Athermal elongated particles are well-known to follow Jeffery orbits when sheared in viscous fluids. It is less clear if similar orbits appear in dense granular flows. We show that when sheared for long enough, sufficiently elongated frictionless granular rods, rather than following noisy Jeffery-like orbits, exist in a quasi-equilibrium state, whose orientational statistics are quantitatively described by classical liquid crystal theory, where the noise is provided by collisions due to shear. At the same time, we demonstrate a systematic breakdown of this equilibrium analogy at two distinct limits: at low aspect ratios, where the equilibrium theory incorrectly predicts an isotropic state, and as inter-particle friction is introduced, where the system moves from steric screening to frictional gearing. Even within this frictionally geared state, the rotational dynamics remain distinct from classical Jeffery orbits. We link this frictional breakdown directly to the system being driven far from equilibrium, as quantified by an effective Ericksen number that compares non-equilibrium rotational driving to steric ordering. Our results provide a quantitative map of the transition from a quasi-equilibrium to a far-from-equilibrium steady state in a dense, driven system, defining the limits of applicability for thermal liquid crystal theory in athermal matter.

Vector embeddings from pre-trained language models form a core component in Neural Information Retrieval systems across a multitude of knowledge extraction tasks. The paradigm of late interaction, introduced in ColBERT, demonstrates high accuracy along with runtime efficiency. However, the current formulation fails to take into account the attention weights of query and document terms, which intuitively capture the "importance" of similarities between them, that might lead to a better understanding of relevance between the queries and documents. This work proposes ColBERT-Att, to explicitly integrate attention mechanism into the late interaction framework for enhanced retrieval performance. Empirical evaluation of ColBERT-Att depicts improvements in recall accuracy on MS-MARCO as well as on a wide range of BEIR and LoTTE benchmark datasets.

We propose a methodology that exploits the contract formalism to characterize the continuous-time safety control problem, which is often difficult to address, in terms of a discrete-time one, for which numerous efficient solution scheme exist. We construct contracts as pairs of assumptions and guarantees which are set-valued mappings that describe the safe boundaries within which the system must operate. By formalizing safety control as contract implementation, we develop a vertical hierarchy according to which we translate implementation from continuous to discrete time. We accomplish this by constructing a discrete-time system and a contract such that a solution to the continuous-time implementation problem can be characterized in terms of a solution to its discrete-time counterpart. We then use this characterization to construct a control input that establishes implementation in continuous time on the basis of the control sequence that achieves implementation in discrete time.

Scanning tunneling microscopy (STM) serves as a powerful pictorial tool for visualizing the local density of states (LDOS) of an individual stripe, which strongly intertwines with superconductivity in the underdoped cuprates. The exotic LDOS map patterns thus appear as the key to uncovering the mystery of the underlying microscopic mechanisms. With the quantum color string model framework, we reveal that the microscopic origin of the ubiquitous $4a_0\times4a_0$ plaquettes is closely related to spinon singlet pairs. Moreover, by comparing our data with LDOS of cuprates, we identify an effect of particle-hole symmetry breaking (PHSB): a $2a_0$ shift, which is confirmed in a longer stripe ($L=18$).Our work offers a fresh wavefunction-based perspective for interpreting STM signals in experiments and may advance the microscopic comprehension of high-$T_c$ cuprates.

Recently the authors solved a long-standing problem and showed that for an arbitrary pair of contractions on Hilbert space with trace class difference has an integrable spectral shift function on the unit circle ${\Bbb T}$ and an analogue of the Lifshits--Krein trace formula holds. It is also known that it may happen that there is no real-values integrable spectral shift function. In this paper we find conditions under which a pair of contractions with trace class difference has {\it a real-valued integrable} spectral shift function. We also consider a similar problem for pairs of dissipative operators. Finally, we find an application of the results in question to dissipative Schrödinger operators.

What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(λ, F)$ plane, where $λ$ is Langton's rule density and $F$ is a background-stability parameter. Of these rules, 20,152 (7.69%) support pattern proliferation, concentrated at low rule density ($λ\approx 0.15$--$0.25$) and low-to-moderate background stability ($F \approx 0.2$--$0.3$), in the weakly supercritical regime (Derrida coefficient $μ= 1.81$ for replicators vs. $1.39$ for non-replicators). Self-replicating rules are more approximately mass-conserving (mass-balance 0.21 vs. 0.34), and this generalises to $k{=}3$ Moore rules. A three-tier detection hierarchy (pattern proliferation, extended-length confirmation, and causal perturbation) yields an estimated 1.56% causal self-replication rate. Self-replication rate increases monotonically with neighbourhood size under equalised detection: von Neumann 4.79%, Moore 7.69%, extended Moore 16.69%. These results identify background stability and approximate mass conservation as the primary axes of the self-replication phase boundary.

