High-voltage direct current (HDVC) transmission systems based on modular multilevel converters (MMCs) have become a key topology in modern power systems. The dynamics of MMCs exhibit strong multivariable coupling, constraints, and uncertainties, motivating the use of model predictive control (MPC) to enhance current regulation performance. However, MPC tuning is nontrivial and does not inherently guarantee stability or robustness, particularly in the presence of model uncertainties. This paper proposes a MPC tuning method that ensures robust performance under bounded model uncertainties. This method solves a convex linear optimization problem to compute the optimal weighting matrices Q, R, and P ensuring optimality and reproducibility. As a result, robustness is enhanced without increasing the online computation burden. The effectiveness of the method is validated through testing on a real-time digital simulator (RTDS) model of a point-to-point HVDC system. Results demonstrate improved performance compared to conventional LQR-based MPC tuning.

Molecular rare-earth-ion complexes offer unique opportunities for quantum technologies by combining the intrinsic coherence properties of rare-earth ions with chemically tunable molecular environments. A crucial capability is the realization of multi-qubit architectures with defined qubit couplings to enable two-qubit quantum gates. Here, we investigate the optical coherence properties and excitation-induced interactions of two Eu$^{3+}$-based molecular complexes, comparing a mononuclear reference system with a dinuclear analogue in which two Eu$^{3+}$ ions are positioned at a well-defined intramolecular distance of about 7 Angstrom. Using cryogenic ensemble spectroscopy, including spectral hole burning, free-induction decay, and photon echo measurements at temperatures down to 100 mK, we demonstrate long optical coherence times $T_{2,\text{o}}$ of up to 9 $μ$s. As a key step toward scalable multi-qubit architectures, a control-target sequence was implemented to probe conditional ion-ion interactions, revealing a stronger interaction-induced dephasing in the dinuclear complex. Finally, we show the integration of the dinuclear complex into a fiber-based optical microcavity, and observe an 380-fold emission enhancement of the $\mathrm{}^5\mathrm{D}_0\rightarrow\mathrm{}^7\mathrm{F}_0$ transition. Together, these results position molecular rare-earth complexes as versatile and chemically tunable building blocks for scalable quantum technologies.

Examiner reports from six major UK exam boards published between 2017 and 2025 are analysed using a mixed-methods thematic analysis. Focusing on questions relating to gravity, the objective is to understand where students commonly drop marks. Findings reveal that the source of difficulty is dependent upon topic and question style. Mathematical errors account for the majority of lost marks in calculation-type questions, while a lack of conceptual understanding commonly results in lost marks on questions relating to fields, energy and gravitational potential. Pedagogical strategies for teaching gravity must emphasise algebraic skills for orbital mechanics topics while prioritising qualitative modelling and precise definitions for field theory.

We establish a complete structural classification for continuum-wise hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw$_F$-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus $\mathbb{T}^2$ or to its standard hyperelliptic quotient on the sphere $\mathbb{S}^2$. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.

We investigate the critical regime $κ(R,T)=0$ in $κ(R,T)$ gravity. While most studies assume a non-vanishing effective gravitational coupling, the existence of critical hypersurfaces where $κ$ vanishes is a generic feature of many admissible coupling functions. We show that the apparent singularity of the non-conservation equation is an artifact of a rewritten form of the conservation law and that the fundamental equations remain regular at $κ=0$. We further analyze the structure of critical hypersurfaces, derive the associated compatibility condition $(\nabla^μκ)T_{μν}=0$, and discuss their interpretation as gravitational screening surfaces separating attractive and repulsive gravitational phases. The existence of critical coupling hypersurfaces also obstructs a global Einstein-frame description, distinguishing $κ(R,T)$ gravity from theories based solely on algebraic redefinitions of the energy-momentum tensor. Possible cosmological and astrophysical consequences are briefly explored.

