In this research note we briefly connect two well-studied topics in computational social choice: metric distortion and the selection of undominated committees. In particular, we show that undominated committees are (in some sense) both necessary and sufficient to achieve bi-criteria metric distortion below $3$ (Banishashem et al., 2026). First, we show that any $\alpha$-undominated committee with $\alpha \le 0.5 - \Omega(1)$ has a bi-criteria metric distortion strictly of $3 - \Omega(1)$. In particular, this implies that a committee of size $5$ with distortion at most $2.7384$ exists. Secondly, we show that if a committee has a bi-criteria metric distortion strictly of $3 - \Omega(1)$, then it must also be $1 - \Omega(1)$-undominated.

The R package bpvars was designed to forecast employment, unemployment, and labour market participation rates of 189 countries. However, it is generally applicable to dynamic panel data due to the flexibility of its modelling framework and robust coding. It includes a family of Bayesian hierarchical panel Vector Autoregressions (VARs) that are characterised by: (i) country-specific VAR models (ii) with their parameters' priors centred around their global counterparts, and (iii) featuring flexible multi-level hierarchical prior distributions (iv) with many variants of well-established in the literature benchmark choices, and (v) four alternative specifications including groupping of country-specific or global parameters. A~distinguishing feature is its implementation of missing observation treatment based on a model-coherent Bayesian approach. These models are accompanied by Bayesian prediction, offering a wide range of possible specifications that aim to increase forecasting precision and comply with various reporting standards. We also implement pseudo-out-of-sample recursive forecasting for evaluating point and density forecast performance. The package implements model specification, estimation, and forecasting routines, facilitating simple workflows and reproducibility, including estimation and forecasting results summaries and visualisations. It achieves extraordinary computational speed thanks to the employment of frontier econometric and numerical techniques, as well as algorithms written in C++.

We investigate the quantum entanglement of Bethe states across a family of integrable spin chains, including the XXX$_{\frac{1}{2}}$ model, its higher-spin generalizations (XXX$_s$), and the non-compact $SL(2,\mathbb{R})$ chain. For on-shell eigenstates, we perform a comprehensive scan of the bipartite entanglement entropy across the entire spectrum of finite chains with periodic boundary conditions, and identify the Bethe solutions that minimize and maximize the entanglement. These extremal solutions follow systematic, spin-dependent patterns in the Bethe quantum numbers. In the XXX$_{\frac{1}{2}}$ spin chain, for the antiferromagnetic chain, the state with minimal entropy always coincides with the lowest-energy state (the ground state) within a given fixed-magnon sector. For the higher-spin XXX$_s$ model, however, the lowest-entropy state is not always identical to the ground state, and can even be the state of highest energy. By contrast, the Bethe roots that maximize entropy exhibit considerably more intricate structure. Our analysis further reveals how special Bethe root configurations, such as singular and strange solutions, affect entanglement, and it uncovers characteristic entanglement features in the non-compact $SL(2,\mathbb{R})$ chain that are absent from compact spin chains. For off-shell Bethe states, we develop an optimization algorithm that extremizes the entanglement entropy over rapidity distributions, enabling us to explore the maximum entanglement achievable by a Bethe state without imposing the Bethe ansatz equations.

Large heat flux is commonly associated with vigorous convection and turbulent mixing. Here, we show that this connection is not fundamental. Using a marginal energy-stability theory, we identify near-optimal convective heat transport with the saturation of an energy-stability constraint rather than with turbulence intensity. The theory selects mean temperature profiles whose fluxes closely approach the best available optimal transport states and rigorous upper bounds, predicting the asymptotic scaling $Nu\sim0.0245Ra^{1/2}$ at large Rayleigh number. These profiles exhibit a hierarchical structure consisting of conductive inner layers, logarithmic-like intermediate layers, and a stably stratified bulk, closely mirroring optimal transport calculations and suggesting that maximal convective heat transport emerges near marginal energy stability. More strikingly, the same profiles can be converted into exact conductive states through prescribed internal thermal forcing. Direct numerical simulations show that an initially turbulent flow then relaxes to a motionless state while maintaining a large wall heat flux. Energy-stability saturation therefore provides both a physical interpretation of transport limits and a route to high-flux heat transfer without turbulence.

