We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter estimation and hypothesis testing to derive ultimate bounds for jointly estimating geometrical features and for deciding the presence or absence of surface defects, and we identify optimal measurements from the geometry of the point-spread-function manifold. As a representative application, we analyse a minimal surface crack model based on three point sources and show that spatial mode sorting can simultaneously enable near-quantum-limited estimation of crack width and depth and markedly enhanced detectability of the crack, compared with direct imaging. Our results pave the way towards enhanced optical inspection and characterisation of sub-diffraction surface features by probing a limited number of spatial modes without any illumination control.

EVMbench, released by OpenAI, Paradigm, and OtterSec, is the first large-scale benchmark for AI agents on smart contract security. Its results -- agents detect up to 45.6% of vulnerabilities and exploit 72.2% of a curated subset -- have fueled expectations that fully automated AI auditing is within reach. We identify two limitations: its narrow evaluation scope (14 agent configurations, most models tested on only their vendor scaffold) and its reliance on audit-contest data published before every model's release that models may have seen during training. To address these, we expand to 26 configurations across four model families and three scaffolds, and introduce a contamination-free dataset of 22 real-world security incidents postdating every model's release date. Our evaluation yields three findings: (1) agents' detection results are not stable, with rankings shifting across configurations, tasks, and datasets; (2) on real-world incidents, no agent succeeds at end-to-end exploitation across all 110 agent-incident pairs despite detecting up to 65% of vulnerabilities, contradicting EVMbench's conclusion that discovery is the primary bottleneck; and (3) scaffolding materially affects results, with an open-source scaffold outperforming vendor alternatives by up to 5 percentage points, yet EVMbench does not control for this. These findings challenge the narrative that fully automated AI auditing is imminent. Agents reliably catch well-known patterns and respond strongly to human-provided context, but cannot replace human judgment. For developers, agent scans serve as a pre-deployment check. For audit firms, agents are most effective within a human-in-the-loop workflow where AI handles breadth and human auditors contribute protocol-specific knowledge and adversarial reasoning. Code and data: https://github.com/blocksecteam/ReEVMBench/.

Coupling between spin, orbital, charge, and lattice degrees of freedom in transition-metal oxides produces a variety of electronic and magnetic phenomena of importance for future technologies. Here, we explore the electronic band structure of a (111)-oriented La0.7Sr0.3MnO3 thin film through soft X-ray angle-resolved photoemission spectroscopy (ARPES). The measurements agree with the electronic band structure calculated with density functional theory using Hubbard U correction. Furthermore, we probe the circular dichroism in ARPES, and observe a pronounced momentum- resolved magnetic circular dichroism in resonant photoemission from the Mn L-edge. The approach combines the momentum- and spin-selectivity of ARPES and X-ray magnetic circular dichroism, respectively, which could provide a useful approach for the study of unconventional magnetism.

The rapid growth of satellite constellations, particularly Starlink, is increasingly affecting ground-based astronomy. In this project, we developed a workflow to detect, identify, and measure the brightness of trails from artificial satellites and other orbiting objects in archival images from the Dark Energy Camera (DECam), available through the NOIRLab Data Archive. We filtered images with visible streaks, retrieved detector-level images, applied the Hough Transform (via satmetrics) to detect and align trails, and performed surface brightness photometry. We also used SatChecker to obtain likely identifications for each trail. Our sample of nine measured streaks includes Starlink satellites, a navigation satellite, a decommissioned science satellite, and a rocket body. Our results show that satellites and other orbiting objects are consistently detectable in DECam images, but their brightness varies significantly, reflecting design and operational differences across object types and models. While the methodology proved effective, detecting faint streaks was challenging, and short-lived glints remain an even harder problem for future work. This proof-of-concept establishes a foundation for larger statistical studies of satellite impacts on astronomical surveys. The code is available at https://github.com/iausathub/reca-streaks

Pulsar timing of double neutron star (DNS) systems is one of the best methodologies to study the neutron star masses distribution. Here we report the discovery of a double neutron star system PSR J0641+0448 in the Five-hundred-meter Aperture Spherical radio Telescope (FAST) Galactic Plane Pulsar Snapshot (GPPS) survey. This pulsar has a 25.7 ms spin period and moves in a 3.73-days eccentric orbit with an eccentricity of 0.145. Using FAST observations, we obtained its phase-connected timing solution with periastron advance and Shapiro delay detected. Using $χ^2$ analysis based on DDGR model, we constrain the pulsar mass to $1.319^{+0.021}_{-0.035}~M_\odot$, and the companion mass to $1.269^{+0.022}_{-0.016}~M_\odot$ with a 68.3\% confidence level. The low companion mass and mild orbital eccentricity is consistent with the correlation between neutron masses and orbital eccentricities.

