We provide a stratification of the $\mathrm{AGL}_r(\mathbb{C})$-representation variety of the fundamental group of the complement of a twisted Hopf link in terms of a stratification of the corresponding $\mathrm{GL}_r(\mathbb{C})$-representation variety. For ranks $1$ and $2$, we explicitly describe this stratification and compute the motives of these varieties in terms of the Lefschetz motive $q=[\mathbb{C}]$ in the Grothendieck ring of complex algebraic varieties $K_0(\mathbf{Var}_{\mathbb{C}})$.

We report the observation of a long-lived non-stationary state of light in a single-mode optical cavity. The observed state is a ghost of a saddle-node bifurcation which creates a bottleneck in phase space. While such ghosts are known to exist, accessing them is challenging because it requires a mechanism that steers the relaxation pathway away from the true attractor and into the bottleneck where the ghost emerges. Here we identify such a mechanism, namely a nonlinear response with memory. Our experimental system leverages this mechanism, enabling us to observe ghost states with lifetimes exceeding the cavity photon lifetime by more than ten orders of magnitude, even in the presence of strong fluctuations. The ghost manifests as a plateau in the relaxation dynamics of the cavity transmission, reminiscent of prethermalization. We show how the ghost lifetime depends on the memory time and the distance to the bifurcation, and we observe signatures of scaling in the distribution of ghost lifetimes at fixed driving conditions. Our work establishes minimal conditions for realizing parametrically long-lived non-stationary states.

This article analyzes the achievable sum-rate of multiuser uplink segmented waveguide-enabled pinching-antenna systems (SWANs). To unveil system-design insights, an upper bound on the achievable sum-rate is derived, based on which the existence of an optimal segment activation level is theoretically established. Motivated by this result, hybrid segment selection and aggregation (HSS/A) schemes are proposed to jointly optimize segment activation and pinching-antenna (PA) placement. Correspondingly, low-complexity greedy algorithms are developed for the considered optimization problem. Numerical results validate the theoretical analysis and demonstrate that the proposed HSS/A schemes outperform conventional full-segment aggregation.

We survey some recent developments on the theory of dual canonical bases for quantum groups and $\imath$quantum groups. The $\imath$quiver algebras were introduced by Wang and the first author, which are used to give two realizations of quasi-split $\imath$quantum groups of type ADE: one via the $\imath$Hall algebras and the other via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke quiver varieties. The geometric construction of the $\imath$quantum groups produces their dual canonical bases with positivity, generalizing Qin's geometric realization of quantum groups of type ADE. Recently, the authors provided a new construction of the dual canonical basis in the setting of $\imath$Hall algebras, and proved that it is invariant under braid group actions, and obtained the positivity of the transition matrix coefficients from the Hall basis to the dual canonical basis. As quantum groups can be regarded as $\imath$quantum groups of diagonal type, we demonstrate that the dual canonical bases of quantum groups coincide with the double canonical bases defined by Berenstein and Greenstein, and resolve several conjectures therein.

Dopant distribution in two-dimensional semiconductors is typically assumed to be stochastic, limiting deterministic defect engineering. Here, we show that non-equilibrium growth kinetics can be harnessed to define dopant-driven strain architectures in vanadium-doped WS$_2$ monolayers. Using synchrotron X-ray fluorescence, we identify preferential vanadium incorporation, anti-correlated with tungsten content, along crystallographic bisectors. An adsorption-growth-diffusion model with a single kinetic parameter quantitatively captures the dopant segregation arising from preferential corner adsorption and limited diffusion during chemical vapor deposition growth. Hyperspectral Raman imaging demonstrates mechanically induced vibrational responses, revealing localized tensile strain ($\varepsilon \approx0.70\%$) channels associated with the anisotropic dopant distribution. This regime is marked by the depletion of W-site-sensitive in-plane modes and the emergence of a localized $J2$ mode (210~cm$^{-1}$), which our ab-initio calculations attribute to antiphase V$-$V oscillations. These findings establish kinetic segregation as a route to deterministic chemical and strain architectures in 2D semiconductors, enabling programmable defect landscapes and strain engineering during synthesis.

In this work, we address the unresolved type III cases of the algebraic reconstruction theorem by integrating crossed product algebras and semiclassical approximations. We first derive that the relative entropy in crossed product algebras factorizes into contributions from the original algebra and observer wavefunctions. By constructing ``holographic'' crossed product algebras for ``bulk'' and ``boundary'' type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi (RT) formula semiclassically, which provides a complete algebraic description of the reconstruction theorem, as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality.

