This work provides a comprehensive overview of the fundamental concepts in continuum mechanics, focusing on the behaviour of materials under mechanical loads. It discusses the distinction between elastic and plastic, highlighting their atomic origins and macroscopic implications. Elastic behaviour is examined via Hooke's law and constitutive matrices, while plasticity is treated through yield surfaces, flow rules, and hardening laws, including isotropic and kinematic hardening. In addition, the theoretical foundations and design principles of pressure vessels and thin axisymmetric shells, focusing on their mechanical behaviour under internal or external pressure, is discussed. The analysis is based on shell theory, assuming thin walls and axisymmetric geometry, which simplifies the stress distribution into membrane stresses. The work also addresses buckling phenomena under external pressure, secondary stresses at geometric discontinuities, and design provisions from the EN 13445 standard.

Detecting cyberattacks in photovoltaic (PV) monitoring and MPPT control signals requires models that are robust to bias, drift, and transient spikes, yet lightweight enough for resource-constrained edge controllers. While deep learning outperforms traditional physics-based diagnostics and handcrafted features, standard fine-tuning is computationally prohibitive for edge devices. Furthermore, existing Parameter-Efficient Fine-Tuning (PEFT) methods typically apply uniform adaptation or rely on expensive architectural searches, lacking the flexibility to adhere to strict hardware budgets. To bridge this gap, we propose Constraint-Driven Warm-Freeze (CDWF), a budget-aware adaptation framework. CDWF leverages a brief warm-start phase to quantify gradient-based block importance, then solves a constrained optimization problem to dynamically allocate full trainability to high-impact blocks while efficiently adapting the remaining blocks via Low-Rank Adaptation (LoRA). We evaluate CDWF on standard vision benchmarks (CIFAR-10/100) and a novel PV cyberattack dataset, transferring from bias pretraining to drift and spike detection. The experiments demonstrate that CDWF retains 90 to 99% of full fine-tuning performance while reducing trainable parameters by up to 120x. These results establish CDWF as an effective, importance-guided solution for reliable transfer learning under tight edge constraints.

We demonstrate all-optical manipulation of magnetic domains in NiO/Pt and CoO/Pt thin films with insulating antiferromagnetic layers. Using magneto-optical birefringence imaging, we show that even a single laser pulse can thermally demagnetize the antiferromagnet, leading to a random redistribution of domains. By sweeping the laser beam, controlled domain wall motion is induced, enabling partial switching of the antiferromagnetic order. The behavior is captured by an analytical model in which temperature gradients generated by the moving beam exert a thermal pressure on domain walls in the form of a ponderomotive force. Importantly, the 90$^{\circ}$ domains can be reversibly toggled solely by reversing the direction of the thermal gradient, demonstrating all-optical switching without the need for electric currents. These findings establish a route toward ultrafast optical manipulation of fully compensated antiferromagnets, with potential impact on non-volatile memory technologies and antiferromagnetic spintronics.

We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These surfaces are obtained by applying the Norman trick to a fixed immersed surface, using non-homotopic tubing arcs. The isotopy classes of these surfaces are distinguished by homotopy classes of the 2-handles (relative to the boundary) in the complement of the image of the $0$- and $1$-handles.

Within the framework of linear response theory, we theoretically investigated the interband longitudinal optical conductivities (LOCs) in two-dimensional (2D) tilted Dirac bands using a tight-binding (TB) model, incorporating the effects of band tilting and Dirac-point shifting. We identified three characteristic critical frequencies in the interband LOCs of the TB model: the partner frequencies, the sharp- peak frequency, and the cutoff frequency. In contrast to conventional critical frequencies, these three types are consistently absent in the corresponding linearized $k\cdot p$ model. Notably, the sharp-peak frequency and cutoff frequency remain robust against variations in band tilting and Dirac-point shifting. By employing analytical expressions derived via the Lagrange multiplier method, we elucidate the origins of the conventional critical frequencies and their partner counterparts. In contrast, the sharp-peak frequency and cutoff frequency are associated with interband optical transitions at high-symmetry points of the energy bands, arising from the Pauli exclusion principle and the finite boundaries of the Brillouin zone. Our theoretical predictions are intended to guide future experimental studies on tilt-dependent optical phenomena in 2D tilted Dirac systems.

