We propose a new approach to inference in tightly identified and large-scale structural vector autoregressions based on a reparameterization that enables imposing identifying inequality restrictions through continuously differentiable mappings. Permitted inequality restrictions include shape and ranking restrictions as well as bounds on economically relevant elasticities, and the approach is also able to accommodate zero restrictions in a straightforward manner. We implement a Hamiltonian Monte Carlo algorithm and show how the posterior density can be rapidly evaluated under the reparameterization, thus facilitating inference in high-dimensional settings. Two empirical applications demonstrate that our approach tends to result in lower serial dependence in Markov chains, larger effective sample sizes and reduced computation time relative to existing methods.

Heat waste is a bottleneck in the development of green information technologies and much effort has been devoted to suppress the heating effect in both electronic and spintronic devices. Here we take an alternative approach and show that controllable heating at the nanoscale can actually benefit information processing. In particular, we study a hybrid nanostructure consisting of a metallic square frame and an antiferromagnetic (AFM) thin film and show that the plasmonic heating can reversibly switch two perpendicularly-oriented AFM domains without the assistance of magnetic fields and electric currents. The required switching energy is at the order 1 nJ, three to six orders of magnitude lower than the current-driven AFM switching. The physical mechanism arises from the thermal-induced strain fields inside the frame, which couple to and manipulate the magnetic orientation via magnetoelastic effect. The strain field direction can be well controlled by selectively exciting the longitudinal and transverse plasmon modes by varying the polarization of the waves, which readily allows for a reversible switching of the AFM vector. Our findings provide tremendous opportunities for optically manipulating the magnetism with ultralow energy consumption and may further promote the interdisciplinary study of photonics, acoustics and spintronics.

Many important statistical models fall outside classical moment-based methods due to the non-existence of moments or moment generating functions. We propose a generalised probabilistic framework in which densities are replaced by pairs $(T,φ)$, where $T \in \mathcal{S}'(\mathbb{R})$ is a tempered distribution and $φ\in \mathcal{S}(\mathbb{R})$ is a Schwartz kernel. Expectations are defined via the action of distributions on regularised test functions, yielding well-defined weak moments, weak characteristic functions, and weak cumulants of all orders. These extend classical quantities and retain key algebraic properties such as additivity under independence and natural affine transformation rules. The main results are: (i) a systematic algebra of weak cumulants; (ii) a weak moment problem where existence of all moments holds unconditionally and uniqueness depends on the kernel, with uniqueness results under Gaussian kernels (via Hermite completeness), positive Schwartz kernels with an exponential tail bound and square-integrable densities (via a Carleman-type criterion), and kernels with exponential decay (via Denjoy-Carleman quasi-analyticity); and (iii) a weak central limit theorem formulated as convergence of weak characteristic functions to a Gaussian limit, covering cases where the classical theorem fails. The framework is illustrated with Student's $t$, stable, and hyperbolic distributions. As a statistical consequence, the weak first moment yields a consistent estimator of the location parameter in the Cauchy model, where no classical moment-based estimator exists. A full statistical treatment is given in a companion paper.

We present a theoretical study of the two-particle spectrum $ω(K)$ for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum $K$ there exist distinct solutions with $\Imω\le 0$ in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of $K$, the calculated spectrum is consistent across all $K$ values. An interesting finding is that the real part of the spectrum $\Re ω(K)$ in the chiral model is gapless. The calculated dispersion law $ω(K)$ provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.

Clinicians lack a principled framework to quantify diagnostic utility in ultrasound reconstructions. Existing standards like PSNR and VGG-LPIPS are inadequate, failing to account for modality-specific physics or the structural nuances of acoustic imaging. We close this gap with a TinyUSFM-based evaluation framework featuring two distinct metrics: TinyUSFM-uLPIPS, a full-reference perceptual distance based on multi-layer token relations, and TinyUSFM-NRQ, a deployable no-reference quality score utilizing clean-manifold modeling and worst-region aggregation to detect localized harmful artifacts. We demonstrate that the presented metrics have four unique advantages: 1) Task-linked quality, where TinyUSFM-uLPIPS achieves superior calibration with semantic task damage, accurately reflecting Dice-score drops in segmentation where VGG-based metrics fail; 2) Cross-organ comparability, maintaining stable scoring scales and consistent severity rankings across diverse anatomical sites and domain-shifted data; 3) PSNR-consistent sensitivity, with TinyUSFM-NRQ providing a reliable quality score without ground-truth images that remains consistent with traditional fidelity benchmarks (i.e. PSNR); and 4) Clinical utility, improving the prediction of expert preference from 47.2$\%$ to 72.8$\%$ accuracy and producing super-resolution reconstructions preferred by sonographers. By integrating these advantages into a unified assessment and optimization loop, this work establishes a modality-aligned standard that finally bridges the gap between algorithmic performance and diagnostic utility. Our code is available at https://github.com/sextant-fable/US-Metrics.

