In this paper we include kinematic power corrections up to twist-four to the deeply virtual Compton scattering dispersion relation. We demonstrate that, both for (pseudo-)scalar and spin-$1/2$ targets, the formal expression of the $n$-subtracted leading-twist dispersion relations is preserved. However, the expression of the subtracted constants is modified by the kinematic powers. Importantly, the minimal-subtracted dispersion relation for the helicity-conserving amplitude, previously thought to depend only on the Polyakov-Weiss $D$-term, now also depends on the double distributions $F$ and $K$. These results are consistent with the ones obtained previously in the literature. Such a mixing may be critical for the Jefferson Lab kinematic range, as it is not suppressed for typical values of $t$ and $Q^{2}$ in the valence region. We therefore expect a strong impact on attempts to extract pressure forces from DVCS data.

Dislocations control the mechanical behavior of crystalline materials, yet their quantitative characterization in bulk has remained elusive. Transmission Electron Microscopy provides atomic-scale resolution but is restricted to thin foils, limiting relevance to structural performance. Dark-field X-ray microscopy (DFXM) has recently opened access to three-dimensional, non-destructive imaging of dislocations in macroscopic crystals. A critical bottleneck, however, is the reliable identification of weak- versus strong-beam conditions. Weak-beam imaging enhances dislocation contrast, while strong-beam conditions are dominated by multiple scattering and obscure interpretation. Current practice depends on manual classification by specialists, which is subjective, slow, and incompatible with the scale of modern experiments. Here, we introduce a deep learning framework that automates this task using a lightweight convolutional neural network trained on small, hand-labeled datasets. By enabling robust, rapid, and scalable identification of imaging conditions, this approach supports scalable DFXM analysis, unlocking statistically significant studies of dislocation dynamics in bulk material

Dependencies between modules can trigger ripple effects when changes are made, making maintenance complex and costly, so minimizing these dependencies is crucial. Consequently, understanding what drives dependencies is important. One potential factor is code smells, which are symptoms in code that indicate design issues and reduce code quality. When multiple code smells interact through static dependencies, their combined impact on quality can be even more severe. While individual code smells have been widely studied, the influence of their interactions remains underexplored. In this study, we aim to investigate whether and how the distribution of static dependencies changes in the presence of code smell interactions. We conducted a dependency analysis on 116 open-source Java systems to quantify these interactions by comparing cases where code smell interactions exist and where they do not. Our results suggest that overall, code smell interactions are linked to a significant increase in total dependencies in 28 out of 36 cases, and that all code smells are associated with a consistent change direction (increase or decrease) in certain dependency types when interacting with other code smells. Consequently, this information can be used to support more accurate code smell detection and prioritization, as well as to develop more effective refactoring strategies.

Lensed quasars are powerful probes of cosmology, the co-evolution of supermassive black holes and their host galaxies, and the distribution of dark matter. We cross-match 1,724 previously identified candidates from KiDS, HSC, and the DESI Legacy Imaging Surveys (DESI-LS) with DESI DR1, obtaining 937 DESI spectra for 677 unique systems. Combining DESI spectroscopy with observations from the Palomar 200-inch Double Spectrograph (P200/DBSP), we confirm two lensed quasars with source redshifts $z_s={1.93,3.23}$ and Einstein radii $θ_{\rm E}={0.39,1.07}$ arcsec, respectively. We further identify 12 likely lensed quasars that are well reproduced by a simple SIE model, exhibit lens galaxies in the image modeling, and have at least one available spectrum; across these, $θ_{\rm E}$ spans $045$-$2.34$ arcsec and $z_s$ spans $1.13$-$2.88$. In 9 of the 12 cases, the systems already satisfy our lensing criteria except that only one quasar image currently has a spectrum; obtaining a second spectrum for the other image would enable immediate confirmation. Moreover, we report eight new static strong lenses spanning galaxy- to group- scale lenses. These results provide valuable targets for follow-up studies and underscore the efficiency of wide-field spectroscopic surveys such as DESI in confirming gravitationally lensed quasars and galaxies.

