This article presents a fully 3D-printed wideband metasurface folded reflectarray antenna (MFRA) operating in the millimeter-wave n257 band. The proposed MFRA integrates a novel polarization-rotating reflective metasurface (RMS), a compact embedded horn feed, and a polarization-selective metasurface polarization grid (MPG), all fabricated using a low-cost in-house 3D-printed method. Unlike conventional PCB-based FRAs constrained to planar unit-cell geometries, the proposed anisotropic meta-element design exploits full three-dimensional dielectric control by tailoring varying unit-cell heights. This volumetric tuning, combined with the spatial distribution of the meta-elements, enables phase compensation exceeding $400^{\circ}$ across the aperture, supporting robust wideband performance. An MFRA prototype is in-house fabricated and experimentally validated. Measured results agree well with simulations, achieving a $-10$ dB impedance bandwidth of 20.7\% (26--32 GHz) and a peak realized gain of 31.1 dBi at 28.2 GHz. The antenna exhibits sidelobe levels below $-20$ dB, cross-polarization below $-30$ dB, and a compact height-to-diameter ratio of 0.20. Stable pencil beams with an average HPBW of $3.7^{\circ}$ are maintained across the operating band. To further validate the robustness of the proposed in-house designed MFRA, a commercially manufactured RMS was also obtained, whose measured performance shows excellent agreement with the in-house 3D-printed version, confirming a cost-effective rapid-prototyping antenna solution. The proposed MFRA is a cost-effective solution for beyond 5G and 6G high-gain point-to-point mmWave wireless applications, such as fixed wireless access, near field communication, and beam focusing.

This work used the γ-activation approach to conduct tests at bremsstrahlung end-point energies of 10-23 MeV utilising the MT-25 microtron beam. The experimental values of relative yields and cross sections per equivalent quantum of photonuclear reactions on stable isotopes of cadmium and tellurium were compared to theoretical calculations obtained from TALYS-2.0 using the default parameters and a combined model of photonucleon reactions (CMPR). The inclusion of isospin splitting in the combined model of photonucleon reactions allows for the description of experimental data on proton escape reactions with energies ranging from 17 to 23 MeV. As a result, isospin splitting must be taken into consideration in order to accurately describe the decay of the giant dipole resonance. For Cd isotopes, essential discrepancies of yet unclear origin between theory (TALYS 2.0 and CMPR) and experimental data are found in the neutron channel.

A general net of quadric surfaces, together with a choice of a base point, defines a net of plane cubics via the Gale transformation of the remaining seven base points. To both nets, one can also naturally associate the same smooth plane quartic. In this paper, we generalize the cycle of correspondences arising from nets of quadrics that define rational elliptic threefolds and provide a complete criterion for GIT stability of the three underlying geometric objects using birational-geometric techniques.

To reduce CO2 emissions and tackle increasing fuel costs, the aviation industry is swiftly moving towards the electrification of aircraft. From the viewpoint of systems and control, a key challenge brought by this transition corresponds to the management and safe operation of the propulsion system's onboard electrical power distribution network. In this work, for a series-hybrid-electric propulsion system, we propose a distributed adaptive controller for regulating the voltage of a DC bus that energizes the electricity-based propulsion system. The proposed controller -- whose design is based on principles of back-stepping, adaptive, and passivity-based control techniques -- also enables the proportional sharing of the electric load among multiple converter-interfaced sources, which reduces the likelihood of over-stressing individual sources. Compared to existing control strategies, our method ensures stable, convergent, and accurate voltage regulation and load-sharing even if the effects of power lines of unknown resistances and inductances are considered. The performance of the proposed control scheme is experimentally validated and compared to state-of-the-art controllers in a power hardware-in-the-loop (PHIL) environment.