Gamma-ray bursts (GRBs) are generally classified as Type~I GRBs, which originate from compact binary mergers, and Type~II GRBs, which originate from massive collapsars. The traditional correspondence between short--Type~I GRBs and long--Type~II GRBs, separated by a duration of 2 seconds, has been challenged by recent observations of long GRBs associated with kilonovae (i.e., Type~I-L GRBs) and a short GRB associated with a supernova. In this paper, we focus on GRBs with precursor emission (PE) and compile 366 GRBs detected by Fermi/GBM. Applying the unsupervised machine learning methods t-SNE and UMAP, we are able to distinguish Type~I (including subclass Type~I-L) and Type~II GRBs for the first time and identify PE as a key feature for distinguishing GRBs of different origins. Inspired by results of machine learning, we propose a diagnostic parameter, the $E_{\rm p,ME}$-precursor index ($EPI$), defined as ${\rm log_{10}}(E_{\rm p,ME}^{2}/(T_{\rm 100,PE}T_{\rm 100,QE1}^{1/2}T_{\rm MVT,PE}))$, where most Type~I GRBs have $EPI > 6.2$ and most Type~II GRBs have $EPI < 6.2$. This parameter can help the community to diagnose the origin of any GRB with PE based solely on its prompt emission and rapidly plan for follow-up observations. The validation using Swift GRBs provides illustrative evidence that our method may also be applicable to GRBs observed by instruments other than Fermi.

We give a systematic account of the soft mode dynamics of QCD critical point and the two-flavor color-superconductivity based on the 2-flavor Nambu--Jona-Lasinio model, and investigate their effects on electromagnetic observables in relativistic heavy-ion collisions (HIC). We first demonstrate that the collective excitations coupled to the fluctuations of the respective order parameters are the soft modes associated with the phase transitions, in the sense that they acquire a prominent spectral strength in the low-energy and low-momentum region near the phase transitions, and the peak energy goes down, i.e., gets softened, and eventually vanishes at the critical point. It is shown that the diquark soft mode of the 2SC gives rise to the pseudogap, i.e., a depression in the density of states of the quark spectra around the Fermi surface above but in the vicinity of the critical temperature. Then, exploiting the ideas that were developed in condensed matter physics for describing the `para-conductivity' in the normal phase of metal superconductors, we show that the soft modes cause an anomalous enhancement of electric conductivity and the dilepton production rate, and discuss their relevance to HIC.

Hardware verification is one of the most challenging stages of the hardware design process, requiring significant time and resources to ensure a design is fully validated and production-ready. Verification teams aim to maximize design coverage while ensuring correct behavior and alignment with the specification. Coverage closure, which relies on iterative constrained-random and directed testing, is still largely manual and therefore slow and labor-intensive. Recent advances show that the code generation capabilities of Large Language Models (LLMs) can be integrated with external tools to build agentic workflows that autonomously perform hardware design and verification tasks. In this work, we introduce Spec2Cov, an agentic framework that automatically and iteratively generates test stimulus directly from design specifications to accelerate coverage closure. Spec2Cov coordinates interactions between an LLM and a hardware simulator, managing compilation and simulation errors, parsing coverage reports, and feeding results back to the model for refinement. We present features that improve Spec2Cov's effectiveness without additional fine-tuning and evaluate their impact. Across 26 designs of varying size and complexity, including problems from the CVDP benchmark suite, Spec2Cov demonstrates promising performance, achieving 100% coverage on simpler designs and up to 49% on more complex designs.

