This paper introduces SixGman, an open-source optical network planning tool for evaluating access-metro-core aggregation network architectures. The framework integrates traffic generation, dual-homed routing, Quality of Transmission (QoT) estimation, spectrum and fiber assignment, techno-economic analysis, energy consumption evaluation, and visualization capabilities. Its modular design, based on standardized interfaces and clearly defined functions, enables flexible, transparent, and reproducible network simulations. SixGman is applied to the Telefónica MAN157 metro-urban topology, composed of 157 optical nodes, 220 links, and four hierarchical layers (HL1-HL4), to compare a conventional full hierarchical architecture with an HL3-bypassed architecture where electrical aggregation at HL3 nodes is removed. The analysis includes traffic distribution, IP router utilization, link congestion, latency, Total Cost of Ownership (TCO), and energy consumption. Results show that HL3 bypassing improves traffic distribution, reduces optical and electrical resource usage, lowers end-to-end latency, and decreases both capital and operational expenditures. Compared to the full hierarchical architecture, the HL3-bypassed scenario achieves reductions of up to 17.5% in TCO and 29.1% in cumulative energy consumption. These results demonstrate the potential of SixGman as a flexible planning platform for cost- and energy-efficient optical network design.

Optical microcavities with rotational symmetry have been widely used for narrowing linewidth and reducing frequency noise, however, the narrow but wavelength dependent optical feedback restricts the narrow linewidth laser works only at some discrete wavelength matching the resonance of the microcavity. Here, we demonstrate a narrow linewidth semiconductor laser with continuous wavelength tunability by hybrid integrating a DFB laser chip with a deformed microcavity fabricated on a 220 nm SOI wafer. The deformed microcavity with vortex radius demonstrates the unique characteristics of unidirectional energy storage, wavelength self-adaptivity, and self-focusing of the Rayleigh scattering based distributed feedback. In addition, the strength of Rayleigh scattering is also significantly enhanced by the high numerical aperture silicon waveguide. The optical feedback signal measured by the optical frequency domain reflectometry (OFDR) shows that the deformed microcavity can effectively lengthen the equivalent propagation distance without wavelength dependence. With the wavelength self-adaptive optical feedback from the deformed microcavity, the intrinsic linewidth of a DFB laser diode is narrowed to 525 Hz and the side mode suppression ratio (SMSR) is improved to 76 dB in a maximum allowable continuous wavelength tuning range of 2.25 nm. The frequency noise and relative intensity noise (RIN) are reduced to 2.98 Hz2 /Hz and -148.74 dB/Hz at the offset frequency of 1 MHz, respectively. The work demonstrated here paves a new way for integrated tunable narrow linewidth lasers, which are of crucial importance in high-speed communication and high-precision spectroscopy

Silicon monoxide (SiO) traces the physical conditions and dynamics in the circumstellar envelopes (CSEs) of AGB stars. We present high-resolution ALMA Band 6 observations of highly excited SiO emission in 14 oxygen-rich AGB stars. We cover transitions from v = 0 to v = 8, including first detections of 28SiO v = 3, 4, 8, J = 6-5, 29SiO v = 6, J = 6-5, and 30SiO v = 4, 5, J = 6-5, some of which are masers. The v = 8 transition is the highest v-state observed in an AGB star yet. Masers in v = 0 are detected clearly in V PsA and IRC+10011 and tentatively in T Mic. R Hya exhibits the richest SiO spectrum. SiO J = 6-5 absorption is seen in R Aql, R Hya, S Pav, and T Mic, with features indicative of both infalls and outflows, and tentative detection of 28SiO v = 8, J = 6-5 absorption is found towards S Pav and R Aql. Highly excited SiO emission is often distributed in arcs or clumps with velocity gradients; components in R Hya and U Her align with predicted shock fronts. Detection rates show no significant difference between low and high mass-loss rate stars, although line overlap may affect some intensities. Maser detections appear uncorrelated with pulsation period or phase. The radius enclosing 90 per cent of compact SiO emission shows a tentative correlation with mass-loss rate. These results highlight the role of mass loss and CSE geometry in shaping high-excitation SiO emission.

