Reliable and precise etching of silicon nanostructures with ultra-high aspect ratios is required in many fields. Metal assisted chemical etching (MacEtch) in vapor is a plasma-free etching method that attracts considerable attention owing to the ability to create smooth, high aspect ratio nanostructures. MacEtch understanding and applications are limited by low fidelity and inconsistent pattern transfer from the catalyst layer to the silicon substrate. The locally constrained electrochemical interactions at the catalyst site make MacEtch particularly sensitive to catalyst contamination reducing the reaction rate and pinning the catalyst during etching. Removing contaminants is essential to improve pattern transfer for reliable processes on a larger area and higher aspect ratio. Physically separating the main source of carbon - the resist - from the catalyst with a sacrificial and functional interlayer solves this issue. The interlayer separates the resist and the catalyst and allows for thorough cleaning of the substrate before catalyst deposition. The resulting clean catalyst has improved stability, quality and reproducibility, enabling reliable fabrication of dense (50% patterned area) high aspect ratio (>250:1) nanostructures. Two different interlayer materials (Cr and Al$_{2}$O$_{3}$) and two patterning approaches are presented, showcasing etching of various high aspect ratio nanostructures, such as X-ray Optics.

In the search for metal-poor stars, large spectroscopic surveys are an invaluable tool. However, the spectra of metal-poor stars can be difficult to analyse because of the relative lack of available lines, which can also lead to misclassification. We aim to identify the stars observed by the APOGEE survey that are below the metallicity limit of APOGEE's analysis. For the highest confidence candidates, we classify the orbital properties of the stars to investigate whether their orbital distribution matches what we would expect for stars that are this metal poor and to select especially interesting targets for spectroscopic follow-up purposes. We examined the properties derived by APOGEE for metal-poor stars from the literature to find signatures of stars with a metallicity below the range of the grid used for spectral analysis. The calibrated APOGEE stellar parameters provide a clear signature of the most metal-poor stars in the survey, indicated by null values for their metallicities while having effective temperatures and surface gravities determined by the pipeline. From comparison with the literature, we find that, within a temperature range of 3700 - 6700 K and above a threshold of S/N > 30, the vast majority of APOGEE stars without calibrated metallicities are very metal poor. The radial velocities provided by APOGEE, Gaia DR3 positions and astrometry along with spectrophotometric distances derived in this work allowed for the computation of their orbits. In this work, we select 289 very metal-poor red giant stars (likely below = -2.5) from the APOGEE results. Our sample contains 16 very metal-poor member candidates of the Magellanic Clouds, 14 very metal-poor stars with orbits confined to the inner Galaxy, and 13 inner Galaxy halo interlopers.

The misanthrope process is an interacting particle system where particles move between neighbouring sites with hop rates depending only on the number of particles at the departure and arrival sites. Motivated by a discretised version of the Hammersley--Aldous--Diaconis process, we introduce a partially asymmetric long range misanthrope process (PALRMP) on a finite one-dimensional lattice with periodic boundary conditions where particles can move between sites that are not necessarily neighbours, as long as there are no particles in between the departure and arrival sites. In this model, each site $\ell$ has an inhomogeneous rate parameter $x_\ell$ associated to it, and the hop rate of a particle moving from site $k$ to site $\ell$ depends upon the parameter associated to the target site $x_\ell$, the direction the particle moves, and the number of particles at sites $k$ and $\ell$. We also consider the homogeneous PALRMP, where all the $x_\ell$'s are 1. We find necessary and sufficient conditions on the hop rates under which the stationary distribution is of factorised form for both the PALRMP and the homogeneous PALRMP, as well as the extreme variants, namely the ones where the particle motion is totally asymmetric (TALRMP) and symmetric (SLRMP). As an illustrative example, we study in detail the discrete Hammersley--Aldous--Diaconis process.

We investigate the Multiple Equilibria phase of generalized Lotka-Volterra dynamics with random, non-reciprocal interactions. We compute the topological complexity of equilibria, which quantifies how rapidly the number of equilibria of the dynamical equations grows with the total number of species. We perform the calculation for arbitrary degree of non-reciprocity in the interactions, distinguishing between configurations that are dynamically stable to invasions by species absent from the equilibrium, and those that are not. We characterize the properties of typical (i.e., most numerous) equilibria at a given diversity, including their average abundance, mutual similarity, and internal stability. This analysis reveals the existence of two distinct ME phases, which differ in how internally stable equilibria behave under invasions by absent species. We discuss the implications of this finding for the system's dynamical behavior.