We consider the Bochner-Schrödinger operator $H_{p}=\frac 1pΔ^{L^p}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry under the assumption of non-degeneracy of the curvature form of $L$. For large $p$, the spectrum of $H_p$ asymptotically coincides with the union $Σ$ of all local Landau levels of the operator at the points of $X$. We study the determinantal point process on $X$ associated with the spectral projection of $H_p$ corresponding to an interval $I=(α,β)$ such that $α,β\not \in Σ$ and compute the asymptotics of its linear statistics as $p$ goes to infinity. When $X$ is compact, this implies the law of large numbers and central limit theorem for the corresponding empirical measures.

The Belle II experiment, operating at the asymmetric SuperKEKB $e^+e^-$ collider, is preparing an upgrade of its vertex detector to cope with an increased luminosity of $6 \times 10^{35}$ cm$^{-2}$s$^{-1}$. The upgraded vertex detector (VTX) will consist of five or six layers of depleted monolithic active pixel sensors (DMAPS), with a total material budget of approximately $3\%$ $X/X_0$. The OBELIX chip, derived from the TJ-Monopix2 sensor and fabricated using Tower Semiconductor 180 nm CMOS technology, is being developed for this upgrade. It features a 33 $μ$m pixel pitch with a time-stamping binning of $50-100$ ns, along with a dedicated digital periphery compatible with the Belle II trigger system, supporting rates up to 30 kHz. The sensor is designed to operate under the high background conditions expected at the target luminosity, with radiation tolerance up to $5 \times 10^{14}$ $n_{eq}$/cm$^2$ and 100 Mrad, while targeting a power density of about 200 mW/cm$^2$. This corresponds to hit rates up to 120 MHz/cm$^2$. Beam test and irradiation studies of TJ-Monopix2 demonstrate that the operating sensor temperature should stay below $40^\circ$C after irradiation up to $5 \times 10^{14}$ $n_{eq}$/cm$^2$. This report reviews the proposed VTX concept, sensor performance, and ongoing R$\&$D activities.

A frequency comb, known for its precision as an "optical ruler", features an evenly spaced spectral pattern. While these combs are vital in photonic quantum technologies, their microwave counterparts are now highly sought after for cryogenic quantum technologies, including semiconducting and superconducting qubits and quantum electrical metrology, which mainly operate in the microwave regime. However, microwave combs are still largely underexplored, and typically rely on complex, high-power optical systems incompatible with the low-power, cryogenic on-chip quantum technologies. In this manuscript, we present an all-electrical, on-chip, cryogenic microwave frequency comb on Strontium Titanate (SrTiO$_3$), exploiting its Pockels-like effect in its quantum paraelectric phase. Our device, utilizing a superconducting microwave cavity, generating the frequency comb via cavity phase modulation enabled by the field-induced effective $χ(2)$ of SrTiO$_3$. The ability to continuously vary the dielectric constant of SrTiO$_3$ by the application of electric field, in its quantum paraelectric phase, makes it possible to control the comb's operating frequency range. The exceptionally high dielectric constant of SrTiO$_3$, > 20,000 in its quantum paraelectric state, enables an ultra-miniature design and on-chip integration with cryogenic quantum technologies.

This Paper presents rapidity-differential measurements of coherent J/$ψ$ and $ψ({\rm 2S})$ photoproduction, as well as rapidity- and mass-differential measurements of exclusive dimuon production, in the forward rapidity region $-4 < y < -2.5$ in ultra-peripheral Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.36$ TeV using data recorded by the ALICE detector at the LHC in 2023, corresponding to an integrated luminosity of $\mathcal{L} = 1170 \pm 50~μ{\rm b}^{-1}$. The J/$ψ$ and $ψ({\rm 2S})$ results reveal the significant role of nuclear shadowing effects. The square root of the ratio of the measured quarkonium cross section to the impulse approximation prediction is about 0.76 for J/$ψ$ and 0.71 for $ψ({\rm 2S})$, at $y \approx -3$, corresponding to typical Bjorken-$x$ values of $10^{-2}$. The exclusive dimuon results highlight the sensitivity of such measurements to precise modeling of the photon flux, particularly at impact parameters near the nuclear radius.

