A signed graph $(G,σ)$ is a graph $G$ together with an assignment $σ$ of either a positive sign or a negative sign to each edge. A signed graph is unbalanced if it contains a cycle with odd number of negative edges. The spectral radius of a signed graph is the spectral radius of its adjacency matrix, in which for vertices $u,v$, the $(u,v)$-entry is $0$, $-1$, or $1$ depending on whether $uv$ represents no edge, a negative edge, or a positive edge, respectively. Recently, Conde, Dratman and Grippo [Discrete Math. 349 (2026) 114942] proved that there is only one unbalanced signed bipartite graph with maximum spectral radius, up to switching isomorphism. In this paper, we establish a spectral Turán type results for signed bipartite graphs. More precisely, we determine the unique graphs containing no negative cycles of length four with maximum spectral radius, up to switching isomorphism, among unbalanced signed bipartite graphs with fixed bipartite sizes and order, respectively.

Complex visual interfaces are powerful yet have a steep learning curve, as users must navigate feature-rich visual interfaces while reasoning about domain-specific operations. Existing approaches either deliver assistance through a separate chat-based interaction, or require substantial application-specific engineering to build support natively into each interface. To address the gaps, we propose in-situ assistance: a mode of support delivered directly within any live web interface through lightweight, browser-level interventions on the Document Object Model (DOM), without rebuilding the application or modifying its underlying logic. We contribute a design space and a computational pipeline for DOM-mediated in-situ assistance, characterizing how GUI agents can insert, mutate, or recompose web elements to make the interface easier for users to understand, use, and navigate. We instantiate in-situ assistance in DOMSteer, a Chrome extension that interprets a user's help request and live interface context, grounds it to relevant UI elements, and executes reversible DOM manipulations directly on the live page to deliver assistance, including contextual tooltips, control highlighting, layout reorganization. Quantitative evaluations on two complex visual interfaces show that DOMSteer delivers reliable and efficient in-situ assistance. Use cases and a comparative user study with baseline ChatGPTAtlas demonstrate the usability and effectiveness of DOMSteer. Altogether, these findings point to a broader role for GUI agents: not just assisting from the sidelines, but actively reconfiguring live interfaces to support users in the moment.

Golay complementary pair (GCP), first introduced by Golay in 1951, has been extensively studied and widely applied in communication systems. A $q$-ary GCP $\{\mathbf{A},\mathbf{B}\}$ consists of two $q$-ary complex sequences $\mathbf{A}=(A_0,\cdots,A_{M-1})$ and $\mathbf{B}=({B}_0,\cdots,{B}_{M-1})$ of equal length $M$, where $\textit{A}_i,\textit{B}_i\in\{ξ^a:0\leq a\leq q-1\}$ with $ξ=e^{\frac{2π\sqrt{-1}}{q}}$.In this paper,we prove that the existence of a quaternary ($q=4$) GCP of length $M$ is equivalent to the explicit constructibility of ($4h$)-ary GCPs of length $2^mM$ for all integers $h,m\geq1$. All proposed sequences are constructed via extended Boolean functions (EBFs), and the direct construction yields GCPs with more flexible length ranges than all previous relevant results.

Affine frequency division multiplexing (AFDM), an emerging multi-carrier modulation scheme, has garnered significant attention due to its resilience to Doppler shifts and capability to achieve full diversity in doubly dispersive channels. However, existing data detection algorithms for AFDM systems face a significant trade-off between computational complexity and accuracy. In this paper, a novel low-complexity data detection scheme, termed the soft-feedback detector (SFD), is proposed. Particularly, building upon a maximum ratio combining (MRC) estimator framework, the SFD leverages the a priori symbol distribution to mitigate error propagation during iterative detection. Specifically, soft-decision feedback is incorporated as extrinsic information derived from the log-likelihood ratios of the transmitted symbols. As a result, the proposed detector significantly enhances detection accuracy while maintaining low computational complexity. Simulation results demonstrate that the SFD consistently outperforms benchmark decision-feedback detectors. In particular, compared with the conventional MRC detector, the proposed scheme achieves approximately a 3 dB signal-to-noise ratio (SNR) gain at the bit error rate (BER) of $10^{-3}$.

