compared with 3.3 dB for ANC RIC (ANC off) and 1.6 dB for the standard RIC. With AI-SE off, enabling ANC added only 0.2 dB. ANC is therefore an enabling technology: on its own it added little, but by attenuating the direct path it allowed SNR-enhancing processing to deliver substantially greater benefit at the eardrum, extending that benefit to much lower frequencies.

Quantum key distribution provides secure communication by relying on physics principles and mathematical reasoning. Security proofs across the field can contain gaps, often between individually valid theorems integrated under mismatched assumptions. We produce an end-to-end security theorem formalized in the Lean proof assistant, eliminating hidden hypotheses by building only on Lean's standard axioms. Our proof covers composable security of the entanglement-based qubit BB84 protocol against coherent attacks by the postselection technique, accounting for finite block size, and is written in a language that enforces local operations and classical communication to help ensure a faithful representation of the protocol. The proof itself was enabled by LLM-based autoformalization, and with the proof complete, we used the same pipeline as a discovery machine, reducing the finite-size penalty on the key rate. Our work sets a reproducible standard for security arguments in quantum cryptography and shows how formal proof engines can accelerate discovery across quantum information science.

Modern neural-network training uses mixed recipes, assigning AdamW-like or sign-based updates to embedding and output layers and spectral updates to hidden matrices. These assignments are usually fixed by layer type, without a clear criterion for selecting the appropriate geometry. We turn sign-versus-spectral assignment into a measurable, layerwise decision problem. For ideal memoryless steps, we derive a finite-batch ratio of conservative descent-lemma lower bounds for spectral and sign updates. Its closed form separates signal efficiency from a geometry-dependent global curvature factor. In the positive-signal regime, the same smoothness assumption gives two-sided bounds that determine which step has the larger conditional expected decrease when the ratio crosses explicit noise-dependent thresholds. We then derive a local directional quadratic score from gradient alignments and Hessian-vector products and use it in Generalized-Scion (G-Scion) to control layerwise routing. In a controlled input-rank experiment, including directional curvature matches the measured same-iterate ordering in all seven aggregate settings, whereas the curvature-free proxy selects the opposite geometry. On 31M GPT-2, the output score routes the output layer from spectral warmup to sign, and G-Scion improves validation loss over fixed Scion in memoryless and matched-momentum comparisons. ViT-B/16 results further show that a spectral edge assignment can outperform fixed Scion outside language modelling. These results suggest that optimizer geometry need not be hard-coded by layer type and are a first step toward understanding how it should be assigned.

Assessing whether disc evolution is driven by viscosity or MHD winds is crucial to determine the conditions in which planets form. The rich statistical information encoded in nearby star-forming regions provides an excellent opportunity to probe disc evolution. In this paper, we apply the Bayesian inference tool DEMOS, designed to exploit the statistical properties of disc populations and infer initial conditions and model parameters, to the Lupus disc population. We consider the observed distributions of stellar mass $M_\star$, disc mass $M$ (from continuum flux), mass accretion rate $\dot{M}$ and CO disc size $R_{90%, CO}$. We constrain all parameters for both the viscous model, with internal photoevaporation, and the MHD winds model, with unprecedented precision. The inferred initial conditions suggest that positive correlations between initial disc properties and $M_\star$ must be present. Both models yield a typical $R_0$ of $3-5$ au for a disc around a $0.3\ \text{M}_\odot$ star, with positive stellar-mass dependence. We infer $\alpha$ (or $\alpha_\text{DW}$) of $3-4 \times 10^{-4}$ for discs around $0.3\ \text{M}_\odot$ stars, with an approximately quadratic dependence on $M_\star$. For the viscous-photoevaporative model, the typical wind mass-loss rate is $\dot{M}_\text{w} \sim 10^{-9}$ M$_\odot$ yr$^{-1}$, scaling with $M_\star$ with an exponent of $\sim 2.5$. The inferred mean age is 1.6 Myr for the MHD winds model and 0.9 Myr for the viscous-photoevaporative model. Despite a slight preference for the latter, Bayesian evidence shows that both models reproduce the data comparably well, and neither can be ruled out. However, their best-fit synthetic populations predict substantially different evolutionary pathways. Applying DEMOS to multiple populations, especially evolved ones like Upper Scorpius, will allow to place stronger constraints on disc evolution mechanisms.