We prove that $4/9$ is a non-jump for $3$-uniform hypergraphs. Our construction perturbs the $ABB$ pattern by inserting, inside the $B$-part, the union of a high-cogirth pair of Steiner triple systems. This goes below the barrier for non-jumps obtainable by Shaw's finite-pattern formulation of the Frankl--Rödl method introduced in 1984. All results employing this approach use patterns where one of the parts has complete shadow. As the $ABB$ pattern is the smallest one with this property, the value $4/9$ is the natural barrier using this technique, and we conjecture that $4/9$ is the smallest non-jump for $3$-graphs. If our conjecture is true, this would answer (in a very strong form) an old question of Erd\Hos.

We study phase ordering dynamics in the three-dimensional nonconserved XY model, via Monte Carlo simulations, for quenches from paramagnetic phase to certain final temperatures $T_f$ within the ferromagnetic region of the phase diagram. The growth in the system occurs via annihilation of vortex and anti-vortex pairs, cores of which, in the three dimensional system geometry, join from different planes, on which the spins lie, to form line defects. In the long-time limit, the associated characteristic length scale, $\ell(t)$, appears to grow with time $(t)$ approximately as $t^{0.15}$, for $T_f=0$. The exponent is much smaller, like in the zero temperature intermediate time ordering in the three dimensional Ising model, than $1/2$, the expected value, that is realized for quenches to $T_f$ value that is sufficiently larger than zero. We carry out quenches from different starting temperatures, $T_s$, that lie above the critical temperature $T_c$. It is observed that the systems with higher $T_s$ approach the final equilibrium faster. This resembles the puzzling Mpemba effect. We present similar results also from the simulations of the two- and three- dimensional Ising model. In the case of the 2D Ising model, we show that the Mpemba effect is observed only if the starting magnetization is restricted to a value close to zero. In $d=3$, on the other hand, for both the models, the effect appears even if the initial configurations at a given $T_s$ are chosen from the full distribution of magnetization. Thus, our results are of much experimental relevance.

Periodically driven systems host topological phases without static analogs, such as the anomalous Floquet phase characterized by trivial bulk bands yet robust boundary modes. In this work, we investigate the scattering problem of a Floquet Chern insulator and reveal the non-Hermitian skin effect (NHSE) of reflected waves. Using a discrete-time scattering formalism, we demonstrate how the non-Hermitian winding number of the reflection matrix is linked to the bulk Floquet invariant via boundary resonances. This reflected-wave NHSE relies on which quasienergy gap the incident wave resides in, leading to a gap-dependent Goos-Hänchen (GH) shift. We further show that the momentum-integrated GH shift quantitatively yields the Floquet topological invariant of the corresponding gap. Our work highlights a frequency-dependent NHSE of reflected waves in driven systems and provides a real-space scattering approach to identify non-equilibrium topology.

Post-Newtonian theory is considered a reliable effective expansion of General Relativity in the weak-field and slow-motion limit. We argue that such a belief is misplaced. In generic many-body relativistic dynamics, the absence of globally conserved charges in the region of interest and non-integrability can drive strong sensitivity to angular-momentum exchange across inhomogeneous curvature, invalidating naive power counting in an effective theory expansion. Building on general lessons from effective field theory, we derive an explicit breakdown criterion that delineates when post-Newtonian truncations become unreliable despite small local potentials and velocities. This supplies a controlled systematic for weak-field mass inference, relevant to the dark matter puzzle in astrophysics and cosmology.

Stochastic forces in natural systems are rarely isotropic. From hydrodynamically coupled colloids to chemical reaction networks, noise contributions are inherently correlated. Together with internal interactions and changing environments, they shape the dependencies between the degrees of freedom of real-world systems, as quantified by their mutual information. In this work, we focus on linearized stochastic systems with both non-diagonal noise matrices and stochastically switching environments. We study how their presence leads to the emergence of information interference, so that the total mutual information cannot be decomposed as the sum of the contributions from deterministic interactions, noise anisotropy, and environmental switching alone. We identify two distinct sources of information interference: a static term, arising from the simultaneous presence of deterministic coupling and noise anisotropy; and a dynamic term, emerging from the interplay between internal processes and environmental switches. We then apply this framework to different physical systems. In the presence of switching temperatures, the mutual information disentangles exactly into internal and environmental contributions. When the noise anisotropy arises instead from hydrodynamic interactions, we find that the presence of a shared fluid can either mask or enhance the information stemming from a non-conservative force depending on its degree of non-reciprocity. Finally, in a fuel-driven chemical reaction network, we show that information interference is controlled by the non-equilibrium driving. These results establish a general information-theoretic perspective on how anisotropic noise and environmental variability shape statistical dependencies in stochastic systems.

Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem has been widely studied, important open problems remain for certain logics. The expressive power of DLs depends on the constructors available for building complex concepts. In this work, we investigate subsumption in the restricted logic $\mathcal{FL}_{\bot \mathit{reg}}$ and its related fragments $\mathcal{FL}_\mathit{reg}$, $\mathcal{FL}_\bot$, and $\mathcal{FL}_0$. These logics support value restrictions over role names, where the subscript $\bot$ denotes the presence of the empty concept and ${reg}$ denotes the use of regular expressions over roles. None of these logics includes concept negation. We show that deciding subsumption between two concept descriptions in $\mathcal{FL}_{\bot \mathit{reg}}$ and $\mathcal{FL}_\mathit{reg}$ is PSpace-complete. When subsumption is considered with respect to a TBox (i.e., a set of axioms), the complexity increases to ExpTime-complete. Our results are obtained via a novel reduction to parity pushdown games.

Marangoni condensation - where surface tension gradients induce instabilities that lead to condensate film breakup into discrete droplets - has traditionally been thought of being restricted to 'positive' binary mixtures, where the less volatile component has higher surface tension. 'Negative' mixtures were expected to exhibit stable filmwise condensation. Here, we demonstrate unexpected spontaneous Marangoni-driven pseudo-dropwise condensation in 'negative' water-ethylene glycol and water-triethylene glycol mixtures. Strong thermo-diffusion in these dilute mixtures enables preferential glycol enrichment in colder condensate film regions during condensation, generating surface tension gradients that trigger film breakup, leading to over 6x wettability-independent heat transfer enhancement compared to filmwise condensation. Our work challenges the conventional framework that restricts Marangoni condensation to 'positive' mixtures - a superficial classification that oversimplifies the underlying interfacial mechanisms that can trigger robust Marangoni condensation, offering new pathways for enhancing phase change heat transfer in industrial applications without the need for expensive and degradation-prone surface coatings.

Causal discovery methods aim to infer causal direction from observational data. Functional causal discovery approaches use structural asymmetries to identify causal directionality but rely on strong modeling assumptions and provide limited tools for uncertainty quantification. We introduce Causal Discovery via Statistical Power (CDSP), a statistical inference framework that connects causal direction estimation with statistical power and enables uncertainty quantification. Considering the foundational setting of bivariate observational data, we show how quantities analogous to statistical power and effect size can be used in causal discovery to determine when data contain sufficient information to favor one direction over the other. We introduce the effect-size asymmetry assumption that characterizes when the probability of correctly detecting the causal direction (i.e., the power of causal discovery) exceeds that of incorrectly favoring the reverse direction. We show that the effect-size asymmetry assumption can be used for causal direction estimation with uncertainty quantification. Simulations show that CDSP direction estimation is robust to mild and moderate model misspecifications. Real data analyses on 100 cause-effect benchmark pairs further demonstrate that CDSP reduces false discovery rates by approximately 18% relative to a commonly used existing method.

Weak gravitational lensing has become a widely used effect to characterise the dark-matter distribution on large scales in the Universe by measuring galaxy ellipticities and their statistical correlations. We present the first weak gravitational lensing catalogue for cosmic-shear cosmology of the Ultraviolet Near Infrared Optical Northern Survey (UNIONS). We analyse approximately $3\,500$ square degrees of sky area in the Northern Hemisphere, observed in the $r$-band by MegaCam on the Canada-France Hawai'i Telescope, achieving a median seeing of 0.7 arcsec. Starting from images calibrated for astrometry and photometry, we describe the steps from image processing to catalogue creation. These steps include masking, source detection and selection, star selection, point spread function (PSF) modelling, shape measurement, and calibration. We conduct extensive validation tests, particularly to assess and mitigate the leakage of PSF ellipticity into galaxy shapes. We demonstrate the robustness of the catalogue by investigating correlations between ellipticity and other observational variables as well as structural elements, such as observer-frame image positions and proximity to bright stars. The final galaxy catalogue contains $62$ million galaxies, corresponding to an effective source density of $4.96$ arcmin$^{-2}$. The ellipticity dispersion, commonly referred to as shape noise, is $σ_ε= 0.27$. Initiating the first major cosmological analysis by the UNIONS collaboration, this is the first in a series of five papers which cover the various aspects of a robust cosmic shear analysis. Two companion papers discuss the robustness of the catalogue, one through the level of $B$-mode contamination and another by producing and analysing dedicated image simulations for shear calibration, while the other two present cosmological results in real and harmonic space.

