Experimental measurements of different decays of charmed mesons have been extensively performed at BESIII. Precision measurements of absolute branching fractions of different decays, the decay constants of $D^+$ and $D^+_s$ mesons, hadronic form factors of $D$ transitions to light hadrons ($K$, $π$, $η$, $η^\prime$, $K^*(892)$, $ρ$, $ω$, $ϕ$, $K_1(1270)$, $f_0(980)$), $c\to s(d)$ Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, tests of lepton flavor universality with various (semi)leptonic $D$ decays, precision measurements of strong phase difference between $D^0$ and $\bar D^0$ decays, amplitude analyses of multibody hadronic $D_{(s)}$ decays, search for rare $D$ decays have been reported. The reported results offer important information to test different theoretical calculations, to test the unitarity of the CKM matrix, and to search for new physics effects beyond the standard model (SM). This paper reviews experimental studies of different decays of $D^0$, $D^+$, and $D^+_s$ as well as their excitations at BESIII as of April 15, 2026. Based on existing results of (semi)leptonic $D$ decays from all experiments, we have presented the most precise averages for the CKM matrix elements $|V_{cs}|=0.9648\pm0.009\pm0.0036$ and $|V_{cd}|=0.2259\pm0.0014\pm0.0013$, the decay constants of $D^+$ and $D^+_s$ $f_{D^+}=(213.1\pm2.0\pm1.5)$ MeV and $f_{D^+_s}=(253.2\pm1.2\pm1.6)$ MeV, as well as the hadronic form factors $f^{D\to K}_+(0)=0.7342\pm0.0007\pm0.0008$, $f^{D\to π}_+(0)=0.6337\pm0.0053\pm0.0037$, $f^{D\to η}_+(0)=0.351\pm0.009\pm0.005$, $f^{D\to η^\prime}_+(0)=0.263\pm0.025\pm0.006$, $f^{D_s\to η}_+(0)=0.4653\pm0.0058\pm0.0069$, $f^{D_s\to η^\prime}_+(0)=0.535\pm0.020\pm0.011$, and $f^{D_s\to K^0}_+(0)=0.627\pm0.036\pm0.009$, where the first and second uncertainties are statistical and systematic, respectively.

We derive finite-blocklength bounds on the minimum achievable energy per bit over a Gaussian unsourced multiple access (UMA) channel in the presence of heterogeneous path-loss conditions. We consider a setting in which the path loss is known to the users, which enables the use of location-based codebook partitioning [Çakmak et al., 2025]. Through numerical simulations and a large-system analysis based on the replica method, we quantify the performance gain of this strategy relative to the conventional UMA approach in which all users employ a common codebook.

The enigmatic puzzle of the Verwey transition in magnetite Fe$_3$O$_4$ has been unresolved for almost a century. We present an ab initio-based model of the polaron transport combining kinetic Monte Carlo and molecular dynamics calculations to directly describe the coupling of polarons with lattice vibrations. Contrary to the Ihle-Lorentz small-polaron model, we find no significant change in the band structure across the Verwey transition, however, trimeron hopping is observed. The proposed model provides dc-conductivity in agreement with experimental data across the Verwey transition.

Recommendation algorithms, used in online social networks, shape interactions between users. In particular, link-recommendation algorithms suggest new connections and affect how individuals interact and exchange information. These algorithms' efficacy relies on key mechanisms governing the creation of social ties, such as triadic closure and homophily. The first is achieved through structural similarity and represents a heightened chance of recommending users to one another given mutual friends; the second is related to opinion similarity and conveys an increased chance of recommending a connection given similar individual characteristics. These two mechanisms jointly shape the evolution of social networks and behaviors unfolding over them. Their combined effect on the co-evolution of opinion and structure dynamics remains, however, poorly understood. Here, we study how social networks and opinions co-evolve given the joint effect of rewiring based on opinion and structural similarity. We show that both similarity metrics lead to polarized states, but differ in how they impact network fragmentation and opinion diversity. While strongly relying on opinion similarity leads to a higher variation of opinion, rewiring via network similarity leads to a larger number of (dis)connected components, resulting in fragmented networks that lean towards one of the signed opinions. Under strong homophilic settings, introducing a weak dependence on structural similarity prevents network fragmentation and favors moderate opinions. This work can inform the design of new recommender algorithms that explicitly account for interacting social and recommendation mechanisms, with the potential to foster moderate opinion coexistence even in inherently polarizing settings.