The success of autoregressive language models trained with Chain-of-Thought~(CoT) supervision raises a fundamental question: How simple can a next-token predictor be while still enabling the efficient simulation of general computation through its autoregressively generated CoT? Surprisingly, we show that a single neuron suffices. For a broad family of activations, including threshold and ReLU, a single autoregressive neuron can simulate any feedforward circuit with the same activation. Specifically, a size-$s$ circuit on $n$ inputs can be simulated by a neuron of dimension $O(ns+s^2)$ using $O(s^2)$ generation steps, with both bounds independent of circuit depth and tight under natural assumptions. For threshold activations, this improves upon the simulation of Joshi et al. (COLT 2025), whose bounds scale exponentially with circuit depth. Consequently, autoregressive threshold neurons can simulate polynomial-time Turing machines, while remaining efficiently learnable from CoT supervision. Our main expressivity result relies on a novel connection to Sidon sets from additive combinatorics. As an experimental illustration, we efficiently train a single autoregressive ReLU neuron to mimic a neural network teacher with nontrivial test accuracy on CIFAR-10.

Standard diffusion processes with isotropic noise corruption are not spectrally neutral. They inherit a coarse-to-fine generation hierarchy from the nonuniform data spectrum, because each frequency band loses signal-to-noise ratio (SNR) at its own rate. For signals on a graph, the relevant spectrum is that of the graph shift operator (GSO). A natural construction, therefore, builds both the diffusion dynamics and the denoiser from graph filters of the GSO, and any such design also takes a position on this hierarchy. We expose this hierarchy as a tunable axis through a family of colored score-based diffusions. Fixing the terminal prior to a Gaussian colored by the GSO couples the drift and diffusion through a positive spectral rate, which acts as a clock for each graph-frequency band. The clock sets when a band loses and recovers information, and the forward processes of standard and certain graph-aware diffusions appear as members of this family. A GSO-valued EDM preconditioning splits the denoiser into an analytic Wiener head that carries the Gaussian second-order structure and a graph neural network (GNN) that learns the remaining non-Gaussian dependencies. Numerical experiments show that colored diffusions reach a given generation quality in far fewer sampling steps than standard diffusion.

SE(3)-equivariance provides a useful geometric inductive bias for visuomotor policies, encoding that actions covary with rigid transformations of the observation. However, existing SE(3)-equivariant visuomotor policies build this bias on a global equivariance assumption that treats the entire observation as governed by a single rigid transformation, which breaks down in real-world manipulation tasks where the task-relevant region changes across different objects. We address this by learning a phase-conditioned affordance field (PAF) over the observed point cloud, a per-point score that the SE(3)-equivariant policy uses in two complementary ways. Its score-weighted centroid serves as a learned, phase-conditioned anchor that canonicalizes the observation and the action around the active region, replacing the fixed gripper-frame reference, and the score itself is appended as a per-point feature. This introduces a local geometric inductive bias, while preserving the policy's global SE(3) equivariance. We validate on multiple MimicGen tasks under varying spatial randomization, and PAF consistently improves the success rate of the underlying policy. On multi-object real-robot tasks, PAF outperforms baselines and keeps its lead under lighting variations.

We present results from a reanalysis of the Green Bank North Celestial Cap (GBNCC) survey, conducted at 350 MHz with the Green Bank Telescope between 2009 and 2020, covering the sky with declinations $\delta>-40^\circ$. We searched the survey data using an FFT-based periodicity search, with candidate selection extending to very low spectral signal-to-noise ratios and summing up to 32 harmonics. From the 60 promising candidates identified in this search, we confirmed 51 new pulsars using the Green bank and CHIME. We also used a direct folding search method (DFSM) to search for slow pulsars between 500 ms and 10 s. Of the 51 pulsars identified in the FFT search, 43 fall within this period range, all of which were found by the DFSM. The DFSM also found an additional pulsar that had been missed during the inspection of the FFT candidates. Most of the new discoveries are canonical pulsars, with spin periods ranging from 299 ms to 4.4 s and dispersion measures from 10 to 192 $\rm pc \, cm^{-3}$. We also found a binary millisecond pulsar with a spin period of 3.2 ms in a 4.5-d orbit. We redetected 855 pulsars in the data, 825 of which were found in the FFT search. Within the effective parameter space of our periodicity search, the FFT search recovered $\sim$98 % of the known pulsars within the survey sensitivity limits. After accounting for previously reported pulsars whose observations were not processed or whose parameters lay outside our search range, the updated GBNCC census now includes 964 pulsars.