In this paper, we investigate the asymptotic behavior of solutions for divergence linear elliptic equations in exterior domains with periodic coefficients. Consequently, we generalise the Liouville type result firstly established by Avellaneda and Lin.

The influence of dispersion on the differential scattering cross section in the vicinity of the first diffraction minimum is revisited for collision energies between 200 and 450 MeV. Transient nuclear excitations in the giant resonance region with angular momentum L \leq 3 are taken into consideration within updated numerics. Moreover, the deviations of the nonperturbative QED corrections from the conventionally used smooth Born predictions are accounted for. A qualitative agreement with the measurements is only obtained for the lowest energy, while dispersion within the present model is too small at the higher energies.

Estimating the meteoroid flux density at centimetre to metre sizes is notoriously difficult. Yet it is an important endeavour, as these sizes represent the transition between small meteoroids that pose a risk to spacecraft, and the Near-Earth Objects that are relevant for planetary defense. We present a novel automated methodology for debiasing meteor observations from multi-camera networks, applied to data from the Desert Fireball Network (DFN). Our approach utilizes the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix) framework to partition the sky into equal-area pixels at 70 km altitude, enabling precise and convenient measurement of effective survey coverage and fireball counting across the network. We developed a comprehensive data processing pipeline that analyses millions of all-sky camera images to determine clear-sky conditions through automated star source detection and flux distribution analysis. As a case study, we apply this methodology to observations of the 2015 Southern Taurid meteor shower, during which there was significant fireball activity. Processing data from 33 cameras over a three-month period (October-December 2015), we calculate an effective observation coverage of $1.58 \times 10^{12}$ km$^2$.h and identified 54 Southern Taurid fireballs from 141 validated detections. Our results are consistent with the extrapolation of previous work done on the same meteor shower at smaller sizes, when we set a $\sim300$ kg.m$^{-3}$ mean meteoroid density, consistent with the cometary origin of the Taurid stream. The HEALPix-based approach successfully automates what was previously a labor-intensive manual process, providing a scalable solution for accurate flux measurements from distributed camera networks; it is directly applicable to other meteor surveys.

This study investigates K--12 teachers' perceptions and experiences with AI-supported rubric generation during a summer professional development workshop ($n = 25$). Teachers used MagicSchool.ai to generate rubrics and practiced prompting to tailor criteria and performance levels. They then applied these rubrics to provide feedback on a sample block-based programming activity, followed by using a chatbot to deliver rubric-based feedback for the same work. Data were collected through pre- and post-workshop surveys, open discussions, and exit tickets. We used thematic analysis to analyze the qualitative data. Teachers reported that they rarely create rubrics from scratch because the process is time-consuming and defining clear distinctions between performance levels is challenging. After hands-on use, teachers described AI-generated rubrics as strong starting drafts that improved structure and clarified vague criteria. However, they emphasized the need for teacher oversight due to generic or grade-misaligned language, occasional misalignment with instructional priorities, and the need for substantial editing. Survey results indicated high perceived clarity and ethical acceptability, moderate alignment with assignments, and usability as the primary weakness -- particularly the ability to add, remove, or revise criteria. Open-ended responses highlighted a ``strictness-versus-detail'' trade-off: AI feedback was often perceived as harsher but more detailed and scalable. As a result, teachers expressed conditional willingness to adopt AI rubric tools when workflows support easy customization and preserve teacher control.

