This paper investigates the design of integrated sensing and communication (ISAC) systems assisted by simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs), which act as multi-functional programmable metasurfaces capable of supporting concurrent communication and sensing within a unified architecture. We propose a two-stage ISAC protocol, in which the preparation phase performs direction estimation for outdoor users located in the reflection space, while maintaining communication with both outdoor and indoor users in the transmission space. The subsequent communication phase exploits the estimated directions to enhance information transfer. The directions of outdoor users are modeled as Gaussian random variables to capture estimation uncertainty, and the corresponding average communication performance is incorporated into the design. Building on this framework, we formulate a performance-balanced optimization problem that maximizes the communication sum-rate while guaranteeing the required sensing accuracy, jointly determining the beamforming vectors at the base station (BS), the STAR-RIS transmission and reflection coefficients, and the metasurface partition between energy-splitting and transmit-only modes. The physical constraints of STAR-RIS elements and the required sensing performance are explicitly enforced. To address the non-convex nature of the problem, we combine fractional programming, Lagrangian dual reformulation, and successive convex approximation. The binary metasurface partition is ultimately recovered via continuous relaxation followed by projection-based binarization. Numerical results demonstrate that the proposed design achieves an effective trade-off between sensing accuracy and communication throughput, by significantly outperforming conventional STAR-RIS-aided ISAC schemes.

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.

Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular, derivations. In this paper, we show that the differential modality of a differential category lifts to a monad on the arrow category and, moreover, that the algebras of this monad are precisely derivations. Furthermore, in the presence of finite biproducts, the differential modality in fact lifts to a differential modality on the arrow category. In other words, the arrow category of a differential category is again a differential category. As a consequence, derivations also form a tangent category, and derivations on free algebras form a cartesian differential category.

We consider the V-A Fermi interaction and apply an earlier developed method for summing up the leading asymptotics for scattering amplitudes in non-renormalizable theories. We consider the amplitude of fermion-antifermion scattering and derive the corresponding RG equation that sums the leading logarithmic contributions just like in renormalizable models. Numerical solution of this equation in the asymptotic regime $s\sim t\sim u \sim E^2 \to \infty$ leads to amplitude logarithmically decreasing with energy, thus restoring the unitarity violated at the tree level.

This paper proposes a scalable Bayesian optimization (BO) framework for dense base-station (BS) configuration design. BO can find an optimal BS configuration by iterating parameter search, channel simulation, and probabilistic modeling of the objective function. However, its performance is severely affected by the curse of dimensionality, thereby reducing its scalability. To overcome this limitation, the proposed method sequentially optimizes per-BS parameters based on block coordinate descent while fixing the remaining BS configurations, thereby reducing the effective dimensionality of each optimization step. Numerical results demonstrate that the proposed approach significantly outperforms naive optimization in dense deployment scenarios.

The application of rare-earth complexes in electrically driven light sources poses a series of challenges that require specific optimization of the molecular photophysical properties. Here, we present a report on films of three different Eu3+ complexes characterized in terms of emission spectra and fluorescence decay. We compare molecular complexes in powder form and sublimed films, in films on glass and on a metal surface, and in films of thicknesses down to less than 3 nm (< 3 ML), approaching electrical coupling. Our photoluminescence experiments supported by scanning tunneling microscopy of sub-monolayers indicate that Eu3+(trensal) complexes are less affected by sublimation and more stable on the metal surface than typical beta diketonate complexes, making them promising candidates for electroluminescence devices.

Online and real-time sensing and monitoring of the health state of complex structures, such as aircraft and critical components of power stations, are essential aspects of research in dynamics. Several types of sensors are used to capture dynamic responses and monitor changes during the operation of critical parts of complex systems. Piezoelectric (PZ) materials belong to a class of electroactive materials that convert mechanical deformation into an electrical response. For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation. This paper focuses on the dynamical response of a cantilever beam structure equipped with a glued PZ sensor and combines experimental and modelling approaches to achieve accurate and reliable results. The time history of the normal velocity at a point on the beam surface was recorded with a laser vibrometer during transient vibrations of the beam, triggered by the sudden removal of a mass load at the beam's free end. Simultaneously, the output voltage of the PZ sensor was measured with an electronic device. An elastodynamic model of a cantilever beam coupled with a piezoelectric sensor is introduced, along with its discretization using the finite element method. The mathematical model includes additional terms that enforce a floating-potential boundary condition to maintain a constant charge on one of the sensor's electrodes and is presented in an extended form suitable for sensitivity analysis or parameter identification. The model implementation is validated using a numerical example corresponding to the experimental setup. The computed results show good agreement with the experimental data. Furthermore, values of the Rayleigh damping parameters were identified based on the experimental measurements.

