We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We conclude with a brief survey of solutions for kin problems which anyhow concern minimization of the output entropy of certain quantum channel and rely upon the symmetry properties of the problem. Key words and phrases: $l_p $-norm, Rényi entropy, tight inequality, maximization of a convex function.

Processing-in-memory (PIM) architectures bring computation closer to data, reducing the processor-memory transfer bottleneck in traditional processor-centric designs. Novel hardware solutions, such as UPMEM's in-memory processing technology, achieve this by integrating low-power DRAM processing units (DPUs) into memory DIMMs, enabling massive parallelism and improved memory bandwidth. However, paradoxically, these PIM architectures introduce mandatory coarse-grained data transfers between host DRAM and DPUs, which often become the new bottleneck. We present PIM-CACHE, a lightweight data staging layer that dynamically eliminates redundant data transfers to PIM DPUs by exploiting workload similarity, achieving content-aware copy (CAC). We evaluate PIM-CACHE on both synthetic workloads and real-world genome datasets, demonstrating its effectiveness in reducing PIM data transfer overhead.

Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes orthogonal, unitary and symplectic. In this work we give a different viewpoint on these results in the case of the soft edge scaled density, and in the Laguerre case we initiate an analogous study at the hard edge. Our tool is the scalar differential equation satisfied by the latter, known from earlier work. Unlike integral representations, these differential equations in soft edge scaling variables isolate the function of $N$ which is the expansion variable. Moreover, they give information on the correction terms which supplements the findings from the work of Bornemann. In the case of the Gaussian ensemble, we can demonstrate analogous features for Dyson index $β= 6$, which suggests a broader class of models, namely the classical $β$ ensembles, with asymptotic expansions exhibiting integrable features. For the Laguerre ensembles at the hard edge, we give the explicit form of the correction at second order for unitary symmetry, and at first order in the orthogonal and symplectic cases. Various differential relations are demonstrated.

We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger equation with general coefficients by variational methods. We study associated minimization problems in the subcritical and critical cases and prove the existence of a minimizer in each case. Finally, we derive Pohozaev-type identities and use them to establish corresponding nonexistence results.

Resolving complex code defects from natural language descriptions remains a fundamental software engineering challenge. Recently, large language models (LLMs) have driven the creation of agent-based automated repair systems. While improving repository-level problem-solving, current methods struggle with complex defects like intricate polymorphic control flows and implicit type degradation. These approaches rely on static analysis and shallow execution feedback, lacking the ability to monitor intermediate execution states. Consequently, agents often fall into speculative exploration, consuming significant tokens without identifying the root cause. We introduce DAIRA (Dynamic Analysis-enhanced Issue Resolution Agent), a pioneering automated repair framework deeply embedding dynamic analysis into the agent's decision loop. DAIRA employs a Test Tracing-Driven workflow, using lightweight tools to capture runtime evidence (e.g., call stacks and variable states) and convert it into structured semantic reports. By illuminating execution paths and causal dependencies, DAIRA enables precise fault localization and prevents context window flooding from irrelevant code retrievals. This shifts the agent's approach from speculative reasoning to deterministic inference. Evaluations on the SWE-bench Verified benchmark show DAIRA achieves a state-of-the-art 79.4% resolution rate when powered by Gemini 3 Flash Preview. Furthermore, it demonstrates robustness in addressing deep-seated logical defects, securing a 44.4% resolution rate on the most demanding tasks. Compared to baselines, DAIRA uniquely resolves complex edge cases and improves operational efficiency. Across various LLMs, it reduces inference costs by approximately 10% and input token consumption by 25%.

We show that $B(H)$ for an infinite dimensional Hilbert space $H$ cannot be realized as the reduced twisted $C^*$-algebra of any locally compact Hausdorff étale groupoid. The proof is based on the canonical conditional expectation $$C_r^*(G,Σ)\to C_0(G^{(0)})$$ and a structural analysis of the resulting diagonal subalgebra inside $B(H)$. We show that this diagonal must be an atomic abelian von Neumann algebra, and then exclude both possibilities for its spectrum. If the unit space is finite, one obtains a tracial state on $C_r^*(G,Σ)$, which is impossible for $B(H)$. If it is infinite, the groupoid structure forces a block-sparsity phenomenon for compactly supported sections, which is incompatible with $B(H)$. This provides the first examples of $C^*$-algebras that cannot be realized as reduced twisted étale groupoid $C^*$-algebras.