We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space. The Ultraviolet Near Infrared Optical Northern Survey (UNIONS) is the largest and deepest photometric survey of the northern hemisphere to date, with the UNIONS-3500 catalogue using high-quality $r$-band imaging across 3500 deg2 of the sky. We perform a 2D cosmic shear analysis with a single tomographic bin, using the two-point correlation function (2PCF) statistic. Assuming a flat LCDM model, we obtain constraints on the clustering amplitude of S_8 = 0.831^{+0.067}_{-0.078}, which is consistent with constraints from Planck CMB measurements and precedent cosmic shear results within 1sigma. We outline the construction of our cosmological inference pipeline, including the estimation of the source redshift distribution, shear calibration, and covariance matrix, and describe methodologies for the mitigation of systematic effects arising from PSF systematics and B-modes. We demonstrate that our results are robust to variations in analysis choices, including scale cuts, prior ranges, and nonlinear modelling. This paper is part of a coordinated release which collectively demonstrates the maturity and readiness of UNIONS to deliver competitive cosmological results, positioning it as a key stepping stone towards the forthcoming era of Stage IV weak lensing experiments.

Integrated photonics has emerged as a promising platform for quantum communication and quantum computation. Thin-film lithium niobate (TFLN) has gained significant attention in this field due to its exceptional optical properties, enabling the realization of numerous integrated photonic devices. However, quantum memory, which serves as a universal building block for the quantum internet, has not yet been demonstrated in TFLN. In this study, we realized the first on-chip quantum memory using erbium ions doped TFLN. The developed quantum memory achieves a storage time of 400 ns with an efficiency of 1.95%, significantly outperforming conventional waveguide delay lines. The multimode capability is demonstrated by successfully storing four temporal modes. Furthermore, single-photon-level coherent pulses are encoded into time-bin qubits and stored with a fidelity of 96.8% , surpassing the classical limit achievable by measure-and-prepare strategy. Our results demonstrate the first on-chip quantum memory for telecom-band time-bin qubits in TFLN, providing a key building block toward integrated quantum registers and repeaters for scalable quantum information processing.

High-order edge-enhanced imaging enables precise feature localization and effective background suppression, offering a powerful tool for real-time recognition and high-contrast visualization. Extending this capability to the mid-infrared (MIR) regime is particularly valuable for applications such as biomedical diagnostics, material inspection, and remote sensing, yet remains limited by inadequate spatial-frequency modulation fidelity and low detection sensitivity. Here, we demonstrate a high-sensitivity MIR upconversion differentiator operating at 3 $μ$m, which achieves isotropic high-order edge enhancement by optically imprinting topological complex-amplitude patterns onto MIR Fourier components via nonlinear parametric interaction. Vortex transfer functions $t(k_r, ϕ) \propto k_r^\ell e^{i\ellϕ}$ are precisely encoded on a phase-only spatial light modulator to enable tunable MIR differentiation from first- to fourth- order, with real-time switching at up to 60 Hz. Benefiting from a low-noise upconversion process and a single-photon-sensitive silicon camera, the system achieves high-contrast edge imaging under low-light conditions. Experimental results confirm accurate edge extraction and background suppression for both amplitude and phase objects, hence underscoring its potential for noninvasive diagnostics and label-free material analysis.

RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the structural organization of viral populations in sequence space remains less explored. Here, we compare genotype network architectures in two RNA viruses with markedly different evolutionary contexts: bacteriophage $Qβ$ evolving in controlled laboratory conditions and SARS-CoV-2 evolving within infected human hosts. Using deep sequencing data, we reconstruct the genotype network of mutationally coupled variants within viral populations and analyze their topological properties. Despite large differences in genome size, mutation rate, and ecological setting, both viruses exhibit a common organization: a highly abundant central haplotype surrounded by layers of variants of diminishing abundance as Hamming distance to the central haplotype increases. All reconstructed networks share qualitative and quantitative topological features, displaying a hierarchical structure. The robust organization of both populations under multiple conditions suggests that RNA viruses may share a common genotype network architecture governed by fundamental properties of sequence space and the generic mechanisms of replication and mutation. Genotype networks provide a unifying framework to describe viral population structure beyond conventional diversity measures and, by revealing how local constraints shape mutational search, offers insights into the predictability of viral evolution.