In this paper we propose a new method for multiple change-point detection for piecewise-constant circular signals, a setting that, despite its importance in many scientific domains, remains comparatively under-explored. The proposed method, Permutation-based Circular Isolate-Detect, denoted PCID, uses an appropriately chosen contrast function and permutation testing to detect change-points in an offline manner, for the data sequence under consideration. Prior to detection, PCID isolates the change-points. The contrast function used is derived under the assumption of von Mises distribution for the noise, but we show that the method is robust and performs well for other distributions as well. Simulations are used to showcase the usability of the method in different signal and noise structures, including serially correlated noise. In order to exhibit the practical relevance of the method in real-world applications, PCID is applied to three real-world datasets, namely flare, acrophase and wave data.

Magnon-photon coupling in cavity magnonic systems offers a promising route toward integrated wave-based information-processing devices. However, in ultrathin magnetic films the weak magnon response is easily buried beneath photon-dominated spectra. We show that a derivative-divide analysis of the microwave transmission parameter in a planar split-ring-resonator cavity isolates the magnetic contribution and resolves clear anticrossings in yttrium iron garnet and CoFeB films, yielding measurable coupling down to thicknesses of 60 nm and 5 nm, respectively. These results establish derivative-divide method as a simple and sensitive probe of magnon-photon coupling in ultrathin insulating and metallic films, and as a practical tool for characterizing miniaturized cavity-magnonic devices.

We consider the problem of private information retrieval (PIR) from MDS coded databases with colluding servers, i.e., MDS-TPIR. In the MDS-TPIR setting, $M$ files are stored across $N$ servers, where each file is stored independently using an $(N,K)$-MDS code. A user wants to retrieve one file without disclosing the index of the desired file to any set of up to $T$ colluding servers. The general problem in studying PIR schemes is to maximize the PIR rate, defined as the ratio of the size of the desired file to the size of the total download. Freij-Hollanti et al. proposed a conjecture of the MDS-TPIR capacity (the maximum achievable PIR rate), which was later disproved by Sun and Jafar by a counterexample with $(M,N,T,K)=(2,4,2,2)$. In this paper, we propose a new MDS-TPIR scheme based on a disguise-and-squeeze approach. The features of our scheme include the following. Our scheme generalizes the Sun-Jafar counterexample to $(M,N,T,K)=(2,N,2,K)$ with $N\geq K+2$ for an arbitrary $(N,K)$-MDS coded system, providing more counterexamples to the conjecture by Freij-Hollanti et al. For $(M,N,T,K)=(2,N,2,K)$ and a GRS (generalized Reed-Solomon codes) coded system, our scheme has rate $\frac{N^2-N}{N^2+KN-2K}$, beating the state-of-the-art results. We further show that this rate achieves the linear MDS-TPIR capacity when $K=2$. Our scheme features a significantly smaller field size for implementation and the adaptiveness to generalized PIR models such as multi-file MDS-TPIR and MDS-PIR against cyclically adjacent colluding servers. Lastly, we provide an $ε$-error MDS-TPIR scheme for $T\geq 3$ based on the disguise-and-squeeze framework.

The uniform Turán density $π_{u}(F)$ of a $3$-uniform hypergraph (or $3$-graph) $F$ is the supremum of all $d$ such that there exist infinitely many $F$-free $3$-graphs $H$ in which every induced subhypergraph on a linearly sized vertex set has edge density at least $d$. Determining $π_{u}(F)$ for a given $3$-graph $F$ was proposed by Erdős and Sós in the 1980s, yet only a few cases are known. In particular, it remains open whether $1/2$ can occur as a value of $π_{u}$. In this paper, we establish a novel connection between Turán-type extremal problems for digraphs and uniform Turán densities of $3$-graphs. Using digraph extremal results, we give the first verifiable conditions for $3$-graphs $F$ with $π_{u}(F) = (r-1)/r$ and $π_{u}(F) = (r-1)^2/r^2$ for all $r \ge 2$, and identify the corresponding $3$-graphs. In particular, these $3$-graph classes contain some specific $3$-graphs, such as $K^{(3)-}_4$. We also present a sufficient condition ensuring $π_{u}(F)=4/27$ and construct $3$-graphs satisfying it; in particular, our examples are different from the tight $3$-uniform cycles whose uniform Turán density $4/27$ was determined in [{Trans. Amer. Math. Soc. 376 (2023), 4765-4809}]. Finally, we give a short proof of the existence of $3$-graphs $F$ with $π_{u}(F)=1/27$, originally established by Garbe, Král' and Lamaison [{Israel J. Math. 259 (2024), 701-726}] via the hypergraph regularity method.

