We study diffusion approximations for a class of interacting stochastic systems with reflection and control. Motivated by interacting stochastic dynamics subject to feedback mechanisms and boundary constraints, we consider diffusion-scaled stochastic processes incorporating stochastic fluctuations, state-dependent interactions, and reflection. Under suitable assumptions, we establish convergence in distribution of the scaled processes to systems of interacting reflected stochastic differential equations of Ornstein-Uhlenbeck type. The limiting dynamics capture key features of constrained multi-agent systems, including mean-reverting behavior, interaction effects, and confinement within bounded domains through Skorokhod reflection. The analysis combines diffusion-scaling arguments, stability estimates, and continuity properties of the Skorokhod map to connect discrete stochastic systems with their reflected diffusion limits. To illustrate the framework, we present numerical examples motivated by crowd dynamics and neural population dynamics. The simulations demonstrate qualitative agreement between the finite stochastic systems and the corresponding reflected diffusion models and illustrate how diffusion approximations can provide tractable descriptions of interacting stochastic systems with constraints.

We develop a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized probabilities can be stationary, respectively invariant. Our results deviate from the setting of classical probability and lead to a new criterion for amenability and for fixed points in cones.

A model-independent parameterization of the low-energy scattering amplitude that incorporates the left-hand cut from one-particle exchange, an extension of the conventional effective-range expansion (ERE), was recently proposed and successfully applied to the low-energy $DD^*$ system [Phys. Rev. Lett. 135, 011903 (2025)]. While the original formulation is based on a nonrelativistic approximation and is thus limited to a [1,1] approximant for self-consistency, we extend the framework by explicitly including the higher-order terms up to $\mathcal{O}(k^6)$. We systematically investigate the reliability and robustness of the generalized ERE by incorporating relativistic kinematic effects. In addition, we develop a relativistic version of the ERE that accounts for lhc contributions. These results affirm the generalized ERE as a robust and systematically improvable framework for near-threshold scattering processes, providing both analytical and numerical reliability for applications in two-body scattering problems with a particle exchange.

Racial disproportionality in stop and search practices elicits substantial concerns about its societal and behavioral impacts. In London, Black individuals are about four times more likely to be stopped and searched than White individuals. Using data on stop and search events in London from January 2019 to December 2023, this paper aims to investigate disproportionality in the volume of stops for expressive crimes involving Black individuals compared to other ethnicities. We employ a semi-parametric partially linear structural regression method and introduce a Bayesian empirical likelihood procedure combined with double machine learning techniques to control for high-dimensional confounding and to accommodate strong prior assumptions. In addition, we show that the proposed procedure yields a valid posterior in terms of coverage. Applying this approach to the stop and search dataset, we find that racial disproportionality aimed at the Black community may be influenced by the borough racial composition when focusing on expressive crimes.

In quantum information, asymmetry, i.e., the lack of symmetry, is a resource allowing one to accomplish certain tasks that are otherwise impossible. Similarly, in a Bell test using any given Bell inequality, the maximum violation achievable using quantum strategies respecting or disregarding a certain symmetry can be different. In this work, we focus on the symmetry involved in the exchange of parties and explore when we have to trade this symmetry for a lower-dimensional quantum strategy in achieving the maximal violation of given Bell inequalities. For the family of symmetric Collins-Gisin-Linden-Massar-Popescu inequalities, we provide evidence showing that there is no such trade-off. However, for several other Bell inequalities with a small number of dichotomic measurement settings, we show that symmetric quantum strategies in the minimal Hilbert space dimension can only lead to a suboptimal Bell violation. In other words, there exist symmetric Bell inequalities that can only be maximally violated by asymmetric quantum strategies of minimal dimension. In contrast, one can also find examples of asymmetric Bell inequalities that are maximally violated by symmetric correlations. The implications of these findings on the geometry of the set of quantum correlations and the possibility of performing self-testing therefrom are briefly discussed.

