Papers

Anatomical continuity provides complementary information for medical image restoration, but its use requires accounting for local anatomy and variations in slice sampling. We introduce ContiLNN, which augments two-dimensional restoration backbones with bidirectional closed-form continuous-time (Bi-CfC) modules for cross-slice modeling while retaining in-plane feature extraction. Slice-index intervals modulate gates determined by local features and hidden states, enabling propagation to respond to sampling variations without numerical ODE integration. Reference-guided consistency aligns first- and second-order cross-slice intensity differences to preserve anatomical variation, while distillation from a frozen backbone helps retain in-plane fidelity. Across five training seeds, ContiLNN improves mean PSNR over Restore-RWKV by 0.1907, 1.0176, and 1.2482 dB for CT denoising, MRI super-resolution, and reduced-count PET restoration, respectively, with lower RMSE in all three tasks. CT results are descriptive for one held-out patient. PET ablations support ordered propagation beyond additional pointwise capacity. Under contiguous training, Bi-CfC achieves higher fidelity than a Bi-GRU with similar parameter counts and arithmetic costs across all tested sampling conditions. Matched seven-slice profiling shows 52.8% lower latency and 57.0% lower peak GPU memory use than Bi-GRU. Mixed-gap training improves sparse and irregular-context performance for both operators, without a uniform ranking across metrics and contexts. Experiments with fewer training patients and a second backbone further support data efficiency and backbone compatibility.

Many tasks in scientific computing and machine learning require the Jacobian or Hessian matrix of a function. Automatic differentiation (AD) computes these derivatives to machine precision, but materializing a dense $m \times n$ Jacobian requires $n$ forward-mode or $m$ reverse-mode AD passes, one per column or row. For a large class of functions, each output depends on only a few inputs, making the derivative matrix sparse. Automatic sparse differentiation (ASD) exploits this structure in four steps: detection of the input-agnostic sparsity pattern, coloring of a graph to group columns or rows that can share an AD pass, compressed differentiation to compute a compressed derivative matrix with one AD pass per color, and finally decompression into the original sparsity pattern. The number of colors, and hence of AD passes, is often independent of the problem dimension: a banded Jacobian with $b$ contiguous bands, for instance, only ever requires $b$ colors, regardless of its size. asdex offers the first standalone ASD toolkit in the popular JAX ecosystem. With $\texttt{asdex.jacobian}$ and $\texttt{asdex.hessian}$, it provides sparse drop-in replacements for $\texttt{jax.jacobian}$ and $\texttt{jax.hessian}$.

We study a Brownian particle in $\mathbb{R}^d$, $d\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The proof uses a renormalization group induction: at each scale, the elliptic operator is well approximated by a Laplacian with effective diffusivity decaying as a power of scale. We compute this exponent exactly in dimension two.

Dense-neutrino flavor evolution is a quantum many-body problem whose fully correlated treatment becomes rapidly more expensive with increasing particle number and spatial structure. We develop a QCNO quantum simulation code that maps a inhomogeneous forward-scattering neutrino Hamiltonian with advection and finite-range interactions to TEBD2 product-formula quantum circuits, and connects ideal many-body simulation, backend-aware execution, and fault-tolerant resource estimation within the same physical model. We reproduce the exact many-body evolution of the suppressed mean-field-like transverse fast flavor instability through $N=30$ and show that even a single open-boundary interaction generates Rënyi entanglement and non-stabilizer magic, although noisy backends still produce polarization RMSEs of order $0.1$–$0.3$. The restricted active interaction graph of this problem allows us to estimate the circuit depth and $T$ gate cost through $N=50$ for both NISQ and fault-tolerant approaches. The measured TEBD2 error in our fiducial ideal simulation of order $10^{-3}$ motivates a synthesis tolerance $\varepsilon_{\rm syn}\sim10^{-7}$, corresponding to about $70$ $T$ gates per $R_Z$ rotation. The generated circuit contains $1.4\times10^4$ $T$ gates per qubit for open boundaries (twice that for closed boundaries), requiring an application-level logical-$T$ error target of order $10^{-7}$ for early fault-tolerant architectures.