When asked what causes the magnetic curvature drift of a charged-particle moving in a curving magnetic field, people respond that there is an `F-cross-B' motion of the `guiding center' due to the centrifugal force on the particle as it follows the magnetic field line. This and similar explanations `beg the question' by assuming that the particle follows the field line. In a curving magnetic field, however, a particle moving parallel to the field direction soon won't be. The convective rotation of the field along the particle trajectory ensures that the Lorentz force switches on, and the resulting acceleration rotates the velocity vector back into alignment periodically. The gyration is not symmetric about the field vector, and the resulting velocity offset is the curvature drift. This explanation is guided by Newton's second law of motion in vector notation. It provides a common framework for explaining the three guiding-center motions of a charged particle in a static nonuniform magnetic field: curvature drift, mirror reflection in a magnetic bottle, and gradient-B drift. The discussion aims to provide insight to instructors of electricity and magnetism or plasma physics at the intermediate- to advanced-undergraduate level.

We present the results from rapid-response 1.3 mm observations of GRB 260127A using the Submillimeter Array (SMA). SMA arrived on-source 12.6 minutes after the initial detection by the Neil Gehrels Swift Observatory, representing the earliest millimeter/submillimeter observations of a GRB to date. From these observations, we find a source with flux density $6.9\pm1.7$ mJy, consistent with the X-ray afterglow position but slightly offset from the optical afterglow position (2.7'' offset, with the SMA detection having a 90% confidence radial position uncertainty of 0.9''). Subsequent observations 1.9 days later show no sources of emission, with a $3σ$ upper limit of 0.70 mJy. If the SMA detection is associated with GRB 260127A, we infer that the 1.3 mm light curve for GRB 260127A declined at least as fast as $t^{-0.5}$, suggesting that peak brightness of the event at this wavelength was reached in under a day. We discuss how these findings may be consistent with both forward shock and reverse shock afterglow scenarios, and implications for future millimeter/submillimeter observations of GRBs on these timescales.

Consider a pair of $S$-dual hyperspherical varieties $G\circlearrowright X$ and $G^\vee\circlearrowright X^\vee$ equipped with equivariant quantizations $Q(X)$, $Q(X^\vee)$. Assume that the local conjecture of Ben-Zvi, Sakellaridis and Venkatesh holds for this pair, and also that $X\simeq T^*_ψ(Y)$ is polarized, so that $Q(X)=D_ψ(Y)$. Let $B\subset G$ (resp. $B^\vee\subset G^\vee$) be Borel subgroups. Then using a variant of the $S^1$-equivariant localization of arxiv:0706.0322, we deduce an equivalence between the ${\mathbb Z}/2$-graded $B$-equivariant category $(D_ψ(Y)\operatorname{-mod}^B)^{{\mathbb Z}/2}$ and the ${\mathbb Z}/2$-graded unipotent $B^\vee$-monodromic category $(Q(X^\vee)\operatorname{-mod}^{B^\vee,\operatorname{mon}})^{{\mathbb Z}/2}$.

Organelle patterning and its heritability remain central mysteries in cell biology, highlighting the fundamental tension between genetic inheritance and self-assembly. Here, we explore the nonequilibrium assembly and emdedded size control of the Golgi cisternae and endosomes, amid a continuous flux of membrane traffic, within a stochastic framework of mechanochemical fusion-fission cycles that violate detailed balance. Using a dynamical systems approach, we identify distinct, robust regimes, ranging from fixed points to limit cycles with definite phase relations between cisternae. We identify these dynamical regimes with diverse phenotypes, from stable cisternae to periodic, cell-cycle-dependent dissolution/reassembly of cisternae to cisternal progression. We analyse its dynamic response to systematic perturbations or driving protocols and make definite predictions that may be tested experimentally. Our analysis reveals that the two competing models of Golgi organization - vesicular transport and cisternal progression - are, in fact, two phases of the same underlying nonequilibrium process. We see that cisternal size homeostasis is brought about by a size-dependent embedded control system driven by fusion-fission kernels. Finally, our framework offers a strategy for controlling cisternal number and chemical identity by modulating the interplay between glycosylation enzymes and membrane fission-fusion dynamics.