The effect of using a graphene layer as a semitransparent contact layer is studied in solar cells based on AlInN on Si (100) substrates. The devices consist of AlxIn1-xN layers deposited on p-type Si (100) substrates incorporating a thin amorphous silicon (a-Si) buffer layer to improve the heterointerface quality. Three aluminum contents are studied, namely: x=0.22, 0.35 and 0.43. Subsequently, a monolayer graphene film was transferred onto the front surface of the devices using a simple and low-temperature transfer process, acting as a semitransparent conductive contact. The photovoltaic characteristics were then evaluated under illumination and dark conditions in devices with and without the graphene layer. The results show that the incorporation of graphene leads to a clear improvement in the short-circuit current density, fill factor, and overall power conversion efficiency for all studied compositions, while the open-circuit voltage remains largely unaffected. These findings demonstrate the potential of graphene as an effective transparent conductive contact for nitride-based solar cells.

The native processing of time-dependent signals from optical sensors by integrated photonic circuits can potentially bring significant advantages in terms of energy consumption, latency and processing power, as it allows skipping or reducing the use of fast digital electronics and directly exploiting optical degrees of freedom and parallelism. However, due to a short memory, optical operations usually struggle to directly process optical signals with relatively slow (<MHz) dynamics from optical sensors. In this work, we experimentally show that these limitations can be overcome by exploiting the self-pulsing dynamics in a microring resonator (MRR) network. In particular, we demonstrate that such dynamics can expand and retain information about perturbations sensed by a fiber sensor. This reduces the minimum sampling rate for the digitization of the sensor signal by at least one order of magnitude. The reduction is achieved by combining fiber sensing measurements at two different perturbation locations and frequencies with MRR network measurements at multiple output ports, input power levels and laser wavelengths. This work represents a first step in bridging time-dependent optical processing and optical sensing at sub-μs time scales.

The dynamics of nanoparticles within nanoscale liquid environments exhibit a range of complex phenomena driven by the interplay of processes at varying length scales. While these dynamics have profound technical implications, such as in nanoscale catalytic kinetics, ion-transport pathways in energy storage, and macromolecular crowding in biological systems, real-space imaging of dense, confined nanoparticle assemblies remains a significant challenge. Here, we present a liquid-phase transmission electron microscopy approach in which dense clouds of gold nanoparticles are formed within microfluidic channels, rendering the particle ensemble visible in bright-field electron imaging. This strategy enables direct imaging of different density-dependent particle ordering phenomena, including a local structuring of the colloidal liquid in nanoscale spaces, disordered dynamic clouds at high nanoparticle densities and the reversible formation of superlattice structures. Our results provide a unique window into the complex processes of colloidal self-organization at the nanoscale.

Fork-join parallelism, popularized by OpenMP, remains the dominant model for shared-memory parallel programming, but its implicit synchronization barriers can penalize algorithms with inhomogeneous workloads. Asynchronous many-task (AMT) runtimes sidestep these barriers by expressing work as a dependency graph of fine-grained tasks. Yet, the actual performance benefit over a carefully written fork-join baseline is rarely quantified. In this work, we introduce Cholesky-Bench and use it to revisit the tiled Cholesky decomposition, a canonical irregular kernel, comparing four parallelization variants of the right-looking algorithm across two runtimes: the OpenMP implementations shipped with GCC and LLVM, and the HPX AMT runtime. The variants span classical fork-join, a collapsed fork-join that exposes additional inner-loop parallelism, synchronous tasking, and asynchronous tasking with explicit data dependencies. We benchmark all eight combinations on a dual-socket 128-core AMD Zen 2 node across multiple tile sizes and problem sizes. Our results show that across all variants, HPX outperforms OpenMP at the optimal tile size by 15%-30%. Specifically, asynchronous HPX tasks are up to 26% faster than their OpenMP counterparts, and exhibit roughly 3.8x smaller task overhead. Furthermore, the collapsed fork-join variants close most of the gap to synchronous tasking. Removing redundant synchronization barriers yields an additional improvement of 7% (OpenMP) to 14% (HPX). A GCC-versus-LLVM comparison further reveals compiler-specific differences in fork-join scheduling and task-creation overheads.

