It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with $\mathrm{Rep}(A_4)$-symmetry, as a matrix product unitary (MPU).

We develop a topological framework for Engel expansions that treats both directions of the correspondence between points of $(0,1]$ and nondecreasing digit sequences. We endow the sequence space with the product topology to study the evaluation map, and we fix a nonterminating digit algorithm to study the digit coding map. We also record the correspondence between cylinder sets and fundamental intervals, and give an application to Baire category results for functions of the digits.

Traditional directed graph signal processing generally depends on fixed representation matrices, whose rigid structures limit the model's ability to adapt to complex graph topologies. To address this issue, this study employed the unified graph representation matrix (UGRM) to propose a generalized graph Fourier transform (UGRM-GFT) method based on singular value decomposition (SVD) for signal analysis on directed graphs and Cartesian product graphs. We defined UGRM-GFT for general directed graphs by introducing a parameterized UGRM that incorporates traditional representations such as the Laplacian matrix and adjacency matrix. The SVD is used to construct spectral transform pairs with both left and right singular vectors. We extended this approach to two types of UGRM-GFTs applied to directed Cartesian product graphs. UGRM-GFT-I performs SVD directly on the composite UGRM matrix of the two-dimensional graph structure, suitable for globally coupled graph signals. UGRM-GFT-II separately applies SVD to the UGRMs of the two-factor graphs and then combines the results, significantly reducing computational complexity while preserving spectral expressiveness. Theoretical analysis confirmed the monotonicity of the proposed method with respect to the parameters alpha and k embedded in the UGRM. Experimental results on real-world datasets demonstrated that the proposed method significantly outperforms traditional fixed-matrix approaches in denoising tasks, with a particular emphasis on signal-to-noise ratio and bandwidth efficiency.

The Mølmer-Sørensen gate, a cornerstone entangling operation in trapped-ion systems, represents a promising alternative to standard entangling gates in superconducting quantum architectures. However, its performance on superconducting hardware has remained unverified. In this work, we present a hardware-efficient implementation of the Mølmer-Sørensen gate and characterize its performance using quantum process tomography (QPT) on IBM Quantum's superconducting processors. Our implementation achieves a process fidelity of 92.47\% on the real quantum hardware, a performance competitive with the 93.02\% fidelity of the device's native controlled-NOT (CX) gate. Furthermore, for the $|00\rangle$ input state, the gate prepares the target Bell state with $94.2\%$ success probability, confirming its correct logical operation. These results demonstrate that non-native entangling gates can be optimized to perform on par with hardware-native operations. This work expands the effective gate set for algorithm design on fixed-architecture processors and provides a critical benchmark for cross-platform gate evaluation, underscoring the role of hardware-aware compilation in advancing noisy intermediate-scale quantum (NISQ) computing.

We study the low-energy dynamics of systems with exact and approximate higher-form symmetries using Gauge-gravity duality. These symmetries are realised holographically via generalised Maxwell/Proca theories for massless/massive $p$-forms in AlAdS spacetimes. Double-trace deformations of the boundary theory are considered via appropriate boundary conditions. We compute thermal correlation functions in isotropic black brane backgrounds to characterise the near equilibrium regimes of the dual boundary theories. In the vanishing-mass limit, the theory exhibits a hydrodynamic regime for weak double-trace deformations (relative to a scale set by the temperature) and a quasihydrodynamic regime for strong deformations. Turning on the bulk mass gives rise instead to a triad of quasihydrodynamic regimes controlled by both the mass and the double-trace coupling. In general, we find the low-energy spectra to be constrained by pole collisions, emergent symmetries and duality relations, the latter originating in part from Hodge-type dualities in the bulk. For nonzero mass, there is an additional strong/weak duality of the double-trace couplings. We further show, in the low-density limit of background charge, that relevant deformations are necessary for stable diffusion of sufficiently high-dimensional charged objects.

