Papers

A variety $\mathcal{V}$ is called a Schreier variety if every subalgebra of a $\mathcal{V}$-free algebra is a $\mathcal{V}$-free algebra. We use ideas from Tame Congruence Theory to classify locally finite Schreier varieties. One version of the classification theorem states that a locally finite variety $\mathcal{V}$ is a Schreier variety if and only if (i) every finite algebra in $\mathcal{V}$ is a $\langle 0,1\rangle$-minimal algebra and (ii) if $\mathcal{V}$ has a constant $1$-ary term operation, then $\mathcal{V}$ also has a constant $0$-ary term operation.

Sequential sentence classification (SSC) is an essential task for structuring scientific publications, and extending SSC research to languages other than English can improve accessibility to scientific knowledge in multilingual digital libraries. Cross-lingual transfer is a promising approach to address the scarcity of training data in non-English languages. Prior work on other natural language processing tasks has shown the benefits of capturing linguistic similarity between source and target languages. However, SSC inherently depends on patterns at the discourse level, such as label sequences and positional regularities, which appear consistently across languages regardless of linguistic differences. To examine the factors that determine transfer success in SSC, we constructed a multilingual SSC dataset covering 13 non-English languages collected from five academic databases. Our cross-lingual transfer experiments, using both encoder-based and generative models, show that linguistic proximity has no consistent predictive power for transfer performance, whereas structural similarity in rhetorical organization shows a weak but consistent positive correlation across models. After controlling for source-language performance, the similarity of label distributions is the most consistent predictor. Building on this finding, we propose a set of three methods that explicitly leverage structural information using generative models. In the in-domain evaluation, the best combination reaches parity with the strongest encoder baselines, and in transfer to languages unseen during training, it outperforms the strongest encoder baseline.

Let $D$ be an odd fundamental discriminant, with $D=1$ permitted, and let $r\geq 1$ be fixed. We prove that, for every sufficiently large integer $\ell$ satisfying $(-1)^\ell D>0$, the first $r$ traced diagonal Rankin–Cohen brackets \[ \mathrm{Tr}_1^{|D|}[G_{\ell-2e,D},G_{\ell-2e,D}]_{2e}, \qquad 1\leq e\leq r, \] are linearly independent in $S_{2\ell}(SL_2(\mathbb Z))$. Here $G_{k,D}$ is the Eisenstein series of weight $k$, level $|D|$, and nebentypus $\chi_D$. The Petersson formula of Kayath, Lane, Neifeld, Ni, and Xue then implies that at least $r$ normalized Hecke eigenforms $f\in S_{2\ell}(SL_2(\mathbb Z))$ satisfy $L(f\otimes\chi_D,\ell)\neq 0$. For $D=1$, this gives, for every fixed $r$ and every sufficiently large $K\equiv 0\pmod 4$, at least $r$ level-one eigenforms of weight $K$ with nonzero central value.

We prove the linear stability of an embedded mean curvature flow shrinker in $\mathbb R^4$ with the topology of the Möbius bundle. This provides a non-flat, non-spherical stable shrinker in higher codimension, in sharp contrast with the classification of stable hypersurface shrinkers. Topologically, the Möbius shrinker models the reversal of a real blow-up, suggesting that stable higher-codimension singularities may encode non-trivial topological operations under mean curvature flow.

A neural turbulence closure defines a new boundary-value problem, $R(U)=N(U)+F(U)=0$, with a coupled Jacobian $J(U)=N'(U)+F'(U)$, where $N$ is the original mean-flow operator and $F$ the learned closure. We establish two consequences of global tangent dissipation. For a monotone original operator, a positive uniform margin supplied by the original operator and closure together guarantees existence, uniqueness and a global inverse-sensitivity bound relating a posteriori solution error to the a priori residual. For a general original operator, a dissipative closure cannot worsen tangent dissipation, but this alone does not guarantee uniqueness. Tangent dissipation depends on both diffusion and reaction. We study two complementary ways to promote it: (1) an exact-integral construction enforcing non-negative tangent diffusion while leaving reaction unconstrained, and (2) a penalty on tangent-reaction violations at sampled states. Tangent diffusion enters the Jacobian, and non-negative secant eddy viscosity alone does not control its coercivity. We conduct tests with channel flow at $Re_\tau=180$–$5200$, which provides a strongly monotone baseline. Both constrained closures reach accurate solutions in all 50 training-seed/Reynolds-number cases. At $Re_\tau=1000$, we conduct tests with 10,000 starts for one fixed network per closure and we find one root for each constrained closure and multiple roots for the other closures. Although this does not prove uniqueness, it provides strong empirical evidence for uniqueness of the tested constrained closures. At $Re_\tau=5200$, the construction and penalty reduce the reported inverse sensitivity relative to the original operator by approximately $372\times$ and $11\times$, respectively.