In complex molecular systems, the reaction coordinate (RC) that characterizes transition pathways is essential to understand underlying molecular mechanisms. This review surveys a framework for identifying the RC by applying deep learning to the committor, which provides the most reliable measure of the progress along a transition path. The inputs to the neural network are collective variables (CVs) expressed as functions of atomic coordinates of the system, and the corresponding RC is predicted as the output by training the network on the committor as the learning target. Because deep learning models typically operate in a black-box manner, it is difficult to determine which input variables govern the predictions. The incorporation of eXplainable Artificial Intelligence (XAI) techniques enables quantitative assessment of the contributions of individual input variables to the predictions. This approach allows the identification of CVs that play dominant roles and demonstrates that the committor distribution on the surface using important CVs is separated by well-defined boundaries. The framework provides an explainable deep learning strategy for assigning a molecular mechanism from the RC and is applicable to a wide range of complex molecular systems.

We demonstrate that the pushforward of the product of Haar measures by the lattice Yang-Mills action concentrates as a Gaussian. It is also sketched how, using this fact, one can recover the strong-coupling expansion.

In highly purified host, the coherence of quantum emitters is ultimately limited by hyperfine interactions between the emitter and lattice nuclei possessing non-zero nuclear magnetic moments. This limitation can only be mitigated through isotopic purification. In this work, we investigate CeO2 as a host composed entirely of nuclei with zero nuclear moment. High-quality CeO2 thin films were grown by PLD and doped with Tm and Er ions. Structural characterization using X-ray diffraction, atomic force microscopy, and ion channeling confirms single-crystalline, atomically smooth films with dopants substitutionally incorporated at Ce lattice sites. Photoluminescence lifetime measurements show significantly longer lifetimes for Er-doped CeO2 (2.9 - 5.3 ms) compared with Tm-doped films (14 - 68 μs). Moreover, the Er-doped PLD films exhibit longer lifetimes at ~1% dopant concentration than previously reported for MBE-grown films. Density functional theory calculations reveal a substantial overlap between unoccupied O 2p and Tm 4f states near the valence band maximum, whereas Er 4f states remain well isolated. This electronic interaction likely introduces non-radiative recombination pathways in Tm-doped CeO2, explaining the reduced lifetimes. These findings highlight the importance of selecting appropriate dopant-host combinations and optimized growth conditions to minimize non-radiative channels for quantum applications.

Earth's long-lived geodynamo is difficult to reconcile with recent high estimates of the core thermal conductivity, a problem known as the new core paradox. At the same time, the long-term thermal evolution of the mantle remains uncertain, largely due to the poorly constrained onset of modern-style plate tectonics, which marks the transition to efficient cooling of the interior through mobile-lid convection. Because core cooling -- and thus magnetic field generation -- depends on the efficiency with which the mantle extracts heat from the core, these two problems are closely linked. Here, we investigate the coupled thermal evolution of mantle and core using a 1D model that incorporates a parametrized transition transition from stagnant- to mobile-lid convection, defined by its onset time and with a prescribed duration. This framework allows us to assess how different tectonic histories influence Earth's thermal and magnetic evolution. We perform a Bayesian inversion using constraints from the palaeomagnetic record, mantle cooling history, and present-day thermal state. Our results favour a transition from stagnant- to mobile-lid convection during the Archean, which promotes core cooling and enables a geodynamo throughout Earth's history, even for core thermal conductivities in excess of 100 W/m/K. A delayed onset of mobile-lid convection provides thus a viable solution to the new core paradox.

We introduce a new flatness index for the boundary of an open subset $Ω$ of $\mathbb{R}^n$, $n\ge 2$. This index provides a necessary condition for $\partialΩ$ to be a harmonic pseudosphere and sufficient conditions for a harmonic pseudosphere to be a Euclidean sphere. These conditions will follow from a stability inequality formulated in terms of a harmonic invariant, the Kuran gap, recently introduced by the last two authors.

