Whether the flash state in electrically driven solids involves non-equilibrium defect production or is accounted for by Joule heating alone has been debated since 2010. Using positron annihilation spectroscopy on copper, we observe a fully reversible, electrically switchable vacancy population: the DBS S-parameter rises above baseline whenever applied current exceeds a critical density and returns on current removal. Positron lifetime spectroscopy independently confirms open-volume defect formation and reveals a void to cluster relaxation hierarchy. The current-induced vacancy concentration exceeds the thermal-equilibrium value at 352C by > 106x, is present only while current is applied, and vanishes within minutes. The nucleation rate scales steeply with the applied current, connecting the minute-scale kinetics resolved here to the sub-second flash events observed in ceramic sintering. These results demonstrate current-induced Frenkel-pair production in a metal and identify a defect-mediated, non-equilibrium contribution to the flash state.

Software Bills of Material (SBOMs) have emerged as an important technology for vulnerability management amid rising supply-chain attacks. They represent component relationships within a software product and support software composition analysis (SCA) by linking components to known vulnerabilities. However, the effectiveness of SBOM-based analysis depends on how accurately SBOMs represent component identities and actual dependencies in software. This paper studies two mismatch patterns: hidden code-level dependencies that are not represented as component-level dependencies, and component variants (clones) that cannot be identified consistently by scanners. We show that these mismatches can lead to inconsistent vulnerability reporting and inconsistent handling of VEX statements across popular SBOM-based vulnerability scanners. These results highlight limitations in current SBOM production and consumption and motivate richer dependency representation and component identity.

Training massive-scale deep learning models on datasets spanning tens of terabytes presents critical challenges in hardware utilization and training reproducibility. In this paper, we identify and resolve profound data-loading bottlenecks within distributed GPU training pipelines using the Petastorm data loader and Apache Parquet datasets. Through systematic profiling, we demonstrate that network I/O and CPU-bound data transformations (e.g., PyArrow to NumPy) constrain GPU utilization to as low as 10-15%. To address this, we propose an optimized architecture that features push-down worker-level transformations coupled with local-disk caching via Fanout-Cache, minimizing redundant I/O and CPU overhead across training epochs. Furthermore, we eliminate race conditions in multi-worker shared queues by implementing dedicated round-robin ventilator and result queues, alongside modernized RNG handling, achieving strict deterministic data loading. Our optimizations yield a 6x speedup, reducing end-to-end training time from 22 hours to 3 hours, increasing GPU utilization to over 60%, and drastically reducing run-to-run variance, enabling robust, high-throughput, and reproducible large-scale model training.

Quantum state tomography (QST) scales exponentially in both measurement and computational cost, making full reconstruction impractical for multi-qubit systems. Existing approaches attempt to reduce this complexity, but do not explicitly restrict the operator space based on physically relevant correlations. We develop a structured QST framework in which the density matrix is reconstructed using a restricted set of observables in a Gibbs representation. The Structured Gibbs Quantum State Tomography (SG-QST) is built by progressively including local, nearest-neighbor, and global correlations. Benchmarking on three, four, and five-qubit. GHZ states shows that comparable fidelity can be achieved with significantly fewer parameters by restricting the operator space to physically relevant observables. These results demonstrate that physically motivated operator-space restriction enables efficient and interpretable quantum state reconstruction.

Toroidal vortices in fluid and gas dynamics underpin a broad spectrum of scientific and technological fields, from elementary particle physics to condensed matter systems, and have recently garnered significant attention in optics because of their inherent topological stability. Here we report the experimental observation of toroidal vortices in stochastic optical wavefields with partial coherence, termed coherence toroidal vortices, which eliminates deterministic topological signatures in conventional optical degrees of freedom while unveiling statistically hidden correlation topologies. These underlying topologies-including both fundamental and higher-order hopfionic textures-emerge exclusively in second-order field correlations and are accessible only through statistical measurements. We further examine the impact of chaotic channels on the stability of these statistically veiled correlation topologies, demonstrating that their topological invariants remain robust under realistic environmental perturbations. These findings are experimentally validated and offer novel insights into the potential of toroidal light vortices serving as controllable channels for directional energy and information transfer within complex media.