We propose and analyze a polytopal discontinuous Galerkin method for the numerical approximation of a coupled non-Newtonian Stokes-Darcy system modeling the interaction between a non-Newtonian free-flow fluid and a non-Newtonian flow through a porous medium. Due to its geometric flexibility and arbitrary-order accuracy, the proposed discretization scheme is well-suited to configurations with complex geometries. We provide a complete a-priori analysis that considers shear-dependent and velocity-dependent non-Newtonian viscosity models for the free-flow and porous media regions, respectively. The well-posedness, stability, and error bounds of the method are established in the framework of generalized inf-sup theory. Error estimates are confirmed by numerical results.

This paper investigates dynamic Resource Unit (RU) allocation strategies for Wi-Fi~6 (IEEE 802.11ax) networks integrated with Time-Sensitive Networking (TSN), targeting the limitations of static RU scheduling under dynamic traffic conditions. We propose a dynamic RU allocation algorithm that maps TSN traffic classes to Wi-Fi~6 Quality of Service (QoS) mechanisms, including Enhanced Distributed Channel Access (EDCA) and aligns TSN control with Ethernet-based TSN domains. The proposed solution is evaluated using the ns-3 DetNetWiFi framework developed by fortiss, focusing on time-sensitive traffic. Simulation results demonstrate improved network efficiency with reductions in latency, jitter, and packet loss compared to static RU allocation schemes. These findings highlight the potential of dynamic RU allocation to support deterministic communication requirements in Wi-Fi~6-based TSN deployments and to enhance the reliability of hybrid industrial networks.

The article deals with the problem of testing conditional axial symmetry within a~multivariate linear heteroscedastic regression framework. A new test based on integrated rank scores is introduced and its asymptotic distribution is derived. The proposed method extends a similar procedure developed for multivariate data to the regression setting. The test may also be employed to assess specific hypotheses concerning distributional properties of the error term. Its performance and application is illustrated in a small simulation study and with real economic data. The article also contains a few theoretical results regarding axial symmetry that may be of independent interest.

In this paper, we study $S$-prime elements and $S$-primary elements within the framework of multiplicative lattices. Furthermore, we define and explore weakly $S$-prime elements and weakly $S$-primary elements, which generalize weakly prime elements and weakly primary elements in multiplicative lattices respectively. We show that the weakly $S$-prime ideals (weakly $S$-primary ideals) of a commutative ring $R$ with $1$ correspond precisely to the weakly $S_L$-prime elements (weakly $S$-primary elements) of the ideal lattice $Id(R)$ of $R$, where $S_L = \{(s) \mid s \in S\}$.

We study the effects of dimension-four and dimension-six nonminimal Higgs couplings to the Ricci scalar $R$ in the $R^2$-Higgs inflation model in light of the recent ACT and SPT observations. We show that the dimension-six operators $|Φ|^2 R^2$ and $|Φ|^4 R$ can accommodate the enhanced scalar spectral index $n_s$ preferred by the combined CMB+BAO analyses. Using a doubly covariant formalism, we find that the same region of parameter space that explains the observed value of $n_s$ can also induce rapid preheating through the production of the Goldstone modes. If thermalization proceeds efficiently through this preheating mechanism, it may help match the inflationary scale with the CMB reference scale.

Halide double perovskites (A$_2$BB'X$_6$) are a long-known class of materials that has recently been rediscovered for diverse applications, including photovoltaics, photocatalysis, and radiation detection. Their doubled unit cell provides immense chemical tunability, allowing the incorporation of magnetic ions and enabling access to a wide range of electronic-structure features, including different band-edge characters, alignments, and symmetries. Magnetic elements may further introduce spin degrees of freedom and magnetic behaviour, thereby broadening the functional landscape of these compounds. Here, we present the first comprehensive database of spin-polarised electronic-structure data for all halide double perovskites predicted to be stable by the recently introduced $τ$ tolerance factor by Bartel et al. The dataset focuses on the Cs$_2$BB'X$_6$ family, with X = I, Br, Cl, and F, and includes density of states (DOS) for $>$2,500 compounds, calculated using hybrid-functional density functional theory. Among these, 719 compounds exhibit band gaps in the visible range and 118 display half-metallic character. In addition, we provide chemical-bonding analysis using \textsc{lobster}, which provides insights into orbital interactions across the dataset. To facilitate exploration, we further offer UMAP-based visualisations and an interactive app for systematic investigation of chemical composition, electronic structure, and magnetic properties.