We study projective unitary (co)representations of compact quantum groups and the associated second cohomology theory. We introduce left/right/bi/strongly projective corepresentations and study them in details. In particular, we prove that given any compact quantum group $\q$, there are compact quantum groups $\tilde{\q_l}, \tilde{\q_r}, {\tilde \q}_{bi}, {\tilde \q}_{stp}$, each of which contains $\q$ as a Woronowicz subalgebra and every left/right/bi/strongly projective unitary corepresentation of $\q$ lifts to a linear corepresentation of these quantum groups respectively. We observe that the strongly projective corepresentations are associated with the second invariant ($S^1$-valued) cohomology $H^2_{uinv}(\cdot)$ of the quantum group. We define a suitable analogue of normalizer of a compact quantum group in a bigger compact quantum group and using this, associate a canonical discrete group $Γ_\q$ to a compact quantum group $\q$ which is an alternative generalization of the second group cohomology and we show by an example that $Γ_\q$ in general may be different from $H^2_{uinv}(\q,S^1) $.

We consider the Casimir force in configurations with magnetic metal plates and analyze the reasons why the predictions of the Lifshitz theory using the dielectric permittivity of the Drude model are inconsistent with the measurement data. For this purpose, the contributions of the electromagnetic waves with the transverse magnetic and transverse electric polarizations to the Casimir force are computed using the Lifshitz theory expressed in terms of the pure imaginary Matsubara frequencies. Furthermore, the fractions of the evanescent and propagating waves in these contributions are found using an equivalent formulation of the Lifshitz theory along the real frequency axis. All computations are performed for Au-Ni and Ni-Ni plates using the Drude model and the experimentally consistent plasma model over the separation region from 0.5 to 6~mum, where the total force value is determined by conduction electrons. It is shown that the transverse magnetic contribution to the Casimir force does not depend on the used model of the dielectric permittivity, so that the total difference between the predictions of the Lifshitz theory using the Drude model and the measurement data is determined by the transverse electric contribution. In doing so, as opposed to the case of nonmagnetic metals, both fractions of the evanescent and propagating waves in this contribution depend on the model of the dielectric permittivity used in computations, whereas the magnetic properties of the plate metal influence the Casimir force solely through the fraction of propagating waves in the transverse electric contribution. The issue of a more adequate theoretical description of the electromagnetic response of magnetic metals is discussed.

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of model theory in our study. In particular, we show that our formal theory is complete, meaning that it entirely determines the behaviour of quantum systems. Moreover, we provide a characterization of the models of our formal theory, thus providing new insights in the study of hidden variable models of quantum theory.

We investigate the global Gevrey hypoellipticity of a class of first-order differential operators associated with tube-type involutive structures on $M\times\mathbb{T}^m$, where $M$ is a non-compact manifold diffeomorphic to the interior of a compact manifold with boundary and $\mathbb{T}^m$ is the $m$-dimensional torus. For $s>1$, we work in Gevrey classes of Roumieu and Beurling type. A key step is the construction, on $M$, of a scattering metric whose coefficients are Gevrey of order $s$ in every analytic chart; this allows us to use Hodge theory and obtain Gevrey regularity for the harmonic forms. Under a natural condition on the defining closed $1$-forms, we obtain a sharp criterion for global Gevrey hypoellipticity in terms of rationality and (Roumieu/Beurling) exponential Liouville behavior.