We prove a number of results related to the size and propagation of boundary pluripolar sets, the exceptional sets for the Dirichlet problem for the complex Monge--Ampère equation. We extend Stout's result that peak sets on strictly pseudoconvex domains $Ω\subset\mathbb{C}^N$ must have topological dimension less than $N$ to also encompass non-propagating boundary pluripolar $F_σ$ sets. In particular, boundary pluripolar sets must propagate into the interior if their topological dimension exceeds $N-1$. We also prove that sets of sufficiently small Hausdorff dimension must be boundary pluripolar and non-propagating, provided that the domain admits peak functions with sufficient boundary regularity. Lastly, we prove that the class of Jensen measures and the class of representing measures do not coincide on any smooth, strictly pseudoconvex domain. This extends a result of Hedenmalm.

The dispersion of Rashba-split heavy-hole subbands in GaAs two-dimensional hole gases (2DHGs) is difficult to access experimentally because strong heavy-hole-light-hole mixing produces non-parabolicity and breaks the usual correspondence between carrier density and Fermi wave vector. Here we use low-field magnetotransport (B < 1 T) to reconstruct the dispersions of the two spin-orbit-split heavy-hole branches (HH-, HH+) in undoped (100) GaAs/AlGaAs single heterojunction 2DHGs operated in an accumulation-mode field-effect geometry. The dopant-free devices sustain out-of-plane electric fields up to 26 kV/cm while maintaining mobilities up to 84 m$^2$/Vs and exhibiting a spin-orbit polarization as large as 36%. Fourier analysis of Shubnikov-de Haas (SdH) oscillations resolves the individual HH-/HH+ subband densities; fitting the temperature dependence of the corresponding Fourier amplitudes yields both branch-resolved SdH effective masses over the same magnetic field window. SdH regimes in which reliable subband parameters can be extracted are delineated. Over 2DHG densities (0.76-1.9) $\times$ 10$^{15}$ /m$^2$, the HH- mass is nearly density independent ($\approx 0.34m_e$), implying a near-parabolic HH- dispersion below the first LH+/HH- anticrossing, whereas HH+ exhibits strong non-parabolicity with an effective mass that increases with density. Combining the extracted dispersions yields a transport-based determination of the spin-orbit splitting energy $Δ_\text{HH}$ between HH and HH+ as a function of in-plane wave vector. Parameter-free Luttinger-model calculations reproduce the qualitative trends but underestimate both masses by a common factor $\approx$ 2, suggesting a many-body renormalization of the heavy-hole mass in this strongly asymmetric regime.

Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where agent capacities are slightly modified to ensure the existence of desirable outcomes. While useful when no stable matching exists, or some agents are left unmatched, it has not previously been investigated whether near-feasible stable matchings satisfy desirable properties with regard to their stability in the original instance. Furthermore, prior works often leave open deviation incentive issues that arise when the centralised authority modifies agents' capacities. We consider these issues in the Stable Fixtures problem model, which generalises many classical models through non-bipartite preferences and capacitated agents. We develop a formal framework to analyse and quantify agent incentives to adhere to computed matchings. Then, we embed near-feasible stable matchings in this framework and study the trade-offs between instability, capacity modifications, and computational complexity. We prove that capacity modifications can be simultaneously optimal at individual and aggregate levels, and provide efficient algorithms to compute them. We show that different modification strategies significantly affect stability, and establish that minimal modifications and minimal deviation incentives are compatible and efficiently computable under general conditions. Finally, we provide exact algorithms and experimental results for tractable and intractable versions of these problems.

High expansion velocity carbon stars (HVCs) are a rare class of evolved stars whose circumstellar envelopes (CSEs) combine C-rich chemistry with unusually high expansion velocities typical of O-rich massive evolved stars. AFGL2233 has been proposed as a high-mass evolved object that exhausted hot-bottom burning. Studying its chemistry is essential to understand the nature and evolution of these objects. We characterize the chemical composition and isotopic ratios of the CSE of AFGL2233 and investigate chemical peculiarities, including the presence of N- and O-bearing species in a C-rich environment. We carried out a complete line survey at 3 mm and 1 mm using the IRAM 30m telescope, complemented by Herschel/HIFI FIR observations and interferometric maps of SiO, C2H, and HCN. Molecular emission was analyzed using rotational diagrams and radiative transfer modeling under the LVG approximation. Column densities and fractional abundances were derived for more than 30 molecular species, including isotopologues, and compared with other evolved stars. The Gaia DR3 distance of 1.236 kpc implies a luminosity of ~2 Lsun, consistent with an initial mass of 4.5-9 Msun. The molecular inventory confirms C-rich chemistry but reveals unusually high abundances of NH3, H2O, and SiN. The isotopic ratios vary among species, with 12C/13C ranging from 7 to 55. The C2H/C4H ratio is abnormally high compared with C-rich AGB stars. The presence of SiN and high NH3 may indicate N-enrichment or the influence of a companion. AFGL2233 is likely a high-mass AGB or super-AGB star with a complex evolutionary history involving nucleosynthesis, shocks, and possible binary interaction.

