Papers

Developing long-acting injectable formulations requires the simultaneous optimization of drug loading, release kinetics, viscosity, injectability, stability and other objectives. To navigate this multidimensional space, Corbion and Intrepid combined Corbion's diverse PURASORB bioresorbable polymer library with Intrepid Labs' proprietary AI algorithm (ANDROMEDA 1) to develop in situ forming depots for a therapeutic peptide. Over approximately 15 weeks, 181 unique formulations spanning drug loadings of 6-12% w/w were prepared and characterized through broad design-space mapping and targeted multi-objective optimization. Four lead candidate formulations were identified at 6%, 9%, and 12% w/w drug loading. Each met the predefined viscosity and injectability criteria while providing distinct 30-day in vitro release profiles. The study evaluated polymers spanning a broad range of molecular weights, including commercially available PURASORB grades and new polymers under development by Corbion to expand its polymer toolbox. ANDROMEDA 1 identified that polymers with intermediate molecular weights provided a favorable balance between sustained release and solution viscosity. Together, these findings demonstrate how integrated polymer expertise and AI-driven optimization can rapidly identify differentiated formulation candidates, focus the development space, and establish a strong data-driven foundation for further optimization and in vivo evaluation.

Several discrete design tasks, such as molecular discovery, require diverse collections of useful candidates at low computational cost. High validity alone does not guarantee a useful candidate library: repeatedly generating the same valid structures leaves few distinct alternatives. Training for both feasibility and diversity is challenging because many relevant criteria can only be evaluated after hard decoding. To address this challenge, we propose EGO (Evolutionary Generators with One-step inference), a framework for training compact generators directly on discrete outputs. The method combines distribution matching with structural constraints and optional diversity or history-dependent rewards, using antithetic low-rank evolution strategies without requiring criterion-specific differentiable surrogates. Once trained, the generator produces the entire graph in a single neural-network evaluation. On molecular generation benchmarks, our compact generator achieves over $50\times$ the valid-and-unique yield per estimated dense operation compared to recent one-step flow-map baselines while retaining high chemical validity. In scaffold completion, EGO achieves an observed $44.3\times$ speedup over MoLeR in generation to SMILES and produces approximately $10\times$ as many filter-passing proposals within matched time budgets for generation and screening. Beyond chemistry, EGO produces $1.54\times$ as many distinct held-out elite architectures as relaxed gradient training on NAS-Bench-101. The low generation cost may enable real-time candidate generation across discrete design tasks, supporting interactive exploration of constrained design spaces and rapid construction of candidate sets for downstream evaluation.

In extensions of the Standard Model with Majorana sterile fermions, additional Dirac and Majorana CP-violating phases can have a significant impact on charged lepton flavour violating (cLFV) transitions and decays. We investigate angular observables associated with polarised $\mu$ and $\tau$ cLFV three-body decays, $\ell_\alpha^+ \to \ell_\beta^+ \ell_\gamma^+ \ell_\delta^-$, including parity- and time-reversal asymmetries. We analyse the correlations between different cLFV observables, showing that sizeable asymmetries can arise over experimentally accessible regions of parameter space. The resulting patterns of angular observables provide powerful probes of this class of Standard Model extensions and, in the event of a cLFV signal, could offer a means to test or potentially falsify the underlying framework.

We adapt Stevens's power law to measure the implicit ability of AI models to read visualizations, which can reveal the built-in perceptual mechanisms of algorithmic models. In our pilot study, AIs see no legend. In the color conditions, no colormap name is provided either. GPT-5.5 first views a reference visual representation and estimates its magnitude, then estimates the magnitude of each subsequent image of the same representation relative to that reference. Our evaluation of twelve visual variables makes how algorithmic models read visual encodings measurable, comparable with human perception, and more transparent to humans.