Robots sharing walkways need to know where people will be, yet semantic occupancy maps show only where they are. We present ReForesight, an open-source ROS 2 toolkit that adds instance-level future occupancy and re-identification after occlusion to a particle-based semantic mapping pipeline. A 36.6k-parameter MLP predicts each tracked person or vehicle up to 3 s ahead, guarded by a Kalman fallback and a stationary gate, and the object's own points are moved to the forecast pose, forming a "ghost" point cloud in the map frame without an occupancy decoder. An optional tracker re-associates objects after occlusion using keypoint descriptors the pipeline already computes and a metric 3D gate. On four held-out CODa sequences, the MLP lowers the mean 3 s final displacement error from 0.728 m (Kalman) to 0.662 m and beats a similar-size GRU (0.692 m) on every sequence, at 0.04 ms per instance on one CPU core. Code, all models, and a ROS-free demo are released; field demonstrations use an outdoor cleaning robot.

Automatic speech recognition (ASR) remains challenging for low-resource languages, where the scarcity of transcribed speech limits the development of accurate systems. This challenge is particularly acute for African languages such as Ewe, which has millions of speakers but remains underrepresented in publicly available ASR resources and benchmarks. In this work, we consolidate, normalize, and partition existing Ewe speech resources into a standardized 174-hour Ewe ASR benchmark, the largest to date to our knowledge. We fine-tune and evaluate pretrained speech models, including Whisper and AfriHuBERT, to establish strong baselines on our benchmark. Whisper-medium achieves a word error rate (WER) of 37.98%, while AfriHuBERT achieves 39.70% on the test set. We further provide a qualitative analysis of common recognition errors. We release the benchmark under the name Nufo, derived from the Ewe word for "talk", accompanied by models and evaluation resources, to facilitate future research on Ewe and other underrepresented African languages.

We study the behavior of saddle connection directions on translation surfaces from the point process viewpoint. We define a direction point process for saddle connections of length at most $R>0$ on every translation surface. Given a general ergodic $\mathrm{SL}(2,\mathbb R)$-invariant measure $\mu$ on a stratum of translation surfaces, we also define a slope point process associated with $\mu$. By utilizing the dynamics and geometry of strata, we show that for almost every translation surface, the direction point processes, rescaled by $R^2$, converge in distribution to the slope point process as $R\to\infty$. Using Palm distribution theory, we prove the existence of limiting joint gap distributions and obtain new regularity results for gap distributions associated with the general $\mu$. Finally, we study how these point processes and joint gap distributions behave as the genus $g$ tends to infinity. In the principal stratum, we show that the slope point processes, rescaled by $g^2$, converge in distribution to a Poisson point process. By passing to the corresponding Palm distributions, we show that the rescaled slope gaps converge jointly to independent exponential random variables, which is in stark contrast to the known non-exponential gap distributions in a fixed genus.

We prove an improved fractal Weyl upper bound for resonances of infinite-area convex cocompact hyperbolic surfaces, expressed in terms of the Hausdorff dimension of the limit set and the Fourier decay exponent of the Patterson–Sullivan measure. This bound also yields a sharper upper bound for the essential spectral gap for these surfaces.