Extreme Edge Computing (XEC) distributes streaming workloads across consumer-owned devices, exploiting their proximity to users and ubiquitous availability. Many such workloads are AI-driven, requiring continuous neural network inference for tasks like object detection and video analytics. Distributed Inference (DI), which partitions model execution across multiple edge devices, enables these streaming services to meet strict throughput and latency requirements. Yet consumer devices exhibit volatile computational availability due to competing applications and unpredictable usage patterns. This volatility poses a fundamental challenge: how can we quantify the probability that a device, or ensemble of devices, will maintain the processing rate required by a streaming service? This paper presents an analytical framework for computational reliability in XEC, defined as the probability that instantaneous capacity meets demand at a specified Quality of Service (QoS) threshold. We derive closed-form reliability expressions under two information regimes: Minimal Information (MI), requiring only declared operational bounds, and historical data, which refines estimates via Maximum Likelihood Estimation from past observations. The framework extends to multi-device deployments, providing reliability expressions for series, parallel, and partitioned workload configurations. We derive optimal workload allocation rules and analytical bounds for device selection, equipping orchestrators with tractable tools to evaluate deployment feasibility and configure distributed streaming systems. We validate the framework using real-time object detection with YOLO11m model as a representative DI streaming workload; experiments on emulated XED environments demonstrate close agreement between analytical predictions, Monte Carlo sampling, and empirical measurements across diverse capacity and demand configurations.

In this article, we study two combinatorial problems concerning the set of reflections of a Coxeter system. The first problem asks whether the language of palindromic reduced words for reflections is regular, and the second is about finding formulas for the Poincaré series of reflections, namely the generating function of reflection lengths. These two problems were inspired by a conjecture of Stembridge stating that the Poincaré series of reflections is rational and by the solution provided by de Man. To address the first problem, we introduce reflection-prefixes, arising naturally from palindromic reduced words. We study their connections with the root poset, dominance order on roots, and dihedral reflection subgroups. Using $m$-canonical automata associated with $m$-Shi arrangements, we prove that the language of reduced words for reflection-prefixes is regular. For the second problem, we focus on affine Coxeter groups. In this case, we derive a simple formula for the Poincaré series using symmetries of the Hasse diagram of the root poset.

We computed Lyapunov times ($T_L$) for a sample of trans-Neptunian objects (TNOs) and outer main-belt asteroids (MBAs) using three numerical approaches: the variational method and two implementations of the renormalization technique. For each object, $T_L$ was derived both from the nominal orbit and from ensembles of 1001 orbital clones, enabling direct comparison between single-orbit and ensemble-based estimates. Across the sample, the methods generally produced consistent results, though larger discrepancies were observed for some MBAs. TNOs, in contrast, displayed greater consistency across methods, likely due to fewer overlapping resonances. Importantly, clone ensembles provided more robust and reliable stability indicators than nominal-orbit computations. Median values from clone populations reduced method-dependent biases and revealed dynamical behaviors that would remain hidden in single-orbit analyses, especially for objects with poorly constrained orbits or evolving in resonant regions. While our study focused on a limited but diverse set of objects, the methodology can be directly extended to larger populations, offering a systematic framework for exploring the long-term stability and dynamical evolution of main-belt asteroids, trans-Neptunian objects or other classes of objects in the Solar System.

Weintroduce a new class of mappings called cyclic p-$ϕ$-contraction mappings and investigate the existence and uniqueness of fixed point for such mappings defined on metric spaces, uniformly convex Banach spaces, or reflex ive Banach spaces.

We consider the recent proposal of steady state coherences in a single qubit in the case of a composite system-bath interaction. Based on a field theoretical approach we reanalyse the issue within a Redfield description. We find that the Redfield approach in accordance with a recent proposal yields steady state coherences but also violates the properties of a quantum map yielding negative populations. The issue is resolved by applying the Lindblad equation which is in accordance with a proper quantum map. The Lindblad equation, however, also implies the absence of steady state coherence. We conclude that steady state coherence in a a qubit is incompatible with a quantum map.