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed by anomalous diffusion while the fractional wave equation describes oscillations and wave propagation in various physical systems. In order to obtain exact invariant solutions of these equations, we firstly determine infinitesimal symmetries with respect to the variable coefficients of the equations. With the help of these symmetries, we then find solutions in terms of Mittag-Leffler functions, generalized Wright functions and Fox H-functions.

There has been intensive research on increasing the utility and performance of Parameterized Quantum Circuits (PQCs) in the past couple of years. Owing to this research, there are now several inductive biases available to a quantum algorithms researchers to design a good circuit for their chosen task. In this paper, we focus on the problem of finding performant initial parameters for a given PQC. Different from previous research that focuses on finding the right \emph{distribution}, we focus on finding the \emph{hyperparameters} for any given distribution. To that end we introduce an evolutionary-search based algorithm that finds optimal hyperparameter given a PQC and quantum task. Our empirical results indicate that our algorithm consistently leads to selection of performant initial parameters tuned specifically to the ansatz and the quantum task leading to faster convergence and performance. More importantly, our algorithm does not \emph{negatively} affect the barren plateau phenomenon. In other words, the initial parameters suggested by algorithm do not worsen the gradient variance scaling for a given initializing distribution.

This paper presents ECCFROG522PP, a 522-bit prime-field elliptic curve in short Weierstrass form, designed with a focus on deterministic generation and public reproducibility. The central design principle is that all critical parameters are derived from a fixed public seed through a transparent and verifiable procedure. While many deployed systems rely on NIST P-256 and secp256k1, which target approximately 128-bit classical security, higher security applications typically consider curves such as NIST P-521, Curve448, and Brainpool P512. ECCFROG522PP is intended for the same general classical security range as P-521, with emphasis on transparency, auditability, and reproducibility rather than performance optimization. The curve parameters are generated through a BLAKE3-based deterministic pipeline with publicly specified indices. The resulting construction has prime order, cofactor one, and a deterministically derived base point of full order. The quadratic twist has a large proven prime factor, and the construction includes a documented lower bound on the embedding degree together with standard sanity checks against low embedding degree reductions and basic CM discriminant anomalies. The full generation and validation procedure can be reproduced end to end from public artifacts and reference scripts, enabling independent verification of all parameters and checks.

This paper proposes a scalable coordination framework with aggregator-side privacy protection for storage-like distributed energy resources (DERs). The framework adopts a two-layer architecture. At the macroscopic layer, building upon an \emph{Eulerian} modeling perspective, the DER population is represented as a continuum whose density evolution is governed by a partial differential equation (PDE), such that the computational complexity is independent of the population size. To address the bilinear non-convexity in this PDE-constrained optimization problem, we develop a convexification method that combines finite-volume discretization with a flux-lifting technique, reformulating the macroscopic problem into a sparse linear program (LP). The LP solution yields a unified, state-dependent broadcast signal for population coordination. Furthermore, a Wasserstein-based relaxation is introduced to replace rigid cyclic constraints and provide additional operational flexibility for improved economic performance. At the microscopic layer, individual resources autonomously recover local setpoints from the broadcast signal and their local states, while an upstream data-mixing protocol aggregates individual states into a macroscopic density histogram without exposing raw individual states to the aggregator. Numerical studies validate the scalability, feasibility, and economic effectiveness of the proposed framework.

Survey data are widely used to study how income inequality, poverty, and welfare evolve over time. A common practice is to estimate the income distribution separately for each year, treating annual observations as independent cross-sections. For population subgroups with relatively small sample sizes, however, this approach can produce unstable parameter estimates, imprecise inference for inequality and poverty measures, and potentially misleading posterior probabilities of Lorenz and stochastic dominance. This paper develops flexible Bayesian models for time-varying income distributions that borrow strength across adjacent years by allowing the parameters of income distributions to evolve dynamically. We consider a random walk specification and an extended model with shrinkage priors. The proposed framework yields coherent inference for the full income distributions over time, as well as for associated inequality measures, poverty indices, and dominance probabilities. Simulation studies show that, relative to independent year-by-year models, the proposed approach produces substantially more precise and stable inference, while avoiding spurious variation in welfare comparisons. An application to the Aboriginal and residents of the Australian Capital Territory (ACT) population subgroups in the Household, Income and Labour Dynamics in Australia survey shows that the dynamic models deliver improved inference for income distributions and related welfare measures, and can change conclusions about distributional dominance over time.