Frontier AI evaluations increasingly use open-ended, agentic, long-horizon tasks whose transcripts can span hundreds of pages of outputs and actions from complex multi-agent networks. The observability envelop-the range of what evaluators can reliably infer about an agent's behaviours-is therefore narrowing. Language model assistants can help classify and interpret agent behaviour but also afford human evaluators significant analytical degrees of freedom, threatening the reproducibility and auditability of language-model-based transcript analysis. Transect is an open source package built on Inspect Scout to help evaluators understand how a long agent run unfolded, identify behaviour worth investigating, and check interpretations against the transcript. Users specify task context and behavioural vocabulary in a reusable evaluation-family configuration, with judge models and analysis settings supplied separately. Transect's navigable reports align recorded events, token use, sub-agent activity, and model-generated behavioural labels on a common turn-based timeline. Reviewers can quickly grasp a run's narrative, trace any label or event to its source turns, and export the underlying data tables for cross-run analysis. We demonstrate the workflow on an AI R&D evaluation that generated almost 13 million tokens, dividing the agents' work into behavioural phases aligned with research-skill classifications, sub-agent delegations and interactions, and token use. The combined view shows a focus on operational work and manuscript production, with little evidence of a sustained hypothesis generation stage-arguably a necessary component for high-quality scientific outputs. Transect's flexible, customisable transcript-analysis pipeline will enable evaluators to keep pace with longer, more complex, more frequent AI evaluations while supporting scientific rigour, transparency, and reproducibility.

Maritime systems operate in highly dynamic environments where unexpected equipment failures can compromise safety, reliability, and operational efficiency. Recent advances in artificial intelligence (AI), machine learning, digital twins, and predictive maintenance enable proactive failure prediction and prevention. However, ensuring trustworthy and explainable decision-making remains a major challenge in safety-critical maritime applications. This chapter reviews key AI technologies required for explainable failure prediction and prevention in maritime systems and presents a conceptual architecture capable of supporting autonomous or human-in-the-loop corrective actions. This architecture integrates data acquisition, time-series forecasting, anomaly detection, risk assessment, decision-making, and explainable AI into a closed-loop framework. With reference to the architectural components, a review and discussion of relevant maritime studies is performed, outlining their methods, advantages, and limitations. Furthermore, it highlights current challenges, including uncertainty and robustness, model generalization, explainability, limited availability of maritime datasets, and operational deployment, and identifies future research directions toward trustworthy AI-assisted maritime decision-making.

We prove that the number of labelled embeddings of any $n$-vertex tree $T$ into an $n$-vertex graph $G$ of maximum degree $d$ satisfies $$ \mathrm{inj}(T,G) \leq (d/e)^n \exp(o_d(1) n). $$ The bound is sharp up to determining $o_d(1)$, even for paths, and the dependence of the error $\exp(o_d(1)n)$ on $d$ is necessary. As an immediate corollary, we obtain an optimal anticoncentration bound for the isomorphism class of a uniformly random spanning tree in a connected $d$-regular graph, answering a conjecture of H. Lee. The proof combines Brégman's inequality with entropy methods.

In this paper, we show that for any coquasi-Hopf algebra $H$ and any $H$-Majid bimodule $M$, the cotensor coalgebra $\operatorname{CoT}_H(M)$ admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.

In this work, we present a comprehensive investigation of the in-medium properties and internal structure of pseudoscalar mesons within the light-front quark model (LFQM), employing both Gaussian and power-law (PL) wave functions. We incorporate in-medium quark properties obtained from the quark-meson coupling (QMC) model into the LFQM, thereby providing a unified description in terms of quark degrees of freedom. We investigate the distribution amplitudes (DAs) and parton distribution functions (PDFs) of $\pi^{\pm}$, $K^{\pm}$, $D^{\pm}$, and $B^{\pm}$ mesons in symmetric nuclear matter. We find that the evolved in-medium pion DA and PDF are strongly suppressed at intermediate $x$, indicating substantial medium-induced modifications to the meson structure. The signs and magnitudes of the modified Gegenbauer coefficients $a_n'$, the parameter $\xi$, and the Mellin moments of the DAs and PDFs in nuclear matter are found to be consistent with other theoretical predictions. In particular, the second Gegenbauer coefficient of the pion DA, $a_2^\pi$, increases substantially with nuclear density, from $0.096$ ($0.057$) in vacuum to $0.232$ ($0.202$) at normal nuclear density for the Gaussian (PL) wave function, respectively. This increase indicates a broader pion DA and an enhanced second Gegenbauer moment in the nuclear medium. We further calculate the pion PDF ratio $R_{\rho/0}^{\pi}$ and find that its $x$ dependence exhibits a behavior qualitatively similar to the observed European Muon Collaboration (EMC) effect, highlighting the important role of QCD evolution in shaping the medium-modified partonic structure. Finally, we compare the calculated free-space $\pi^{\pm}$ and $K^{\pm}$ DAs with available free-space lattice QCD results and find reasonable agreement.