Understanding how galaxies ignite and extinguish their star formation remains a cornerstone question in modern astrophysics. Recent JWST surveys have revealed an overabundance of massive quiescent galaxies in the first billion years of the Universe, challenging current models of galaxy evolution. In the nearby Universe, ram pressure stripping (RPS) is a major environmental mechanism capable of rapidly shutting down star formation, yet direct observation remains scarce at redshift $z\gtrsim1$, and its role at $z>2$ is even poorly constrained by simulations. Here, we utilize JWST and ALMA observations to present direct evidence of RPS in the post-starburst galaxy A2744-JF-z3, residing in a galaxy group at redshift 3.06, the earliest such detection to date. Spectroscopic diagnostics and spectral energy distribution modeling reveal the ongoing removal of cold gas and dust, coincident with the abrupt cessation of star formation. Contrary to hydrodynamical simulations that predict a reduced incidence of RPS at high redshift, our results instead imply that RPS can operate at $z>3$, suggesting a highly stochastic and impulsive stripping within a clumpy, filamentary intra-group and circumgalactic medium. These observations extend environmental quenching well into the epoch of galaxy assembly, highlighting RPS as a previously overlooked decisive pathway to rapid quenching in nascent groups and protoclusters in the early Universe.

Let $K$ be any field, and let $E$ be any graph. We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra $L_K(E)$ associated to cycles and irreducible polynomials. Then we study the dimension of the $K$-vector space of the extensions between two such simple modules.

We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and study tropical notions of volume associated to both divisors and tropical modules. We prove optimal asymptotic results for each case. In addition, we show that the tropical volume is compatible with the tropicalization of curves.

The cosmological gravitational wave background provides a powerful window on parity-violating physics at energies far beyond the reach of terrestrial experiments. However, any colocated planar detector network is insensitive to isotropic circular polarization, independent of its relative orientation. In this Letter, we show that this no-go result can be evaded by a new class of colocated 3D interferometer designs, which we call Squashed Pyramid, whose non-coplanar configuration geometrically isolates chirality. The design can be viewed as a minimal extension of the Einstein Telescope geometry, obtained by introducing a slightly tilted arm relative to the ET planar configuration. The coplanar correlation channel is blind to circular polarization, whereas the colocated non-coplanar channel is insensitive to the unpolarized background and acquires a response only in the presence of nonzero net helicity. Squashed Pyramid interferometer networks therefore furnish a unique probe of cosmological gravitational wave chirality, opening a realistic terrestrial pathway to test parity violation and fundamental symmetry breaking in the early Universe.

We prove a deterministic analogue of Rudelson's sampling theorem for sums of positive semidefinite matrices. Let $A_1,\dots,A_m$ be positive semidefinite \(d\times d\) matrices, and let $λ_1,\dots,λ_m \ge 0$ satisfy \[ \sum_{i=1}^m λ_i = 1, \qquad \sum_{i=1}^m λ_i A_i = I_d, \qquad \|A_i\| \le M \quad\text{for all } i=1,\dots,m. \] We show that there exists a deterministic sequence of indices $i_1,i_2,\dots \in \{1,\dots,m\}$ such that for every integer $k \ge 1$, \[ \left\| \frac{1}{k}\sum_{r=1}^k A_{i_r} - I_d \right\| \le \begin{cases} \displaystyle \frac{2M\ln(2d)}{k}, & \text{if } k \le M\ln(2d),\\[2ex] \displaystyle 3\sqrt{\frac{M\ln(2d)}{k}}, & \text{if } k > M\ln(2d). \end{cases} \] In particular, if $0<\varepsilon\le 1$ and $N \ge 9M\ln(2d)\varepsilon^{-2}$, then one can choose indices $i_1,\dots,i_N \in \{1,\dots,m\}$ such that \[ \left\| \frac{1}{N}\sum_{r=1}^N A_{i_r} - I_d \right\| \le \varepsilon. \]

Production logistics (PL) is increasingly exposed to variability, dynamic interdependencies, and operational disturbances that challenge conventional centralized planning and control. These characteristics are particularly pronounced in circular production systems, but are increasingly relevant across PL more generally. This paper addresses this challenge through the concept of Self-Organizing Production Logistics (SOPL) using the Design Science Research Methodology (DSRM) as a structuring framework. The paper identifies key technological and systemic drivers motivating SOPL, including autonomous logistics resources, distributed AI-based decision-making, and increasing operational uncertainty in circular production. Based on these drivers, system-level objectives and design requirements for SOPL are derived. Building on these requirements, an initial multi-agent architecture is proposed that combines embodied and non-embodied agents, event-driven coordination, semantic knowledge structures, and digital twins. In addition, a three-phase demonstration roadmap is presented, ranging from an initial laboratory demonstrator toward increasingly distributed and adaptive SOPL systems. The Phase I demonstrator serves as an experimental setup for investigating disturbance handling, human involvement, and supervisory coordination in an order-driven kitting and supply scenario. Overall, the paper contributes a conceptual foundation for the design, implementation, and experimental evaluation of SOPL systems.