Controlling optical and tribological properties of metal surfaces, like color and wear rate, without altering their chemical composition is a highly desirable process across numerous fields of science and industry. It represents a cost-effective alternative to traditional chemical methods, particularly for copper, one of the most important metals widely used where high electrical and thermal conductivity, alongside resistance to corrosion, are required. We investigated the control of copper surface texture through a controlled micromodification process, utilizing constant force and velocity with abrasive silicon carbide sandpaper on ultrapure copper pellets exhibiting elongated crystallographic grains, and its impact on optical properties. Systematically varying grit size and rubbing direction, both along and across the grains, resulted in tunable microgroove morphology, demonstrating a marked difference in wear rate between single-grain and multi-grain abrasion. Furthermore, modification along copper grain boundaries yielded a change in the wear rate by a factor of two, related to single-grain and multi-grain abrasion regime changes, enabling precise control over material performance via tuned abrasion conditions. Colorimetric analysis via C-Microscopy revealed a strong, statistically significant relationship between abrasive parameters, microgroove geometry (inclination angle, depth, and size), and optical spectral signatures, which were then parametrized to achieve targeted control. This research demonstrates a simple yet effective approach to color and reflectance modification via microgroove engineering, offering a pathway to customized material properties by uniquely coupling contact mechanics, surface morphology, and colorimetry at the microscale level.

Randomized experiments (or A/B tests) are widely used to evaluate interventions in dynamic systems such as recommendation platforms, marketplaces, and digital health. In these settings, interventions affect both current and future system states, so estimating the global average treatment effect (GATE) requires accounting for temporal dynamics, which is especially challenging in the presence of nonstationarity; existing approaches suffer from high bias, high variance, or both. In this paper, we address this challenge via the novel Truncated Policy Gradient (TPG) estimator, which replaces instantaneous outcomes with short-horizon outcome trajectories. The estimator admits a policy gradient interpretation: it is a truncation of the first-order approximation to the GATE, yielding provable reductions in bias and variance in nonstationary Markovian settings. We further establish a central limit theorem for the TPG estimator and develop a consistent variance estimator that remains valid under nonstationarity with single-trajectory data. We validate our theory with two real-world case studies. The results show that relative to existing approaches, a well-calibrated TPG estimator can achieve a favorable balance between bias and variance in nonstationary settings, highlighting the value of the policy-gradient perspective for designing effective estimators under complex dynamics.

This paper investigates a cooperative jamming (CJ)-aided secure wireless communication system. Conventional CJ schemes transmit Gaussian noise (GN) to improve security, which inherently degrades the legitimate receiver's performance. While encoded jamming (EJ) mitigates this interference, its superiority over GN is highly channel-dependent. To overcome this limitation, we introduce a joint optimization framework integrating a reconfigurable intelligent surface (RIS) with EJ to maximize the secrecy rate. \RED{We first establish the information-theoretic relationship between the EJ and GN schemes, identifying the spatial channel conditions that limit EJ performance. For the multiple-input single-output (MISO) scenario, we analytically derive the ergodic secrecy gap as the number of RIS elements grows large and obtain a positive EJ-over-GN gap under explicit power and channel conditions.} Furthermore, for the general multiple-input multiple-output (MIMO) setup, we develop a low-complexity algorithm based on the weighted minimum mean-square-error (WMMSE) framework to handle the resulting non-smooth max-min structure through a WMMSE-based mode-selection framework. By introducing a parameterized function abstraction, the transmit precoding matrices and the RIS phase shift matrix are jointly optimized via block coordinate descent (BCD). Simulation results support the analysis and show that, under the evaluated settings, RIS-assisted EJ can overcome the identified spatial bottlenecks and outperform the optimized GN baseline.

