This article is devoted to the study of the evolution of the properties of nucleons bound in nuclear matter within the framework of the chiral confining model. The in-medium nucleon trial states (either localized factorized wave functions or momentum-projected states) are determined by imposing the von Laue stability condition, according to the formal results established in a preliminary companion paper (labeled as I). The main results concern the response of the composite nucleon to the scalar field, as well as the respective roles of confinement and chiral symmetry breaking in the evolution of the in-medium nucleon mass. This evolution governs the repulsive three-body forces required for the nuclear saturation mechanism. We also analyze the modification of the energy density distribution and the pressure distribution inside the in-medium nucleon. We also draw some perspectives concerning the mapping between bound nucleon properties and the equation of state of dense matter as realized in the deep interior of neutron stars.

We discuss the issue of the mechanical stability of the nucleon within a class of models in which massive constituent quarks are subject to a confining potential and are coupled to a surrounding pion cloud enveloping the quark core. The nucleon trial states (either localized factorized wave functions or momentum-projected states) are determined by imposing the von Laue stability condition. This article is primarily devoted to the formal aspects related to the detailed expressions for the total energy (mass), the average pressure, the energy density and the pressure distribution inside the nucleon. It will be accompanied by a complementary article addressing the evolution of nucleon properties with density, associated with the restoration of chiral symmetry.

We investigate Kerr-Schild-AdS geometries in quadratic f(R) gravity without imposing the constant-curvature condition R=R_0 a priori. We show that the field equations dynamically enforce constant scalar curvature and uniquely select the Kerr--AdS family of solutions. Thus, quadratic f(R) gravity admits no Kerr--AdS solutions beyond the Einstein branch, establishing a no-go theorem for this class of geometries.

Identifying crack generations from microscopic images of hierarchical crack patterns is challenging due to the lack of temporal information and sensitivity to image boundaries. Existing algorithms often fragment individual cracks or lose stability when the observed fragment is shifted. We propose a method that reduces the classification problem to topological sorting of a directed acyclic graph (descendant$\to$parent), built from T-junctions and nearly collinear edges. Sequential removal of leaf vertices assigns generation numbers starting from the youngest. On 100 computer-generated networks, our method correctly classifies $\approx 70$\% of cracks at a window size of only three mean edge lengths, whereas a conventional approach that starts from primary cracks drops nearly to zero. The classification is highly stable against reasonable shifts of image boundaries but remains limited to strictly hierarchical networks.

I present EXOVEIL, a transit detection system that learns what a star's brightness should look like and flags when reality disagrees. Unlike existing systems that require phase-folded input, EXOVEIL operates on raw flux time series and can detect planets that transit only once.A Transformer world model, trained on 16,499 Kepler light curves with transit-masked self-supervised learning, predicts expected stellar flux. A matched-filter detector with variance weighting extracts transit signals from the prediction residuals. A learned classifier (XGBoost) separates planets from false positives, achieving AUC 0.938 on Kepler DR25. Applied to single-transit injection-recovery, EXOVEIL recovers 32% of transits at 1000 ppm depth a task where all classification-based systems score 0% by construction. A blind search of 3,737 Kepler stars yields 179 new transit-like signals not present in the DR25 TCE catalogue, including 46 monotransit candidates. Applied withoutretraining to 47 confirmed TESS planets in the PLATO LOPS2 field, EXOVEIL achieves 100% recovery, demonstrating zero-shot cross-mission transfer. At PLATO's 25-second cadence, detection reaches 100 ppm -- approaching the Earth-analog regime. I provide the first application of conformal prediction to transit detection (95.9% empirical coverage) and release the system as pip install exoveil with pretrained weights and a candidate catalogue.