We present a Python/CuPy FX software correlator for small radio interferometer arrays and evaluate it on QUEST (Qilu University Explorer Survey Telescope). The system combines multi-threaded data ingest, pinned-memory host-device transfers, GPU-accelerated correlation, Polyphase Filter Bank channelization, MAD-based RFI flagging, and delay/phase calibration in a single workflow aimed at array commissioning. On a single NVIDIA RTX 4090D GPU, the implementation reaches a peak throughput of 1.51 GB/s, which is sufficient for real-time operation in the four-antenna mode tested here. After calibration, the visibility phase across a clean 1.32-1.38 GHz band is flattened to a residual scatter of a few degrees. Using the calibrated visibilities, we form a four-antenna synthesis image of Cassiopeia A; the CLEANed image recovers a compact source at the phase center and reduces image-domain background fluctuations from order 0.1 to a few 0.01 Jy/beam. These results indicate that the software is suitable for small-array commissioning and initial synthesis imaging on QUEST. A GNSS-based beam measurement is included as a supporting commissioning check.

Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex functions. While quantum optimization offers a potential alternative, mapping continuous problems onto near-term quantum hardware introduces severe scaling limits and barren plateaus. To bridge this gap, we propose the Distributed Quantum-Enhanced Optimization (D-QEO) framework. Instead of forcing the quantum processor to find the exact minimum, we use it simply as a topographical preconditioner. The QPU maps the landscape to locate the most promising basin of attraction, generating high-quality seed points for a classical GPU-accelerated solver to refine. To make this approach viable for utility-scale problems, we exploit the mathematical structure of separable functions. This allows us to cut a 50-qubit (i.e., $2^{50}$) global search space into independent and manageable sub-spaces using 5-qubit subcircuits. By executing these fragments concurrently with CUDA-Q, we completely bypass the overhead of cross-register entanglement and classical tensor knitting for separable functions. Benchmarks on the 10-dimensional Rastrigin and Ackley functions show that D-QEO prevents the exponential failure rates observed in purely classical algorithms. Furthermore, this quantum warm-start significantly reduces the number of classical BFGS iterations required to converge, providing a highly practical blueprint for utilizing near-term quantum resources in complex global search.

Climate change concerns emphasize the need for sustainable computing. Modeling the carbon footprint (CFP), including operational and embodied CFP from semiconductor use, manufacture and design, is essential. Field programmable gate arrays (FPGAs) stand out as promising platforms due to their reconfigurability across various applications, enabling the amortization of embodied CFP across multiple applications. This paper introduces GreenFPGA, a tool estimating the total CFP of FPGAs over their lifespan, considering uncertainties in CFP modeling. It accounts for CFP during design, manufacturing, reconfigurability (reuse), operation, disposal, testing, and recycling. GreenFPGA identifies deployment regimes in which FPGAs can be more sustainable than ASICs, GPUs, and CPUs under the modeled iso-performance assumptions. Experimental results highlight the importance of analyzing applications across different computing platforms to assess their CFP while varying parameters such as application type, lifetime, usage time, and volume impact their total CFP. Across the evaluated pairwise iso-performance case studies with ASICs, GPUs, and CPUs, FPGAs can be more sustainable under specific deployment regimes involving frequently changing, diverse workloads and low-volume applications.

We study finite-node conifold degenerations of Calabi--Yau threefolds from the point of view of interacting light sectors. Although each ordinary double point contributes a rank-one local vanishing sector, the corrected global object need not assemble as a freely independent sum of nodewise pieces. Using the corrected perverse and mixed-Hodge-module degeneration package, the global gluing law for corrected extension classes, and the rigid-flexible atom decomposition on the \(F\)-bundle side, we define an interacting multi-node light-sector package and prove a block-reduced structure theorem. In the block-separated cycle family, the finite-node package separates into two logically distinct layers: relation collapse, controlled by a common relation lattice on the corrected-extension, smoothing, and resolution sides, and residual interaction among the surviving global sectors, controlled by a reduced block interaction matrix on the transport and atom sides. The result isolates the geometric and Hodge-theoretic precursor of coupled conifold light states and provides the mathematical input for a later multi-node reformulation of Strominger's conifold mechanism.

