Electromagnetic resonances play a central role in nanophotonics by enabling efficient confinement of electromagnetic energy and enhanced light-matter interaction. Traditionally, resonant phenomena have been described using platform-specific concepts developed within distinct research communities, including photonic crystals, plasmonics, and dielectric metasurfaces. In this Perspective, we propose a unified framework that distinguishes electromagnetic resonances as eigenmodes of open systems from their experimentally observed manifestations as scattering features. We show how resonances evolve from isolated particles to coupled oligomers and periodic structures, highlighting the roles of geometry, material response, and dimensionality. Particular attention is given to interference-driven phenomena such as bound states in the continuum, lattice resonances, anapoles, and superscattering, some of which cannot always be associated with a single eigenmode. By clarifying the relationship between eigenmodes, scattering channels, and interference effects, this Perspective provides a coherent language for interpreting resonant phenomena and identifies key challenges and opportunities for designing robust resonant photonic systems.

People often express opinions that differ from their privately held views, a phenomenon known in economy as preference falsification. Expressed-private opinion (EPO) models capture this by assigning each agent two dynamical variables: a private (internal) and an expressed (external) opinion. Within the nonlinear $q$-voter model, two EPO variants have been studied so far: with and without self-anticonformity. In both formulations, agents update private and expressed binary opinions, one after another and at the same rate, which has led to two update schemes studied previously: AT (act then think), in which an agent first updates its expressed and then its private opinion, and TA (think then act), in which the order is reversed. To eliminate this ad hoc distinction and quantify the interplay between private and expressed opinions, we introduce the $α$-EPO $q$-voter model with asynchronous updating -- in each elementary step, an agent updates its private opinion with probability $α$ or its expressed opinion with complementary probability $1-α$. We derive mean-field theory and, for the first time for EPO $q$-voter dynamics, a pair approximation, and validate them with Monte Carlo simulations on artificial and real organizational networks. Comparing the two model variants, we show that the collective outcome controlled by $α$ strongly depends on self-anticonformity: with self-anticonformity the results are robust to $α$, whereas without it $α$ shifts the agreement-disagreement threshold and can change the type of phase transition. In the mean-field limit this change occurs only for $q=3$, but the pair approximation reveals an additional low-connectivity regime in which both $α$ and the average degree $k$ control the emergence and width of hysteresis also for larger influence groups.

Multiphase gas can be found in many astrophysical environments, such as galactic outflows, stellar wind bubbles, and the circumgalactic medium, where the interplay between turbulence, cooling, and viscosity can significantly influence gas dynamics and star formation processes. We investigate the role of viscosity in modulating turbulence and radiative cooling in turbulent radiative mixing layers (TRMLs). In particular, we aim to determine how different amounts of viscosity affect the Kelvin-Helmholtz instability (KHI), turbulence evolution, and the efficiency of gas mixing and cooling. Using idealized 2D numerical setups, we compute the critical viscosity required to suppress the KHI in shear flows characterized by different density contrasts and Mach numbers. These results are then used in a 3D shear layer setup to explore the impact of viscosity on cooling efficiency and turbulence across different cooling regimes. We find that the critical viscosity follows the expected dependence on overdensity and Mach number. Our viscous TRMLs simulations show different behaviors in the weak and strong cooling regimes. In the weak cooling regime, viscosity has a strong impact, resulting in laminar flows and breaking previously established inviscid relations between cooling and turbulence (albeit leaving the total luminosity unaffected). However, in the strong cooling regime, when cooling timescales are shorter than viscous timescales, key scaling relations in TRMLs remain largely intact. In this regime -- which must hold for gas to remain multiphase -- radiative losses dominate, and the system effectively behaves as non-viscous regardless of the actual level of viscosity. Our findings have direct implications for both the interpretation of observational diagnostics and the development of subgrid models in large-scale simulations.