In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and induce complete synchronization at a specified small coupling value in oscillators governed by phase-frustrated bi-harmonic coupling. We derive an optimal set of natural frequencies that is robust against added noise and correlated with the network degree heterogeneity, along with the parameters involved in the bi-harmonic coupling function that lead to complete synchronization ($r = 1$). In addition, we find complete synchronization transitions accompanied by hysteresis in scale-free networks, indicating a first-order (discontinuous) phase transition, whereas Erdős--Rényi networks exhibit complete synchronization through a second-order (continuous) phase transition. Furthermore, we use the mean-field approximation in the presence of optimal frequencies to determine the critical coupling strength associated with the synchronization transition in the pure second-harmonic Sakaguchi--Kuramoto model. Here, the obtained optimal natural frequencies scale linearly with the node degree, and the critical coupling strength for the onset of synchronization is derived analytically from the self-consistent equations. In this specific regime, we observe a perfectly ordered two-cluster synchronized state. These findings remain robust for higher-order harmonic coupling schemes, as well as across a diverse range of synthetic and empirical networks, including scale-free, Erdős--Rényi, Zachary Karate Club, and the \textit{C.~elegans} neural network, demonstrating their general applicability.

Quasi-periodic eruptions (QPEs) are a recently discovered class of highly variable X-ray bursts originating in galactic nuclei. These high-amplitude bursts exhibit periodicity ranging from tens of minutes to several days. QPEs are also characterized by variable peak amplitudes that can vary by a factor of few. While multiple physical models have been proposed to explain QPE light curves, none can fully account for all the observed features. A possible connection between QPEs and tidal disruption events (TDEs) has been suggested, particularly due to the past optical/UV outbursts that can be traced back for several sources, the long-term decay in the continuum luminosity, and the soft, thermal-dominated X-ray spectrum. Our primary goal is to verify whether the long-term decrease in eruption amplitudes detected for some QPE sources is consistent with the accretion disk being formed following a TDE. In this work, we adopt a simplified extreme mass ratio inspiral (EMRI) scenario, where a Solar-type star orbits a supermassive black hole (SMBH) and collides with an accretion disk twice per orbit, generating eruptions. We assume a post-TDE disk that follows a temporal power-law decline in mass accretion ($\propto t^{-p}$, $p>0$). As our aim is to develop a toy-model scenario, we have used purely analytical methods without considering all intervening processes in their full generality. Indications are that (i) the observed long-term decline in QPE amplitudes can be reproduced if the first monitored epoch occurs years to a few decades after the tidal disruption, (ii) stellar mass loss caused by ablation can play an important role in the evolution of QPE amplitudes in systems with heavy main-sequence (MS) stars.

While experiments and computer simulations to study biological phenomena are usually performed in diluted in vitro conditions, such phenomena happen inside the cell, an environment densely packed with diverse macromolecules. Here, we revise recent computational methods to investigate crowded and cellular environments. Protein crowders, inert crowders and small molecules were used to mimic crowding. Simulations were performed for models of the cytoplasm. New methods were developed to simulate crowded systems, reaching up to 200 microseconds of simulation time. Apart from the challenges, modeling and simulations to investigate biological phenomena inside cells is a growing field, and has a lot of potential to improve our understanding of how such phenomena happen in vivo.