Let $(M,g)$ be a $C^{\infty}$ smooth compact connected Riemannian manifold with boundary $\partial M$. Consider the Dirichlet problem: $\Delta_gu=0,\ u|_{\partial M}=f$ for $f\in C^{\infty}(\partial M)$. The Dirichlet-to-Neumann (DN) operator $\Lambda_g:C^\infty(\partial M)\longrightarrow C^\infty(\partial M)$ is defined by $\Lambda_gf=\left.\frac{\partial u}{\partial\nu}\right|_{\partial M}$, where $\nu$ is the unit outer normal to the boundary and $u$ is the unique solution to the Dirichlet problem. Let $g_\partial$ be the Riemannian metric on $\partial M$ induced by $g$. The Calderón problem is as follows: To what extent is $(M,g)$ determined by the data $(\partial M,g_\partial,\Lambda_g)$? In the two-dimensional case the surface $(M,g)$ is determined by the DN data uniquely up to conformal equivalence. Knowledge of the DN data is equivalent to knowledge of the Hilbert transform ${\mathcal H}_\Omega:C^\infty(\Gamma)\to C^\infty(\Gamma)$ on the boundary curve $\Gamma=\partial\Omega$ of a planar domain $\Omega$. We study properties of the Hilbert transform. In particular, we obtain an integral formula for ${\mathcal H}_\Omega$ for a simply connected $\Omega$ which generalizes the classical integral formula for the Hilbert transform on the unit circle. This formula is the base of our algorithm for reconstructing a simply connected planar domain from the DN data. Several numerical reconstructions are presented.

Constructing predictive models of nonlinear dynamical systems from measurement data is a longstanding problem in systems identification and control. Although Neural ordinary differential equations~(Neural ODEs), Koopman operator approximations, and input-aware architectures have each moved the field forward, none simultaneously addresses environment-varying operating conditions, rigorous stability guarantees, and input-to-state stability (ISS) certification within a unified trainable framework. This paper introduces Environment-Aware Stable Neural Koopman Dynamics Learning (ESNKD), which integrates four components: (i)~a bundle-structured encoder that maps environmental observations to a geometrically regularized latent manifold, drawing on the fiber bundle framework; (ii)~an input-conditioned Neural ODE whose residual term handles arbitrary external signals, extending the input concomitant philosophy; (iii)~a contraction synthesis layer enforcing convergence via Persidskii-type tractable linear inequalities, analogous to the certification mechanism; and (iv)~a Koopman lifting stage with LMI-based ISS verification that follows the theoretical pipeline of. Theoretical guarantees cover solution existence and uniqueness, incremental exponential stability, ISS with explicit gain bounds, and robustness to environmental perturbation. Experiments on five benchmark systems, including two robotic manipulation platforms, show consistent improvements over five competitive baselines in both prediction accuracy and safety certification rates.

Quantum gases of polar molecules have recently emerged as a powerful platform for exploring exotic many-body dynamics and correlated quantum behavior. To achieve the full potential of this platform, the production of deeply degenerate quantum gases of molecules in arbitrary confinement geometries is necessary. Here, we successfully evaporate fermionic KRb molecules in both 3D and quasi-2D geometries to well below their Fermi temperatures utilizing dipolar collisions. As we evaporate deeper into degeneracy in both geometries, we enter the Pauli-blocked regime with polar molecules, which we independently confirm for the first time by measuring the Pauli suppression of elastic collisions. Moreover, the Pauli suppression of collisions contributes to the limitation of our final molecular temperature to about 25% of the Fermi temperature in both geometries, particularly limiting quasi-2D evaporation where the Pauli blockade drastically reduces an otherwise large elastic to inelastic scattering ratio. This work demonstrates the production of degenerate Fermi gases of polar molecules both in a 3D harmonic trap and in mono- and bi-layer 2D configurations. Further, our work explores the fundamental limits on evaporation of molecular Fermi gases set by the Pauli-exclusion principle, which could be overcome in the future by introducing distinguishable scattering partners.

