Fair scores reward ensemble forecast members that behave like samples from the same distribution as the verifying observations. They are therefore an attractive choice as loss functions to train data-driven ensemble forecasts or post-processing methods when large training ensembles are either unavailable or computationally prohibitive. The adjusted continuous ranked probability score (aCRPS) is fair and unbiased with respect to ensemble size, provided forecast members are exchangeable and interpretable as conditionally independent draws from an underlying predictive distribution. However, distribution-aware post-processing methods that introduce structural dependency between members can violate this assumption, rendering aCRPS unfair. We demonstrate this effect using two approaches designed to minimize the expected aCRPS of a finite ensemble: (1) a linear member-by-member calibration, which couples members through a common dependency on the sample ensemble mean, and (2) a deep-learning method, which couples members via transformer self-attention across the ensemble dimension. In both cases, the results are sensitive to ensemble size and apparent gains in aCRPS can correspond to systematic unreliability characterized by over-dispersion. We introduce trajectory transformers as a proof-of-concept that ensemble-size independence can be achieved. This approach is an adaptation of the Post-processing Ensembles with Transformers (PoET) framework and applies self-attention over lead time while preserving the conditional independence required by aCRPS. When applied to weekly mean $T_{2m}$ forecasts from the ECMWF subseasonal forecasting system, this approach successfully reduces systematic model biases whilst also improving or maintaining forecast reliability regardless of the ensemble size used in training (3 vs 9 members) or real-time forecasts (9 vs 100 members).

Current bounds on the tensor-to-scalar ratio imply that the energy scale of inflation may lie below the grand-unified scale. In this paper, we show that in a broad class of single-field inflation models with sufficiently small energy scales, an extremely efficient tachyonic instability develops at the end of inflation. This instability rapidly drives the system into a nonlinear regime before coherent oscillations can be established, leading to a first-order phase-transition--like phenomenon without tunneling or barrier crossing. The resulting ultra-relativistic shock fronts surrounding the bubble interiors expand to near the Hubble scale, corresponding to the most strongly enhanced tachyonic modes, and collide with one another, producing energetic inflaton particles and gravitational waves. As a result, the post-inflationary dynamics can differ significantly from the conventional high-scale inflationary scenario. Interestingly, inflation at MeV--EeV energy scales can be probed via gravitational-wave observations, including pulsar timing arrays, ground-based detectors, and future space-based experiments. Recent limits from the LIGO--KAGRA--Virgo collaboration already constrain EeV-scale inflation, while pulsar timing array results may be interpreted as evidence for gravitational waves generated by GeV-scale inflation. We also briefly discuss further implications of the resulting tachyonic shocks.

Radial oscillations provide a clean dynamical test of the high-density stiffness of neutron-star equations of state. We study spherically symmetric pulsations of nonrotating relativistic stars built from cold, charge-neutral, $β$-equilibrated pure nucleonic matter described within relativistic mean-field theory. As a baseline we adopt the UCIa parameter set [Astron. Astro-phys. 689, A242 (2024)], and we implement high-density stiffening via the $σ$-cut scheme by adding a regulator potential $U_{\rm cut}(σ)$ [Phys. Rev. C 92, no.5, 052801 (2015), Phys. Rev. C 106, no.5, 055806 (2022)]. For representative choices $f_s=0$ (no cutoff) and $f_s=0.58$ (stiffened), we solve the Tolman-Oppenheimer-Volkoff and tidal perturbation equations to obtain equilibrium sequences, mass-radius relations, and tidal deformabilities. We then derive and solve the linear general-relativistic radial pulsation equations to compute the eigenfrequencies and eigenfunctions of the fundamental and overtone modes. The $σ$-cutoff suppresses the growth of the scalar field at supranuclear density, increases the pressure, and shifts the maximum mass, radii, and $Λ_{1.4}$ accordingly, while systematically raising the radial-mode frequencies at fixed mass. Using the sign change of $ω_0^2$ as a stability criterion, we identify stiffened models that remain radially stable up to the observed $\sim 2M_\odot$ mass scale and are consistent with current multimessenger constraints, demonstrating how radial spectra complement static EoS tests.