Utilization of Faraday rotation (FR) properties of topological materials offers a promising route toward novel magneto-optical devices. We systematically investigated the effect of Rashba spin-orbit coupling (SOC) on FR spectra in an extended Haldane model, which incorporates Rashba SOC and exchange splitting into the original spinless Haldane framework. Using the Kubo formalism, we calculated the FR spectra across the model's rich topological phase diagram. We found that in the Chern number C=2 region, in the absence of exchange splitting, the FR angle can exceed 4$^\circ$ and its peak position is tunable by the Rashba SOC. In contrast, with the inclusion of exchange splitting, a nearly flat FR profile emerges over a broad frequency range, and the FR peak values increase monotonically with the Rashba SOC strength. The Rashba SOC opens additional transition channels, whose net contribution constructively enhances the FR peak. Furthermore, we derived a low-energy effective Hamiltonian expanded up to quadratic terms, the results of which are in good agreement with tight-binding model calculations, thereby validating our numerical results. Our findings suggest that magneto-optical device characteristics can be designed and optimized through Rashba SOC engineering.

We analyze five photonic microring tensor core designs with a common optical power model. The results show that circuit ordering, unary encoding, and homodyne accumulation shape scalability, with the last two offering the strongest path to higher parallelism.

Federated learning (FL) enables collaborative intrusion detection without raw data exchange, but conventional FL incurs high communication overhead from full-precision gradient transmission and remains vulnerable to gradient inference attacks. This paper presents EdgeDetect, a communication-efficient and privacy-aware federated IDS for bandwidth-constrained 6G-IoT environments. EdgeDetect introduces gradient smartification, a median-based statistical binarization that compresses local updates to $\{+1,-1\}$ representations, reducing uplink payload by $32\times$ while preserving convergence. We further integrate Paillier homomorphic encryption over binarized gradients, protecting against honest-but-curious servers without exposing individual updates. Experiments on CIC-IDS2017 (2.8M flows, 7 attack classes) demonstrate $98.0\%$ multi-class accuracy and $97.9\%$ macro F1-score, matching centralized baselines, while reducing per-round communication from $450$~MB to $14$~MB ($96.9\%$ reduction). Raspberry Pi-4 deployment confirms edge feasibility: $4.2$~MB memory, $0.8$~ms latency, and $12$~mJ per inference with $<0.5\%$ accuracy loss. Under $5\%$ poisoning attacks and severe imbalance, EdgeDetect maintains $87\%$ accuracy and $0.95$ minority class F1 ($p<0.001$), establishing a practical accuracy, communication, and privacy tradeoff for next-generation edge intrusion detection.

Photonic state engineering in waveguide QED is typically based on local light-matter interactions. This limits its control over the spatial structure of bound photonic states. Here, we demonstrate a distinct mechanism arising from the interplay between nonlocal giant-atom coupling and topological band structure. Specifically, we consider giant atoms coupled to a Su-Schrieffer-Heeger waveguide and show that this configuration enables a controllable energy-level crossing protected by the topological gap. Adiabatically sweeping the atomic detuning across the crossing leads to a controlled exchange between distinct photonic bound states. In a two-giant-atom configuration, this mechanism achieves high-fidelity conversion of a spatially splitting state into a combining state. Extending this scheme to three-giant atoms, we further realize robust, shape-preserving photon transfer mediated by sequential in-gap crossings. Our results demonstrate how topology and nonlocal light-matter coupling can be combined to achieve programmable control of bound photonic states in waveguide QED platforms.

A new weighted Hardy-type inequality for functions from the Sobolev space $W_{p}^{1}$ is proved. It is assumed that functions vanish on small alternating pieces of the boundary. The proved inequality generalizes the classical known weighted Hardy-type inequalities.

Hurricanes are causing unprecedented damage to the natural environment, infrastructure, and communities. Understanding evacuation behavior is essential for improving emergency preparedness. Past studies have relied on surveys and interviews, which are prone to recall bias. Additionally, they urge incorporating social vulnerability in evacuation research, emphasizing its impact on evacuation capability and destination choice. This study addresses these gaps by analyzing evacuation behavior using mobile device location data from Hurricane Ian, one of Florida's deadliest hurricanes, and directly incorporating variables from the Social Vulnerability Index (SVI) into a zone-to-zone (census tract level) evacuation demand model. We find that vehicle availability, residence in group quarters, road density, and English proficiency have significant effects on evacuation demand, shaping both the ability to evacuate from origin tracts and the attractiveness of destination tracts. Travel impedance, measured as distance, also plays a significant role, with evacuees substantially less likely to travel longer distances.