This article offers an introduction to metaprogramming in Isabelle/HOL for beginners, based on a running example for working with multivariate polynomials. The example is motivated by our formalisation of universal Diophantine pairs. We describe the implementation of the poly_degree command, which computes upper bounds on the total degrees of multivariate polynomials and automatically proves their correctness. The complete metaprogram handles a variety of special cases but herein we present a simplified version for the sake of exposition. We describe our development process and design decisions; our goal is to offer a small and self-contained tutorial on Isabelle/ML, for mathematicians who want to get started with metaprogramming.

Post-training quantization is a standard route to fitting vision transformers (ViTs) into edge compute and memory budgets, yet quantized models become especially brittle under distribution shift. Test-time adaptation (TTA) addresses such shifts without labels, but most existing approaches are poorly aligned with the constraints of quantized inference. Prevailing TTA methods recover accuracy through backpropagation, while backprop-free methods often still incur overhead from extra forward passes or parameter updates, and lightweight feature- or logit-level methods recover only part of the loss. Across these approaches, a quantization-specific failure mode that amplifies the drop is not directly targeted: under shift, activations occupy frozen quantizers' calibrated ranges differently, distorting their code distribution. We propose Quantizer-Aligned Recalibration (QuAR), a single-pass TTA method tailored to quantized ViTs that neither backpropagates nor updates any model parameters. QuAR recalibrates activations at the input to a frozen quantizer, mapping the test stream's running per-channel statistics back toward the source calibration. On ImageNet-C with ViT-B, QuAR achieves the highest mean accuracy among state-of-the-art backprop-free TTA methods at 3-, 4-, 6- and 8-bit weight/activation precision, outperforming the strongest baseline by 2.28 points at 8 bits and 4.00 at 3 bits, with 46% lower latency and a memory overhead of only 0.17 MB (0.01% of peak inference memory). Analysis and diagnostics trace the gain to a reduced per-channel mismatch at these quantizers, which restores the code distribution the baselines leave unchanged or distort further. A single fixed configuration remains ahead across continual streams, non-i.i.d. label shift, seven out-of-distribution suites, and three other backbones.

We construct an example of a smooth embedding of $\mathbb{S}^{p+q-1}$ in $\mathbb{R}^{p+q}$ whose evolution under the mean curvature flow forms an isolated singularity at one point, after which it is a smoothly embedded copy of $\mathbb{S}^{p-1}\times \mathbb{S}^q$. In doing so, we prove some general results about $SO(p)\times SO(q)$-invariant mean curvature flow whose initial data is generated by the rotation of a graphical profile curve, including an analysis of bubblesheet singularities. The most involved part of our analysis is an instant smoothness result, which requires a delicate approximation and pseudolocality.

Waterfall-like spectral features observed by angle-resolved photoemission spectroscopy (ARPES) are commonly associated with strong electronic correlations or electron-boson coupling. Here, we investigate this connection in the kagome metal LuFe6Ge6, a structurally simple member of the FeGe-derived family, using polarization-dependent ARPES, density functional theory and dynamical mean-field theory. We observe a pronounced vertical spectral feature at the L point extending over several hundred meV in binding energy. Its orbital character is identified as predominantly Fe dyz, and its energy onset coincides with a van Hove singularity located approximately 0.3 eV below EF . Despite the waterfall-like spectral response, dynamical mean-field theory (DMFT) reveals only weak electronic correlations, while the calculated electronic structure closely reproduces the experimental bulk bands. We propose that the anomalous spectral weight may arise from inelastic scattering of the outgoing photoelectrons, potentially associated with the large density of states near the van Hove singularity. Our results suggest that waterfall-like features can emerge without strong electronic correlations and highlight the possible role of the underlying band structure and photoelectron energy-loss processes in their interpretation.