We build a three-dimensional (3D) red supergiant (RSG) stellar model for common envelope evolution (CEE) simulations by transporting a 1D stellar model to a 3D numerical grid, mimicking core nuclear power by depositing energy to an inner shell, and mimicking stellar emission by cooling grid cells with densities below the photospheric density. We do not relax the model; rather, we let it perform its natural pulsation. We find that when we mimic photospheric emission by cooling low-density grid cells, the oscillations slowly decay on a time scale much longer than in the absence of photospheric cooling. When we mimic both nuclear energy production, by depositing the stellar luminosity in an inner shell above the inert core of the stellar model, and the photospheric cooling, the oscillations do not decay and their amplitude slowly increases with time. The main pulsational period is about 1 year, comparable to the stellar dynamical time, suggesting a fundamental radial pulsation mode. The non-spherical structure of the stellar model and rapid low-amplitude temporal variations in the average stellar radius testify to the presence of non-radial oscillation modes on top of the fundamental radial mode. We also obtain vigorous convection, as RSG stars have. We conclude that the best way of preparing a giant star to simulate CEE and grazing-envelope evolution is to deposit energy with the stellar luminosity in an inner shell, and to cool the outer low-density numerical shell. There is no need to relax the model.

Given $n \in \mathbb{N}$, an Ahlors--David $n$-regular set $S \subset \mathbb{R}^{n+1}$, and a weight $γ$ satisfying the local Muckenhoupt $A_{1}$-condition, we present a complete intrinsic description of the trace-space $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ of the weighted first-order Sobolev space $W_{1}^{1}(\mathbb{R}^{n+1},γ)$ to $S$. Furthermore, we construct a new family of nonlinear bounded extension operators acting from $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ to $W_{1}^{1}(\mathbb{R}^{n+1},γ)$. Finally, we find conditions on $γ$ that sufficient for the existence of a bounded linear extension operator from $W_{1}^{1}(\mathbb{R}^{n+1},γ)|_{S}$ to $W_{1}^{1}(\mathbb{R}^{n+1},γ)$.

The propagation of very-high-energy (VHE; $E_γ \geq 100$ GeV) gamma rays from extragalactic sources is affected by interactions with photons of the extragalactic background light (EBL), resulting in pair production that attenuates the intrinsic gamma-ray flux. This interaction renders the Universe increasingly opaque to VHE photons at high energies and redshifts. New physics scenarios involving axion-like particles (ALPs) could modify this expected optical depth. In particular, ALPs with masses $m_a \sim 10$ eV can decay into two photons over cosmological timescales, thereby contributing to the diffuse EBL. If such ALPs constitute a significant fraction of the dark matter density, their decay would enhance the EBL intensity and consequently increase the gamma-ray optical depth. In this study, we investigate this scenario using a large sample of gamma-ray spectra observed with the High Energy Stereoscopic System (H.E.S.S.) and the Fermi Large Area Telescope. We model the contribution of decaying ALPs to the EBL and assess their impact on the spectra of blazars across redshifts. By comparing these observations with standard EBL models, we place constraints on the properties of heavy ALPs, specifically their mass and photon coupling, and evaluate their viability as a dark matter candidate capable of modifying the gamma-ray transparency of the Universe. From the combined analysis, and under the assumption that ALPs constitute the entire dark matter density, we derive 95% confidence exclusion limits on the photon-ALP coupling down to $g_{aγ} \sim 7 \times 10^{-12}$ GeV$^{-1}$ for masses $m_a\sim 15$ eV. These constraints are competitive with existing astrophysical bounds and provide complementary sensitivity to other techniques, closing a previously unconstrained region of parameter space in the $m_a \sim 2.5$-$20$ eV range.