We develop a rigorous evaluation of Dirac brackets for classical observables on the phase space of radiative gravitational modes at null infinity that naturally incorporates memory effects. Considering the Ashtekar-Streubel phase space, with boundary conditions in time given by vanishing {\it news} and purely electric {\it shear}, and taking into account the infinite dimensionality of the phase space, we identify the algebra of proper observables (understood as functions on phase space that can be associated with smooth symplectic flows). We show that the action of supertranslation charges generate the correct transformations on the shear. We also show that the conventional definition of the ``Goldstone mode'' adopted in the literature cannot be associated with a proper observable, but nevertheless there exists an infinite family of proper observables, which we call {\it Goldstone probes}, that are capable of measuring the Goldstone mode. We notice that there are no Goldstone probes constructed only out of the shear {\it or} the news, providing a possible explanation for why attempts to construct a (separable) Hilbert space with different memory states have failed so far. Finally, we derive formulas for distributional Dirac brackets between local shear and news, and show that they contain non-local corrections.

The Ultraviolet Near Infrared Optical Northern Survey (UNIONS) is a photometric survey in the northern sky. The quality of the data in the $r$ band provides precise shape measurements to measure the growth of structures using cosmic shear. This work aims to constrain cosmological parameters using a harmonic-space estimator of the cosmic shear signal, known as pseudo-$C_\ell$, in a non-tomographic analysis. We perform our analysis in the context of the standard $Λ$CDM cosmology. We model astrophysical systematic effects such as baryonic feedback and intrinsic alignments of galaxies. We verify that the point spread function systematic contribution does not affect our results. We assess the impact of different scale cuts and modelling choices on the constraints. We find $S_8 \equiv σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.891^{+0.057}_{-0.084}$, consistent at the $0.79 \, σ$ level with \emph{Planck} and between $0.87$ to $1.51 \, σ$ with other weak lensing surveys. Our results are robust to analysis choices, and we use lognormal simulations to assess the consistency between configuration and harmonic space results, finding a $2.18 \, σ$ agreement between the two statistics. The degeneracy between $S_8$ and the amplitude of the intrinsic alignment, $A_{\rm IA}$, sampled from a prior obtained from direct measurements, is one of the largest sources of uncertainty. This work is part of the first cosmological analysis of the UNIONS survey using cosmic shear and paves the way for future tomographic and $3 \times 2$ point cross-correlation analyses, exploiting the unique overlap of UNIONS with deep spectroscopic surveys in the northern hemisphere.

We prove that any complex local representation of the flat virtual braid group, $FVB_2$, into $GL_2(\mathbb{C})$, has one of the types $λ_i: FVB_2 \rightarrow GL_2(\mathbb{C})$, $1\leq i\leq 12$. We find necessary and sufficient conditions that guarantee the irreducibility of representations of type $λ_i$, $1\leq i\leq 5$, and we prove that representations of type $λ_i$, $6\leq i\leq 12$, are reducible. Regarding faithfulness, we find necessary and sufficient conditions for representations of type $λ_6$ or $λ_7$ to be faithful. Moreover, we give sufficient conditions for representations of type $λ_1$, $λ_2$, or $λ_4$ to be unfaithful, and we show that representations of type $λ_i$, $i=3, 5, 8, 9, 10, 11, 12$ are unfaithful. We prove that any complex homogeneous local representations of the flat virtual braid group, $FVB_n$, into $GL_{n}(\mathbb{C})$, for $n\geq 3$, has one of the types $γ_i: FVB_n \rightarrow GL_n(\mathbb{C})$, $i=1, 2$. We then prove that representations of type $γ_1: FVB_n \rightarrow GL_n(\mathbb{C})$ are reducible for $n\geq 6$, while representations of type $γ_2: FVB_n \rightarrow GL_n(\mathbb{C})$ are irreducible if and only if $b\neq y$, for $n\geq 3$. Then, we show that representations of type $γ_1$ are unfaithful for $n\geq 3$ and that representations of type $γ_2$ are unfaithful if $y=b$. Furthermore, we prove that any complex homogeneous local representation of the flat virtual braid group, $FVB_n$, into $GL_{n+1}(\mathbb{C})$, for all $n\geq 4$, has one of the types $δ_i: FVB_n \rightarrow GL_{n+1}(\mathbb{C})$, $1\leq i\leq 8$. We prove that these representations are reducible for $n\geq 10$. Then, we show that representations of types $δ_i$, $i\neq 5, 6$, are unfaithful, while representations of types $δ_5$ or $δ_6$ are unfaithful if $x=y$.