The role of AI-generated synthetic data has recently been expanded to support realistic Monte Carlo simulations. However, guidance is limited on generating data with multilevel structures and designing simulations based on such data. This study proposes a general framework for AI-based simulation studies to evaluate the predictive performance and parameter recovery of quantitative methods, specifically using multilevel data commonly observed in the social sciences. Our proposed six-stage workflow consists of (i) specifying a method and real data, (ii) training Generative AI with real data, (iii) assessing synthetic data quality, (iv) designing and conducting simulations, (v) evaluating method performance, and (vi) checking robustness. To enhance fidelity in multilevel data generation, we also introduce targeted modifications to diffusion models and Generative Adversarial Networks (GANs). Furthermore, we develop a systematic quality evaluation framework that assesses both within-table and between-table fidelity, and discuss how AI-based simulation designs should differ depending on whether the simulation's objective is predictive performance or parameter recovery. Finally, using empirical multilevel data and multilevel modeling methods, we demonstrate the utility of the proposed AI-based simulation framework. This approach leads to more accurate and honest evaluations of quantitative methods in the real world, unlike traditional simulation studies based on arbitrary simulated scenarios.

As Edge Intelligence (EI) becomes increasingly prevalent in domains such as smart healthcare, manufacturing, and critical infrastructure, ensuring data privacy while maintaining system efficiency is a growing challenge. This paper presents a new privacy-preserving machine learning (PPML) framework tailored for EI applications, including a four-layer system architecture and training and inference algorithms. We focus on three leading approaches: Differential Privacy (DP), Secure Multi-party Computation (SMC), and Fully Homomorphic Encryption (FHE), and assess their impact on key performance metrics, including model accuracy, response time, and energy consumption. Results from real implementation and extensive trace-based simulations of inference tasks show that DP generally preserves throughput and latency close to plaintext baselines, while accuracy drops with model complexity (up to 35 percent on AlexNet and under 18 percent on LeNet for FordA). SMC performance is driven by communication; network bandwidth and round complexity determine end-to-end latency. For AlexNet, increasing link capacity from 250 Mbps to 500 Mbps reduces latency by about 30 percent. FHE is highly sensitive to model structure and numerical precision bit width, with tighter parameters imposing substantial compute overhead; we observe roughly a 1000 times increase in response time compared to DP. Beyond efficiency, DP shifts the privacy-utility-extractability frontier by reducing the attacker's data efficiency in black-box model stealing, whereas SMC and FHE, while protecting inputs and parameters during inference, require complementary output controls to achieve similar resistance to extraction. These findings provide critical insights into the trade-offs between privacy, performance, and resource efficiency in edge computing scenarios.

Depth sectioning in reflection microscopy has predominantly relied on temporal coherence gating. Here we show that volumetric reflection tomography at diffraction-limited resolution can be achieved under monochromatic illumination by engineering spatial, rather than temporal, coherence. In programmable spatial coherence tomography (PSCT), a sequence of pupil-coded illumination patterns with angular-spectrum diversity generates measurement redundancy enabling the system to calibrate itself, jointly retrieving aberrations, illumination profiles, and sample motion without guide stars or modal priors. We demonstrate label-free volumetric imaging of thick human tissues, organoids, frequency-resolved dynamic contrast, and high-resolution in vivo brain imaging through a cranial window. These results position PSCT as an alternative to temporal coherence based reflection imaging in complex biological systems.