This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values and the function values, as well as the derivative values. Compared with the classical compact schemes, which employ a Taylor expansion method to determine the coefficients, our approach adopts an equivalent and more generalized method to achieve this goal. Via this method, the problem of constructing a high-order compact scheme is transformed into solving the null space of undetermined homogeneous linear systems. This null space constitutes the complete set of schemes that meet the specified accuracy under a given stencil, and is termed the 'scheme space'. Schemes within the scheme space possess the same accuracy level yet exhibit distinct dispersion and dissipation characteristics. Through Fourier analysis, we can get the dissipation and dispersion properties of all schemes in the scheme space. This facilitates the control of scheme dispersion and dissipation without altering the stencil compactness. Combined with the WENO (Weighted Essentially Non-Oscillatory) concept, multi-stencil schemes are employed to construct the nonlinear weighted compact finite volume scheme (WCFV). The WCFV is capable of eliminating unphysical oscillations at discontinuities, thereby enabling the capture of strong discontinuities. One-dimensional schemes are discussed in detail, and numerical results demonstrate that the proposed method exhibits high-order accuracy, robustness, and shock-capturing capability.

Newcomers are crucial for the growth of online communities, yet their successful integration into these spaces requires overcoming significant initial hurdles. Social Virtual Reality (VR) platforms are novel avenues that offer unprecedented online interaction experiences. Unlike well-studied two-dimensional online environments, the pathways to successful newcomer integration in online VR spaces are underexplored. Our research addresses this gap by examining the strategies used by newcomers to navigate early challenges in social VR and how they adapt. By focusing on active participants (ranging from newcomers currently navigating these hurdles to veterans who have successfully integrated) we isolate the specific strategies necessary for retention. We interviewed 24 active social VR users and conducted a reflexive thematic analysis. While participants identified barriers such as unfamiliar user interfaces, social norms, and overwhelming sensory input, our analysis reveals the adaptation strategies required to overcome them. Our findings expand on understanding newcomer persistence beyond traditional 2D environments, emphasizing how social dynamics influence the management of VR-specific issues like VR sickness during onboarding. Additionally, we highlight how successful newcomers overcome the lack of clear objectives in social VR by proactively constructing social meaning. We propose design suggestions to scaffold these successful integration pathways.

Automated benchmarks dominate the evaluation of large language models, yet no systematic study has compared user satisfaction, adoption motivations, and frustrations across competing platforms using a consistent instrument. We address this gap with a cross-platform survey of 388 active AI chat users, comparing satisfaction, adoption drivers, use case performance, and qualitative frustrations across seven major platforms: ChatGPT, Claude, Gemini, DeepSeek, Grok, Mistral, and Llama. Three broad findings emerge. First, the top three platforms (Claude, ChatGPT, and DeepSeek) receive statistically indistinguishable satisfaction ratings despite vast differences in funding, team size, and benchmark performance. Second, users treat these tools as interchangeable utilities rather than sticky ecosystems: over 80% use two or more platforms, and switching costs are negligible. Third, each platform attracts users for different reasons: ChatGPT for its interface, Claude for answer quality, DeepSeek through word-of-mouth, and Grok for its content policy, suggesting that specialization, not generalist dominance, sustains competition. Hallucination and content filtering remain the most common frustrations across all platforms. These findings offer an early empirical baseline for a market that benchmarks alone cannot characterize, and point toward competitive plurality rather than winner-take-all consolidation among engaged users.

It was once conjectured that two graph states are local unitary (LU) equivalent if and only if they are local Clifford (LC) equivalent. This so-called LU-LC conjecture was disproved in 2007, as a pair of 27-qubit graph states that are LU-equivalent, but not LC-equivalent, was discovered. We prove that this counterexample to the LU-LC conjecture is minimal. In other words, for graph states on up to 26 qubits, the notions of LU-equivalence and LC-equivalence coincide. This result is obtained by studying the structure of 2-local complementation, a special case of the recently introduced r-local complementation, and a generalization of the well-known local complementation. We make use of a connection with triorthogonal codes and Reed-Muller codes.

This paper introduces a new extension of the Conditional Autoregressive Value at Risk (CAViaR) model aimed at improving tail risk forecasting across assets. The proposed component-based model, CAViaR with Spillover Effects (CAViaR-SE), decomposes the conditional Value at Risk into a proper-risk component and a spillover component driven by a linear combination of tail risks from influential assets. These assets are selected via a recursive partial correlation algorithm, allowing multiple spillover sources with minimal parameterization. The spillover component acts as a predictable quantile shifter, directly affecting the conditional quantile dynamics rather than the volatility scale. Empirical results on Dow Jones Industrial Average stocks show that spillover effects account for a substantial share of total tail risk and significantly improve out-of-sample tail risk forecasts. Backtesting procedures, together with Model Confidence Set (MCS) analysis, confirm that CAViaR-SE provides well-calibrated risk measures and statistically superior forecasts compared to standard and augmented CAViaR models.