In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient time. In this paper, we focus on the case of Boolean networks. We define a reduced graph on the dominant vertices and an induced dynamics on this graph, which we prove is asymptotically equivalent to the original Boolean dynamics. Asymptotic conjugacy ensures that the systems, restricted to their respective attractors, are dynamically equivalent. For a significant class of networks, the induced dynamics is indeed a reduction of the original system. In these cases, the reduction, which is obtained from the structure of dominant vertices, supplies a more tractable system with the same structure of attractors as the original one. Furthermore, the structure of the induced system allows us to establish bounds on the number and period of the attractors, as well as on the reduction of the basin's sizes and transient lengths. We illustrate this reduction by considering a class of networks, which we call clover networks, whose dominant set is a singleton. To get insight into the structure of the basins of attraction of Boolean networks with a single dominant vertex, we complement this work with a numerical exploration of the behavior of a parametrized ensemble of systems of this kind.

The problem of constrained stabilization on the n-sphere under star-shaped constraints is considered. We propose a control strategy that allows to almost globally steer the state to a desired location while avoiding star-shaped constraints on the n-sphere. Depending on the state's proximity to the unsafe regions, the state is either guided towards the target location along the geodesic connecting the target to the state or steered towards the antipode of a predefined point lying in the interior of the nearest unsafe region. We prove that the target location is almost globally asymptotically stable under the proposed continuous, time-invariant feedback control law. Nontrivial simulation results on the 2-sphere and the 3-sphere demonstrate the effectiveness of the theoretical results.

This paper introduces a reinforcement learning framework that employs Proximal Policy Optimization (PPO) to dynamically optimize the weights of multiple large language model (LLM)-generated formulaic alphas for stock trading strategies. Formulaic alphas are mathematically defined trading signals derived from price, volume, sentiment, and other data. Although recent studies have shown that LLMs can generate diverse and effective alphas, a critical challenge lies in how to adaptively integrate them under varying market conditions. To address this gap, we leverage a DeepSeek model to generate fifty alphas for ten stocks, and then use PPO to adjust their weights in real time. Experimental results indicate that the PPO-optimized strategy does not consistently deliver the highest cumulative returns across all stocks, but it achieves comparatively higher Sharpe ratios and smaller maximum drawdowns in most cases. When compared with baseline strategies, including equal-weighted, buy-and-hold, random entry/exit, and momentum approaches, PPO demonstrates more stable risk-adjusted performance. The findings highlight the importance of reinforcement learning in the allocation of alpha weights and show the potential of combining LLM-generated signals with adaptive optimization for robust financial forecasting and trading.

In the framework of quasi-topological (QT) gravity, we propose a novel model which is characterized by a bounce of the spacetime such that the singularity in standard general relativity can be avoided in both cosmological and black hole setups. Specifically, in the cosmological background, this model reproduces the modified Friedmann equation proposed in loop quantum cosmology, while in a black hole background, it produces a black bounce metric identical to that of the quantum Oppenheimer-Snyder (qOS) model. This model resolves the singularity presented in the qOS model as well as in QT gravity coupled to linear electromagnetic fields, and provides a unified, manifestly covariant framework for general spacetimes, from which both the modified Friedmann equation and the qOS black hole metric can be derived. Furthermore, it establishes a profound correspondence between the effective dynamics of loop quantum cosmology and the QT gravity theory, suggesting that certain quantum gravitational effects in loop quantum gravity can be captured by adding an infinite tower of higher-curvature corrections to the Einstein-Hilbert action.

The ultrarelativistic collisions of heavy ions provide rich spectrum of possibilities to discuss the response of the nucleus to photons. Newly published neutron and proton multiplicities measured in the ALICE experiment in ultraperipheral collisions allow investigating the influence of the electromagnetic fields on colliding nuclei for the $^{208}$Pb+$^{208}$Pb at $\sqrt{s_{NN}}$=5.02~TeV. The theoretical predictions are done within hybrid model including equivalent photon approximations (EPA), GiBUU modeling of pre-equilibrium processes and generation of the exited nuclear remnants, which decay is modeled by statistical approach: GEM2 or GEMINI++. The cross-sections of the mass-charge distributions of nuclear remnants as well as the neutron, proton and other charged particle multiplicities are estimated. We concentrate on production of protons and isotopes coming from the electromagnetic dissociation. Special attention is devoted to emission of a single proton. The cross section for $1p$ emission is very close to maximal available one based on reactions of photon with individual nucleons. Our pre-equilibrium processes explain simultaneously the tail of neutron energy distributions in the nuclear rest frame observed in $γ+ A$ collisions.