In this article we use Gaussian measure on $\mathbb{R}^N$ to define the coefficients of an elliptic diffusion on an open cone of $\mathbb{R}^2$. We prove the existence and uniqueness of a stationary distribution for this diffusion. In a companion article, we show that the diffusion constructed in this work is the inviscid limit of the laws of the ``enstrophy-energy'' process of a stationary $N$-dimensional Galerkin-Navier-Stokes type evolution with Brownian forcing and random stirring (the strength of which can be made to go to zero in the inviscid limit). In the present work, owing to the special properties of the coefficients constructed with the Gaussian measure, we bound the distance to $1$ of the ratio of the expected energy to the expected enstrophy (this ratio is at most $1$ with our normalization). Together with our companion article, this shows that for suitable Brownian forcings an inviscid condensation inducing an attrition of all but the lowest modes takes place.

Microwave synthesizers are central to test and measurement systems across applications including wireless communications, radar, spectroscopy, and time and frequency metrology. State-of-the-art microwave sources, however, are fundamentally constrained by trade-offs between frequency tunability and spectral purity. Electro-optic frequency division (eOFD) is an emerging technique for dividing down the purity of optical sources to the microwave domain. Previously reported eOFD-based synthesizers generally have limited tunability due to feedback stabilization requirements. Here we demonstrate a feed-forward eOFD architecture in which the frequency tunability of a microwave source is preserved while optical spectral purity is divided through feed-forward cancellation, without any downstream electronic frequency synthesis. By canceling the phase noise of the microwave source without feedback, this eOFD approach removes loop bandwidth and source noise constraints observed in prior eOFD architectures. We achieve octave-spanning tunability, including the entire X-band, with phase noise below -140 dBc/Hz at kilohertz offsets and a high-frequency noise floor between -155 dBc/Hz and -145 dBc/Hz for carrier frequencies from 8 to 16 GHz. This performance corresponds to single-femtosecond integrated timing jitter, enabling, to our knowledge, the first demonstration of coherent, optically referenced microwave synthesis under wide tuning with this level of spectral purity.

In this article we consider a stationary $N$-dimensional Galerkin-Navier-Stokes type evolution with Brownian forcing and random stirring (of arbitrarily small strength). We show that the stationary diffusion in an open two-dimensional cone constructed in a companion article, stands as the inviscid limit of the laws of the ``enstrophy-energy'' process of the $N$-dimensional diffusion process considered here, this regardless of the strength of the stirring. With the help of the quantitative condensation bounds of the companion article, we infer quantitative inviscid condensation bounds, which for suitable forcings show an attrition of all but the lowest modes in the inviscid limit.

21cm radiation from neutral hydrogen serves as a direct probe of the Epoch of Reionization. However, both its detection and physical interpretation are severely hindered by contamination from astrophysical foreground emission and instrumental noise that are several orders of magnitude brighter than the signal of interest. A promising way to tackle these challenges is to cross-correlate the 21cm signal with other independent tracers of large-scale structure, most notably high-redshift galaxies. Besides validating putative 21cm detections, such joint analyses are expected to provide independent insights into the properties of ionizing sources and the evolving morphology of ionized regions during reionization. The 21cm signal, however, is intrinsically highly non-Gaussian, limiting the effectiveness of conventional two-point cross-correlation statistics, which capture information only up to the second order. In this work, we therefore investigate the utility of k-nearest-neighbour cumulative distribution functions (kNN CDF), which encode information from the joint clustering at all orders, as an alternative framework for probing 21cm-galaxy cross-correlations. Using self-consistently simulated mock 21cm fields and a catalog of line-emitting galaxies at z = 7, we conducted a proof-of-concept study comparing the kNN CDF formalism and the two-point cross-correlation approach. We find that the kNN CDF statistics outperform the two-point statistics in detecting 21cm-galaxy cross-correlations, even in the presence of instrumental noise and aggressive foreground filtering. Moreover, at a fixed global ionized fraction, it is even able to differentiate between reionization models that remain indistinguishable using two-point statistics. These results demonstrate the power and unexplored potential of exploiting higher-order statistics for extracting maximal information from 21cm-galaxy synergies.