Higher-order spacing statistics in the $m$ superposed spectra of circular random matrices of the same class are studied numerically. We conjecture that for given $m$ (or order $k$) and $β$, the sequence of modified Dyson index $β'(k)$ (or $β'(m)$) obtained using the sum of absolute differences between the cumulative distribution functions method (denoted as $D(β')$) is unique. Also, for a given $k$, the distribution tends to the corresponding $k$-th order Poisson statistics in the limit $m\rightarrow \infty$. The quantum chaotic kicked top model for various Hilbert space dimensions is studied, and it is found to satisfy our conjecture. This involves the numerical verification of $m=2$ case of COE results. Our result can be used as a tool for the characterization of a system and to determine the symmetry structure of the system without desymmetrization of the spectra. Additionally, the comparative study of the higher-order spacing and ratio distributions in both $m=1$ and $m=2$ cases of COE as well as GOE is performed within and across these ensembles numerically using the $D(β')$ method. This study is carried out both by varying the dimension and keeping the number of realizations constant, and vice-versa. The same asymptotic higher-order statistics are observed across COE and GOE in terms of a given spectral fluctuation measure. But, within a given ensemble of COE or GOE, the results of higher-order spacing and ratio distributions agree with each other only up to some lower $k$, and beyond that, they start deviating from each other. Further, the spectral fluctuations of the intermediate map of various dimensions are studied. Various important observations and discussions from the analysis of our extensive numerical computations are presented.

The detailed functioning of the human brain remains incompletely understood. Large-scale brain simulations complement experimental research but face substantial computational challenges: the human brain comprises approximately $10^{11}$ neurons connected by $10^{14}$ synapses, collectively forming the connectome. Empirical evidence indicates that modifications of the connectome -- specifically the formation and elimination of synapses, referred to as structural plasticity -- are essential for processes such as learning and memory formation. Connectivity updates can be computed efficiently using a Barnes--Hut-inspired approximation that reduces computational complexity from $O(n^2)$ to $O(n \log n)$, where $n$ denotes the number of neurons. Despite this improvement, communication overhead still limits scalability. Synapse updates rely heavily on remote memory access (RMA), and spike transmission requires all-to-all communication at every simulation time step. We introduce a novel algorithm that reduces communication by migrating computation rather than data. This approach reduces connectivity update time by a factor of 6 and spike transmission time by more than 2 orders of magnitude.

If $f=u+iv$ is analytic in the unit disk $\mathbb{D}$, it is known that the integral means $M_p(r,u)$ and $M_p(r,v)$ have the same order of growth. This is false if $f$ is a (complex-valued) harmonic function. However, we prove that the same principle holds if we assume, in addition, that $f$ is $K$-quasiregular in $\mathbb{D}$. The case $0<p<1$ is particularly interesting, and is an extension of the recent Riesz type theorems for harmonic quasiregular mappings by several authors. Further, we proceed to show that the real and imaginary parts of a harmonic quasiregular mapping have the same degree of smoothness on the boundary.

We study the problem of discrete distribution estimation under utility-optimized local differential privacy (ULDP), which enforces local differential privacy (LDP) on sensitive data while allowing more accurate inference on non-sensitive data. In this setting, we completely characterize the fundamental privacy-utility trade-off. The converse proof builds on several key ideas, including a generalized uniform asymptotic Cramér-Rao lower bound, a reduction showing that it suffices to consider a newly defined class of extremal ULDP mechanisms, and a novel distribution decomposition technique tailored to ULDP constraints. For the achievability, we propose a class of utility-optimized block design (uBD) schemes, obtained as nontrivial modifications of the block design mechanism known to be optimal under standard LDP constraints, while incorporating the distribution decomposition idea used in the converse proof and a score-based linear estimator. These results provide a tight characterization of the estimation accuracy achievable under ULDP and reveal new insights into the structure of optimal mechanisms for privacy-preserving statistical inference.

We formalize a new type system for Elixir, a dynamically typed functional programming language of growing popularity that runs on the Erlang virtual machine. Our system combines gradual typing with semantic subtyping to enable precise, sound, and practical static type analysis, without requiring any changes to Elixir's compilation pipeline or runtime. Type soundness is ensured by leveraging runtime checks -- both implicit, from the Erlang VM, and explicit, via developer-written guards. Central to our approach are two key innovations: the notion of "strong functions", which can be assigned precise types even when applied to inputs that may fall outside their intended domain; and a fine-grained analysis of guards that enables accurate type refinement for case expressions and guarded function definitions. While type information is erased before execution and not used by the compiler, our "safe erasure" gradual typing strategy maintains soundness and expressiveness without compromising compatibility or performance. This work lays the theoretical foundation for Elixir's new type system, outlines its integration into recent versions of the language, and demonstrates its effectiveness on large-scale industrial codebases.