The potential field source surface (PFSS) model is a cornerstone of many state-of-the-art space weather forecasting frameworks. It includes a single physical free parameter, the source surface (SS) height. Traditionally, a fixed SS height of 2.5 solar radii has been adopted in most studies. However, several studies have investigated the SS height in the PFSS model using various datasets and temporal intervals. Earlier efforts primarily aimed to improve estimates of the heliospheric open magnetic flux. Our recent study Kumar et al. (2025), showed that optimising the SS height substantially improves the performance of the Wang Sheeley Arge (WSA) solar wind speed prediction model at L1. That analysis employed two types of GONG synoptic magnetic field maps, namely standard (STD) and zero-point-corrected (ZPC) maps, over selected periods of solar cycles (SCs) 24 and 25. In this study, we perform a comprehensive investigation of SCs 23 to 25 using synoptic magnetic field maps derived from ground-based (GONG) and space-based (SDO/HMI) observatories. Our results demonstrate that optimising the SS height in the PFSS model significantly improves the WSA model performance compared to the commonly adopted fixed SS height. We find that during solar minimum, higher SS heights (less than or equal to 2.5 solar radii) yield better solar wind speed predictions at L1, whereas during active phases the opposite trend is observed. Although the absolute optimised SS height varies across SCs, the overall distribution pattern remains similar. These finding suggests a relationship between SS height and SC phase over long time scales. Overall, the SS height optimisation enhances the background solar wind speed prediction models in the heliosphere.

We study the collective dynamics of independent particles that diffuse outside a spherical surface, on which they are replicated with a prescribed catalytic rate. In spatial dimensions three and higher, the transient nature of diffusion creates the competition between autocatalytic and escape events, thus leading to a rich phase diagram between subcritical (extinction), critical (steady-state), and supercritical (growth) regimes at long times. The rotational symmetry of the domain and an explicit form of the single-particle diffusion propagator allow us to obtain the statistics of the population size (i.e., the number of particles). In this way, we analyze the mean population size, its variance and higher-order moments, as well as the full distribution. In particular, we obtain a fully explicit form of the distribution at long times and describe a slow, power-law approach to this steady-state limit.

Valid treatment effect inference in survival studies is fundamental yet challenging when the treatment assignments and outcomes are confounded by many baseline covariates. To this end, in this paper we propose a high-dimensional survival causal inference (HSCI) framework that delivers valid inference under a sparse high-dimensional Cox proportional hazards outcome model and a high-dimensional logistic propensity score working model. To mitigate the nuisance estimation bias, we develop a Neyman near-orthogonal score for the treatment effect and implement it with cross-fitting. Under doubly robust nuisance-rate conditions, we establish the root-n asymptotic normality and consistent variance estimation. We also extend the framework to inference on high-dimensional survival covariate effects. Simulation examples confirm that HSCI reduces sharply the bias relative to the regularized Cox estimators and maintains valid confidence interval coverage across different dimensionality, censoring, and misspecified propensity-model settings. An application to diffuse large-B-cell lymphoma data further showcases its value for high-dimensional biomedical survival studies.

Observational studies frequently involve hierarchical data structures in which individuals are nested within higher-level units. In such settings, unmeasured cluster-level factors may confound the treatment-outcome relationship and may additionally induce treatment effect heterogeneity across clusters, complicating causal effect estimation. We formalize the use of g-computation for hierarchical observational data by incorporating random-effects models (REM) as outcome models and propose a within-group g-computation strategy designed to reduce bias arising from unmeasured cluster context. The approach groups clusters according to their observed treatment prevalence and performs g-computation within groups before aggregating group-specific estimates. Through extensive Monte Carlo simulations, we compare the standard and within-group implementations of g-computation using both linear models and REM. Results show that both standard and within-group REM-based implementations substantially reduce bias when the unmeasured cluster-level variable acts solely as a confounder, whereas the proposed within-group REM estimator achieves the lowest RMSE when the unmeasured cluster-level factor acts as both a confounder and a source of treatment effect heterogeneity. We apply the proposed within-group REM estimator to estimate the causal effect of adolescent pregnancy on the child height-for-age Z-score using 2019 Bangladesh MICS data, obtaining an estimated effect of -0.12 (95% bootstrap CI: [-0.18, -0.06]). The proposed within-group g-computation framework offers a strategy for reducing bias from unmeasured cluster-level confounding and treatment effect heterogeneity in hierarchical observational studies.