A new excited charm-strange meson is observed through an amplitude analysis of the full phase space of $B^0\to D^+ D^- K^+ π^-$ decays. The analysis is based on a proton-proton collision data sample collected by the \lhcb experiment at a center-of-mass energy $\sqrt{s} = 13\,\text{TeV}$, corresponding to an integrated luminosity of $5.4\text{fb}^{-1}$. The statistical significance of the new state exceeds $10$ standard deviations. Its Breit--Wigner mass and width are measured to be $m_0 = {2933}^{+6}_{-5}(\text{stat})^{+4}_{-3}(\text{syst}) \,\text{MeV} $ and $Γ_0 = {72}^{+18}_{-12}(\text{stat})^{+\phantom{0}7}_{-10}(\text{syst}) \,\text{MeV} $, respectively, and its spin-parity quantum numbers are determined to be $J^P = 1^+$. This new meson, denoted as $D_{s1}(2933)^+$, is a candidate for a $D_s(2P^{(\prime)}_{1})^+$ state.

Additive manufacturing and welding processes are highly sensitive to heat dissipation, where improper thermal management leads to residual stresses, distortions, and cracking. Existing heat transfer models, such as Rosenthal's solutions, fail to handle finite 3D geometries, cooling effects, or transient behavior, limiting their accuracy. We overcome these limitations by developing an analytical framework that incorporates cooling boundary conditions mimicking Newton's Law of Cooling. Using two different and proven-equivalent approaches, Laplace transform and Fourier series, we derive closed-form solutions for transient and steady-state temperature profiles under various heat sources, including Gaussian, ellipsoidal, double-ellipsoidal, and time-dependent on/off switch sources. We compare our analytical solutions to numerical implementations, demonstrating strong agreement while providing deeper physical insight. This approach significantly reduces computational cost and experimental requirements, making it a scalable tool for optimizing thermal predictions and mitigating residual stresses in metal-based manufacturing. Additionally, our framework enables the generation of synthetic datasets for machine learning models to predict heat distribution efficiently.

The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point or a terminal node, and with the placements minimising the sum of all the edge lengths of the associated tree. We consider a problem in which we start with a known solution to a Steiner tree problem, and the terminal positions are then perturbed. A first-order approximation theorem is established for efficiently updating the Steiner point positions to recover a Steiner tree solution after the perturbations to terminal nodes. Numerical examples illustrate the effectiveness of our approach (including a stepwise application for large perturbations) as well as its limitations.

The pursuit of compact, programmable light sources with high coherence and spectral purity hinges on establishing a precise set of phase relationships in light-matter interactions. Here, we demonstrate that the quadratic dispersion of freely propagating electron wavepacket serves as a programmable quantum medium. Prepared in a coherent momentum-state ladder via a single laser interaction, the electron subsequently undergoes deterministic phase evolution during free propagation-an intrinsic process that compiles its quantum state into two distinct emission channels. This mechanism, quantified by a quantum bunching factor, enables: (i) Talbot-resonant bunching, where the electron density self-structures into sub-cycle combs with tunable harmonic selectivity, and (ii) coherent phase transfer of the programmed quadratic phase to light, generating nonclassical photon states such as multi-component Schrodinger cat states via measurement-conditioned interaction. This quadratic-phase programming establishes a versatile platform for on-demand quantum state synthesis, bridging beam engineering with electron wavefunction shaping for compact quantum light sources, coherent radiation control, and scalable quantum information processing.