RED-2400 is a public benchmark of 6,660 algorithmically-rejected trading events from a live Solana decentralised-exchange filter stack, observed continuously over 22 calendar days (2026-04-10T21:10Z through 2026-05-02T21:48Z, UTC). Each rejection event is linked to its post-rejection price-and-liquidity trajectory. The deposit contains 169,123 forward-outcome observations and 1,837 graveyard-tracker lifecycle snapshots, covering 1,076 distinct mints in the rejection registry and 1,075 in the forward-observation file. Outcome labels follow the five-tier classification rule introduced by a related methodology paper [Kamat 2026c]. The deposit includes a lifecycle-tracker file that permits external validation of any subset of those labels against observed token-lifecycle ground truth. Filter labels are anonymised to filter_1 through filter_8; source-collector identifiers to source_a and source_b. Liquidity and 24-hour volume are quantised to the nearest power of two, preserving heavy-tailed shape while preventing operational-threshold inference. This is the first window of a planned series; subsequent windows will extend the time horizon and enable regime-stratified analysis. "RED-2400" is a brand name, not a count; current cohort sizes are listed below and do not equal 2,400.

Exact diagonalization (ED) is a workhorse technique in computational quantum many-body physics, but published ED results are rarely accompanied by machine-checkable evidence of their numerical correctness. The community typically relies on the implicit trust chain LAPACK $\to$ user code $\to$ result, with at most informal agreement against another package treated as confirmation. We argue that this practice is inadequate for a method whose output frequently underpins theoretical claims, and we present \textsc{certify-ed}, a verification framework designed to be used \emph{alongside} existing ED packages (QuSpin, XDiag, ALPS) rather than as a replacement for them. The framework consists of (i) a multi-oracle eigensolver that runs three independent LAPACK paths and reports their pairwise disagreement, (ii) thirteen logically independent validation layers covering algebraic invariants, analytic limits, alternative algorithms, arbitrary-precision reference computation, conservation laws, dynamical consistency, and finite-size scaling, and (iii) tamper-evident SHA-256 hashed certificates that downstream consumers can verify. The framework also ships an error-injection layer that confirms the entire pipeline detects six injected error classes. Running on sixteen physics models from one-dimensional spin chains to two-dimensional Kitaev honeycomb clusters, our reference implementation passes 53 of 53 unit tests and 81 of 81 individual validation tests in under thirty seconds, with maximum disagreement against QuSpin of $1.6\times 10^{-14}$ across 320 eigenvalue comparisons, and agreement with 50-digit \texttt{mpmath} reference values to $1.6\times 10^{-15}$. The package is released under the MIT license on Zenodo and Github

Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing methods targeting conditional coverage are largely analyzed case by case, leaving limited general theory for understanding where conditional miscoverage comes from, how different procedures should be compared, and how such guarantees can be extended beyond i.i.d.~data. We address these gaps through a unified framework and theory for conformal methods targeting conditional coverage. Our central contribution is a non-asymptotic decomposition of conditional miscoverage into three interpretable components: score-estimation error, finite-sample calibration error, and intrinsic conditional-mismatch error. This decomposition clarifies the mechanisms behind asymptotic conditional validity and places existing methods within a common analytical lens. Building on this framework, we derive principled guidance for conditional-coverage-oriented model selection, and develop localized methods with asymptotic conditional guarantees under covariate shift. Finally, we extend the framework to structured data, with concrete applications to graph-structured and hierarchical settings. Numerical experiments corroborate the theory and demonstrate the effectiveness of the proposed procedures.