Accurate simulation of rigid-body interactions is essential for predictive physical world models. Despite recent progress in modeling object dynamics, capturing how local contacts between surfaces shape object motion remains challenging. While end-to-end world models predict interactions across entire scenes or objects, in practice, rigid-body contact is inherently local, and only nearby surfaces can directly exchange contact forces. Motivated by this observation, we introduce Rigid-body Contact Reasoning (RiCo), which represents interactions between objects through sparse neighborhoods of contact surface points. RiCo combines each point's state with the relative geometry, motion, and physical properties of nearby surfaces, then reasons across the object's points to determine how these local contacts jointly affect its motion. By confining cross-object reasoning to nearby surfaces while propagating contact information within each rigid body, RiCo retains fine-grained interaction details without the cost of modeling every pair of scene points. Such properties enable RiCo a higher accuracy and contact fidelity. Experiments on MOVi-benchmark demonstrate that RiCo reduces 100-frame position and orientation errors by 31-35% and approximately 38%, respectively, compared with baselines. Moreover, RiCo achieves high contact fidelity, with ground-truth-relative penetration-time and mean-depth differences of 11.0% and 2.22 mm, respectively. RiCo further generalizes zero-shot from small-scale training scenarios to scenes containing 270 objects. Our real-world multi-ball collision experiments further provide preliminary evidence of sim-to-real transfer.

Randomized controlled trials (RCTs) identify treatment effects without confounding but are often small, whereas observational studies (OBS) are large but may be confounded. Many estimators combining a small RCT with a large OBS have been developed for the average treatment effect (ATE) and the conditional ATE (CATE). However, existing ATE estimators either make assumptions on the OBS or do not borrow enough power from them. The CATE has been studied less than the ATE. Existing CATE methods either assume the OBS are unconfounded, rely on a model of the confounding function, or accept bias in exchange for lower variance. We therefore propose a framework that, without special assumptions on the OBS, fuses the OBS and the RCT by preserving the unbiasedness of RCT-based estimation while borrowing power from the large OBS to boost precision. Applying this principle, we build an ATE estimator, AIPW-Fusion, with closed-form weights and confidence intervals, and two CATE learners, DR-Fusion and R-Fusion. Experiments corroborate our findings.

In this paper, we study the nature of wave packets and their decay behavior in the $\kappa$-Minkowski space. We employ techniques from singularity theory throughout our analysis. Specifically, we use methods from the theory of Lagrangian singularities and caustics to study the topology of the energy-level manifold. The Newton polyhedron method from the theory of oscillatory integrals is applied to analyze the decay behavior of wave packets. We find that for a generic Hamiltonian in the $\kappa$-Minkowski space, the associated wave packets exhibit different decay rates depending on the control parameter of the system. When the control parameter takes values on the cusp, the system exhibits decay of order $t^{-1/4}$; otherwise, it exhibits decay of order $t^{-1/2}$. This distinctive behavior of wave packets in the $\kappa$-Minkowski makes it fundamentally different from commutative spacetime.

We show that the characteristic cycle multiplicities of $A$-hypergeometric systems are upper semicontinuous in the parameter for every rational projective weight, thereby proving a conjecture of Schulze and Walther [Duke Math. J. 142 (2008), 465–509]. The proof uses a specialization formula for filtered families satisfying a fixed product support condition, expressing the difference between the special and generic characteristic cycles as the characteristic cycle of the first Tor module. Combined with the Gevrey index theorem, this yields upper semicontinuity of generic Gevrey irregularity and of each of its graded dimensions. We also construct non-Cohen–Macaulay semigroup rings whose Gevrey dimensions are constant in the parameter despite the presence of a genuine irregular slope, showing that the Gevrey jump locus need not coincide with the full exceptional arrangement defined by Ext.