Impacts of octupole correlations on the low-lying $0^+$ states and two-neutron transfer intensities in rare-earth nuclei are investigated in terms of the interacting boson model that is based on the nuclear density functional theory. The octupole degrees of freedom are not only essential building blocks to describe properties of negative-parity states in the model, but also influence low-spin positive-parity states including excited $0^+$ states. The calculation produces a large number of low-energy $0^+$ states that contain significant amounts of octupole components, indicating important roles played by the octupole degrees freedom in this mass region. Octupole correlations are shown to make sizable contributions to the $(p,t)$ and $(t,p)$ transfer intensities and, in particular, to reproduce the discontinuous changes of these quantities near those nuclei with $N\approx88$ or 90, which are observed experimentally as a signature of the shape phase transition.

The impacts of the mass imbalance and Coulomb interaction on the complex phase structures of the polaritonic condensates and their Bardeen-Cooper-Schrieffer (BCS)--Bose-Einstein condensation (BEC) crossover in semiconductor and semimetal microcavities are investigated. In the framework of the unrestricted Hartree-Fock approximation, a two-band electron-hole model involving photon mode is analyzed by treating Coulomb attraction and light-matter coupling on equal footing. The single-particle spectral functions and the luminescence properties are then examined. In the semiconducting regime, a positive band gap stabilizes tightly bound excitons and yields predominantly BEC-type excitoniclike polaritonic condensates at low density, while increasing excitation density and reducing mass imbalance drives a continuous crossover toward BCS-type pairing with intermediate and photoniclike polaritonic character. In contrast, the semimetallic regime favors itinerant electron-hole pairing, with BCS-type condensates dominating and BEC excitoniclike coherence emerging only at sufficiently strong Coulomb interaction and large mass imbalance situations. The evolution of luminescence spectra provides clear spectroscopic signatures of these crossover phenomena, offering a unified framework for understanding and controlling polaritonic condensates in microcavity systems.

Elasto-inertial turbulence (EIT) is primarily driven by polymer elasticity, yet the modulating role of fluid inertia is non-negligible and remains largely unexplored. To investigate the effect of inertia, we perform direct numerical simulations of two-dimensional EIT in channel flow over a wide range of Reynolds numbers ($Re$). We show that increasing inertia promotes both the enhancement of dynamic amplitudes and the wallward migration of core structures. Specifically, inertia intensifies the turbulent fluctuations, facilitates the fragmentation of large-scale structures, and amplifies statistical quantities such as the root-mean-square of velocity fluctuations and polymer extension. The peak location of nonlinear elastic shear stress follows a scaling law $y^+ \propto Re_τ^{1/2}$, closely resembling that of Reynolds shear stress in Newtonian turbulence, indicating a change of the momentum transfer mechanism. Meanwhile, the peak location of energy conversion between elastic and turbulent kinetic energies exhibits a $y^+ \propto Re_τ^{0.1}$ scaling law migration, remaining mostly confined to the near-wall region. Remarkably, despite the inertial modulation, the probability density functions (PDFs) of velocity and elastic stress fluctuations extracted at the energy-conversion peak collapse convincingly over the range of $Re$ investigated. This reveals a robust statistical self-similarity across a wide range of inertia magnitude. Furthermore, the PDFs of wall-normal velocity and elastic stress fluctuations exhibit pronounced exponential heavy tails.

Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on the blow-up of projective space along the embedded surface. This can be thought of as a weak analogy of Saint-Donat's Theorem on the generators of the ideal of a curve embedded by an adjoint linear series. Next, Reider-type inequalities give a sharp estimate for the ample cone of the Hilbert schemes of length d subschemes of the surface. The proofs consist of (a) finding a natural family of objects parametrized by the base (either the blow-up along the surface or the Hilbert scheme) and (b) finding the largest chamber in the stability manifold of the surface where the objects in the family are all Bridgeland semistable. A Theorem of Bayer-Macri then gives nefness of the determinant line bundle on the base of the family.