The global topology of the Universe can affect long-range gravitational forces via boundary conditions. Detailed studies of non-trivial topologies require simulations that natively adopt such geometries. Cosmological $N$-body simulations typically evolve matter in a periodic cubic box. While numerically convenient, this imposes a non-trivial three-torus topology that affects long-range gravitational forces, potentially biasing large-scale statistics. We introduce a compactified simulation framework that is only periodic along a single axis, characterised by an infinite topology with isotropic boundary conditions towards the perpendicular directions, namely, a $\mathrm{S}^1\times\mathbb{R}^2$ (slab) topology. This new simulation geometry is ideal for simulating systems with cylindrical symmetries such as filaments or certain anisotropic cosmological models. We compactified the comoving space via an inverse stereographic projection along the radial direction of a periodic cylinder. Then, we evolved the particles based on Newtonian dynamics. A smoothly varying spatial and mass resolution with radius suppresses edge artefacts at the free outer boundary. Our implementation in the StePS (STEreographically Projected cosmological Simulations) framework uses a direct force calculation that maps efficiently to GPUs, as well as an Octree force calculation for use on large CPU clusters. The cylindrical domain's topology enables fully self-consistent simulations to be run in the $\mathrm{S}^1\times\mathbb{R}^2$ manifold, while mitigating any periodic-image artefacts with respect to targets whose symmetries are mismatched to a cubic box. The main trade-off is a radially varying resolution with distinct systematics and analysis requirements. Finally, we demonstrate the accuracy of the new simulation method via a standard lambda cold dark matter cosmological simulation.

Every distributed system is a message-passing system, and every message-passing system is a growing causal DAG observed by a set of observers. We treat each observer's consistency as two operators on its visible sub-DAG (a causal-closure filter $C$, fixing which dependencies it must have seen, and a fork resolution $O$, ordering the concurrent forks the filter admits) and give the resulting space the structure the flat catalog of named models lacks. The operators are coupled, asymmetrically: an order that refines causality supplies closure its filter never demanded. That coupling yields a decidable readability order (which configuration's data another can read honestly) with a factoring dichotomy: the order splits across the $C$ and $O$ axes exactly when ordering does not refine causality, and refuses to when it does, the cross-axis gap being the closure ordering supplies. On that order sit a consistency ratchet (a level lost under migration is never regained) and a Detection = Prevention bound: a system can tell its order inverted causality only if it retained exactly what would have prevented the inversion. The classical results land at clean coordinates in the same system, not as new claims: resolving a fork demands retaining the causal history that distinguishes its branches (database folklore, here an impossibility for every message-passing system) and linearizability resolves as a composite of two systems, a store and a global real-time serializer supplying an order no single observer's light cone can. The named models are configurations of $(C, O)$, exact over the standard-safety fragment and generative past it, predicting configurations the catalog has not named. LCC is a formalization of the observer-relative consistency model of Burgess and Gerlits.

The power spectrum (PS) of the density field in supersonic turbulence is a fundamental quantity that characterizes the statistical properties of the structures formed in compressible flows. It is also widely used to estimate the Mach number in the interstellar medium from simulation-derived relations. In this paper, we provide a first quantitative explanation for the evolution of the slope of the PS of the density field with the Mach number in homogeneous isotropic isothermal turbulence using a time-invariant quantity derived by Chandrasekhar (1951). For simulated turbulent flows, the model reproduces the measured slopes for different widths of the inertial range and density variances very well. Our model also provides a comprehensive interpretation of the characteristic slopes of the PS of the density field measured in the interstellar medium. Based on these results, we stress that the Mach number cannot be reliably deduced from the slope of the PS of the density field. In closing, we discuss a resolution criterion that must be fulfilled to correctly simulate a turbulent flow with a given density PS slope.

We construct two families of regular hairy black holes within gravitational decoupling using a fixed exponential deformation profile for an effective tensor-vacuum sector. The first family is generated from a Bardeen-type seed and produces a de Sitter-like core. The second family is generated from a hollow seed with an asymptotically Minkowski core so that the central density vanishes and no de Sitter core is produced. For each branch we determine the critical deformation strengths separating horizonless, extremal, and two-horizon geometries in the static case, and we obtain the corresponding Kerr-like rotating extension by promoting the mass parameter to the deformed mass function. Representative parameter choices are used to illustrate the horizon structure and to verify the weak energy condition in the exterior region.

