Papers

We establish the weak type \((1,1)\) endpoint estimate for operator-valued rough singular integrals with kernels satisfying the classical \(L\log L\) integrability and cancellation conditions. This extends Seeger's endpoint theorem [{J. Amer. Math. Soc.} 9 (1996)] to the noncommutative setting. A key ingredient is an off-diagonal analysis that controls interactions between different kernel scales and avoids an additional logarithmic loss.

Propositional Dynamic Logic (PDL) is a well-established modal logic of programs. Among its many extensions, the loop operator stands out for capturing the cyclic behaviour of programs: a world satisfies loop(pi) precisely when it can return to itself along a path matching the regular expression pi. While the satisfiability problem for the resulting logic LPDL was settled already in the 1980s, the decidability of its finite satisfiability problem has remained open ever since. The core difficulty is inherent to the finite setting: requiring and forbidding cycles at once is easily reconciled over arbitrary models, but over finite ones it defeats the existing finite-model-theoretic techniques. We make the first substantial progress towards closing this gap. We prove that finite satisfiability is ExpTime-complete for LPDL formulae (also in the presence of the converse operator) in negation normal form, under the restriction that every negated non-atomic loop has the form loop(pi^+) for some arbitrarily complex program pi – a generalised form of self-reachability; positive occurrences of loops remain unrestricted. At the heart of our approach lies a novel way of representing intended finite models as their infinite, cactus-like unravellings: these are recognisable by two-way tree automata and satisfy a tailored omega-regular foldability condition that lets us finitise the accepted structures.

Codes in the Levenshtein metric that can correct multiple edits (including deletions, insertions, and substitutions) have attracted a lot of attention recently owing to their application in DNA-based storage and racetrack memories. In this work, we present new techniques for designing explicit binary codes of length $n$ that correct $t$ edits with at most $(2t+1)\log n+O_t(\log\log n)$ bits of redundancy. We first propose to use a polynomial hash to construct a systematic code that corrects $t$ edits with $(4t+2)\log n+O_t(\log\log n)$ bits of redundancy. Then we observe that there are many polynomial hashes like this, some are good, some are bad. So, we propose the second technique, called entropy recycling, to use the indices of good hashes to carry information. As a consequence, we obtain a partial-systematic code of length $n$ that corrects $t$ edits with at most $(2t+1)\log n+O_t(\log\log n)$ bits of redundancy. Finally, we provide deterministic polynomial-time encoding and decoding algorithms for our code.

Hidden beneath the vanishing charge Hall response of altermagnets are spin-up and spin-down Hall currents of opposite sign—concealed, not absent—whose cancellation is enforced by symmetry. When these spin states are locked to distinct valleys, the hidden currents constitute a spin-valley Hall effect. Here we show that in 2D altermagnets with spin-valley-layer coupling (SVLC), a gate field unveils this hidden spin-valley Hall response.~By lifting the symmetry-enforced compensation between valleys with opposite layer polarizations, the field converts the hidden response into a net charge Hall signal, yielding a gate-switchable electric Hall effect (EHE) enabled by SVLC. Using collinear spin layer group (cSLG) theory, we classify all 158 altermagnetic cSLGs, identify 32 that support SVLC, and predict monolayer Mg$_2$Os$_2$(SO$_5$)$_2$ and the Ca(CoN)$_2$-family as candidate materials. First-principles calculations for Mg$_2$Os$_2$(SO$_5$)$_2$ reveal reversible valley splitting, a gate-switchable Hall response, and a Kerr rotation exceeding 1 mrad whose sign reverses together with the EHE signal. These results establish a symmetry-based route to all-electrical valley-spin control and identify altermagnets as promising platforms for high-performance valley transport and electrically switchable magneto-optics.

Choosing a mixed-precision configuration for large language model (LLM) serving trades speed against accuracy. Allocators that use average bit-width or a memory budget as a speed proxy can miss changes in the resource that limits execution. We argue that served speed can be limited by compute, weight loading, or key-value (KV) cache access, depending on the phase, batch size, and context length. A byte-based proxy does not capture all of these costs, so fewer bits do not always mean faster serving. To address this gap, we build a cost model that accounts for the binding resource and use it in two ways. First, as a predictor: given a configuration and operating point, it estimates serving latency using constants calibrated for the model, GPU, and serving stack. We evaluate its accuracy across three hardware classes. Second, as an allocator: we combine modeled time costs with measured per-tensor accuracy costs and use a dynamic program to select a configuration under a latency or accuracy budget. We compare its configurations against byte-aware and sensitivity-only allocation.