Fast Fourier Transform (FFT)-based preconditioners provide an efficient approach for approximating inverse operators in large-scale linear inverse problems when the underlying operator structure can be exploited in the Fourier domain. Optical Fourier transforms (OFTs), the analog of digital Fourier transforms, exploit light propagation through optical systems and offer the potential for greater throughput and energy efficiency than conventional digital FFT implementations. However, practical optical systems are inherently imperfect and introduce a variety of errors into the computed output. Thus, OFTs can only provide approximations to their digital counterpart, and the implications of these inexact transforms for iterative solvers remains largely unexplored. This work investigates the feasibility of OFT-based preconditioning of iterative Krylov subspace methods for the solution of discrete inverse problems. We digitally simulate the optical Fourier transform using the FFT and incorporate sources of error expected in practical optical systems into the simulation. Numerical experiments suggest that given sufficient optical system quality, iterative methods utilizing OFT-based preconditioners can maintain reconstruction quality and convergence comparable to those with fully digital FFT-based preconditioners.

Model reduction can substantially reduce the computational burden of model predictive control (MPC) for high-dimensional systems, but a reduced dimension chosen for performance may be insufficient for safety-critical operation. This paper introduces a safety-aware dimension-selection framework in which the prediction model adapts to the order of the model required to maintain a certified finite-horizon safety condition. Dynamic active subspaces provide a performance-oriented ordering of reduced coordinates, while finite-horizon error bounds robustly enforce discrete-time control barrier function constraints. The controller selects the smallest prediction order for which the resulting safety-critical MPC problem remains feasible. We establish full-order horizon safety, recursive feasibility, and closed-loop invariance of the safe set under the proposed reduced-order formulation. The proposed approach therefore adapts the prediction complexity to safety requirements, avoiding unnecessary high-dimensional prediction during benign operation.

We derive a local upper bound on the coordinate-time Lyapunov exponent of unstable circular null orbits in static, spherically symmetric, asymptotically flat Einstein–Gauss–Bonnet gravity in $n\geq5$ dimensions with nonnegative Gauss–Bonnet coupling. On the regular Einstein branch, the tangential null energy condition suffices; no additional density-pressure inequality is required for the principal result. The bound retains the local matter-density contribution dictated by the field equations. Using the spherical mass relation, we express the departure of its dimensionless coefficient from the Einstein value $n-3$ in terms of the difference between the local density and the enclosed generalized Misner–Sharp mass per areal volume. This gives a sufficient density-contrast criterion for the Einstein optical bound to remain valid at nonzero coupling. Optical Gaussian curvature and tangential null convergence provide geometrical interpretations that distinguish radial tidal instability from the focusing of a null congruence. Vacuum solutions saturate the bound, while a Maxwell field with nonzero charge produces a strictly positive gap. The smooth Einstein limit and explicit vacuum and charged solutions provide consistency checks. A separate matter condition yields a density-free corollary. We also discuss consequences for strong-deflection lensing and test-field eikonal damping within their respective regimes of validity.

This paper addresses trajectory tracking for a class of nonlinear mechanical systems with input delay. The delayed actuator channel is represented as an equivalent transport partial differential equation, thereby transforming the original delayed system into a coupled plant-channel representation. A finite-dimensional approximation of the delay channel is then constructed through Galerkin projection, resulting in an explicit ODE model of the delayed actuator dynamics. Using this reduced-order plant-channel model, a backstepping controller is developed, and Lyapunov analysis establishes uniform exponential stability of the nominal tracking error dynamics for the reduced-order Galerkin model. To enhance practical implementation, a command-filtered version is also introduced to avoid direct differentiation of virtual controls, for which a corresponding uniform ultimate boundedness result is obtained. Simulation studies are provided to validate the proposed design and illustrate the effectiveness of the method.

Propaganda detection systems usually operate as black boxes, lacking explanations. To address this, we hypothesise that persuasive techniques contain definitional characteristics with respect to their social-political setting. We introduce ReCoT, a reasoning-conditioned detection framework that captures definitional cues of persuasive techniques via population-level refinement and performance-guided resampling, without requiring additional explanation annotations. On INDI-PROPspan, ReCoT achieves a macro F1_LCS of 0.364, surpassing baselines and reaching 88% of the SFT upper bound on Avg F1_LCS. Similarly, on PTC, ReCoT reaches 85% of the SFT upper bound on Avg F1_LCS, closing much of this gap while remaining interpretable. Importantly, the analysis of the reasoning pool's convergence and update pattern for ReCoT shows effective refinement of reasoning CoTs.