Given an undirected graph $G=(V, E)$, the Personalized PageRank (PPR) of $t\in V$ with respect to $s\in V$, denoted $π(s,t)$, is the probability that an $α$-discounted random walk starting at $s$ terminates at $t$. We study the time complexity of estimating $π(s,t)$ with constant relative error and constant failure probability, whenever $π(s,t)$ is above a given threshold parameter $δ\in(0,1)$. We consider common graph-access models and furthermore study the single source, single target, and single node (PageRank centrality) variants of the problem. We provide a complete characterization of PPR estimation in undirected graphs by giving tight bounds (up to logarithmic factors) for all problems and model variants in both the worst-case and average-case setting. This includes both new upper and lower bounds. Tight bounds were recently obtained by Bertram, Jensen, Thorup, Wang, and Yan for directed graphs. However, their lower bound constructions rely on asymmetry and therefore do not carry over to undirected graphs. At the same time, undirected graphs exhibit additional structure that can be exploited algorithmically. Our results resolve the undirected case by developing new techniques that capture both aspects, yielding tight bounds.

A smooth Hermitian surface $X$ is a projective surface isomorphic to the Fermat surface of degree $q+1$ in positive characteristic. We study incidence relations of the rational curves of degree $q+1$ contained in $X$, and show that such curves produce a family of certain strongly regular graphs and association schemes.

Due to their high kinetic inductance, highly disordered superconducting thin films are a potential hardware for the realization of compact, low-noise elements in cryoelectronic applications. However, high disorder typically results in structural defects that cause spatial inhomogeneity of the superconducting order parameter, thereby impairing the film's properties. Here, we employ scanning tunneling microscopy to demonstrate that NbN thin films fabricated by plasma-enhanced atomic layer deposition (PE-ALD) exhibit unusual spatial homogeneity, even at thicknesses approaching the superconductor-insulator transition. Tunneling spectra acquired across the sample surface show only small variations of the order parameter with a standard deviation of 2-3%, on length scales that significantly exceed the film's grain size. At the same time, the films achieve a relatively high sheet resistance (up to 1400 Ohm) and, consequently, a high sheet kinetic inductance (up to approximately 200 pH), making them well-suited for applications.

We provide theoretical guarantees for convergence of discrete-time policy mirror descent with inexact advantage functions updated using temporal difference (TD) learning for entropy regularised MDPs in Polish state and action spaces. We rigorously derive sufficient conditions under which the single-loop actor-critic scheme is stable and convergent. To weaken these conditions, we introduce a variant that performs multiple TD steps per policy update and derive an explicit lower bound on the number of TD steps required to ensure stability. Finally, we establish sub-linear convergence when the number of TD steps grows logarithmically with the number of policy updates, and linear convergence when it grows linearly under a concentrability assumption.

This study presents an efficient field-programmable gate array (FPGA) implementation of a polynomial spline function-based statistical compression algorithm designed to address the critical challenge of massive data transfer bandwidth in emerging high-spatial-resolution single-photon avalanche diode (SPAD) arrays, where data rates can reach tens of gigabytes per second. In our experiments, the proposed hardware implementation achieves a compression ratio of 512x compared with conventional histogram-based outputs, with the potential for further improvement. The algorithm is first optimized in software using fixed-point (FXP) arithmetic and look-up tables (LUTs) to eliminate explicit additions, multiplications, and non-linear operations. This enables a careful balance between accuracy and hardware resource utilization. Guided by this trade-off analysis, online sketch processing elements (SPEs) are implemented on an FPGA to directly process time-stamp streams from the SPAD sensor. The implementation is validated using a customized LiDAR setup with a 192 x 128-pixel SPAD array. This work demonstrates histogram-free online depth reconstruction with high fidelity, effectively alleviating the time-stamp transfer bottleneck of SPAD arrays and offering scalability as pixel counts continue to increase for future SPADs.