Deep learning is now central to radiology, helping detect changes on X-rays, CTs, and MRIs. However, these systems are highly vulnerable to adversarial attacks - small, crafted perturbations that mislead models while appearing unchanged to humans. Such errors risk missed cancers or false positives. Studies show over 90% attack success on medical scans. Almost 30% of US hospitals use AI in imaging in 2023. Thus, an effective method of detecting such attacks and their directionality is crucial to ensure the credibility and reliability of medical systems based on DNNs. We propose a novel detection framework that leverages subsequent attacks using random noise to identify adversarial perturbations. Our approach uses the analysis of variations in the Sigmoid function to distinguish genuine medical images from adversarially manipulated ones. Specifically, we compare prediction differences between clean and attacked images, as well as between different adversarially altered versions, to improve detection accuracy. We evaluated our method on three popular medical datasets including 'Chest X-Ray Images for Classification', 'Retinal Fundus Multi-disease Image Dataset' and 'Brain Tumor Dataset' under various attack scenarios, including random noise. Our framework achieved up to 99.8% ACC in identifying adversarial directional attacks, significantly outperforming existing defense mechanisms. It consistently identified adversarial samples across varying attack strengths while keeping false positives low, showing strong reliability and potential for clinical use. Furthermore, our proposal highlights its potential for real-world deployment.

The feasibility of real-time track fitting of straight tracks for online event selection is shown in the context of the MUonE experiment. In order to reach the high throughput and low latency required for real-time track fitting, the tracking algorithm is implemented using High-Level Synthesis for an FPGA, which provides provides a balance between flexibility and performance. Hardware tracking results from a test with high-rate muons at the CERN M2 beam are presented. This test, a joint effort by the MUonE and Compact Muon Solenoid (CMS) experiments, operated with Two-Strip (2S) modules provided by the CMS tracker group. The prototype version of the fitter used in this test achieves 3.75 $\mu$s latency and 7.75 % resource use. A comparison of the results with those obtained from a pure software implementation shows agreement well below relevant uncertainty scales. Developments since the test are also presented, with the hardware algorithm now reaching 1.35 $\mu$s latency and producing pipelined fitting results above 50 MHz while requiring less resources than the initial version. Doing so required including certain assumptions in the algorithm, but these assumptions hold for linear track fitting in general and algorithm remains useful in contexts other than MUonE.

Electroencephalography (EEG) recorded for motor-imagery (MI) brain-computer interfaces (BCIs) carries subject-identifying structure that persists across sessions, allowing separately released sessions from the same person to be linked. Existing EEG identity protections use learned or additive perturbations and operate on representations other than the covariance geometry underlying MI pipelines. We ask whether cross-session identity leakage can be suppressed directly in this covariance representation without learning a privacy model. We introduce a Riemannian transform that equalizes two subject-conditioned geometric statistics: the Riemannian mean covariance and the tangent-space scatter around it, with two optional band-specific refinements. Ablations show that mean alignment and scatter whitening carry nearly all of the suppression, while the optional stages contribute small, dataset-dependent refinements. Across two public datasets and five attackers spanning four covariance-space representations, the worst attacker falls from 90.8% to 15.6% on BCI Competition IV-2a and from 90.8% to 9.9% on OpenBMI, at a cost of 7.0 and 2.1 points of MI decoding accuracy relative to the 8-30 Hz input, and no aggregation rule exceeds chance by more than two points at any batch size. The transform requires no learned privacy model, surrogate network, or gradient-based training, and is fitted on one session and applied unchanged to a held-out later session.