Calculations of the lowest valence π* as well as the 3s and higher energy 3pσ Rydberg excited states of the CO2 molecule are carried out using density functionals with variational optimization of the orbitals, an approach involving relatively little computational effort. Five functionals with varying degree of exchange are used in combination with real or complex-valued orbitals that are optimized by finding saddle points on the electronic energy surface corresponding to the excited states. When the PBE functional is used in combination with complex orbitals, the calculated excitation energy is found to be within 0.3 eV of multireference configuration interaction reference values, and the results are further improved with hybrid functionals. In contrast, linear-response time-dependent density functional theory calculations give errors up to 1.9 eV for the most diffuse 3pσ excitation and exhibit stronger dependence on both the excitation character and the functional used. Calculated C-O dissociation curves using the PBE functional and the orbital-optimized approach compare remarkably well with the reported multireference configuration interaction and equation-of-motion coupled-cluster singles and doubles calculations. Thanks to the low computational cost, these results demonstrate that orbital-optimized density functional calculations can be a promising route for modelling photorelaxation in condensed-phase CO2, for example in the context of interstellar cosmic-ray radiation driven process involving high-energy Rydberg states.

Gravitational waves from intermediate-mass black-hole (IMBH) binaries is a probe of strong-field gravity and black-hole evolution. Detection of IMBH is challenging because of their typically low frequency where the seismic noise, radiation pressure noise, and thermal noise dominate. The Cryogenic sub-Hz cROss torsion bar detector with quantum NOn-demolition Speed meter (CHRONOS) has been proposed to reach a strain sensitivity of $10^{-18} {\rm Hz}^{-1/2}$ at 2 Hz. It aims to detect GW from IMBH mergers with the mass of $\mathcal{O}(10^4)$ M$_{\odot}$ and to explore stochastic gravitational background of $Ω_{\rm GW} \sim 2\times 10^{-3}$ at 2 Hz. We present the overview of the CHRONOS hardware which is designed to integrate key techniques for improving low frequency sensitivity; torsion bar, speed meter, and cryogenic mirror. As a demonstration of the interferometer operation, we also report the commissioning status of a Michelson interferometer in National Central University in Taiwan which has been assembled as a partial component of CHRONOS.

How do European publics debate a geopolitical crisis on social media, and do they inhabit a shared informational reality? We analyze over 38 million geolocated tweets from 20 European countries during the first eight months of the Russian invasion of Ukraine. Using retweet community detection and stance annotation across six issues, we identify 'hawkish' and 'doveish' opinion clusters present within almost every country studied. We find that structural polarization is driven not by radicalization, but by the exit of casual users. Crucially, whether opposing sides orient to the same events depends on the issue. On pragmatist issues, both sides react to the same high-profile events, forming an agonistic public sphere. Instead, on interpretive issues, they operate as affective publics and counterpublics constructing divergent meanings. We propose conditional publics to describe formations whose relational structure, sharing or fracturing a referential frame, depends on the epistemic character of the debated issue.

We extend latent representation methods for safety control design to set-valued states. Recent work has shown that barrier functions designed in a learned latent space can transfer safety guarantees back to the original system, but these methods evaluate certificates at single state points, ignoring state uncertainty. A fixed safety margin can partially address this but cannot adapt to the anisotropic and time-varying nature of the uncertainty gap across different safety constraints. We instead represent the system state as a zonotope, propagate it through the encoder to obtain a latent zonotope, and evaluate certificates over the worst case of the entire set. On a 16-dimensional quadrotor suspended-load gate passage task, set-valued evaluation achieves 5/5 collision-free passages, compared to 1/5 for point-based evaluation and 2/5 for a fixed-margin baseline. Set evaluation reports safety in 44.4% of per-head evaluations versus 48.5% for point-based, and this greater conservatism detects 4.1% blind spots where point evaluation falsely certifies safety, enabling earlier corrective control. The safety gap between point and set evaluation varies up to $12\times$ across certificate heads, explaining why no single fixed margin suffices and confirming the need for per-head, per-timestep adaptation, which set evaluation provides by construction.

This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional subspace using bounds based on n-widths and a greedy algorithm for basis reduction. For kernels whose native spaces are norm-equivalent to Sobolev spaces, we derive how the required basis size scales with kernel smoothness and input dimension. This finite-dimensional representation enables the use of convex scenario optimization to obtain violation guarantees for the learned predictor without requiring an a priori bound on the true system's RKHS norm or Lipschitz constant. The method is demonstrated on an obstacle-avoidance task. We also discuss the main limitations of the current analysis, including dimensional scaling and dependence on i.i.d. data.