A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the present paper, we propose a position deformation of Heisenberg algebra with both maximal length and minimal momentum uncertainties. By using a pseudo-similarity transformation to the non-Hermitian operators, we prove their Hermiticity with a suitable positive-definite pseudo-metric operator. We then construct Hilbert space representations associated with these pseudo-Hermitian operators. Finally, we study the eigenvalue problem of a free particle in this deformed space and we show that this deformation curved the quantum levels allowing particles to jump from one state to another with low energy transitions.

In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a tensor-based parametrization where the diagonal entries of these states are encoded as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors. Our results bridge multipartite entanglement theory with semialgebraic geometry and the theory of completely positive and copositive tensors. This dictionary maps separability to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sum of squares tensors. Using this framework, we construct explicit PPT entangled states in three or more qutrits. In this class of states, we establish that PPT entanglement exists for all multipartite systems with three qutrits or more, disproving a recent conjecture in [J. Math. Phys. 66, 022203 (2025)]. We also show that, for mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies PPT with respect to any other bipartition. We further connect bosonic extendibility of mixtures of Dicke states to the duals of known hierarchies for non-negative polynomials, such as the ones by Reznick and Polya. We thus provide semidefinite programming relaxations for separability and entanglement testing in the Dicke subspace.

Understanding how polymer architecture governs transport through nanopores is essential for nanocomposite fabrication, membrane design, and polymer upcycling. However, the effect of the nanoscale structure of copolymers on chain transport through nanoporous media remains poorly understood. In this study, we demonstrate that simply inverting the surface orientation of lamellar poly(styrene-block-2-vinylpyridine) (PS-b-P2VP) diblock copolymers, composed of two monomers with strongly contrasting affinities for SiO2, at the entrance of nanoporous silica significantly alters the kinetics of capillary rise infiltration. Using in situ spectroscopic ellipsometry, we find that infiltration of symmetric PS-b-P2VP into silica nanoparticle (SiO2 NP) packings is significantly faster when the P2VP domain is the top layer of the film and first contacts the nanoparticles, compared to when the PS domain is the top layer. Coarse-grained molecular dynamics simulations reveal that this difference originates from block-specific adsorption pathways that reorganize the nanophase structure around nanoparticles: P2VP-first infiltration forms thin adsorbed layers that drive PS into the pore interiors, generating continuous interfacial pathways that enable rapid, interface-mediated transport. In contrast, PS-first infiltration produces thicker P2VP layers that isolate PS domains and disrupt pathway connectivity, forcing chains to rely on a slower, connectivity-limited transport mechanism through P2VP-rich interstitial regions. Above the order-disorder transition, or upon silanizing nanoparticles to neutralize surface affinity, the rate difference disappears. These findings demonstrate how the interplay between nanoscale domain configuration and polymer-surface affinity governs infiltration dynamics, providing mechanistic insight into tuning transport in nanostructured block copolymers.

Aimed at the simulation, design, and interpretation of advanced pulse experiments crossing the boundaries between nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), including the rapidly emerging, hybrid discipline of pulsed dynamic nuclear polarisation (DNP), we present a host of novel features in the widely used SIMPSON software package addressing these aspects. Along with this come new features for advanced pulse sequence evaluation in terms of propagator splitting, high-order spin operator cross terms, and pulse phase transients. These fundamental new tools are introduced in a C++-based next generation of the SIMPSON software, which improves calculations speed in some aspects, is better prepared for further developments, and facilitates easier community contributions to the open-source software package.