We propose a data-efficient workflow to optimize the efficiency of a radial turbine design under a strict budget of high-fidelity computational fluid dynamics simulations. Assuming anisotropic parameter impact, we use a maximum-projection initial experimental design to ensure space-filling and strong projection properties on low-dimensional subspaces. Bayesian optimization is performed using Gaussian process surrogates with an upper confidence bound acquisition function. In parallel, polynomial chaos expansions provide variance-based global sensitivity analysis metrics, which allow to identify a reduced subspace with the most influential parameters, wherein the optimization is continued. Turbine efficiency is increased from 85.77% initially to 91.77% at the end of the workflow, with a total budget of 330 simulations.

Motivated by the simplification of decomposition formulas for fibred bisets, we study the homomorphism extension problem for subdirect products of finite groups when the codomain is an abelian group satisfying certain hypothesis. We prove that every homomorphism of subdirect products whose Goursat quotients have trivial Schur multipliers is extensible. We also examine the case where subdirect products contain a twisted diagonal subgroup and investigate the functoriality of the extensibility property.

Recent advancements in AI-generated content (AIGC) have introduced new challenges in intellectual property protection and the authentication of generated objects. We focus on scenarios in which an author seeks to assert authorship of an object generated using latent diffusion models (LDMs), in the presence of adversaries who attempt to falsely claim authorship of objects they did not create. While proof-of-ownership has been studied in the context of multimedia content through techniques such as time-stamping and watermarking, these approaches face notable limitations. In contrast to traditional content creation sources (e.g., cameras), the LDM generation process offers greater control to the author. Specifically, the random seed used during generation can be deliberately chosen. By binding the seed to the author's identity using cryptographic pseudorandom functions, the author can assert to be the creator of the object. We refer to this stronger guarantee as proof-of-authorship, since only the creator of the object can legitimately claim the object. This contrasts with proof-of-ownership via time-stamping or watermarking, where any entity could potentially claim ownership of an object by being the first to timestamp or embed the watermark. We propose a proof-of-authorship framework involving a probabilistic adjudicator who quantifies the probability that a claim is false. Furthermore, unlike prior approaches, the proposed framework does not involve any secret. We explore various attack scenarios and analyze design choices using Stable Diffusion 2.1 (SD2.1) as representative case studies.

Significant gamma-ray emission between 1 TeV and 20 TeV from a point source, 1LHAASO J1219+2915, consistent with the location of the LINER/LLAGN galaxy NGC 4278 was recently reported by the LHAASO collaboration. These data were later split into active and quasi-quiet states, with most of the LHAASO significance coming from the active state (MJD 59449-59589). Subsequent analysis of Fermi-LAT and Swift-XRT observations have been used to explore the double-peaked broad-band emission. Models of the spectral energy distribution (SED) are currently unconstrained due to the lack of contemporaneous multi-wavelength data at either peak. Here we report serendipitous observations of NGC 4278 with VERITAS, made possible by the contemporaneous observations of the nearby blazars 1ES 1218+304, 1ES 1215+303, and W Comae, each of which are located within $2^\circ$ of NGC 4278. VERITAS did not detect any gamma-ray emission and a flux upper limit was calculated. The flux upper limits constrain the photon spectrum of the quasi-quiet period, and together with Fermi-LAT, indicate a peak in the SED between 100 GeV and 2 TeV. We present an interpretation of the broadband SED that is based on acceleration of protons in the corona of the AGN, followed by p-$γ$ interactions and optically thin $γ$-ray emission. Within this framework, the implied neutrino signal is slightly below the current sensitivity of IceCube.

I propose and investigate the use of continuous functional equations for the study of meta-Fibonacci integer sequences. This exploratory study includes three sequences with quite different behavior: Conway's famous sequence $A(n)= A(A(n-1))+A(n-A(n-1))$, the sequence $D(n)= D(D(n-1))+D(n-1-D(n-2))$ introduced by the present author more than 25 years ago, and Hofstadter's well-known $Q(n)= Q(n-Q(n-1))+Q(n-Q(n-2))$. The sequences are studied in their equivalent detrended forms $(a,d,q)(n)=2\,(A,D,Q)(n)-n$. For $a(n)$ and $d(n)$, a highly symmetric functional equation admits exact continuous solutions that nicely model the global behavior (backbone) of the sequences. For the Hofstadter sequence, a continuous functional model is developed that leads to a random matrix approach for the generation and study of fractal solutions. Two remarkable properties of the Q-sequence are reproduced by the model: the anomalous scaling of the generation length, which scales $\sim (2-η)^k$, and the anomalous amplitude growth that scales like $2^{αk}$.

Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing (QA) is promising, yet its native binary nature supports only discrete variables, making accurate and efficient encodings of continuous quantities a central challenge. Existing approaches either split the coupled problem, mapping discrete decisions to QA while solving continuous fields classically, or use fixed-bit-depth encodings. The former compromises QA's global search advantages; the latter can underrepresent dynamic range or inflate the number of binary variables. We show that simply increasing bit depth can even degrade performance on current QA hardware, underscoring the need for alternative encodings. In response, we introduce an adaptive encoding strategy for continuous variables in QA that enables efficient treatment of coupled mixed-variable problems. We propose an update strategy for the representable ranges of the continuous variables and demonstrate its utility by integrating it into the minimum complementary energy formulation for structural design optimization, which provides a single, coupled constrained problem. We apply a quadratic penalty method where we update the representation of the continuous variables while targeting the full original objective, preserving QA's global search capability. On a published benchmark, the size optimization of a composite rod, our adaptive encoding improves solution quality under a fixed binary variable budget, demonstrating a superior precision-resource trade-off. Since the framework generalizes beyond structural design, it offers practical guidance for encoding continuous variables for QA and indicates that adaptive representations can enhance precision on current hardware.

We study the pseudoscalar ($J^{PC}=0^{-+}$) and vector ($1^{--}$) top--antitop (toponium) systems within the rainbow--ladder truncation of the Dyson--Schwinger and Bethe--Salpeter equations, employing the Qin--Chang effective interaction. After validating the framework in the charmonium and bottomonium sectors, we extend it consistently to the top sector, incorporating renormalisation-group running of the current quark mass and a careful treatment of the number of active flavours. We compute masses and leptonic decay constants for $N_f=5$ and $6$, then analyse their dependence on the renormalisation scale in the range $μ=400-800\,\text{GeV}$. The resulting toponium masses lie near $344-346\,\text{GeV}$ with hyperfine splittings below $0.14-0.17\,\text{GeV}$, while the decay constants are large, $6-7\,\text{GeV}$, and exhibit the expected heavy-quark scaling behaviour. We find only mild sensitivity to the renormalisation point and a systematic reduction of binding when increasing $N_f$. Although the physical top quark decays weakly before hadronisation, our results demonstrate that, within a Poincaré-covariant nonperturbative framework, quantum chromodynamics (QCD) generates tightly correlated pseudoscalar and vector toponium systems in that extreme heavy-quark limit.

This article summarises the methods used by the team ``Ca' Foscari" for the EVA 2025 Data Challenge. The questions of the challenge concern the estimation of exceedance probabilities across several locations. Rather than modelling the spatial dependence structure, we reduce the problems to univariate ones by considering relevant spatial order statistics across the sites. Within a Peaks over Threshold framework, we model the marginal distributions of exceedances using generalised Pareto distributions. Generalised additive models are employed to allow the parameters to vary as functions of external predictors, which for all questions are reduced to the month. For questions 1 and 2, the required estimates and confidence intervals are obtained by generating samples from our fitted models. Question 3 involves the dependence between two consecutive observed statistics. To account for this temporal dependence, we fit a conditional extreme value model and derive empirical estimates of persistent extreme events by simulating from this model.