The cosmic vorticity field, an essential tracer of nonlinear structure formation, has remained observationally inaccessible because transverse galaxy motions are difficult to measure and analytic models struggle to capture shell-crossing. Here we report an empirical reconstruction of this field by applying an artificial intelligence framework trained on simulations of the concordance LambdaCDM model to Sloan Digital Sky Survey galaxies. The recovered three-dimensional velocity and vorticity fields reveal coherent vortical structures, including spiral flows in clusters, filaments, and voids, and the cosmic web inferred from vorticity closely matches that derived from density segmentation. The power spectra of the reconstructed velocity and vorticity fields agree statistically with LambdaCDM predictions, and the inferred velocity field effectively removes redshift-space distortions, yielding an almost isotropic clustering signal. These converging lines of evidence, obtained from an independent perspective, reinforce the concordance cosmological model. By closing a long-standing observational gap, our results highlight the potential of AI-driven reconstruction to access otherwise unobservable quantities and to address fundamental questions in cosmology and galaxy formation.

The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor dimension diverges: in such regimes, the limiting null and alternative distributions of the ICM statistic degenerate to fixed constants. Moreover, when the number of predictors diverges, the commonly used wild bootstrap no longer approximates the null distribution of the ICM statistic well, leading to size distortion and substantial power loss. To address these challenges, we propose a new specification test based on weighted residual processes for evaluating the parametric form of the regression mean function in high-dimensional settings where the number of predictors increases with the sample size. We establish the asymptotic properties of the test statistic under the null hypothesis and under global and local alternatives. The proposed test maintains the nominal significance level and can detect local alternatives that deviate from the null hypothesis at the parametric rate $1/\sqrt{n}$. Furthermore, we propose a smooth residual bootstrap to approximate the limiting null distribution and establish its validity in high-dimensional settings. Two simulation studies and a real-data example are conducted to evaluate the finite-sample performance of the proposed test.

Recently, Abo Khamis et al. showed how to upper bound the size of a join of multiple tables, a problem essential to query optimization in database theory. They unified earlier works by the following information-theoretical framework. 1. Let $(X_1,..., X_n)$ be a row selected from the join uniformly at random. 2. The size of the join is now $\exp(H(X_1,..., X_n))$. 3. To upper bound $H(X_1,..., X_n)$, break it into several $\textit{local entropies}$, such as $H(X_1)$, $H(X_2, X_3)$, and $H(X_4|X_5)$, using Shannon-type inequalities. 4. Upper bound local entropies using statistics of the tables being joined. The statistics Abo Khamis et al. considered are the counts of graph homomorphisms from stars to the tables. In a follow-up work, we generalized stars to bi-stars. In this paper, we generalize bi-stars to caterpillars, an even larger class of graphs inspired by Sidorenko's conjecture. Simulations show that, while Abo Khamis et al.'s star bound overestimates the join size by $m$, our bi-star bound overestimates by about $m^{3/4}$, and this paper's new caterpillar bound overestimates by about $m^{3/5}$. These exponents are obtained by log-log regressions with R-square $> 0.98$. All homomorphisms are counted in time linear in the size of the tables being joined.

Synthetic-template subtraction is widely used to measure chromospheric activity in large spectroscopic surveys. However, many solar-like FGK stars show systematically negative Ca II infrared triplet (IRT) residual indices, implying that the observed line cores are deeper than those predicted by parameter-matched templates. We investigate this effect using solar-like stars from LAMOST DR9, MaStar, and XSL DR3, measuring activity indices (R+) for both the Ca II H&K and IRT lines in a uniform framework. We find that observational effects, including atmospheric-parameter offsets, treatment of the instrumental line-spread function, and propagated measurement uncertainties, contribute to scatter but do not explain the systematic negative bias in R+_IRT. The results instead suggest that the negative bias most likely arises because photospheric templates underestimate the depth of the IRT cores, likely owing to missing chromospheric structure and, to a lesser extent, NLTE effects. An empirical increase in the adopted microturbulent velocity deepens the synthetic IRT cores and partially mitigates the negative offset. In addition, R+ values derived from different synthesis configurations show systematic offsets but generally preserve strong linear correlations, indicating that they can be cross-calibrated. These results clarify the origin of negative Ca II IRT residual indices and help interpret template-dependent systematics in chromospheric activity measurements based on synthetic-template subtraction.