We completely solve part (a) of Problem 17.112 in the Kourovka Notebook. We prove that a non-abelian finite simple group $G$ has a proper non-trivial ordinary $G$-permutable subgroup if and only if $G$ is isomorphic to ${\rm PSL_2(q)}$ where $q\geq4$ is a prime power and $q\not\equiv3\pmod4$, ${}^2B_2(2^{2a+1})$ where $a\geq1$, $J_1$, ${\rm Sp}_4(4)$, or ${\rm PSp}_4(p)$ where $p$ is prime and $p\equiv1,13,17\pmod{24}$. Moreover, we classify all proper non-trivial ordinary $G$-permutable subgroups of these groups. Every other non-abelian finite simple group $G$ has no proper non-trivial ordinary $G$-permutable subgroup.

We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks. The objective is the sum of a possibly nonsmooth nonconvex Lipschitz function and a convex regularizer, and the function is accessed through stochastic gradients or function values. The goal is to find a point that satisfies a Goldstein-type stationarity condition designed for composite objectives. To our knowledge, no oracle complexity bound for this setting is known under first-order access, and existing complexities under zeroth-order access are suboptimal. To handle this issue, we employ the framework of online-to-nonconvex conversion, which chooses update directions by an online learner and is known to achieve optimal rates for noncomposite problems. We extend the framework to our composite scenario by introducing new losses for the learner, which contain the regularizer itself rather than its linearization and for which a variant of online mirror descent achieves low regret. We show that the resulting algorithm finds such a point with $O(\delta^{-1}\varepsilon^{-3})$ stochastic gradient queries or $O(d\delta^{-1}\varepsilon^{-3})$ function-value queries, where $\delta$ is the Goldstein radius, $\varepsilon$ is the stationarity tolerance, and $d$ is the dimension. These rates match the optimal ones for noncomposite nonsmooth nonconvex optimization, demonstrating that the additional convex regularizer does not worsen the oracle complexity. We also give rates for the smooth case and present numerical experiments.

The memory-bound nature of the decoding stage of large language model (LLM) inference incurs significant latency. Layer-wise training-free network pruning approaches guided by the Hessian have been a prominent solution to this problem, as pruning reduces the number of nonzero parameters read from memory during decoding. Nevertheless, typical methods in this line compute the Hessian using pre-collected natural sequences, whereas the model is fed self-generated tokens during decoding, creating a distribution shift between the two sequences. The Hessian calculated on the natural sequence is different from that calculated on the generated sequence. We observe that this discrepancy causes the activation distribution during generation to deviate from that used for pruning, further hurting the pruned model performance. Moreover, most existing LLM pruning methods that bring actual speedup primarily target the sparse matrix-matrix (SpMM) multiplication, providing limited support for the sparse matrix-vector (SpMV) operations, which dominate decoding. To solve these problems, we introduce SparseDecoding, a principled decoding-aware pruning framework tailored for accurate and efficient LLM decoding. Specifically, at the algorithmic axis, SparseDecoding constructs calibration matrices from layer-wise activations collected during the dense-model autoregressive generation, excluding prefill, thereby aligning the pruning objective with the decoding activations. At the system axis, we develop an optimized N:M sparse matrix-vector kernel with bitmask indexing and fixed-step traversal. Substantial empirical results on representative LLMs (Llama-3.1-8B, Llama-3.3-70B, Qwen3-14B / 32B) demonstrate that our method consistently outperforms standard fixed-text calibration on the long-form generation benchmarks while achieving up to 1.48x end-to-end wall-clock decoding speedup on A100 GPUs.