The model of backward proton production in the exclusive reaction $pd \to ppn$ at proton beam momenta up to several GeV/c is constructed on the basis of Feynman diagrams for one- and two-step amplitudes. The latter include nucleon and $Δ(1232)$ resonance intermediate scattering states with propagators reduced to eikonal form using the generalized eikonal approximation. The model calculations are compared with available experimental data on the energy spectra of protons at backward polar angles in the deuteron rest frame. It is shown that inclusion of two-step amplitudes significantly increases the production of backward protons with energies above $\sim$ 50 MeV, thereby significantly improving the agreement with experiment. The remaining theoretical problem related to the description of the off-shell behavior of the elementary amplitudes of the $NN \to NN$ and $NN \leftrightarrow NΔ$ transitions is discussed. Partial discrepancies between different sets of experimental data do not allow for conclusion that exotic effects, such as proton interactions with density fluctuations and/or $6q$ clusters in the deuteron, are present.

We analyze the quantum dynamics of a relativistic homogeneous superfluid in a complex scalar field theory. Unlike zero-charge condensates, which undergo quantum evaporation due to internal number-changing processes, we show that $U(1)$ superfluids preserve their internal coherence indefinitely in this theory. In particular, although not Hamiltonian eigenstates, these configurations are stable in the full quantum theory to all orders in perturbation theory. This is demonstrated by explicitly constructing the corresponding quantum state and studying its dynamics. Crucially, maintaining stability requires the quantum state to go beyond a naive coherent-state construction: specific non-Gaussian corrections are essential for having a stationary state. The resulting state is identified as the interacting vacuum of the superfluid fluctuations, which also serves as the ground state of the modified Hamiltonian $\hat{H}-μ\hat{Q}$, with $μ$ the full-fledged quantum chemical potential and $\hat{Q}$ the $U(1)$ charge. Finally, we check that the phonon mode remains gapless once one-loop corrections are included, confirming the robustness of the Goldstone theorem beyond the semiclassical regime, even in systems with a spontaneously broken Lorentz symmetry.

Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In support of our findings, several examples and counter examples are provided, illustrating the applicability of the theoretical results. Additionally, we extend the discussion to an important application in probabilistic erasure, highlighting how weaving frames can be used to mitigate data loss in such scenarios. This work contributes to the broader understanding of frame theory in indefinite inner product spaces.

Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on a large lattice, which is, in most cases, computationally very challenging. In this work an alternative method is proposed to solve Euclidean path integrals in quantum field theories, using radial basis function-type neural networks. The method allows us to approximate observables in a very efficient manner, taking only seconds to do calculations that would otherwise take hours or even days with other existing methods. The model is used to describe phase transitions in the scalar $ϕ^4$ theory for a wide range of coupling strength. The obtained phase transition line is compared to previous lattice results, giving very good agreement between them.

Magnetic monopoles, elusive in high-energy physics, have been realised as emergent quasiparticles in solid-state systems, where their unique properties hold promise for novel spintronic applications. Magnetic monopoles have been invoked in diverse platforms, including skyrmion lattices, chiral magnets, soft ferromagnets, aritifical nanomagnets. Yet, a demonstration of their role in magnetic transport has remained elusive. Here, we report such an observation via the spin Seebeck effect in the bulk insulating pyrochlore oxide, spin ice $\mathrm{Dy_2Ti_2O_7}$. By applying a thermal gradient perpendicular to a $[111]$-oriented magnetic field, we detect a transverse spin Seebeck voltage marked by a dominant peak at the onset of monopole proliferation, accompanied by a secondary feature and frequency-dependent behavior. Our findings establish a direct link between monopole dynamics and magnetic transport in an insulating medium, establishing a new pathway for probing fractionalized excitations and advancing towards novel spintronic applications.