Designing rapid transportation routes requires balancing efficiency and reachability. Shortest-path models ensure direct, cost-efficient routes but ignore coverage, while centrality-based approaches maximize accessibility but do not enforce operational constraints. We study the problem of selecting a shortest path that maximizes reachability, measured as the number of nodes within a fixed distance of the path. To do this, we introduce the $k$-Step-Central Shortest Path problem and analyse its structural properties. We show that optimal solutions on unweighted graphs can be found in polynomial time and propose an algorithm with a novel pruning rule. We also prove that the problem becomes NP-hard when edge weights are introduced. Additionally, we show that our algorithm can be used to solve the NP-hard problem of finding the closeness-central shortest path in a graph. We demonstrate the efficiency and scalability of our algorithm on synthetic and real-world networks with up to 2,000 nodes. Our results show that improving reachability can substitute for route expansion: increasing the reach of transit lines drastically increases their coverage with shorter routes. This suggests that investments in active transport infrastructure that improve reachability can be more effective than extending primary routes, providing a data-driven basis for allocating resources in network design.

We study quantum gravitational effects inside hyperbolic black holes with both outer and inner horizons by solving the Wheeler--DeWitt (WDW) equation in the minisuperspace approximation. The WDW equation contains a tachyonic region where the effective potential becomes negative. We develop a numerical method that consistently evolves the wave function across this region and obtain stable solutions throughout the entire minisuperspace. For small values of the parameter $\kappa$, which controls the strength of quantum gravitational effects, the wave packet propagates along the classical trajectory with only mild quantum spreading. As $\kappa$ increases, enhanced quantum effects lead to significant spreading of the wave packet during its propagation. Nevertheless, when the initial state is localized near the outer horizon, the wave packet becomes localized again in the vicinity of the inner horizon. We refer to this recovery of localization as a refocusing phenomenon. This result suggests that, if the geometry is classical near the outer horizon, it becomes classical again near the inner horizon. Within the minisuperspace approximation, inner-horizon formation is not obstructed by quantum gravitational effects.

Large-format heterodyne focal plane arrays require highly integrated receiver architectures while maintaining low noise and sufficient sideband rejection, which remains challenging for superconducting SIS mixers at millimeter wavelengths. In this work, we demonstrate, for the first time, a monolithic dual-polarization sideband-separating superconductor-insulator-superconductor (SIS) mixer operating at 2 mm wavelengths (125-163 GHz) on a silicon-on-insulator substrate. The integrated SIS mixer achieves a sideband rejection ratio exceeding 10 dB over the 4-8 GHz intermediate-frequency (IF) band across most of the radio-frequency (RF) range, with a minimum single-sideband (SSB) receiver noise temperature as low as approximately 60 K. As a key building block of the hybrid planar integration (HPI) architecture, this result verifies the feasibility of highly integrated large-format heterodyne focal plane arrays, providing a practical path toward substantially expanding the field of view of millimeter and submillimeter-wave radio telescopes.

NOvA has reported a significance of mass ordering determination using ten years of data together with external constraints from reactor-based experiments. The JUNO collaboration is poised to provide a more precise reactor-based constraint on $|\Delta m^2_{32}|$. In this Letter, we explore the potential impact of this anticipated measurement on the determination of the neutrino mass ordering by NOvA. We find that $3\sigma$ evidence of the normal ordering is achievable over a range of plausible JUNO measurements within the next five years.