Flow-matching models start from an isotropic Gaussian source, the standard choice when the correlation structure of the data is unknown in advance. For multi-channel brain recordings, however, part of this structure is known in advance. Electrodes sit at fixed positions on the head, and volume conduction through the skull and scalp makes nearby electrodes co-vary in a way that is shared across subjects. Existing EEG generative models nonetheless leave the network to learn this from scratch. We put this structure into the source instead. From the sensor coordinates alone, we build a k-nearest-neighbor graph and take a graph-Matérn function of its Laplacian as the source covariance, so the flow starts from spatially coherent patterns rather than channel-independent noise. The change adds no learned parameters, works with any coupling and any drift network, and uses the same three hyperparameters on every dataset. Across eight EEG datasets and four flow-matching methods, the graph-Matérn source lowers the spectral discrepancy between generated and real signals in the five clinical bands (PSD-KL) on most datasets. PSD-KL falls by 12% to 17% in geometric mean over datasets depending on the method and by up to 40% on PhysioNet-MI, the densest montage. We show that the improvement stems from the spatial eigenvectors of the local graph of sensor positions, since randomizing the eigenvectors while preserving the eigenvalue spectrum eliminates the gain. Furthermore, a prior fitted directly to the empirical data covariance performs worse than isotropic noise. The same construction applies unchanged to MEG, intracranial EEG with patient-specific grids, and a traffic-sensor network, lowering PSD-KL for every method on each. https://jd730.github.io/projects/GraphPrior

Nuclear matrix elements (NMEs) for neutrinoless beta-beta decays (DBD) and inverse-beta decays (IBD) are crucial for studying neutrino properties beyond and within the standard model by using DBDs and IBDs. The charge exchange nuclear reaction (CER) is a realistic probe for studying experimentally these NMEs. The present work shows for the first time an experimental way to extract the Gamow-Teller (GT) and tensor (T) NMEs associated with DBDs and IBDs from the q (momentum transfer) dependence of the CER cross-section by taking into accounts explicitly both the central and tensor interactions. The present method was applied for CERs on 71Ga used for the solar-neutrino and the Ga anomaly and on 100Mo and 128Te used for DBD and IBD. Impacts of the CER with the tensor interaction on the DBD and IBD NME studies are discussed.

While graph neural networks (GNNs) have shown substantial promise in connectome-based diagnostic classification, deterministic models inevitably suppress pipeline-induced noise and model ambiguities, yielding overconfident predictions. Although uncertainty quantification (UQ) is widely adopted in voxel-level segmentation, its role in connectomic graph learning remains largely unaddressed. This paper presents a comprehensive narrative review of UQ frameworks tailored to connectome graph learning alongside an empirical case study demonstrating the perils of uncalibrated predictions. We delineate sources of aleatoric and epistemic uncertainty across neuroimaging pipelines and review prominent UQ paradigms, from Bayesian approximations and ensemble methods to evidential learning and conformal prediction. In our case study, a temporal Graph Attention Network (GAT) trained on dynamic functional connectivity (dFC) matrices from the SUDMEX CONN dataset achieves 80.0% diagnostic accuracy (F1 = 0.794) for Cocaine Use Disorder. However, a post-hoc uncertainty audit via Monte Carlo dropout reveals severe overconfidence (ECE = 0.127), with misclassified subjects assigned prediction confidences up to 95%. This empirical divergence between discrimination and calibration underscores the confidence paradox in deep connectomics. Our findings establish that rigorous UQ, calibration, and selective prediction mechanisms are indispensable for deploying trustworthy graph-based biomarkers in clinical neuroscience.