We present the design and implementation of a RAG-based AI system benchmarking (RAGPerf) framework for characterizing the system behaviors of RAG pipelines. To facilitate detailed profiling and fine-grained performance analysis, RAGPerf decouples the RAG workflow into several modular components - embedding, indexing, retrieval, reranking, and generation. RAGPerf offers the flexibility for users to configure the core parameters of each component and examine their impact on the end-to-end query performance and quality. RAGPerf has a workload generator to model real-world scenarios by supporting diverse datasets (e.g., text, pdf, code, and audio), different retrieval and update ratios, and query distributions. RAGPerf also supports different embedding models, major vector databases such as LanceDB, Milvus, Qdrant, Chroma, and Elasticsearch, as well as different LLMs for content generation. It automates the collection of performance metrics (i.e., end-to-end query throughput, host/GPU memory footprint, and CPU/GPU utilization) and accuracy metrics (i.e., context recall, query accuracy, and factual consistency). We demonstrate the capabilities of RAGPerf through a comprehensive set of experiments and open source its codebase at GitHub. Our evaluation shows that RAGPerf incurs negligible performance overhead.

This review traces the evolution of precision timing in particle physics experiments, from the first large-scale applications of scintillator and photomultiplier tube (PMT) systems in the 1990s to the picosecond-precision detectors of future colliders. Four technological generations are identified: (i) the era of discrete electronics (NIM, CAMAC, VME) and PMTs, which established the three canonical uses of timing -- particle identification via time-of-flight, background and pile-up rejection, and directionality triggering; (ii) the silicon revolution enabled by Silicon Photomultipliers (SiPMs), Low-Gain Avalanche Diodes (LGADs), and Application-Specific Integrated Circuits (ASICs); (iii) the current transition to ubiquitous four-dimensional (4D) tracking, in which time is a coordinate measured at every point along a particle trajectory. Under-construction systems at the HL-LHC (CMS MTD, ATLAS HGTD, CMS HGCAL) demonstrate the maturity of 30--50\,ps silicon timing at the million-channel scale. The EIC, LHCb VELO Upgrade~II, and ALICE~3 push this technology into new regimes of radiation hardness, material budget, and granularity. (iv) The Far-future facilities such as the Muon Collider and FCC require a further leap to $\sim$10\,ps, setting the agenda for the next decade of detector R\&D.

Observations made by the Juno spacecraft above Jupiter's polar regions have revealed that electrons accelerated toward Jupiter, which contribute to auroral emissions, are frequently accompanied by electrons accelerated away from Jupiter. These electrons should be observable as narrow electron beams in the middle magnetosphere, in accordance with the principles of adiabatic particle motion. The existence of such beams has been previously reported using data from the Galileo mission, and their relation to auroral processes has been hypothesized. In the present study, we analyze electrons measured by Juno's JEDI instrument in the middle magnetosphere between 13 RJ and 50.5 RJ radial distance and within energies of 30-1,200 keV. The pitch angle distributions of potential electron beams are fitted with an intensity 'beamness' function. The presence of narrow beams is demonstrated throughout the observation range. The energy fluxes of auroral and equatorial electron beams are compared by including pitch angle scattering processes along the magnetospheric field lines. This is achieved by solving the pitch angle diffusion equation for different sets of diffusion coefficients. The statistical occurrence distribution and the energy fluxes of the beams are consistent with auroral upward accelerated electrons observed in studies of the polar space environment. This finding provides further support for the hypothesis that the electron beams observed in the middle magnetosphere originate from the auroral acceleration region.