Superhard materials are critical for wear-resistant and high-stress applications. Conventional approaches correlating hardness with elastic moduli derived from DFT calculations enable rapid screening but overlook the strong load dependence of hardness. In this work, machine learning (ML) models were developed using a large, curated dataset of load-dependent experimental Vickers hardness (Hv) measurements. Moderate correlation was observed between experimental and DFT-based Hv values, whereas a single-task ML model trained solely on experimental data outperformed multi-task models that combined experimental and computed data. The superior performance of the single-task model highlights that explicit inclusion of indentation load, along with compositional, electronic, and structural descriptors, is essential and sufficient for accurate hardness prediction, beyond what can be achieved using DFT-accessible bulk and shear moduli alone (or in tandem with experimental data). These results emphasize the importance of high-quality experimental data and explicit inclusion of measurement conditions, particularly load, in the development of reliable hardness prediction models.

Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is restricted to smooth solutions and does not directly accommodate shock discontinuities. Addressing this limitation within a variational framework has long been a challenging issue. In this paper, we develop a variational framework that extends Hamilton's principle to shock solutions in compressible fluid dynamics. For the barotropic Euler equations, we introduce a modified action principle that incorporates additional contributions localized at discontinuities. This allows the Rankine--Hugoniot conditions for mass and momentum to emerge directly from unrestricted variations, without imposing continuity across shocks. The additional term admits a natural interpretation as a dissipation potential, linking the variational structure to energy loss at shocks. We then extend the approach to the full compressible Euler equations. Using a variational formulation of nonequilibrium thermodynamics together with suitable variational and phenomenological constraints, we recover the Rankine--Hugoniot relations for mass, momentum, and energy. This yields a unified variational description of shock dynamics in compressible fluids and highlights a fundamental distinction between barotropic and full compressible models in the treatment of energy and entropy at discontinuities.

A new method for including systematic errors in the regression with Poisson data is reviewed in this contribution, with emphasis on applications to astronomical spectra. The method consists of generalizing the usual Poisson log-likelihood, known as the Cash statistic $C_{min}$, and its associated likelihood-ratio statistic $ΔC$, to include the presence of systematic sources of uncertainty. Advantages of this new method include its modeling simplicity and its ability to assess both the level of systematics and the goodness of fit at the same time, including for a nested model component.

Missing confounders are common in observational studies and present fundamental challenges for causal effect estimation by weakening identification and increasing sensitivity to model misspecification. Within the missing-indicator framework, existing methods rely on a single working model and achieve consistency only when that model is correctly specified, and are therefore singly robust. In this article, we develop a doubly robust missing indicator weighted ordinary least squares (MI-WOLS) estimator with partially observed confounders. The MI-WOLS estimator incorporates the treatment assignment mechanism, commonly known as the propensity score model, into the weighting structure of the outcome regression. Building on the missing-indicator framework, we define propensity score based regression weights that satisfy a covariate-balancing condition in the presence of confounder missingness. Under the missingness-strongly-ignorable treatment allocation assumption and assuming either a Conditionally Independent Treatment or Conditionally Independent Outcome structure, the MI-WOLS estimator is consistent when at least the treatment or the outcome model is correctly specified. Simulation studies support the theoretical robustness of the MI-WOLS estimator, demonstrating negligible bias, accurate sandwich-based variance estimation, and near-nominal coverage probability across a wide range of data-generating scenarios. An illustrative application to kidney function outcomes further demonstrates the interpretability and practical feasibility of the method, offering a flexible, doubly robust alternative to existing singly robust estimators.

The sequentially Markov coalescent (SMC) is a Markov jump process which models correlations in local genealogies across a chromosome. It has been used as a theoretical tool for studying linkage disequilibrium and identity-by-descent, and it also forms the basis of a class of statistical procedures for estimating population history and inferring ancestry. In this paper, we study the rate at which SMC forgets its initial condition in the pairwise setting. For the embedded jump chain, we prove geometric ergodicity in total variation, with explicit constants. For the continuous process, by contrast, the total variation distance from stationarity decays as $\asymp 1/\ell$ in genetic distance $\ell$. We obtain analogous results for the closely related SMC' process using a novel time-change argument. One application of these results is to justify heuristic approximations used in the literature that treat distant loci as evolving independently.