Li$_2$CO$_3$ (LC) is a cornerstone material for clean energy technologies, including high-temperature molten carbonate fuel cells, electrochemical carbon capture, and lithium-based batteries. However, capturing the complex, many-body interactions governing the structure and transport in LC in its molten state has remained a challenge, constrained by the computational cost of \textit{ab initio} methods and the accuracy limitations of classical force fields. To address this gap, we deploy equivariant graph-based machine learned interatomic potentials, specifically, the multi atomic cluster expansion (MACE) and neural equivariant interatomic potential (NequIP) architectures that are trained on melt-quench \textit{ab initio} molecular dynamics data. Our benchmarking demonstrates that MACE provides superior transferability and precision in predicting energies and forces compared to NequIP. Subsequently, we use the optimized MACE model to perform large-scale molecular dynamics simulations to probe the properties of molten LC. Besides describing the structural features, such as the dominant presence of C-O pair correlations under molten conditions, our MACE model reproduces experimentally-measured static structure factors and shear viscosity values. Further, our simulations indicate that Li transport in LC is fundamentally dominated by concerted motion, as evidenced by Haven's ratios being significantly below unity (0.20-0.40). Notably, we identify a temperature-driven transition from anisotropic (and highly concerted) Li transport, supported by persistent oxygen-centered Voronoi cages at 1000~K, to isotropic (and less concerted) diffusion at 1400~K. Thus, we provide fundamental insights into the structural and transport properties of molten LC and also demonstrate a robust and scalable framework for the accelerated design of molten salt electrolytes and ionic liquids.

We investigate the hydrodynamic properties of a strongly coupled non-Abelian plasma dual to a four-dimensional AdS black brane with a nonminimal coupling of the form $q_2 F^{(a)\alpha\beta}F^{(a)\gamma\lambda}R_{\alpha\gamma}R_{\beta\lambda}$ in the bulk action. This higher-derivative term introduces a direct interaction between the Yang-Mills field strength and the Ricci tensor, leading to corrections beyond the minimal Einstein-Yang-Mills theory. Using a perturbative expansion in the small coupling $q_2$, we construct the black brane solution up to first order and employ the fluid-gravity correspondence to compute two key transport coefficients: the DC color conductivity $\sigma$ and the shear viscosity to entropy density ratio $\eta/s$. In holography, $\eta/s$ is inversely proportional to the square of the coupling constant of the boundary theory, while $\sigma$ in Einstein-Maxwell theory satisfies a universal lower bound $\sigma \ge 1$ (in units where $\hbar=1$), saturated for uncharged black holes and characterizing a perfect quantum critical fluid. Our results reveal that the nonminimal coupling significantly alters these transport quantities. For the DC conductivity, we find $\sigma = 1 - q_2 \bigl(9\kappa Q^2/(L^2 r_h^4) + 7\kappa^2 Q^4/(4 r_h^8)\bigr)$, indicating a violation of the conductivity bound for $q_2>0$ while the bound is preserved for $q_2<0$. For the shear viscosity, we obtain $\eta/s = (1/(4\pi))\bigl(1 + q_2\, 7\kappa^2 Q^4/(2 r_h^8)\bigr)$, showing that the KSS bound is modified by a term linear in $q_2$. The sign of $q_2$ determines whether the ratio increases above or decreases below the universal value $1/(4\pi)$. These findings highlight the sensitivity of holographic transport to curvature-coupled gauge interactions and provide a controlled example of how higher-derivative corrections influence the hydrodynamic regime of strongly coupled plasmas.

The rapid development of the low-altitude economy (LAE) has created growing demand for reliable aerial communication systems. Extremely large-scale multiple-input multiple-output (XL-MIMO) is a promising enabler for such systems due to its high spatial resolution and robust connectivity. However, three-dimensional (3D) mobility together with near-field propagation makes it difficult to obtain dedicated high-fidelity wireless datasets, hindering systematic algorithm development and evaluation. To address this issue, we develop LAETwin-XL, a digital twin (DT)-based toolchain and dataset for XL-MIMO research in LAE scenarios. Built on the Sionna ray-tracing (RT) module, the proposed toolchain simulates near-field and far-field channels with diverse wireless labels for practical environments. Building on this dataset, we further develop a conditional denoising diffusion implicit model (CDDIM)-based generative foundation model that is pretrained to learn transferable XL-MIMO channel representations from incomplete channel observations. Unlike conventional task-specific or foundation models that rely on relatively complete channel inputs, the proposed model can generatively infer informative channel representations from partially observed channels. Experimental results demonstrate that the proposed framework achieves effective zero-shot channel extrapolation performance. Furthermore, using lightweight task heads and limited training data, it enables parameter-efficient transfer to various downstream tasks (e.g., channel estimation, classification, and localization), delivering high accuracy and robustness even under sparse antenna observations. The codes and dataset are available at this https URL.