Superradiant instability of ultralight bosons can produce clouds around rotating black holes, whose continuous gravitational wave (GW) emission is a promising observational target. Precise predictions of the signal frequency and its evolution are essential for detecting such continuous GWs. For axions, self-interactions can populate multiple superradiant modes via nonlinear couplings, and GW emission can occur through various channels. To calculate the frequency shifts of GWs emitted through these channels, we employ relativistic perturbation theory based on a bilinear form. We apply this framework to self-interaction effects for the first time, and also revisit the treatment of the self-gravity contribution. Our results provide a simple and unified framework for calculating frequency shifts, including cases in which multiple modes are excited, and are relevant for next-generation GW observations.

We study the late-time evolution of an anisotropic Bianchi-I universe with radiation in the framework of asymptotically safe gravity. We first discuss the radiation-dominated universe for the perfect fluid with the equation of state $p=ρ/3$, and find that the classical evolution involves logarithmic terms, which lead to a slow approach toward isotropy. The quantum effects introduce subleading corrections that soften the anisotropy in the intermediate stage. Next we discuss the universe with magnetic fields. For a vanishing classical cosmological constant, we find that the universe in general evolves toward a Kasner-type regime with persistent anisotropy while the expansion rate is enhanced by quantum effects, leading to a faster decay of the magnetic field. In contrast, for a nonzero classical cosmological constant, the late-time dynamics are dominated by the cosmological constant, and the universe asymptotically approaches an isotropic de Sitter phase with exponential decay of both anisotropies and the magnetic field. Finally, we employ Hodge duality to demonstrate that these cosmological findings apply equally to environments dominated by electric fields.

We demonstrate, for the first time to our knowledge, ultra-low-noise supercontinuum (SC) generation in normal-dispersion fluoride fibres pumped by femtosecond (fs) pulses. We have investigated two elliptical-core polarisation-maintaining (PM) ZBLAN fibres with core dimensions 6.7$\times$2.7 $μ$m and 8.9$\times$4.1 $μ$m, experimentally measured to have normal dispersion up to 3.77 $μ$m and 3.25 $μ$m, respectively; the smaller-core fibre yields ultra-low-noise SC spanning 1.537-2.196 $μ$m with a minimum relative-intensity noise (RIN) of 0.22% at 1.7 $μ$m, and the larger-core fibre yields 1.507-2.250 $μ$m with 0.36% at 2.0 $μ$m. To aid the generation of low-noise SC, we developed an all-PM thulium chirped-pulse amplifier delivering 58 fs pulses at 1.85 $μ$m, 210 mW average power at 40 MHz, with 0.41% RIN, seeded by a part of an ultra-low-noise SC using a 1.55 $μ$m fs laser and an all-normal-dispersion (ANDi) silica fibre for precise seed control. These results establish a robust, alignment-free pathway to extend ultra-low-noise ANDi-fibre SC towards the mid-infrared using PM fluoride fibres.

We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by grid-following (GFL) IBRs. The linearizability and time invariance of the framework enables us to perform eigen decomposition, which is a powerful tool for root-cause analysis of the SSO modes and damping controller design. The same framework also enables analysis of excitation of the SSO modes in presence of data center (DC) loads. The GFL IBRs are modeled in their respective $dq$-frame DPs and the detailed model of synchronous generators (SGs) along with dynamic transmission network models are represented in $pnz$-frame DPs. Several case studies are performed on the modified IEEE two-area benchmark system, where $2$ SGs are replaced by GFL IBRs and validated with EMTDC/PSCAD simulations. First, time- and frequency-domain analyses of the SSO mode are presented followed by the design of a robust decentralized $\mathcal{H}_\infty$ damping controller based on local signals of the GFL IBRs. Second, the dynamic behavior of the system following an unbalanced fault is demonstrated that is damped by the proposed damping controller. Finally, excitation of the SSO mode in presence of DC load is exhibited and its locational impact is analytically quantified.