Let $χ$ be a subgroup-theoretical property. We introduce an \emph{antichain condition} $\operatorname{ac}_χ$ which forbids the existence of infinite antichains of mutually permutable non-$χ$ subgroups whose infinite joins remain non-$χ$. This is a ''width'' analogue of the real chain condition on non-$χ$ subgroups, and it extends the usual hierarchy of weak chain conditions (double chain condition, deviation, and $\operatorname{RCC}$). Our main results show that, within the universe of generalized radical groups, the antichain condition is as rigid as the corresponding chain conditions. For the properties $χ$ of normality, almost normality, near normality, permutability, modularity, and pronormality, we prove that a generalized radical group satisfies $\operatorname{ac}_χ$ if and only if it satisfies $\operatorname{RCC}$ on non-$χ$ subgroups; equivalently, it satisfies any of the standard weak chain conditions on non-$χ$ subgroups. In particular, we obtain minimax-type dichotomies: either the group is minimax, or \emph{every} subgroup satisfies $χ$. This yields characterizations in terms of Dedekind groups, quasi-Hamiltonian groups, groups with modular subgroup lattice, and $\overline{T}$-groups. In the pronormal case, one has to deal with locally finite simple groups and a use of the Classification of Finite Simple Groups seems unavoidable.

Social media platforms have become critical infrastructures for public communication, where large-scale interaction can both support socially beneficial collective pressure and amplify polarization and conflict. While opinion-dynamics research has long modeled how beliefs evolve through interpersonal influence, the central challenge for healthier online environments increasingly lies in algorithmic interventions: mechanisms that steer collective opinion toward desirable outcomes or dampen harmful dynamics. This survey offers a structured synthesis of this fast-growing, interdisciplinary literature. We organize prior work by the objective optimized -- overall opinion (e.g., consensus or mean opinion), polarization and disagreement, and other quantities -- and review the associated optimization formulations and representative algorithms with mathematical rigor. We also compile intervention-relevant theoretical and empirical findings. Finally, we outline concrete future directions that emerge from this survey.

We study the Emery model (three-band Hubbard model) for superconducting cuprates on three distinct ladder-like lattices that are supercell of the CuO$_2$ plane and thus preserve the ratio of copper to oxygen atoms. Using the density-matrix renormalization group method we confirm that these Emery ladders are charge-transfer insulators for the hole concentration corresponding to undoped cuprates but become Luther-Emery liquids with enhanced pairing correlations upon doping. The preservation of the Cu to O ratio allows us to study the distribution of charges between these atoms in the Luther-Emery phase. We show that these Emery ladders can describe the relations between charge distribution, pairing strength, and interactions that have been observed in the Emery model on two-dimensional clusters and in experiments.

So called cartesian cut cell meshes provide efficient ways to generate meshes but do require tailored numerical methods to not suffer from stabilization issues, especially in the hyperbolic regime where the application of explicit time stepping schemes is common. In this scenario, due to potentially arbitrarily small cut cells, an infeasible restriction is imposed on the time step size. The Domain of Dependence (DoD) stabilization allows for a time step size based on the underlying Cartesian mesh. Being an extension of a discontinuous Galerkin (DG) method, one would expect similar accuracy properties as in the pure DG case. While numerical results do support this expectation, on the analytical level this has only been investigated thoroughly for $k=0$. Error analysis typically hinges on a consistency result. In this contribution we prove such a result for the DoD stabilization given an arbitrary polynomial degree and an exact solution of sufficient regularity. This in turn could open the way towards a more refined analysis of the method even in the high-order case.

The Lunar Electromagnetic Monitor in X-rays (LEM-X) is a proposed wide-field X-ray observatory designed for deployment on the Moon's surface. Its primary scientific goal is to enhance multi-messenger astrophysics by detecting, localizing, and monitoring high-energy transient phenomena and variable X-ray sources across the sky. Building on the heritage of the eXTP and LOFT mission proposals, LEM-X employs pairs of coded-aperture cameras equipped with large-area linear Silicon Drift Detectors (SDDs), offering excellent spectral resolution ($\leq$350 eV at 6 keV) over the 2-50 keV energy range. Each camera provides a field of view of ~1 steradian at 25% effective area and achieves a Point-Source Location Accuracy (PSLA) of 1 arcminute, with an on-axis sensitivity better than 5 mCrab in 50 ks and 700 mCrab in 1 s. In this paper we describe the experiment and focus on the detailed design and optimization of the LEM-X coded mask, analyzing its scientific performance, imaging capabilities, and thermo-mechanical properties. We describe the mask code generation, decoding algorithms, and the trade-offs involved in achieving the required angular resolution, sensitivity, and structural integrity. Imaging simulations and mechanical analyses confirm the effectiveness of the proposed design, demonstrating its suitability for high-precision, wide-field X-ray imaging devoted to multi-messenger astrophysics and transient events detection.