Digital twin (DT) technology offers transformative potential for vehicular networks, enabling high-fidelity virtual representations for enhanced safety and automation. However, seamless DT synchronization in dynamic environments faces challenges such as massive data transmission, precision sensing, and strict computational constraints. This paper proposes an integrated sensing, computing, and semantic communication (ISCSC) framework tailored for DT-assisted vehicular networks in the near-field (NF) regime. Leveraging a multi-user multiple-input multiple-output (MU-MIMO) configuration, each roadside unit (RSU) employs semantic communication to serve vehicles while simultaneously utilizing millimeter-wave (mmWave) radar for environmental mapping. We implement particle filtering at RSUs to achieve high-precision vehicle tracking. To optimize performance, we formulate a joint optimization problem balancing semantic communication rates and sensing accuracy under limited computational resources and power budget. Our solution includes a hybrid heuristic algorithm for vehicle-to-RSU assignment and an alternating optimization approach for determining semantic extraction ratios and beamforming matrices. Performance is extensively evaluated via the Cramér-Rao bound (CRB) for angle and distance estimation, semantic transmission rates, and resource utilization. Numerical results demonstrate that the proposed ISCSC framework achieves a 20% improvement in transmission rate while maintaining the sensing accuracy of existing integrated sensing and communication (ISAC) schemes under constrained resource conditions.

As artificial intelligence continues to grow, so does the need for more efficient ways to process data. Besides moving from electronic to photonic circuits, a promising approach is to integrate phase-change materials. Vanadium dioxide (VO$_2$) exhibits an ultrafast, near-room-temperature phase transition, characterized by hysteresis and large optical modulation -- making it a promising candidate for short-term memories and for mimicking neural behavior in brain-like computing systems. While the hysteresis behavior of VO$_2$ has been well studied in thin films and nanostructures, practical control and device integration have been limited only to thin films. Here, we demonstrate control over the phase transitions of VO$_2$ nanocylinders via lithographic patterning, controlled crystallization, and controlled dewetting. Because nanostructures are easier to address and consume less power than films, the ability to fabricate them with tailored geometry and hysteresis properties directly on integrated platforms is a key step toward scalable, energy-efficient memory and neuromorphic photonic devices.

This paper studies a feedback driven configuration tuning framework for adaptive sensing feedback in Integrated Sensing and Communication (ISAC) systems. We propose a framework in which the User Equipment (UE) adapts sensing parameters under dynamic conditions while satisfying network defined constraints. The problem is formulated as a stochastic constrained optimization problem, to improve sensing reliability and latency. We consider a bistatic ISAC sensing feedback setup and instantiate the framework via threshold optimization as a representative case study, enabling benchmarking against baseline methods. To ensure efficiency under UE computational limits, we propose Ranking Aware, Constrained, and Efficient CMAES (RACE CMA), which integrates two stage racing, common random numbers, noise aware ranking, and feasible constraint handling. Results show that the proposed approach improves sensing reliability by about 35 percent while reducing computational cost by about 25 percent, yielding roughly a twofold gain in performance cost efficiency. This highlights that UE side configuration tuning is a promising mechanism for enhancing closed loop ISAC performance under practical system constraints.

Axion electrodynamics extends Maxwell's theory by postulating a hypothetical pseudoscalar axion field sourced by a scalar product of electric and magnetic fields. In this work, we demonstrate that a superposition of toroidal electromagnetic pulses propagating in free space naturally exhibits localized regions, where $\bm{E}\cdot\bm{B}\ne0$. As a consequence of axion electrodynamics, these structured light pulses generate a space-time localized pseudoscalar field co-propagating with the pulses. This result should not be interpreted as a mechanism for generating axion particles by light, but rather as a consequence of adopting the axion electrodynamics extension to Maxwell's equations.

With the growing pervasiveness of artificial intelligence, the ability to explain the inferences made by machine learning models has become increasingly important. Numerous techniques for model explainability have been proposed, with natural-language textual explanations among the most widely used approaches. When applied to tabular data, these explanations typically draw on input features to justify a given inference. Consequently, a user's ability to interpret the explanation depends on their understanding of the input features. To quantify this feature-level understanding, Rossberg et al. introduced the Feature Understandability Scale. Building on that work, this proof-of-concept study collects understandability scores across two datasets, proposes a co-optimisation methodology of understandability and accuracy and presents the resulting explanations alongside the model accuracies. This work contributes to the body of knowledge on model interpretability by design. It is found that accuracy and understandability can be successfully co-optimised while maintaining high classification performances. The resulting explanations are considered more understandable at face value. Further research will aim to confirm these findings through user evaluation.