Molecular gas is crucial to understanding star formation and galaxy evolution, but the giant molecular clouds (GMCs) of early-type galaxies (ETGs) have rarely been studied. Here, we present analyses of the spatially resolved GMCs of the lenticular galaxy NGC 1387, exploiting high spatial resolution (0.15" or 14 pc) 12CO(2-1) line observations from the Atacama Large Millimeter/submillimeter Array. We identify 1285 individual GMCs and measure the fundamental properties (radius, velocity dispersion, and molecular gas mass) of each with a modified version of the CPROPStoo package. Unusually for an ETG, the GMCs of NGC 1387 follow scaling relations very similar to those of the Milky Way disc and Local Group galaxy clouds, and most are virialised. GMCs with large masses and radii and/or small galactocentric distances have their angular momenta aligned with the large-scale galactic rotation, while other GMCs do not. These results show that ETGs have more diversified GMC properties than previously thought. We discuss potential reasons for such diversity, and viewing-angle dependency is a plausible candidate.

In this work, we provide an overview of general solutions for displacement fields in static problems of isotropic strain gradient elasticity (SGE). We not only review existing solutions but also derive new representations, showing that all classical elasticity solutions - including those of Boussinesq-Galerkin, Papkovich-Neuber, Naghdi, Lame, Love and Boussinesq - can be simply generalized to SGE framework. In general, it is shown that SGE enables the use of any classical general solution representation combined with a Helmholtz decomposition for the gradient part of the displacement field. Consistency is also established between the presented Papkovich-Neuber representation and the general solutions of SGE proposed previously by Mindlin (1964), Lurie et al. (2006) and Charalambopoulos et al. (2020). Furthermore, we establish the relationships between the stress functions of different general solutions and show their completeness.

We establish results on the dynamics of interacting charged null fluids in general relativity, specifically in the context of the bouncing continuation proposed in [Ori91]. In this model - the setting for a number of prominent case studies on black hole formation - charged massless particles may instantaneously change direction (bounce) after losing all their 4-momentum due to electrostatic repulsion. We initiate the study of timelike bounce hypersurfaces in spherical symmetry: scenarios in which an incoming beam of charged null dust changes direction along a timelike surface $\mathcal{B}$, which is the (free) boundary of an interacting 2-dust region. We identify a novel decoupling of the equations of motion in this region. First, it is shown that every timelike curve segment $γ$ in the spherically symmetric quotient of Minkowski or Reissner-Nordström spacetimes arises as the bounce hypersurface $\mathcal{B}$ of a charged null dust beam incident from past null infinity $\mathcal{I}^-$. We construct a spacetime $(\mathcal{M},g_{μν})$ describing the full trajectory of the beam, which includes gluing to Reissner-Nordström and Vaidya regions. Across $\mathcal{B}$ the metric has regularity $g_{μν}\in C^{2,1}$ and satisfies Einstein's equation classically, while $C^\infty$ gluing may be achieved across all other interfaces. We also obtain examples of timelike bounce hypersurfaces terminating in a null point. Since these constructions are teleological, we secondly consider a given charged incoming beam from past null infinity. We formulate and solve a free boundary problem which represents the formation of a timelike bounce hypersurface. The result is conditional, applying only in the exterior region of a Reissner-Nordström spacetime, and subject to a technical regularity condition.