The discrete Pareto (or Zeta, Zipf) distribution, arises naturally in modeling rank-frequency data across diverse fields such as linguistics, demography, biology, and computer science. Despite its widespread applicability, goodness-of-fit testing for the discrete Pareto distribution remains underdeveloped, particularly in the presence of heavy tails and infinite support. This article introduces a novel goodness-of-fit test based on a new Stein-type characterization of the discrete Pareto distribution, formulated using its probability generating function. The proposed method is applicable even when the shape parameter is unknown and avoids binning or smoothing techniques. We study the asymptotic properties of the test and assess its empirical size and power through extensive simulation experiments. The results show that the proposed test either outperforms or matches the performance of existing method across various alternatives. Applications to real datasets are provided to demonstrate its practical relevance and robustness.

This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem admits a unique global solution provided that the initial oxygen concentration is suitably small.

We present a detailed analysis of the evolution of type-C quasiperiodic oscillations (QPOs) observed during the flaring state of the recently discovered black hole X-ray binary Swift J1727.8-1613, utilizing data from the Insight Hard X-ray Modulation Telescope. By examining the relation between the QPO fractional rms amplitude and QPO frequency across various energy bands, we discover that the behavior significantly differs between these energy bands. Below 10 keV, the QPO fractional rms generally decreases with increasing QPO frequency, whereas above 10 keV, the QPO fractional rms remains relatively stable with frequency. Additionally, we report, for the first time, the detection of a common break at around 4 Hz in the relation between QPO fractional rms and frequency in both the 2-4 and 50-100 keV energy bands. We also find that the evolution of all the spectral parameters alters its behavior at around 4 Hz, with the changes in all parameters becoming flatter. This suggests a significant change in the geometry of the accretion flow. We attribute the observed break to the overall changes in the spectrum.

Femtosecond electron beams with complex modulation play a crucial role in applications such as X-ray Free Electron Lasers (XFELs) and plasma wakefield accelerators. However, diagnostics for the electron beam current profile still face challenges with complex structure. In this letter, we propose a novel temporal retrieval algorithm for the coherent transition radiation (CTR) diagnostics of complex modulated electron beams. Starting from the time-frequency analysis of the electron bunch train, the algorithm separates and reconstructs the high- and low-frequency components. A temporal kernel was derived from the inverse sampling of the measured spectrum to construct the high-frequency component, while the low-frequency envelope was composed of several basis functions. Tested on the electron bunch trains from the complex multi-gaussian model and bunching-enhanced coherent harmonic generation, the algorithm successfully reconstructed the temporal signals and achieves better performance than the Kramers-Kronig method. This method is expected to crucial provide temporal evidence for potential electron beam modulation schemes, and will enable broad prospects for future applications.

Machine learning interatomic potentials (MLIPs) offer first-principles accuracy with reduced computational cost, but their transferability across different thermodynamic states remains questionable, particularly for fluid systems where molecules experience local environments far from crystalline equilibrium. Here, we demonstrate that diversifying the density of training configurations, rather than temperature, is the most effective strategy for building thermodynamically transferable MLIPs within a fixed computational budget. We first show that foundation MLIPs trained on solid-state databases accurately describe liquid-like densities but fail at gas-like conditions, while molecular-database-trained models exhibit the opposite behavior. Controlled from-scratch training and distillation experiments confirm that density-diverse datasets resolve both failure modes, whereas temperature-diverse datasets cannot compensate for missing density regimes. Coordination number analysis reveals the physical origin of this behavior: local coordination topology is more susceptible to density than temperature, leading to further structural diversity. These results establish density diversity as a design principle for thermodynamically transferable MLIPs and provide a validation framework for assessing the thermodynamic coverage of both foundation and from-scratch models, enabling reliable atomistic simulation of fluid-phase processes across diverse operating conditions.