World Action Models (WAMs) unify visual world modeling and action generation, yet their real-world deployment is heavily bottlenecked by iterative action denoising and the sequential execution of visual prefilling and action prediction. We demonstrate that the action-denoising trajectories in WAMs are approximately straight, rendering the first-step velocity a strong estimate of the final action direction. Building on this observation, we introduce 1Step-WAM, a framework that transforms multi-step action denoising into one single forward. Specifically, we employ a lightweight calibrator to directly correct the first step velocity, and use bandwidth-constrained action decoding to further reduce errors in the calibrated one-step actions. Compressing action generation into a single step enables it to execute in parallel with visual prefilling, completely breaking the sequential bottleneck of the traditional imagination-then-action paradigm. Evaluations on RoboTwin and LIBERO show that 1Step-WAM largely preserves multi-step task success with only about 13.4M trainable parameters, while achieving inference speedups of $7.44\times$, $5.98\times$, and $24.84\times$ for FastWAM, ImageWAM and Kairos, respectively. Furthermore, real-world robotic deployments using the FastWAM backbone confirm a consistent 7.44$\times$ speedup while maintaining close success rate to the multi-step baseline. Code is avaliable at https://github.com/changdong1687/1Step-WAM.

A random geometric graph is a random graph model whose vertex set is a binomial point process, where two vertices are connected by an edge if each lies within the ball of radius $r$ centered at the other. In this paper, we investigate the asymptotic fluctuations of the threshold radius required for the maximum degree of the graph to reach a target value. Assuming this target value grows with the number of vertices $n$ at an order of at least $\log n$ but strictly less than $(\log n)^d$, we show that these fluctuations follow a Gumbel distribution. We also investigate the spatial configurations of vertices with extremely large degrees, and show that the point process marked by their degrees converges in distribution to a Poisson point process.

Hybrid federated semantic communication enables user equipment (UEs) to contribute model updates or semantic features under a shared training framework. However, heterogeneous role costs and the interaction between model aggregation and feature reconstruction (FR) remain key challenges in practical radio access network (RAN) deployment. To address these issues, we propose ARC-FedSC, a RAN-aware framework that coordinates UE role assignment and server-side controlled FR under a fixed communication budget. Within ARC-FedSC, RAN Aware Role-Bandit learns the historical contribution of UEs in different roles together with current uplink conditions, while Temporal Consistency Alignment (TCA) regulates FR according to recent model aggregation directions. Experiments on CIFAR-10 with time-varying RAN channels show that ARC-FedSC outperforms baselines across all five tested role configurations in the later training stage, with the best configurations achieving about 24.17 dB average PSNR over the last 20 rounds. Component level results further show that Role-Bandit maintains an average rolling UE coverage of 85.3%, compared with about 65.7% for baseline, while TCA reduces the probability of harmful FR events from 0.245 to 0.093, corresponding to a 62.0% reduction. Ablation and sensitivity studies further support the effectiveness and robustness of the proposed design.

Structural disorder is generally regarded as detrimental to magnetism. Since magnetic properties are governed by both the arrangement of magnetic atoms and the crystal environment, including non-magnetic atoms that mediate exchange interactions, the distinct role of magnetic and non-magnetic disorder remains less understood. The recently reported anti-Heusler alloy, Al$_2$MnCu, forming with $\sim$50% intra-symmetry site disorder (B2) involving the magnetic Mn atom and $\sim$5% inter-symmetry site disorder associated with non-magnetic Al and Cu atoms, offers a good platform to disentangle the individual roles of magnetic and non-magnetic atomic disorder. Our magnetic critical analysis, in the vicinity of the Curie temperature ($T_{\rm C}$), does not lead to any conventional single universality class expected for a standard ferromagnet; instead, the non-monotonic temperature dependence of effective critical exponents points towards more complex magnetic interactions, akin to inhomogeneous ferromagnets. Dc magnetometry complemented by higher-harmonic ac magnetic susceptibility data, further confirms the persistence of locally ordered magnetic clusters above $T_{\rm C}$. Theoretical analysis establishes that the enhancement of the local magnetic ordering temperature arises directly from the strengthening of exchange interactions due to the small degree of non-magnetic disorder, whereas $T_{\rm C}$ is hardly influenced by the much larger level of magnetic-atom disorder. The combined experimental and theoretical investigations on the anti-Heusler alloy Al$_2$MnCu reveal and explain the unusual observation of nonmagnetic disorder-induced elevation of $T_{\rm C}$, providing a paradigm for the counterintuitive role of disorder in magnetic materials.