The success of Large Language Models (LLMs) has established that scaling compute, through joint increases in model capacity and dataset size, is the primary driver of performance in modern machine learning. While machine learning has long been an integral component of High Energy Physics (HEP) data analysis workflows, the compute used to train state-of-the-art HEP models remains orders of magnitude below that of industry foundation models. With scaling laws only beginning to be studied in the field, we investigate neural scaling laws for boosted jet classification using the public JetClass dataset. We derive compute optimal scaling laws and identify an effective performance limit that can be consistently approached through increased compute. We study how data repetition, common in HEP where simulation is expensive, modifies the scaling yielding a quantifiable effective dataset size gain. We then study how the scaling coefficients and asymptotic performance limits vary with the choice of input features and particle multiplicity, demonstrating that increased compute reliably drives performance toward an asymptotic limit, and that more expressive, lower-level features can raise the performance limit and improve results at fixed dataset size.

We present the development of a data-driven, AI-based model of the Point Spread Function (PSF) that achieves higher accuracy than the current state-of-the-art approach, "PSF in the Full Field-of-View'' (PIFF). PIFF is widely used in leading weak-lensing surveys, including the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) Survey, and the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The PSF characterizes how a point source, such as a star, is imaged after its light traverses the atmosphere and telescope optics, effectively representing the "blurred fingerprint'' of the entire imaging system. Accurate PSF modeling is essential for weak gravitational lensing analyses, as biases in its estimation propagate directly into cosmic shear measurements -- one of the primary cosmological probes of the expansion history of the Universe and the growth of large-scale structure for dark energy studies. To address the limitations of PIFF, which constructs PSF models independently for each CCD and therefore loses spatial coherence across the focal plane, we introduce a deep-learning-based framework for PSF reconstruction. In this approach, an autoencoder is trained on stellar images obtained with the Hyper Suprime-Cam (HSC) of the Subaru Telescope and combined with a Gaussian process to interpolate the PSF across the telescope's full field of view. This hybrid model captures systematic variations across the focal plane and achieves a reconstruction error of $3.4 \times 10^{-6}$ compared to PIFF's $3.7 \times 10^{-6}$, laying the foundation for integration into the LSST Science Pipelines.

The focusing of particle beams for collider experiments is crucial for maximizing the luminosity and thus the discovery potential of these machines. In recent years, plasma wakefield acceleration has emerged as a leading candidate for achieving higher energy collisions with smaller facility footprints due to the large accelerating gradients in the plasma. This higher beam energy poses significant challenges for the final focusing system of the collider. Here, we discuss the various challenges of final focusing for TeV-scale plasma accelerators and propose possible solutions. Finally, we present the first design of a final focusing system for a 10 TeV linear wakefield collider, evaluate its performance, and discuss its shortcomings as well as improvements for future designs.

We propose a minimal tight-binding model for the electronic interface layer of the LaAlO$_3$/SrTiO$_3$ heterostructure with oxygen vacancies. In this model, the effective carriers are subject to oxygen vacancy induced magnetic impurities. Both the effects of random on-site potentials and Zeeman-like exchange interactions between correlated carriers and magnetic impurities are taken into account. By applying the combined coherent potential approximation (CPA) and dynamical mean-field theory (DMFT) for a ferromagnetic state, we uncover a disordered Fermi-liquid regime for the majority-spins and a low energy scale which controls the transport of the minority-spin carriers, both induced by the magnetic impurities.

Latent heat flux is a primary pathway for ocean-atmosphere exchange of heat and moisture, yet the influence of sea surface temperature variability at fine scales ($\leq$ 100 km) on latent heat flux variability, particularly over the Southern Ocean, remains poorly understood. Here we quantify the scale-dependent drivers of latent heat flux (LHF) variability using a year-long, global, fully coupled ocean-atmosphere simulation with kilometer-scale resolution. Annual-mean LHF in eddy-rich regions reaches $\approx$ 215 W m$^{-2}$, approximately three times larger than in eddy-poor regions. Spectral analyses show that ocean mesoscale [$\mathcal{O}$(100 km)] and submesoscale [$\mathcal{O}$(1-10 km)] variability accounts for up to $\approx$ 80% of the total LHF variance in eddy-rich sectors, but as little as 10% in eddy-poor regions, and increases proportionally with eddy kinetic energy and sea surface temperature (SST) variance. We also find that strong submesoscale SST fronts ($\approx$ 5 $^\circ$C over 10 km) force a localized secondary circulation that extends well above the marine boundary layer into the mid-troposphere. Comparison with ERA5 shows that fine ocean scales, responsible for about 17% of the ocean-driven LHF variance in the simulation, are largely unresolved in the reanalysis, leading to a muted atmospheric response lacking any secondary circulation. Despite a strong heterogeneity in LHF variability, the atmospheric dynamics are mostly uniform across the domain, suggesting a non local atmospheric response to ocean forcing. These results highlight the potential for ocean meso- and submesoscales, commonly under-resolved in climate models and reanalysis, to influence Southern Ocean air-sea coupling and atmosphere both locally and remotely.