The differential $λ$-calculus studies how the quantitative aspects of programs correspond to differentiation and to Taylor expansion inside models of linear logic. Recent work has generalized the axioms of Taylor expansion so they apply to many models that only feature partial sums. However, that work does not cover the classic web based models of K{ö}the spaces and finiteness spaces . First, we provide a generic construction of web based models with partial sums. It captures models, ranging from coherence spaces to probabilistic coherence spaces, finiteness spaces and K{ö}the spaces. Second, we generalize the theory of Taylor expansion to models in which coefficients can be non-positive. We then use our generic web model construction to provide a unified proof that all the aforementioned web based models feature such Taylor expansion.

Thin films of functional inorganic materials, particularly oxides, play a vital role in optoelectronics, enabling applications that range from active optical components to MEMS-based architectures. Achieving high aspect ratio patterning of these functional materials remains a significant challenge, as many of their constituent elements do not readily form volatile compounds required for conventional reactive ion etch processes. We introduce a novel approach, Pulsed Laser Template ENgineering (PLATEN), which offers a more accessible route for patterning materials that are typically difficult to etch. This technique involves depositing functional films using the Pulsed Laser Deposition (PLD) process onto silicon substrates that have been pre-patterned using reactive ion etching to create high aspect ratio features. Due to the highly forward-directed nature of the PLD process, the deposited films replicate closely the topography of the patterned silicon, without coatings the sidewalls. This process remains effective even at feature sizes down to approximately 50 nm. The oxide films replicate the underlying silicon pattern to a thickness of 80 nm. For thickness beyond 80 nm the patterns develop a waist at the midpoint which scales with film thickness and is not dependent on the feature size. In this paper, we present a detailed analysis of the PLATEN process, including deviations from ideal pattern replication in sub-micron features as a function of film thickness, and demonstrate near single crystalline growth of oxides on the patterned silicon substrate, demonstrating the potential of PLATEN technique for active opto-electronic materials.

Transmitter localization in vessel-like molecular communication channels is a fundamental problem with potential applications in healthcare. Existing analytical solutions either assume knowledge of emission time or require multiple closely spaced receivers, which limits their applicability in realistic scenarios. In this letter, we propose a simple closed-form approximation that exploits the temporal variance of the received molecular signal to estimate the distance between the transmitter and the receiver without emission time information. The method is derived from a Gaussian approximation of the received signal near its peak and gives an explicit variance-distance relation. Simulation results in physically relevant capillary vessel scale show that the proposed method achieves distance prediction with error on the order of 1%.

Calculations of the self-energy corrections to ionization energies of the $3s$, $3p_{1/2}$, and $3p_{3/2}$ states in sodium-like ions with nuclear-charge numbers $Z=30$, $50$, $70$, and $92$ are presented. The calculations are performed using two approaches: the rigorous bound-state QED formalism and the model-QED-operator method. Within the first method, the first and second orders of the QED perturbation theory formulated in the Furry picture are evaluated. Various screening potentials are included into the initial approximation to partially take into account the electron-electron interaction effects already at the lowest order, thereby accelerating the convergence of perturbation series. Within the second approach, different implementations of the model-QED operator, including its incorporation into the relativistic configuration-interaction calculations, are considered. A detailed comparison of the results obtained by these two independent methods is presented, demonstrating good agreement and thus validating the accuracy and efficiency of the model-QED-operator approach for many-electron systems.

We investigate the optical and radiative signatures of an accretion disk around a Schwarzschild black hole (BH) immersed in a uniform magnetic field. The spacetime geometry is described by the Schwarzschild-Bertotti-Robinson (SBR) metric, which represents the non-rotating sector of the recently discovered Kerr-Bertotti-Robinson exact solution to the Einstein-Maxwell equations. We begin with the study of null geodesics and demonstrate that the self-consistent magnetic field fundamentally alters photon propagation, causing an expansion of light bundles relative to the Schwarzschild case due to modified initial conditions in the orbital equation. We then compute the magnetic field-dependent shifts of key characteristic radii: the event horizon ($r_h$), photon sphere ($r_{ph}$), and innermost stable circular orbit ($r_{ISCO}$). We find that all three increase monotonically with field strength $B$, revealing a magnetic amplification of the effective gravitational field. For $B=0.05$, we find that the lensed emission bands contract to a narrower impact parameter range, $b\in(4.976,5.149)\cup(5.19,6.128)$. Employing ray-tracing formalism, we construct observed accretion disk images and quantify magnetic modifications, showing that the direct image contracts while maximum energy flux, radiation temperature, and redshift factor are enhanced. Complementing these numerical findings, we develop an analytical framework for the accretion disk dynamics. We derive the modified Keplerian frequency $Ω_K$, along with the specific energy $E$ and angular momentum $L$ for circular orbits. From these, we obtain the exact ISCO radius $r_{\text{ISCO}}$, which shows an outward shift. This outward shift reveals that the radiative efficiency decreases dramatically with increasing magnetic field strength $B$. For $β= BM \sim 0.1$, the efficiency drops by approximately $91\%$.