Diffusion MRI enables non-invasive probing of tissue microstructure, but accurate parameter estimation is challenged by noise-related effects. In supervised machine learning frameworks trained on simulated data, discrepancies between the noise characteristics of simulated and acquired signals introduce a form of covariate shift, whereby the input signal distribution differs between training and inference. We investigated the impact of this mismatch on microstructure parameter estimation and propose a realistic noise synthesis (RNS) framework to mitigate it. RNS incorporates both the Rician expectation and the effective post-processing noise variance into simulated training signals. The Rician expectation was modelled using a noise standard deviation estimated with MPPCA, while the effective standard deviation was derived from spherical harmonic residuals of preprocessed data. The method was evaluated using the cylinder-zeppelin and the SANDI models on simulated datasets across multiple SNR levels and on in vivo diffusion data with repeated acquisitions. Sensitivity to noise misestimation was also assessed. Ignoring magnitude-induced noise effects during training produced systematic, SNR-dependent parameter bias, particularly at low SNR. Incorporating the Rician expectation substantially reduced bias to the level of noise-aware nonlinear least-squares fitting. Modelling the effective standard deviation further improved precision. Performance was largely independent of regression architecture but sensitive to accurate noise estimation. These findings demonstrate that realistic noise modelling in simulated training data mitigates signal-domain covariate shift and is essential for unbiased supervised microstructure estimation, particularly in low-SNR regimes associated with high b-values or high spatial resolution.

Clifford+T synthesis of rotation gates is an important routine in fault-tolerant quantum compilation. While Clifford+T synthesis is scalable, it has a high overhead of tens of T gates per rotation in practice, translating to high resource estimates for many fault-tolerant algorithms. However, these well-known results, including those using probabilistic mixtures [Quantum 7, 1208 (2023)], are independent of the rotation angle $\theta$, requiring $O(\log 1/\delta)$ T gates. We show that it is possible to do much better for small angles, reducing the T cost to $\tilde{O}(\theta^2/\delta)$, and returning to existing $O(\log1/\delta)$ results in the worst case. This is particularly important since many algorithms, such as Trotterization, are dominated by small-angle rotations. Further, we perform a detailed theoretical and numerical study of quasi-probabilities, which can further reduce the total T cost of large circuits by orders of magnitude with only a small overhead in sample complexity. We also develop a scheme based on quasi-probability mixtures of Clifford+T fallback channels. We derive new $\theta$-dependent formulas that can be used for resource estimation of fault-tolerant quantum algorithms. As an application of our results, we show that the gate cost of Trotterization circuits compiled to a Clifford+T gate set is constant in the small Trotter step size limit, and can be reduced by orders of magnitude even for large step sizes. The cost of fault-tolerant Trotterization for a variety of applications should be re-examined in light of these results. Our work dispels the widely-stated claim that Clifford+T rotation synthesis has a high cost independent of $\theta$, and further develops a scalable quasi-probability method for rotation synthesis. We also expect our results to bring forward useful early fault-tolerant quantum computing by reducing required magic state resources.

Let $B(\Lambda_a) \, (a=0,1)$ be the crystal of the level 1 integrable irreducible highest weight representation of the affine quantum group $U_q(\widehat{\mathfrak{sl}}_2)$. We consider the crystal graphs of degree $n$ associated with the irreducible $(2r+1)$-dimensional (resp. $(2r+2)$-dimensional) $U_q(\mathfrak{sl}_2)$ module in $B(\Lambda_0)$ (resp. $B(\Lambda_1)$). In this paper, we construct an explicit combinatorial procedure providing a bijection between the set of highest weight paths in these graphs with respect to the action of the Kashiwara operator $\tilde{f}_{1}$, and the set of integer partitions of $n$ with sqrank (resp. rerank) $r$, which is a recently introduced partition statistic. As a byproduct, we also obtain a precise interpretation of the motif description of spinons suggested by Bernard-Pasquier-Serban in the spinon picture for Wess-Zumino-Witten conformal field theory models.

Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not determine a unique effective response, and a low-resolution observation may correspond to many plausible high-resolution fields. In such settings, deterministic surrogates may learn a well-defined mathematical object while still missing application-relevant uncertainty. This tutorial develops a self-contained module centered on the conditional-mean barrier: the point at which a squared-loss predictor has reached the conditional mean and the remaining error is irreducible aleatoric variance. We give two diagnostics for locating this barrier, residual-feature orthogonality and the coefficient of determination against its explained-variance ceiling, and prove that adding latent randomness to a squared-loss predictor collapses it back to the conditional mean. Crossing the barrier therefore requires a loss that scores distributions rather than point predictions. We briefly organize common distributional objectives, including negative log-likelihood, moment and observable matching, variational objectives, adversarial divergences, and score matching, by the feature of the conditional law each targets. The emphasis is the boundary itself and a finite-data procedure for recognizing it, rather than a survey of methods beyond it. CPU-based demonstrations on a two-branch law and a two-scale Lorenz-96 closure problem show how the diagnostics distinguish deterministic underfitting from residual distributional variability.

Given the canonical seesaw mechanism as a most natural extension of the standard model in its neutrino sector, we find out a special but brand new solution to the exact seesaw equation: $m^{}_i/M^{}_i = - R^2_{\alpha i}/U^2_{\alpha i}$ for the masses and flavor mixing matrix elements of light and heavy Majorana neutrinos of the $i$-th family (for $i = 1, 2, 3$ and $\alpha = e, \mu, \tau$). This family-separated seesaw scenario allows us to establish simple relations between the original seesaw parameters and the active degrees of freedom, and thus offers a number of testable predictions in neutrino phenomenology.

Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the closure problem). Offline-trained machine-learning (ML) closures suffer distribution shift in predictive simulations, while ML methods that bypass the governing equations struggle to generalise from scarce high-fidelity data. We develop a physics-derived deep learning closure model for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on small datasets and accurately generalise across Reynolds numbers, to unseen geometries, and to different flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure for efficient optimisation. On canonical square-duct and periodic-hill benchmarks, DARSM reduces average test velocity error over baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can reconstruct a trajectory that is consistent with both the data and the governing equations. A key open question is how many measurements are required for accurate reconstruction, making the full system trajectory observable from sparse data. We establish observability criteria for variational state estimation applied to the Kuramoto-Sivashinsky equation by linking its observability to embedding theory for dissipative dynamical systems. For a system whose attractor lies on an inertial manifold of dimension $d_M$, we show that $m \geq d_M$ measurements ensures local observability from an arbitrarily good initial guess, and $m \geq 2d_M + 1$ implies global observability using a gradient-based smoother since the only critical point on $M$ is the global minimum. We also analyze optimization-dynamic limitations that persist even when these topological conditions are met, including drift off the manifold, degeneracy of the Hessian, negative curvature, and vanishing gradients. To address these issues, we introduce a robust reconstruction strategy that combines non-convex Newton updates with a novel pseudo-projection step. Numerical simulations of the Kuramoto-Sivashinsky equation validate our analysis and show practical limits of observability for chaotic systems with low-dimensional inertial manifolds.

This paper explores the sensitivity gains afforded by spin-squeezed states in atom interferometry, in particular using Bragg diffraction. We introduce a generalised input-output formalism that accurately describes realistic, non-unitary interferometers, including losses due to velocity selectivity and scattering into undesired momentum states. This formalism is applied to evaluate the performance of one-axis twisted spin-squeezed states in improving phase sensitivity. Our results show that by carefully optimising the parameters of the Bragg beam splitters and controlling the degree of squeezing, it is possible to improve the sensitivity of the interferometer by several dB with respect to the standard quantum limit despite realistic levels of losses in light pulse operations. However, the analysis also highlights the challenges associated with achieving these improvements in practice, most notably the impact of finite temperature on the benefits of entanglement. The results suggest ways of optimising interferometric setups to exploit quantum entanglement under realistic conditions, thereby contributing to advances in precision metrology with atom interferometers.