In this paper, we consider a two-parameter ($l$ and $a$) generalization of a sequence that Glasby and Paseman considered. Based on computer experiments, we conjecture its unimodality, log-concavity, peak positions, and the asymptotic behavior of the maximum values. Then we prove this conjecture for the case where $l=2$ and $a=1$. We finish the paper by making some comments about the conjecture on the generalized sequence.

Most existing assistive navigation tools focus on providing real-time guidance for Blind and Low-Vision (BLV) people, but few support building a holistic spatial understanding of unfamiliar environments before travel. Such cognitive map construction (e.g., knowing that a fountain is south of a tower and west of a hotel) is important for pre-travel planning, yet remains underexplored in prior work. To address this gap, we present Touching Space, an end-to-end system that retrieves map data for a target place and loads it into a frontend interface for exploration. The system combines haptic and audio feedback: users explore spatial layouts through touch and ask spoken questions to a conversational agent during exploration. Touching Space contributes a conversational interface that supports BLV users in building cognitive maps on commodity hardware.

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can propagate from and return to the particle trajectory, under the additional assumption that the flow has nonzero vorticity.

We present a randomized augmenting paths-based algorithm to compute the maximum flow in a directed, uncapacitated graph in almost $m+nF$ time, matching the algorithm of Karger and Levine for undirected graphs (SICOMP 2015). Combined with an initial $\sqrt n$ rounds of blocking flow to reduce the value of $F$, we obtain a maximum flow algorithm with running time $mn^{1/2+o(1)}$. For combinatorial, augmenting paths-based algorithms, this is the first improvement over Dinic's algorithm for moderately sparse graphs. To obtain our algorithm, we introduce a new technique to re-weight the edges of a strongly connected directed graph so that each cut is approximately balanced: the total weight of edges in one direction is within a constant factor of the total weight in the other direction. We then adapt Karger and Levine's technique of sampling edges from the newly weighted residual graph, ensuring that an augmenting path exists in the sampled graph with high probability. One technical difficulty is that our balancing weights have to be dynamically maintained upon changes to the residual graph. Surprisingly, we can black box the dynamic data structure from the recent interior point method-based flow algorithm of van den Brand et al. (FOCS 2024).

We study the parametrization of the energy-momentum tensor for the case of a proton in momentum space in terms of gravitational transverse momentum-dependent distributions (TMDs). These gravitational TMDs are investigated with the inclusion of higher-twist contributions to predict the mechanical properties, specifically the transverse pressure and shear force distributions, along with the polarization-dependent $Π^q_S$ and $Π^q_A$ terms. The corresponding distributions are computed individually for both $u$ and $d$ quark flavors. The calculations have been performed in the light-cone framework using the spectator diquark model. A strong binding contribution to the transverse pressure is observed in the low-momentum space for both quark flavors of the proton.

This study maps the quantum landscape of superconducting diodes (SDs) \cite{nadeem23} onto the quantum technology architecture, which is currently constrained by fundamental challenges in control and scalability. In the existing non-integrated quantum technology hardware, control and scalability related issues emerge at two fronts: First, nonlinear and nonreciprocal circuit elements, which are essential building blocks for quantum processors, are often complex, bulky, and dissipative. Second, the temperature gradient between classical control electronics ($T_C\gtrsim$ K), which is also dissipative, and the quantum processor at cryogenic temperatures ($T_Q\sim$ mK) makes scalability even more challenging. The main focus is to reveal how the built-in nonlinearity, nonreciprocity, and quantum functionalities of SDs are significant for on-chip integrated circuit quantum electrodynamics (c-QED), enabling scalable integration of noise-resilient qubit and qubit-interfaces for efficient power delivery, coherent control and memory, high-fidelity readout, and quantum-limited amplification. To this end, this study will also shed light on how thermodynamic constraints and field effects can be harnessed within a quantum-enhanced SD platform, thereby enabling thermal compatibility between classical and quantum workflows, isothermal all-electrical control, and on-chip scalability. This perspective is expected to play a pivotal role in the advancement of superconducting circuit-based quantum hardware with temperature-matched classical, quantum, and hybrid workflows.