The conversion rate (CVR) is a crucial metric for evaluating the effectiveness of platforms, as it quantifies the alignment of content with audience preferences. However, the limited nature of customers' conversion actions presents a significant challenge for training ranking models effectively. In this paper, we propose an Effective Knowledge Transfer method for Multi-task Recommendation Models (EKTM). This method enables the ranking model to learn from diverse user behaviors, thereby enhancing performance through the transfer of knowledge across distinct yet related tasks. Each specific CVR task can directly benefit from the insights provided by other tasks. To achieve this, we first introduce a router module that integrates and disseminates knowledge across tasks. Subsequently, each CVR task is equipped with a transmitter module that facilitates the transformation of knowledge from the router. Additionally, we propose an enhanced module to ensure that the transferred knowledge benefit the original task learning. Extensive experiments on several benchmark datasets demonstrate that our proposed method outperforms existing state-of-the-art approaches. Online A/B testing on a commercial platform has validated the effectiveness of the EKTM algorithm in large-scale industrial settings, resulting in a 3.93% uplift in effective Cost Per Mille (eCPM). The algorithm has since been fully deployed across two of the platform's main-traffic scenarios.

Oral cancer is a significant global health burden, and early detection remains a critical clinical need. Electrical impedance spectroscopy (EIS) offers a promising non-invasive approach for real-time tissue characterization, but classification frameworks that jointly leverage multiple impedance features for in vivo oral lesion discrimination remain underdeveloped. This paper presents a machine-learning (ML) pipeline to optimize classification of in vivo oral pathology from EIS data collected using a handheld, bedside device. Impedance measurements were acquired from 104 patients undergoing oral cancer resection or biopsy. Three classification tasks were evaluated: (1) healthy vs. cancer, (2) multi-class lesion-type discrimination (cancer, high-grade dysplasia, non-malignant), and (3) multi-class discrimination between the three lesion pathologies and healthy tissue. For each task, signal frequencies were independently ranked and reduced using PCA, and different current injection/voltage measurement (IIVV) pattern geometries were tested. Classification performance was assessed through leave-one-patient-group-out cross-validation to ensure robustness on unseen patients. Input data dimensionality was reduced by up to 99% across all tasks while improving diagnostic accuracy over baseline models trained on the full dataset. A logistic regression model achieved the highest binary classification accuracy of 80% with an AUC of 0.90, while multi-class scenarios maintained AUCs above 0.82. All top-performing models utilized the significantly reduced IIVV set as input. The proposed pipeline advances EIS-based cancer detection by providing a robust, computationally efficient, and clinically practical framework for early diagnosis of oral cancer lesions, with a methodology readily generalizable to other EIS devices and applications.

This paper introduces the $α$-Wasserstein mechanism for achieving Rényi Pufferfish Privacy using Laplace and Gaussian noise. By leveraging Hölder's inequality, we demonstrate that the scale parameter of the Laplace mechanism can be calibrated via an upper bound on the $W_α$ metric to satisfy $(α, ε)$-Rényi Pufferfish Privacy for $α\in (1, \infty]$. We show that at the limit $α= \infty$, this framework recovers the established $W_\infty$ mechanism for $ε$-pufferfish privacy. This result is subsequently extended to the exponential mechanism. Furthermore, we propose a $W_α$ mechanism for Gaussian noise for $α\in (1, \infty)$, demonstrating that it generalizes existing results within the Rényi Differential Privacy framework. Experimental evaluations reveal that our $α$-Wasserstein mechanism significantly reduces noise power compared to the conventional $W_\infty$-based approach, with the Gaussian mechanism providing superior utility over the Laplace mechanism. Notably, the mechanisms derived in this work achieve exact $(α, ε)$-Rényi Pufferfish Privacy without requiring additional relaxations, such as $δ$-approximations.