We investigate whether the Lagrangian density for an interacting vector field or an interacting massless spin-2 field can be determined by imposing Poincaré invariance and the conservation of energy-momentum for the entire system. We adopt the Belinfante-Rosenfeld energy-momentum tensor for systems involving either a vector field or a spin-2 field. For the vector field coupled to a system of point masses, it is not possible to determine the Lagrangian density of the vector field. On the other hand, we show that for the spin-2 field coupled to a material system such as a system of point particles, its Lagrangian density is uniquely given by the Einstein Lagrangian density. Furthermore, the Belinfante-Rosenfeld tensor for the spin-2 field becomes Papapetrou's gravitational energy-momentum pseudotensor.

We present a Renormalization Group (RG) framework based on a nonlocal effective action ansatz to analyze the strong coupling dynamics of the three-dimensional relativistic $\phi^{4}$ theory. By implementing a Hubbard-Stratonovich transformation, we decouple the quartic interaction into the primary field $\phi$ and an auxiliary field $\varphi \sim \phi^2$, allowing both exponents $\Delta_{\phi}$ and $\Delta_{\varphi}$ to act as independent, unconstrained variables rather than fixed scaling dimensions. Within this nonlocal propagator framework, both the field self-energies and vertex corrections are evaluated at the one-loop order. The resulting one-loop logarithmic derivatives determine the renormalization group flows of the couplings and the scaling exponents. For $d = 3$ and $\epsilon = 0.5$, the self-consistent equations yield a physical fixed point at $\Delta_{\phi} \approx 0.81479$ and $\Delta_{\phi^2} \approx 1.37042$. These exponents result in a kinematic anomalous dimension $\eta_{\phi} \approx 0.37042$, an energy operator dimension $\Delta_{\phi^2} \approx 1.37042$, and a thermal correlation length exponent $\nu \approx 0.61366$. For $\epsilon\approx-0.28996$, the self-consistent equations yield another fixed point at $\Delta_{\phi}\approx0.87284$, $\Delta_{\varphi}\approx-0.53564$, and $\Delta_{\phi^2}\approx1.25432$, corresponding to $\eta_{\phi}\approx0.25432$ and $\nu\approx0.57284$. Although these leading-order results show deviations from high-precision Quantum Monte Carlo (QMC) and conformal bootstrap benchmarks, they characterize the baseline scaling behavior of the Wilson-Fisher universality class.

We demonstrate that novel limits on prompt axion-like particles (ALPs) in the hard-to-probe mass range near the neutral pion - the so-called pion chimney - may be obtained from recasting $K_L \to 3\pi^0 \to 6\gamma$ data taken by the J-PARC KOTO experiment, to search for $K_L \to 2\pi^0a \to 6\gamma$. We also explore the power of KOTO $6\gamma$ data to probe $K_L \to 2\pi^0a$ for a broader range of ALP masses, incorporating displaced decays.

Transition-metal halides V$X_3$ ($X$ = Br and I) have emerged as promising candidates for two dimensional spintronic and quantum applications due to their layer-dependent magnetism and tunable electronic states. However, experimental insights into their ground state electronic structures remain limited. Here, we present a comprehensive investigation of V$X_3$ using high resolution resonant inelastic x-ray scattering (RIXS) combined with ligand field multiplet calculations. The RIXS spectra reveal distinct $dd$ and charge-transfer excitations, allowing precise determination of electronic structure parameters, including the crystal field splitting, trigonal distortion, and Racah parameters. The determined parameters showed clear variation, indicating an increase in covalency from Br to I. The trigonal distortion parameters $\Delta_{D_{3d}}$ were determined to be -0.096 eV in VBr$_3$ and 0.07 eV in VI$_3$, indicating a sign opposition between the two compounds, reflecting good agreement with experimental RIXS data. Cluster model calculations yield a high-spin V$^{3+}$ $(S = 1)$ configuration, with an $e'^2_g$ ground state in VBr$_3$ and an $e'^1_ga^1_{1g}$ ground state in VI$_3$, consistent with trigonal elongation and compression, respectively. Our findings provide the most complete experimental determination of the low energy electronic structure in V$X_3$, offering valuable insights for designing 2D magnetic and spintronic materials based on vanadium halides.