Given a symplectic manifold, can one pack uncountably many Lagrangian submanifolds in a given Hamiltonian isotopy class of this symplectic manifold? We address $C^\infty$ and $C^0$ versions of this question.

Overall survival (OS) is the gold standard for assessing patient benefit and cost-effectiveness of new cancer drugs. However, it is often difficult to use OS as the primary endpoint in randomized clinical trials (RCTs) for patients with metastatic cancer due to multiple reasons. In recent years, progression-free survival (PFS) has increasingly been used as the primary endpoint in metastatic cancer RCTs to accelerate development. However, regulatory authorities often seek mature OS data for approval. Therefore, it is critical to determine the target time when OS data are expected to be mature for reliable statistical inference. Motivated by an advanced renal cell carcinoma (RCC) clinical trial, we develop and investigate different prediction models leveraging information from disease progression to improve target OS prediction times. We propose a multivariate joint modeling approach considering components of progression and OS and extend three models commonly used for association to be used for OS prediction. To the best of our knowledge, this is the first comprehensive statistical study exploring the prediction of OS using different levels of information on disease progression and illustrating these models using a real, complex dataset. Our findings have significant implications for OS prediction.

We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge depicting the gap-resolved topology, the topological word captures both the global non-Abelian topology corresponding to the homotopy classification, and the band-adjacency information. The latter, though crucial for the edge-state pattern across multiple gaps, is often overlooked in previous studies. We confirm our framework using both static models and periodically driven Floquet systems, and discuss its connection and distinction with existing descriptions, such as the phase-band singularities and braiding representations. Intriguingly, topological word continues to provide insight regarding topology and edge states, even as the global non-Abelian topology becomes ill-defined under broken parity-time symmetry.

Autonomous vehicles (AVs) increasingly rely on multi-sensor perception pipelines that combine data from cameras, lidar, radar, and other modalities to interpret the environment. This SoK systematizes 48 peer-reviewed studies on perception-layer attacks against AVs, tracking the field's evolution from single-sensor exploits to complex cross-modal threats that compromise multi-sensor fusion (MSF). We develop a unified taxonomy of 20 attack vectors organized by sensor type, attack stage, medium, and perception module, revealing patterns that expose underexplored vulnerabilities in fusion logic and cross-sensor dependencies. Our analysis identifies key research gaps, including limited real-world testing, short-term evaluation bias, and the absence of defenses that account for inter-sensor consistency. To illustrate one such gap, we validate a fusion-level vulnerability through a proof-of-concept simulation combining infrared and lidar spoofing. The findings highlight a fundamental shift in AV security: as systems fuse more sensors for robustness, attackers exploit the very redundancy meant to ensure safety. We conclude with directions for fusion-aware defense design and a research agenda for trustworthy perception in autonomous systems.

Interconnecting heterogeneous quantum systems is an important step toward realizing the quantum internet. We propose a quantum network hub that interfaces local quantum devices with dense wavelength-division multiplexing (DWDM) networks in the telecom band via quantum frequency conversion (QFC) with frequency-channel selectivity. We show that standard periodically poled lithium niobate waveguides used for QFC exhibit a dispersion sweet spot, for example around the 780 nm band, enabling wide tunability of the pump wavelength while maintaining phase matching. Experimentally, we demonstrate the network hub by implementing a channel-selective and polarization-insensitive QFC from 780 nm to telecom wavelengths around 1540 nm. We achieve a pump tuning range of 2 THz and successfully distribute polarization-encoded single photons into 16 frequency channels on the ITU-T DWDM grid with 25 GHz channel spacing, while preserving the quantum information. These results position the QFC-based hub as a versatile backbone for connecting a wide range of quantum devices, spanning both photonic and matter-based systems, across frequency-multiplexed telecom networks.

In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture survives, albeit in a fundamentally altered form, once the system is coupled to an environment.Using a Schwinger-Keldysh formulation of the full counting statistics of the Krylov position, we derive an effective action for operator growth under Lindblad dynamics. Even for the minimal case of dephasing, the phase-space dynamics ceases to be Hamiltonian; environmental coupling generates diffusion in the variable conjugate to Krylov depth, converting deterministic trajectories in to stochastic ones. The hyperbolic mechanism underlying exponential complexity growth is therefore broadened and, beyond a parametrically controlled scale, destroyed.This identifies dissipation as a relevant perturbation of the chaotic Krylov fixed point and reveals operator growth in open systems as a problem of stochastic dynamics in an emergent phase space.