Fast qubit reset is essential for qubit reuse in the noisy intermediate-scale quantum computing era, yet it conflicts with the weak decoherence required for high-fidelity computation. We solve the time-optimal reset problem for a frequency-tunable qubit coupled to a structural environment under realistic spectral and control constraints. The optimal strategy consists of a switch--restore--switch sequence, where the qubit is moved from a low-decoherence computational configuration to a high-decoherence restoring configuration and then returned for reuse. For superconducting qubits in four representative environments, this strategy reduces the reset time from typically $\gtrsim\SI{100}{\nano\second}$ to $\SI{20}{\nano\second}$, about $40\%$ of a typical two-qubit gate time, while achieving a reset precision of $10^{-5}$. Our results identify environmental spectral structure as a practical resource for rapid, high-fidelity qubit reset and provide a design principle for qubit reuse on qubit-limited processors.

We record a Lean-certified theorem package for the four-point Heil--Ramanathan--Topiwala configuration \[ Λ=\{0,a,b,ν\}\subset \R^2, \qquad \Lzero=\Z a+\Z b, \qquad ν=r a+s b, \] with $a$ and $b$ linearly independent. The principal certified theorem states that if $|\symp(a,b)|>1$ and $1,r,s$ are linearly independent over $\Q$, then for every nonzero $f\in L^2(\R)$ the four vectors \[ f,\qquad π(a)f,\qquad π(b)f,\qquad π(ν)f \] are linearly independent. A second certified theorem treats the rational-coordinate case $r,s\in \Q$, where the configuration lies in a finer full-rank lattice and linear independence follows from Linnell's theorem. The paper is written in standard mathematical prose. An appendix records the precise Lean certification ledger and the explicit analytic inputs used by the formal development and a download link is provided.

This paper establishes a ${C^{n,\varepsilon }}$-smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior can be completely determined by explicit smooth first-order ODEs. We first devise a new framework for an abstract equation with two nonlinear terms, where one preserves regularity and the other reduces regularity, and derive sufficient conditions for constructing the ${C^{n,\varepsilon}}$-smooth extension of the IM by treating these two nonlinear terms separately.

The electron velocity-electric field characteristics in short channel length (50-100 nm) amorphous oxide field-effect transistors (FETs) are described using measured experimental data from indium gallium zinc oxide (IGZO) FETs in conjunction with a physics-based model. Such understanding is crucial for the design of FETs for emerging applications such as in back-end-of-line circuitry for advanced memories and artificial intelligence hardware. In such semiconductor systems, there is an interplay between trapping and extended state (band) transport that has to be considered in detail for a more complete physical understanding of device operation. The approach described in this paper demonstrates such a method and its use for an exemplary semiconductor IGZO. It can be used in many emerging thin-film semiconductors, including several amorphous oxide semiconductors. The carrier mobility is calculated for dominant scattering mechanisms such as trapped carrier scattering and optical phonon scattering. The carrier velocity is computed from the mobility using a modified Caughey-Thomas equation. The physical model considers contact resistance, Joule heating, and electric-field-induced carrier heating, all of which are very important in small geometry FETs. The carrier velocity exhibits a tendency to saturate at high electric fields and reaches values > 2*10^6 cm/s when averaged over all induced carriers (both trapped and in the band) and > 4*10^6 cm/s for carriers in the band.

We investigate whether the observed radio-infrared-$γ$-ray correlation in star-forming galaxies is a geometric effect rather than a signature of local cosmic-ray (CR) calorimetry. Using the GALPROP framework, we generate synthetic observations for external viewers from a grid of 3D Milky Way models with varied CR source, gas, interstellar radiation, and magnetic field distributions, all normalised to reproduce local CR data. We find that a tight, quasi-linear correlation arises naturally from line-of-sight integration through the extended, radially-structured disc, even when local calorimetry is absent. The correlation's properties depend strongly on viewing geometry, preserving its form under moderate inclination but breaking down in edge-on views where galactic components are stratified. We conclude that the correlation is primarily an emergent property of geometric projection, not local physics. This implies that its scatter is likely not random noise but a diagnostic of underlying galactic structure and viewing angle.