We report a comprehensive measurement of the environmental $γ$-ray flux in Hall C of the Gran Sasso National Laboratory. A spatial mapping of the radiation was carried out using a high-purity germanium detector mounted on a movable cart and deployed at eight locations within the hall. The detector response function and full-energy-peak efficiencies were determined through Geant4 simulations validated with calibrated $γ$-ray sources, with particular attention devoted to the efficiency modeling and associated systematic uncertainties. In the energy range of 57-2800 keV, the average $γ$-ray flux is measured to be $(\mathrm{0.46} \pm \mathrm{0.06}_{stat} \pm \mathrm{0.03}_{syst})$ $\mathrm{cm}^{-2}$ $\mathrm{s}^{-1}$. The radon level was monitored for about a month using a radon detector mounted on the same cart, and a clear correlation is observed between the environmental $γ$-ray rate and the ambient radon concentration, consistent with the short-lived daughters of $^{222}\mathrm{Rn}$. This result represents the first high-precision and efficiency-corrected mapping of the $γ$-ray flux in Hall C, substantially improving its radiological characterization and providing key input for future rare-event experiments operating in this hall.

We study the rational coefficients that arise when the Eisenstein series $G_k$ is expressed as a polynomial in $G_4$ and $G_6$, proving a conjecture that gives an exact formula for their minimal 2-adic valuation in terms of the binary expansion of the weight. The proof uses lacunary recurrences for Eisenstein series and yields refined information about the first valuation levels. As an application, we prove irreducibility results for Faber polynomials associated to dyadic linear combinations of powers of Eisenstein series.

We examine the instabilities of a confined active nematic subjected to an orienting field using a low Reynolds number Ericksen-Leslie framework with active stresses and field-induced torques. Linear analysis reveals two distinct modes, with odd and even director symmetry, the instabilities of which depend on the interplay between activity and field strength. We derive exact and approximate analytic forms of the stability boundaries and show that an orienting field that aligns the director perpendicular to the substrate anchoring direction cooperatively lowers activity thresholds and enables a field-driven even symmetry mode instability, while an orienting field that aligns the director parallel to the substrate anchoring tends to stabilise the system. Numerical solutions of the full nonlinear equations show that the linear stability analysis correctly identifies the symmetries of long-time states. These results demonstrate how orienting fields can promote an instability below the classical critical activity and can be used to both tune the instability onset and control the mode selection in confined active nematics.

Quantum entanglement is a key resource for quantum information processing and sensing, but it is severely degraded by environmental noise. We extend the previous study by Moosavi Khansari and Kazemi Hasanvand [27] of entanglement dynamics in a qubit qubit system with Dzyaloshinskii Moriya (DM) interaction and static magnetic fields to the realistic case of time varying, stochastic magnetic fields. We derive a stochastic Lindblad master equation and simulate quantum trajectories to quantify the negativity under colored noise. We then design a proportional integral feedback protocol that dynamically adjusts the DM interaction strength D_z (t) to maintain negativity near a target value. The feedback stabilized state is used as a probe for quantum metrology: we compute the quantum Fisher information (QFI) for estimating an unknown static field B_0. Our simulations show that feedback increases the time averaged negativity from 0.21 to 0.42 for α=1 at noise amplitude σ=0.5, leading to a factor 2.5 improvement in sensitivity over the classical shot noise limit. This work provides a practical route to protect entanglement in noisy environments and enhances quantum sensing performance.

The electric Aharonov-Bohm effect -- a time-dependent scalar potential imparting a measurable phase shift on electrons in a region free of electromagnetic fields -- has never been experimentally tested in its original formulation with shielded, time-dependent potentials. This unexplored regime offers a rare opportunity: the Lorenz condition $\partial_μA^μ= 0$, a choice that eliminates a scalar degree of freedom from the electromagnetic potential, may not be the last word. If the Stueckelberg scalar $B = \partial_μA^μ$ survives as a physical field and couples to matter, it would produce a phase shift with a distinctive $1-\cos(ωT)$ signature -- orthogonal to the standard $\sin(ωT)$ and separable by a frequency sweep even if both contributions coexist. We propose a measurement protocol based on single-electron interferometry with picosecond time resolution, within reach of current technology. The experiment asks a question that has lingered since 1959: is the Lorenz gauge a matter of convenience, or a matter of principle?