The definition of the sixth generation mobile communication is in the full swing. Mobile communication aims for the convergence of physical, human and digital world. Research project 6G NeXt is considering two demanding use cases, holographic communications and drones anti-collision system, which set heterogeneous requirements on the communication as well as the computing infrastructure. In both use cases, the clients are widely spread in the network and are cooperatively interacting with each other. Especially for holographic communication, also high processing power is required. This makes a high-speed distributed backbone computing infrastructure, which realises the concept of split-computing, inevitable. Furthermore, tight integration between processing facilities and wireless network is required in order to provide adequate quality of service to the users. This paper illustrates the use case scenarios and their requirements. Afterwards, an appropriate solution approach to realise those is elaborated. Here, the novel technological approaches are discussed based on the developed overall communication and computing architecture.

In this paper, we study the regularity of free boundaries for Monge-Ampère obstacle problem up to the boundary. We mainly focus on how the growth order of boundary value near the contact point impact the regularity. We also find an interesting phenomena that under quadratic growth boundary value, the free boundary enjoys better regularity in high dimensions than in two dimension.

Visual world models enable goal-directed control through decision-time action search, but their deployment efficiency is often limited by conservatively large planning budgets. We show that competitive task performance can be achieved without agreement with the Full-budget action, that sufficient budgets vary across model–task pairs, and that iterative planners repeatedly encode solve-invariant context. To address these inefficiencies, we propose {SufficientPlan}, a simple deployment framework that requires no modification to pretrained world models or planner updates. Its {Paired Sequential Budget Certification (PSBC)} component uses paired closed-loop evidence to search for and certify a reduced model–task-specific budget within a predefined Full-performance tolerance. Its {Static-Context Reuse (SCR)} component caches observation and goal representations across search iterations while preserving candidate-dependent planning and selected actions. Experiments across multiple world-model backbones and visual-control tasks show that SufficientPlan substantially reduces search budgets and planning latency while maintaining competitive control performance.

Erasure codes are widely used in distributed storage systems to provide fault tolerance. An $[n,k]$ erasure code encodes $k$ data symbols into $n$ coded symbols and distributes them across $n$ storage nodes. Once the code parameters are fixed, the achievable fault tolerance is also fixed. However, the failure rates of storage nodes may vary over time, and dynamically adapting the code parameters to these variations can substantially reduce storage overhead. Motivated by this observation, Maturana and Rashmi introduced convertible codes, which allow an $[n^I,k^I]$ initial code with redundancy $r^I=n^I-k^I$ to be transformed into an $[n^F,k^F]$ final code with redundancy $r^F=n^F-k^F$, while preserving the required code properties. Convertible codes whose initial and final codes are both MDS codes are called MDS convertible codes. They are of particular interest because MDS codes provide the maximum erasure tolerance for a given amount of storage overhead. Several works have established lower bounds and constructions for the bandwidth cost of MDS convertible codes in the split regime. However, the tight bound in the parameter range $r^F<k^F<r^I$ remains unknown. In this work, we establish a family of new rank inequalities for stable MDS convertible codes with linear conversion procedures and derive an improved lower bound on the bandwidth cost consisting of three cases for this remaining range. We prove that the bound is tight by presenting three explicit constructions, one for each case.

We construct distinct high-dimensional mean-zero finite range lattice random walks having pairwise-equal return probabilities for all step counts. The same examples provide pairwise-distinct shapes of discretizations of the standard Laplacian with pairwise-equal density state functions. The main contribution is a reconstruction theorem: to a colored trivalent graph one associates a quantum Clebsch–Gordan polytope, and this association is a full functor, in particular from the polytope one can uniquely recover the original graph. These polytopes appear as moment polytopes of toric degenerations of character varieties (moduli spaces of rank-2 bundles on curves), yielding a combinatorial non-abelian Torelli theorem. In symplectic geometry, the reconstruction theorem implies that monotone Lagrangian tori on odd character varieties associated with these degenerations are pairwise non-Hamiltonian isotopic. These results, and some of the applications, arose from the study of mirror symmetry for moduli spaces of vector bundles, and of the related Laurent phenomenon for mutations of graph potentials.