Alignable nets are grid structures that can collapse to a planar strip, which is in fact the real-world counterpart of a curve. This property simplifies on-site assembly and enables compact transport and storage. These grid structures can then be deployed by a scissor motion at each vertex in a desired location. In this article, we classify all surfaces supporting an alignable net that additionally have the geodesic and conjugate net property, namely, the alignable Voss surfaces. In doing so, we use Cartan's theory of moving-frames and we obtain a coordinate-free classification of these surfaces. In the next step we express our findings in local coordinates and at the level of the fundamental forms. We show that the alignable Voss surfaces consist of two classes where each in turn consists of two two-parameter families of surfaces. A surprising feature of one of these classes is that they admit an isothermal-conjugate geodesic net, thereby providing a counterexample to Eisenhart's earlier classification claim for Voss surfaces of this type. Finally, we derive explicit immersion formulas for one of the classes as functions of the deformation and alignability parameters. Additionally, we show that, upon disregarding certain singularities, the above immersions of alignable Voss surfaces give rise to infinitely many explicit immersions of other Voss surfaces still depending on the deformation parameter. Since explicit immersion formulas for Voss surfaces that include the deformation parameter are seldom obtainable, this provides a rare result in the literature. Finally, we examine several notable subclasses in detail, including the well known example of infinitely many geodesic-conjugate nets on a helicoid, and we give a kinematical explanation for why this phenomenon appears in computations.

Context. Gamma-ray bursts (GRBs) reach redshifts beyond Type Ia supernovae (SNe Ia) and can extend distance measurements into the early Universe, but their use as distance indicators is limited by the circularity problem in calibrating empirical luminosity relations. Aims. We present a model-independent methodology to overcome this circularity by combining Pantheon$+$ SNe Ia, a distance reconstruction based on artificial neural networks (ANNs), and two GRB correlations (Amati and Combo) into a distance ladder from low to high redshift, with the goal of constraining cosmological parameters in $Λ\mathrm{CDM}$ and $w_0 w_a \mathrm{CDM}$. Methods. We use the ReFANN to reconstruct the luminosity distance $d_L(z)$ and distance modulus $μ(z)$ from the Pantheon$+$ dataset, with hyperparameters optimized via approximate Bayesian computation rejection and a risk function. This model-independent reconstruction calibrates the Amati and Combo relations using a low-redshift ($z<1$) GRB sample from Fermi GBM and Swift-XRT. The calibrated relations then provide distance estimates for GRBs at $z \geq 1$. Finally, a joint Bayesian analysis simultaneously constrains the cosmological and GRB correlation parameters, ensuring self-consistent uncertainty propagation. Results. We obtain consistent cosmological constraints from two independent GRB correlations. The Hubble constant $H_0$ agrees with SNe Ia values, though potentially influenced by Pantheon$+$ dataset. High-redshift GRBs favour a higher matter density $Ω_m$ than the Pantheon$+$ and hint at possible dark energy evolution.Conclusions. We present a framework that mitigates GRB cosmology's circularity problem, extending the distance ladder to $z \sim 9$ and establishing GRBs as a high-redshift probe.

Generalised Parton Distributions (GPDs) provide multidimensional insight into hadron structure and are particularly relevant for the pion, whose dynamics are intimately linked to chiral symmetry breaking. We introduce a novel modelling strategy for pion GPDs that satisfies all QCD constraints by construction: support, polynomiality, positivity, and the soft-pion theorem. The approach is illustrated with a simple algebraic model, which is evolved and used to compute deeply virtual Compton scattering (DVCS) Compton Form Factors at next-to-leading order. Our results indicate that gluons dominate the pion response at the Electron Ion Collider kinematics.