We study the Lax operator for Macdonald symmetric functions introduced by Nazarov and Sklyanin in 2015, extending the spectral theory developed by Mickler-Moll in the Jack case. We extend the NS operator to a Lax operator acting on symmetric functions with coefficients in polynomials in an auxiliary variable, and prove it has an orthogonal eigenbasis indexed by partitions and their addable corners, with the corner contents as eigenvalues, and leading terms given by Macdonald symmetric functions. We obtain the Macdonald analogue of the author's earlier Jack box-sum identity for Littlewood-Richardson coefficients. We then strengthen this box-sum identity to a two-parameter formula, proved using a finite-rank product formula of Warnaar. Its residues give explicit linear relations among Macdonald Littlewood-Richardson coefficients.

Do LLM scientific agents rely only on their initial task context, or do they adapt their decisions in response to experimental feedback? We study this question in neural operator adaptation, where a large language model (LLM) selects fine-tuning configurations under a limited trial budget. Across transfers within and between partial differential equation (PDE) families, the LLM achieves lower held-out test nRMSE than random search and Bayesian optimisation in nearly every matched comparison. Endpoint performance alone cannot distinguish what happens, so we verify each attribution with controlled interventions. Before observing any validation score, the LLM's first configuration already ranks near the top of the corresponding random-search pool, indicating a useful initial bias. A complementary cold-start intervention shows that the selected base learning rate shifts with the PDE description. Once feedback becomes available, reassigning validation scores among evaluated configurations changes the next proposal in every case tested, whereas a value-preserving rewrite produces no comparable aggregate effect. These interventions establish that the LLM's decision-level actions respond to the given task and observed outcomes, showing that it combines a task-dependent prior with sensitivity to experimental feedback.

The discrete-time control barrier function condition for a safe set that is a union of convex sets is nonconvex in the control input. For safe sets defined by a matrix concave function through the number of its nonnegative eigenvalues, this paper shows that the set is a union of convex sets, and that the nonconvexity arises because at least one member of the union must hold, not every member. Selecting eigenvectors of the matrix function at the current state yields a convex input constraint that acts only on the eigenvalues determining membership in the set. This constraint is implied by the matrix-wide condition of prior work, and it guarantees a geometric lower bound on each of those eigenvalues along closed-loop trajectories. A double-integrator simulation with a polytope obstacle and a spectrahedron obstacle compares the proposed filter with the matrix-wide condition.

OB stars exhibit line profile variability, often associated with rotation; notably, in their UV wind-sensitive lines where discrete absorption components tend to recur cyclically. We searched for periodicity in spectral regions of the O7.5III(n)((f)) star xi Persei formed very close to the star. The NIV 1718 A line was identified as the most uncontaminated spectral with a large and homogeneous available dataset is available: 307 IUE spectra over 12 years and 11 STIS spectra taken 21 years later. We also studied 322 time-resolved HeII 4686 A spectra and MOST, BRITE, and TESS space photometry, covering a time span of 13 years. We also reconsidered X-ray studies with Chandra. A CLEAN analysis and subsequent weighted least-squares fit of the flux in this region resulted in a unique period of 2.040514(20) d, attributed to rotation. The phase of maximum flux in the NIV, SiIV, Ha, and HeII line profiles coincide with the results of X-ray variability studies. This period was also found in the photometric data. Given the coherent periodic behaviour probing the region of the wind nearest the stellar surface, we propose that xi Per has an as-yet undetected weak global surface magnetic field. The sinusoidal behaviour suggested that only one magnetic pole is visible, implying an inclination of i approximately 51 deg, and therefore, 39 deg for the magnetic obliquity. We present a conceptual framework within which weak wind confinement by a global magnetic field can create a small magnetospheric disc, while allowing for the formation of more classic corotating interaction regions at higher magnetic latitudes. The periodic variations are then understood to result from the changing projected area of the magnetospheric disc as a function of rotational phase, both along the line of sight and off the stellar limb.