We provide a mathematically rigorous derivation of the first order expansion of the motion of a charged particle in a strong magnetic field. In contrast to the derivations that can be found in the physics literature we solely assume throughout that the magnetic field is strong. In particular we do not need to make any structural assumptions on the particle motion, such as the gyroradius being small in comparison to the magnetic length scale. Instead, some of the additional assumptions which are usually made in the physics literature turn out to be an a posteriori consequence in our approach. Our approach further justifies the utilisation of the guiding centre approximation at "bounce points" within magnetic mirrors, a situation which violates the usual assumptions which are made in the physics literature when deriving the guiding centre approximation.

In this paper, the problem of tracking a given reference output trajectory is investigated for the class of Boolean control networks, by resorting to their algebraic representation. First, the case of a finite-length reference trajectory is addressed, and the analysis and algorithm first proposed in [17] are extended to be able to deal with arbitrary initial conditions and to identify all possible solutions. The approach developed for the finite-length case is then adjusted to cope with periodic reference output trajectories. The results of the paper are illustrated through an example.

The investigation of the inhomogeneities in modern inflationary Universe scenarios is related, in particular, with the study of the role played by scalar fields in cosmological evolution. We present the model described by one of the extensions of the Abelian-Higgs theory, where the scale-invariant approach to the Standard Model (SM) is achieved by introducing the complex scalar fields and the vector fields in the hidden (dark) sector, where the latter and the SM are minimally coupled to gravity. The formation of the cosmological compact objects intuitively is explained in terms of the topological line defects - the string like tubes. The strings can get an energetically preferable configuration corresponding to the magnetic flux quantum inside an area defined by the mass of dark vector field.

This study employs linear regression and structural equation modeling to explore how Thinking Skills, Design Thinking, Creative Self-Efficacy (CSE), and Collective Creative Efficacy (CCE) drive Design Creativity & Innovation, and analyzes the structural stability of the model across different levels of experience. Path analysis results indicate that the four Design Thinking Skills, Problem-driven Design (beta = 0.198, p < 0.01), Information-driven Design (beta = 0.241, p < 0.001), Solution-driven Design (beta = 0.227, p < 0.001), and Knowledge-driven Design (beta = 0.263, p < 0.001) all significantly and positively influence Design Thinking. Furthermore, Design Thinking has a significant positive predictive effect on Design Creativity & Innovation (beta = 0.286, p < 0.001). Mediation analysis confirms three significant mediation paths: the CSE mediation path (beta = 0.128, p < 0.001), the CCE mediation path (beta = 0.073, p < 0.01), and the "CSE to CCE" chain mediation path (beta = 0.025, p < 0.01). Multi-group comparison results reveal significant differences between the student and professional groups under the full equivalence model. After relaxing specific constraints, there were no significant differences between the nested models of the baseline model, partial measurement invariance, structural weight invariance, and structural covariance invariance. These findings elucidate the multi-dimensional pathways of Design Creativity & Innovation, providing a robust empirical basis for optimizing differentiated pedagogical models and professional practice guidelines.

We investigate the quasisymmetric uniformization of a special class of metric surfaces known as paper surfaces, constructed as quotients of planar multipolygons via segment pairings, including infinite Type W identifications. These spaces, which arise naturally in dynamical settings, exhibit conic singularities and complex geometric structure. Our goal is to prove that a broad class of such surfaces satisfies Ahlfors 2-regularity and linear local contractibility, which together ensure the existence of a quasisymmetric parametrization onto the standard 2-sphere.

We define PSTCTL, a probabilistic variant of Strategic Timed CTL (STCTL), interpreted over stochastic multi-agent systems with continuous time and asynchronous execution semantics. STCTL extends TCTL with strategic operators in the style of ATL. Moreover, we demonstrate the feasibility of verification with irP-strategies.

In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution equations that capture the free-boundary dynamics up to quadratic order. In the long-wave thin-film regime, we rewrite the kinematic condition in flux form, flatten the moving domain, and derive a lubrication-type equation. Moreover, we establish well-posedness for these models in suitable Wiener spaces.