Bright squeezed vacuum (BSV) is an intense quantum state of light with zero mean electric field and huge photon number fluctuations, sufficiently intense to drive extreme nonlinear processes and imprint nonclassical statistics. However, the temporal structure of single BSV shots has not been fully characterized. Here, we retrieve the spectral and temporal pulse characteristics of a set of single-peak BSV shots. It is obtained by realizing a femtosecond BSV source at 1040 nm with a single spatial mode and perform single-shot spectral interferometry with a fully characterized coherent-state reference pulse. Our approach reveals that the group delay is consistent between the various shots, resulting in an average pulse duration of 27.2 fs, much shorter than the pump pulse, and a variation of 5.5 fs (standard deviation). We also observe a characteristic nodal structure in the spectral interferograms, demonstrating the BSV's random phase ambiguity of $π$ rad. Our approach demonstrates that BSV is a viable source of femtosecond light pulses for attosecond sub-cycle metrology of ultrafast electron dynamics.

We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high Péclet numbers. Our construction builds on the multiscale spectral generalized finite element method (MS-GFEM), wherein the coarse space is spanned by locally optimal basis functions obtained from local generalized eigenproblems on operator-harmonic spaces. Extending the theory of Ma (2025) to convection-diffusion problems in conservation form, we establish exponential convergence of the MS-GFEM approximation with respect to the dimension of the local approximation space. Rewriting MS-GFEM as a RAS-type iteration, we show for coercive problems that this exponential convergence property is inherited by the RAS-type iterative method (at least in the continuous setting). Employed as a preconditioner within the generalized minimal residual method (GMRES), the resulting method requires only a few iterations for high accuracy even with low-dimensional coarse spaces. Through extensive numerical experiments on problems with high-contrast diffusion and non-divergence-free, rotating velocity fields, we demonstrate robustness with respect to the grid Péclet number and the number of subdomains (tested up to $10^5$ subdomains), while coarse-space dimensions remain small as grid Péclet numbers increase. By adapting the coarse space and oversampling size, we are able to achieve arbitrarily fast convergence of preconditioned GMRES. As an extension, for which we do not have theory yet, we show effectiveness of the method even for indefinite problems and in the vanishing-diffusion limit.

This paper considers identification and estimation of distributional effect parameters that depend on the joint distribution of an outcome and another variable of interest ("treatment") in a setting with "two-sided" measurement error -- that is, where both variables are possibly measured with error. Examples of these parameters in the context of intergenerational income mobility include transition matrices, rank-rank correlations, and the poverty rate of children as a function of their parents' income, among others. Building on recent work on quantile regression (QR) with measurement error in the outcome (particularly, Hausman, Liu, Luo, and Palmer (2021)), we show that, given (i) two linear QR models separately for the outcome and treatment conditional on other observed covariates and (ii) assumptions about the measurement error for each variable, one can recover the joint distribution of the outcome and the treatment. Besides these conditions, our approach does not require an instrument, repeated measurements, or distributional assumptions about the measurement error. Using recent data from the 1997 National Longitudinal Study of Youth, we find that accounting for measurement error notably reduces several estimates of intergenerational mobility parameters.

Group awareness--the ability to perceive the activities of collaborators in a shared space--is a vital mechanism to support effective coordination and joint data analysis in collaborative visualization. We introduce collaborative attention-aware visualizations (CAAVs) that track, record, and revisualize the collective attention of multiple users over time. We implement this concept in HeedVision, a standards-compliant WebXR system built with React Three Fiber that runs on modern AR/VR headsets, and complement it with proof-of-concept implementations covering the remaining three quadrants of our design space--varying presentation (embedded vs. separated) and situatedness (world space vs. camera space). Through a mixed-methods exploratory study where pairs of co-located analysts performed visual search tasks in a shared immersive AR environment, we investigate how attention revisualization affects collaborative coordination in immersive analytics. Our results show that CAAVs improve spatial coordination, search efficiency, and task load distribution among collaborators, though benefits vary by context, favoring abstract environments lacking natural landmarks. This work extends attention awareness to multi-user settings and provides empirical evidence for its context-dependent benefits in collaborative immersive analytics environments.