In this work, we investigate several phenomenological aspects of a covariant quantum-corrected Reissner-Nordström black hole characterized by the mass $M$, electric charge $Q$, and the quantum correction parameter $ζ$. We first study the motion of neutral test particles and derive the fundamental orbital and epicyclic frequencies, which are then employed to analyze different quasi-periodic oscillation (QPO) models. Using observational QPO data from stellar-mass, intermediate-mass, and supermassive black hole candidates, we perform a Bayesian parameter estimation through a Markov Chain Monte Carlo (MCMC) analysis and obtain constraints on the black hole parameters. The results show that the presence of the quantum correction significantly affects the location of the QPO radii and the separation between the QPO orbit and the ISCO. We then examine the scalar perturbations by deriving the Schrödinger-like radial equation and the corresponding effective potential. The influence of the parameters $Q$ and $ζ$ on the perturbation potential and stability of the spacetime is discussed. Furthermore, we compute the greybody factor and the energy emission rate in the high-frequency (geometric-optics) regime, showing how the quantum correction modifies the absorption probability and radiation spectrum. Finally, we study the effect of thermal fluctuations on the black hole entropy and obtain the logarithmic corrections to the Bekenstein-Hawking area law. We show that these corrections become important for small black holes, while for large horizon radius the standard thermodynamic behavior is recovered. Our analysis demonstrates that the quantum correction parameter leaves observable imprints on both dynamical and thermodynamical properties of the spacetime and can be constrained through QPO observations.

The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure. Instead of rolling forward the cumulative claims with estimated CL factors, we estimate multi-period factors that project the latest observations directly to the ultimate claims. This alternative perspective on CL reserving creates a natural pathway for the application of machine learning techniques to individual claims reserving. As a proof of concept, we present a small-scale real data application employing neural networks for individual claims reserving.

Or should we talk about dS/CFT correspondence or dS/SFT correspondence in cosmological correlators? In non-unitary field theories -- which are conjectured to be dual to cosmological correlators -- scale invariance does not necessarily imply full conformal invariance. While general relativity predicts the emergence of conformal invariance (or boost symmetry in the bulk), various modified theories of gravity suggest only scale invariance, characterized by the absence of bulk boost symmetry. We demonstrate this distinction using Einstein-Aether theory as a canonical example.

We consider the problem of maximizing the volume of hermitian ellipsoids inscribed in a given pseudoconvex domain in complex Euclidean space. We prove existence and uniqueness, and give a characterization of the maximizer.

We incorporate a canonical polyadic decomposition (CPD) based low-level solver as a means to accelerate the environment-level solver for the recently developed MPCC embedding framework. Using CPD, we both factorize the three dominant order-three density-fitting two-electron integral (DF TEI) tensors and develop a novel formulation that reduces the storage complexity of the low-level solver from ${O}(N^3)$ to $O(NR)$, where $R$ is the CPD rank, and the computational scaling of the most time-consuming contractions from ${O}(N^4)$ to ${O}(NR^2)$. We provide benchmarks on representative chemical environments, namely water clusters $\mathrm{(H_2O)_n}$ with $n = 1$ to $6$ and linear alkane chains $\mathrm{C_nH_{2n+2}}$ with $n = 1$ to $6$. For both test sets, using the CPD-compressed DF TEI tensors reproduces the DF reference convergence behavior of the low-level solver, the subsequent high-level step, and the fully self-consistent MPCC iterations, while introducing only small, rank-controlled shifts in absolute energies. At a fixed tolerance in the absolute MPCC energy, the CP ranks required for these tensor approximations increase linearly with system size. Chemically relevant energy differences are likewise preserved, as demonstrated for water-cluster dissociation energies and in a proof-of-concept embedding calculation of methane in a four-water cluster.

Generalized partially linear single-index models (GPLSIMs) provide a flexible and interpretable semiparametric framework for longitudinal outcomes by combining a low-dimensional parametric component with a nonparametric index component. For repeated measurements, valid inference is challenging because within-subject correlation induces nuisance parameters and variance estimation can be unstable in semiparametric settings. We propose a profile estimating-equation approach based on spline approximation of the unknown link function and construct a subject-level block empirical likelihood (BEL) for joint inference on the parametric coefficients and the single-index direction. The resulting BEL ratio statistic enjoys a Wilks-type chi-square limit, yielding likelihood-free confidence regions without explicit sandwich variance estimation. We also discuss practical implementation, including constrained optimization for the index parameter, working-correlation choices, and bootstrap-based confidence bands for the nonparametric component. Simulation studies and an application to the epilepsy longitudinal study illustrate the finite-sample performance.

We investigate the phase structure of Quantum Chromodynamics (QCD) in the vacuum as a function of quark flavor number $N_f$ within the chiral limit. By self-consistently solving the coupled DSEs for the quark and gluon propagators in a minimal QCD scheme, we elucidate the nonperturbative dynamics governing dynamical chiral symmetry breaking. Our calculations determine a critical flavor number of $N_f^c=6.81$ which marks the chiral symmetry restoration of quarks. Further analysis reveals the critical exponents of the chiral condensate as $ -\langle\barψ ψ\rangle\sim |N_f-N_f^c|^{0.53(9)}$, characterized the second order feature of this phase transition of chiral symmetry. Additionally, we discuss the implications for the walking regime towards the conformal window at larger flavor.