The rapid deployment of electric vehicles (EVs) in public parking facilities and fleet operations raises challenging intra-day charging scheduling problems under tight charger capacity and limited dwell times. We model this problem as a variant of the Partition Coloring Problem (PCP), where each vehicle defines a partition, its candidate charging intervals are vertices, and temporal and resource conflicts are represented as edges in a conflict graph. On this basis, we design a branch-and-price algorithm in which the restricted master problem selects feasible combinations of intervals, and the pricing subproblem is a maximum independent set problem. The latter is reformulated as a quadratic unconstrained binary optimization (QUBO) model and solved by quantum-annealing-inspired algorithms (QAIA) implemented in the MindQuantum framework, specifically the ballistic simulated branching (BSB) and simulated coherent Ising machine (SimCIM) methods, while the master problem is solved by Gurobi. Computational experiments on a family of synthetic EV charging instances show that the QAIA-enhanced algorithms match the pure Gurobi-based branch-and-price baseline on small and medium instances, and clearly outperform it on large and hard instances. In several cases where the baseline reaches the time limit with non-zero optimality gaps, the QAIA-based variants close the gap and prove optimality within the same time budget. These results indicate that integrating QAIA into classical decomposition schemes are a promising direction for large-scale EV charging scheduling and related PCP applications.

The IllustrisTNG simulation suite, particularly TNG50, was reported to have generated a notable population of elongated, bar-like structures within galaxies classified as Early-Type Galaxies (ETGs). In this work, we revisit the nature of these structures at $z=0$ using a morphology-agnostic census. We find that these features are ubiquitous ($f_{\rm bar} \sim 75-80\%$) in dispersion-dominated galaxies ($D/T < 0.2$) in TNG50-1. They are not prolate rotators (rotating around their long axis), but genuine non-axisymmetric instabilities characterized by coherent, albeit slow, pattern speeds. Unlike the fast bars found in Late-Type Galaxies, these bar-like structures in ETGs are physically longer ($\gtrsim 3$ kpc), rotate significantly slower ($Ω_p \lesssim 20$ km s$^{-1}$ kpc$^{-1}$), and reside in red, gas-poor, dispersion-dominated systems. By tracing the evolutionary history of these systems, we demonstrate that such structures originate as typical fast bars in gas-richer discs at higher redshifts ($z \gtrsim 0.2$). They survive the galaxy quenching phase, undergoing secular deceleration and lengthening due to dynamical friction, ultimately appearing as slow, fossilized rotators in the $z=0$ red sequence. We conclude that the specific excess of bar-like structures in TNG50 ETGs likely reflects a combination of the imperfect baryonic physics of the simulation (over-producing these bar-like structures or their host ETGs) and a potential observational blind spot regarding long-lived, secularly evolved bars in hot stellar systems.

The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coefficients are allowed to depend on the whole trajectory of the process up to the current time. We investigate the existence and uniqueness (aka the strong well-posedness) of solutions to such equations in the $L^p$ setting, $p>0$, locally in time and their properties specifically their path regularity and flows. Then, we introduce a numerical approximation method based on an interpolated $K-$integrated Euler-Maruyama scheme to simulate numerically the process, and we prove the convergence, with an explicit rate, of this scheme towards the strong solution in the $L^p$ norm.

We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a surrogate model for the limit state and then construct an IS proposal to estimate failure probability using separate oracle evaluations, we propose a \emph{single stage} approach where a Gaussian process surrogate and a surrogate for the optimal (zero-variance) IS density are trained from shared evaluations of the oracle, making better use of a limited budget. With such an approach, small failure probabilities can be learned with relatively few oracle evaluations. We propose \emph{kernel density estimation adaptive importance sampling} (\texttt{KDE-AIS}), which combines Gaussian process surrogates with kernel density estimation to adaptively construct the IS proposal density, leading to sample efficient estimation of failure probabilities. We show that \texttt{KDE-AIS} density asymptotically converges to the optimal zero-variance IS density in total variation. Empirically, \texttt{KDE-AIS} enables accurate and sample efficient estimation of failure probabilities compared to the state of the art, including previous work on Gaussian process based adaptive importance sampling.