Polarimetric interferometry is a powerful tool for probing both black hole accretion physics and the background spacetime. Current models aimed at explaining the observed multiwavelength flares in Sgr A* often assume hotspots moving on geodesic, Keplerian orbits. In many scenarios, though, a hotspot may instead follow an inspiraling trajectory, potentially transitioning into a plunge toward the black hole. In this work, we present a general framework to simulate the polarized emission from generic equatorial inspiraling hotspots in Kerr spacetime using a parametric four-velocity profile. This parametrization defines a continuous family of flows, ranging from Cunningham's disk model (fixed radius orbits outside the innermost stable circular orbit and plunging motion within the innermost stable circular orbit) to purely radial motion, thereby extending the standard assumptions. Within this framework, we show that inspiral motion produces a distinctive observational signature: a precessing, unwinding evolution of the polarimetric Stokes Q-U looping pattern, in sharp contrast with the closed Q-U loops associated with stable orbits at a fixed radius. We then explore how the morphology of these signatures depends on black hole spin, observer inclination, and magnetic-field configuration. The presented model can be applied to current and near-future interferometric observations of linear polarization, offering a new avenue to probe the physics of matter spiraling inward and the relativistic velocities of plunging plasma.

The calculation of inclusive processes that involve the production of many particles is a challenge for lattice QCD, a Euclidean-space method that is far removed from real-time, multiparticle production. A new approach to this problem based on Nevanlinna-Pick interpolation has been proposed by Bergamaschi et al. Here we extend their method by exploring the propagation of the statistical and systematic errors that accompany a lattice QCD calculation through this interpolation process. A simplified example of a multiparticle spectral function is studied with a focus on the possible applications of these methods to the calculation of inclusive heavy-particle decays.

The function of the zebra's striped coat has been debated since Darwin and Wallace. A growing body of comparative and experimental evidence supports the hypothesis that the stripes act primarily as a defence against visually orienting biting Diptera - in particular tabanids (horse flies), glossinids (tsetse flies) and culicids (mosquitoes). The mechanisms proposed for this protection range from polarotactic disruption and silhouette break-up to motion-based illusions arising in the Reichardt-type motion detectors of the insect visual system. In this work we focus on a complementary, purely optical mechanism: the Moiré interference that arises when a periodic striped stimulus is sampled by the periodic ommatidial lattice of an insect compound eye. We develop a linear, shift-invariant Fourier model of the diptera compound eye, parameterised from published optical data on diurnal Culicidae, and apply it to images of zebra coats observed at biologically relevant viewing. The model predicts that, in a band of approach distances of approximately 1-5 m, the interaction of the stripe pattern with ommatidial sampling generates parasitic spatial frequencies that are absent from the physical stimulus and that fall within the spatial-frequency window most relevant to host fixation and landing control. A post-retinal motion-detector stage demonstrates that these parasitic frequencies translate into spurious local motion vectors, consistent with the empirical observation that tabanid and glossinid flies fail to land cleanly on striped surfaces. Our results are therefore consistent with the biting-fly hypothesis of zebra striping.

One of the fundamental challenges of quantum gravity is to understand how the microscopic degrees of freedom of the cosmological horizon shape the evolution of the Universe. One possible approach to this problem is based on the Barrow--Tsallis entropy. This entropy accounts for both quantum gravitational effects and the nonextensive effects inherent in any long-range interaction. By employing an inverse cosmographic reconstruction of the model parameters, we derive a relation between the Barrow parameter, which encodes the microscopic deformation of the horizon geometry, and the Tsallis parameter, which characterizes macroscopic nonextensivity. Within the IR--UV correspondence, this relation determines the scaling of the microscopic length uncertainty in terms of the current cosmographic parameters and demonstrates how long-range nonextensive effects alter the standard Karolyhazy-type scaling. We also used our method for finding the parameters of cosmological models to evaluate the feasibility of using fractional derivatives to describe the late evolution of the Universe. The resulting relationships are exact. Therefore, the uncertainty in the relationship between the model parameters depends only on the current uncertainty in the values of the cosmographic parameters.

