We investigate Brunn-Minkowski-type inequalities for the torsional rigidity $T_γ$ and the first eigenvalue $λ_γ$ associated with the Ornstein-Uhlenbeck operator. Counterexamples are provided showing that neither concavity nor convexity properties hold for $T_γ$ on general bounded convex sets. We also demonstrate that log-concavity and log-convexity properties fail in this setting. In the case of centrally symmetric sets, we answer a question raised by Cordero-Erausquin and Eskenazis by showing that $T_γ^{1/(n+2)}$ is neither convex nor concave. On the positive side, we prove that $T_γ^{1/3}$ is convex with respect to Minkowski addition when restricted to Euclidean balls centered at the origin. For $λ_γ$, we answer negatively a question posed by Colesanti, Francini, Livshyts, and Salani by showing that the inequality $λ_γ(Ω_t)^{-1/2} \geq (1-t)λ_γ(Ω_0)^{-1/2} + tλ_γ(Ω_1)^{-1/2}$ does not hold, even for centrally symmetric sets.

We present a comprehensive global analysis of Energy-Energy Correlation (EEC) data in electron-positron annihilation into hadrons, spanning a wide range of center-of-mass energies ($7.7\,\,\text{GeV}\!\leq\!\sqrt{s}\!\leq\! 91.2\,\,\text{GeV})$. In the back-to-back (two-jet) region, we resum to all orders the logarithmically-enhanced contributions up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. The resummed results are consistently matched to fixed-order calculations up to $\mathcal{O}(α_S^3)$. Our resummation formalism also incorporates dominant heavy-quark mass effects and models non-perturbative power corrections by means of an analytic dispersive approach. A simultaneous fit yields an excellent description of experimental data across all energies, enabling a precise determination of the strong coupling, $α_S(m_Z^2) = 0.119 \pm 0.002$, as well as the non-perturbative parameters, including those characterizing the Collins--Soper evolution kernel. Our analysis includes, for the first time in a global fit, datasets from the ALEPH and AMY collaborations.

We propose a non-perturbative description of the moduli spaces encoding p-form generalized Maxwell theories in any dimension, using derived differential geometry. Our approach synthesizes the Batalin--Vilkovisky formalism with differential cohomology. Within this framework we formulate Dirac charge quantization and show how such charge-quantized moduli spaces exhibit abelian duality between generalized Maxwell theories of different types. We also describe the compactification of generalized Maxwell theories along closed Riemannian manifolds by computing the pushforward of the underlying sheaves of cochain complexes that model differential cohomology.

Prediction-powered inference (PPI) is a rapidly growing framework for combining machine learning predictions with a small set of gold-standard labels to conduct valid statistical inference. In this article, I argue that the core estimators underlying PPI are equivalent to well-established estimators from the survey sampling literature dating back to the 1970s. Specifically, the PPI estimator for a population mean is algebraically equivalent to the difference estimator of Cassel et al. (1976), and PPI plus corresponds to the generalized regression (GREG) estimator of Sarndal et al. (2003). Recognizing this equivalence, I consider what part of PPI is inherited from a long-standing literature in statistics, what part is genuinely new, and where inferential claims require care. After introducing the two frameworks and establishing their equivalence, I break down where PPI diverges from model-assisted estimation, including differences in the mode of inference, the role of the unlabeled data pool, and the consequences of differential prediction error for subgroup estimands such as the average treatment effect. I then identify what each framework offers the other: PPI researchers can draw on the survey sampling literature's well-developed theory of calibration, optimal allocation, and design-based diagnostics, while survey sampling researchers can benefit from PPI's extensions to non-standard estimands and its accessible software ecosystem. The article closes with a call for integration between these two communities, motivated by the growing use of large language models as measurement instruments in applied research.

Spectral reconstruction is a well studied numerically ill-posed problem which arises due to the relation of the Euclidean correlator to the spectral function via an inhomogeneous Fredholm equation of the first kind. Several different methods are on the market to resolve this issue, each taking different approaches and assumptions. In this proceedings we focus on implementing and testing a machine learning framework for spectral reconstruction, as well as implementing a novel method of estimating the behavior of the spectral function in the vicinity of vanishing frequency, which we denote as multipoint method, and compare these methods to well established spectral reconstruction techniques from the literature using mock data. As a physics application, we apply the reconstruction techniques to quenched lattice data for the correlation function in the vector channel at non-zero external magnetic field to extract the spectral function and the electric conductivity through its behaviour at vanishing frequency via a Kubo formula.