We study purification dynamics in monitored quantum processes governed by ensembles of quantum circuits in different random-matrix symmetry classes. We analyze the universal aspects that emerge away from the measurement induced phase transition and inside the volume/weak measurement phase and in the scaling limit of large time and Hilbert space dimension. We present two toy models that reveal two complementary visions and provide quantitative access to universal scaling: i) a discrete-time dynamic in which each time step corresponds to multiplication by a Gaussian random matrix; ii) weak continuous-time monitoring that induces a Dyson brownian motion of the eigenvalues of the density matrix. The first approach provides an algebraic characterization based on rotational invariance emerging in Kraus's operator space, focusing in particular on the unitary and orthogonal cases, respectively $β=2$ and $β=1$, with $β$ the Dyson random-matrix index. The second approach, on the other hand, allows for a unified treatment for any $β$, thanks to the mapping of the Fokker-Planck evolution of eigenvalues onto the Calogero-Sutherland integrable Hamiltonian diagonalized in terms of Jack polynomials. We provide explicit expressions for the universal decrease of Rényi entropies. We show that, approaching the universal scaling limit, numerical simulations of different models agree with each other and with our theoretical predictions. Our results clarify the existence of different classes of universality for the purification process in hybrid quantum systems, accessible in random circuit architectures and weak measurement protocols.

When faced with data problems, many data workers cannot articulate their information need precisely enough for software to help. Although LLMs interpret natural-language requests, they behave brittly when intent is under-specified, e.g., hallucinating fields, assuming join paths, or producing ungrounded answers. We present Pneuma-Seeker, a system built around a central idea: relational reification. Pneuma-Seeker represents a user's evolving information need as a relational schema: a concrete, analysis-ready data model shared between user and system. Rather than answering prompts directly, Pneuma-Seeker iteratively refines this schema, then discovers and prepares relevant sources to construct a relation and executable program that compute the answer. Pneuma-Seeker employs an LLM-powered agentic architecture with conductor-style planning and macro- and micro-level context management to operate effectively over heterogeneous relational corpora. We evaluate Pneuma-Seeker across multiple domains against state-of-the-art academic and industrial baselines, demonstrating higher answer accuracy. Deployment in a real organization highlights trust and inspectability as essential requirements for LLM-mediated data systems.

Generalizing our previous work on ``toroidal averages'', we study the average of special values of $L$-functions of the form $L(1/2,χ^a)L(1/2,χ^b)L(1/2,χ^c)$ for integers $a$, $b$ and $c$, where $χ$ varies over Dirichlet characters of a given prime modulus. We highlight connections with estimates for bilinear forms of trace functions and with bounds for the number of solutions of monoidal equations in three variables in small boxes over finite fields.

With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical properties, most of which exhibit pronounced nonlinear, especially large-deformation, behaviors. The main numerical challenge therefore lies in performing nonlinear simulations of such lattice structures, which may contain thousands of geometrically intricate unit cells, while lacking sufficient scale separation for multiscale homogenization schemes to be applicable straightforwardly. In this work, we propose a dedicated solver for the full volumetric fine-scale simulation of nonlinear hyperelastic lattice structures that drastically reduces both memory and computational costs. The key idea is to exploit the intrinsic self-similarity of the cells through a reduced-order modeling strategy applied within a domain-decomposition framework. At each Newton iteration, a limited set of principal cells is identified through a dedicated, weakly intrusive, EIM-like approach, allowing all local tangent operators to be expressed as linear combinations of a few principal ones. This enables fast and memory-efficient operator assembly, and then feeds an efficient inexact FETI-DP based preconditioner at the solution stage, resulting in a quasi matrix-free algorithm for the nonlinear analysis. Numerical experiments in two and three dimensions demonstrate significant computational gains, with runtime reductions from several hours to a few tens of minutes and memory savings by factors of about three, while maintaining full fine-scale accuracy. Notably, the proposed strategy enables the computation of problems involving thousands of cells (i.e., millions of degrees of freedom) within a few minutes on an off-the-shelf laptop.