Alternative theories of quantum statistics provide an avenue for exploring novel physics beyond bosons and fermions, yet experimental verification of their existence in nature proves a challenging task. Among these theories, it has recently been suggested that $R$-parastatistics can be realized as quasiparticle excitations in many-body systems. In this paper, we build on this idea by showing that signatures of $R$-parastatistics can be observed as flavor-charge separation in 1D systems. We consider a generalized version of the Luttinger model and show that bosonization persists when the $R$-paraparticles have fermi-surface-like structures. These $R$\textit{-parafermions} can satisfy generalized exclusion principles beyond conventional Pauli's. We show that density waves of all $R$-parafermions can always be bosonized, but flavor waves act like bosons only for a certain sublcass of $R$-parafermions. We derive the conditions for bosonization by analyzing the LM spectrum, showing that bosonization applies only to low-temperature systems. Signatures of flavor-charge separation then become apparent as distinct dispersion profiles when we turn on inter-particle interactions. This points to potential observations of flavor-charge separation in 1D systems that host emergent $R$-paraparticles.

The recent work of Dafydd and Porter [2024] on the attenuation of waves propagating through floating broken ice of random thickness is extended to consider water of non-shallow depth. A theoretical model of broken floating ice is analysed using a multiple scales analysis to provide an explicit expression for the attenuation of waves as they propagate from a region of constant thickness ice into a semi-infinite region of ice whose thickness is a slowly-varying random function of distance. Theoretical predictions are shown to compare well to numerical simulations of scattering over long finite regions of ice of randomly-varying thickness computed from an approximate depth-averaged model derived under a mild-slope assumption. The theory predicts a low-frequency attenuation proportional to the eighth power of frequency and a roll-over effect at higher frequencies. The relationship between the results and field measurements are discussed.

The discovery of ambient-pressure nickelate high-temperature superconductivity provides a new platform for probing the underlying superconducting mechanisms. However, the thermodynamic metastability of Ruddlesden-Popper nickelates Lnn+1NinO3n+1 (Ln = lanthanide) presents significant challenges in achieving precise control over their structure and oxygen stoichiometry. This study establishes a systematic approach for growing phase-pure, high-quality Ln3Ni2O7 thin films on LaAlO3 and SrLaAlO4 substrates using gigantic-oxidative atomic-layer-by-layer epitaxy. The films grown under an ultrastrong oxidizing ozone atmosphere are superconducting without further post annealing. Specifically, the optimal Ln3Ni2O7/SrLaAlO4 superconducting film exhibits an onset transition temperature (Tc,onset) of 50 K. Four critical factors governing the crystalline quality and superconducting properties of Ln3Ni2O7 films are identified: 1) precise cation stoichiometric control suppresses secondary phase formation; 2) complete atomic layer-by-layer coverage coupled with 3) optimized interface reconstruction minimizes stacking faults; 4) accurate oxygen content regulation is essential for achieving a single superconducting transition and high Tc,onset. These findings provide valuable insights for the layer-by-layer epitaxy growth of diverse oxide high-temperature superconducting films.

We introduce the notion of 0-shifted cosymplectic structure on differentiable stacks and develop a corresponding moment map theory for Hamiltonian cosymplectic actions. We present a reduction procedure, establish a version of the Kirwan convexity theorem, and obtain examples of Morse-Bott Lie groupoid morphisms.