Dynamic metasurface antennas (DMAs) are an emerging hybrid-MIMO technology distinguished by an ultrathin form factor, low cost, and low power consumption. In real-world DMA prototypes, mutual coupling (MC) between meta-elements is generally non-negligible; some architectures even deliberately exploit strong MC to enhance wave-domain flexibility. In this paper, we address channel estimation (CE) for DMAs with known MC by formulating it as a tensor-decomposition problem. We develop a generalized block Tucker alternating least squares (BTALS) algorithm, together with specialized variants for cases with known direct and/or feed channel. We also develop a reciprocity-aware bilinear factorization method for the case with known direct channel. We experimentally validate our algorithms using an 18 GHz DMA prototype whose 7 feeds and 96 meta-elements are strongly coupled via a chaotic cavity. Our general BTALS algorithm reaches an accuracy of 43.1 dB, only 0.3 dB below the upper bound imposed by experimental noise. All proposed algorithms generally outperform the prior-art reference scheme thanks to the superior noise rejection enabled by the tensor-based framework. We further study the minimum number of required measurements as a function of the number of feeds and demonstrate the importance of MC awareness by comparison with an MC-unaware benchmark. Finally, we apply BTALS to a second setup enabling the prediction of the DMA's full dual-polarization 3D radiation diagram. We also measure the latter for DMA configurations optimized for channel-gain enhancement based on the estimated channels. Altogether, our work establishes the practical relevance of MC-aware tensor methods; beyond DMAs, it applies to all wireless systems with wave-domain programmability enabled by tunable lumped elements.

We assess the impact of non-ideal, continuously rotating half-wave plates (HWPs) on cosmic microwave background (CMB) polarization measurements targeting large angular scale signal. Such hardware solutions are used in or planned for multiple modern CMB efforts, both ground-based, for instance, small aperture telescopes of Simons Observatory or satellite borne, such as LiteBIRD. Using a frequency-dependent parametric model based on the Mueller matrix formalism, we characterize the induced mixing of Stokes parameters. Through end-to-end simulations, we propagate these effects from time-ordered data to cosmology via map-making and component-separation stages, quantifying their impact on the $B$-modes power spectrum and the tensor-to-scalar ratio, $r$. Our analysis shows that neglecting the frequency dependence of a three-layer HWP gives rise to significant polarization leakage, biases foreground spectral parameters, and leads to residual contamination in the recovered CMB maps. To mitigate these effects, we investigate multiple analysis strategies progressively incorporating a more complete description of the instrumental response. At the map-making level, this requires generalizing the standard pointing matrix to account for the full time- and frequency-dependent instrumental response. We find that standard HWP models, reduce the biases only down to $r \sim 10^{-2}$, while a more advanced approach based on a generalization of both map-making and component separation, implemented using JAX, can suppress it down to $r \sim 7 \times 10^{-4}$. Finally, we extend this approach to a time-domain component-separation, enabling a statistically consistent treatment of instrumental response in the presence of time-domain features. We demonstrate its feasibility and validate it by performing a full end-to-end analysis, recovering results in good agreement with the map-based ones.

We systematically investigate the electromagnetic properties of exotic states whose internal structures remain uncertain and for which different models have been proposed. In this work, we focus on the magnetic dipole moments of hidden-charm pentaquark states using QCD light-cone sum rules with four distinct interpolating currents. The analysis accounts for contributions from both light and charm quark sectors, as well as higher-dimensional operators, ensuring convergence of the operator product expansion and dominance of the ground-state pole. Our results demonstrate a strong dependence of the magnetic moments on the internal quark configurations and spin alignments, revealing substantial variations among the different currents despite identical quark content and quantum numbers. Comparisons with existing studies indicate that while molecular-type predictions show general agreement, compact configurations yield markedly different values, including significant differences in sign and magnitude. These findings therefore underscore the sensitivity of electromagnetic observables to the internal structure of exotic hadrons and highlight their potential as probes to discriminate between competing structural models for spin-parity assignments and underlying quark dynamics.