Understanding the formation of social ties requires disentangling the roles of individual traits and local network structure. We analyse signed social relationships among 3,395 students using an interpretable machine learning model -- the Explainable Boosting Machine (EBM) -- to predict link polarity from individual attributes (prosociality, cognitive reflection, and gender) and a structural metric, triadic influence. Our results show that triadic influence overwhelmingly dominates link prediction, confirming that local network structure is the primary driver of social relationships. Nevertheless, a small subset of links (0.24\%) is primarily explained by individual-level traits. A detailed characterisation of this subset reveals that these links do not arise from distinct structural conditions, but rather correspond to weaker and less structurally embedded relationships. In particular, they are more likely to be negative ties and exhibit lower levels of structural balance, whereas triadic-dominant links are strongly associated with positive relationships and highly balanced configurations. Furthermore, we find that links without indirect structural paths are not explained by individual traits, but by the absence of structural reinforcement itself. These findings support a layered view of social tie formation, in which structural mechanisms dominate globally, while individual-level effects emerge in specific, less constrained contexts. More broadly, our work highlights the value of explainable machine learning for uncovering the mechanisms underlying social network formation.

In this paper, we pursue an investigation of the consequences of a mixing between supersymmetric partners - the photon and photino - analogous to the so-called Primakoff effect, but induced by a Lorentz-symmetry violating (LSV) fermionic-condensate background. In our framework, the LSV parameters are introduced as members of a non-dynamical superfield. As a consequence, we show that naturally there appears a mixing term between the gauge boson and the gaugino, which can be readily seen in the superspace/superfield approach. We inspect the kinetic photon-photino mixing matrix in the scenario of stellar physics which we apply our results to. Bounds on the strength of the fermionic LSV background are can be set by invoking the energy loss argument and the solar data we adopt.

We present a time-resolved analysis of the persistent emission in 4U 1728--34 using AstroSat observations from 2016 to 2019. We detect kilohertz quasi-periodic oscillations (kHz QPOs) during all epochs, with centroid frequencies ranging from $\sim 350$ to $1180~\mathrm{Hz}$, although some detections are of lower significance ($< 3σ$). We model the simultaneous spectra from the Soft X-ray Telescope and the Large Area X-ray Proportional Counter using a combination of an absorbed disk component (diskbb), a blackbody component (bbodyrad), a thermal Comptonization model (thcomp), and a broad Gaussian line. From the diskbb parameters, we estimate the accretion rate and find that all observations fall into two accretion regimes, namely AR1 and AR2, with accretion rates of $\sim 3 \times 10^{16}~\mathrm{g\,s^{-1}}$ and $\sim 7 \times 10^{16}~\mathrm{g\,s^{-1}}$, respectively. Interestingly, we find that for AR1, the lower kHz QPO frequency ($ν_{\mathrm{L}}$) is always $< 500~\mathrm{Hz}$, while for AR2 it is $\gtrsim 500~\mathrm{Hz}$. We found that the spectral index showed no clear correlation with $ν_{\mathrm{L}}$. For AR1, the coronal electron temperature ($kT_{\mathrm{e}}$) and optical depth ($τ$) are $\sim 10~\mathrm{keV}$ and $\sim 5$, respectively. In contrast, for AR2, $kT_{\mathrm{e}}$ decreases to $\sim 3~\mathrm{keV}$ and $τ$ increases to $\sim 12$, showing correlations with $ν_{\mathrm{L}}$, with Spearman's rank correlation coefficients of $-0.78$ and $0.71$, respectively. The transition of the spectral parameters at $ν_{\mathrm{L}} \sim 500~\mathrm{Hz}$ indicates the existence of a critical QPO frequency governed or influenced by the accretion state of the source.

Optical thermodynamics offers a distinctive framework for understanding complex phenomena in multimode systems, yet standard ideal-gas-like formulation neglects the effect of nonlinear interaction on thermodynamic quantities, significantly restricting its range of validity. Here, we overcome this limitation by developing a mean-field thermodynamic theory that incorporates the nonlinear renormalization of the mode spectrum. The resulting nonlinear equation of state, analogous to that of the van der Waals for gases, enables the prediction of power-dependent mode localization and the description of optical cooling and heating in photonic Joule-Thomson expansion. Our work establishes a unified thermodynamic perspective on the nonlinear control and transport of optical waves.