Strange hidden-charm pentaquark states have been systematically investigated within a diquark-triquark model. Through a Gaussian expansion method, masses of some diquarks, triquarks and strange hidden-charmed pentaquark states from S-wave to P-wave excitations have been calculated with the non-relativistic Semay and Silvestre-Brac potentials in terms of the same parameters employed for tetraquark states. Masses of pentaquark states in S-wave excitations are found between $4200$ MeV and $4590$ MeV, while masses of all P-wave excitations are found above $4600$ MeV. Mass splittings between the S-wave and P-wave pentaquark states are about $350-570$ MeV. In comparison to the experimental data, $P_{c\bar cs}(4459)^{0}$ observed by LHCb in decay channel $Ξ_{b}^{-}\rightarrow J/ψΛK^-$ is assumed as the $|1; 0, 1/2; 3/2, 0\rangle_{3/2}$ $[sq][\bar{c}cq]$ pentaquark state with $J^P={3\over 2}^-$, while $P_{c\bar c s}(4338)^0$ observed in the decay channel $B^{-}\rightarrow J/ψΛ\bar{p}$ is very possibly the $|0; 1, 1/2; 1/2, 0\rangle_{1/2}$ $[cq][\bar{c}sq]$ pentaquark state with $J^P={1\over 2}^-$. We predict a lowest strange hidden-charm pentaquark state with $J^P={1\over 2}^-$ around $4200$ MeV.

Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We study the limiting statistical distribution of the eigenvalues of matrices of the form $R_n(a) = T_n(a) + σ_n X_n$, where $T_n(a)$ is a sequence of non-Hermitian tridiagonal twisted Toeplitz matrices, $X_n$ is a sequence of tridiagonal random matrices whose entries have mean $0$ and finite variance, and $σ_n\to0$. The limiting distribution turns out to be a two-dimensional measure which is in general different from the push-forward of the Lebesgue measure by the symbol. We also explain how the results could extend to banded non-Hermitian twisted Toeplitz matrices.

NA61/SHINE is a multipurpose, fixed-target spectrometer operating at the CERN SPS. The studied regime of collision energies, 5.1<\sqrt{s_{NN}}<16.8/27.4 GeV, places the project in-between the two main European heavy ion activities of the coming decade, the continued LHC (0.9<\sqrt{s_{NN}}<14 TeV) and the announced FAIR SIS100 (2.7<\sqrt{s_{NN}}<4.9 GeV) programs. Also, the project partially overlaps with RHIC BES and STAR-FXT (3<\sqrt{s_{NN}}<62.4 GeV, with data taking completed). This contribution gives a subjective summary of the recent results from NA61/SHINE, with particular emphasis on these of greatest importance for the other research programs.

Discovery of high-$T_c$ superconductivity (SC) in the bilayer nickelate series La$_3$Ni$_2$O$_7$ have attracted substantial interest, providing a new platform for exploring unconventional SC. Certain experimental evidence has pointed to a correlated electronic nature, which is the driving force responsible for its high critical temperature ($T_c$). This work reviews the SC in La$_3$Ni$_2$O$_7$, with a particular focus on theoretical understanding of its pairing mechanism driven by this strong-coupling, Hund-assisted scenario. The electronic landscape is governed by two $E_g$-orbitals within the bilayer structure of NiO$_2$ planes. The $3d_{z^2}$ orbital is nearly half-filled and exhibits a stronger localized character, while the $3d_{x^2-y^2}$ is approximately quarter-filled and remains highly itinerant. The localized $3d_{z^2}$ orbitals experience robust interlayer hybridization, mediated by the $2p_z$ orbitals of the inner apical oxygen atoms. This hybridization generates a strong interlayer antiferromagnetic (AFM) exchange. In the strong coupling regime, Hund's rule coupling aligns the spins of the two $E_g$ orbitals on the same nickel site. The strong interlayer AFM exchange is effectively transferred to the itinerant $3d_{x^2-y^2}$ orbital, generating an effective coupling $J_{\perp}$ within this orbital. This mechanism is captured by a minimal strong-coupling bilayer $t$-$J$-$J_{\perp}$ model for the $3d_{x^2-y^2}$ band. Driven by $J_{\perp}$, $3d_{x^2-y^2}$ electrons can form interlayer Cooper pairs, leading to an extended $s$-wave pairing SC with high $T_c$. Meanwhile, the strongly localized $3d_{z^2}$ electrons tend to form interlayer rung singlets. Due to a lack of phase coherence, these singlets do not directly participate in the SC condensate, but instead give rise to a pseudogap phase.