With the aim to study the spectral properties of some X-ray sources from recently observed {\it Chandra} data, 9 galaxies which have been observed by {\it Chandra} ACIS-S during the year 2018 to 2022 have been considered for the present work. 27 sources with net source counts $ \ge$ 100 have been considered. The spectra of all the sources were fitted using two empirical models -- an absorbed powerlaw and an absorbed disk blackbody. From their estimated bolometric luminosities, the 27 X-ray sources are categorized as 6 X-ray binaries (XRBs) and 21 Ultraluminous X-ray sources (ULXs). All the six XRBs are found to be in the spectrally hard state ($Γ\sim$ 1.52-2.29) which indeed may be due to thermal comptonization. Only one ULX, CXOUJ032251.2-370950 (X-5), was found to be spectrally soft while the remaining 20 ULXs were spectrally hard. The spectral parameters of X-5 with an inner disk temperature (kT$_{in}$) $\sim $ 0.5 keV and an estimated bolometric luminosity, L$_X \sim$ 3.26 $\times$ 10$^{39}$ erg s$^{-1} $ requires a black hole of mass, M$_{BH} \sim$ 137.86$^{+66.62}_{-47.41}$ M$_\odot $ accreting at $ \sim$ 0.19 times its Eddington limit. 8 ULXs, X-4, X-8, X-9, X-10, X-11, X-12, X-20 and X-21, were found to be in the Extremely luminous X-ray sources (ELXs) regime with even their lower limit of luminosity $>$ 10$^{40}$ erg s$^{-1}$. Softening/Hardening of spectra with or without changes in the luminosity were also observed in some ULXs/ELXs. In the hard ELX, X-8, spectral softening with almost consistent luminosity was observed. While in the ULXs X-20 and X-25 spectral softening with increasing luminosity was observed. However spectral hardening with increase in luminosity were observed in the ULXs X-21 and X-26.

We establish the Kazhdan isomorphism for the $n$-fold metaplectic cover of the reductive group $\mathrm{SL}_2$ over two sufficiently close non-archimedean local fields $F$ and $F'$, both of which have residue characteristic coprime to $n$ and contain all distinct $n$th roots of unity.

Angular momentum coupling manifests widely in diverse physical systems, underpinning the emergent properties and collective dynamics across different scales. The tidal locking, which originates from the synchronization of rotational and orbital motions, has far-reaching impacts in celestial mechanics, reflecting fundamental processes of angular momentum transfer, energy dissipation, and evolution toward dynamical equilibrium. However, its counterpart in mesoscopic quantum fluids has remained largely unexplored. Here we demonstrate the emergence of quantum tidal locking in Bose-Einstein condensates undergoing central force motion in an anharmonic potential. The condensate follows a well-defined orbital trajectory in a static trap and experiences an effective rotating potential induced by the trap anharmonicity. The sustained geometric squeezing continuously deforms the condensate and drives a self-organized synchronization process, in which the intrinsic rotation gradually locks to the orbital motion. Numerical simulations further reveal the formation of a ring-shaped vortex array over longer timescales, arising from the coherent evolution of the rotating matter wave during the locking dynamics. Our findings establish quantum tidal locking in mesoscopic systems as a robust self-organized mechanism for generating and stabilizing circulating states.

We present femtoscopy as a new way to search for saturated gluonic matter in inclusive photonuclear processes, such as inclusive ultraperipheral collisions at the Large Hadron Collider (LHC) and the inclusive photonuclear reactions at the Electron-Ion Collider (EIC). As the femtoscopic approaches are sensitive to the space-time structure of the particle emitting source, they are ideal in providing insights also about the initial stage of the collision, where the gluon distributions may impact the effective size of the dipole the quasireal photons oscillate into. This technique demonstrates its capabilities in isolating nuclear shadowing and gluon saturation effects. Finally, we show how a femtoscopic approach is highly sensitive to sub-fermi scale structures typically observed in ultraperipheral collisions, such as gluonic hot spots.