The gas-kinetic scheme (GKS) integrates the characteristics of flux difference scheme (FDS) and flux vector splitting (FVS) scheme, providing high accuracy in smooth regions and strong robustness near discontinuities across all Mach regimes. Leveraging these properties, an implicit discrete adjoint GKS is developed for aerodynamic shape optimization over a wide range of Mach numbers. The adjoint solver is constructed using the source-transformation-based algorithmic differentiation tool Tapenade. To enhance computational efficiency, both the flow and adjoint GKS equations are solved using an implicit time-marching strategy, also known as the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method. The effectiveness of the implicit formulation is demonstrated through comparisons with the explicit approach. To accurately impose solid wall boundary conditions, particularly in hypersonic regimes, kinetic boundary conditions and their adjoint counterparts are formulated for both adiabatic no-slip and isothermal walls. Four benchmark test cases covering subsonic, transonic, supersonic, and hypersonic flows are used to verify the effectiveness of the developed adjoint-based design optimization system.

Coarse-grained (CG) molecular simulations offer an efficient alternative to atomistic molecular dynamics to study large and complex biological systems. The accuracy of CG simulations has been increased dramatically by the introduction of machine-learned coarse-grained (MLCG) models. However, these models are typically designed to be used at a single thermodynamic point, lack temperature transferability, and can not be used to predict temperature dependent quantities like the heat capacity. Here we introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins that explicitly decomposes the CG potential of mean force (PMF) into its energetic and entropic components. The model architecture enforces an exact thermodynamic relation between the energetic and entropic components of the PMF and guarantees physically consistent extrapolation and interpolation across temperature regimes. We validate this framework on an extensive dataset spanning a total of 250 $\mu$s of molecular dynamics simulations across five temperatures between 300 K and 400 K for the Chignolin protein, and demonstrate that it reproduces the temperature dependency of the reference atomistic free energy surfaces, correcting the temperature-unaware baselines. Furthermore, we show that it is possible to apply an inexpensive, post-hoc temperature-dependent correction that does not require retraining the MLCG potential, accurately recovering the atomistic heat capacity at different temperatures. Overall, this work provides a physically grounded pathway toward thermodynamically transferable MLCG simulations of complex biomolecular systems.

Let $G$ be a connected affine algebraic group defined over a field of positive characteristic. We prove that the action of $G$ on a smooth projective variety can be lifted to its associated Artin-Schreier root stacks, whenever $G$ has no non-trivial characters. The existence of a $G$-linearization on a certain tautological invertible sheaf on such Artin-Schreier root stacks is also shown.

The Fornax galaxy cluster constitutes a suitable laboratory to explore the evolution of galaxies in a dense environment. Recently, the Southern Photometric Local Universe Survey (S-PLUS) has obtained unprecedented photometric information of Fornax, revealing new features regarding its galaxy populations and surrounding regions. In this context, simulations are invaluable tools to interpret the past, present and fate of such observational findings. We aim to deliver a robust photometric catalog of simulated Fornax-like systems in cosmological context, to consistently contrast them with S-PLUS data. We analyze Fornax analogs from the EAGLE and IllustrisTNG simulations, selected using observed properties of the Fornax cluster and its central galaxy NGC 1399. For each system, we generated synthetic photometry in the 12 S-PLUS bands using the SKIRT radiative transfer code, reproducing the instrumental configuration of the S-PLUS survey. Simulated data cubes, mock images, spectral energy distributions, magnitudes and colors were obtained for each galaxy in our selected simulated Fornax analogs. The synthetic photometry and spectra derived from simulations show a good agreement with the S-PLUS observations. We identify particular systems which show some similarity with the spatial distribution of galaxies in Fornax. Such simulated candidates reproduce the observed color-magnitude relation and the spatial substructure between the cluster core and the Fornax A region. Also, simulated galaxies are bluer at higher cluster-centric distances, in agreement with observations. Although modest discrepancies were obtained between the observed and simulated color-magnitude diagrams in some cases, our results support the suitability of our selection criteria and synthetic photometry, and the reliability of current cosmological simulations to reproduce key general features of the Fornax cluster.