We predict an intrinsic orbital Nernst effect in reciprocal photonic lattices with real Bloch modes. In the collisionless regime, a thermal gradient generates a transverse angular-displacement response although band angular moments and ordinary Berry curvatures vanish. The response is carried by angular-density dipoles formed through virtual mixing of distinct spatial modes. Their correlation with band velocity survives thermal averaging and is independently recovered from the angular-density readout of unitarily evolved wave packets. Two controls expose the mechanism: a fixed-generator two-level system has zero antisymmetric intrinsic response, and flattening the dispersion suppresses transport without changing the eigenstates. A canonical scalar Maxwell calculation realizes the effect through symmetry-selected virtual channels, even when one band dominates the thermal population. These findings establish an orbital-dipole mechanism for intrinsic thermal angular transport in real photonic bands.

Multimodal Chain-of-Thought (MCoT) substantially enhances the complex reasoning capabilities of Multimodal Large Language Models (MLLMs) by explicitly modeling intermediate reasoning processes. However, most learning-based MCoT methods follow a stage-centric paradigm, where different reasoning behaviors are assigned to predefined stages and optimized separately. This results in fragmented reasoning and a training-inference reasoning-state gap. To address these limitations, we propose ReState, a unified iterative reasoning framework that reformulates multimodal reasoning from a stage-driven pipeline into a state-driven dynamic process. It comprises two complementary components: Unified Reasoning State Modeling (URSM) and Closed-Loop Reasoning-State Learning (CRSL). URSM unifies reasoning construction, correct reasoning preservation, and erroneous reasoning correction as reasoning-state transitions within a shared state space, enabling these heterogeneous reasoning behaviors to be learned jointly. CRSL further incorporates self-generated historical reasoning states during training and recursively updates the current state during inference, thereby mitigating the reasoning-state gap and enabling iterative self-refinement without requiring an additional reflection module, critic, or independent correction stage. Furthermore, we construct VersaCoT-10K, a high-quality CoT dataset spanning eight visual reasoning domains, which provides diverse supervision for multi-domain reasoning and reasoning-state refinement. Extensive experiments demonstrate that ReState exhibits strong adaptability across different MLLM backbones and achieves strong performance on multiple public reasoning benchmarks, supporting the shift from stage-centric reasoning toward state-centric reasoning. Our data and code are available at https://github.com/YuChuang1205/ReState

This thesis investigates the application of techniques developed in supersymmetric gauge theories to physical problems in Quantum Field Theory and Gravity, focusing on the Seiberg-Witten (SW) curve and its quantum version. After reviewing the essential concepts of Supersymmetry and the derivation of the SW curve, we explore its applications in both fields. In Quantum Field Theory, we investigate the emergence of Argyres-Douglas theories in the moduli space of supersymmetric models, focusing on extremal correlators. We analyze a conformal model to compute their instanton corrections, finding agreement with predictions from Effective Field Theory, and discuss the implications for analogous observables in Argyres-Douglas theories. In Gravity, we exploit the quantum SW curve and its relation to differential equations describing physical systems. We establish the linear stability of Topological Stars, arising in the fuzzball proposal, under massive charged scalar perturbations. We also investigate charge superradiance in configurations with a horizon and derive a novel hypergeometric representation of the confluent Heun function, relevant to gravitational-wave propagation in the Schwarzschild background. This result yields a new resummed expression for waveform tail contributions, in excellent agreement with numerical data. Finally, beyond the SW formalism, we develop a Machine Learning algorithm based on Hamiltonian Neural Networks to reproduce the geodesics of a neutral particle in a fuzzball geometry. For critical trajectories, our method outperforms standard numerical integrators in both efficiency and accuracy.