We give new algorithms for tree evaluation (S. Cook et al. TOCT 2012) in the catalytic-computing model (Buhrman et al. STOC 2014). Two existing approaches aim to solve tree evaluation in low space: on the one hand, J. Cook and Mertz (STOC 2024) give an algorithm for TreeEval running in super-logarithmic space $O(\log n\log\log n)$ and super-polynomial time $n^{O(\log\log n)}$. On the other hand, a simple reduction from TreeEval to circuit evaluation, combined with the result of Buhrman et al. (STOC 2014), gives a catalytic algorithm for TreeEval running in logarithmic $O(\log n)$ free space and polynomial time, but with polynomial catalytic space. We show that the latter result can be improved. We give a catalytic algorithm for TreeEval with logarithmic $O(\log n)$ free space, polynomial runtime, and subpolynomial $2^{\log^εn}$ catalytic space (for any $ε> 0$). Our result opens a new line of attack on putting TreeEval in logspace, and immediately implies an improved simulation of time by catalytic space, by the reduction of Williams (STOC 2025). Our catalytic TreeEval algorithm is inspired by a connection to matching-vector families and private information retrieval, and improved constructions of (uniform) matching-vector families would imply improvements to our algorithm.

We present the absolute flux and wavelength calibration of the James Webb Space Telescope (JWST) Near-Infrared Camera (NIRCam) Wide Field Slitless Spectroscopy (WFSS) mode. Each of NIRCam's two modules (A and B) provides independent long wavelength (LW) grism spectroscopy over the 2.4-5.0 micron range, with orthogonally oriented R and C grisms. Using commissioning and calibration data from programs 01076, 01536, 01537, 01538, 01479, 01480, 04449, 04498, 06606, and 06628, we have measured the field-dependent geometry and wavelength dispersion of both first and second order spectra across the full detector area. The trace geometry was modeled using two-dimensional third-order polynomials that reproduce the observed spectral positions with an RMS accuracy better than 0.1 pixel. Wavelength calibration, derived from observations of the planetary nebula SMP LMC 58, achieves a precision of 0.65-0.91A for the +1 orders and 0.5A for the +2 orders. Absolute flux calibration, established from observations of the G-type star standard P330E, provides a consistent sensitivity function across all grisms and modules with an absolute flux accuracy of 3\%. The resulting calibration framework defines the geometric, wavelength, and photometric reference for all NIRCam WFSS observations and ensures cross-consistency between modules and grism orientations. These calibrations form the basis for accurate slitless spectroscopy with NIRCam and will support ongoing improvements to the JWST calibration pipeline and data products.

Femtosecond laser modification of fused silica enables precise surface tailoring for the fabrication of micro-optical components such as microlenses and diffractive elements. However, the process is governed by laser-matter interactions where the local fluence determines the processing depth, often limiting control over feature geometry and efficiency. Here, we present a hybrid approach combining localized Au implantation (1.8 MeV Au2+ ions) into SiO2 samples with femtosecond laser irradiation (250 fs), effectively tuning the laser-matter interaction and resulting morphology. At both 515 nm and 1030 nm irradiation wavelengths, single-shot femtosecond pulses produce cylindrical craters with sharp edges and flat-bottom profiles. Independently of the fluence, these craters exhibit a constant depth of 550 nm, corresponding to the region of maximum Au concentration. The effect manifests already at moderate fluence (app. 4 J/sq.cm) and yields high ablation efficiency, up to 15 cubic micrometers per microjoule. The hybrid method also works effectively at lower implantation doses that preserve the excellent transmission of fused silica, offering a promising pathway for the high-quality fabrication of flat optical components such as binary phase masks, phase lenses, or fused-silica micromolds.