Classical equations for predicting one-repetition maximum (1RM) from submaximal performance were derived from small samples performing a single exercise, yet are routinely applied to hundreds of exercises. All use a fixed conversion factor relating repetitions to estimated 1RM, regardless of exercise or load. We used large-scale observational data from a consumer fitness app (303,494 near-failure sets from 14,966 users across 388 exercises spanning 16 muscle groups) to derive and evaluate a generalization in which the conversion factor varies logarithmically with the weight lifted: 1RM = w * (1 + (r - 1)^0.85 / (-2.55 + 4.58 * ln(w))). Because the dataset contains no directly measured maxima, we optimized and evaluated the formula using an internal consistency criterion -- the degree to which different weight-repetition combinations from the same person, exercise, and time window yield the same estimated 1RM. The proposed formula reduced inconsistency by 17-22% relative to four classical benchmarks, with the improvement positive for every one of the 183 exercises with sufficient data. Five-fold user-level cross-validation confirmed near-zero overfitting. An ablation analysis attributed 91% of the improvement to the weight-dependent conversion factor and 9% to the sub-linear repetition exponent. The conversion factor increases with load: at light weights each additional repetition implies a larger fraction of maximal capacity than at heavy weights, consistent with prior evidence that the repetitions-%1RM relationship varies by exercise. Classical equations, by applying a single conversion factor across all loads, systematically underestimate this variation -- and the discrepancy is largest for the lighter, more diverse exercises that dominate real-world training programs.

We show that anyonic statistics fundamentally reshapes non-Hermitian many-body physics by intrinsically breaking pseudo-Hermiticity, leading to a unique real-complex spectral transition with characteristically dense states in Im$E$. This anyon-induced transition occurs even when bosonic and pseudofermionic counterparts remain entirely real, revealing a form of non-Hermitian criticality driven purely by exchange statistics. The resulting spectrum exhibits enhanced gaps in Im$E$ that dynamically isolate dominant eigenstates, producing anomalously stable short-time quench dynamics for anyons. Our results identify anyonic statistics as an intrinsic mechanism for generating unconventional non-Hermitian critical behavior usually associated with highly non-local systems.

We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue spaces L p for all integrability exponents p $\in$ (1, $\infty$) with regularity assumptions in the transport and diffusive directions according to the scaling of the Kolmogorov equation. The regularity scale accommodates weak and strong solutions. We prove that the proposed spaces satisfy sharp embeddings quantifying the transfer-ofregularity {à} la Bouchut-H{ö}rmander, continuity-in-time in the spirit of Lions and the gainof-integrability of Sobolev and Hardy-Littlewood-Sobolev type. A core tool are mapping properties of the Kolmogorov operator, given by the fundamental solution, established between anisotropic homogeneous Sobolev spaces. To achieve this, we prove L^p boundedness of related singular integral operators, for which we deduce novel kernel estimates by a Littlewood-Paley decomposition and geometric considerations. Moreover, we provide a new uniqueness criterion which allows us to show well-posedness of the Cauchy problem.

OpenMC can be used to computationally model depletion and produce estimates of decay heat. As an input to depletion simulations, OpenMC requires a depletion chain that details nuclide transmutation pathways. The simplified CASL depletion chain was designed to track relatively few nuclides while still accurately modeling the effective neutron multiplication factor and nuclide number densities. However, the CASL chain dramatically underestimates decay heat due to the many nuclides it does not contain. In this work, we modify the CASL depletion chain to improve its accuracy while maintaining its computational efficiency. We demonstrate the effectiveness of adding pseudo-nuclides to the CASL chain, with each pseudo-nuclide capturing the behavior of a large group of nuclides. We further introduce "delay nuclides," which dramatically improve the accuracy of decay heat estimates.

In this paper, we consider the reflection and transmission problem of waves by a rapidly oscillating rough interface that exhibits general mixing properties. Using an asymptotic analysis based on a separation of scales, corresponding to a paraxial (parabolic) scaling regime, we precisely characterize the specular and speckle (diffusive) components of the reflected and transmitted fields. A critically scaled interface is considered, in the sense that the amplitudes of the interface fluctuations and the central wavelength are of the same order. When the correlation length of the interface fluctuations is of the same order as the beam width, random specular components arise in both the reflected and transmitted waves, while no speckle component is observed. Equivalently, the reflected and transmitted fields are essentially confined to the cones formed by the specular components (specular cones) with directions given by the classical Snell's law of reflection and refraction. When the correlation length is smaller than the beam width, a specular homogenization regime emerges. In this case, the rough interface can be approximated by an effective flat interface, yielding deterministic specular reflected and transmitted cones. However, broader cones containing the specular cones appear, within which the wavefields form speckle patterns (speckle cones) whose total energy is of leading order. We provide the two-point correlation functions of these speckle patterns and establish a central-limit-theorem-type result, showing that they can be modeled as Gaussian random fields. These results enable the identification of generalized Snell's laws of reflection and transmission, which depend on an effective scattering operator at the interface.