Understanding how optical excitation couples with polarization and interfacial electrostatics in van der Waals (vdW) ferroelectrics (FEs) is essential for the development of light-programmable nanoelectronic and optoelectronic devices. Here, we present direct nanoscale evidence of photoferroionic coupling in the vdW FE semiconductor CuInP2S6 (CIPS), where optical excitation jointly modulates electronic band bending, FE switching, and Cu+ ionic relaxation. The use of correlated Kelvin probe force microscopy, piezoresponse force microscopy, and conductive atomic force microscopy under above-bandgap illumination reveals illumination-induced enhancement of surface work function, persistent surface photovoltage, reduced coercive field, and positive imprint shifts. These effects arise from synergistic photocarrier redistribution and slow Cu+ migration that reshape interfacial depletion widths and internal electric fields. Illumination-assisted barrier lowering further enhances carrier injection and produces sweep-rate-dependent ferroionic transport hysteresis. Our results establish photoferroionic coupling as the governing mechanism for light-controlled band modulation and polarization stability in CIPS, providing a nanoscale framework for designing light-addressable FE memories, optoelectronic switches, and neuromorphic devices based on layered ferroionic materials.

Direct air carbon capture and storage (DACCS) is a promising CO2 removal technology, but its deployment at scale remains speculative. Yet, its technological, economic, and policy-related uncertainties have often been overlooked in mitigation pathways. This paper conducts the first uncertainty quantification and global sensitivity analysis of DACCS on technological, market, financial and public support drivers, using a detailed-process Integrated Assessment Model and newly developed sensitivity algorithms. We find that DACCS deployment exhibits a fat-tailed distribution: most scenarios show modest technology uptake, but there is a small but non-zero probability (4-6%) of achieving gigaton-scale removals by mid-century. Scaling DACCS to gigaton levels requires subsidies that always exceed 200-330 USD/tCO2 and are sustained for decades, resulting in a public support programme of 900-3000 USD Billions. Such an effort pays back by mid-century, but only if accompanied by strong emission reduction policies. These findings highlight the critical role of climate policies in enabling a robust and economically sustainable CO2 removal strategy.

We investigate the phenomenon of black hole superradiance in the presence of torsion within the framework of Poincaré gauge theory. In particular, in contrast to the classical approach of General Relativity, we show that the inclusion of torsion in the space-time geometry enables the energy extraction from rotating black holes by Dirac fermions via chiral asymmetry, while preserving the Pauli exclusion principle.

This paper presents a Hamiltonian reduction procedure for field theories over affine principal bundles introducing a canonical identification to describe the reduced multisymplectic space without the introduction of a connection. The main goal is to provide a Hamiltonian analogue of the Lagrangian reduction theory developed in M. Castrillón López, P. M. Chacón, and P. L. García. J. Geom. Mech., 5(4):399-414, 2013. The core of this work lies in the derivation of this canonical identification, the reduced Hamilton-Cartan equations, and a reduced covariant bracket that describes the dynamics. Finally, this theoretical framework is illustrated with a fundamental example: molecular strands.

The growing use of inverter-based resources in modern power systems has made grid-following inverters a central topic in power-system modeling, control, and simulation. Despite their widespread deployment, introductory material that explains grid-following inverter operation from first principles and connects control design to time-domain simulation remains limited. To address this need, this tutorial presents a circuit-theoretic introduction to the modeling and simulation of a grid- following inverter connected to an electrical power grid. We describe the inverter synchronization with the grid (PLL), power control, and current control structure and show how these elements can be represented within an electromagnetic transient (EMT) simulation framework using companion model-based formulations similar to those used in circuit simulators such as SPICE and Cadence. In this tutorial, we use the grid-following inverter as the primary example to illustrate how its governing equations, control loops, and network interface can be formulated and simulated from first principles. By the end of the document, readers should gain a clear introductory understanding of how to model and simulate a grid-following inverter in an EMT platform.

Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. This process takes polylogarithmic time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.