Nucleation rates are exponentially sensitive to the thermodynamic driving force and can therefore depend strongly on the treatment of long-range intermolecular interactions. Here, using the Lennard–Jones (LJ) system as a benchmark, we combine molecular dynamics (MD) simulations, jumpy forward-flux sampling (jFFS), and free-energy calculations to quantify the effect of potential truncation on melting thermodynamics, homogeneous crystal nucleation kinetics, and computational cost. Within the cutoff-radius range $2.5\sigma\le r_c\le 6\sigma$, the melting temperature at zero pressure varies by approximately 11%, while the nucleation rate changes by approximately ten orders of magnitude. By invoking classical nucleation theory (CNT), we show that this pronounced kinetic sensitivity originates primarily from cutoff-induced changes in the chemical potential difference between the liquid and crystalline phases. Building on this observation, we develop a CNT-based framework for extrapolating finite-cutoff rates to the full-potential limit and for estimating the expected rate deviations at other cutoff radii and temperatures. These findings also provide a systematic basis for cutoff selection: the optimal cutoff should minimize computational cost while keeping the deviation from the full-potential rate within acceptable bounds. At $kT/\epsilon=0.5$, $r_c=4\sigma$ provides a reasonable compromise according to these criteria. We further demonstrate that conventional homogeneous tail corrections do not offer a reliable alternative, as they cannot consistently account for the liquid, crystalline, and interfacial environments present during nucleation. Our findings highlight the need to specify and validate the truncation scheme as an integral component of force-field development in simulations of nucleation and other interfacial phase transitions within inhomogeneous environments.

Crustal strength is often characterized using a strength-depth profile where laboratory-derived friction and flow laws are connected at depth (i.e., the so-called Christmas Tree diagram). Large, destructive earthquakes frequently nucleate within the transition zone from a frictional-to-viscous deformation regime, which represents the strongest part of the crust. However, microscale deformation mechanisms controlling bulk frictional-to-viscous transitional behavior remain unclear. To investigate the deformation mechanisms, we conducted shear experiments on room-dry, powdered quartz-albite mixtures under upper- to mid-crustal pressure-temperature conditions using a Griggs-type deformation apparatus. We simulated depth conditions in the range 7-30 km, by varying temperatures and confining pressures (210-900 C and 185-870 MPa, respectively, by assuming 30 C/km and 2,700 kg/m3). To assess the rate dependence and stability of shear deformation, we sequentially stepped shear strain rates between 10^-3/s and 10^-4/s. At shallower depth conditions, friction coefficients follow Byerlee's law, while at greater depth conditions they deviate from it and strain weakening is observed. Post-mortem microstructures indicate changing deformation mechanisms with increasing simulated depths. The samples deformed at shallower depth conditions (<18 km) show a predominance of cataclastic grain comminution. At greater depth conditions (>24 km), nano-grains are observed, as well as polygonal quartz grains at the greatest depth condition (30 km). These results indicate that the controlling deformation mechanisms at the frictional-viscous transition zone are grain boundary sliding and dynamic recrystallization. We conclude that nano-scale deformation mechanisms govern the frictional-viscous transitional deformation in the upper crust, and propose their importance for understanding seismic rupture processes there.