Graph Signal Processing (GSP) and Graph Neural Networks (GNNs) rely fundamentally on the matrix representation of the underlying graph topology. This representation defines key operators such as the graph Fourier transform, spectral filtering, and convolution. Existing parameterized operator families interpolate only partial subsets of classical graph matrices, while broader formulations become non-compact when representing transition-type operators, limiting both theoretical analysis and stable learning. To address this issue, we propose the Generalized Linear Graph Representation (GLGR), denoted by $\mathbf{Q}_{\alpha,l}$, as a compact two-parameter operator family defined on a bounded linear domain. GLGR unifies major classical operators together with transition-type operators without requiring asymptotic parameters. Theoretically, we show that $\mathbf{Q}_{\alpha,l}$ admits a variational decomposition balancing local smoothness and global degree-weighted energy, derive spectral perturbation bounds, and establish graph-aware sufficient conditions for positive semi-definiteness. Building on this formulation, we develop Adaptive GLGR Convolution (AG-Conv), which makes the propagation operator itself learnable within end-to-end GNNs. Experiments on graph classification and node classification benchmarks show that GLGR improves both fixed-operator representation search and adaptive graph learning across multiple backbones.

We report the first evidence for the hadronic transition $\psi(3770) \to \pi^0 J/\psi$ using a data sample of $20.3~\mathrm{fb}^{-1}$ collected at $\sqrt{s} = 3.773$~GeV with the BESIII detector. The $e^+ e^- \to \pi^{0}J/\psi$ process is observed with a statistical significance of $6.1\sigma$, while the significance specifically attributed to $\psi(3770) \to \pi^{0}J/\psi$ is $4.5\sigma$. We measure the dressed cross section for $e^+e^- \to \pi^0 J/\psi$ to be $(249 \pm 44 \pm 15)~\text{fb}$ and determine the branching fraction $\mathcal{B}(\psi(3770) \to \pi^0 J/\psi) = (2.08 \pm 0.36 \pm 0.21\pm 0.25) \times 10^{-5}$, where the first uncertainty is statistical, the second is systematic, and the third due to a possible interference with the $\psi(3686) \to \pi^{0}J/\psi$ decay. This is the first determination of this branching fraction. It lies significantly below tetraquark model predictions but aligns with calculations that incorporate meson loop effects, providing crucial insight into the isospin-violating nature of $\psi(3770)$ decays.

We consider the existence of vortex solutions to the complex sine-Gordon II (CSG2) equation, which can be viewed as an analogy of the Ginzburg-Landau (GL) equation. Using the nontrivial kernels $\eta_{\pm}$ of the linearized CSG2 equation at the standard degree-2 vortex solution $\Psi_2$, we show that it bifurcating to a one-parameter family of symmetry-breaking solutions $\Psi_{2,\alpha}$. Explicit formulas of these solutions are also available, from which we propose a new bilinear system for this equation. Our method can be generalized to higher degree case. Nondegenracy and stability of degree-1 solution are also proved. Finally, we formally discuss the Lyapunov-Schmidt reduction procedure for the multivortex solutions of the CSG2 and GL equation.

Wafer-level 3D integration of superconducting interconnects requires low-thermal budget bonding processes compatible with superconducting materials. Rapid native oxide formation on tantalum (Ta) surfaces limits low-temperature, low-pressure direct Ta-Ta thermocompression bonding. In this study, we develop an oxidation-resistant bonding process using an ultrathin Au passivation layer to suppress oxide formation during bonding. The engineered interface enables blanket Ta-Ta wafer bonding at 300 $^\circ$C under 4.93 bar, significantly reducing the bonding thermal budget and generation of $\alpha$-Ta across the interface, which potentially improves coherence time as reported in literature. Structural and interfacial analyses confirm oxide suppression and continuous metallic bonding, having a bond strength of 169 MPa. This work demonstrates a low-temperature, low-pressure Ta-Ta thermocompression bonding strategy for scalable 3D superconducting interconnect integration.