The differential scalar polarizability $Δα_0(ω)$ of the Ba$^+$ S$_{1/2}$-to-D$_{5/2}$ clock transition has a zero crossing near 481nm, which is measured to be 623.603\,13(17)\,THz. From this measurement, we infer a ratio of reduced matrix elements $\langle P_{3/2}\|r\|S_{1/2}\rangle/\langle P_{1/2}\|r\|S_{1/2}\rangle=1.411\,81(13)$, which provides a stringent test of atomic structure calculations and experimental determination of matrix elements. Additionally, it enables the construction of an accurate approximation to $Δα_0(ω)$, valid for frequencies up to 450\,THz, with only one reduced matrix element, $\langle P_{1/2}\|r\|S_{1/2}\rangle$, appearing in the model's parameterization. We discuss the achievable accuracy of the model, the application to the assessment of blackbody radiation (BBR) shifts in ion-based clocks, and the applicability of the approach to other alkaline-earth ions.

We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon transform. Such a representation enables us to recover the source function directly. The efficiency and robustness of the novel indicator function are verified by several numerical examples.

We investigate the pairwise negative correlation (p-NC) property for uniform probability measures on several families of spanning subgraphs of the complete graph $K_n$. Motivated by conjectured negative dependence properties of the random-cluster model with $q<1$, we focus on three natural families: the set of all connected spanning subgraphs, the set of forests with exactly $k$ components, and the set of connected spanning subgraphs with excess $k$, where $k$ is a fixed integer. We prove that for each of these families, the associated uniform measure satisfies the p-NC property provided $n$ is sufficiently large. Our results extend earlier work on uniform forests and provide the first verification of the p-NC property for uniform connected subgraphs and their truncations on complete graphs.

In this paper we develop the theory of discrete averaging designed to study discrete time dynamical systems defined by iterates of a map. The discrete averaging uses weighted averages over a segment of trajectory to find an autonomous vector field that approximates the original map. The method provides a simple and effective tool for finding adiabatic invariants, both numerically and analytically. It is capable of strengthening various theorems of the classical averaging theory because it eliminates two intermediate steps used in the classical averaging: the suspension procedure that assigns a rapidly oscillating flow to the map and time-dependent coordinate changes that eliminate the dependence on time. We discuss two applications of the discrete averaging - to the dynamics of a near-identity map and to the dynamics of a map in a neighbourhood of a resonant fixed point. We show that the discrete averaging provides explicit uniform bounds for approximation errors. We also show that the discrete averaging can be used to establish domain of validity of adiabatic approximations in numerical experiments.

We study the properties of galaxy cluster 2-point correlation function covariance matrices estimated using the linear-construction (LC) method, which is computationally up to 20 times faster than the standard sample-covariance method. Our goal is to assess how well the LC method performs in cosmological parameter estimation compared to the sample covariance. We use a set of 1000 mock dark matter halo catalogues to compute both the LC-covariance and the sample-covariance estimates in four redshift shells. These numerical matrices are used to fit a theoretical four-parameter model for the covariance. We then use the two fitted covariance models in a likelihood function to estimate two cosmological parameters - the matter density parameter $Ω_{\rm m}$ and the amplitude of the matter density fluctuations $σ_8$ - from the simulated mock catalogues. The purpose of this is to validate the LC-covariance-based model against the sample-covariance model. The catalogues were simulated assuming the spatially flat $Λ$CDM cosmology, with $Ω_{\rm m} = 0.30711$ and $σ_8=0.8288$. We find that the parameter posteriors obtained using the sample- and LC-covariance models agree well with each other and with the simulation cosmology. The two pairs of marginalized constraints are $Ω_{\rm m} = 0.307 \pm 0.003$ and $σ_8 = 0.826\pm 0.009$ (sample covariance), and $Ω_{\rm m} = 0.308 \pm 0.003$ and $σ_8 = 0.825 \pm 0.009$ (LC covariance). The posterior widths are the same, and the difference in the median values is less than $0.16\,σ$ for both parameters.