The standard cosmological paradigm assumes that the inflaton field becomes dynamically negligible during the post-reheating evolution of the Universe. We demonstrate that this assumption fails for a broad class of inflationary models where the potential behaves as a monomial form $V(ϕ) \propto ϕ^k$ (with $k \ge 4$) around the minimum. In such scenarios, the effective inflaton mass depends on the field amplitude and vanishes asymptotically as the Universe expands. This vanishing-mass mechanism renders the inflaton kinematically accessible to the thermal plasma long after reheating, facilitating the regeneration of inflaton quanta through 1-to-2 decays and 2-to-2 scatterings of bath particles. This mechanism is quite generic and the coupling responsible for reheating can be constrained if the inflaton is overproduced, while the inflaton quanta can constitute dark matter in specific scenarios. Furthermore, if reheating occurs via the Standard Model Higgs portal, the process can be further constrained by big bang nucleosynthesis, cosmic microwave background, and colliders such as the LHC. This mechanism provides a new framework for probing post-inflationary reheating.

Solid phase of dense granular matter is inevitable because of jamming transition when the packing fraction or the pressure suffered is high enough. The experiment suggests that active Brownian granular matter will keep fluid phase even under the highest packing fraction (higher than the packing fraction of crystallization) if crystallization is prevented by mixing granular particles of different sizes. The findings encourage us to reconsider the role of activity in affecting the global dynamical properties of matter.

We present the maximum ejecta mass $(M_{\rm ej})_{\rm max}$ and the maximum ratio of ejecta mass and accreted mass $(M_{\rm ej}/M_{\rm acc})_{\rm max}$ of a nova for various white dwarf (WD) masses ($M_{\rm WD}=0.6$ - 1.38 $M_\odot$) and mass accretion rates ($\dot{M}_{\rm acc}=1\times 10^{-11}$ - $3\times 10^{-7} ~M_\odot$ yr$^{-1}$) based on the energy balance with nuclear burning. These maximum values serve as an upper bound of mass ejection for individual novae. Recently, B. E. Schaefer concluded that the WD masses in the recurrent novae U Sco and T CrB decreased at nova explosions, because the ejected mass is much larger than the accreted mass, i.e., $M_{\rm ej}/M_{\rm acc}= 26$ and $540$, respectively. These values are derived from the orbital period change at the nova explosions. Recurrent novae have been considered to be a progenitor system of Type Ia supernovae (SNe Ia) because their WD masses are now close to, and will possibly grow up to, 1.38 $M_\odot$ at which WDs explode as SNe Ia. From the different view point of energy generation at the thermonuclear runaway, we have obtained the much smaller value of the maximum ratio of $M_{\rm ej}/M_{\rm acc}\lesssim 2.6$ for a $1.37 ~M_\odot$ WD. This conclusion simply means that the nuclear (hydrogen) burning cannot release energy enough to expel such a large ejecta mass as B. E. Schaefer's claims. We also conclude that $(M_{\rm ej}/M_{\rm acc})_{\rm max}$ hardly increases even if we include the effect of frictional mass ejection process in the common envelope phase of a nova.

Universal speech enhancement (USE) aims to restore speech signals from diverse distortions across multiple sampling rates. We propose UniPASE, an extension of the low-hallucination PASE framework tailored for USE. At its core is DeWavLM-Omni, a unified representation-level enhancement module fine-tuned from WavLM via knowledge distillation on a large-scale supervised multi-distortion dataset. This module directly converts degraded waveforms into clean and linguistically faithful phonetic representations, ensuring robust enhancement with minimal linguistic hallucination. Based on these enhanced phonetic representations, an Adapter generates enhanced acoustic representations containing rich acoustic details, which a neural Vocoder uses to reconstruct corresponding high-fidelity 16-kHz waveforms. A PostNet then converts the waveforms to 48~kHz before resampling them to their original rates, enabling seamless handling of inputs and outputs at multiple sampling rates. Experimental results on several evaluation datasets, covering sub-tasks and full tasks, demonstrate that UniPASE achieves superior or competitive performance compared with existing state-of-the-art models. The proposed model also serves as the backbone of our submission to the URGENT 2026 Challenge, which achieved 1st place in the objective evaluation. The source code and audio demos are available at https://github.com/xiaobin-rong/unipase/.