We investigate two massive young stellar objects (YSOs), IRAS21078+5211 and G035.02+0.35, where evidence for magnetohydrodynamic (MHD) disk winds (DWs) has been obtained at scales of 10-100 au through measurements of the 22GHz water maser velocity distribution within the Protostellar Outflows at the EarliesT Stages (POETS) survey. We employ IRAM Northern Extended Millimeter Array and archival Atacama Large Millimeter Array observations of IRAS21078+5211 and G035.02+0.35, respectively, to study kinematics and physical conditions of the corresponding protostellar winds on scales of 100-1000 au using the same molecular tracers. In IRAS21078+5211, the emissions of several molecules, particularly SO, SO2, CH3CN and CH3OH, are distributed along the axis of the radio jet, and present a LSR velocity (Vlsr) gradient transversal to the jet axis. Position-velocity (PV) plots of the SO lines show patterns consistent with Keplerian rotation. The SO2 emission comes from high velocity gas flowing close to the jet axis, while CH3CN and CH3OH present larger radial extension than the S-bearing species. In G035.02+0.35, the same molecules are instead distributed along the major axis of the rotating disk, and their Vlsr gradients consistently trace the disk rotation. The corresponding PV plots present Keplerian profiles. SO is the only molecular species whose emission extends well outside the disk. In both YSOs, the spatial and velocity distributions of SO are consistent with a rotating wind magneto-centrifugally launched from the YSO disk. The comparison with models of molecule formation and excitation in shocks indicates that the different radial extension of the molecular species observed in the protostellar wind of IRAS21078+5211, as well as the lack of molecules, except SO, in the G035.02+0.35's wind, can be explained in terms of a radially extended MHD DW, rather than a compact X-wind.

Adaptive context selection is critical for retrieval-augmented generation (RAG) systems, as fixed Top-K retrieval fails under query-dependent and heavy-tailed similarity distributions. While Extreme Value Theory (EVT) offers a principled framework for adaptive truncation, existing approaches apply EVT globally across the entire ranked list, incurring prohibitive computational costs and statistical instability. We propose Tail-Aware Adaptive-k(TAA-k), a training-free framework that operationalizes EVT through a localized validation strategy. The key insight is that ranked similarity curves exhibit a characteristic steep--flat--steep pattern reflecting a transition from relevance-dominated to noise-dominated regimes. TAA-k exploits this geometric structure via knee detection to identify a compact candidate region, then applies EVT-based goodness-of-fit testing within this window to validate the onset of tail behavior. This coarse-to-fine design reduces computational complexity from O(N^2M) to O(sqrt{N\log N}*M) while maintaining statistical rigor. Under mild monotone likelihood ratio assumptions, TAA-k yields a stable, query-adaptive cutoff corresponding to the earliest noise-dominated position. Experiments on WebQuestions, 2WikiMultiHopQA, and MuSiQue demonstrate that TAA-k achieves near-oracle retrieval quality (F1 within 2-3% of oracle) with orders-of-magnitude efficiency gains over global EVT methods, while maintaining robustness across embedding models and compression dimensions.

We consider a multi-receiver status update system in which a transmitter monitors a finite-state semi-Markov source and decides whether to stay idle, unicast an update, or broadcast a common update. We formulate a risk-aware scheduling problem that minimizes the long-term average sum of the average Age of Incorrect Information (AoII), average risk ratio, and transmission cost. The risk state is defined by whether the AoII exceeds a prescribed threshold. We solve the problem using model-based and model-free policies and compare them with two baselines. Numerical results show that the proposed policies outperform the baselines, exploit both unicast and broadcast transmissions, and capture the effect of the dwell-time law on scheduling performance.