We introduce a sparse classical representation, a truncation strategy and a shot-efficient sampling method to push the classical prediction of quantum error correction thresholds beyond Clifford operations and Pauli errors. As two illustrations of the potential of our method, we first show that coherent noise error thresholds, when computed at the circuit level (i.e taking into account full syndrome circuits) for distances up to d=9, are systematically overestimated (by a factor of about 4) by a Pauli-twirling approximation of the noise. We then apply our method to the recently introduced magic-state cultivation protocol. We show, through shot-efficient importance sampling, that, at distance d=5, the multiplicative factor between the T-gate and the S-gate injection error rate is not the one conjectured from low-d computations: it can be as large as 7.

Sensitivity analysis methods such as the Cornfield inequality and the E-value were developed to assess the robustness of observed associations against unmeasured confounding -- a major challenge in observational studies. However, the calculation and interpretation of these methods can be difficult for clinicians and interdisciplinary researchers. Recent advances in large language models (LLMs) offer accessible tools that could assist sensitivity analyses, but their reliability in this context has not been studied. We assess four widely used LLMs, ChatGPT, Claude, DeepSeek, and Gemini, on their ability to conduct sensitivity analyses using Cornfield inequalities and E-values. We first extract study-specific information (exposures, outcomes, measured confounders, and effect estimates) from four published observational studies in different fields. Using such information, we develop structured prompts to assess the performance of the LLMs in three aspects: (1) accuracy of E-value calculation, (2) qualitative interpretation of robustness to unmeasured confounding, and (3) suggestion of possible unmeasured confounders. To our knowledge, there has been little prior work on using LLMs for sensitivity analysis, and this study is an early investigation in this area. The results show that ChatGPT, Claude, and Gemini accurately reproduce the E-values, whereas DeepSeek shows small biases. Qualitative conclusions from all the LLMs align with the magnitude of the E-values and the reported effect sizes, and all models identify biologically and epidemiologically plausible unmeasured confounders. These findings suggest that, when guided by structured prompts, LLMs can effectively assist in evaluating unmeasured confounding, and thereby can support study design and decision-making in observational studies.

In [4] Camps-Moreno et al. treated (relative) generalized Hamming weights of codes from extended norm-trace curves and they gave examples of resulting good asymmetric quantum error-correcting codes employing information on the relative distances. In the present paper we study ramp secret sharing schemes which are objects that require an analysis of higher relative weights and we show that not only do schemes defined from one-point algebraic geometric codes from extended norm-trace curves have good parameters, they also posses a second layer of security along the lines of [11]. It is left undecided in [4, page 2889] if the ``footprint-like approach'' as employed by Camps-Moreno herein is strictly better for codes related to extended norm-trace codes than the general approach for treating one-point algebraic geometric codes and their likes as presented in [12]. We demonstrate that the method used in [4] to estimate (relative) generalized Hamming weights of codes from extended norm-trace curves can be viewed as a clever application of the enhanced Goppa bound in [12] rather than a competing approach.

Spectral induced polarization (SIP) is a geophysical method used to characterize subsurface materials. It measures the frequency-dependent complex resistivity of rocks and soils through the application of a small alternating current in the subsurface or in laboratory samples. Debye decomposition (DD) is a standard method for analyzing and interpreting SIP data, as it allows estimation of the relaxation time distribution (RTD) of geomaterials. However, conventional DD approaches treat measurements independently, work in real-valued spaces despite the complex-valued nature of SIP data, and provide limited uncertainty quantification. These limitations reduce the effectiveness of conventional DD on heterogeneous datasets. We reformulate DD as an unsupervised machine learning problem and introduce a conditional variational autoencoder (CVAE) that learns a shared mapping from resistivity spectra to continuous RTDs. The model is validated on a dataset comprising 140 laboratory and field SIP measurements of granular mixtures, mineralized rocks, and cementitious materials. The CVAE operates in complex-valued data space and achieves reconstruction errors of 0.45 % and 0.24 % for the imaginary and phase components of resistivity, respectively, with statistically significant improvements over conventional methods (p-values of 4x10^-6 and 2x10^-3). The inferred RTDs are stable and physically consistent, and their total chargeability and mean relaxation time correlate with polarizable grain content and grain size, respectively, with coefficients of determination up to 0.98. An additional contribution of the proposed method is the learned latent representation, which organizes SIP spectra into a structured space. Unsupervised clustering in a two-dimensional projection of this space improves the Davies--Bouldin index by nearly a factor of three relative to conventional RTD parameters.