JWST/NIRCam imaging has enabled efficient selection of a large number of galaxy candidates at very high redshifts. Accurate and robust selection is crucial for statistical analyses, such as measurement of the ultraviolet luminosity function (UV LF). A variety of selection methods and criteria have been proposed in the literature. We evaluate the selection methodology of galaxy candidates at $z\geq8.5$ using 183 candidates with secure spectroscopic redshifts obtained from the CAPERS JWST/NIRSpec PRISM program. The success of high-$z$ confirmation is strongly correlated with the photometric signal-to-noise ratio (SNR) in the detection filter, the strength of the Lyman-$\alpha$ break, and the $\Delta \chi^2$ between the best-fitting low-redshift and high-redshift spectral energy distribution model. However, the most efficient selection method is the use of a UV LF prior on the inferred $p(z)$ of a source, raising the success rate from $\simeq 35\%$ to $\simeq 77\%$ while achieving greater completeness than conservative SNR and $\Delta \chi^2$ cuts. Out of the 183 candidates we spectroscopically confirm 48 sources at $z\geq8.5$ via detections of emission lines and/or the Lyman-$\alpha$ break (particularly important for those with no emission line detection). We report the highest-redshift source in CAPERS as UDS-111893 at $z_{\mathrm{spec}}=12.98$, with no sources confirmed at $z>13$. This work provides spectroscopic quantification of JWST/NIRCam photometric selection at $z\geq8.5$, and demonstrates the effectiveness of a UV LF prior for high-redshift photometric selection.

Spatial public goods models show that prescribed movement toward richer locations can generate spatial patterns. We ask how such patterns emerge when agents learn where to move and how learning rates shape their consequences for collective welfare. Fixed populations of cooperators and defectors independently learn movement policies using tabular Q-learning and local observations. Cooperator learning generates clusters around resource peaks, while co-adaptation changes their strength and motion. At a fixed training budget, the largest welfare losses occur when cooperators learn at high rates and defectors at low rates. In part of this regime, learned policies also generate traveling bands supported by a shared directional preference. The conditions supporting travel change with further training, so these patterns reflect training history rather than an established asymptotic outcome. Across the tested learning-rate conditions with cooperator learning, mean collective welfare falls below random movement because increased crowding outweighs gains in resource benefit. Charging agents for the crowding they impose on others during learning recovers much of the welfare loss in the tested conditions. These results connect learning rates to the emergence and welfare costs of spatial organization driven by individual rewards.

Full Pauli-basis tomography of an arbitrary $n$-qubit state uses the expectation values of all nonidentity Pauli observables. For multiqubit systems, prior knowledge that the state is pure allows some of these observables to be omitted while retaining uniqueness. We study two resulting notions of uniqueness: whether every pure state is uniquely determined among pure states (UDP), and whether every pure state is uniquely determined among all states, including mixed states (UDA). We derive quartic uniqueness certificates from the fourth elementary symmetric polynomial of operators in the real span of the omitted Pauli observables. An exact quartic identity shows that, for $n$-qubit systems with $n\geq 3$, every pure state is UDA whenever the omitted Pauli observables contain no four distinct operators that commute pairwise and multiply to $\pm I$. For three qubits, this condition is also necessary for UDP, yielding an exact characterization of both UDP and UDA. We further prove that UDP and UDA coincide for any number of qubits whenever the omitted Pauli observables commute pairwise. These results provide directly checkable structural criteria for certifying pure-state tomography from restricted Pauli measurements.

Rate-induced tipping ("R-tipping") in ecological modelling is characterised by too-rapid change of an environmental parameter causing collapse of a population without any bifurcation being crossed ("B-tipping"). A well-known example of a slow-fast predator-prey model in which R-tipping is observed [Vanselow, Wieczorek, Feudel, Journal of Theoretical Biology, 479, 64-72 (2019)] suffers from unecological "resurgence", whereby populations driven to functional extinction recover towards stable coexistence. We propose an analytically tractable model, incorporating a strong Allee effect into the prey dynamics in a slow-fast Lotka-Volterra-type predator-prey system, which induces bistability and thus renders the extinction state a genuine attractor. Applying geometric singular perturbation theory (GSPT), we describe the dynamics of the extended model that is obtained by "ramping" of the inverse prey carrying capacity. We show the presence of a parabolic-shaped, folded critical manifold which admits a folded saddle singularity, the strong canard of which separates solutions that track the moving coexistence state from those that tip to extinction. The analytical simplicity of our model allows us to derive explicit expressions for the critical rate that separates "tracking" from "tipping" dynamics. Finally, we argue that our system represents a minimal model for rate-induced tipping to extinction, in that it incorporates three essential ingredients: bistability, a folded critical manifold, and a folded-saddle-type canard.