Single-photon sources that are bright, pure, and interference-ready are essential for quantum communication and photonic quantum information processing, but many solid-state platforms still rely on bulky optical excitation, careful alignment, and post-selection to achieve useful linewidth, stability, and brightness. Scalable quantum photonics instead requires turnkey quantum-light engines that can be triggered on demand, stabilized against environmental noise, and efficiently interfaced with fibers or photonic circuits. This review surveys recent progress in electronic and photonic integration of single quantum emitters in two-dimensional materials, focusing on localized excitonic emitters in transition metal dichalcogenides and defect-based color centers in hexagonal boron nitride. On the electronic side, we discuss electrical injection, fast modulation, electrostatic stabilization, and Stark tunability as routes to suppress blinking, spectral wandering, and charge-noise-induced broadening. On the photonic side, we review waveguide and resonator platforms that funnel emission into well-defined optical modes and, in some cases, enhance radiative rates through the Purcell effect. We connect these integration strategies to key source metrics, including single-photon purity, brightness, spectral stability, and photon indistinguishability. We conclude that the next stage of progress will depend on co-designed electronic and photonic architectures that jointly optimize on-demand operation, stabilization, tunability, and packaging-compatible optical interfacing.

We demonstrate a compact piezoelectric-driven micropipette launcher for localized in-vacuum delivery of nano- and microparticles into optical traps. The launcher has been integrated into multiple optical trapping setups, including a single-beam trap, a non-interfering dual beam trap, and a standing-wave dual beam trap, showcasing the versatility and ease of integration of the setup. Using the micropipette launcher, we have successfully trapped silica spheres of $170\text{ nm}$, $300\text{ nm}$, 3 $μ\text{m}$ diameter, as well as 6 $μ\text{m}\times$ 0.2 $μ\text{m}$ $β$-NaYF hexagonal prisms and $\sim 100$ nm diameter high-purity nanodiamonds. We characterize the performance of the device including the peak acceleration, angular distribution of emitted particles, and the dependence on vertical displacement between the pipette tip and optical trap. Trapping efficiency as high as 93\% is achieved.

Iridium-based photosensitizers have attracted significant attention in photodynamic therapy (PDT) due to their exceptional photophysical properties and chemical stability, as well as tunable phosphorescence emission spectrum and high triplet state production yields. Photosensitizers with large two-photon absorption (TPA) and mitochondrial targeting capabilities are particularly promising for clinical PDT, as they enable deeper tissue penetration and reduced damage to normal cells. In this study, we theoretically studied photophysical, photodynamic properties and photosensitization reaction mechanism of a series of iridium-based photosensitizers with modified C^N and N^N ligands (a2-a6, b1/b1-r and b2/b2-r) by TDDFT/DFT methods. The photophysical properties, including one- and two-photon absorption spectra, frontier molecular orbitals, and singlet and triplet excitation energies, were calculated. Additionally, rate constants for intersystem crossing, fluorescence, and phosphorescence, along with water solubility and lipophilicity metrics (logP), were determined to assess both efficacy and biocompatibility. The results elucidate the modulation roles of the chelated ligands and ancillary ligands in TP-PDT efficiency, indicating that the asymmetric iso-fused-benzene ring modification to the N^N ligand is a robust design strategy for comprehensively enhancing photosensitization performance. Complexes a2, b2 and b1-r show greater promise as candidates for two-photon PDT photosensitizers, owing to their large TPA cross-sections, extended triplet state lifetimes, and balanced water solubility and lipophilicity. Notably, the b1-r complex can undergo both Type I and Type II PDT photosensitization mechanisms, which will help address the issue of drug resistance arising from the hypoxic environment in deep-seated tumors.

Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework for analyzing spatial and temporal diversity in dynamical state estimation on product Lie groups, drawing structural parallels to diversity gains in space-time coding. Three main results are established: (i) coupling-based necessary and sufficient conditions for cross-factor observability, showing that a sensor local to one group factor renders another factor observable if and only if the dynamics propagate error directions across the corresponding Lie algebra components; (ii) a spatial diversity saturation theorem identifying precisely when additional observation channels fail to expand the propagated observation subspace and thus provide no structural benefit; and (iii) a time-space diversity decomposition that exactly separates instantaneous spatial information from accumulated temporal information in the estimation error covariance. The framework is applied to planar SE(2) and spatial SE(3) navigation, yielding exact observability guarantees for redundant and non redundant sensor architectures in modern robotics and autonomous vehicles. These results extend classical observability theory beyond Euclidean state spaces, exposing structural constraints invisible to standard rank-based analysis that fundamentally govern robust inference in coupled dynamical systems.