All observational evidence for dark matter and dark energy is so far exclusively gravitational. Hence, the dark sector may be equivalently described by a theory of the spacetime metric whose dynamics is affected by interactions with an unknown environment. Adapting open-system techniques, we have recently constructed such a general theory of open gravitational dynamics. Here we study a minimal and concrete realization of this theory that describes the late-time acceleration of the Universe. Our model provides a good fit to recent baryon acoustic oscillation measurements by construction, while avoiding violations of the null energy condition. Moreover, it leads to a set of correlated and observationally testable predictions. Studying the modified cosmological perturbation theory and compared to the $Λ$CDM model we find: a dissipative suppression of the gravitational-wave luminosity distance relative to the electromagnetic one; a modification in the evolution of the Bardeen potentials with a clear signal in the gravitational slip; and an enhancement of structure formation at low redshift. We present semi-analytical estimates of the magnitude of these effects and show that they lie within the reach of current constraints while providing clear targets for upcoming cosmological surveys.

The origin of the mass scaling relation between supermassive black holes (SMBHs, $M_{\rm BH}$) and galaxies ($M_*$) remains a key open question. Rather than invoking AGN feedback, a non-causal mechanism has been proposed in which multiple mergers average out the $M_{\rm BH}/M_*$ ratio, thus decreasing its scatter ($σ$) and forming a tight local mass relation over cosmic history. A larger scatter in the relation at higher redshift suggested from a non-causal evolutionary scenario may be evident from recent JWST observations of overmassive SMBHs at high redshift. Here, we carry out a Monte Carlo simulation of solely merger-induced evolution of galaxies and their SMBHs which incorporates recent high-redshift observational constraints on $σ$ and the galaxy merger rate. We find that the dispersion in the local mass relation can be reproduced, even when starting from a highly scattered population at $z\sim6$ with $σ=0.8\,{\rm dex}$ or $1.0\,{\rm dex}$, which are in agreement with recent JWST studies. The redshift evolution of the scatter is highly sensitive to the mass ratio between merging pairs and the merger rate, and minor mergers with higher frequency than major mergers can also contribute to the scatter evolution, highlighting the importance of accurately constraining these parameters at high redshift through observations. Furthermore, statistical surveys aimed at determining the $M_*$-dependence of $σ$ and constraining $σ$ at $z\sim3-4$ will be effective in testing this scenario.

Thermal correlators in holographic conformal field theories are known to exhibit singularities in complex time, sometimes referred to as ``bouncing singularities", which are believed to be related to bulk geodesics probing the black hole interior. These singularities correspond to exponentially suppressed contributions in the high-frequency limit of the thermal correlators. We revisit in detail the calculation of retarded two-point functions of local operators dual to bulk scalar fields in the planar AdS black hole background. We confirm that these correlators develop bouncing singularities, and highlight the agreement of two independent methods: a large frequency WKB analysis with infalling boundary conditions at the horizon; and an asymptotic OPE analysis that relies only on the near-boundary expansion, without any direct input from the black hole interior. We then extend these calculations to the case of the retarded two-point function of displacement operators on a Wilson line in the finite temperature gauge theory. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. We find that these defect correlators also exhibit bouncing singularities, and again observe exact agreement between the WKB analysis sensitive to the black hole interior and the asymptotic OPE analysis. This agreement suggests that the bouncing singularities and the corresponding OPE data encode a universal high-frequency structure of the retarded correlators, and we propose a factorization formula that encodes the deviations from this universality.