We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $Λ>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $Λ$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,Λ)$ locally in the slow-rotation regime away from $a=0$.

We show how the micro-focused BLS signal of forward volume spin waves is formed and why it remains observable despite symmetry-based "suppression" expectations. A reciprocity-theorem based model with vectorial diffraction-limited focusing identifies the nonnegligible longitudinal focal-field component as the key element responsible for BLS sensitivity in the forward volume geometry. We further demonstrate that full polarization analysis, implemented through polarizer-analyzer maps of coherently excited spin waves, provides information beyond the conventional crossed polarizer-analyzer readout. In a BiYIG thin film, the measured maps exhibit Stokes/anti-Stokes polarization asymmetries and nontrivial patterns that stem from quadratic magneto-optical coupling terms. Fitting the data with a model including Voigt and Cotton-Mouton contributions yields an effective Cotton-Mouton constant and shows that the quadratic response is comparable to the linear Voigt contribution.

Despite significant advances in lead-free perovskite photovoltaics, achieving a balance among environmental safety and high optoelectronic performance remains challenging. The inorganic double perovskite Cs2AgBiBr6 has emerged as a promising candidate owing to its robust three-dimensional crystal structure and suitable visible-range bandgap. However, best power conversion efficiencies (PCEs) for Cs2AgBiBr6 solar cells reported so far - 6.37% experimentally and 27.78% in numerical studies - remain below the theoretical performance potential, largely due to suboptimal charge transport layers, and interface-related recombination losses. Here, we address this gap using a 3D finite-element method (FEM) implemented in COMSOL Multiphysics, which couples optical simulations with semiconductor drift-diffusion transport. To our knowledge, this work represents the first comprehensive 3D FEM-based study of a double halide perovskite solar cell. Screening of 25 electron transport layer (ETL)-hole transport layer (HTL) combinations identifies CeO2 and P3HT as the optimal ETL and HTL respectively. Device performance is further analyzed through systematic variation of layer thicknesses, doping concentrations and defect densities within the FTO/CeO2/Cs2AgBiBr6/P3HT/Au architecture. Under optimized parameters, the simulated device achieves a PCE of 31.76%, representing the theoretical upper bound predicted by the model. Overall, this work demonstrates 3D physics-based device engineering as a decisive pathway for overcoming efficiency bottlenecks in lead-free double perovskite photovoltaics.

This paper presents the first demonstration of a viable, ultra-fast, radiation-hard machine learning (ML) application on FPGAs, which could be used in future high-energy physics experiments. We present a three-fold contribution, with the PicoCal calorimeter, planned for the LHCb Upgrade II experiment, used as a test case. First, we develop a lightweight autoencoder to compress a 32-sample timing readout, representative of that of the PicoCal, into a two-dimensional latent space. Second, we introduce a systematic, hardware-aware quantization strategy and show that the model can be reduced to 10-bit weights with minimal performance loss. Third, as a barrier to the adoption of on-detector ML is the lack of support for radiation-hard FPGAs in the High-Energy Physics community's standard ML synthesis tool, hls4ml, we develop a new backend for this library. This new back-end enables the automatic translation of ML models into High-Level Synthesis (HLS) projects for the Microchip PolarFire family of FPGAs, one of the few commercially available and radiation hard FPGAs. We present the synthesis of the autoencoder on a target PolarFire FPGA, which indicates that a latency of 25 ns can be achieved. We show that the resources utilized are low enough that the model can be placed within the inherently protected logic of the FPGA. Our extension to hls4ml is a significant contribution, paving the way for broader adoption of ML on FPGAs in high-radiation environments.