Scientific discovery is defined by the ability to identify the boundaries of existing knowledge and venture into unexplored territory. The ultimate vision for AI in science is problem-driven autonomous research: given a fundamental challenge by a human expert, the AI independently navigates the scientific landscape, uncovers theoretical and empirical bottlenecks, and systematically expands the frontier of knowledge. In this paper, we introduce ScientistTwo, a fully autonomous multi-agent framework designed to realize this vision. Specifically, ScientistTwo takes an initial problem as input, establishes state-of-the-art baselines, formulates novel hypotheses, and coordinates specialized agents to orchestrate an end-to-end discovery cycle without human intervention. Moreover, the framework rigorously conducts experiments using diverse datasets and metrics, refines methodologies through automated ablation studies, and validates research findings via a closed-loop simulated peer-review rebuttal engine. To evaluate ScientistTwo's capabilities against the highest standards of human scientific achievement, we benchmark it across papers accepted at top-tier conferences such as ICLR, ICML, and NeurIPS. As a result, ScientistTwo autonomously generates expert-level, publishable papers and fully verified, executable codebases. Its solutions consistently outperform human state-of-the-art models, and achieve higher average review ratings than human-authored papers under automated AI review agents. These results show that ScientistTwo is not merely an assistive tool but an autonomous scientific pioneer capable of pushing the frontiers of human discovery. Project website: https://scientist-two.github.io/

We present a unified analytical treatment of carrier transport relaxation in bilayer graphene (BLG), including scattering by surface roughness, charged and neutral impurities, acoustic and optical phonons, and substrate polar phonons. The calculation is formulated within the low-energy two-band approximation using Fermi's golden rule and the semiclassical Boltzmann transport equation. Closed-form expressions for the transport relaxation rates are derived and verified by numerical evaluation of the corresponding scattering integrals. Particular attention is given to Pauli blocking, whose influence becomes important under degenerate carrier conditions owing to the approximately parabolic low-energy dispersion and nearly constant density of states of BLG. We find that Pauli blocking modifies the relaxation rates in a mechanism- and energy-dependent manner for both suspended and substrate-supported BLG. For the parameters considered, neutral-impurity scattering provides the dominant contribution over a substantial energy range, while acoustic-phonon and charged-impurity scattering remain important competing mechanisms. Optical-phonon scattering is suppressed below its emission threshold, whereas substrate polar phonons provide an additional relaxation channel in supported BLG. Comparison with monolayer graphene and a conventional two-dimensional electron gas highlights the role of band dispersion, density of states, screening, and chirality in determining the distinct scattering behavior of BLG. These results provide analytical insight into the relative importance of the principal momentum-relaxation mechanisms and the role of Pauli blocking in BLG transport.

Peptide-HLA binding prediction is a critical step in neoantigen identification for personalized cancer immunotherapy and holds significant clinical value. However, the training data available for many HLA alleles are extremely limited, which severely constrains the performance of conventional methods on this task. Parameterized quantum circuits are hypothesized to induce inductive biases beneficial for learning from small datasets, yet their application to biological sequence prediction remains underexplored. To address this, we propose a hybrid quantum-classical neural network (HQNN) specifically designed for peptide-HLA binding prediction. HQNN integrates multi-source biological feature encoding with parallel quantum feature extractors and a quantum-enhanced classifier. On two HLA alleles (A*02:01 and B*07:02), HQNN outperforms a parameter-matched classical CNN baseline across all training sizes, with the performance gap widening as training data decreases. Ablation studies confirm the respective contributions of the quantum feature extraction module and the quantum classifier. In noise-aware simulations, performance degrades only mildly, and such degradation is reasonable and acceptable under realistic quantum hardware noise levels. These results suggest that hybrid quantum-classical architectures can provide practical sample-efficiency gains for immunoinformatics tasks in low-data regimes.

Epidemic mitigation comes with a price in practice, and when budget is limited, its effective allocation becomes an important question on public policy. In this paper, we study epidemic control through a Stackelberg mean-field game in which a principal, representing the government, chooses social distancing guidelines and vaccination levels for a large population of rational minor agents subject to a budget-spending process. The principal anticipates the minor agents mean-field Nash equilibrium (MFNE) and selects intervention policies to minimize her own objective, inducing a bi-level optimal control problem. We define the Stackelberg mean-field game equilibrium (SMFE) and give its necessary condition by a forward-backward ordinary differential equation (FBODE) system, and provide existence and uniqueness results. We further propose an iterative fixed-point algorithm to solve the FBODE numerically and present computational observations that illustrate the resulting equilibrium behavior.