The phenomenon of salt creeping along a free surface remains only partially understood, particularly with respect to its dynamics. In this work, combining a theoretical model with controlled experiments, we identify three distinct kinetic regimes: an initial exponential growth of the height of the crystallized salt deposit on vertical walls, followed by a linear regime, and a final stage where the height saturates while the crystal deposit thickens logarithmically. This unified description makes it possible to follow the macroscopic kinetics of salt growth on a free surface from its nucleation to saturation. In addition, we complement this macroscopic analysis with numerical simulations that shed light on the evolution of the microscopic crystal structure under varying external conditions (humidity and temperature).

This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point vortex initial data and the boundary, which complicates the derivation of a valid asymptotic expansion. To overcome this, we carry out a precise matching between the point vortex and boundary-layer profiles to accurately capture the correct viscous behavior of the vortex in the half-plane. Based on this matched asymptotic analysis, we decompose the vorticity into three components: vorticity near the point vortex, vorticity near the boundary, and vorticity in the transition layer. A key point is that each component must be analyzed in its own distinct region. On this basis, we establish refined estimates and thereby achieve the inviscid limit for the point vortex. Finally, we rigorously prove that solutions to the Navier-Stokes equations converge to the Lamb-Oseen vortex away from the boundary, while approaching the Prandtl boundary-layer system in the near-boundary region.

A linkage $\mathcal{L}$ consists of a graph $G=(V,E)$ and an edge-length function $\ell$. Deciding whether $\mathcal{L}$ can be realized as a planar straight-line embedding in $\mathbb{R}^2$ with edge length $\ell(e)$ for all $e \in E$ is $\exists\mathbb{R}$-complete [Abel et al., JoCG'25], even if $\ell \equiv 1$, but a considerable part of $\mathcal{L}$ is rigid. In this paper, we study the computational complexity of the realization question for structurally simpler, less rigid linkages inside an open polygonal domain $P$, where the placement of some vertices may be specified in the input. We show XP-membership and W[1]-hardness with respect to the size of $G$, even if $\ell \equiv 1$ and no vertex positions are prescribed. Furthermore, we consider the case where $G$ is a path with prescribed start and end position and $\ell \equiv 1$. Despite the absence of any rigid components, we obtain NP-hardness in general, and provide a linear-time algorithm for arbitrary $\ell$ if $G$ has only three edges and $P$ is convex.

Employing the generalized free energy landscape and solving the associated Fokker-Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation.

We present a comprehensive experimental investigation of the temperature evolution of magnetic states in triangular-lattice delafossite YbCuSe$_2$. Magnetization measurements on high-quality single crystals reveal easy-plane anisotropy. Specific heat, magnetization, and muon spin relaxation ($μ$SR) establish the absence of magnetic order or spin freezing down to 0.03 K ($\leq J_{\mathrm{avg}}/250$), demonstrating a dynamically fluctuating quantum spin liquid (QSL) ground state. Thermodynamic measurements uncover multiple characteristic energy scales at $T_H \approx 4.5$ K, $T_L \approx 1.8$ K, and $T^* \approx 0.7$ K. Below $T^*$, $μ$SR detects a dynamical phase separation in which the majority of the spins are forming a QSL state whereas the remaining spins form a sporadic, disorder-induced state decoupled from the dominant QSL component. Remarkably, the unconventional temperature dependence of the $μ$SR relaxation rate indicates roton-like excitations emerging between $T_H$ and $T_L$, a feature not previously observed in any QSL system, preceding the stabilization of the low-temperature QSL at 0.3 K. These findings identify YbCuSe$_2$ as a unique QSL platform, providing valuable insights for further experimental and theoretical exploration.