Shallow ensembles provide a convenient strategy for uncertainty quantification in machine learning interatomic potentials, that is computationally efficient because the different ensemble members share a large part of the model weights. In this work, we systematically investigate training strategies for shallow ensembles to balance calibration performance with computational cost. We first demonstrate that explicit optimization of a negative log-likelihood (NLL) loss improves calibration with respect to approaches based on ensembles of randomly initialized models, or on a last-layer Laplace approximation. However, models trained solely on energy objectives yield miscalibrated force estimates. We show that explicitly modeling force uncertainties via an NLL objective is essential for reliable calibration, though it typically incurs a significant computational overhead. To address this, we validate an efficient protocol: full-model fine-tuning of a shallow ensemble originally trained with a probabilistic energy loss, or one sampled from the Laplace posterior. This approach results in negligible reduction in calibration quality compared to training from scratch, while reducing training time by up to 96%. We evaluate this protocol across a diverse range of materials, including amorphous carbon, ionic liquids (BMIM), liquid water (H$_2$O), barium titanate (BaTiO$_3$), and a model tetrapeptide (Ac-Ala3-NHMe), establishing practical guidelines for reliable uncertainty quantification in atomistic machine learning.

Laser guide stars (LGSs) have been deployed for the last 20-30 years in ground-based astronomical telescopes to overcome the limited sky coverage of classical adaptive optics (AO) systems. Unfortunately, slow altitude drifts of the sodium layer compromise focus measurements, generating the so-called slow focus error, and, consequently, a natural guide star (NGS) is needed to compensate for that error. Our goal is to develop and operationalize a focal plane wavefront sensing (FPWFS) technique for slow focus tracking for the Keck I telescope, which can significantly increase sky coverage and allow slow focus tracking at higher frequencies, reducing the lag error. We develop, characterize, and compare three different FPWFS algorithms, namely Gerchberg-Saxton (GS), linearized focal plane technique (LiFT), and Gaussian fit (Gf). These algorithms were studied for the specific purpose of slow focus sensing in the NIR (H and K bands) using numerical simulations and data collected at Keck in 2025 (bench and on-sky). The three algorithms were studied and characterized against different criteria such as linearity, computational costs, and resistance to low signal-to-noise ratio and/or residuals. From the results obtained, the main candidate for an on-sky deployment was GS. On-sky tests showed promising results, with GS successfully compensating for purposely introduced focus errors, even under the presence of high turbulence conditions. This work can also be extrapolated to other existing 8-10 m class telescopes, or even future 30-40 m class telescopes, where the use of FPWFS can significantly improve sky coverage and reduce the lag error.

An analytical tool is presented to compute the parametric regions of flutter instabilities of a two-dimensional flexible foil elastically mounted. It is based on a new analytical formulation of the unsteady fluid-estructure interaction valid for small-amplitude oscillations and deformations of the foil immersed in an inviscid fluid. The formulation extends a previous analysis by including the effects of gravity and a second flexural mode, increasing its validity range to much smaller rigidities. The analytical results are validated with available numerical results, capturing the first two natural flexural modes down to values of the stiffness parameter $S$ of order $10^{-1}$. When only passive heave, or only passive pitch, is allowed, the rigid foil is stable, existing an upper stiffness bound for the flexural instabilities, wich become coupled with the spring instability mode for small spring constant increasing the growth rate. These coupled spring (linear or torsional) and flexural instability modes occur below a threshold value of $S$ and above a threshold value of $R$, both depending on the corresponding spring constant. Coupled pitch-heave flutter instabilities of a rigid foil occur in a region below a curve of the parametric plane of the two springs constants that depends on $R$, which shrinks to zero as $R$ decreases. For a flexible foil, the flexural unstable modes become coupled with the springs unstable mode as $S$ decreases from infinity, enlarging the mass ratio range for flutter instability and increasing its growth rate, the more so the smaller the springs constants. The parametric regions for flutter instabilities are easily characterized with the present analytical tool, providing the corresponding frequency and critical flutter velocity. The present results can be useful as a guide in the design of future turbines based on flexible oscillating foils.