We study price regulation for a monopolist operating in networked markets with demand spillovers. Achieving efficiency requires price reductions proportional to consumers' Katz-Bonacich centralities, which generally cannot be implemented by commonly used price regulations. Moreover, these regulations become asymptotically welfare neutral as spillovers grow. Nevertheless, some price regulations may still benefit consumers. In particular, average-price regulation robustly increases consumer surplus. By contrast, banning price discrimination increases consumer surplus only when more central consumers have higher intrinsic willingness to pay.

LuSEE-Night is a pathfinder radio telescope on the lunar far side employing four 3-m monopole antennas arranged as two horizontal cross pseudo-dipoles on a rotational stage and sensitive to the radio sky in the 1-50 MHz frequency band. LuSEE-Night measures the corresponding 16 correlation products as a function of frequency. While each antenna combination measures radiation coming from a large area of the sky, their aggregate information as a function of phase in the lunar cycle and rotational stage position can be deconvolved into a low-resolution map of the sky. We study this deconvolution using linear map-making based on the Wiener filter algorithm. We illustrate how systematic effects can be effectively marginalised over as contributions to the noise covariance and demonstrate this technique on beam knowledge uncertainty and gain fluctuations. With reasonable assumptions about instrument performance, we show that LuSEE-Night should be able to map the sub-50 MHz sky at a ~5-degree resolution.

Momentum current density (MCD) $T^{ij}$ is a general physics concept describing the momentum conservation through momentum flow generated from both the kinetic motion of particles and the interacting forces among them. It has been suggested by M. Polyakov et al. that the MCD in the nucleon, characterized by the form factor $C/D$ of the QCD energy-momentum tensor, can be interpreted as the pressure and shear forces between adjacent parts of the system because the nucleon interior approximates a continuous medium. While intuitively appealing, we find that the interpretation is hard to justify from a detailed examination of the physical mechanisms for the momentum flow in QCD. After reviewing through a broad range of classical and quantum systems, we find that while thermal and/or quantum average of isotropic motion contributes to kinetic MCD a pressure term proportional to $δ^{ij}$, when there is an anisotropic motion, the pressure cannot simply be identified from the MCD tensor. Furthermore, kinetic pressure cannot be considered as the surface force between adjacent parts of a system. More importantly, at the scale of the nucleon dimension, the color forces among quarks and gluons is by no means short-ranged as in a continuous medium, and the resulting interaction MCD cannot be interpreted as normal or shear ``stress'' force, although an isotropic term from the QCD trace anomaly may be interpreted as a ``vacuum pressure.'' Following our previous study of force densities through divergences of kinetic MCDs, we affirm that the vacuum pressure term provides a confining potential on the quarks through color Lorentz forces.

The discovery of Ruddlesden-Popper (R-P) nickelate superconductors under high pressure heralds a new chapter of high-transition temperature (high-Tc) superconductivity. Recently, ambient-pressure superconductivity is achieved in R-P bilayer nickelate thin films through epitaxial compressive strain, unlocking the potential for understanding the nature of the unconventional superconductivity. Here, through electrical transport study, we report the discovery of time-reversal symmetry (TRS) breaking superconductivity with electronic glass in bilayer nickelate (La, Pr, Sm)3Ni2O7 films. It emerges in the lower-temperature regime of superconducting transition to the zero-resistance state, and is captured by three remarkable characteristics: 1. Unconventional magnetoresistance hysteresis, the direct evidence of TRS breaking, which is robust under different magnetic field orientations and differs fundamentally from trapped vortices or long-range-ordered magnetism. Successive oxygen reductions simultaneously weaken both the superconductivity and hysteresis, revealing their mutual connections to selective electronic orbitals. 2. Magnetic field history-dependence and zero-field non-reciprocity in the current-voltage responses, further substantiating the intrinsic and spontaneous TRS breaking. 3. Logarithmically slow resistance relaxations upon the removal of magnetic field, the hallmarks of glassy dynamics. Distinguished by the striking magnetic field history- and time-dependent properties, our findings uncover an unprecedented superconducting state in the nickelate superconductors, providing phenomenological and conceptual advances for future research on high-Tc superconductivity.