We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one under any non-null distribution with a sequence of i.i.d. observations, and consistent set-valued mode estimators that eventually equal the true set of modes. Additionally, we characterize the set of all e-values, and therefore the set of all valid tests, with one monotone and unimodal observation, as well as the most powerful e-value for a fixed alternative. We then show that many of our results can be generalized to continuous random variables, relating them to the existing results in the shape-constrained inference literature.

Incomplete reporting of diagnostic accuracy data remains a persistent problem in medical research. In many studies, only part of the 2x2 diagnostic table is reported, leaving denominators for diseased and non-diseased groups unknown and preventing direct calculation of sensitivity, specificity, predictive values, and related operating characteristics. To address this limitation, we develop hierarchical Bayesian models for reconstructing incomplete 2x2 diagnostic tables from such partial information. Two motivating scenarios are considered: one in which only a single test-outcome row is observed, and another in which true positives, false positives, and the total sample size are reported but the remaining cells are missing. The proposed models are illustrated on a benchmark breast MRI study with complete counts, treated as partially observed in order to assess reconstruction performance under controlled missingness. The framework yields posterior inference for the missing cell counts and associated diagnostic measures, together with uncertainty quantification in weakly identified settings.

The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these sharp waves effectively requires a mesh with high resolution, making the scheme computationally expensive. In this work, adaptive mesh refinement is used with the high-order Lax-Wendroff flux reconstruction (LWFR) method to solve the system of RHD equations, which is closed with general equations of state. To make the scheme Jacobian-free, the idea of automatic differentiation is incorporated for computing the temporal derivatives in the time average flux approximations. The high-order method is blended with an admissible low-order method at the subcell level to control the Gibbs oscillations and maintain the physical admissibility of the solution. Finally, several test cases involving high Lorentz factors, low densities, low pressures, strong shock waves, and other discontinuities are used to demonstrate the robustness, accuracy, and effectiveness of the proposed method. These simulations are performed with AMR using various linear and curved meshes to show the scheme's efficiency and ability to handle complex geometries.

Surface deformations of optical cavities and plasmonic nanoparticles are inevitable in nanophotonics. The random morphology changes of different realizations modify the associated resonance frequencies and quality factors, which may be characterized by specified distributions instead of their nominal values. As an alternative to statistical analyses based on direct numerical calculations, we present an approximate method using first-order perturbation theory with shifting boundaries. For an example resonator in the form of a plasmonic nanowire, the approach explains the bivariate frequency distribution observed in direct numerical calculations involving 1000 realizations of random surface deformations and provides the average and the associated covariance matrix with relatively high accuracy.

Phase-gradient metasurfaces provide powerful wavefront control through two-dimensional arrangement of nanostructures acting as metaatoms. While dynamic tuning forms a major driver for future breakthroughs and applications in this area, current metaatoms are generally static or limited to operation in the infrared. Here, we present a metaatom that is both electrically tunable and operates in the visible. Its function originates from an excitonic absorption band of a dedoped conducting polymer, which together with low background permittivity induces optical metallicity in a selected part of the visible. This allows anisotropic nanostructures to support excitonic resonances along one direction and not the other, promoting polarization-dependent optical response which can be toggled off and on through reversible doping induced by small bias potentials. Our study details the mechanism of these metaatoms and demonstrate their use in electrically tunable phasegradient metasurfaces for visible light, including erasable and rewritable holograms.

In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process for the classification of simple birepresentations of almost finitary bicategories, and consider in detail the case of Soergel bimodules in extended affine type A.

We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant variations in the point construction. We show how the situation simplifies in the case of semicontinuous relations, allowing for straightforward correspondences between modal axioms and relational properties.