We study tree-level completions of four-dimensional $\mathcal N=4$ Yang–Mills theory coupled to $\mathcal N=4$ supergravity. Six-point factorization and supersymmetry Ward identities, supplemented by a peculiar-parity restriction on scalar contact terms, impose nonlinear relations between the single- and double-trace Wilson coefficients, $a_{k,q}$ and $b_{k,q}$, of the four-gluon amplitude. The simplest relation, $\kappa^2a_{0,0}=0$, excludes the single-trace $F^4$ interaction at nonzero gravitational coupling, despite its compatibility with four-point supersymmetry. On this gravitational branch, five double-trace parameters determine all coefficients through $a_{7,q}$ and $b_{8,q}$, which are reproduced by a common exponential generating form. Both the heterotic string and a family of infinite-spin-tower (IST) amplitudes realize this structure. Combining these relations with dispersion relations and partial-wave positivity in $SO(N)$ color channels yields a narrow numerical band closely bounded by the heterotic and simplest IST amplitudes. A spin-dependent mass gap excludes the IST spectrum and further localizes the region near the heterotic trajectory. An analytic unitarity analysis of the simplest IST gives $N\leq48$ and $g^2/(\kappa^2 m^2)\leq4$, matching the upper limits of the heterotic amplitude, where $m$ is the mass of the first massive level. Along the heterotic trajectory, the numerical bounds also sharply constrain the gauge-to-gravity coupling ratio at $N=48$.

Distinguishing between faint extended X-ray sources is a fundamental yet challenging task in X-ray surveys. This paper presents a benchmark comparison of convolutional neural network models for classifying simulated XMM-Newton observations of AGN and galaxy clusters, focusing on the impact of data representation and interpretability of that data. We evaluate 1D, 2D, 2D+1D, and 3D CNNs trained on distinct data representations derived from simulated XMM-Newton observations of AGN and clusters: 1D (spectral), 2D (imaging) and 3D (event cube) data. We further apply 3D-GradCAM to interpret the learned features and assess the physical basis for the model's decision making to move beyond black-box classification. Our results demonstrate that increased spectral resolution enhances classifier performance using 1D and 2D information provides a strong baseline, the integration of both domains yields significant diagnostic gains. We find that a 3D CNN architecture applied directly to spatio-spectral event cubes provides the most robust performance, with superior consistency across cross-validation folds. Interpretability analysis reveals that the 3D model autonomously learns to distinguish the diffuse thermal emission of the intracluster medium from the localized, non-thermal power-law signatures of AGN. It exploits multi-dimensional correlations that are lost in lower-dimensional projections. While the performance gain over combined 2D and 1D baselines is marginal, the 3D approach demonstrates an ability to perform implicit background characterisation. By operating directly on total photon counts within event cubes, this method bypasses the need for manual background subtraction and modelling, offering a consistent, streamlined, end-to-end pipeline for automated classification of X-ray sources in large-scale catalogues.