Spin-orbit obliquity measurements of hot-Jupiter systems constrain giant planet migration and tidal evolution. In binary systems, combining stellar obliquities with the orbit-orbit angle ($γ$) between the planetary and stellar companion orbits provides further insight into the dynamical influence of stellar companions. Here we aim to determine the projected obliquity ($λ$) of the hot Jupiter TOI-1333Ab ($P\approx4.72$ d, $M_{\rm p}\approx2.4$ M$_{\rm J}$) and place the system in the context of hot-Jupiter migration and tidal realignment in binary systems. We analysed spectroscopic observations obtained during planetary transit to model the Rossiter-McLaughlin effect and derive the projected obliquity. We combined this measurement with published system parameters and constraints on the wide stellar companion orbit to assess plausible migration scenarios. We measure a projected obliquity of $λ=-5 \pm 10^\circ$, showing that TOI-1333Ab is well aligned with the stellar spin axis of its F-type host star. The low obliquity and its modest eccentricity ($e=0.073^{+0.092}_{-0.052}$) are consistent with either disc-driven migration or high-eccentricity migration followed by efficient tidal circularisation and realignment. With an effective temperature of $6274\pm94$ K, the host star lies above the canonical Kraft break where the systems are frequently misaligned. Despite this, we find the system to be well aligned. In comparison with other planetary systems in binaries, TOI-1333 occupies a relatively isolated region in projected obliquity-orbit-orbit angle ($γ=81.5\pm1.1^\circ$) space, making it a valuable system for studying the interplay between migration, tides, and stellar companions.

Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite dimensional spectral triple. Motivated by the fundamental question of the dependence of the spectra of Dirac operators under change of metrics, we prove the continuity of the spectra of Dirac operators for almost commutative models as functions of the underlying Riemannian metric. We allow both the Riemannian metric (in the $C^1$ topology) and the Dirac operator of the finite-dimensional factor to vary simultaneously. Since the physics of the system is fundamentally encoded in this spectrum, this result is a form of stability result regarding the geometry, or physical, content of these models. This result is based upon a novel approach to prove continuity of spectra of Dirac operators using the spectral propinquity. Notably, this method provides a new, different proof of the classical results as well. To illustrate the versatility of our new method, we also apply our results to completely non-commutative family of examples, including quantum tori and quantum solenoids.

We describe an empirical approach to identify low-weight combinations of columns of the decoding matrices of a quantum circuit-level noise model, for which belief-propagation (BP) algorithms converge possibly very slowly. Focusing on the logical-idle syndrome cycle of the low-density parity check gross code, we identify criteria providing a characterization of the Tanner subgraph of such low-weight error syndromes. We analyze the dynamics of iterations when BP is used to decode weight-four and weight-five errors, finding statistics akin to exponential activation in the presence of noise or escape from chaotic phase-space domains. We study how BP convergence improves when adding to the decoding matrix relevant combinations of fault columns, and show that the suggested decoder amendment can result in the reduction of both logical errors and decoding time.

We study the affine variety $L_{n}(\mathfrak{g})$ of Lie algebra representations, the collection of all homomorphisms from an arbitrary $n$-dimensional Lie algebra into a fixed real semi-simple Lie algebra $\mathfrak{g}$. Using techniques from real Geometric Invariant Theory, we equip this variety with a natural moment map and associated energy functional arising from the action of the real reductive group $GL(n,\mathbb{R}) \times \text{Inn}(\mathfrak{g})$. We analyze the critical points of the energy functional and describe their structure. In particular, we prove that every semi-simple pair, that is representations of semi-simple Lie algebras, will globally minimize the energy in its orbit. As consequences, we obtain an elementary proof of the rigidity of semi-simple homomorphisms and derive a new proof of the Mostow theorem on the existence of compatible Cartan involutions for semi-simple subalgebras. Subsequent results concerning the structure of critical points of higher energy are also obtained.