Croissant is the de facto machine-readable descriptor for ML datasets: JSON-LD over schema.org. Since version 1.1 it also carries data use conditions, recommending DUO and ODRL for them. What no version specifies is how any of them is evaluated: no decision procedure, no bound on evaluation cost, no outcome for a condition an implementation cannot evaluate, no record of what was checked, and nothing on composition with caller-side authority. We supply that half. An additive profile lets a dataset declare the operations it admits and the conditions under which it admits them, over a closed set of five operators whose decision procedure is given in full, so a gate decides from the descriptor alone and records what it checked. Two corpora evaluate it and their evidence is kept apart. Three descriptors that gated a real nf-core pipeline give the deployment result: decisions from a profile document match the gate's native descriptor record for record, stripping the layer leaves a valid Croissant document, and the added cost is 11.7 $\mu$s against a 119 $\mu$s decision. A corpus generated from the profile's grammar gives the breadth, covering every operator, refusal class and conformance clause. Across its valid cases, 552 complete decision records agree three ways – native descriptor, profile terms, and the same policy as ODRL in usageInfo. The carrier is therefore not the contribution; the evaluation semantics is. Finally, caller-bound and data-bound policies range over non-overlapping state spaces, so neither permit set contains the other.

Quantum computers are technologically novel and unusual, but at system scale they should be engineered using many of the same principles that govern classical heterogeneous accelerators. This paper argues that utility-scale quantum architecture is primarily a cost-performance problem across a coupled quantum-classical system, leading to a blueprint for scalable quantum processing unit (QPU) design. Our architecture blueprint is organized around clean logical abstractions, hiding details and complexity of physical qubit modalities below the instruction set architecture (ISA) boundary, and specializes recurring functions aggressively to minimize the cost for utility scale quantum computations. Its low-level implementation through specialized local hardware for control, readout, and quantum error correction (QEC) closely resembles the architecture of high-performance network stacks. One of our main insights is that the design principles and the resulting architecture closely follow established practice from classical computing and networking.

Broken symmetry and topology are distinct descriptions for how matter organizes itself. Here, we propose one gives rise to the other. A mixed singlet-triplet $d$-density wave, which is a particle-hole condensate, has a hidden bond order that breaks translation symmetry and generates a time-reversed pair of Chern bands, without producing conventional charge or spin density order. At fractional fillings with odd denominators, finite size exact diagonalization studies show how repulsive interactions can transform this symmetry-broken topological state into a fractional quantum spin Hall liquid. Its opposite chiralities produce a crossed response in which charge flux transports spin, and spin flux transports charge. The same setting also reveals what borders such a phase. Strong interspin coupling and increasingly dilute fillings favor charge order and make residual band dispersion decisive, while at half filling, the spin-decoupled limit gives a homogeneous correlated liquid with signatures consistent with the physics of a composite Fermi liquid.

Recently, Ferroni constructed a family of counterexamples to the well-known conjecture in Ehrhart theory stating that the $h^*$-polynomial of a lattice polytope with the integer decomposition property is unimodal. This raises the question of whether the $h^*$-polynomial of a lattice simplex with the integer decomposition property remains unimodal. In this note, we prove that every lattice simplex with the integer decomposition property and prime normalized volume has a unimodal $h^*$-polynomial. Furthermore, we establish several sufficient conditions for the unimodality of the $h^*$-polynomial of such simplices.