A planner in a network of strategic agents faces three entangled challenges: the optimum depends on agents' private information, queried agents may misreport to steer the outcome, and exact computation does not scale. We study these challenges in multi-activity network games with heterogeneous private technologies, in which the planner sets non-discriminatory prices. We show that the optimal prices admit a centrality-based decomposition of the welfare kernel: each agent's contribution scales with its squared centrality in a network reweighted by agents' preferences across activities. This decomposition motivates Poll, a polling algorithm in which the planner samples one agent per round, walks briefly through the agent's neighborhood, and updates the price from a local report. From the same decomposition flow three forms of efficiency: computationally, Poll uses significantly fewer operations than exact computation and other distributed methods, requiring up to three orders of magnitude less communication on a real-world network with over 300,000 agents; statistically, its query complexity scales with topology and preference heterogeneity rather than explicitly with population size; and economically, it converges to welfare-maximizing prices while admitting behavior-specific implementations that induce truthful reports and detect adversarial deviations.

Polarization imaging provides physical cues beyond intensity imaging but typically requires specialized hardware. Recent methods infer polarization from RGB-like inputs, yet predict only normalized Stokes components or relative descriptors, from which the radiometric scale needed for full Stokes reconstruction has been divided out. We introduce PolarScale, a benchmark that makes this scale an explicit prediction and evaluation target. Built on existing trichromatic full-Stokes measurements, PolarScale takes the per-scene normalized total-intensity image $s_0$ (a scene-referred linear image, not a consumer sRGB photograph) and asks models to predict normalized Stokes components, AoLP/DoLP/DoCP, and a per-scene scale. Because the scale is divided out of the input, it is not physically identifiable; PolarScale therefore evaluates dataset-conditioned semantic scale estimation against a constant-scale control, together with angular, self-consistency, and physical-bound metrics. Across seven restoration-based and generative backbones and three prediction strategies, the strongest restoration models estimate the scale with 3.6-4.3% mean relative error versus 5.7% for the constant control and violate physical bounds on fewer than 0.25% of pixels, whereas two generative baselines collapse to a near-zero scale; explicit descriptor supervision improves descriptor accuracy (23.66 vs. 18.88 dB PSNR for MAE). Predicted full-Stokes representations improve diffuse/specular separation, material segmentation, and glare classification, although in diffuse/specular separation the learned scale performs only on par with the constant control.

Using a replica-symmetric high-dimensional characterization, we develop an inferential framework for sparse support vector machines when the sample size and number of features grow proportionally. The main challenge is the nonsmooth hinge loss, which prevents direct application of debiasing arguments developed for smooth classification losses. We overcome this difficulty by representing the $L_1$-penalized support vector machine (SVM) as a linear program and identifying the hinge-loss subgradient through its dual variables. This yields a computationally accessible debiased estimator whose coordinates are asymptotically Gaussian under the proportional asymptotic regime. The resulting distributional characterization provides confidence intervals and hypothesis tests for individual features and enables false-discovery-rate-controlled variable selection. Extensive simulations examine calibration, power, and variable-selection performance under a range of covariance structures, including strongly correlated designs. An analysis of high-dimensional breast cancer gene-expression data illustrates how the proposed inference can distinguish statistically significant features from variables selected by the original sparse SVM.

Assistance in collaborative manipulation is often initiated by user instructions, making high-level reasoning request-driven. In fluent human teamwork, however, partners often infer the next helpful step from the observed outcome of an action rather than waiting for instructions. Motivated by this, we investigate an event-driven formulation of proactive assistance, where human–object interaction outcomes initiate assistive reasoning without user-provided task specifications at inference time. To this end, we propose an event-driven framework that monitors workspace state changes with an event monitor and, upon event completion, extracts stabilized pre/post snapshots that characterize the resulting state transition. A frozen pretrained Vision-Language Model (VLM) then uses its semantic priors to infer the task context, decide whether assistance is appropriate, and, when needed, generate a sequence of assistive actions from the observed transition. To make outputs executable and verifiable, we restrict actions to a set of action primitives and reference objects via integer IDs. We evaluate the same framework across three distinct real world tabletop collaboration tasks without task-specific training or fine-tuning. The event-driven framework achieves performance comparable to variants given user instructions.