We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any choice of lift of the dynamics to the real line, and prove that they are equivalent to the standard random rotation number. We then prove that the mean random rotation number may be approximated within an error of $1/n$ when using $n$ iterations of the dynamics. Finally, we develop numerical algorithms for approximation of the random rotation number which we test with several examples.

Patient-specific computational modeling has emerged as a powerful tool for surgical planning in complex congenital heart disease. One promising application is complex biventricular repair, which often requires construction of a custom intraventricular baffle to establish a physiologic left ventricle-to-aorta outflow pathway. In current practice, baffle geometry is designed and shaped intraoperatively and preoperative planning remains largely manual, limiting the ability to generate anatomically conformal, watertight models suitable for quantitative hemodynamic assessment. In this work, we present a semi-automated computational framework for the design and assessment of patient-specific intraventricular baffles. The method constructs an explicit VSD-to-aorta flow pathway, preserves native right ventricular geometry, and reshapes only the baffle region using section-wise area constraints along a physiologically aligned centerline. The resulting geometry is integrated into a closed, multi-labeled domain for computational fluid dynamics analysis. We retrospectively applied this framework to four patients with double outlet right ventricle (DORV) who previously underwent biventricular repair. For each case, a patient-specific baffle was generated and its hemodynamic performance was evaluated using CFD. Predicted pressure gradients across the reconstructed outflow were within clinically acceptable ranges and comparable to the patients' postoperative echocardiographs. This approach enables quantitative, pre-operative design and evaluation of candidate baffle geometries and provides a reproducible method for generating simulation-ready models. By combining physiologically constrained geometric design with CFD-based assessment, the framework represents a step toward computational, patient-specific decision support for biventricular flow restoration in a complex heterogeneous patient population.

Error-controlled lossy compressors have been widely used in scientific applications to reduce the unprecedented size of scientific data while keeping data distortion within a user-specified threshold. While they significantly mitigate the pressure for data storage and transmission, they prolong the time to access the data because decompression is required to transform the binary compressed data into meaningful floating-point numbers. This incurs noticeable overhead for common analytical operations on scientific data that extract or derive useful information, because the time cost of the operations could be much lower than that of decompression. In this work, we design an error-controlled lossy compression and analytical framework that features multi-stage decompression and homomorphic analytical operation algorithms on intermediate decompressed data for reduced data access latency. Our contributions are threefold. (1) We abstract a generic compression pipeline with partial decompression to multiple intermediate data representations and implement four instances based on state-of-the-art high-throughput scientific data compressors. (2) We carefully design homomorphic algorithms to enable direct operations on intermediate decompressed data for three types of analytical operations on scientific data. (3) We evaluate our approach using five real-world scientific datasets. Experimental evaluations demonstrate that our method achieves significant speedups when performing analytical operations on compressed scientific data across all three targeted analytical operation types.

In this article, we improve the classical Bukhgeim-Klibanov method presented in [1],which can be used to prove the conditional stability of inverse source problem for a hyperbolic equation from the measurement on the subboundary. A major ingredient of our proof is a novel Carleman estimate. This inequality eliminates the need to extend the solution in time, therefore simplifies the existing proofs, which is widely applicable to various evolution equations.