In this paper, by considering the anhedral angle, we for the first time study the problem of supersonic flow of a Chaplygin gas over a conical wing with $Λ$-shaped cross sections, where the flow is governed by the three-dimensional steady isentropic irrotational compressible Euler equations. This work is motivated by the design of the Nonweiler wing, which is one of the simplest waveriders. Mathematically, the problem reduces to a boundary value problem for a nonlinear mixed-type equation in conical coordinates. By introducing a viscosity parameter to treat the degenerate boundary, we use the continuity method to establish the existence of a piecewise smooth self-similar solution to the problem, in the case that the shock is attached to the leading edge of the conical wing. Our results verify part of Küchemann's speculation on the conical flow field structures of this type, and also find a new conical flow field structure.

Atmospheric aerosols strongly influence daytime sky quality for solar coronal imaging, yet few studies directly link aerosol properties and sky-brightness measurements within ~2° of the Sun. Here we compare externally occulted coronagraphic measurements of near-Sun radiance with aerosol-constrained inferences derived from direct-Sun and sky photometry. Our analysis focuses on Mauna Loa Observatory, a well-characterized high-altitude site for atmospheric and solar observations. We present coronagraphic measurements of near-Sun radiance at 1.54 +/- 0.77° from solar disk center acquired between 2006 and 2007 by an ATST Sky Brightness Monitor (SBM). These data are directly compared with circumsolar radiances inferred at 1.54° using AERONET almucantar measurements and aerosol optical retrievals. We find quantitative agreement between these two approaches, enabling extension to multi-decadal analyses of circumsolar radiance and its relationship to aerosol properties and related proxies (e.g., the Angstrom exponent) using AERONET data from 2000-2025. Near-Sun radiances are expressed relative to the solar disk-center radiance, facilitating direct comparison with related studies. Finally, we synthesize physically based true-color images of the circumsolar sky under representative aerosol conditions as an observational aid, in part to illustrate that visually enhanced solar aureoles do not necessarily imply poor infrared coronal observing conditions. This methodology provides an extended framework for assessing daytime coronal sky quality at existing and future observing sites.

The entanglement entropy in $d+1$ dimensional conformal field theories can be calculated using the area of $d$ dimensional minimal surfaces in $AdS_{d+2}$. Therefore, the existence of surfaces anchored in the boundary of an asymptotically anti-de Sitter (AdS) spacetime is crucial for the calculation of entanglement entropy. In particular, in $d=3$ the extremal surfaces are geodesics with two ends in the boundary. In the Schwarzschild-AdS black hole the space-like geodesics can connect timelike-separated points by winding around the horizon multiple times. This result can be extended to other asymptotically AdS spacetimes. For geodesics joining time-like separated points, if there is a photon ring then the timelike entanglement entropy in the $\text{AdS}_3/\text{CFT}_2$ will not have an imaginary part. We present an exhaustive analysis about the existence of geodesics anchored in the boundary of the three dimensional quantum BTZ (quBTZ) black hole and its charged counterpart. We found conditions for the existence of geodesics with two ends in the boundary in all branches of the quBTZ and determine the type of distance between the points in the boundary. We use a criteria for the existence of light rings to shed some light over the conjecture for spacetimes that are spherically symmetric and have a photon sphere: there are always points with time-like separation that can be connected by space-like or null geodesics.

We prove limit theorems for the number of fixed points, descents, and inversions of iterated random-to-top shuffles in two asymptotic regimes. Our proofs are analytic, and they utilize new combinatorial decompositions that represent each statistic as a randomly indexed statistic of a uniformly random permutation. This perspective gives new combinatorial proofs of the expected number of fixed points and inversions. In particular, we solve an open problem of Pehlivan on fixed points, and we answer a question of Diaconis and Fulman on inversions.

Electroweak, QCD, and QED radiative corrections to the nucleon low-energy coupling constants $g_V$ and $g_A$ are enhanced by large perturbative logarithms between the electroweak and hadronic scale, as well as between the hadronic scale and the low-energy MeV scale. Additionally, higher-order pion-mass splitting corrections to the nucleon axial-vector charge might be large. By consistently incorporating these effects, we provide an updated relation between the lattice-QCD and physical $g_A$, finding a total radiative correction of $3.5(2.1)\%$ ($5.6(0.7)\%$). This leads to an expected lattice-QCD result of $g^{\mathrm{QCD}}_A = 1.265(26)$ ($g^{\mathrm{QCD}}_A = 1.240(9)$) when based on a combination of lattice-QCD and data-driven (or only data-driven) inputs, respectively. Future phenomenological, chiral perturbation theory, and lattice-QCD studies can improve both the central value and the uncertainty of this estimate.