We propose a unified $A_4\times Z_2\times U(1)_L$ framework for generating small Dirac neutrino masses and address dark matter through feeble interactions in an extended particle physics model. The model extends the Standard Model with a pair of heavy vector-like neutral $A_4$ fermions $N(N_{L,R})$, two additional flavon fields $\eta$ and $\phi$, among which $\eta$ being a $Z_2$-odd inert scalar and a dark-sector vector-like fermion field $\chi$. We numerically explore the Dirac-sector Yukawa couplings and identify the parameter region that is consistent with the NuFit 6.1 neutrino oscillation data at the $3\sigma$ level. The dark matter candidate $\chi$, stabilized by the $Z_2$ symmetry, is produced non-thermally through the decay $N_L\rightarrow\chi+\eta$. By solving the Boltzmann equation, we find that the observed relic abundance, $\Omega_{\rm DM}h^2\simeq0.12$, can be reproduced for freeze-in couplings of order $\lambda\sim10^{-5.5}$–$10^{-7.5}$ over the considered dark matter mass range. For the chosen parameter space, we also verify the interaction rate remains below the Hubble expansion rate, confirming $\chi$ never reaches thermal equilibrium. Thus, our results demonstrate that the model provides a consistent realization of Dirac neutrino masses and FIMP dark matter within a common symmetry-based setup. The presence of light Dirac RH neutrinos can contribute to the dark radiation and hence the effective degrees of freedom via thermal and non-thermal processes. We further estimate the contribution of the light right-handed neutrinos to \(\Delta N_{\rm eff}\), finding a maximum characteristic value of \(\Delta N_{\rm eff}\simeq0.14\) in the benchmark parameter region.

Recursive synthetic-data training can degrade a fitted model, but its effects on the variable-screening stage that precedes model fitting are less understood. When each generation labels data for the next, a marginal screener ranks variables against the current pseudo-label target rather than the original response. Across generations, this target drift can erode or reverse the active–inactive score margin and cause screening to discard variables that clean-label screening would retain. We call this process screening collapse. In a Gaussian linear model with minimum-norm recursive generators, we establish finite-sample screening bounds, characterize a late-generation information-loss limit, and derive a minimax impossibility result. Screening collapse can precede and compound ordinary model collapse: omitted variables incur a covariance-weighted loss that no refit restricted to the selected variables can eliminate, while recursive labels further degrade estimation on the retained variables. We also examine two approaches to mitigating screening collapse. Fixed-fraction real-label retention preserves a clean-label component but leaves resolution fixed, whereas data accumulation can avoid screening collapse if the pooled target preserves a positive margin and the growing sample resolves it. Numerical experiments on gene-expression data support the theoretical findings.

Dietary transitions away from animal-based meat could reduce food-related environmental burdens, but plant-based alternatives must compete on flavor, texture, and overall liking. Here we extend a generative AI framework with 469 plant-based burger recipes and use it to create six formulations across five primary ingredients: bean, chickpea, lentil, mushroom, and oat. An executive chef translates the AI-generated formulations into standardized preparation protocols and refines the ingredient quantities based on culinary expertise. The integration of generative modeling and culinary expertise defines a human-centered generative AI framework for food design. We evaluate the six burgers in a blinded sensory survey with 101 participants in an operating restaurant and quantify their land use, greenhouse gas emissions, eutrophication potential, and scarcity-weighted water use. We use Big Mac scores from a previous survey as an iconic commercial benchmark. The mushroom burger achieves mean flavor, texture, and overall liking scores similar to the Big Mac, with less than one-third of its estimated environmental impact. The other formulations reduce the estimated impact further, in several cases to near one-tenth of the Big Mac value, but receive lower liking scores. Mixed-effects models quantify associations between sensory attributes and human liking and retain predictive accuracy on independent survey data, with mean absolute errors no greater than 0.52 points on a seven-point scale. Together, these results demonstrate how generative design, culinary expertise, human sensory response, and environmental assessment can converge to create sustainable foods that people want to eat.

Computational research in physics requires continuous interplay between simulation and scientific interpretation, demanding substantial specialist effort. Here we introduce Brilliance, a research agent that combines large language models, reusable physics knowledge and numerical simulation to conduct adaptive investigations in accelerator physics. Given a single user prompt, Brilliance designs a fourth-generation synchrotron light source that meets coupled emittance and nonlinear-acceptance requirements. Further exploration yields a design combining sub-10-pm emittance with a large dynamic aperture under realistic engineering constraints, suggesting a route towards hard-X-ray diffraction-limited operation, although the momentum-acceptance target remains unmet. Brilliance also calibrates a model of an operating light source against measured responses, accurately inferring its lattice and calibration errors. Across these studies, Brilliance autonomously revises its computational strategies in response to numerical evidence. These results demonstrate a route towards delegating sustained scientific investigations to agents equipped with domain expertise and numerical tools.