Gravitational waves (GWs) can resonate with magnetic fields through the Gertsenshtein-Zeldovich effect, producing electromagnetic signals at the same frequency. In pulsar magnetospheres, this conversion may yield a faint radio-band signal that could be detected. In this work, we focus on two specific pulsars, PSR J1856-3754 and PSR J0720-3125, and use numerical simulations to evaluate how well the FAST and SKA2-MID telescopes could detect such signals. We consider transient events, including primordial-black-hole-like mergers, as well as stochastic backgrounds, including primordial GWs. To improve detection sensitivity, we propose four observational methods to lower the detectable energy-density limit of very high-frequency (VHF) GWs; the "Multiple Pulsars with Multiple Telescopes" (MPMT) method performs best because it allows cross-validation and rejection of false candidates. Under the assumption of nearly 6000 hours of observation at 3 GHz and a $5σ$ detection threshold, the minimum detectable characteristic strain is projected to be $h_c \approx 10^{-23}$ for transient events and $h_c \approx 10^{-33}$ for stochastic backgrounds. Under optimistic assumptions on integration time and conversion efficiency, these projections suggest that radio-band searches may approach the sensitivity needed to begin testing representative VHF GW scenarios. More broadly, this conversion in pulsar magnetospheres could be relevant to the origin of some repeating fast radio bursts in the our galaxy.

In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the superposition method. An explicit representation of the solution and the corresponding Green's function is obtained. The explicit form of the Green's function is expressed in terms of a bivariate Mittag-Leffler type function. Then, it is proved that the obtained solution indeed constitutes the solution of the considered problem.

Many integer sequences arise as numbers of $G$-orbits on $\binom{X}{n}$ as $n$ varies, for a permutation group $G\subseteq \operatorname{Sym}(X)$. For finite $X$, Stanley proved that these finite sequences increase towards the middle using an action of the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$. For infinite sets $X$, and hence infinite sequences, Cameron provided an argument for monotonicity by identifying orbits with a vector space basis of the orbit algebra $\mathsf{H}_{G,X}^{\star}$, and proving injectivity of a certain operator $\mathsf{H}_{G,X}^{\star}\to \mathsf{H}_{G,X}^{\star+1}$. In this paper we generalize Stanley's approach to oligomorphic groups, and in particular extend Cameron's operator to a full $\mathfrak{sl}_2(\mathbb{C})$-action on $\mathsf{H}_{G,X}^{\star}$. As intermediate step, we define for every oligomorphic permutation group $G\subseteq \operatorname{Sym}(X)$ the $X$-th tensor power $(k^r)^{\otimes X}$, generalizing work of Entova-Aizenbud. We show that this space carries natural commuting actions of $G$ and the Lie algebra $\mathfrak{gl}_r(k)$, the latter depending on a Harman-Snowden measure $μ$ on $G$. We then show that $\mathsf{H}_{G,X}^{\star}\subseteq (\mathbb{C}^2)^{\otimes X}$ has an ascending filtration by $\mathfrak{sl}_2(\mathbb{C})$-Verma modules. We explain how our approach applies to Fibonacci numbers, Tribonacci numbers, etc. by constructing measures on products with $(\mathbb{Q},<)$.

Atomistic structural data are central to materials science, condensed matter physics, and chemistry, and are increasingly digitised across diverse repositories and databases. Interoperable access to these heterogeneous data sources enables reusable clients and tools, and is essential for cross-database analyses and data-driven materials discovery. Toward this aim, the OPTIMADE (Open Databases Integration for Materials Design) specification defines a standard REST API for atomistic structures and related properties. However, deploying and maintaining compliant services remains technically demanding and poses a significant barrier for many data providers. Here, we present optimade-maker, a lightweight toolkit for the automated generation of OPTIMADE-compliant APIs directly from raw atomistic structure and property data. The toolkit supports a wide range of raw datasets, enables conversion to a standardised OPTIMADE data representation, and allows for rapid deployment of APIs in both local and production environments. We further demonstrate it through an automated service on the Materials Cloud Archive, which automatically creates and publishes OPTIMADE APIs for contributed datasets, enabling immediate discoverability and interoperability. In addition, we implement data transformation pipelines for the Cambridge Structural Database (CSD) and the Inorganic Crystal Structure Database (ICSD), enabling unified access to these curated resources through the OPTIMADE framework. By lowering the technical barriers to interoperable data publication, optimade-maker represents an important step toward a scalable, FAIR materials data ecosystem integrating both community-contributed and curated databases.