Reinforcement learning (RL) is widely used to improve language-model agents, and its gains are usually measured by final task success. However, an agent's earlier actions shape the states in which its later decisions are made, so final task success conflates the ability to reach useful states with the ability to complete the task once there. Comparing agents only on the states each one reaches does not separate the two, since each agent is then scored on states selected by its own actions. To address this conflation, we introduce checkpoint handoff, an evaluation protocol that decouples reaching from completing without retraining. One checkpoint acts as a reacher up to a handoff point, and another continues as the solver from the same replayed history. In detail, (1) Reach measures how often a reacher arrives at states that a replayable environment verifies to be a fixed number of actions from success, and (2) Solve measures how often a solver completes the task from identical cloned copies of those states. Crossing supervised fine-tuning (SFT) and RL checkpoints in both roles across two benchmarks and two independently released training pipelines, we find that the gain from switching the solver from SFT to RL is consistently larger when RL is the reacher, at all three model scales on TravelPlanner and on both ALFWorld splits. Further analyses on ALFWorld show that RL improves both Reach and Solve. The solver gain is larger under an RL reacher because RL reaches solvable states more often, and separately measured Reach and Solve gaps recover most of this difference. Because handoff only requires replaying one checkpoint's history under another, agentic RL evaluations can report arrival and completion alongside final success.

Conversational agents are increasingly used to guide reflection. A recent randomized trial compared a GPT-4o career reflection agent with the same program in a static journaling survey. Agent participants ended less committed to their career plans and more doubtful. We coded all 17,930 turns from its two studies, checked our coding against human coders and linked conversations to the trial's surveys. The rules the agent followed were the easy-to-check ones, like a reply length cap. Told not to flatter, it praised participants in half of its turns; told to challenge gently, it almost never did, and such a break leaves no visible trace. The behavior tied to the worse outcome was the demand to decide: the survey posed each decision once, while the agent asked again when participants hesitated, and those pressed most ended most doubtful. Our findings inform reflection agent design and the writing of checkable instructions.

This paper proposes a Retrieval-Augmented Generation (RAG) framework for scientific image quality assessment, designed to simultaneously address both the understanding track (SIQA-U) and the scoring track (SIQA-S) of the SIQA challenge. We construct a multimodal index that integrates textual semantics with fine-grained visual features, and develop a multi-route retrieval and fusion mechanism to provide large language models with highly relevant reference cases, thereby enhancing their capability to evaluate complex scientific images. Experimental results demonstrate that the proposed framework effectively aligns with the judgment criteria of human experts. Ultimately, our method achieves 1st place in the SIQA-U track of the SIQA challenge at the ICME 2026 Grand Challenges.

Photomultiplier tubes (PMTs) are widely used in imaging atmospheric Cherenkov telescopes. Their response can depend on the telescope pointing direction through changes in their orientation relative to the geomagnetic field. Such a dependence was indicated during the calibration campaign of the CTAO LST-1. In this work, the LST-1 calibration data are analyzed to quantify the gain dependence in terms of the geomagnetic field, and dedicated laboratory measurements are performed to test the hypothesis that the observed dependence originates from magnetic-field effects. Both the on-site and laboratory measurements show a consistent dependence of the PMT gain on the magnetic field, while the laboratory measurements further separate the effects on the gain and the excess noise factor. These results provide a clearer understanding of the gain variation observed in LST-1 in terms of magnetic-field effects.

For ordered graphs $H_1,\ldots,H_t$, let $\rt(H_1,\ldots,H_t)$ denote the least integer $N$ such that every $t$-coloring of the edges of the naturally ordered complete graph on $[N]$ contains an ordered copy of $H_i$ in color $i$ for some $i\in[t]$. We prove that a uniformly random ordered matching $M$ on $n$ vertices with interval chromatic number two asymptotically almost surely satisfies \[ \rt(K_3,M) =\Omega\left(\frac{n^{4/3}}{(\log n)^{1/3}}\right). \] This strengthens the lower bound $\Omega((n/\log n)^{5/4})$ of Balko and Poljak for such random matchings and improves the general existential lower bound of Conlon, Fox, Lee and Sudakov by a factor of $\log n$. The proof combines pseudorandom triangle-free graphs, a coarse encoding of order-preserving embeddings, and a permutation avoidance estimate derived from Brègman's inequality.