In this paper, we introduce a convolution based short time offset linear canonical transform (STOLCT) and investigate its fundamental mathematical properties. Specifically, we establish its continuity, orthogonality relations, inversion formulas, range theorem, and convolution theorem. We further explore several important applications of STOLCT, including the Poisson summation formula, the Paley Wiener criterion, and a sampling theorem. In addition, numerical simulations and graphical analyses are presented to compare signal reconstruction performance under different scenarios. A comparative study between STOLCT and STLCT is conducted with respect to their reconstruction formulas, demonstrating the effectiveness and potential advantages of the proposed transform.

We study appearance of bond-nematicity in insulating altermagnetic materials induced by increased frustration and quantum-fluctuations driven melting of the altermagnetic order. Using novel machine learning approach that combines symmetry enhanced neural network architectures and variational Monte Carlo we consider the spin-$1/2$ square lattice $J_1-J_2-\delta$ model known to have altermagnetic ordering in the regime of small geometric frustration and a gapless spin liquid phase in the regime of strong frustration and small exchange interaction modulation parameter $\delta$. In the regime where exchange modulation is relatively large, resulting in the significant splitting of the magnon modes with different chiralities in the altermagnetic regime, we find that melting of the altermagnetic order by increased frustration leads to an intriguing phase that hosts coexisting symmetry protected topological valence bond solid and bond-nematic orders. The phase is characterized by condensation of magnon pairs that results in bond-nematicity, breaking of U(1) spin rotation and $\mathbb{Z}_2$ spin inversion symmetries and chiral splitting of the triplon-like energy levels in the excitation spectrum. Whilst numerous recent studies address non-trivial impact of altermagnetic moments on various properties in altermagnetic materials, like electronic band structure and superconductivity, influence of strong quantum fluctuations and phases that can result from melting of the altermagnetic order are much less explored. Our study therefore presents an important step in identifying exotic phases of matter that can emerge in vicinity of the altermagnetic order.

Probing surfaces with optical beams is a powerful technique utilised for material characterisation, and more recently, measuring surface magnetisation with vortex beams has opened new avenues by utilising OAM beams for metrology. In this paper, we focus on extending the theoretical framework of unit order vortex beam reflection to spatially homogeneous magnetic surfaces, and derive expressions for the Goos-Hänchen (GH) and Imbert-Federov (IF) shifts. We calculate closed form expressions for the plane wave eigenpolarisations, polarisations which remain in the same vectorial direction after reflection, for both dielectric and homogeneous magnetic surfaces. These are found by extending the singularimetry formalism for dielectric surfaces, where the position of the phase vortex can be analytically approximated by taking into account the finite beam width, to homogeneous magnetic surfaces. From this we find the eigenpolarisations of the unit order vortex beam for reflection from both dielectric and homogeneous magnetic surfaces. We discuss with relation to the analytical forms of the Jones matrices for GH and IF shifts the additional reflection behaviour observed for homogeneous magnetic surfaces.

Let $n\geq 2$, and let $\mathcal{S}(1,n)$ be the Lie superalgebra of zero-superdivergence superderivations of $\mathbb{C}[t^{\pm1}]\otimes\Lambda(n)$. Its derived algebra $\mathcal{S}^\prime(1,n):=[\mathcal{S}(1,n),\mathcal{S}(1,n)]$ is well known as a superconformal algebra. In this paper, we first study Shen-Larsson modules over $\mathcal{S}^\prime(1,n)$. These modules, introduced by G. Shen and T. A. Larsson, are constructed from modules over the Weyl superalgebra $K_{1,n}$ and the special linear Lie superalgebra $\mathfrak{sl}(1,n)$. We establish necessary and sufficient conditions for the simplicity of Shen-Larsson modules and investigate their simple subquotients in the non-simple case. Then as an application, building on the classification of simple cuspidal $\mathcal{S}^\prime(1,n)$-modules by C. Martínez, O. Mathieu and E. Zelmanov, we obtain an explicit construction of all simple cuspidal modules over $\mathcal{S}^\prime(1,n)$.