We obtain several new results on the simultaneous packing and covering constant $γ(\mathcal{X})$ of a Banach space $\mathcal{X}$, and its lattice counterpart $γ^*(\mathcal{X})$. These constants measure how efficient a (lattice) packing by unit balls in $\mathcal{X}$ can be, the optimal case being that $γ(\mathcal{X})= 1$ and the worst that $γ(\mathcal{X})= 2$. Our first main result is that $γ(\mathcal{X})> 1$ whenever $B_\mathcal{X}$ admits a LUR point, which leads us to a negative answer to a question of Swanepoel. We also develop general methods to compute these constants for a large class of spaces. As a sample of our findings: (i) $γ^*(\mathcal{X})= 1$ when $\mathcal{X}$ is a separable octahedral Banach space, or $\mathcal{X}= \mathcal{C}(\mathcal{K})$, where $\mathcal{K}$ is zero-dimensional; (ii) $γ(\ell_p(κ)\oplus_r \mathcal{X})= γ^*(\ell_p(κ)\oplus_r \mathcal{X})= \frac{2}{2^{1/p}}$, whenever $\rm{dens}(\mathcal{X})< κ$ and $1\leq r\leq p< \infty$; (iii) $γ(L_p(μ))= γ^*(L_p(μ))= \frac{2}{2^{1/p}}$ for $1\leq p\leq 2$ and every measure $μ$; (iv) there exist reflexive (resp. octahedral) Banach spaces $\mathcal{X}$ with $γ(\mathcal{X})= 2$. We leave a large area open for further research and we indicate several possible directions.

Generative artificial intelligence (GenAI) has engrossed the mainstream culture, expanded AI's creative user base, and catalyzed economic, legal, and aesthetic issues that stir a lively public debate. Unsurprisingly, GenAI tools proliferate kitsch in the hands of amateurs and hobbyists, but various shortcomings also induce kitsch into a more ambitious, professional artists' production with GenAI. I explore them in this paper. Following the introductory outline of digital kitsch and AI art, I review GenAI artworks that manifest five interrelated types of kitsch-engendering expressive flaws: the superficial foregrounding or faulty circumvention of generative models' formal signatures, the feeble critique of AI, the mimetics, and the unacknowledged poetic similarities, all marked by an overreliance on AI as a cultural signifier. I discuss the normalization of these blunders through GenAI art's good standing within the art world and keen relationship with the AI industry, which contributes to the adulteration of AI discourse and the possible corruption of artistic literacy. In conclusion, I emphasize that recognizing different facets of artists' uncritical embrace of techno-cultural trends, comprehending their functions, and anticipating their unintended effects is crucial for reaching relevance and responsibility in AI art.

Air quality and climate are major issues in Italian society and lie at the intersection of many research fields, including public health and policy planning. There is an increasing need for readily available, easily accessible, ready-to-use and well-documented datasets on air quality and climate. In this paper, we present the GRINS AQCLIM dataset, created under the GRINS project framework covering the Italian domain for an extensive time period. It includes daily statistics (e.g., minimum, quartiles, mean, median and maximum) for a collection of air pollutant concentrations and climate variables at the locations of the 700+ available monitoring stations. Input data are retrieved from the European Environmental Agency and Copernicus Programme and were subjected to multiple processing steps to ensure their reliability and quality. These steps include automatic procedures for fixing raw files, manual inspection of stations information, the detection and removal of anomalies, and the temporal harmonisation on a daily basis. Datasets are hosted on Zenodo under open-access principles.

We study $\mathbb{S}_n$-equivariant weight-graded and topological Euler characteristics of the universal Picard stack $\mathrm{Pic}_{g, n}^d \to \mathcal{M}_{g, n}$ of degree-$d$ line bundles over $\mathcal{M}_{g, n}$. We prove that in the weight-zero and topological cases, the generating function for Euler characteristics of $\mathrm{Pic}_{g, n}^d$ is obtained from the corresponding one for $\mathcal{M}_{g, n}$ by an extremely simple combinatorial transformation. This lets us deduce closed formulas for the two generating functions, taking as input the Chan--Faber--Galatius--Payne formula in the weight-zero case and Gorsky's formula in the topological case. As an immediate corollary, we obtain closed formulas for the weight-zero and topological Euler characteristics of $\mathrm{Pic}^d_g$. Our weight-zero calculations follow from a general result passing from the weight-graded Euler characteristics of $\mathcal{M}_{g, n}$ to those of $\mathrm{Pic}_{g,n}^d$.