We define a generalized Golomb--Dickman constant $λ_θ$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $θ> 0$. Exploiting the independence properties of Kingman's Poisson process construction of the Poisson--Dirichlet distribution, we obtain an explicit integral representation for $λ_θ$ in terms of the exponential integral. The dependence of $λ_θ$ on $θ$ reflects the transition between regimes dominated by long cycles (small $θ$) and those with many small cycles (large $θ$). We also derive the asymptotic behavior of $λ_θ$ for small and large $θ$ and illustrate our results with numerical computations, Monte Carlo simulations of the Hoppe urn, and an application.

Transmission Kikuchi diffraction in the scanning electron microscope has gained popularity as a materials characterization technique for its high throughput and nanometer-level spatial resolution. While conventional diffraction pattern analysis routines focus on Kikuchi bands on the diffraction patterns, the full physical picture of electron scattering and diffraction pattern formation is more complex. Analysis that accounts for additional diffraction features such as diffraction spots and excess-deficiency effects should provide more robust and accurate indexing, if they can be incorporated in pattern indexing or simulation routines. A more accurate understanding of their physics of formation and geometry is required to enable this change. In this work, we demonstrate geometric and full contrast dynamical simulation of on-axis transmission Kikuchi patterns, based on experimental patterns captured using a modular, direct electron detector-based set-up in the scanning electron microscope. First, a diffraction geometry calibration routine is proposed based on the electron channeling pattern of the direct electron detector. This allows us to accurately account for the position of diffraction spots in both geometric and dynamical simulations with good agreement with experimental patterns. Further, by introducing appropriate weight factors, simulation of incoherent diffuse intensity, and calculation of the energy spectra of diffracted electrons, simulated patterns can be obtained which accurately capture the many diffraction features on experimental patterns. Workflows and findings of this work can be used to improve pattern indexing routines, as well as the understanding of the physical processes in the formation of on-axis transmission Kikuchi patterns.

Protoplanetary discs contain a wide range of dust sizes that influence their thermal structure and planet formation processes such as planetesimal formation and pebble accretion. Dust evolution models are therefore essential for both planet formation simulations and the interpretation of disc observations. Several open-source dust evolution codes are available, each adopting different model assumptions. We present a comparison of 1D radial simulations using (in order of complexity) two-pop-py, TriPoD, and DustPy, and 2D radial-vertical simulations with TriPoD, cuDisc, and mcdust. The comparison includes dust size distributions, dust disc masses, planetary gap structures, millimetre fluxes and disc sizes from synthetic observations, planetesimal formation regions, and planetary growth via pebble accretion. We also perform a parameter study to assess how key dust-evolution parameters influence disc evolution, planet formation, and code agreement. In 1D, two-pop-py depletes dust masses faster and produces higher dust concentrations outside planetary gaps than DustPy or TriPoD. The latter two generally agree well, except when size distributions deviate strongly from a power law. While the calculated millimetre fluxes and disc radii agree well, planetesimal formation locations and pebble accretion rates vary significantly between codes. In 2D, we compare cuDisc, mcdust, and TriPoD in simulations of turbulence- and sedimentation-driven coagulation. The dust size distributions agree well, despite the completely different numerical approaches used to model dust coagulation. The largest differences arise in the upper atmosphere, where mcdust suffers from low mass resolution and TriPoD fails to reproduce the exact shape of size distributions that deviate from a power-law.

We construct examples of non-smoothable surfaces in the $4$-sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of order $2$, thus simultaneously answering Question 4.29(a) on the K3 problem list.

This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI) systems. Starting from the definition of geometric frequency, which provides a geometrical interpretation of frequency in electric circuits that admits a natural decomposition into symmetric and antisymmetric components associated with amplitude variation and rotational motion, respectively, we show that complex frequency arises as its restriction to the two-dimensional Euclidean plane. For LTI systems, it is shown that the complex frequencies computed from the system's states subject to a non-isometric transformation, coincide with the original system's eigenvalues. This equivalence is demonstrated for diagonalizable systems of any order. The paper provides a unified geometric interpretation of eigenvalues, bridging classical linear system theory with differential geometry of curves. The paper also highlights that this equivalence does not generally hold for nonlinear systems. On the other hand, the geometric frequency of the system can always be defined, providing a geometrical interpretation of the system flow. A variety of examples based on linear and nonlinear circuits illustrate the proposed framework.