Patterned-transducer thermoreflectance enhances sensitivity to low-thermal-conductivity materials by suppressing lateral heat spreading in the metal transducer, but its wider use is limited by the cost of repeated high-fidelity forward evaluations in iterative fitting. Here, we develop a transfer-learning-enhanced POD-FNN surrogate for rapid phase prediction in patterned-transducer thermoreflectance, using patterned FDTR as a representative case. A validated COMSOL model is first constructed, and proper orthogonal decomposition is applied directly to the phase signals to build a compact reduced-order representation. A feedforward neural network is then trained to predict the POD coefficients from thermophysical and geometric parameters. Within the original parameter domain, the surrogate achieves mean and median RMSE values of 0.19 and 0.17 degrees, with a maximum RMSE below 0.47 degrees, while reducing the average prediction time per signal from 5.39 s to 0.01 s (about 534x). In inverse analysis, the fitting time for a representative case is reduced from about 18950 s to about 65 s with comparable accuracy. The framework is further applied to measured Al/SiO2 samples, yielding stable silica thermal conductivities of 1.44 +/- 0.088, 1.43 +/- 0.093, and 1.50 +/- 0.079 W/(m K) for conventional FDTR and patterned FDTR with pattern radii of 5.3 and 3.25 um, respectively. Transfer learning further improves performance in expanded parameter domains, with the TL-FR strategy giving the best overall results. Reducing the additional target-domain dataset from 6000 to 1000 samples also lowers the high-fidelity data-generation time from about 34179 s to about 5885 s. The proposed framework provides an accurate and efficient route for repeated forward evaluation, rapid inverse fitting, and cost-effective model updating in patterned thermoreflectance workflows.

We obtain exact expressions for various factors involved in the Hadamard form of the retarded Green function for the (Bardeen-Press-)Teukolsky equation on Schwarzschild spacetime. We use these to improve on previous results for the calculation of this Green function. We work in a spacetime $\mathcal{M}_2\times\mathbb{S}^2$ conformal to Schwarzschild, in which the metric takes a direct product form. This allows us to derive a separable form for the direct (i.e., singular) part of the Hadamard form of the retarded Green function. The angular factor in this quantity is calculated explicitly. This shows an interesting interplay between geodesics of $\mathbb{S}^2$, spin-weighted spherical harmonics, and Euler angles. The $\mathcal{M}_2$ factor equates to a spin-dependent factor that satisfies a transport equation along geodesics, times the square root of the van Vleck determinant. Both terms are calculated in an exact form for constant radius orbits (which includes the cases of circular timelike geodesics and static worldlines of Schwarzschild spacetime). This separable form also allows us to obtain the multipolar $\ell$-modes of the direct part for electromagnetic and gravitational field perturbations. We then use these $\ell$-modes to calculate, in the gravitational case, the retarded Green function minus its direct part: this is a better representation in practise of the retarded Green function for points near coincidence.

Models predict that chemical enrichment and gas redistribution should proceed rapidly once star formation begins, yet direct observational constraints at the earliest cosmic epochs have been scarce. Here we present evidence that metal-enriched gas in multiple ionic phases was already present around galaxies before the midpoint of cosmic reionization. Using JWST/NIRSpec rest-frame ultraviolet spectroscopy of three galaxies at redshifts $z=7.2-9.3$, we detect blueshifted metal absorption in all three systems; across the sample, the detected transitions span neutral, low-ionization, and high-ionization species, including O I, Si II, C II, Si IV, and C IV. These absorption features show velocity offsets of order $|Δv| \sim 50$--$250\,\mathrm{km\,s^{-1}}$, predominantly blueshifted relative to the systemic redshifts of the host galaxies derived from nebular emission lines. This ionic coexistence within a broadly shared velocity structure, together with the observed equivalent-width ratios, is consistent with outflowing or otherwise kinematically disturbed galaxy-associated gas, similar to that seen at lower redshift. The observations therefore indicate that metal-enriched gas associated with galaxies was already kinematically disturbed at very early times, requiring rapid metal production in the early generations of stars. These results show that key conditions for baryon cycling were established in at least a subset of luminous galaxies within the first several hundred million years of cosmic time, well before the completion of reionization.