A principal delegates choice to an agent whose decision depends on both beliefs and tastes. The principal can steer the delegated decision using two costly instruments: (i) an information policy that determines a Bayes--plausible distribution of posteriors, and (ii) a bias-management policy that shifts the agent's effective taste. We study a binary-state, two-action, convex hull of two benchmark tastes specialization with posterior-separable information costs. The analysis admits an inner--outer decomposition: optimal bias management is bang--bang (either no intervention or the minimal intervention needed to flip the agent's action), while the optimal information policy is characterized by concavification of an endogenous posterior value function that already incorporates optimal management and information costs. This structure clarifies how information acquisition and bias management interact; they can be complements, substitutes, or both depending on the primitives of the model. Information changes which posteriors are realized and hence where management is used; management reshapes the curvature and kinks of the posterior value function and hence the marginal value of information. The model delivers regime classifications for pooling vs. informativeness and for management at different posteriors within informative signals, and highlights how comparative statics can be monotone or non-monotone depending on how concavification contact points move with costs.

The coexistence of terrestrial networks (TN) and non-terrestrial networks (NTN) in the frequency range 3 (FR3) upper mid-band presents considerable interference concerns, as dense TN deployments can severely degrade NTN downlink performance. Existing studies rely on interference-nulling beamforming, precoding, or exclusion zones that require accurate channel state information (CSI) and static coordination, making them unsuitable for dynamic NTN scenarios. To overcome these limitations, we develop an optimization framework that jointly controls TN downlink power, uplink power, and antenna downtilt to protect NTN links while preserving terrestrial performance. The resultant non-convex coupling between TN and NTN parameters is addressed by a Proximal Policy Optimization (PPO)-based reinforcement learning method that develops adaptive power and tilt control strategies. Simulation results demonstrate a reduction up to 8 dB in the median interference-to-noise ratio (INR) while maintaining over 87% TN basestation activity, outperforming conventional baseline methods and validating the feasibility of the proposed strategy for FR3 coexistence.

Efficiently scaling industrial Click-Through Rate (CTR) prediction has recently attracted significant research attention. Existing approaches typically employ early aggregation of user behaviors to maintain efficiency. However, such non-unified or partially unified modeling creates an information bottleneck by discarding fine-grained, token-level signals essential for unlocking scaling gains. In this work, we revisit the fundamental distinctions between CTR prediction and Large Language Models (LLMs), identifying two critical properties: the asymmetry in information density between behavioral and non-behavioral features, and the modality-specific priors of content-rich signals. Accordingly, we propose the Efficiently Scalable Transformer (EST), which achieves fully unified modeling by processing all raw inputs in a single sequence without lossy aggregation. EST integrates two modules: Lightweight Cross-Attention (LCA), which prunes redundant self-interactions to focus on high-impact cross-feature dependencies, and Content Sparse Attention (CSA), which utilizes content similarity to dynamically select high-signal behaviors. Extensive experiments show that EST exhibits a stable and efficient power-law scaling relationship, enabling predictable performance gains with model scale. Deployed on Taobao's display advertising platform, EST significantly outperforms production baselines, delivering a 3.27\% RPM (Revenue Per Mile) increase and a 1.22\% CTR lift, establishing a practical pathway for scalable industrial CTR prediction models.

IMITATOR4AMAS supports model checking and synthesis of memoryless imperfect information strategies for STCTL, interpreted over networks of parametric timed automata with asynchronous execution. While extending the verifier IMITATOR, IMITATOR4AMAS is the first tool for strategy synthesis in this setting. Our experimental results show a substantial speedup over previous approaches.

We present the analytic expressions of the three-loop virtual corrections to the helicity amplitudes of 2 -> 2 four-fermion scattering processes in massless QED. The contributing Feynman diagrams are grouped into integrand families characterised by independent Symanzik polynomials and decomposed in terms of master integrals using an optimised integration-by-parts strategy. Upon the renormalisation of the ultraviolet divergences and the extraction of the universal infrared pole structure, the finite results are expressed in terms of generalised polylogarithms up to transcendental weight six. Amplitudes for dimuon production in electron-positron annihilations, electron-muon scattering, and Bhabha scattering are explicitly derived.

We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep velocities to oscillatory behavior at slow sweeps. We show that, under a stochastically driven field, the critical sweep velocity at which the spin correlation functions undergo an abrupt change decreases with increasing noise strength and scales linearly with the square of the noise intensity. Remarkably, when the noise intensity and sweep velocity are comparable, the excitation probability becomes locked to pk = 1/2 over a finite momentum window, signaling the emergence of noise-induced maximally mixed modes. This gives rise to a highly oscillatory region in the dynamical phase diagram, whose threshold sweep velocity increases with noise and likewise exhibits quadratic scaling with the noise strength. Finally, we identify a universal scaling function under which all boundary sweep-velocity curves collapse onto a single universal curve.