We explore the origin of the rotation rates of massive stars. Contrary to their low-mass siblings, most massive stars do not have detectable magnetic fields, so that star-disk interaction models used for the formation of rotating low-mass stars do not apply. We investigate whether the magnetic fields of protostellar jets present in the parent molecular cloud prevent the protostar from reaching the critical angular velocity. Starting from the gravitational collapse of a molecular cloud, we run two two-dimensional radiation-gravito-magnetohydroynamical simulations to study the formation of an accretion disk and the launching of magnetically-driven protostellar outflows (of particular interest is the formation of a magnetocentrifugal jet originating from the protostar and inner disk). We then study the angular momentum transfer from the disk and jet onto the protostar. Finally, we compute one-dimensional stellar evolution models of the pre-main sequence including our results from the disk-jet simulations and follow the angular momentum redistribution within the structure of the protostar. We find that the angular momentum transported outwards by the magnetically-driven protostellar outflows is sufficient for keeping the protostar below the critical speed at all times. Moreover, we are able to link the strength of the jet, and thus the rotation rate at the end of the accretion epoch, to the initial conditions for star formation. Our results show that the jet strength produces a variety of stellar rotation rates, suggesting that protostellar jets fix the rotation rate of massive stars.

A broad experimental program is targeting the QCD axion band predicted by single-axion solutions to the strong CP problem. Multi-axion theories provide a well-motivated departure from this canonical picture, since additional states generically modify the mass-photon-coupling relation. We investigate the general structure of multi-axion solutions to the strong CP problem and study the different qualitative mass-coupling patterns that arise, including axions to the right of the QCD band, axions in the experimentally accessible region to its left, and scenarios in which the QCD axion band itself is displaced. This general treatment reveals a broad set of phenomenological possibilities that are not captured by more restrictive assumptions. In particular, we identify the structure of Peccei-Quinn symmetry breaking and the relative alignment between the QCD and electromagnetic anomalies as key ingredients determining the location of the axions in parameter space. Combining these ingredients, we derive a general sum rule for $N$-axion systems that incorporates both general PQ breaking and non-universal anomaly coefficients. We apply the framework to the two-axion system and to general multi-axion setups, identifying UV-complete theories in which the different phenomenological regimes arise naturally. Our results motivate an extended axion search program and have implications for our understanding of fundamental physics and the ultraviolet completion of the Standard Model.

A higher extremal Kähler metric is defined (motivated by analogy with the definition of an extremal Kähler metric) as one whose top Chern form equals a smooth function multiplied by its volume form such that the gradient of the function is a holomorphic vector field. A special case of this is a higher cscK metric which is defined (again by analogy with the definition of a cscK metric) as one whose top Chern form is a constant multiple of its volume form or equivalently whose top Chern form is harmonic. In our previous paper on higher extremal Kähler metrics we had looked at a certain class of minimal ruled surfaces called as pseudo-Hirzebruch surfaces all of which contain two special divisors (viz. the zero and infinity divisors) and serve as example manifolds in the momentum construction which is used for producing explicit examples of the above-mentioned kinds of canonical metrics. We had proven that every Kähler class on such a surface admits a higher extremal Kähler metric which is not higher cscK and we had further proven by using the top Bando-Futaki invariant that higher cscK metrics do not exist in any Kähler class on the surface. In this paper we will see that if we allow our metrics to develop conical singularities along at least one of the two special divisors then we do get conical higher cscK metrics in each Kähler class by the momentum construction. We will show that our constructed metrics satisfy the polyhomogeneous condition for conical Kähler metrics and we will interpret the conical higher cscK equation globally on the surface in terms of the currents of integration along the two divisors. We will introduce the top $\log$ Bando-Futaki invariant and then employ it to arrive at a certain conjectural linear relationship between the cone angles of the conical singularities along the two divisors.

The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this within the framework of quantum reservoir computing by introducing a tunable $N$-qubit random circuit model, where a fraction $p$ of Clifford gates are probabilistically substituted with nonstabilizing conditional-$\hat{T}$ gates. We establish a direct correspondence between the reservoir's performance on temporal processing tasks and its entanglement spectrum statistics and long-range nonstabilizer resource content. To assess scalability, we study the scaling of the anti-flatness of states in the large-$N$ limit at a fixed circuit depth ratio $d/N \sim \mathcal{O}(1)$. This is taken as a witness to concentration of measures, a known impediment to learning in thermalizing systems. We demonstrate that the learnability and scalability of the reservoir can be continuously controlled by the parameter $p$, allowing us to navigate from classically tractable to maximally expressive quantum dynamics. These architecture-agnostic results provide a general strategy for designing tunable and expressive quantum reservoirs, highlighting how certain nonclassical properties control average-case intrinsic learnability and functionality.