Active galactic nuclei (AGN) hosting water megamaser disks provide precise geometric measurements of black hole mass, distance, maser disk orientation, and dynamical center. In anticipation of space-based very long baseline interferometry, these systems offer a path to black hole shadow (BHS) imaging beyond Sgr A* and M87*. We present new Submillimeter Array continuum observations of water megamaser galaxies, supplemented by archival ALMA and VLA measurements, to assess whether their AGN cores are bright enough for BHS-scale imaging. For a 21-source parent sample, we map the predicted BHS diameters of systems with published SMBH masses to submillimeter/millimeter (submm-mm) baseline requirements, estimate AGN core flux densities at 230 GHz while bounding thermal dust and extended-jet contamination and checking whether variability could affect the continuum estimates, and evaluate the astrometric precision required to detect spin-dependent BHS offsets for NGC 4258. NGC 4258 is the only source resolvable on Earth-L2 baselines; other targets require longer baselines approaching Earth-L4/L5 distances, and only a handful have $S_{230} \gtrsim 10$ mJy beam$^{-1}$. We also find a submillimeter excess in NGC 4258, suggesting that its disk remains geometrically thin to $\lesssim 100$ Schwarzschild radii before transitioning to an advection-dominated flow. Even for maximal spin, the formal 230 GHz BHS centroid precision is not the limiting term: the measurement would require locating the 22 GHz water maser dynamical center and registering it to the 230 GHz BHS image roughly seventy times more precisely than current maser astrometry allows, making the spin-offset measurement infeasible with present data.

We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of Bollobás and Riordan and generalizes it to higher dimensions. As a consequence, we prove a sharp phase transition for the emergence of i-dimensional giant cycles in Voronoi percolation on the 2i-dimensional torus.

Bilayer graphene cavities where electrons are confined within finite graphene flakes provide an alluring platform not only for the future nanoelectronic devices owing to the tunable energy gap but also for investigating the quantum nature of chaos due to the trigonal warping of their Fermi surface. Here we demonstrate that rotating the cavity boundary relative to the underlying lattice structure drives a quantum transition from nearly integrable dynamics to chaotic regime, observed as a concomitant crossover of eigenvalue statistics and eigenstate profiles. Complementing the full quantum treatment, we examine the classical backbone of this onset of chaos by employing semiclassical ray dynamics. Our results position bilayer graphene cavities as a promising venue for investigating and engineering quantum-chaotic behavior in graphene-based devices.

Online joint estimation of a dynamical model's unknown parameters and states with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to support prediction and decision-making. Reliability and computational speed are vital for DTs. Online parameter-state estimation ensures computational efficiency, while uncertainty quantification is essential for making reliable predictions and decisions. In parameter-state estimation, the joint distribution of the state and model parameters conditioned on the data, termed the joint posterior, provides accurate uncertainty quantification. Because the joint posterior is generally intractable to compute, this paper presents an online variational inference framework to compute its approximation at each time step. The approximation is factorized into a marginal distribution over the model parameters and a state distribution conditioned on the parameters. This factorization enables recursive updates through a two-stage procedure: first, the parameter posterior is approximated via variational inference; second, the state distribution conditioned on the parameters is computed using Gaussian filtering based on the approximate parameter posterior. The algorithmic design is supported by a theorem establishing upper bounds on the joint posterior approximation error. Numerical experiments demonstrate that the proposed method (i) accurately infers both unobserved states and unknown parameters of dynamical and observation models; (ii) remains robust under noisy, partial observations and model discrepancies in a chaotic Lorenz'96 system; and (iii) scales effectively to a high-dimensional state-space system arising from the spatial discretization of a convection-diffusion equation. outperforming the joint ensemble Kalman filter in this setting.