We propose that X-ray absorption and emission magnetic circular dichroism (XAS-MCD and XES-MCD) are promising measurements to directly detect ferroic higher-rank multipoles as candidate order parameters in altermagnets. Using the sum rules for XES-MCD and connecting them to multipole language, we demonstrate that the expectation value of the magnetic octupole moment is finite in the $d$-wave altermagnetic candidate rutile-type compounds TF$_2$ (T=transition metal). We also perform spectral calculations of XAS-MCD and XES-MCD based on an effective model with a full multiplet approach. While the intensity of the XAS-MCD spectra vanishes, the XES-MCD spectra exhibit finite intensity, whose spectrum becomes opposite by inverting the Nèel vector. These results clearly indicate ferroic magnetic octupole order in these compounds.

We present the status and goals of the readout electronics system we are developing to support the detector arrays in the coronagraph instrument on the NASA Habitable Worlds Observatory (HWO) mission currently in development. HWO aims to revolutionize exoplanet exploration by performing direct imaging and spectroscopy of 25 or more habitable exoplanets, and to resolve a broad range of astrophysics science questions as well. Since exoplanet yield depends critically on the detector dark count rate, as we show in this paper, the ambitious goals of HWO require arrays of single-photon energy-resolving detectors. We argue that Kinetic Inductance Detectors (KIDs) are best suited to meet these requirements. To support the detectors required for HWO and future far-IR missions, at the required power consumption and detector count, we are developing a radiation-tolerant reconfigurable readout system for both imaging and energy-resolving single photon KID detector arrays. We leverage an existing RFSoC-based system we built for NASA balloons that has a power consumption of 30 Watts and reads out 2000-4000 detectors (i.e. 7-15 mW/pixel), and move to a radiation tolerant Kintex Ultrascale FPGA chip to bring low-power wide bandwidth readout to a space-qualified platform for the first time. This improves significantly over previous spaceflight systems, and delivers what is required for NASA's future needs: ~100,000 pixels with less than 1 kW total power consumption. Overall, the system we are developing is a significant step forward in capability, and retires many key risks for the Habitable Worlds Observatory mission.

We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an approximate version of this condition.

The overlap matrix of electronic energy eigenstates, sometimes referred to as the form factor, determines the quantum geometric tensor of electrons in solids. Here, we show that the variation in the overlap of two eigenstates with opposite momenta can be directly observed via quasiparticle interference (QPI) imaging. We study the QPI in twisted bilayer graphene using a real-space tight-binding model combined with the kernel polynomial method. The resulting QPI patterns, which are largely independent of whether the two graphene layers are commensurate or incommensurate, reveal all intralayer and interlayer interference processes. While the intralayer interference signals resemble those of monolayer graphene, the interlayer interference - which vanishes at large twist angles - displays a chiral structure that reverses between the two layers and between the valence and conduction bands. Furthermore, the QPI patterns explicitly demonstrate the approximate translational symmetries and valley charge conservation in twisted bilayer graphene, validating the topological obstruction to constructing the Wannier orbitals of states at the Dirac cones. Using a continuum model of twisted bilayer graphene, we show that all characteristics of the observed QPI patterns can be explained by the form factor of eigenstates projected onto a single layer. Our results provide fundamental insights into the electronic spectrum and wave functions of twisted bilayer graphene, and establish QPI as an experimental probe for the form factor of back-scattering states.