Multi-label learning typically pursues model construction through the joint optimization of label fitting, correlation modeling, and structural regularization. While empirically effective, such a coupled paradigm imposes multiple learning objectives on a single predictive parameter matrix, forcing it to simultaneously fit observed labels and encode structural priors. This coupling may induce ill-conditioned optimization geometry, increase hyper-parameter sensitivity, and complicate capacity control. To address the these issues, this paper proposes a Progressive Multi-Label Learning (ProML) framework, which decouples direct label fitting from predictor learning via the introduction of an auxiliary predictive variable. This auxiliary variable admits a closed-form solution, yielding an equivalent profiled objective in which the supervised fitting term is scaled by a trade-off parameter. This result provides a unified view of ProML and conventional coupled learning, with the latter recovered as a limiting case. We theoretically analyze the optimization geometry of ProML and show that, under quadratic positive semidefinite structural regularization, ProML attenuates the dominant curvature of the fitting term, enlarges the stable learning rate range, and provides a controllable fidelity-regularization trade-off. Further, we instantiate the ProML for multi-label feature selection task by integrating global-local label priors and row-sparse regularization. Extensive experiments and controlled optimization analyses on 12 benchmark datasets empirically corroborate the theoretical analysis and demonstrate the robust and competitive performance of the proposed method.

Effective unsupervised domain adaptation (UDA) requires a representation that captures transferable structure from both the labeled source domain and the unlabeled target domain. We introduce Joint Contrastive-Adversarial Representation Learning (JCAR), a two-stage framework that learns a common representation from the union of unlabeled source and target samples by combining contrastive learning with adversarial domain alignment, and then freezes the representation to fit a source-supervised predictor. We establish a non-asymptotic excess-risk bound for this procedure that couples representation and domain-discriminator estimation while separating downstream prediction, with explicit neural-network approximation errors. Under the stated assumptions and common Hölder smoothness $\beta\geq1$, the bound identifies a sufficiently large unlabeled-sample regime in which the downstream rate is $\widetilde{\mathcal{O}}(m^{-\beta/(2\beta+d)})$, where $m$ counts labeled source samples and logarithmic factors are suppressed. The labeled-sample exponent is governed by the latent dimension $d$ rather than the ambient dimension $p$, which enters the pretraining cost. Experiments on Office-31, Office-Home, and DomainNet demonstrate clear transfer gains across diverse domain shifts, with particularly strong performance when representations are learned from scratch.

Accurate lesion segmentation in mammography is important for computer-aided breast cancer diagnosis, but dense pixel-level annotations remain costly and limited. Existing public segmentation datasets usually cover only a small set of lesion types with manually delineated masks, whereas larger mammography datasets often provide only image-level diagnostic labels. This annotation mismatch makes it difficult to train segmentation models that can generalize to rare or weakly annotated lesion categories. To address this problem, we study open-vocabulary mammographic lesion segmentation under a mixed-supervision setting, where pixel-level masks are available for base lesion categories and image-level labels are available for a broader set of categories. We propose a two-branch framework that jointly learns from segmentation data and classification data. The segmentation branch learns lesion boundaries from annotated masks, while the classification branch introduces additional image-level semantic supervision. To better transfer image-level supervision to lesion-relevant regions, we further introduce a Lesion-wise Attentive Classifier that maintains category-specific feature prototypes and generates lesion-aware attention maps for foreground feature pooling. This design reduces the influence of background tissue and encourages more compact lesion representations. Experiments on multiple mammography datasets show that the proposed method consistently improves open-vocabulary segmentation baselines on both base and novel lesion categories, while reducing the gap to fully supervised models that require dense target-domain masks. Qualitative results further indicate that our method produces more complete lesion localization for small, low-contrast, and visually subtle mammographic findings.