Spatiotemporal optical vortices carry transverse orbital angular momentum (t-OAM), which give rise to spatiotemporal topological charge (ST-TC). To unleash the full potential of t-OAM in expanding the capacity of communication and computing, we demonstrate the first optical information-processing pipeline capable of performing addition and subtraction on ST-TC values, regardless of whether they are integer or fractional. Additionally, we established a readout method for those mathematical operations through imaging spectral analysis, providing a robust optical basis toward arithmetic operations and verification. These new capabilities mark crucial advancements toward full arithmetic operations on the ST-TC of light for bosonic state computation and information processing.

Fisher's fiducial probability has recently attracted renewed attention under the notion of epistemic confidence. Epistemic confidence statements can be formulated through extended likelihoods, thereby clarifying several long-standing controversies regarding its fiducial probability properties. It establishes a direct connection between Fisher's epistemic notion of confidence for observed data and Neyman's frequentist aleatory coverage probability for future data, thereby enabling extension of epistemic confidence statements for multidimensional parameters. We demonstrate how higher-order asymptotic theory can be applied to refine the first-order asymptotic epistemic confidence statements of the observed region, as a direct consequence of extended likelihood property.

Defects trap photocarriers and hinder solar water splitting. The nanoscale photocarrier transport, trapping, and recombination mechanisms are usually inferred from ensemble-averaged measurements and remain elusive. Because an individual high-performing nanoparticle photocatalyst may outperform the ensemble average, design rules that would otherwise enhance catalytic efficiency remain unclear. Here, we introduce photomodulated electron energy-loss spectroscopy (EELS) in an optically coupled scanning transmission electron microscope (STEM) to map photocarrier localization. Using rhodium-doped strontium titanate (SrTiO3:Rh) solar water-splitting nanoparticles, we directly image the carrier densities concentrated at oxygen-vacancy surface trap states. This is achieved by separating photothermal heating from photocarrier populations through experimental and computational analyses of low-loss spectra. Photomodulated STEM-EELS enables angstrom-scale imaging of defect-induced photocarrier traps and their impact on photocatalytic efficiency.

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken symmetries. Various examples of group and non-invertible symmetries are studied. In particular, the origin of the distinguishability of the vacua resulting from spontaneously broken non-invertible symmetries is made manifest with an information-theoretic perspective, where certain operators in the SymTFT are excluded from observation.

The gluon emission from an energetic heavy quark is suppressed in the forward direction below the angle $Θ\lesssim m_Q/E$ for a quark of mass $m_Q$ and energy $E$ according to perturbative Quantum Chromodynamics (QCD) (``dead cone"). Another consequence is the suppression of energetic particles in the jet which has been observed already for c- and b-quark jets. The suppression of the forward particles can be explained by an application of the Modified Leading Logarithmic Approximation (MLLA) of perturbative QCD. In this paper we investigate whether this type of analysis can be carried out also for top-quark jets with the much higher heavy quark mass allowing for QCD tests in this new kinematic regime. The new aspect of this analysis is the finite lifetime of the top quark. We consider for simplicity the decay $t\to b\ellν$, where the b-quark radiates gluons as well and partially obscures the dead cone. Guided by the decay amplitude in leading order in $α_s$ for $e^+e^- \to t \bar t$ we propose a method to separate the radiation by the $\widehat{tb}$ dipole in the decay process which is superimposed to the primary radiation from the $\widehat{t \bar t}$ dipole involving the top-quark dead cone effect. The momentum distributions of partons or hadrons are determined for finite decay angles of the b-quark $Θ_b$ and extrapolated into forward direction $Θ_b=0$ where the radiation from the decay process is expected to vanish. This method is successfully tested at the parton level and results obtained for hadrons are compatible with the MLLA relation within an accuracy of around 15\%. Our calculations are carried out with the Pythia 8.3 Monte Carlo Event Generator.