Cryptocurrency markets are highly volatile and influenced by both price trends and market sentiment, making effective portfolio management challenging. This paper proposes a dynamic cryptocurrency portfolio strategy that integrates technical indicators and sentiment analysis to enhance investment decision-making. Market momentum is captured using the 14-day Relative Strength Index (RSI) and Simple Moving Average (SMA), while sentiment signals are extracted from news articles with VADER and further validated using the Google Gemini large language model. These signals are incorporated into expected return estimates and used in a constrained mean-variance optimization framework. Backtesting across multiple cryptocurrencies shows that the integrated approach outperforms traditional benchmarks, including momentum strategy, Bitcoin Long-Short strategy, and an equal-weighted portfolio, achieving stronger risk-adjusted returns and more consistent cumulative growth. Furthermore, comparing the sentiment-only and technical-only strategies shows that incorporating sentiment information alongside technical indicators can lead to more consistent performance gains. However, the strategies exhibit substantial drawdowns that coincide with known periods of market stress, indicating that additional risk-management components are required to improve stability.

Active living matter continuously creates and annihilates topological defects in a process that remains poorly understood. Here, we investigate these dynamics in two distinct active living systems: swarming bacteria and human bronchial epithelial cells. Despite their entirely different evolutionary origins, biological functions, and physical scales, both systems exhibit half-integer defects, consistent with the nematic phase. However, in contrast to active nematic theory, we find that defect creation and annihilation undergoes spatial symmetry breaking. We propose that these results stem from a fundamental dualism between nematic structural organization and generated polar forces, which are intrinsic to living systems. Furthermore, estimation of entropy production reveals that creation and annihilation are not reversed processes. Our findings challenge conventional nematic models and emphasize the role of defect-mediated dynamics in non-equilibrium biological systems as a major source of entropy production.

We analyze the performance of quantum key distribution (QKD) protocols that rely on discrete phase randomization (DPR). For many QKD protocols that rely on weak coherent pulses (WCPs), continuous phase randomization is assumed, which simplifies the security proofs for such protocols. However, it is challenging to achieve such a perfect phase randomization in practice. As an alternative, we can select a discrete set of global phase values for WCPs, but we need to redo the security analysis for such a source. While security proofs incorporating DPR have been established for several QKD protocols, they often rely on computationally intensive numerical optimizations. To address this issue, in this study, we derive analytical bounds on the secret key generation rate of BB84 and measurement-device-independent QKD protocols in the DPR setting. Our analytical bounds closely match the results obtained from more cumbersome numerical methods in the regions of interest.

We systematically derive an exact coarse-grained description for interacting particles with thermodynamically consistent stochastic dynamics, applicable across different observation scales, the mesoscopic and the macroscopic. We implement the coarse-graining procedure using the Doi-Peliti field theory, which preserves microscopic noise effects on the meso/macro scale. The exact mapping reveals the key role played by Poissonian particle occupancy statistics. We show the implications of the exact coarse-graining method using a prototypical flocking model, namely the active Ising model, which exhibits a mismatch between the microscopic and macroscopic mean-field coarse-grained descriptions. Our analysis shows that the high- and low-density regimes are governed by two different coarse-grained equations. In the low-density regime, noise effects play a prominent role, leading to a first-order phase transition. In contrast, the second-order phase transition occurs in the high-density regime. Due to the exact coarse-graining methods, our framework also opens up applicability to systematically analyze noise-induced phase transitions in other models of reciprocally and non-reciprocally interacting particles.

Mobile application performance is a vital factor for user experience. Yet, performance issues are notoriously difficult to detect in development environments, where they often manifest less conspicuously, making their diagnosis more challenging. In this setting, app reviews from users with diverse device configurations can provide timely and context-rich information about emerging performance issues. However, unlike structured bug reports, app reviews are written by end-users and tend to be more ambiguous, with individual reviews often providing only partial descriptions of the underlying issue. To bridge this gap, we present RevPerf, the first approach to automatically reproduce mobile application performance issues by leveraging and synthesizing information from app reviews. RevPerf retrieves complementary reviews via semantic retrieval and uses prompt engineering to integrate them, enriching the original review with performance issue details. An execution agent is then employed to generate and execute commands to reproduce the issue. After executing all necessary steps, the system incorporates multifaceted detection methods to identify performance issues by monitoring Android logs, GUI changes, and system resource utilization during the reproduction process. Experimental results demonstrate that our proposed framework achieves a 72.73% success rate in reproducing performance issues on the constructed dataset, outperforming the best baseline by 27.28%.