Accurate instance-level and functional understanding of urban buildings in large-scale point clouds is essential for digital city modeling and urban analysis. However, the extensive spatial coverage of urban scenes leads most existing methods to rely on predefined blocks for training and evaluation, although such partitions are rarely available in real-world applications and introduce additional preprocessing while fragmenting complete building structures. To address this issue, we propose an adaptive region-dividing strategy with unified scene-level evaluation. Specifically, the 3D point cloud is projected onto a bird's-eye-view (BEV) plane, where a pretrained segmentation model is used to detect building regions. The detected bounding boxes are then back-projected to the original point cloud to construct structure-aligned adaptive training blocks, enabling semantically guided dynamic partitioning without manual design. Furthermore, beyond instance-level understanding, few methods have explored fine-grained classification for urban buildings, and thus we also put forward a fine-grained classification model for urban buildings with a spatially-supervised contrastive loss. First, for each segmented building, a point transformer classifier jointly encodes its body and local context using geometric, color, and core-context information. Then, the class-balanced weighted cross-entropy is used to alleviate severe class imbalance. The proposed spatially-supervised contrastive loss further enhances inter-class discriminability by assigning greater weight to spatially proximate, same-category buildings, encouraging compact functional representations while separating easily confused categories. Extensive experiments on UrbanBIS and STPLS3D demonstrate the advantages of the proposed method in building instance segmentation and fine-grained classification compared to existing SOTA methods.

Large language models (LLMs) are increasingly integrated into vehicle voice assistants. But linking natural-language requests to vehicle functions creates a safety-critical authorization problem. Before executing a command, the system must choose whether to execute, refuse, clarify, require confirmation, defer to manual control, trigger an emergency response, or make no tool call. To our knowledge, prior evaluations do not isolate this pre-action decision across speaker role, authentication status, vehicle state, and tool availability. We introduce a 202-scenario benchmark with Reference Decisions under a seven-class taxonomy. We evaluate two local open-weight models and three API-based LLMs using Decision Alignment and safety-specific error metrics. Alignment ranges from 40.1% for Llama 3.2 3B to 89.1% for Gemini 3.1 Pro Preview. The API-based models score between 83.2% and 89.1%, with no statistically significant differences among them. Even these models produce two to three False Executes among 161 non-execution scenarios, and persistent errors remain in confirmation and manual-control decisions. A controlled Llama 3.2 3B ablation increases alignment to 40.1% under the structured authorization policy, versus 28.2-29.2% under schema-only and generic-safety baselines, but it does not eliminate False Executes. Structured LLM decisions are therefore insufficient as a standalone safety mechanism, and deployment requires an independent enforcement layer that verifies tool permissions and vehicle-state constraints before invoking any vehicle function.

Symmetry plays a fundamental role in modern physics by guiding the classification of phases and the construction of effective theories of critical systems. Identifying collective symmetry remains challenging because tests based on preselected order parameters can overlook hidden components. A central goal is therefore to extract symmetry and critical information from a single accessible component. We pursue this goal using Lee–Yang zero ratios generated by a single ordering field. Unmeasured components shape the projected fluctuation distribution and hence the relative zero positions. Deep in a phase with spontaneous symmetry breaking, we show analytically that the zero ratios for an isotropic order parameter approach a parameter-free Bessel sequence fixed by the number of collective components. Near quantum criticality, fluctuations deform this distribution. The resulting ratio deviations and their finite-size coupling dependence carry additional critical information. We demonstrate these results with large-scale quantum Monte Carlo simulations of many-body systems with conventional and enlarged continuous symmetries. This approach provides quantitative access to collective symmetry and criticality without measuring every competing order.

We present VGGT-GS SLAM, a monocular 3D Gaussian Splatting SLAM system designed for uncalibrated videos. Starting from feed-forward VGGT pose and depth priors, our system performs submap differentiable bundle adjustment that jointly refines camera poses and a 3D Gaussian map, while optimizing submap-shared intrinsics and radial–tangential distortion through analytic calibration Jacobians. To improve global consistency, we introduce Gaussian-native alignment (GNA) for camera-anchored scale refinement between sequential submaps and verification of loop-closure candidates. Extensive experiments on standard indoor benchmarks show consistent improvements in localization accuracy and strong rendering quality under uncalibrated settings, establishing a strong baseline for uncalibrated Gaussian SLAM.