Public access to pulse-level and control-electronics interfaces in commercial quantum computing has bifurcated. This paper proposes a six-axis rubric for measuring control-plane openness, the layer between gate-level circuit specification and physical control electronics, defined operationally so that the same evidence produces the same grade across vendors. The rubric is validated three ways: a blinded re-grading pass, thirty-nine days after the evidence cutoff, that tests whether the cited evidence and the level definitions alone reproduce the recorded grades; a boundary-case methodology that fixes where each level begins and ends; and a published grading protocol that lets others reproduce and contest any cell. We establish that the rubric measures change rather than describing a snapshot by comparing the catalog against the documented control plane before the February 2025 removal of pulse-level access from IBM hardware, and reporting the cells that moved. The rubric is applied to thirteen commercial vendors across superconducting, trapped-ion, neutral-atom, and photonic modalities as of May 1, 2026, as its first application, and one of the three harms the rubric is designed to detect is demonstrated through a reproduction-access audit of five pre-2025 IBM Qiskit Pulse experiments against the access available on current hardware, carried through to a client-side structural port of the audit's selected target to Rigetti Quil-T. The catalog ships as a separate machine-readable artifact under CC-BY-4.0 with per-cell source URLs ( this https URL ). The catalog readings will change as vendor policies shift; the rubric is the contribution that survives them.

With the next generation of both electromagnetic and gravitational wave observatories beginning to come online, rapid analysis methods for kilonova data are becoming increasingly important in astronomy. Traditional Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) is time-consuming and relies on explicit likelihood approximations that can break down when modeling uncertainties are significant. We develop a simulation-based inference (SBI) framework for kilonova parameter estimation using density-estimation likelihood-free inference. The framework uses a Gaussian process emulator trained on $\sim 1300$ POSSIS simulations. We demonstrate that SBI provides a rapid alternative to MCMC that is robust to likelihood misspecification. The standard Gaussian likelihood approximation fails to capture the non-Gaussian, correlated structure of emulator uncertainty; SBI learns this structure directly from forward simulations. Simulation studies show that the SBI method accurately recovers injected parameters, while the MCMC suffers from systematic bias caused by likelihood misspecification. This problem persists when analyzing AT2017gfo, where a subset of the MCMC posteriors pile up at prior boundaries and the SBI posteriors do not. The SBI framework infers a total ejecta mass of $\sim 0.087 M_{\odot}$ dominated by lanthanide-poor ejecta and excludes toroidal and peanut ejecta geometries at the 99th percentile for both components. The SBI framework generates $\sim 2 \times 10^{4}$ posterior samples in seconds.

Soft, slender structures are ubiquitous in natural and engineered systems, with broad application potential from biomimetic materials to soft robotics. However, there is a notable lack of computational tools that simultaneously preserve high-fidelity continuum rod mechanics, scale to large interacting ensembles, and remain flexible across diverse biophysical settings. Here we introduce Elastica++, an open-source, high-performance implementation of the Cosserat-rod model for large-scale simulations of slender-body dynamics. Elastica++ combines performance-oriented kernels with shared-memory parallelism to sustain teraflop-scale throughput despite complex discretization domains and physical interactions. The framework further interoperates with external numerical solvers, supporting efficient multiphysics workflows. We demonstrate robustness and breadth through case studies spanning passive nest-like metamaterials, collective active-matter dynamics, cilia carpets, soft magnetic microrobots, and schooling swimmers. Elastica++ thus provides a missing foundation for high-throughput studies of emergent behavior in interacting assemblies of elastic slender structures.

Two constructions of the Darboux-Halphen system are discussed. In the Jacobi construction we start with transcendental functions which are fixed as the first integrals. In the Lie construction we use a single-valued representation of the simple Lie algebra $sl(2,\mathbb R)$ which is non-integrable in Lie's terminology.

Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical tools for fermionic many-body systems in the coherent-state path-integral representation. Despite their vast potential for both condensed-matter and particle-physics communities, Grassmann tensor network methods are somewhat underexploited in practical simulations. In this work, we provide a detailed, self-contained introduction to Grassmann tensor network methods, from the basics of the Grassmann tensor operations to the Grassmannization of typical tensor network algorithms. Furthermore, the resulting Grassmann tensor network methods are validated in several interesting models in both particle physics and condensed matter physics.

Large foundation models (FMs) are transforming Earth science by integrating heterogeneous multimodal data, such as multi-platform imagery, gridded reanalysis data, diverse geophysical and geochemical observations, and domain-specific text, to support tasks ranging from basic perception to advanced scientific discovery. This paper provides a unified review of Earth science foundation models (Earth FMs) through two complementary dimensions: depth, which traces the evolution of model capabilities from perception to multimodal reasoning and agentic scientific workflows, and breadth, which summarizes their expanding applications across the atmosphere, hydrosphere, lithosphere, biosphere, anthroposphere, and cryosphere, as well as coupled Earth system processes. Using this framework, we review representative multimodal Earth foundation models and compile more than 200 datasets and benchmarks spanning diverse Earth science tasks and modalities. We further discuss key challenges in multimodal data heterogeneity, scientific reliability and continual updating, scalability and sustainability, and the transition from foundation models to agentic and embodied Earth intelligence, and outline future directions toward more integrated, trustworthy, and actionable AI Earth scientists. Overall, this paper offers a structured roadmap for understanding the development of Earth foundation models from both capability depth and application breadth.

We introduce a method for error-corrected quantum metrology where only partial quantum error correction (QEC) is needed to suppress local noise and maintain the probe states' super-standard-quantum-limit (super-SQL) sensing performance. This stands in contrast to the existing QEC-assisted sensing schemes in Phys. Rev. Lett. 112, 080801 (2014) and Phys. Rev. Lett. 112, 150802 (2014), where a probe state is encoded into the logical subspace of a quantum code and error correction involves measurements on all checks of the code. Here, we encode the probe states into superpositions of energetically different states of the underlying quantum code. For our probe states, error correction using a subset of checks is enough to suppress noise both before and after phase imprinting. We analyze the tradeoff in noise suppression. For noise parallel to our phase imprinter of weight $l$, we achieve a suppression of $p^\delta$ where $p$ is the noise strength and $\delta = \lfloor (l+1)/2 \rfloor$. We propose an adaptive imprinter weight increasing strategy to maintain super-SQL performance as we scale up the system. In all our examples, checks and phase imprinters are chosen to be local operators avoiding non-local connectivity.

We investigate the spectrum and polarization of radiation emerging from a subcritical X-ray pulsar using self-consistent radiation-hydrodynamic simulations of an accretion channel in a strong magnetic field. The polarized radiative transfer in the channel above the hot spot is simulated for the two normal modes, taking into account resonant Compton scattering in a strongly magnetized plasma and the effects of vacuum polarization. We show that the deceleration of the accreting matter in the subcritical regime is mainly governed by resonant scattering. Our simulations provide the velocity profiles of the plasma flow and demonstrate that vacuum polarization dominates over plasma birefringence, enhancing both the cyclotron spectral feature and the radiative deceleration of the plasma. We also find that the energy of the cyclotron feature increases with accretion luminosity, indicating a positive correlation consistent with previous observational results and theoretical interpretation.

The no-boundary wavefunction for slow-roll inflation on the 3-sphere exponentially favors a small universe, in sharp disagreement with observations. We show that this problem is resolved by changing the spatial topology to the 3-torus. The sum over the ${\rm SL}(3,\mathbb{Z})$ family of geometries, computed using the theory of automorphic forms for ${\rm GL}(3)$, produces a wavefunction favoring a large inflating universe with ${\cal N} \gtrsim 250$ e-folds. We also compute corrections to the CMB power spectrum induced by torus moduli fluctuations.