We report on the implementation of a dynamical method for the determination -- in an extended temperature range around room temperature -- of the saturation vapor pressure and enthalpy of vaporization of low-volatility liquid substances. The method relies on isolating a \textit{precooled} substance in a heated chamber under static vacuum conditions and monitoring the chamber pressure as the sample slowly thermalizes to the chamber temperature. We apply the method to four reference substances -- diethyl phthalate, 1-decanol, 1-heptanol, and 1-hexanol -- and provide accurate data for their saturation vapor pressure and enthalpy of vaporization in the range from $-10$ to $35^\circ$C.

We propose an accurate, efficient, and low-memory sum-of-Gaussians tensor neural network (SOG-TNN) algorithm for solving the high-dimensional Schrödinger equation. The SOG-TNN utilizes a low-rank tensor product representation of the solution to overcome the curse of dimensionality associated with high-dimensional integration. To handle the Coulomb interaction, we introduce an SOG decomposition to approximate the interaction kernel such that it is dimensionally separable, leading to a tensor representation with rapid convergence. We further develop a range-splitting scheme that partitions the Gaussian terms into short-, long-, and mid-range components. They are treated with the asymptotic expansion, the low-rank Chebyshev expansion, and the model reduction with singular-value decomposition, respectively, significantly reducing the number of two-dimensional integrals in computing electron-electron interactions. The SOG decomposition well resolves the computational challenge due to the singularity of the Coulomb interaction, leading to an efficient algorithm for the high-dimensional problem under the TNN framework. Numerical results demonstrate the outstanding performance of the new method, revealing that the SOG-TNN is a promising way for accurately tackling quantum systems.

The radiometric integral is the fundamental radiance--to--flux relation in imaging, whereas étendue is typically used as a compact system-level descriptor. For quantitative imaging and calibration, however, the operative mapping must be explicit at the level of individual detector pixels, including pixel acceptance and field-dependent pupil visibility. This work packages the pixel-restricted radiometric integral into a reusable geometric throughput factor by defining a per-pixel optogeometric (optical-throughput) factor $F_{\mathrm{opg},i}$ (units \si{m^2.sr}) such that, under weak radiance variation, $Φ_i \approx L_i\,F_{\mathrm{opg},i}$. Making throughput explicit at the pixel scale yields an optics-delivered photon budget in which the incident photon count at the detector, $N_{\mathrm{inc},i}$ (before quantum efficiency), scales linearly with geometry: $N_{\mathrm{inc},i}\propto F_{\mathrm{opg},i}$ for a given scene radiance distribution and fixed acquisition settings (bandwidth, integration time, and optical transmission). The corresponding optics-delivered (pre-detection) shot-noise ceiling is set by the incident photon count $N_{\mathrm{inc},i}$, with $\mathrm{SNR}_{\mathrm{inc},i}\le \sqrt{N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, while in photoelectron units one has $\mathrm{SNR}_i \le \sqrt{N_{\mathrm{ph},i}}=\sqrt{η(\barν)\,N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, where $N_{\mathrm{ph},i}$ is the detected photoelectron count and $η(\barν)$ is the (narrowband) quantum efficiency; additional detector/electronics noise sources (e.g.\ dark current and read noise) can only reduce the achieved SNR below these shot-noise limits.