Recent motion generative models have demonstrated strong capabilities in synthesizing physically plausible character motion, but often overlook established animation principles used by professional animators to ground and design their animation work. Understanding and incorporating these principles into motion generative pipelines is essential for producing motions that serve not only physically grounded applications but also the needs of the character animation community. This enables the creation of characters that not only move in physically plausible ways but also feel alive, expressive, and engaging. To close this gap, we focus on the Exaggeration principle of animation and investigate how it can be incorporated into modern motion generative pipelines to produce more expressive character motions. To this end, we introduce a framework that operates at two stages of existing motion generative pipelines. The first stage introduces exaggeration during training, where we perform supervised fine-tuning of pre-trained text-to-motion models on our curated exaggeration dataset. The second stage operates at inference time, where we: (i) introduce a mathematical formulation of exaggeration based on dynamic movement primitives (DMPs); and (ii) leverage this formulation as an exaggeration guidance signal to guide existing diffusion and flow-matching text-to-motion generation models toward exaggerated motion without additional training. Through qualitative and quantitative evaluations against three strong motion generation models, we show that our methods generate more exaggerated and expressive motions while preserving neutral reference motion intent and physical plausibility.

Energy extrapolation is a well-established strategy for approaching quantum-chemical limits without performing prohibitively expensive calculations. Complete basis set extrapolation is widely used, whereas extrapolation across electronic structure methods remains much less developed. Method-Space Effective-Rank Correlation Energy Extrapolation (MERCE) is introduced as an adaptive effective-rank framework for estimating high-rank finite-basis correlation energies from second-order Moller-Plesset perturbation theory (MP2), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triples [CCSD(T)]. The method assigns adaptive effective ranks to MP2 and CCSD(T) from the local MP2-CCSD-CCSD(T) correlation energy pattern and fits a compact three-point extrapolation form for each system. A hierarchical model-selection protocol balances cross-dataset transferability, maximum dataset-level mean absolute error (MAE) ratios, robustness on developmental sets referenced to full configuration interaction (FCI), size-consistency defects, and performance for A24 noncovalent interaction energies. Across the chemically diverse benchmarks used during model development, the selected MERCE model substantially reduces CCSD(T) errors and frequently improves upon the tested higher-rank coupled cluster baselines. Transferability is further assessed using calculations performed only after the functional form and parameters were frozen. Formal nonadditivity is quantified using artificial noninteracting pairs and the actual A24 and selected S66 component calculations.

Trapped-ion quantum simulators are powerful platforms for exploring many-body physics, yet engineering of arbitrary interaction graphs remains a central challenge. To leverage the intrinsic structure of native motional modes and thereby enhance programmability, a residual-guided optimization protocol is introduced for the systematic design of multi-tone global drive spectra. While the achievable interaction fidelity is fundamentally bounded by the available motional modes, this adaptive strategy converges on the theoretical limit using a number of laser tones that scales nearly linearly with system size. The versatility of this method enables the synthesis of both long-range and traditionally difficult short-range coupling topologies. Additionally, by incorporating a penalty for residual motional excitation, the algorithm effectively mitigates errors associated with incomplete closure of phase-space trajectories. Overall, this scalable framework significantly expands the programmable capabilities of trapped-ion architectures while maintaining low computational overhead and high potential for experimental implementation.

Large language model compliance systems are deployed on the assumption that a verdict depends on the regulatory rule it is given. We test this directly across five models and 20 regulatory and platform-policy domains: delete, swap, or negate the governing rule while holding the case fixed, and check whether the verdict changes (OCS) or the model's internal representation of compliance shifts at all (ICS-delta). Neither moves much: models' verdicts are often invariant to substantial perturbations of the supplied rule, and the guard model, evaluated here under a custom-rule adaptation of its native taxonomy, is the least rule-sensitive and least accurate of the five, barely above chance (51%, versus 90-92% for general-purpose models). This reflects easy cases more than blanket neglect: on cases where deleting the rule changes a previously correct model prediction, models do track it closely. Neither better prompting nor direct intervention on the model's internal representations closes this gap. Accuracy alone does not establish that a compliance verdict is grounded in the supplied rule.