IY Lyr, historically misclassified as an eclipsing binary, is now established as a first-overtone RR Lyrae star (RRc star). Using multi-band photometry (ASAS-SN, ZTF, TESS, and our BVRI data), LAMOST spectroscopy, and Gaia astrometry, we investigate its pulsation, binarity, and Galactic population. From O-C analysis, we detect a long-term period decrease and a light-travel time effect with an orbital period of 3.94 years, eccentricity of 0.46, and a mass function of 0.65 M$_{\odot}$. The companion is independently confirmed by radial velocity residuals and Gaia proper motions. Combined constraints yield an orbital inclination of 94.8$^{\circ}$ and a companion mass of 1.37 M$_{\odot}$. Chemical abundances ([Fe/H] $\simeq$ -1.0, [$α$/Fe] $\simeq$ +0.27, Xiang et al. 2019) and dynamics ($L_{\rm z}$ $\simeq$ 1250 kpc km s$^{-1}$, $Z_{\rm max}$ $\simeq$ 1.31 kpc) identify IY Lyr as an old, high-$α$, thick-disk star. The companion mass lies at the peak of the neutron star mass distribution, and the system's age excludes a main-sequence star; we conclude the companion is most likely a typical neutron star, although a massive white dwarf near the Chandrasekhar limit cannot be ruled out. IY Lyr is among the few RRc binaries with a compact companion verified by multiple methods, and it has important implications for thick-disk binary evolution and neutron star formation.

A well-known theorem by Ruh and Vilms states that the Laplacian of the Gauss map for a smooth immersion into Euclidean space is given by the covariant derivative of the mean curvature vector field. For hypersurfaces, this implies that the Gauss map is harmonic iff the mean curvature is constant. In this paper, we extend this result to hypersurfaces in Weitzenböck geometry. While Riemannian geometry corresponds to the curved geometry without torsion, Weitzenböck geometry is a flat geometry with torsion. They represent two opposite extremes of Riemann-Cartan geometry.

The Hubble tension is usually expressed as a discrepancy between the low H_0 inferred from Planck CMB data within base \LambdaCDM and the higher value obtained from late-time distance-ladder measurements. This scalar comparison compresses distinct inference problems into one derived parameter: Planck CMB, DESI DR2 BAO, and Pantheon+SH0ES constrain physical densities and acoustic scales, ruler-normalized distances, and calibrated luminosity-distance relations, respectively. We reformulate the comparison in terms of the dimensionless expansion history E(z)=H(z)/H_0. This does not remove the absolute-scale discrepancy, but separates the normalization encoded in $H_0$ from the redshift-dependent shape of the expansion history. Within a common flat-\LambdaCDM framework, each probe posterior is mapped onto posterior-implied E(z) histories. Since the reconstructed values E(z_k) are strongly correlated across redshift, we quantify the global mismatch with a covariance-subspace history displacement S_{hist}, alongside pointwise redshift differences. The histories are not identical, but the discrepancies are moderate: the pointwise significance is typically 1-2σ, while S_{hist} simeq 1.65 for DESI DR2 and S_{hist} \simeq 2.55 for Pantheon+SH0ES relative to Planck. With two retained covariance eigenmodes, these correspond to two-sided one-dimensional Gaussian equivalents of approximately 1.1σand 2.1σ, both below the conventional \simeq 4.9σPlanck-SH0ES scalar-H_0 discrepancy.