We present a categorical theory of monads and distributive laws in substructural contexts. In the study of distributive laws, the roles of (the absence of) structural rules for variable contexts have been recognized; our theory formalizes these substructural situations using Tronin's verbal categories $\mathbf W$, in a uniform and presentation-independent manner. We introduce the classes of $\mathbf W$-operadic monads (those defined via the structural rules in $\mathbf W$) and of $\mathbf W$-commutative monads (those invariant under the structural rules in $\mathbf W$). We give a canonical construction of a distributive law $ST\to TS$ of monads on $\mathbf{Set}$; it is applicable when $S$ is $\mathbf W$-operadic and $T$ is $\mathbf W$-commutative (under mild conditions). This accounts for many known and new distributive laws. Even when $S$ fails to be $\mathbf W$-operadic, we can refine $S$ and force $\mathbf W$-operadicity; this captures Varacca and Winskel's construction of indexed valuations.

In this paper, we study the following nonlinear Hartree system: $-Δu_i + V_i(x)u_i = μ_i ϕ_{u_i}u_i + \sum_{j\neq i}β_{ij}ϕ_{u_j}u_i$ for $x\in\mathbb{R}^3$, with $u_i\in H^1(\mathbb{R}^3)$ ($i=1,2,3$), where $ϕ_u(x):=\int_{\mathbb{R}^3}\frac{u^2(y)}{|x-y|}dy$ for any $u\in H^1(\mathbb{R}^3)$, $V_i(x)$ ($i=1,2,3$) are continuous bounded radial functions, and $β_{ij}$ are coupling constants. We mainly investigate the effects of the potentials and the nonlinear coupling terms on the structure of solutions. Applying the Lyapunov-Schmidt reduction method, we prove the existence of infinitely many solutions to the system. Specifically, the solutions we obtain satisfy that some components are synchronized with each other but segregated from the others, and that some components are positive while others are sign-changing. To the best of our knowledge, it is the first time that solutions possessing some positive components and some sign-changing ones have been constructed using Lyapunov-Schmidt reduction methods. Moreover, it is also the first attempt to investigate systems consisting of three Hartree equations with mixed couplings.

This paper proposes a decentralized method for regional pole placement, or $\mathcal{D}$-stability, in linearized networked systems. Existing LMI-based methods are hindered by confidentiality concerns regarding proprietary subsystem models and the absence of communication infrastructures. To overcome these barriers, we map the target region $\mathcal{D}$ of pole placement to an auxiliary left-half plane and introduce positive functions to handle the resulting complex-coefficient dynamics. We prove that $\mathcal{D}$-stability is guaranteed via local frequency-domain criteria without requiring shared subsystem models or inter-subsystem communication. This method is then tailored to DC microgrids, where a loop transformation is utilized to reallocate the burden of stability certification, deriving a broadcastable grid code for decentralized parameter synthesis. Numerical examples verify the efficacy of the proposed method.

Further development of nuclear power plant technology relies heavily on materials durability under operating conditions. Estimating the materials performance in the operando tests is crucial. In this paper, the mechanical behavior of thin amorphous nuclear-dedicated Al2O3 coatings deposited by pulsed laser deposition was investigated by nanoindentation over the temperature range of 25-650C. Experimental nanomechanical analysis was supported by MD simulations. The results indicate that the hardness of the amorphous coating experiences a gradual, constant decrease with temperature, while the Young modulus value remains constant in the whole temperature range. Observed phenomena confirm the increasing plasticity of the material and it is postulated to be related to the bond-switching mechanism that accelerates at high temperatures. The post-mortem transmission electron microscopy characterization confirmed that the loaded material was non-crystalline over the entire range of the indentation temperatures. The thermal stability of the structure was further studied in-situ up to 1050C by X-ray diffraction. The implemented methodology allowed us to follow the dynamic process of phase transitions occurring in the material above 650C. First, thermally activated crystallization was observed at 700C. Intermediate alumina phases were present up to 950C, while above this temperature, exclusively the thermodynamically stable alpha-Al2O3 was observed. The in-situ high-temperature characterization of the evolution of thin films boosts the understanding of the application limits of the coating systems at elevated temperatures. The added value is that the paper demonstrates the potential usefulness of combining high-temperature techniques to characterize the complete behavior of thin films at elevated temperatures.