Aumann defined common knowledge mathematically and established his now famous Agreement Theorem. We present a novel approach to quantifying how close individuals are to commonly knowing events, $(δ,ε)$-common knowledge, which is defined for any (and not just countable) probability spaces, and provide quantitative versions of the key results in this field. Specifically, we do this for Aumann's Agreement Theorem and Nielsen's extension thereof to random variables, as well as for the setting in which posteriors are communicated back and forth between individuals. Our results apply in particular to noisy communication settings.

Most galaxies host supermassive black holes (SMBHs) that remain weakly accreting or dormant for much of their lifetimes. At the lowest accretion rates, these systems may represent the transition between active nuclei and dormant black holes, but whether they can still launch collimated jets remains unclear. The nuclei in our Galaxy (\sgra) and M31 are key examples of this regime, although no clear jet structure has yet been detected in either source. Here we report multi-frequency very long baseline interferometric observations of \Msixty\ (NGC~4649), a nearby elliptical galaxy hosting a nearly dormant SMBH with an Eddington ratio of $\sim10^{-8}$. We detect a compact two-sided jet with an unusually steep synchrotron spectrum, demonstrating that collimated outflows can persist even under nearly dormant accretion conditions. The apparent radio core exhibits an unprecedentedly steep frequency-dependent position shift toward the SMBH, locating the central engine only $\sim57\,μ$as, corresponding to a projected distance of $\sim10$ Schwarzschild radii, upstream of the 8.37-GHz core. The observed jet morphology and steep core-shift behaviour are reproduced by general relativistic magnetohydrodynamic and radiative-transfer simulations, indicating a magnetically dominated, non-equipartition jet-launching region that departs from the standard conical equipartition picture. These results provide direct observational evidence that jet production can survive near the dormant SMBHs and establish \Msixty\ as a unique laboratory for probing jet formation on event-horizon scales in the lowest-accretion SMBH regime.

To a full $m\times n$ Mealy automaton $A$ we associate a bijection $θ_A$, a one-vertex rank-two graph $F_{θ_A}$, and a one-vertex $VH$-square complex $Y_A$ tiled by $mn$ Wang tiles. We prove that $Y_A$ contains an anti-torus if and only if $A$ is bi-reversible and $F_{θ_A}$ is aperiodic. The two hypotheses are independent and play disjoint roles: bi-reversibility is exactly what makes $Y_A$ a complete square complex, so that its universal cover splits as a product of two trees and anti-tori can be discussed at all; and, within that setting, an anti-torus is precisely a period-free configuration in the two-sided path space of $F_{θ_A}$, whose existence is the aperiodicity condition. Working at the level of configurations removes any appeal to the geometry of products of trees from the main equivalence; the geometric (loop-spanned) form of Wise is shown to be strictly stronger, the lamplighter being aperiodic with no loop-spanned anti-torus.

Play-based parent-child interaction offers preschoolers rich opportunities for everyday foreign language learning, yet many parents struggle to turn open-ended play into effective English-as-a-Foreign-Language (EFL) learning experiences at home. To explore how AI might support this process, we conducted formative studies through interviews and a Wizard-of-Oz study. We identified four key challenges: content selection, language expression, balancing instruction and play, and problem solving. To address these challenges, we present PAPEL, a parent-AI collaborative system that grounds suggestions in the ongoing play scene and organizes support into four core modules: content generation, language adaptation, balance assessment, and extended response. In a counterbalanced within-subjects study with 16 parent-child dyads, PAPEL was associated with more integrated parent utterances that combined playful and instructional content, as well as more parent-child conversational turns, than the lightweight chatbot baseline used in our study.

We extend the dendroidal Rezk nerve to the setting of relative $\infty$-operads. Our main theorem relates it to localization of $\infty$-operads, generalizing a theorem of Mazel-Gee. By exploiting the relation, we obtain a surprisingly effective tool to prove localization results in operadic contexts. As applications, we obtain a number of new results on operadic localizations, including a generalization of Willwacher's recent result on cyclic operads and operadic modules, and a description of locally constant factorization algebras on spheres in terms of discrete geometry.