Electrostatic modulation of graphene provides a tunable route to engineering miniband structures. We perform quantum transport simulations on a gate-defined graphene superlattice junction, formed by confining a two-dimensional superlattice graphene (SGr) region between two normal graphene (NGr) regions. In the low-field regime at low carrier densities, robust Fabry-Pérot interference fringes emerge even in the unipolar regime due to Fermi-velocity renormalization in the SGr region. At stronger magnetic fields but only up to 3 T, the conductance map clearly reveals the Hofstadter butterfly spectrum. At intermediate fields, our finite-width transport simulations reveal a new type of snake state, the supersnake state, composed of alternating anomalous cyclotron arcs on the SGr side and conventional semicircular arcs on the NGr side, forming a weaving trajectory along the junction. The resulting conductance oscillations agree well with geometrical conditions derived from semiclassical cyclotron orbits. Our results demonstrate that gate-defined NGr-SGr-NGr junctions provide a versatile platform hosting multiple transport regimes within a single device architecture and can be generalized to other types of superlattices not restricted to graphene.

This paper presents a scalable framework for high-precision near-field multipath channel parameter estimation in extremely large antenna array (ELAA) systems, enabling joint recovery of path number, path gains, angles, and ranges from a single noisy observation. The key idea is to interpret the near-field multipath channel as a superposition of spatial chirp components with spatially varying frequencies and exploit this structure through a partitioned ELAA architecture. Specifically, we establish a Chirp-coupled Subarray Far-field (CSF) model, where each near-field path is locally represented as a far-field sinusoid with a constant spatial frequency within each subarray, while these local spatial frequencies are coupled across subarrays through a linear relationship induced by the underlying spatial chirp, forming a path-specific chirp trajectory. Based on this model, we propose the CHirp-coupled Angular-Range estiMation (CHARM) algorithm, which performs gridless local frequency estimation followed by cross-subarray trajectory recovery. To mitigate the potential modeling mismatch of the CSF model, we further propose the enhanced CHARM (E-CHARM) algorithm, which refines the CHARM estimate under the near-field channel model through maximum likelihood. The computational complexity of the proposed algorithms scales linearly with the array size. Moreover, simulation results show that the proposed algorithms achieve reliable path-number detection, high-precision angle-range estimation, and accurate channel reconstruction.

Quantum imaginarity is a distinct resource in quantum information theory, yet its nonlocal properties have not been fully explored. Here, we report an experimental study of the nonlocal advantage of quantum imaginarity (NAQI), in which local measurements on one subsystem can steer the average imaginarity of the conditional states of the other subsystem beyond the corresponding classical bound. The $l_1$-norm of imaginarity inequality is adopted as an experimentally accessible witness. A hybrid optimization algorithm that combines a genetic algorithm with sequential quadratic programming is developed to avoid local optima and accelerate the search for optimal measurement settings. Using polarization-encoded photonic qubits, we prepare two classes of two-qubit Bell-diagonal states and experimentally characterize the imaginarity of the conditional states following local measurements. Clear violations of the $l_1$-norm of imaginarity inequality are observed, providing an experimental certification of NAQI. We further investigate the relationship among NAQI, the nonlocal advantage of quantum coherence (NAQC), and Bell nonlocality based on their respective inequality criteria. For the two-qubit Werner states considered in this work, the regions of states that violate the respective criteria satisfy $\mathcal{D}_{\rm NAQC}\subset\mathcal{D}_{\rm NAQI}\subset\mathcal{D}_{\rm BN}$. Our work provides an experimental realization of NAQI and a comparison of different forms of quantum nonclassicality in a photonic platform.

Characterization, control, and calibration of stringiness, the propensity to form long, thin, persistent threads, are key to the design and application of polymer solutions and formulations transferred to substrates by dropwise dispensing, jetting, spraying, or coating, and are used in manufacturing fibers, membranes, or spray-dried products. For Newtonian fluids, enhancing shear viscosity translates into increasing stringiness as can be easily perceived during dripping of water vs. sugar syrups or glycerol-water mixtures. In contrast, even polymer solutions with comparable shear viscosity can display a significant contrast in extensional rheology and apparent stringiness. However, there are no quantitative maps, formulas, or scales for stringiness, which motivates this study. In this contribution, we contrast the stringiness for a series of aqueous polymer solutions by determining the filament lifespan using dripping-onto-substrate (DoS) rheometry and filament length and lifespan in using dripping-into-air (DiA). We investigate the influence of polymer chemistry and molecular weight on stringiness and rely on DoS rheometry to characterize pinching dynamics and extensional rheology response. We show that an increase in stringiness correlates with steady, terminal extensional viscosity, and extensional relaxation time, respectively. Lastly, we provide a framework, which compares the stringiness of different polymer solutions through an extensional Ohnesorge-Deborah ($Oh-De$) plot or $Oh_E-De_E$ map, by computing the two dimensionless groups $Oh_E$ using steady, terminal extensional viscosity and $De_E$ using extensional relaxation time, respectively