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.

We investigate critical restricted solid-on-solid models associated to Dynkin diagrams of type $A$, $D$ and $E$, with fixed, periodic and twisted periodic boundary conditions. These models are endowed with an action of the diagrams of the Temperley-Lieb category. For each model, we obtain the decomposition of the state space as a direct sum of irreducible modules over the Temperley-Lieb algebra $\mathsf{TL}_N(β)$ or its periodic incarnation $\mathsf{\mathcal EPTL}_N(β)$. This allows us to recover the known conformal partition functions for these models in the continuum scaling limit. For each irreducible factor arising in the decompositions, we define an associated local operator on the lattice, which behaves like a connectivity operator. Using knowledge from the Temperley-Lieb representation theory at roots of unity, we show that these operators satisfy certain linear difference relations, which are lattice counterparts of the singular-vector relations in conformal field theory.

Identifying influential nodes and edges in directed networks remains a fundamental challenge across domains from social influence to biological regulation. Most existing centrality measures face a critical limitation: they either discard directional information through symmetrization or produce sparse, implementation-dependent rankings that obscure structural importance. We introduce a unified spectral framework for centrality analysis in directed networks grounded in the Singular value decomposition of the incidence matrix. The proposed approach derives both vertex and edge centralities via the pseudoinverse of Hodge Laplacians, yielding dense and well-resolved rankings that overcome the sparsity limitations commonly observed in betweenness centrality for directed graphs. Unlike traditional measures that require graph symmetrization, our framework naturally preserves directional information, enabling principled hub/authority analysis while maintaining mathematical consistency through spectral graph theory. The method extends naturally to hypergraphs through the same mathematical foundation. Experimental validation on real-world networks demonstrates the framework's effectiveness across diverse domains where traditional centrality measures encounter limitations due to implementation dependencies and sparse outputs.

Fast directional solidification during Laser Additive Manufacturing (LAM) produces a complex microstructure in nickel-based superalloys, comprising columnar grains with cellular sub-grain structures and carbides. Using non-destructive Scanning 3D X-ray Diffraction (S3DXRD), we reveal spatially complex orientation and intergranular strain relationships that couple strongly to processing-induced cellular sub-grain networks and a primary cubic metal carbide (MC) phase. We have examined 3D orientation and elastic strain tensor fields across 82 $γ$ grains together with the spatial distribution of over 37,000 MC carbides in an ABD-900AM alloy sample manufactured by the Directed Energy Deposition (DED) LAM process. Carbides are spatially associated with the cellular sub-grain network with a weak but present orientation relationship with their parent $γ$ grains. The MC carbides, known to be Ti, Ta and Nb rich, form in regions of high solute segregation, resulting in a significant volumetric lattice parameter patterning in the associated $γ$ phase regions. These chemically distinct solute-rich regions possess a higher associated elastic modulus compared to intercellular regions and determine the local residual stress patterning. These results provide the first non-destructive 3D study of the relationship between rapid solidification-induced segregation, deformation heterogeneity and carbide architectures in an additively manufactured Ni-based superalloy. The insights provide crucial detail to rationalise LAM process parameter optimisation and the coupled spatially governed structural performance.