Photonic flat bands offer significant potential for strong light-matter interactions, nonlinear optics, and sensing thanks to their localization of light and high density of states. However, realizing these flat bands typically requires intricate fabrication, perfect alignment and/or specialized geometries, and a general design strategy is missing. In this work, we demonstrate a simple yet versatile strategy to engineer radiative flat bands above the light line, using only a single-layer honeycomb photonic crystal slab. By applying a density wave like geometric perturbation-a spatially periodic displacement of the lattice air holes-we couple intrinsic flat band states from below the light cone into the radiative continuum. This structural modulation creates a highly anisotropic band structure that exhibits linear, Dirac-like dispersion in one direction and nearly flat dispersion in the orthogonal direction, forming an extended van Hove singularity at band extrema. Furthermore, by tuning the Fourier components of the modulation, we can manipulate the Dirac mass term to realize band inversion and switch between two topologically distinct phases. As an application, we demonstrate a Jackiw-Rebbi interface state positioned at the junction of two domains with opposite Dirac mass, that also shows flat band dispersion along the interface. This density-wave perturbation approach provides a conceptually clear and fabrication friendly platform for programming complex photonic band dispersions, opening new avenues for both topological photonics and practical flat-band optoelectronic devices.

Differential item functioning (DIF) arises alongside latent population heterogeneity in many applications, and both must be accounted for when assessing measurement invariance. In many practical settings, however, the comparison groups are unobserved and anchor items are unknown. A further challenge is that item response theory models traditionally assume symmetric link functions, yet empirical response processes may exhibit substantial asymmetry. This paper proposes a general framework for jointly analysing impact and DIF under asymmetric item response models. Unobserved group differences are represented by latent classes within a mixture item response model, while item-specific shifts capture DIF effects. Assuming the number of DIF items is relatively small, an $\ell_1$-regularised estimator is used to simultaneously identify the latent classes and select DIF items without requiring observed group labels or pre-specified anchor items. A simulation study evaluates recovery of impact, item parameters, and DIF effects across a range of configurations. The method is illustrated using two empirical applications from educational testing. In one dataset, the selected model reveals both impact and item-level DIF, whereas in the other, the results indicate substantial impact but little evidence of item-level DIF.

Previous work showed that ultralight-dark-matter solitons can provide dynamical friction for supermassive black-hole binaries, suppressing low-frequency power in the pulsar-timing-array gravitational-wave background and constraining the particle mass and effective ultralight-dark-matter fraction. Here we extend that analysis by comparing the predictive performance of four models: simplified and realistic ultralight-dark-matter implementations, a phenomenological environmental-hardening model, and a gravitational-wave-only model. We use Bayesian leave-one-out cross-validation on the five lowest pulsar-timing-array frequency bins. The phenomenological model gives the largest expected log predictive density, but its advantage over the other models is not large compared with the estimated standard errors. The current data therefore do not decisively prefer one model overall. The clearest pairwise result is within the ultralight-dark-matter framework: the simplified model outperforms the realistic implementation in all five frequency bins. Current pulsar-timing-array data are therefore compatible with ultralight-dark-matter-induced low-frequency suppression, but do not yet distinguish ultralight-dark-matter significantly from more generic environmental descriptions of supermassive-black-hole-binary evolution.

The extended affine Weyl group of a root system is the semidirect product of the corresponding Weyl group by its coweight lattice. The stabilizer subgroup of the extended affine Weyl group with respect to the corresponding fundamental alcove induces a subgroup of automorphisms of the extended Dynkin diagram. In this paper, we construct a finite root system by folding by the elements of the subgroup.

We introduce a scalable, translationally invariant variational theory for ab initio polarons that remains applicable across coupling regimes without resorting to supercells. Our approach combines a momentum-projected Toyozawa-type wavefunction with a low-rank factorization of the electron-phonon kernel, enabling near-linear scaling with the number of $\mathbf{k}$-points while capturing both delocalized and self-trapped carriers. Benchmarks for the Fröhlich model, LiF, and anatase and rutile TiO$_2$ yield accurate polaron binding energies, thermodynamic-limit band structures, and transparent real-space measures of polaron extent. For LiF, comparison with first-principles diagrammatic Monte Carlo (DiagMC) reveals close agreement for the weak-coupling electron-polaron ground state and band structure. However, in the hole-polaron of LiF, which is in the strong-coupling regime, we found a significant bias in DiagMC results. These results establish momentum-projected variational wavefunctions as a systematically improvable route to thermodynamic limit studies of polarons in real materials.