We followed scientists who started publishing in 2000 and who continued publishing until 2020-2023 (N = 41,424). These survivors in science authored 2 million articles (N = 2,089,097) with more than 70 million cited references (N = 73,118,395) and worked in 38 OECD countries. Using a raw Scopus dataset, we examined gender disparities in publishing intensity, international collaboration, journal selection, productivity, citations, team formation, and publishing breaks in 16 STEMM and social science disciplines. Several author-level metrics were computed. Our data show a gender productivity gap for both lifetime scholarly output and annual journal prestige-normalized productivity. Surprisingly, in the context of extant literature, the data do not show a gender international collaboration gap, a gender journal selection gap, a gender citation gap, or a gender team formation gap. Men were on average 23% more productive than women cumulatively in 2000-2023 and 19% more productive in the last 5 years studied (2019-2023). Men and women published in equally prestigious journals, received the same number of citations (field-normalized), and worked in equally sized teams. In all, 80% of scientists in STEMM disciplines and 70% in the social sciences had published every year. Our data indicate interesting disciplinary differences in gender disparities.

Software Bills of Materials (SBOMs) improve software release transparency by documenting components and dependencies, but their practical value depends on the tools that generate, analyze, and manage them. This paper compares the tool ecosystems of the two dominant SBOM formats: SPDX and CycloneDX. We analyze 108 open-source and 62 proprietary SBOM tools, compare ecosystem-level health metrics across 470 SPDX and 171 CycloneDX tools, examine 36,990 issue reports from open-source tools, and study the top 250 open-source projects using each format. Our results show that CycloneDX-using projects often exhibit stronger developer engagement and selected project health indicators, while SPDX benefits from a larger, more mature tool ecosystem and broader industry adoption. These findings highlight the complementary strengths of both ecosystems and identify opportunities for improving SBOM tooling across formats.

The discovery of superconducting nickelates provides a unique opportunity to explore the pairing mechanism of high-temperature superconductivity. Here, we use ultrafast terahertz spectroscopy to probe the temperature-dependent superfluid density in an infinite-layer samarium nickelate film with a Tc of 20 K. The superfluid density decreases linearly with rising temperature, consistent with clean limit d-wave pairing. From this linear relation, we extract a superconducting gap of 2.5 meV and a gap-to-Tc ratio of 3, suggesting that this sample lies in the weak-coupling limit. Furthermore, the ratio of the mean free path to the coherence length, is determined to be 1.5, confirming the clean-limit behavior. These findings establish strong parallels between the pairing mechanisms in nickelate and cuprate superconductors.

We present remarkably simple covariant expressions for the graviton and ghost propagators in Anti-de Sitter (AdS) spacetime valid in any spacetime dimension. In gravity there is a $2$-parameter family of covariant gauge-fixing conditions and the simplification occurs for a special choice of these parameters. In this gauge the graviton propagator satisfies $\nabla^μμ\nabla^νμ\, G_{μν,α'β'}(μ)=0$, where $μ$ is the geodesic distance between two points, and this condition implies an improved infrared behavior. This gauge choice is not possible in flat spacetime.

In three-dimensional variational data assimilation (3DVar) for numerical weather prediction (NWP), the observation operator $\mathcal{H}$ plays a central role by mapping model state variables to an observation equivalent. For weather radar, however, specifying $\mathcal{H}$ is particularly challenging: reflectivity is a nonlinear, microphysics-dependent diagnostic quantity that only indirectly relates to the model's prognostic variables, making traditional parameterised radar operators complex, regime-dependent and difficult to tune. In this study, we propose a neural-network (NN)-based observation operator for radar reflectivity and apply it within a 3DVar framework. Using five years (2019-2023) of radar reflectivity data from the Lisca radar and 4.4 km-resolution short-range forecasts from ALADIN model over Slovenia, we train a convolutional encoder-decoder neural network to map model temperature, humidity, horizontal wind components and surface pressure fields to radar reflectivity. Across independent test cases spanning clear-sky, stratiform, and convective regimes, the NN-based operator accurately reproduces the spatial structure and intensity of observed reflectivity, relying primarily on the model state near the observation point. In the extreme precipitation case, which caused widespread floods in Slovenia on August 4, 2023, assimilating the full radar disc reduces the domain-averaged reflectivity root-mean-square error from 5.99 dBZ to 3.47 dBZ and improves the alignment between the analysed and observed convective bands. Embedded within 3DVar, the Jacobian of the NN observation operator allows radar reflectivity observations to inform model state variables, producing corresponding analysis increments. The proposed NN radar observation operator offers a flexible alternative to traditional parameterised radar operators for improving convective-storm forecasts.