Traditionally, traders and quantitative analysts address alpha decay by manually crafting formulaic alphas, mathematical expressions that identify patterns or signals in financial data, through domain expertise and trial-and-error. This process is often time-consuming and difficult to scale. With recent advances in large language models (LLMs), it is now possible to automate the generation of such alphas by leveraging the reasoning capabilities of LLMs. This paper introduces a novel framework that integrates a prompt-based LLM with a Transformer model for stock price prediction. The LLM first generates diverse and adaptive alphas using structured inputs such as historical stock features (Close, Open, High, Low, Volume), technical indicators, sentiment scores of both target and related companies. These alphas, instead of being used directly for trading, are treated as high-level features that capture complex dependencies within the financial data. To evaluate the effectiveness of these LLM-generated formulaic alphas, the alpha features are then fed into prediction models such as Transformer, LSTM, TCN, SVR, and Random Forest to forecast future stock prices. Experimental results demonstrate that the LLM-generated alphas significantly improve predictive accuracy. Moreover, the accompanying natural language reasoning provided by the LLM enhances the interpretability and transparency of the predictions, supporting more informed financial decision-making.

Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests.

Single atomic adsorbates on ultrathin insulating films provide a promising route toward bottom-up quantum architectures based on atomically identical yet individually addressable spin qubits on solid surfaces. A key challenge in engineering quantum-coherent spin nanostructures lies in understanding and controlling the spin state of individual adsorbates. In this work, we investigate single titanium (Ti) atoms adsorbed on MgO/Ag(100) surfaces using a combined scanning tunneling microscopy and electron spin resonance. Our measurements reveal two distinct spin states, $S = 1/2$ and $S = 1$, depending on the local adsorption site and the thickness of the MgO film. Density functional theory calculations suggest a Ti$^+$ configuration for the Ti adsorbates with approximately 3 electrons in the 4$s$ and 3$d$ valence shells. Using a multi-orbital atomic multiplet calculations the site dependence of the spin can be rationalized as a charge redistribution between spin-polarizing and depolarizing orbitals. These findings underscore the potential of surface-supported single atoms as spin qubits with tunable spin and charge states, enabling atom-by-atom control in the realization of a versatile quantum platform on surfaces.

We consider the filtering problem with the partially observed Lorenz 96 model. Although the accuracy of the 3DVar filter in this problem has been established, the theoretical guarantee for the ensemble Kalman filter (EnKF) remains limited due to the analytical difficulty of handling non-symmetric matrices that emerge in the partial observation setting. This study establishes uniform-in-time error bounds of a stochastic variant of the EnKF, known as the perturbed observation (PO) method. By utilizing additive covariance inflation, we successfully obtain the bounds both with and without projecting the background covariance onto the observation space. Our analysis with the projection complements existing results for the deterministic variant of the EnKF, while our approach without the projection offers an extended mathematical framework to handle the non-symmetric matrix products directly. A numerical example validates the theoretical findings and shows comparable accuracies between the two settings.

The simulation of quantum field theories, both classical and quantum, requires regularization of infinitely many degrees of freedom. However, in the context of field digitization (FD) -- a truncation of the local fields to $N$ discrete values -- a comprehensive framework to obtain continuum results is currently missing. Here, we propose to analyze FD by interpreting the parameter $N$ as a coupling in the renormalization group (RG) sense. As a first example, we investigate the two-dimensional classical $N$-state clock model as a $\mathbb{Z}_N$ FD of the $U(1)$-symmetric $XY$-model. Using effective field theory, we employ the RG to derive generalized scaling hypotheses involving the FD parameter $N$, which allows us to relate data obtained for different $N$-regularized models in a procedure that we term $\textit{field digitization scaling}$ (FDS). Using numerical tensor-network calculations at finite bond dimension $χ$, we further uncover an unconventional universal crossover around a low-temperature phase transition induced by finite $N$, demonstrating that FDS can be extended to describe the interplay of $χ$ and $N$. Finally, we analytically prove that our calculations for the 2D classical-statistical $\mathbb{Z}_N$ clock model are directly related to the quantum physics in the ground state of a (2+1)D $\mathbb{Z}_N$ lattice gauge theory which serves as a FD of compact quantum electrodynamics. Our study thus paves the way for applications of FDS to quantum simulations of more complex models in higher spatial dimensions, where it could serve as a tool to analyze the continuum limit of digitized quantum field theories.