Movable antenna (MA) can enhance the physical layer security (PLS) performance of integrated sensing and communications (ISAC). However, most existing works assume either near-field (NF) or far-field (FF) propagation models for both communication users (CUs) and targets. This paper considers a more practical scenario where multiple CUs, an eavesdropper (Eve), and multiple targets are in a mixed near- and far-field environment due to the changes in the propagation field caused by antenna position updates in MA with a unified array response and continuous NF/FF weights. To evaluate the PLS performance of MA-aided ISAC in mixed-field environments, we formulate an optimization problem to maximize the sum secrecy rate (SSR) of CUs by jointly designing the transmit beamforming and antenna positions at the transmitter. The problem is highly non-convex, so a two-layer algorithm is proposed to iteratively solve the problem using the projected gradient ascent (PGA) method and the Lagrangian dual transform. Since the abrupt switch between the NF and the FF models during antenna movement can cause the objective function to oscillate during iteration, the unified array response is combined with the Barzilai-Borwein step, Armijo line search, and precise projection to ensure that the SSR does not decrease during the iteration and the objective function is differentiable on the Rayleigh boundary. Numerical results show that the MA-ISAC using the mixed-field model achieves almost identical PLS performance to that of using the full NF model in terms of SSR, and both outperform the FF model. Using the mismatched FF model during antenna position updates results in a loss of MA gain, potentially making MA inferior to the FA-based system using the correct model.

We consider the recovery of functions of the weighted Wiener classes $W_s^\mu$ from perturbed Fourier–Hermite coefficients in the metric of $L_\infty(\mathbb R)$. For the summation methods of the class $\mathcal S^\theta$ we find error estimates on $W_s^\mu$. The estimates take into account the behaviour of the Hermite functions both in the oscillatory region and near the turning point: the maxima of functions with different indices are attained at different points, and the supremum of a sum over a block of indices is substantially smaller than the sum of the suprema. Owing to this, in particular, we establish a common lower bound for all finite diagonal methods; for $s\ne4/3$ and $p\ne4/3$ it matches the upper bound and gives the exact order of the error in this class, while at the critical points the gap between the bounds does not exceed $(\log(e/\delta))^{1/4}$ up to a constant. If, in addition, $s>4/3$ or $p<4/3$, then this order is also optimal among all recovery operators that use the whole sequence of data.

Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 $^{40}\mathrm{Ca}^{+}$ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the $10^{-18}$ level and an expected 20-fold improvement in frequency stability compared to single ion clocks.

The Unified Field Bosonization Technique (UFBT) is employed to investigate the single-particle properties of inhomogeneous Luttinger liquids containing localized clusters of impurities in the presence of forward-scattering interactions. Within this framework, fermionic two-point correlation functions are used to derive the leading-order singular contributions to the dynamical density of states (DDOS) and the cross-barrier tunneling conductance. The results reveal distinct power-law behaviours of the DDOS near the impurity cluster and in the far-field regime. The tunneling conductance exhibits a power-law temperature dependence, decreasing with decreasing temperature for repulsive interactions and increasing for attractive interactions, while remaining temperature-independent in the noninteracting limit. The impurity cluster modifies the amplitudes and spatial structure of these observables, whereas their characteristic power-law exponents are determined solely by the interaction parameters. The formulation accommodates arbitrary impurity strengths without requiring perturbative expansions in the impurity or interaction strengths. The characteristic scaling behaviour emerges directly from the fermionic correlation functions, without an explicit renormalization-group (RG) treatment of the impurity strength, while the weak-interaction limit recovers the leading perturbative correction to the tunneling response. These findings establish UFBT as a unified framework for describing local spectral properties and cross-barrier transport in inhomogeneous Luttinger liquids.

We construct smooth irreducible plane curves whose complete amoeba contour is a smooth embedded curve equal to the amoeba boundary, although the curves are not torically equivalent to simple Harnack curves. Finite monomial coverings yield explicit infinite families with higher logarithmic multiplicity and nonmaximal normalized amoeba area. We classify the Newton polygons admitting such covering constructions through their exponent lattices, give an exact connectedness criterion in terms of monodromy, and treat primitive polygons by a separate phase-sensitive construction. Exact triangular and trapezoidal families are complemented by positive-genus investigations exhibiting bounded amoeba-complement components. These results show that a perfectly exposed amoeba contour does not determine the real structure, logarithmic sheet number, or Harnack type of the underlying curve.