In the $\gamma$-gap $k$-SetCover problem, we are given a family $\mathcal{S}$ over a universe $U$, and the goal is to distinguish between the case where $\mathcal{S}$ contains $k$ sets covering $U$, and the case where at least $\gamma k$ sets in $\mathcal{S}$ are needed to cover $U$. We show that, for every $k^{\Omega(k^2)}\le\rho\le n^{O(1)}$, it is W[1]-hard to approximate $k$-SetCover within ratio $\Omega\big(\frac{\log\rho}{k^2\log\log\rho}\big)$ on instances with $n$ sets and universe size at most $\rho\log n$. We also show that under the randomized $k$-OV Hypothesis, there is no bounded-error randomized $f(k)n^{o(k)}$-time $o\big(\frac{\log N}{\log\log N}\big)$-approximation algorithm for $k$-SetCover. These results improve on the previous $(\log n)^{1/O(k)}$-inapproximability. For fixed $k$, this matches the polynomial-time $(\ln\rho+O(1))$-approximation up to a $\log\log\rho$ factor. We further establish a connection between small universes and large approximation gaps. We show that for every $1\le\gamma\le\min\big\{\frac{\log u}{\log\log N},\frac{\log u}{k^2\log\log u}\big\}$, exact $k$-SetCover with universe size $u^{\Theta(1/\gamma)}$ is equivalent to $\gamma$-gap $k$-SetCover with universe size $u$ under randomized Turing reductions. This suggests a barrier to proving superconstant-gap W[2]-hardness: such a result would also make exact $k$-SetCover with universe size $n^{o(1)}$ W[2]-hard under randomized FPT Turing reductions. Finally, we analyze the VC dimensions of the set systems produced by our reduction. Write $d$ and $d^*$ for the primal and dual VC dimensions respectively. We show that for $\gamma=o(\frac{\log N}{\log\log N})$, $\gamma$-gap $k$-SetCover is W[1]-hard even when $d=O(k^{2}\gamma\log(k\gamma))$ and $d^*=O(k\gamma)$. The bound for $d^*$ matches the $O(d^*\log k)$-approximation algorithm up to a $k\log k$ factor.

Existing Retrieval-Augmented Generation (RAG) systems struggle with multi-hop reasoning due to a fundamental inability to balance relevance and novelty. Traditional dense retrievers are constrained by surface-level matching, falling into a homogenized "Similarity Trap". Conversely, emerging Graph RAGs attempt to explore novel documents via heuristic entity extraction, but they introduce prohibitive Large Language Model (LLM) overhead and easily drift into off-topic "Novelty Traps". To fundamentally resolve this contradiction, we propose Geometric Gain Graph (G$^3$RAG), the novel zero-token graph construction paradigm for RAG. G$^3$RAG completely discards the expensive heuristic extraction by LLMs, aiming instead to directly quantify the information gain between nodes through the native document feature space. To this end, we designed a concise edge weight criterion, $\cos\theta \cdot \sin\theta$, which naturally maps the trade-off between relevance and novelty into a geometric measurement of directional consistency and orthogonality in the vector space, thereby driving the token-free topological construction of the graph. Furthermore, we introduce a topological penalty to suppress the excessive connectivity of high-frequency hubs, forcing the transient diffusion process toward long-tail peripheral nodes that carry critical indirect evidence. Extensive experiments demonstrate that, while entirely eliminating LLM token costs during graph construction, G$^3$RAG significantly outperforms state-of-the-art Graph RAG baselines on complex multi-hop QA benchmarks. The code is available at: https://github.com/deeplearning-LI/G3RAG