We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli b-divisor are compatible with restriction to arbitrary open subsets. We also discuss the boundedness of complements in this setting.

We study the thermodynamic geometry of the one-dimensional Blume--Capel model within the Tsallis nonextensive framework to understand how generalized statistics modify correlation structure and pseudo-critical behaviour. Using the transfer matrix method, we construct the Tsallis entropy based thermodynamic metric as its negative Hessian on the parameter space $(β, J)$, with the crystal-field anisotropy $D$ as a control parameter, and compute the associated scalar curvature $R(T)$ as a measure of correlations. Although no true phase transition occurs in one dimension, $R(T)$ exhibits finite peaks signaling pseudo-critical crossovers. We analyze both $D < J$ and $D > J$ regimes and show that deviations from the Boltzmann--Gibbs limit ($q=1$) systematically deform the curvature profile: for $q>1$ the peak shifts and correlations persist beyond the crossover, whereas for $q<1$ the peak is weakened or suppressed. Our results demonstrate that the Tsallis parameter $q$ geometrically reshapes the entropy surface, providing a clear information-geometric interpretation of nonextensive effects in spin-1 systems.

Unresolved thin-film dynamics often causes spurious coalescence in diffuse-interface simulations of multiphase flows. We address this issue by introducing a fully local repulsive near-contact flux in a conservative Allen--Cahn phase-field model coupled to lattice Boltzmann hydrodynamics. The interaction activates only for oppositely oriented nearby interfaces, with a strength that self-adjusts based upon an analytical estimate of the local film thickness extracted from the phase field. The resulting method circumvents nonlocal geometric procedures, preserves computational efficiency, and is well suited to massively parallel implementations. Tests on collision benchmarks and three-dimensional bubble swarms demonstrate robust suppression of artificial merging and physically consistent near-contact dynamics.

We establish an integration by parts formula for the semi-group in time $T > 0$ of the kinetic Brownian motion in the Euclidean plane together with its speed in the circle. The stochastic differential equation of our kinetic Brownian motion is driven here by one real-valued Brownian motion constructed with an orthonormal basis of $L^2([0,T],\mathbb R)$ and an independent sequence of $\mathscr N(0,1)$ random variables. Our method is based on an explicit computation of a Malliavin dual in the Gaussian space. We are mainly interested in large time $T$. From our integration by parts, we obtain gradient estimates including a reverse Poincar{é} inequality for the semi-group. As a direct consequence, we also obtain a Liouville property for the generator of the kinetic Brownian motion and its speed: all bounded harmonic functions are constant.

Hydrogen uptake in complex multicomponent alloys, including high-entropy alloys (HEAs), governs both hydrogen storage capacity and resistance to hydrogen-induced degradation. We combine high-pressure experiments, density-functional theory (DFT), and a GRACE universal interatomic potential to investigate hydrogen absorption in Al$_{0.3}$CoCrFeNi and Al$_3$CoCrFeNi HEAs. In H$_2$ as a pressure-transmitting medium, the FCC Al$_{0.3}$CoCrFeNi alloy forms hydrides at ambient temperature above 3 GPa, whereas the Al-rich B2 Al$_3$CoCrFeNi alloy shows no evidence of hydride formation even upon heating at pressures up to 50 GPa. Experiments and calculations show that aluminum suppresses hydrogen uptake by increasing solution energies and destabilizing interstitial sites. The universal potential, employed in the calculations and pretrained on large DFT databases, closely reproduces DFT energetics and demonstrates transferability from the dilute limit to the hydride-forming regime. Simulations further disentangle the roles of local ordering, volume changes, composition, and crystal structure. Overall, our results indicate that hydrogen solubility in Al-containing HEAs is governed primarily by composition, with Al-driven B2 ordering as a strong secondary effect.