This paper presents the Battery Modelling Toolbox (BattMo), a flexible finite volume continuum modelling framework in MATLAB\textsuperscript{\textregistered} (\citeproc{ref-MATLAB}{The MathWorks Inc., 2025}) for simulating the performance of electro-chemical cells. BattMo can quickly setup and solve models for a variety of battery chemistries, even considering 3D designs such as cylindrical and prismatic cells. The simulation input parameters, including the material parameters and geometric descriptions, are specified through JSON schemas. In this respect, we follow the guidelines of the Battery Interface Ontology (BattINFO) to support semantic interoperability in accordance with the FAIR principles (\citeproc{ref-fair}{Wilkinson et al., 2016}). The Doyle-Fuller-Newman (DFN) (\citeproc{ref-Doyle1993ModelingCell}{Doyle et al., 1993}) approach is used as a base model. We include fully coupled thermal simulations. It is possible to include degradation mechanisms such as SEI layer growth, and the use of composite material, such as a mixture of Silicon and graphite. The models are setup in a hierarchical way, for clarity and modularity. Each model corresponds to a computational graph, which introduces a set of variables (the nodes) and functional relationship (the edges). This design enables the flexibility for changing and designing new models. The solver in BattMo uses automatic differentiation and support adjoint computation. We can therefore compute the derivative of objective functions with respect to all parameters efficiently. Gradient-based optimization routines can be used to calibrate parameters from experimental data.

Scaling quantum computers to large sizes requires the implementation of many parallel qubit readouts. Here we present an ultrastable superconducting-qubit readout method using the multi-tone self-phase-referenced Pound-Drever-Hall (PDH) technique, originally developed for use with optical cavities. In this work, we benchmark PDH readout of a single transmon qubit, using room-temperature heterodyne detection of all tones to reconstruct the PDH signal. We demonstrate that PDH qubit readout is insensitive to microwave phase drift, displaying $0.73^\circ$ phase stability over 2 hours, and capable of single-shot readout in the presence of phase errors exceeding the phase shift induced by the qubit state. We show that the PDH sideband tones do not cause unwanted measurement-induced state transitions for a transmon qubit, leading to a potential signal enhancement of at least $14$~dB.

We present argon abundances from a sample of 46 star-forming galaxies at $z=2-3.5$ from the Assembly of Ultradeep Rest-Optical Observations Revealing Astrophysics (AURORA) program. Although argon is an $α-$element produced by Core Collapse Supernovae (CCSNe), the latest supernova yield models suggest additional argon production and enrichment by Type Ia supernovae (SNe Ia), unlike other $α-$elements such as oxygen. To study the relationship between argon and oxygen abundances, we construct two median-stacked composite spectra for separate $z=2.0-2.6$ and $z=2.8-3.5$ redshift bins, presenting more representative measurements than previous samples that require individual detection of faint lines. Abundance ratios were determined using an empirical calibration based on the strength of the [ArIII]$\lambda7137$ emission line relative to the [OIII]$\lambda5008$ emission line. With this calibration, we estimate argon abundances (Ar/O) of $0.42^{+0.12}_{-0.10}\mbox{(Ar/O)}_{\odot}$ for the $\langle z \rangle = 2.26$ bin and $0.42^{+0.12}_{-0.11}\mbox{(Ar/O)}_{\odot}$ for the $\langle z \rangle = 3.15$ bin, suggesting minimal SNe Ia and dominant CCSNe enrichment in this sample. Comparison of our abundance measurements of $z\sim 2-3$ AURORA galaxies with chemical evolution modeling of Milky Way stars shows consistency with the Milky Way Bulge component, suggesting a rapid star-formation timescale. However, even larger samples of actively star-forming galaxies with available argon abundances, as well as comparisons between argon abundance and other critical galaxy properties (e.g., sSFR) and models (e.g., one tuned specifically to this redshift range) are needed to draw stronger conclusions on the role of argon in galactic chemical enrichment at Cosmic Noon.