We present the first results from a program searching for extended Ly$α$ halos around high redshift ($ z \gtrsim 6.5$) quasars using the red channel of the Keck Cosmic Web Imager (KCWI). Our observations reveal a Ly$α$ halo extending to $\simeq11$ pkpc around the $z=6.64$ broad absorption line quasar J0910$-$0414. The Ly$α$ velocity field displays a rotation-like gradient, and the gas velocity dispersion is consistent with gravitationally dominated motion ($σ_{\mathrm{Lyα}}<300$ km s$^{-1}$). Comparison with the $[\mathrm{C\;II}]$ kinematics of the host galaxy core from ALMA observations shows that the Ly$α$-emitting gas extends over a much larger region, shows distinct kinematics, and has a smaller velocity dispersion ($σ_{\mathrm{Lyα}} \simeq 0.6σ_{\mathrm{[C\;II]}}$). The Ly$α$ spectral region of the quasar is largely obscured by a deep $\mathrm{N\;V}$ absorption trough, and as a result, roughly $55\%$ of the total Ly$α$ flux is from the extended halo. These observations demonstrate the potential of KCWI for probing the cool gas reservoir that fuels the growth of quasars and their hosts in the epoch of reionization.

The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing constant terms in their q-expansions. In this paper, we remove the assumption and establish the relationship between modular iterated integrals and multiple modular L-functions for general modular forms, including those with nonzero constant terms. We also provide a proof of a functional equation for modular iterated integrals, which is a specialization of a general result obtained by Brown [2]. This leads us to a generalization of the result of Choie-Ihara [3]. In the final part of the paper, we compute explicit examples of modular iterated integrals. These calculations essentially reproduce the explicit initial computations carried out by Brown [2], but they also serve to validate the broader framework developed in this work.

Polar brightening (PB) observed at microwave frequencies serves as an important probe to study the thermal and magnetic properties in the Sun's polar regions. Building on earlier studies that linked microwave PB to polar faculae, small-scale loops, and the polar coronal holes (PCHs), we present a comprehensive analysis of the long-term behaviour of 17 GHz microwave PB and its relation to polar magnetic field and coronal hole evolution. Using daily Nobeyama Radioheliograph observations spanning 1992 to 2018, we quantify microwave PB peak temperature variations and compare them with the temporal evolution of PCH area extracted from SDO/AIA-based SPoCA coronal hole catalogues during the period 2010-2018. We also examine the correspondence between microwave PB and the polar magnetic field to assess the nature of their association. Our results show a strong correlation between microwave PB peak temperature and PCH area, as well as with the polar magnetic-field strength. In addition, we found that regions of enhanced microwave emission are frequently associated with small-scale loop structures, consistent with Coronal Bright Points (CBPs), which are often associated with the eruption of jets. Overall, this study aims to investigate the impact of coronal holes, polar magnetic fields, and small-scale polar activity on polar brightening observed at 17 GHz and its long-term evolution.

In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{$\ast$} \end{equation} on a closed manifold $M$ with a non-identically vanishing discount factor $λ(x)$. There is a critical value $c_0\in[-\infty,\infty)$ such that \eqref{hjs1} admits a viscosity solution if $c>c_0$ and no solution if $c<c_0$. Inspired by the recent development [34] on the stability theory of viscosity solution, we show that the equation admits an asymptotically stable solution if and only if $c>c_0$. In this case, we determine the basin of the stable solution and investigate the long time behavior of the solution semigroup associated to \eqref{hjs1}. In particular, we relate the lowest convergence rate to the integral of $λ$ over Mather measures, which leads to an asymptotic behavior of Mather measures when $c$ goes to infinity. Assume $c\geqslant c_0$ and the equation admits a solution, we classify ergodic Mather measures and locate their distribution in the phase space.