Space-efficient streaming estimation of quantiles in massive datasets is a fundamental problem with numerous applications in data monitoring and analysis. While theoretical research led to optimal algorithms, such as the Greenwald-Khanna algorithm or the KLL sketch, practitioners often use other sketches that perform significantly better in practice but lack theoretical guarantees. Most notably, the widely used $t$-digest has unbounded worst-case error. In this paper, we seek to get the best of both worlds. We present a new quantile summary, SplineSketch, for numeric data, offering near-optimal theoretical guarantees, namely uniformly bounded rank error, and outperforming $t$-digest by a factor of 2-20 on a range of synthetic and real-world datasets. To achieve such performance, we develop a novel approach that maintains a dynamic subdivision of the input range into buckets while fitting the input distribution using monotone cubic spline interpolation. The core challenge is implementing this method in a space-efficient manner while ensuring strong worst-case guarantees.

The pursuit of high-temperature quantum anomalous Hall (QAH) insulators faces fundamental challenges, including narrow topological gaps and low Curie temperatures ($T_C$) in existing materials. Here, we propose a strategy using bilateral hydrogenation to engineer a robust QAH state in the topologically trivial ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$ via covalent orbital reconstruction. First-principles calculations reveal that by rewiring the orbital hybridization network, hydrogenation alters orbital occupations to shift preexisting Dirac points, originally embedded in the conduction bands, to the vicinity of the Fermi level in Cr$_2$Ge$_2$Te$_6$H$_6$. This electronic restructuring, coupled with spin-orbit coupling, opens a global topological gap of 118.1 meV, establishing a robust QAH state with Chern number $C=3$. Concurrently, this orbital reconstruction tunes the energy difference between the ligand $p$ and transition metal $d$ orbitals. This shift enhances ferromagnetic superexchange via the $d{z^2}-p_z-d_{xz}$ channel, strengthening the nearest-neighbor coupling $J_1$ by 3.06 times and switching $J_2$ from antiferromagnetic to ferromagnetic. Monte Carlo simulations based on extracted exchange parameters indicate a pronounced enhancement of ferromagnetic stability compared with pristine Cr$_2$Ge$_2$Te$_6$. While absolute Curie temperatures depend on the mapping to an effective spin model and represent relative trends, the enhanced stability after hydrogenation is a salient effect. This work establishes targeted orbital reconstruction driven by surface hydrogenation as a powerful route to simultaneously control topology and magnetism in 2D materials, providing a general route to engineer QAH phases with large gaps and high Chern numbers in van der Waals ferromagnetic semiconductors.

Menger's theorem tells us that if $S,T$ are sets of vertices in a graph $G$, then (for $k\ge0$) either there are $k+1$ vertex-disjoint paths between $S$ and $T$, or there is a set of $k$ vertices separating $S$ and $T$. But what if we want the paths to be far apart, say at distance at least $c$? One might hope that we can find either $k+1$ paths pairwise far apart, or $k$ sets of bounded radius that separate $S$ and $T$, where the bound on the radius is some $\ell$ that depends only on $k,c$ (the ``coarse Menger conjecture''). The last three authors showed in an earlier paper that this is false for all $k\ge 2$ and $c\ge3$, by constructing a sequence of finite graphs giving counterexamples for larger and larger values of $\ell$ with $k=2$ and $c=3$. These counterexamples contained subdivisions of uniform binary trees with arbitrarily large depth as subgraphs, and so had unbounded path-width. Here we show that, if $H$ is a graph that can be drawn in the plane such that each region shares a vertex with the infinite region, then the coarse Menger conjecture is true for all graphs not containing $H$ as a minor. Consequently, the conjecture is true for all graphs with bounded path-width (by taking $H$ to be a sufficiently large tree), and it is true for series-parallel graphs (by taking $H=K_4$). The first is somewhat surprising, since the conjecture is false for bounded tree-width.

We propose a novel feedback controller for a class of uncertain higher relative degree nonlinear systems, subject to delays in both state measurement and control input signals. Building on the prescribed performance control framework, a delay-dependent performance correction mechanism is introduced to ensure the boundedness of all signals in the closed-loop and to keep the output tracking error strictly within a dynamically adjusted performance envelope. This mechanism adapts in response to large delays that may cause performance degradation. In the absence of delays, the correction term vanishes, and the controller recovers the nominal (user-defined) performance envelope. The effectiveness of the proposed approach is validated through simulation studies.