Problem Definition: Managing inpatient flow in large hospital systems is challenging due to the complexity of assigning randomly arriving patients -- either waiting for primary units or being overflowed to alternative units. Current practices rely on ad-hoc rules, while prior analytical approaches struggle with the intractably large state and action spaces inherent in patient-unit matching. Scalable decision support is needed to optimize overflow management while accounting for time-periodic fluctuations in patient flow. Methodology/Results: We develop a scalable decision-making framework using Proximal Policy Optimization (PPO) to optimize overflow decisions in a time-periodic, long-run average cost setting. To address the combinatorial complexity, we introduce atomic actions, which decompose multi-patient routing into sequential assignments. We further enhance computational efficiency through a partially-shared policy network designed to balance parameter sharing with time-specific policy adaptations, and a queueing-informed value function approximation to improve policy evaluation. Our method significantly reduces the need for extensive simulation data, a common limitation in reinforcement learning applications. Case studies on hospital systems with up to twenty patient classes and twenty wards demonstrate that our approach matches or outperforms existing benchmarks, including approximate dynamic programming, which is computationally infeasible beyond five wards. Managerial Implications: Our framework offers a scalable, efficient, and explainable solution for managing patient flow in complex hospital systems. More broadly, our results highlight that domain-aware adaptation is more critical to improving algorithm performance than fine-tuning neural network parameters when applying general-purpose algorithms to specific applications.

In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,λ)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier results of Sharma to the generalized setting. Moreover, we show that divergence-free vector fields are Killing in this context, and we derive consequences under sign conditions on $m$ and $λ$, including triviality results. We also revisit a recent theorem of Ghosh \cite{ghosh}, discuss a subtle issue in the argument, and provide a new formulation and proof. Finally, we establish rigidity results for manifolds with geodesic potential vector fields.

Multivariate time series (MTS) are frequently affected by co-occurring quality issues, such as missing values, outliers, and constraint violations, which significantly undermine downstream analytics. Existing cleaning approaches fix only a limited set of such issues, making them ill-suited for scenarios where multiple quality problems arise simultaneously. Furthermore, these methods commonly depend on the availability of ground truth data or domain-specific rules, both of which are rarely accessible in real-world applications. In this paper, we introduce AegisTS, an agent system with reinforcement learning designed to clean multiple data quality issues in MTS. We cast the cleaning process as a joint optimization problem that simultaneously handles quality issue order and cleaning model selection, allowing efficient navigation of the large space of possible cleaning pipelines. Our framework relies on a hierarchical agent architecture, where a high-level agent determines the order in which data quality issues should be processed, while a low-level agent identifies the most suitable cleaning method for each issue. To guide the agent toward an optimal cleaning pipeline, we propose a dual-stage reward mechanism that couples upstream (cleaning) and downstream performance, enabling effective optimization without relying on ground truth. Our experimental results show that AegisTS consistently outperforms existing methods, achieving up to 96% improvement in data cleaning quality and 27% improvement in downstream performance.

We develop a nonperturbative framework for generic nonintegrable many-body systems that reorganizes the expansion of diagonal Green's functions. Starting from exact projection identities and the spectral representation of the resolvent, we derive a recursive hierarchy for the self-energy in which cross-correlated propagation processes are systematically rewritten in terms of diagonal resolvents. Under a diagonal closure approximation, the hierarchy becomes formally closed yet remains systematically improvable. The framework combines two nonperturbative mechanisms. First, a Lanczos continued-fraction representation provides a recursive single-resolvent structure that naturally produces non-Lorentzian spectral features beyond self-consistent Born approximations. Second, an exact projected multi-resolvent hierarchy introduces nonlocal frequency couplings through products of resolvents and their Hilbert transforms. These contributions mix parity sectors under energy reflection and generate spectral skewness, which is absent in single-resolvent closures. To solve the resulting equations, we employ a hierarchy of Lorentzian, Gaussian, and Voigt-type ansätze together with an effective Faddeeva self-energy representation ensuring analyticity and causality. Spectral broadening, distribution tails, and higher-order fluctuations emerge from the interplay between continued-fraction recursion and multi-resolvent correlations. The framework requires no small expansion parameters or diagrammatic truncations, relying instead on ETH-type statistical assumptions appropriate for dense chaotic spectra. It provides a unified route from microscopic interactions to emergent spectral structure, revealing a progression from single-pole self-consistent dynamics to continued-fraction renormalization and finally to multi-resolvent interference effects.