Understanding the prevalence of disk-like galaxies at very high redshifts is crucial for constraining the early formation of angular momentum-supported structures. The advent of JWST now permits rest-frame UV and optical morphological studies deep into cosmic epochs where disks have traditionally been considered uncommon. We apply an identical denoising VAE-GCNN classification pipeline to multi-filter JWST/NIRCam cutouts in order to obtain homogeneous, morphology-based disk fractions across the sample. Our approach comprises two steps: (i) a U-Net Variational Autoencoder (VAE) is trained to remove astrophysical and instrumental contaminants while preserving intrinsic morphology, and (ii) a rotation - and reflection - equivariant GCNN classifier is applied to the denoised cutouts to distinguish disk-like galaxies from non-disks. We determine the fraction of disk-like galaxies as 0.34 for a sample of JWST 100 galaxies over the redshift range 4 < z < 7.7, also in dependence on the galaxy mass range. Our GCNN-based morphological analysis indicates that disk-like systems constitute a significant fraction of the considered high-redshift population and underscore the importance of such studies for the models of disk formation in the first billion years.

In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian regular $F$-finite $\mathbb{F}_p$-scheme $X$, and define their Bernstein--Sato roots as $p$-adic integers. When the D-module is the structure sheaf $O_X$, this recovers Bitoun's definition. When the D-module arises from a locally finitely generated unit $F^e$-module and $X$ is of finite type over an $F$-finite field, we show that the roots are finite and rational, generalizing Bitoun's result. In the course of the proof, we also develop a related theory for Cartier modules.

Heterogeneous sequential recommendation (HSR) aims to learn dynamic behavior dependencies from the diverse behaviors of user-item interactions to facilitate precise sequential recommendation. Despite many efforts yielding promising achievements, there are still challenges in modeling heterogeneous behavior data. One significant issue is the inherent sparsity of a real-world data, which can weaken the recommendation performance. Although auxiliary behaviors (e.g., clicks) partially address this problem, they inevitably introduce some noise, and the sparsity of the target behavior (e.g., purchases) remains unresolved. Additionally, contrastive learning-based augmentation in existing methods often focuses on a single behavior type, overlooking fine-grained user preferences and losing valuable information. To address these challenges, we have meticulously designed a behavior-aware dual-channel preference learning framework (BDPL). This framework begins with the construction of customized behavior-aware subgraphs to capture personalized behavior transition relationships, followed by a novel cascade-structured graph neural network to aggregate node context information. We then model and enhance user representations through a preference-level contrastive learning paradigm, considering both long-term and short-term preferences. Finally, we fuse the overall preference information using an adaptive gating mechanism to predict the next item the user will interact with under the target behavior. Extensive experiments on three real-world datasets demonstrate the superiority of our BDPL over the state-of-the-art models.

Understanding and controlling vortex motion in superconductors are important both for suppressing dissipation in superconducting devices and for device applications that exploit vortices. In this work, we quantitatively imaged the stray magnetic field distribution of vortices in an NbN thin film by wide-field magnetic imaging using a perfectly aligned diamond NV ensemble. By continuously measuring while stepwise varying the applied magnetic field under local laser heating, we captured a rearrangement of the vortex configuration in real space and in real time over more than 100 min. The observed vortex rearrangement is consistent with a reduction of the pinning force due to local laser heating and with the Lorentz force exerted by shielding currents induced by the field variation. These results provide insight into vortex dynamics and suggest potential applications, including vortex exclusion from sensitive regions of superconducting devices and vortex positioning in vortex-based devices.

Optical vortices are singularity lines where the light field intensity vanishes and its phase is undefined. These threads of darkness are adorned by Gauss's law as lines of pure longitudinal polarization where the polarization plane tilts and winds around. We unveil the resulting spin field as a unique structure which unifies both topological textures and defects, as it includes a point defect of undefined spin surrounded by a meronic texture which spans half the spin unit sphere. Moreover, this intricate topological structure of transverse spin does not spread in propagation, is localized arbitrarily below the wavelength of light and presents highly anisotropic features. Here we describe these hidden topologies of transverse spin embedded in simple scalar vortex beams, highlighting the diversity of topological structures that arise in two different spaces -- the spin unit sphere and the transverse-axial Poincaré sphere -- and discuss the underlying aspects behind their subwavelength localization.

This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate the problem into the study of Hamilton-Jacobi equations. Through a detailed analysis of the structure of viscosity solutions, we provide a complete classification of explicit formulas for the spreading speed of the prey population, especially in cases where it invades the habitat more rapidly than predators, yielding two fundamentally distinct ``nonlocal determinacy'' results derived by different mechanisms. We also obtain an upper bound for spreading speed of the predators, incorporating the decay rate of the initial data and the speed of shifting habitats. These findings demonstrate that there are complex connections among spreading speeds, habitat shifting speed and initial conditions, and emphasize the significance of nonlocal dispersal in determining the propagation dynamics of predator-prey systems.