Bound states in structured reservoirs require exact interference conditions and are therefore sensitive to imperfections in the coupling geometry. In this paper, we study a two-level giant atom coupled at multiple points to a mirror-terminated semi-infinite waveguide. The exact atom-photon bound state requires both cancellation of the outgoing radiation amplitude and dispersive matching to the atomic detuning. Generalized delay-equation dynamics, continued-pole spectra, and real-space photon fields verify this criterion for coupling-strength, position, and coupling-phase imperfections. For representative realizations, retuning restores one-, two-, and three-root responses after strength errors and one- and two-root responses after position errors. The specified position-imperfect three-root configuration fails because its $2\pi$ root is no longer dark, consistent with a $58.77\%$ spectral mismatch. Ensembles of 1000 realizations at each error amplitude show near-unity target-state recovery for strength errors, unity recovery of the specified one- and two-root targets but no three-root recovery for position errors, and no nontrivial exact recovery for independent phase errors. Optimized phase-imperfect responses instead retain finite linewidths. Root matching with realization-dependent control retuning therefore constitutes a compensation procedure, rather than generic passive robustness against arbitrary disorder.

Let $H>0$ and $\kappa,\tau\in\mathbb{R}$ satisfy $4H^2+\kappa>0$ and $\kappa\leq 4\tau^2$. We prove that an immersed stable disk of constant mean curvature $H$ and circular boundary in the space $\mathbb{E}(\kappa,\tau)$ is a spherical cap of the canonical rotational $H$-sphere.

Recent training-free pruning approaches for Multimodal Large Language Models (MLLMs) effectively cut computational overhead by exploiting visual redundancy or text-vision attention. However, they frequently suffer from semantic degradation due to their task-agnostic design or unreliable attention estimates. Based on our empirical analysis, we have found that this issue arises because salient tokens in shallow layers persistently suppress emerging semantic ones through numerical inertia, leading to premature discarding of signals crucial for deep reasoning. To address the aforementioned issue, from the task-oriented aspects, we first reformulate training-free pruning as a minimization of the distortion in the final task loss and derive a tractable, token-wise upper bound to serve as a surrogate objective. Specifically, this formulation inherently reveals a previously neglected inter-layer term that accounts for gradients across layers. Accordingly, for the implementation, we propose DIPrune, a rank-based framework that employs a dual importance scoring mechanism to jointly optimize intra-layer static feature saliency and inter-layer dynamic semantic evolution. Extensive experiments on LLaVA and Qwen-VL demonstrate that DIPrune consistently achieves state-of-the-art results.

We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.

Camera-based 3D perception for autonomous driving relies heavily on large annotated datasets, and deploying such a system to a new target region typically requires data collection and annotation. Generative augmentation has been proposed to reduce this cost, but existing approaches face a fundamental trade-off: label-conditioned methods consume the very annotations they aim to replace, while simulator-conditioned methods offer free annotations but lack visual grounding to specific real environments. This work investigates the extent to which a digital-twin-driven Real2Sim2Real pipeline (DT-R2S2R) can substitute for target-region real data. By reconstructing recorded driving clips inside a georeferenced digital twin (DT-R2S), we condition a diffusion model on geometrically aligned simulator renderings, establishing a digital twin-grounded Sim2Real model (DT-S2R). As a result, DT-S2R synthesizes photorealistic driving images given low-cost yet georeferenced simulator data across both reconstructed and novel simulator scenes within digital-twin coverage. The efficacy of generated data is verified on diverse 3D detectors. DETR3D, especially, reports 93.18% of mAP obtained by a target-region real-data oracle, without employing target images for detector training. Furthermore, simple co-training with existing out-of-target real data outperforms the oracle. Thus, DT-R2S2R can substantially reduce the cost of manual on-site data collection and annotation in digital twin-available districts, providing a practical foundation for scaling 3D perception.