Nonparanormal models describe the joint distribution of multivariate responses via latent Gaussian, and thus parametric, copulae while allowing flexible nonparametric marginals. Some aspects of such distributions, for example conditional independence, are formulated parametrically. Other features, such as marginal distributions, can be formulated non- or semiparametrically. Such models are attractive when multivariate normality is questionable but interpretability paramount. Most estimation procedures perform two steps, first estimating the nonparametric part. The copula parameters come second, treating the marginal estimates as known. This is sufficient for some applications. For other applications, e.g. when a semiparametric margin features parameters of interest or when standard errors are important, a simultaneous estimation of all parameters might be more advantageous. We present suitable parameterisations of nonparanormal models, possibly including semiparametric effects, and define four novel nonparanormal log-likelihood functions. In general, the corresponding one-step optimisation problems are shown to be non-convex. In some cases, however, biconvex problems emerge. Several convex approximations are discussed. From a low-level computational point of view, the core contribution is the score function for multivariate normal log-probabilities computed via Genz procedure. As a demonstration for the versatility of the theoretical and computational framework, we present a series of nonparanormal models for transformation discriminant analysis when some biomarkers are subject to limit-of-detection problems. Possible empirical gains of full maximum likelihood estimation compared to two-step approaches are illustrated in a simulation study targeting semiparametric efficient polychoric correlation analysis where a theoretical benchmark is available.

We report on the sympathetic cooling and Coulomb crystallization of xenon highly charged ions (HCIs) with laser-cooled Ca$^+$ ions. The HCIs are produced in a compact electron beam ion trap, then charge selected, decelerated, and finally injected into a cryogenic linear Paul trap. There, they are captured into $^{40}$Ca$^+$ Coulomb crystals, and co-crystallized within them, causing dark voids in their fluorescence images. Fine control over the number of trapped ions and HCIs allows us to realize mixed-species crystals with arbitrary ordering patterns. By investigating Xe$^{q+}$--Ca$^+$ strings, we confirm the HCI charge states, measure their lifetime and characterize the mixed-species motional modes. Our system effectively combines the established quantum control toolbox for Ca$^+$ with the rich set of atomic properties of Xe highly charged ions, providing a resourceful platform for optical frequency metrology, searches for signatures of new physics, and quantum information science.

The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. We make use of the rely-guarantee approach to concurrency that facilitates reasoning about interference from concurrent threads in a compositional manner. Recursive programs can be defined as fixed points over a lattice of commands and hence we develop laws for reasoning about fixed points. Loops can be defined in terms of fixed points and hence the laws for recursion can be applied to develop laws for loops. Unlike many approaches to concurrency, we do not assume that expression evaluation is atomic.

We present exact analogies between the tautochrone problem of classical mechanics and the squeezed states of quantum optics to optical lattices. Both phenomena emerge in the same physical system, that of waveguide arrays with nonuniform couplings. Extension to two dimensions yields Lissajous-type trajectories and multidirectional tautochrone focusing. Furthermore, we investigate the impact of Kerr nonlinearity and show that it determines the diffraction behavior, namely coherent-state-like or squeezed propagation. These quantum inspired classical lattices highlight the role of the coupling coefficients to beam engineering and light control in complex media.