Large-scale information retrieval systems, including retrieval-augmented generation (RAG) and recommendation engines, widely use multi-layered hierarchical data structures for ultra-fast approximate nearest-neighbor search in high-dimensional vector spaces. However, the geometric conditions that ensure accurate and efficient greedy navigation remain poorly understood. In this work, we study the efficiency of greedy navigation on a hierarchy of proximity graphs constructed from \(n\) data points on the \(d\)-dimensional torus~$\mathbb{T}^d$. We identify a deterministic coverage condition under which, given any query $q\in \mathbb{T}^d$, greedy search returns a point within $(1+\varepsilon)$-factor of the distance to the closest point. This coverage property holds with high probability when the data is distributed as a homogeneous Poisson process, a Hermitian determinantal process, or a bounded-density Cox process, as long as $d = o(\log n/\log \log n)$. Under the same assumptions, the expected number of greedy hops for a fixed query is \(O\!\left(\exp\!\left(\tfrac12 d\log d+O(d)\right)\log n\right)\), yielding logarithmic expected hop count in fixed dimension.

We study the near-horizon geometry of near-extremal NS5 branes, which admits an exact worldsheet description in terms of the $SL(2,\mathbb{R})_k/U(1)$ coset. In the supergravity limit, the analytically continued time-domain reflection amplitude exhibits a singularity associated with a null geodesic bouncing off the black-hole singularity, analogous to the bouncing singularities of boundary correlators in asymptotically AdS spacetimes. We show that finite-string-length effects render this amplitude an entire function of complex time, completely resolving the bouncing singularity. This resolution is nonperturbative in the inverse coset level: the singularity persists at every finite order in the expansion.

A single multimodal large language model (MLLM) struggles to excel simultaneously at detection, localization, description, and reasoning in multimodal industrial anomaly understanding (MM-IAU). We show that in-domain training does not close this gap. On MMAD, a widely adopted MM-IAU benchmark, trained specialists reach at most 75.5% accuracy in defect localization, against 92.3% for human experts, and even detect anomalies less accurately than their untrained base model. Meanwhile, different MLLMs offer complementary strengths but share this weakness in fine-grained perception, so combining them alone cannot remove it. We therefore propose SiGMA, a spatially grounded multi-agent framework that divides labor between heterogeneous MLLM agents and a dedicated visual defect expert. A multimodal searcher supplies industrial knowledge and normal references, the defect expert turns query-reference comparison into calibrated anomaly evidence, and a label-free reliability controller weighs each source by task-wise competence and query-level evidence quality. SiGMA reaches 85.2% average accuracy on MMAD, 4.0% above the strongest trained specialist and Gemini-2.5-Pro and within 1.5% of human experts. Even with three agents of at most 9B parameters, it reaches 84.4%, and new MLLMs join without retraining.

Let $n \geq 3$. We prove that if $j \colon (\Sigma^n,g) \to (\mathbb{R}^N,dx^2)$ is an isometric immersion, then \begin{equation*} \int_\Sigma \left( \lvert \nabla u \rvert^2 + \frac{n(n-2)}{4}\lvert H \rvert^2 u^2 \right) \geq \frac{n(n-2)}{4}\mathrm{Vol}(S^n)^{2/n}\left( \int_\Sigma \lvert u \rvert^{\frac{2n}{n-2}} \right)^{\frac{n-2}{n}} \end{equation*} for all $u \in W^{1,2}(\Sigma)$, and characterize immersions for which equality is realized. Our proof exploits the conformal invariance of the inequality, and hence extends to sharp Michael–Simon inequalities for submanifolds of the sphere, of hyperbolic space, and of other conformally developable manifolds. As an application, we derive Chen–Fenchel–Willmore-type inequalities relating $L^p$-norms of the mean curvature vector to the volume of a compact submanifold of a simply-connected spaceform.

In recent years, simulation-based inference (SBI) methods have been proposed to address several data-analysis challenges faced by existing and planned gravitational-wave experiments. For example, SBI classification has recently been shown to significantly improve the prospects for detecting anisotropies in pulsar timing array (PTA) data. In this work, we use a simple toy model of a PTA to provide a more pedagogical explanation of how, and under which circumstances, SBI-based detection can improve on classical detection statistics for gravitational-wave background anisotropies.