Three-dimensional (3D) localization microscopy using rotational point spread functions (PSFs) is fundamentally challenged by limited axial range, poor PSF compactness, and depth-decoding ambiguity – particularly in dense specimens with heavy PSF overlap. To address these limitations, we introduce a 3D localization approach based on tornado wave (ToW)-PSFs, combined with a convolutional neural network (CNN) designed to decode continuous rotational patterns and resolve multi-period axial ambiguity. Our engineered PSF encodes the 3D position of each nanoparticle into a compact double-lobe pattern whose orientation rotates with axial position. This design yields a clean, well-defined structural evolution across an unprecedented 15 um axial range, with an average rotation rate of 21.8 degrees/um, ensuring robust long-range depth encoding. To recover coordinates from overlapping emitters, we systematically benchmark a conventional matching-pursuit (MP) algorithm against our CNN. While MP performs adequately in sparse scenes, the CNN demonstrates exceptional robustness in dense fields, achieving a 70.24% localization accuracy at 20 particles per image-substantially outperforming MP's 22.52% – while also significantly suppressing axial period-jump errors. Experimental validation on nanoparticles confirms reliable single- and multi-particle localization throughout the entire working range. Our results establish ToW-PSFs as a powerful and practical optical encoding strategy for high-density, extended-range 3D localization imaging.

Functional electrical stimulation (FES) assists movement, but fixed schedules cannot track how a repeatedly activated muscle changes, and surface electromyography (EMG) near the stimulation electrodes is often obscured by artifacts. Prior work recorded mechanomyography (MMG) passively during closed-loop FES cycling and estimated FES-induced fatigue or predicted fatigue for FES control, without gating stimulation with stimulated-site MMG. In this study, we present VG-FES, a wearable module co-locating microphone-based MMG, programmable charge-balanced biphasic stimulation, and embedded state-gated control at one on-skin thigh site. After each action, we compare rectus femoris (RF) mean power frequency (MPF) with an early-session baseline of the same direction, giving a relative state. A threshold on its window means enables fixed-duration bursts separated by rest periods. During onboard stimulation, MMG remained recordable, whereas near-site EMG was artifact-dominated. Under prolonged external stimulation, cycle-wise MMG tracked an independent local-pressure reference (Spearman rho = 0.968). In leave-one-session-out evaluation on 2284 squat actions (11 sessions, eight participants), MMG-based action segmentation reached an event-detection F1 of 0.923 and direction classification a balanced accuracy of 0.925. Online, over 15.69 min of self-paced squats, one participant received four bursts while MMG acquisition and action monitoring continued. Mechanical feedback from the stimulated site offers wearable FES and assistive robotics a per-action basis for state-gated stimulation.

Traffic sign detection plays a vital role in intelligent transportation systems, supporting the safe operation of advanced driver assistance systems and autonomous vehicles. Despite significant progress in real-time object detection, accurately identifying traffic signs under challenging conditions remains difficult. Variations in lighting, adverse weather, motion blur, and partial occlusion often reduce detection performance, especially for small or visually degraded signs where important spatial information can be lost. To address these challenges, we propose Squeeze-Aware-YOLO, a lightweight traffic sign detection framework that introduces a multi-branch bottleneck module combining convolutional kernels of different sizes with a Squeeze-and-Excitation mechanism to improve feature extraction and adaptive channel weighting. In addition, we integrate the Multi-Branch Auxiliary Feature Pyramid Network and Re-parameterized Heterogeneous Multi-Scale modules to strengthen multi-scale feature representation and feature fusion while preserving real-time inference efficiency for practical deployment. The proposed approach is evaluated on the Bangladeshi Traffic Sign Detection Dataset, the CSUST Chinese Traffic Sign Detection Benchmark 2021, and the German Traffic Sign Detection Benchmark, achieving mAP@0.5 scores of 74.7%, 79.4%, and 84.0%, respectively, while consistently outperforming recent state-of-the-art YOLO-based traffic sign detectors. These findings demonstrate that combining multi-scale receptive fields, channel attention, and enhanced feature fusion enables more accurate and robust traffic sign detection while maintaining the computational efficiency required for real-world deployment.