Spanwise wall oscillation (SWO) of turbulent boundary layers (TBLs) is investigated via direct numerical simulations over an extended actuation region with oscillation periods up to T_{sc}^+=600, scaled by the uncontrolled friction velocity u_{τ0} at the onset of SWO (i.e. Re_θ=344). For low periods (T_{sc}^+<200), drag reduction (DR) decreases with increasing Re_θ, consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods, DR increases with Re_θ. For example, at T_{sc}^+=600, DR rises from 1.3% at Re_θ=713 to 7.0% at Re_θ=2340. This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as TBL develops, u_{τ0} decreases downstream, reducing the local-scaled period T^+ and thereby enhancing suppression of near-wall turbulence. Interestingly, even the results are compared at approximately fixed T^+, DR for T^+>350 still exhibits a weak positive dependence on Re_θ, consistent with recent experiments by Marusic et al. Nat. Commun., vol. 12, 2021, 5805. We further develop a new analytical relationship that links DR to the upward shift of mean velocity in the wake region. Unlike previous formulations, the relationship avoids logarithmic-region fitting and does not rely on an invariant Karman constant under SWO, while maintaining good agreement with DNS data. Flow diagnostics -- including Reynolds stresses, skin-friction decomposition, and energy spectra -- demonstrate that the observed variation of DR with Reynolds number (Re) arises from period-dependent modulation of near-wall turbulence. Overall, these findings challenge the conventional view that DR inevitably deteriorates with Re and demonstrate that out-scaled actuation can instead enhance DR performance -- offering new physical insights for high-Re control strategies.

Effective instruction in tutoring requires promptly providing instructional materials that match the needs of each student (e.g., in response to questions). In this study, we introduce an agent that automatically delivers supplementary materials on demand during one-on-one tutoring sessions. Our agent uses a multimodal large language model to analyze spoken dialogue between the instructor and the student, automatically generate search queries, and retrieve relevant Web images. Evaluation experiments demonstrate that our agent reduces the average image retrieval time by 44.4 s compared to cases without support and successfully provides images of acceptable quality in 85.7% of trials. These results indicate that our agent effectively supports instructors during tutoring sessions.

In the present work, the form factors of $B_{(s)}$ to light P-wave axial vector mesons are calculated via the light cone sum rules (LCSR) in the framework of heavy quark effective field theory (HQEFT). Firstly, the expressions of form factors in terms of the light cone distribution amplitudes (DAs) of axial vector mesons are derived via the LCSR at the leading order of heavy quark expansion. It is found that the penguin type form factors can be obtained directly from the corresponding semileptonic ones, which is similar to the case of S-wave mesons. Considering the light axial vector meson DAs to twist-3, we give the numerical results of form factors systematically. As applications, we investigate the branching ratios, longitudinal polarization fractions and forward-backward asymmetries of relevant semileptonic decays induced by charged current. Our results may be tested by more precise experiments in the future.

Deploying synchronous condensers (SynCons) near grid-following renewable energy sources (GFLRs) is an effective and increasingly adopted strategy for grid support. However, the potential transient instability risks in such configurations remain an open research question. This study investigates the mechanism of dominant synchronization instability source transition upon SynCon integration and proposes a straightforward approach to enhance system stability by leveraging their interactive characteristics. Firstly, a dual-timescale decoupling model is established, partitioning the system into a fast subsystem representing phase-locked loop (PLL) dynamics and a slow subsystem characterizing SynCon rotor dynamics. The study then examines the influence of SynCons on the transient stability of nearby PLLs and their own inherent stability. The study shows that SynCon's voltage-source characteristics and its time-scale separation from PLL dynamics can significantly enhance the PLL's stability boundary and mitigate non-coherent coupling effects among multiple GFLRs. However, the dominant instability source shifts from the fast-time-scale PLL to the slow-time-scale SynCon after SynCon integration. Crucially, this paper demonstrates that the damping effect of PLL control can also be transferred from the fast to the slow time scale, allowing well-tuned PLL damping to suppress SynCon rotor acceleration. Consequently, by utilizing SynCon's inherent support capability and a simple PLL damping loop, the transient stability of the co-located system can be significantly enhanced. These conclusions are validated using a converter controller-based Hardware-in-the-Loop (CHIL) platform.

In this paper, we study the $[k]$-Roman domination number of cylindrical graphs $C_m \Box P_n$. Our analysis begins with a general lower bound based on local neighborhood constraints, showing that $γ_{[k]R}(C_m\Box P_n) > (k+1)\left\lceil\frac{mn}{5}\right\rceil.$ By exploiting the connection between $[k]$-Roman domination and efficient domination, we characterize those cylindrical graphs whose optimal $[k]$-Roman domination number is realized by configurations with minimum possible local neighborhood weight. For fixed small values $m\in\{5,\ldots,8\}$, we construct explicit periodic $[k]$-Roman dominating functions that yield constructive upper bounds. These constructions are further refined using ceiling-type adjustments and reductions based on packing sets. A systematic comparison of the resulting bounds shows how their relative strength depends on the parameter $k$ and on the length of the path.