We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based optimization. We employ the methodology in a variational data assimilation problem for the chaotic Kuramoto-Sivashinsky equation and show that it successfully reconstructs the full trajectory for up to 0.25 Lyapunov times given full state measurements at the final time. The proposed algorithm provides 3.5 times speed-up when compared to the full-order model. The proposed method opens up new possibilities for the reduced order modelling of spatiotemporally chaotic systems.

The Tremaine-Weinberg (TW) method and its variations provide the most direct means to measure the pattern speeds of galactic bars. We establish a unifying framework by deriving an integral form of the continuity equation over an arbitrary closed loop. This naturally defines a local pattern speed for any chosen region in a galactic disk (including bars and spirals). We demonstrate that this intuitive formalism recovers all standard variants of the TW method as special cases corresponding to specific choices of the integration loop. In this paper, we validate this framework and demonstrate its diagnostic power. By applying it to a diverse set of test cases from the TNG50 simulation, including face-on prototype barred galaxies and highly constrained Mock Milky Way standard configurations, we show that this formalism accurately recovers both constant global pattern speeds and radially varying profiles. Rather than relying on rigid geometric approximations, our method naturally differentiates coherent solid-body rotators (bars) from spirals. Our results validate that this unified integral framework provides a robust, geometrically flexible, and practically extensible tool for decoding complex dynamics of galactic structures.

We formulate and validate an equivalent circuit model describing mutual resistive coupling between three microwave cavity resonators interconnected via thin metallic foils. Each cavity is represented as a lumped LCR circuit, while the foils act as a dissipative interface that mediates energy exchange via mutual resistance. This coupling mechanism produces interference effects and a controllable anti-resonance when the input resonators are amplitude- and phase-balanced, a behavior not achievable with standard microwave antenna probes. All three resonators operated in the TM$_{010}$ mode, where two input resonators each excited the third via a thin copper foil. Analytical expressions are derived for the mutual resistance and coupling coefficient of these foils in this geometry. Under balanced conditions, a sharp anti-resonance emerges with a near order-of-magnitude enhanced phase sensitivity at the resonant frequency of the output cavity, consistent with model predictions. The experimentally extracted mutual coupling coefficients, $Δ_{13}=(5.00\pm0.01)\times10^{-6}$ and $Δ_{23}=(4.10\pm0.01)\times10^{-6}$, fall within the calculated range $Δ_{n3}\approx(1\text{--}48)\times10^{-6}$ derived from the foil's electromagnetic properties, where the spread is dominated by the estimated foil thickness uncertainty of $(9\pm1)\,μ\mathrm{m}$. These results confirm that resistive coupling can occur across a number of skin depths of a metallic interface, providing a new means of engineering controlled interference in multi-resonator systems. The approach offers potential applications in precision microwave experiments, phase-sensitive detection, and tests of fundamental electromagnetic interactions.

Large language models (LLMs) enable a new form of advertising for retrieval-augmented generation (RAG) systems in which organic responses are blended with contextually relevant ads. The prospect of such "generated native ads" has sparked interest in whether they can be detected automatically. Existing datasets, however, do not reflect the diversity of advertising styles discussed in the marketing literature. In this paper, we (1) develop a taxonomy of advertising styles for LLMs, combining the style dimensions of explicitness and type of appeal, (2) simulate that advertisers may attempt to evade detection by changing their advertising style, and (3) evaluate a variety of ad-detection approaches with respect to their robustness under these changes. Expanding previous work on ad detection, we train models that use entity recognition to exactly locate an ad in an LLM response and find them to be both very effective at detecting responses with ads and largely robust to changes in the advertising style. Since ad blocking will be performed on low-resource end-user devices, we include lightweight models like random forests and SVMs in our evaluation. These models, however, are brittle under such changes, highlighting the need for further efficiency-oriented research for a practical approach to blocking of generated ads.