In this paper, we propose a structure preserving method using a Crank-Nicolson's type method with an implicit Gauss-Seidel fractional iteration. Such a method is of first-order accuracy in time and second-order accuracy in space, stable and length preserving. Such a proposed method brings great benefits for the theoretical analysis. The numerical accuracy, norm preserving and stability are verified for 1D and 3D tests.

Let $\mathsf{mSt}_n$ be the plactic-like monoid obtained by factoring the free monoid over a finite alphabet $\mathcal{A}_n$ by the meet of the stalactic congruence and its dual. In this paper, we prove that $\mathsf{mSt}_n$ can be equipped with multiple involutions, and divide these involutions into $\lfloor\frac{n}{2}\rfloor+1$ types. A faithful representation of $\mathsf{mSt}_n$ under each of these involutions is obtained. We give transparent combinatorial characterizations of identities for $\mathsf{mSt}_n$ under each involution, and so the finite basis problem and identity checking problem for them are solved.

Team sports represent complex phenomena characterized by both spatial and temporal dimensions, making their analysis inherently challenging. In this study, we examine team sports as complex systems, specifically focusing on the tactical aspects influenced by external constraints. To this end, we introduce a new generic graph-based model to analyze these phenomena. Specifically, we model a team sport's attacking play as a directed path containing absolute and relative ball carrier-centered spatial information, temporal information, and semantic information. We apply our model to union rugby, aiming to validate two hypotheses regarding the impact of the pedagogy provided by the coach on the one hand, and the effect of the initial positioning of the defensive team on the other hand. Preliminary results from data collected on six-player rugby from several French clubs indicate notable effects of these constraints. The model is intended to be applied to other team sports and to validate additional hypotheses related to team coordination patterns, including upcoming applications in basketball.

Hidden Markov models (HMMs) are powerful tools for analysing time series data that depend on discrete underlying but unobserved states. As such, they have gained prominence across numerous empirical disciplines, in particular ecology, medicine, and economics. However, the increasing complexity of empirical data is often accompanied by additional latent structure such as spatial effects, temporal trends, or measurement perturbations. Gaussian fields provide an attractive building block for incorporating such structured latent variation into HMMs. Fast inference methods for Gaussian fields have emerged through the stochastic partial differential equation (SPDE) approach. Due to their sparse representation, these integrate well with novel frequentist estimation methods for random-effects models via the use of automatic differentiation and the Laplace approximation. Scaling to high dimensions requires tools such as (R)TMB to exploit sparsity in the Hessian w.r.t. the latent variables - a property satisfied by SPDE fields but violated by the HMM likelihood. We present a modified forward algorithm to compute the HMM likelihood, constructing sparsity in the Hessian and consequently enabling fast and scalable inference. We demonstrate the practical feasibility and the usefulness through simulations and two case studies exploring the detection of stellar flares as well as modelling the movement of lions.

We consider the time-harmonic Maxwell equations with impedance boundary conditions on a bounded Lipschitz domain $Ω$ with analytic boundary $Γ$. We suppose that $Ω$ consists of multiple subdomains, and that the permeability and permittivity tensors are analytic on every subdomain, but may jump across subdomain interfaces. Under these conditions we show that for any wavenumber $k\in\mathbb{C}$ with $|k|\geq 1$ for which Maxwell's equations are polynomially well-posed, a Galerkin discretization based on Nédélec elements of order $p$ on a mesh with mesh width $h$ is quasi-optimal, provided that there holds the wavenumber-explicit scale resolution condition a) that $|k|h/p$ is sufficiently small and b) that $p/\log |k|$ is bounded from below.