Large language models (LLMs) have rapidly evolved from general-purpose systems to multimodal models capable of processing text, images, and audio. As both general-purpose LLMs (GLLMs) and multimodal LLMs (MLLMs) gain widespread adoption, understanding user perceptions in real-world settings becomes increasingly important. However, existing studies often rely on surveys or platform-specific data (e.g., Reddit or GitHub issues), which either constrain user feedback through predefined questions or overemphasize failure-driven, debugging-oriented discussions, thus failing to capture diverse, experience-driven, and cross-model user perspectives in practice. To address this issue, we conduct an empirical study of user discussions on Hugging Face, a major model hub with diverse models and active communities. We collect and manually annotate 662 discussion threads from 38 representative models (21 GLLMs and 17 MLLMs), and develop a three-level taxonomy to systematically characterize user concerns. Our analysis reveals that LLM access barriers, generation quality, and deployment and invocation complexity are the most prominent concerns, alongside issues such as documentation limitations and resource constraints. Based on these findings, we derive actionable implications for improving LLM ecosystem.

The ISOKANN (Invariant Subspaces of Koopman Operators Learned by Artificial Neural Networks) framework provides a data-driven route to extract collective variables (CVs) and effective dynamics from complex molecular systems. In this work, we integrate the theoretical foundation of Koopman operators with Krylov-like subspace algorithms, and reduced dynamical modeling to build a coherent picture of how to describe metastable transitions in high-dimensional systems based on CVs. Starting from the identification of CVs based on dominant invariant subspaces, we derive the corresponding effective dynamics on the latent space and connect these to transition rates and times, committor functions, and transition pathways. The combination of Koopman-based learning and reduced-dimensional effective dynamics yields a principled framework for computing transition rates and pathways from simulation data. Numerical experiments on one-, two-, and three-dimensional benchmark potentials illustrate the ability of ISOKANN to reconstruct the coarse-grained kinetics and reproduce transition times across enthalpic and entropic barriers.

Amplitude Amplification offers a provable speedup for search problems, which is leveraged in combinatorial optimization by Grover Adaptive Search (GAS). The protocol demands deep circuits that are challenging with regards to NISQ capabilities. We propose a nested Amplitude Amplification protocol for the binary knapsack problem that splits the decision tree at a tunable depth, performing a partial amplification on the first variables before executing a global GAS on the full search space. The partial amplification is implemented by an Inner Iteration Finder that selects the rotation count maximizing marked-subspace amplitude. The resulting biased superposition serves as the initial state for the outer Amplitude Amplification. Using the Quantum Tree Generator for feasible-state preparation and an efficient classical amplitude-tracking scheme, we simulate the protocol on knapsack instances of sizes intractable by statevector simulation. Our results show that the nested approach reduces the cost of improving an incumbent solution compared to baseline GAS, particularly for a specific subset of knapsack instances. As combinatorial problems in domains such as semiconductor supply-chain planning grow in scale, methods that reduce circuit cost are an important step toward eventual quantum advantage for such applications.

Geometric representations provide a useful perspective on critical phenomena in the Ising model. In a recent study [Phys. Rev. E 112, 034118 (2025)], we found that the two-dimensional critical Ising model exhibits two consecutive percolation transitions for geometric spin clusters as the bond-occupation probability $p$ between parallel spins increases. Here, through extensive Monte Carlo simulations, we show that this phenomenon does not persist in three dimensions, where we observe only a single percolation transition on critical Ising configurations. Further theoretical analysis of the Ising model on the complete graph also yields the same scenario. In addition, we study percolation on a two-dimensional layer embedded in the three-dimensional critical Ising model. For this layer system, we estimate the red-bond exponent $y_p = 0.426(6)$ and the fractal dimensions of the largest cluster, hull, and shortest path as $d_f = 1.8926(20)$, $d_{\rm hull} = 1.663(4)$, and $d_{\rm min} = 1.080(10)$, respectively. These values indicate a distinct universality class induced by coupling to out-of-plane critical correlations.

Structured light pulses hold significant promise for their ability to overcome dephasing in laser-wakefield accelerators, that should facilitate applications in high-energy physics and XFEL. Numerical studies have shown that sculpting a pulse into a flying focus and using it to drive a wakefield can achieve dephasing-free acceleration of electrons, with gain in excess of 100\,GeV within reachable with existing laser facilities. This work reports on novel experiments using a flying-focus generated laser-wakefield accelerator to accelerate electrons to relativistic energies. The flying-focus pulse is achieved by sculpting the laser-pulse before focusing using spatio-temporal couplings and generating a quasi-Bessel beam with an axiparabola. This combination allows for the tuning of the propagation velocity of the wakefield, which, we demonstrate, has an impact on the maximum achievable electron energy. Optical and particle-in-cell simulations are used to support the data and to provide direct evidence of the partial mitigation of dephasing through this flying-focus scheme. These results are further elucidated in our companion letter [1].