Biophysical models in diffusion MRI (dMRI) hold promise for characterizing gray matter tissue microstructure. Yet, the reliability of their parameter estimates remains largely under-studied, especially in models that incorporate water exchange. In this study, we investigate the accuracy, precision, and presence of degeneracy of two recently proposed gray matter models, NEXI and SANDIX, using established acquisition protocols, on both simulated and \textit{in vivo} data. We employ $μ$GUIDE, a Bayesian inference framework based on deep learning, to quantify parameter uncertainty and detect degeneracies, enabling a more interpretable assessment of model fits. Our results show that while some microstructural parameters, such as extra-cellular diffusivity and neurite signal fraction, are robustly estimated, others, including exchange time and soma radius, are often associated with high uncertainty and estimation bias, particularly under realistic noise conditions and reduced acquisition protocols. Comparison with non-linear least squares fitting highlights the critical advantage of uncertainty-aware methods: the ability to flag and filter out unreliable estimates. Together, these findings emphasize the need to report uncertainty and account for model degeneracies when interpreting model-based estimates. Our study advocates for the integration of probabilistic fitting approaches into imaging pipelines to improve reproducibility and biological interpretability.

We classify the inertial Weil-Deligne types arising from elliptic curves over all finite extensions $F/\mathbb Q_p$. Based on this classification, we give a fully explicit description of the types and implement an algorithm that computes all inertial types of elliptic curves defined over a given $F$. As an application, we determine all inertial types arising from elliptic curves over any extension $F/\mathbb Q_p$ of degree at most 3.

Joint Species Distribution Models are essential for understanding how ecological covariates shape species communities. However, most existing approaches are limited by rigid parametric distributions for count data and the inability to model how interspecific associations change with those covariates. We introduce joint count transformation models, a novel framework designed to overcome these limitations. Our approach combines distribution-free marginal count transformation models for multiple species with a covariate-dependent latent Gaussian copula to model interspecific correlations, interpretable as Spearman's rank correlation on the observed count scale. All model parameters are estimated efficiently via joint maximum likelihood estimation, implemented in the R package tram. We apply this framework to model the joint abundance of three fish-eating bird species, using seasonality as the primary covariate. Our model successfully captured the complex, species-specific seasonal abundance patterns, including periods of high zero-counts and seasonal shifts in variance. Furthermore, the model revealed strong, seasonally-varying correlations between the species. These findings are consistent with an empirical approach and similar to those from the computationally expensive parametric Bayesian Hierarchical Modelling of Species Communities (HMSC) framework. Consistency, accuracy and feasibility of our approach are demonstrated in a simulation study for up to 10 species.

In collisionless astrophysical plasmas, turbulence mediates the partitioning of free energy among cascade channels and its dissipation into ion and electron heat. The resulting ion heating is often anisotropic, with ions observed to be preferentially heated perpendicular to the local magnetic field; understanding the mechanisms responsible for this heating is a key step in understanding the evolution of such plasmas. In this paper, we use the framework of quasi-linear theory to compute analytically the heating rates of ions interacting with turbulent, large-scale Alfvénic fluctuations. We show how the imbalance of the turbulence (the difference in energies between Alfvénic fluctuations travelling parallel and antiparallel to the magnetic field) modifies the spatiotemporal spectrum of these fluctuations, allowing the heating mechanism to smoothly transition between stochastic heating in balanced turbulence and cyclotron-resonant heating in imbalanced turbulence. The resultant heating rate is found to have a general form regardless of the level of imbalance, exhibiting a suppression related to the conservation of the ions' magnetic moment at small turbulent amplitudes and recovering previous empirical results in a formal calculation. The results of this work help to consolidate our qualitative understanding of ion heating within astrophysical plasmas, as well as yielding specific quantitative predictions to analyse simulations and observations.