We determine the magnetic ground state of the kagome lattice magnet Nd3Ru4Al12 by single-crystal neutron diffraction, supported by experiments with polarized neutrons. We identify this material as a collinear ferromagnet ("hex-FM") with uniform moment length mc = 2.1 μB/Nd and ordering vector Q = 0, in contrast to a previous, seminal report that proposed unequal moment lengths on two Nd sites, here called the "ortho-FM" state. Our analysis of the flipping ratio in polarized neutron scattering is consistent with the hex-FM state. The results provide a microscopic basis for understanding the large fluctuation-induced Hall and Nernst responses near TC = 41 K, as previously reported for Nd3Ru4Al12.

Quantum entanglement and Bell-inequality violation in $τ^+τ^-$ pairs provide a sensitive probe of quantum correlations in high-energy interactions. We present a feasibility study of $e^+e^- \to τ^+τ^-$ at the proposed Super Tau-Charm Facility based on full Monte Carlo simulation at $\sqrt{s} = 7$ GeV, focusing on the $ππ$ channel ($τ^\pm \to π^\pmν$), which offers the maximal spin-analyzing power $|κ| = 1$ and the simplest final-state topology for validating the quantum-tomography framework. We establish a consistency chain from the tree-level QED prediction through truth-level and detector-level reconstruction, yielding a reconstructed concurrence of $0.279 \pm 0.007$ with the good-solution approach. A complementary full-simulation study of the $ρρ$ channel is also briefly reported. These results demonstrate that the STCF can provide a competitive platform for precision studies of quantum correlations in $τ$-lepton pairs.

We present a systematic high-throughput density-functional-theory investigation of the structural and magnetic stability of 312 substitutional compounds in the magnetic kagome AT6X6 family. Our screening confirms the stability of many previously reported structures and predicts several additional stable candidates. Within collinear spin configurations, we find that Fe-based systems predominantly adopt antiferromagnetic ground states, whereas Mn-based analogues exhibit a more balanced distribution between ferromagnetic and antiferromagnetic order. For compounds exhibiting several nearly degenerate collinear configurations, we analyze the nature of their magnetic ground states, assess the possible emergence of non-collinear order, and discuss the limitations and uncertainties inherent to standard density-functional approaches. Our electronic-structure analysis further reveals that newly predicted ferromagnetic kagome systems display characteristic features of topological metals, with rich magnetic configurations that can be tuned by chemical substitution. Overall, these ferromagnetic kagome compounds constitute a broad and still largely unexplored materials platform for the emergence of exciting magneto-transport phenomena.

We study feedback control of the Kuramoto model with uniformly spaced natural frequencies defined on uniform graphs which may be complete, random dense or random sparse. The control objective is to drive all nodes to the same constant rotational motion. For the case of node number $n\ge 3$, we establish the existence of exactly $2^n$ synchronized solutions in the controlled Kuramoto model (CKM) and their saddle-node and pitchfork bifurcations, and determine their stability. In particular, we show that only a solution converging to the desired motion in the limit of infinite feedback gain is stable and the others are unstable. Based on the previous results, it is shown that (i) the solution to which the stable synchronized solution in the CKM converge as $n\to\infty$ is always asymptotically stable in the continuous limit (CL) if it exists, and (ii) the asymptotically stable solution of the CL captures the asymptotic behavior of the CKM when the node number is sufficiently large, even if the graphs are random dense or sparse. We demonstrate the theoretical results by numerical simulations for the CKM on complete simple, and uniform random dense and sparse graphs.