Empirical force fields remain the primary tool for large-scale molecular simulation, yet their limited flexibility and transferability often hinder predictive modeling in chemically complex condensed-phase systems. Here we present ORION, a universal machine-learning force field for C, H, O, N, S, and P systems developed within the Neuroevolution Potential (NEP) framework. To enhance transferability across diverse chemical environments, ORION was trained on a chemically rich dataset constructed through an integrated top-down and bottom-up strategy, enabling accurate descriptions of complex organic configurations, reactive intermediates, and weak intermolecular interactions. ORION achieves near-density-functional-theory accuracy while retaining the efficiency required for large-scale molecular dynamics simulations. On the test set, it predicts atomic forces with substantially higher accuracy than ReaxFF while running 215.5 times faster under identical hardware conditions, making simulations on the hundreds-of-nanoseconds timescale readily accessible. The model provides a balanced description of bond breaking and formation, aromatic growth, hydrogen bonding, van der Waals interactions, and π-stacking, demonstrating strong transferability across both reactive and nonreactive systems. These results establish ORION as a practical and general force field for predictive simulations in chemistry and materials science, and provide an effective route toward universal machine-learning force fields with both high accuracy and broad applicability.

Bergelson et al. observed that Furstenberg's proof of Szemeredi's theorem provides a positive lower bound on the density of arithmetic progressions in sets of positive density in the integers. Namely, for every $δ\in(0,1]$ and every $k\in \mathbb{N}$, there exists a positive constant $c=c(k,δ)>0$ such that $$\{n\in \mathbb{N} : d(E\cap (E-n)\cap\dots\cap (E-(k-1)n))>c(k,δ)\} \neq \emptyset$$ whenever $d(E)\ge δ$. Similarly, Furstenberg and Katznelson proved the IP Szemeredi theorem, establishing in particular the existence of a constant $c_{\mathrm{IP}}=c_{\mathrm{IP}}(k,δ)>0$ such that $$\{n\in \mathbb{N} : d(E\cap (E-n)\cap\dots\cap (E-(k-1)n))>c_{\mathrm{IP}}(k,δ)\}$$ is $\mathrm{IP}^*$ whenever $d(E)\ge δ$. In this paper, we study analogues of $c$ and $c_{\mathrm{IP}}$ and their ergodic-theoretic counterparts, $c^{\mathrm{rec}}$ and $c_{\mathrm{IP}}^{\mathrm{rec}}$, for vector spaces over finite fields. We provide a qualitative result and in special cases such as Roth's theorem and the IP-Roth theorem, we also provide strong quantitative bounds for these constants. Our tools are primarily ergodic theoretic; we study the characteristic factors and limit of multiple ergodic averages along $\mathrm{IP}$s in vector spaces over finite fields.

Benchmark collections have long enabled controlled comparison and cumulative progress in Information Retrieval (IR). However, prior meta-analyses have shown that reported effectiveness gains often fail to accumulate, in part due to the use of weak or outdated baselines. While large language models are increasingly used in retrieval pipelines, their impact on established IR benchmarks has not been systematically analyzed. In this study, we analyze 143 publications reporting results on the TREC Robust04 collection and the TREC Deep Learning 2020 (DL20) passage retrieval benchmark to examine longitudinal trends in retrieval effectiveness and baseline strength. We observe what we term an \emph{LLM effect}: recent systems incorporating LLM components achieve 8.8\% higher nDCG@10 on DL20 compared to the best result from TREC 2020 and approximately 20\% higher on Robust04 since 2023. However, adapting a data contamination detection approach to reranking reveals measurable contamination in both benchmarks. While excluding contaminated topics reduces effectiveness, confidence intervals remain wide, making it difficult to determine whether the LLM effect reflects genuine methodological advances or memorization from pretraining data.

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the existence and uniqueness of solutions subject to the non-slip boundary condition. This result was established in \cite{Ken} under the condition that the total mass is sufficiently small. Here, we eliminate the smallness assumption by analyzing the linearized operator near the point vortex and constructing a tailored functional framework-one designed to capture the distinct behaviors of the solution in the vicinity of the point vortex and the boundary, respectively.

Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.