This work develops a spherical-multipole expansion of Goldstein's acoustic analogy, for the prediction of tonal noise from rotating propellers. The acoustic field is expressed through spherical multipoles, which separate source integrals from the observer dependence. This decoupling leads to computational efficiency: once the multipole coefficients are computed from blade geometry and aerodynamics, the sound field at any observer location is obtained by a simple evaluation of spherical harmonics and radial propagation factors, avoiding repeated integrations for each observer point. Moreover, this enables a straightforward radiated power calculation, without resorting to far-field pressure integrals. For hovering subsonic propellers, the results show a rapid convergence of the expansion. For each harmonic, the dominant radiation is accurately captured by the first two non-zero multipoles, corresponding to the leading symmetric and antisymmetric contributions with respect to the plane of rotation. To interpret the physical content of these leading terms, two simplified descriptions of the source integral are developed. The first is a lifting-surface formulation, suited to blades at small incidence, in which the thin-airfoil approximation allows to separate lift-like loading, drag-like loading, and thickness contributions. The second is a lifting-line formulation, suited to high-aspect-ratio blades, in which the surface integral is reduced to spanwise integrals of compact sectional moments. The validity of the two formulations is assessed through comparisons of directivity, power distribution over harmonics and time-domain waveforms. The results show good accuracy in their respective regimes of validity, together with substantial computational savings.

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.

Analog multiplexing for sigma delta modulated Digital to Analog Converters has been recently proposed as a means of achieving robustness. This preprint analyses said scheme via simulations. The main limitation introduced by the proposed architecture comes from mismatch in the DACs gain, which can drastically impact performances. A new technique of dynamic elements matching is proposed here to overcome this problem.

We present BSTModelKit.jl, an open-source Julia package for constructing, solving, and analyzing Biochemical Systems Theory (BST) models of biochemical networks. The package implements S-system representations, a canonical power-law formalism for modeling metabolic and regulatory networks. BSTModelKit.jl provides a declarative model specification format, dynamic simulation via ordinary differential equation (ODE) integration, steady-state computation, and global sensitivity analysis using the Morris and Sobol methods. The package leverages the Julia scientific computing ecosystem, in particular the SciML suite of differential equation solvers, to provide efficient and flexible model analysis tools. We describe the mathematical formulation, software design, and demonstrate the package capabilities with illustrative examples.

We study the solvability and uniqueness for several degenerate Monge--Ampère equations including the Monge--Ampère eigenvalue problem in real Euclidean spaces that involve singular Borel measures. Our approach systematically analyzes the Monge--Ampère energy from the variational point of view and appropriately exploits monotonicity arguments. Our main tools consist of the mixed Monge--Ampère measure, Aleksandrov--Blocki--Jerison-type maximum principles, integration by parts, convex envelope, and comparison principles for subcritical equations. For the Monge--Ampère eigenvalue problem, we contrast the analysis within and without the energy class; even if it might not have solutions in the energy class, we show that the infimum of the Rayleigh quotient can be approximated from above by Monge--Ampère eigenvalues of the truncated measures, and by Rayleigh quotients of an inverse iterative scheme. We give examples showing that for very singular Borel measures, the Monge--Ampère eigenvalue problem has only solutions outside the energy class together with symmetry breaking and nonuniqueness.

The paper describes a numerical method for solving acoustic multibody scattering problems in two and three dimensions. The idea is to compute a highly accurate approximation to the scattering operator for each body through a local computation, and then use these scattering matrices to form a global linear system. The resulting coefficient matrix is relatively well-conditioned, even for problems involving a very large number of scatterers. The linear system is amenable to iterative solvers, and can readily be accelerated via fast algorithms for the matrix-vector multiplication such as the fast multipole method. The key point of the work is that the local scattering matrices can be constructed using potentially ill-conditioned techniques such as the method of fundamental solutions (MFS), while still maintaining scalability and numerical stability of the global solver. The resulting algorithm is simple, as the MFS is far simpler to implement than alternative techniques based on discretizing boundary integral equations using Nyström or Galerkin.

We derive analytical expressions for chemical potentials within the random phase approximation (RPA), equivalently the $GW$ energy functional evaluated using non interacting Green's functions ($G_s$). The chemical potential is obtained using two formally equivalent approaches: a direct derivative of the total energy with respect to particle number, and a functional derivative via the chain rule through $G_s$, both validated with finite difference benchmarks. We show that the functional derivative of the $GW$ correlation energy$\unicode{x2013}$i.e., the $GW$ correlation self energy$\unicode{x2013}$exhibits a discontinuity at integer particle numbers with finite jumps. This resolves the apparent inconsistency between accurate $GW$ quasiparticle energies and the large delocalization errors observed in RPA total energies, as standard $GW$ self energies neglect this nonanalytic behavior. Our results suggest that derivative discontinuities are a fundamental feature of correlation energy functionals, analogous to the known discontinuity in the exact exchange correlation energy.

Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this paper we develop an embedding theory for variable Hajłasz-type smoothness spaces on metric measure spaces whose ``dimension'' is allowed to vary pointwise through a bounded exponent $Q(\cdot)$ that governs a lower Ahlfors growth condition on the measure. We introduce variable exponent Hajłasz-Sobolev spaces $M^{s(\cdot),p(\cdot)}$, Hajłasz-Triebel-Lizorkin spaces $M^{s(\cdot)}_{p(\cdot),q(\cdot)}$, and Hajłasz-Besov spaces $N^{s(\cdot)}_{p(\cdot),q(\cdot)}$, and establish Sobolev, Morrey, and Moser-Trudinger type embeddings into variable exponent Lebesgue and Hölder spaces. These embeddings are proved both locally (on balls) under a lower Ahlfors $Q(\cdot)$-regularity condition on the measure and regularity assumptions on the exponents (notably log-Hölder continuity), and globally under additional geometric hypotheses such as geometric doubling and mild uniform bounds on the measure of unit balls. We also identify geometric conditions that are not only sufficient but, in appropriate forms, necessary for the validity of these embeddings, showing in particular that such inequalities force a lower growth bound on the measure of order $r^{Q(x)}$.

Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes -- a quantum analog of the well-studied LPN problem -- is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practical: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE, and our OT is round-optimal. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suit of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions.

We perform a search for an X-ray monochromatic line arising from dark matter (DM) decay in the halo of the Large Magellanic Cloud. An emission line can be expected from two well-motivated DM candidates: sterile neturinos and axion-like particles (ALPs). We analyze the eROSITA-DE DR1 datasets in the energy range between 1 and 9 keV. No evidence for a DM line is found, and we set lower limits on the DM lifetime. We then recast these bounds into upper limits on the active-sterile neutrino mixing angle $\sin^2(2θ)$ and on the ALP to photon coupling $g_{aγ}$, for DM masses between 2 and 18 keV. These results set new strong constraints for masses below 5 keV.

This report examines numerical aspects of constructing Karhunen-Loève expansions (KLEs) for second-order stochastic processes. The KLE relies on the spectral decomposition of the covariance operator via the Fredholm integral equation of the second kind, which is then discretized on a computational grid, leading to an eigendecomposition task. We derive the algebraic equivalence between this Fredholm-based eigensolution and the singular value decomposition of the weight-scaled sample matrix, yielding consistent solutions for both model-based and data-driven KLE construction. Analytical eigensolutions for exponential and squared-exponential covariance kernels serve as reference benchmarks to assess numerical consistency and accuracy in 1D settings. The convergence of SVD-based eigenvalue estimates and of the empirical distributions of the KL coefficients to their theoretical $\mathcal{N}(0,1)$ target are characterized as a function of sample count. Higher-dimensional configurations include a two-dimensional irregular domain discretized by unstructured triangular meshes with two refinement levels, and a three-dimensional toroidal domain whose non-simply-connected topology motivates a comparison between Euclidean and shortest interior path distances between the grid points. The numerical results highlight the interplay between the discretization strategy, quadrature rule, and sample count, and their impact on the KLE results.

Couplings between ferroelectric and magnetic orders offer promising routes toward low-dissipation electronics. However, such couplings are notably rare, largely due to the poor compatibility between insulating band structures and ferromagnetism. Here, we study a different strategy: we identify previously overlooked time-reversal-symmetric $p$- and $f$-wave spin-polarized insulating electronic states in ferroelectrics with noncollinear magnetic sublattices. We show that combining spin and magnetic group theory enables a systematic classification of the origin of polar symmetry breaking. We distinguish crystallographic, exchange-, or spin-orbit-driven mechanisms. Furthermore, we identify more than 50 candidate materials. Using first-principles calculations, we demonstrate a pristine, time-reversal-symmetric $p$-wave spin-polarized electronic structure in the well-known multiferroic $\mathrm{GdMn_2O_5}$. We further show that its $p$-wave order can be switched electrically, opening alternative paths toward spintronic and multiferroic functionalities in this class of materials.