We prove a regret lower bound for Gaussian-process bandits on a smooth compact Riemannian manifold $\M$ of dimension $d$ with intrinsic Matérn-$ν$ kernel ($ν>d/2$) that exposes how the geometry of the arm space enters the constant. For any algorithm and time horizon $T$ exceeding an explicit threshold, the worst-case expected regret over the RKHS-ball $\|f\|_{\Hil_{k_ν}}\!\le\!B$ satisfies \begin{multline*} \E[R_T(f)]\;\ge\;c_*(d,ν)\,B^{d/(2ν+d)}\,σ_n^{2ν/(2ν+d)} \\ \cdot\,\vol_g(\M)^{ν/(2ν+d)}\,T^{(ν+d)/(2ν+d)}(\log T)^{ν/(2ν+d)}. \end{multline*} The exponent matches the Vakili--Khezeli--Picheny upper bound \cite{vakili2021information}; the $\vol_g(\M)^{ν/(2ν+d)}$ factor is, to our knowledge, the first explicit volume-dependent geometric constant in a manifold GP-bandit lower bound. We extend the analysis in five directions: (i)~a companion Assouad-style proof gives a different lower bound with a strictly smaller $T$-exponent $(2ν+3d)/(4(ν+d))$ but with a polylog factor of the form $1/(\log\log T)^{(2ν+d)/(4(ν+d))}$, sharpening the $(\log T)^{ν/(2ν+d)}$ Fano polylog of Theorem~\ref{thm:main}; (ii)~we prove a $|G|^{1/2}$ upper bound on the regret of an extrinsic-kernel GP-UCB algorithm on a quotient space $\M=\Mt/G$, plus a bracketing theorem (Theorem~\ref{thm:gauge-bracket}); the precise constant is conjectured to take the modulated form $(1+(|G|-1)h(\rinj/κ))^{1/2}$ (Conjecture~\ref{conj:gauge-modulated}), validated numerically on $\SO(3)$; (iii)~we write the leading constant $c_*(d,ν)$ out fully; (iv)~we extract a curvature dependence $1+O(K\eps_T^2)$ via Bishop--Gromov; (v)~we transfer the bound to the Bayesian regret framework via the Yang--Barron / Castillo et al.\ Bayesian-Fano transfer.

High-resolution spectropolarimetry has opened new avenues for understanding how chromospheric waves shape coronal plasma composition. All modeling efforts so far highlight wave activity and, in particular, the ponderomotive force associated to Alfvénic perturbations, as a key ingredient. Over recent years, studies based on spectropolarimetric measurements in the solar chromosphere have identified magnetic perturbations associated to waves linked to regions in the corona with enhanced FIP bias. Building on this established framework, the present work explores the diagnostic potential of Stokes V amplitude asymmetries as an alternative diagnostic tool for investigating wave behavior relevant to compositional fractionation processes.

We study a class of interacting nonlinear Hawkes point processes on the integer lattice in which each component is reset after its own jumps. The intensity of a component depends on the post-reset activity of its nearest neighbours, which produces a variable-length memory structure. We develop a graphical construction based on a dominating Poisson environment and introduce the clan of ancestors of a space-time point. The clan is the finite or infinite backward exploration of all events whose acceptance decisions may influence the target value. Our main result is a constructive subcriticality criterion: if the sure-event rate exceeds the candidate-event rate, equivalently if $β_*/(β^*-β_*)>1$, then the clan is almost surely finite. The proof is based on an explicit dominating branching process associated with the genealogical structure of the exploration. The finiteness of the clan yields a measurable local construction of the stationary regime. We prove existence and uniqueness of the stationary solution by a coupling argument and obtain an exact backward--forward perfect simulation algorithm. The algorithm terminates almost surely in the subcritical regime and returns exact samples from the stationary law. Numerical experiments, together with reproducibility details and R code, illustrate the finite-clan mechanism and the computational behaviour near the theoretical threshold.