Altermagnetism (AM) and its associated spin-transport phenomena are typically linked to spin-split electronic band structures in bulk materials. However, the crystal surface has a reduced symmetry with respect to the bulk, which can induce AM at the surface of conventional antiferromagnets (AFMs) $\unicode{x2013}$ a local effect which cannot be detected using bulk properties. In this work we define the symmetry conditions necessary for surface AM and show how it can be topologically protected, rendering it a robust effect. We provide a minimal model for one trivial and two topological examples of surface AM. We show that the spin spectral density, accessible by spin- and angle-resolved photoemission spectroscopy, can exhibit a $d$-wave-like altermagnetic character at the surface, even when the full band structure is completely spin degenerate. Our topological model describes the Dirac semimetal CuMnAs, which provides an existing realization of our theory. Our results identify crystal surfaces as a platform to realize robust, topology- and symmetry-driven unconventional magnetism beyond the bulk classification of magnetic materials.

The advent of quantum computation compels the cryptographic community to design digital signature schemes whose security extends beyond the classical hardness assumptions. In this work, we introduce Spinel, a post-quantum digital signature scheme that combines the proven security of SPHINCS+ (CCS 2019) with a new family of algebraic hash functions (Adv. Math. Commun. 2025) derived from the Tillich-Zemor paradigm (Eurocrypt 2008) with security rooted in the hardness of navigating expander graphs over $\mathrm{SL}_n(\mathbb{F}_p)$, a problem believed to be hard even for quantum adversaries. We first provide empirical evidence of the security of this hash function, complementing the original theoretical analysis. We then show how the hash function can be integrated within the SPHINCS+ framework to give a secure signature scheme. We then model and analyze the security degradation of the proposed scheme, which informs the parameter selection we discuss next. Finally, we provide an implementation of the hash function and the proposed signature scheme Spinel as well as detailed empirical results for the performance of Spinel showing its feasibility in practice. Our approach lays the foundations for the design of algebraic hash-based signature schemes, expanding the toolkit of post-quantum cryptography.

We study two central qubits interacting with a transverse-field Ising chain that serves as their environment. The environment is driven linearly in time across its quantum critical points (QCPs) and, during the evolution, is subjected to quantum reset (QR), where it is returned at random times to its initial state. We investigate how such QR of the environmental spin chain modifies the dynamics of entanglement and quantum discord between the qubits. Our results show that in the strong-coupling regime, entanglement and discord exhibit pronounced revivals within the interval bounded by the Ising QCPs, but these revivals diminish as the QR rate increases. In contrast, weak coupling leads to a monotonic reduction of quantum correlations. Numerically, we find that the revival peaks of concurrence decay and scale exponentially with the QR rate, while quantum discord shows no clear scaling behavior. In the weak-coupling regime without QR, the correlations decay monotonically as the driven field crosses the second QCP. When QR is applied, however, both entanglement and discord undergo oscillatory suppression, with the oscillation period increasing as either the QR rate or the ramp time scale is reduced.

A study of the unbalanced magnetic polarity distribution of 70 coronal holes was performed. Data from the Helioseismic and Magnetic Imager (HMI) were used to examine the photospheric line-of-sight magnetic field ($B_{\mathrm{LOS}}$) beneath these coronal holes. The skewness ($S$) values of the $B_{\mathrm{LOS}}$ distributions revealed significant asymmetry, characterized by the dominance of one magnetic polarity, with $\sim88\%$ of the coronal holes exhibiting a skewness value ranging from $\pm(0.20~\text{to}~0.40)$. The corresponding magnetic flux imbalance ($Φ_{\mathrm{imb}}$) ranges from $20\%$ to $45\%$. In contrast, quiet-Sun regions show symmetric magnetic field distributions with skewness values less than$~0.11$ and flux imbalance less than $11.0\%$. A study of a coronal hole as it traverses across the disk shows that the magnetic field distribution does not evolve significantly over this time, remaining stable across half a solar rotation. A moderate correlation ($r = 0.60$) between the magnetic flux imbalance and the speed of associated high speed solar wind streams ($v_{\mathrm{HSS}}$) suggests that flux imbalance may contribute to the generation of these faster solar wind streams. These results imply that regions with higher flux imbalance ($Φ_{\mathrm{imb}}$), indicative of more open magnetic field structures, present more favorable conditions for plasma acceleration as compared to closed bi-polar field, but the moderate correlation indicates that other factors may also play important roles.