Deterministic channel modeling maps a physical environment to its site-specific electromagnetic response. Ray tracing produces complete multi-dimensional channel information but remains prohibitively expensive for area-wide deployment. We identify line-of-sight (LoS) region determination as the dominant bottleneck. To address this, we propose D$^2$LoS, a physics-informed neural network that reformulates dense pixel-level LoS prediction into sparse vertex-level visibility classification and projection point regression, avoiding the spectral bias at sharp boundaries. A geometric post-processing step enforces hard physical constraints, yielding exact piecewise-linear boundaries. Because LoS computation depends only on building geometry, cross-band channel information is obtained by updating material parameters without retraining. We also construct RayVerse-100, a ray-level dataset spanning 100 urban scenarios with per-ray complex gain, angle, delay, and geometric trajectory. Evaluated against rigorous ray tracing ground truth, D$^2$LoS achieves 3.28~dB mean absolute error in received power, 4.65$^\circ$ angular spread error, and 20.64~ns delay spread error, while accelerating visibility computation by over 25$\times$.

This paper investigates the characteristics of quasinormal modes (QNMs) of static, spherically symmetric black holes under the combined influence of spontaneous Lorentz symmetry breaking (LSB) induced by the Kalb-Ramond (KR) field and perfect fluid dark matter (PFDM). Using M87$^\ast$ shadow data from the Event Horizon Telescope (EHT), we constrain the LSB factor $τ$ and PFDM parameter $ζ$ at 1$σ$ confidence. By combining the sixth-order WKB approximation method with timedomain numerical integration, we systematically compute the complex frequency spectrum of QNMs for black holes in this spacetime background. The numerical results reveal an intriguing conclusion: as the LSB factor $τ$ or the PFDM parameter $ζ$ increases, both the real part and the absolute value of the imaginary part of the QNMs frequencies exhibit a monotonic increase, demonstrating a unique "stiffening" effect. This characteristic stands in stark contrast to the decreasing trend of QNMs frequencies observed in models that consider only traditional dark matter, revealing the critical influence of the coupling between the KR field and PFDM on the dynamic evolution of black holes. This study not only enriches and deepens the understanding of black hole perturbation theory within the framework of modified gravity but also, by identifying the distinctive spectral features of QNMs, offers the potential to distinguish whether the KR field and dark matter are coupled in future observations. Thus, it provides a theoretical foundation for testing mechanisms of spacetime symmetry breaking beyond the standard model and for exploring the nature of dark matter.

A complete structural characterization of graphs with no $K_{3,4}$ minor is obtained, and the following consequences are established. Every $4$-connected non-planar graph with at least seven vertices and minimum degree at least five contains both $K_{3,4}$ and $K_6^-$ as minors, thereby proving a conjecture of Kawarabayashi and Maharry in a strengthened form. Moreover, every $4$-connected graph with no $K_{3,4}$ minor is hamiltonian-connected, extending a theorem of Thomassen, and admits an embedding on the torus.

We introduce a new framework for multiagent decision-making in queueing systems that leverages the agility and robustness of nonlinear opinion dynamics to break indecision during queue selection and to capture the influence of social interactions on collective behavior. Queueing models are central to understanding multiagent behavior in service settings. Many prior models assume that each agent's decision-making process is optimization-based and governed by rational responses to changes in the queueing system. Instead, we introduce an internal opinion state, driven by nonlinear opinion dynamics, that represents the evolving strength of the agent's preference between two available queues. The opinion state is influenced by social interactions, which can modify purely rational responses. We propose a new subclass of queueing models in which each agent's behavioral decisions (e.g., joining or switching queues) are determined by this evolving opinion state. We prove a sufficient parameter condition that guarantees the Markov chain describing the evolving opinion and queueing system states reaches the Nash equilibrium of an underlying congestion game in finite expected time. We then explore the richness of the new framework through numerical simulations that illustrate the role of social interactions and an individual's access to system information in shaping collective behavior.

We determine the thickness of the Cartesian product $K_{6p+4} \square P_2$ for $p \ge 0$ and of the Cartesian product $K_8 \square P_m$ for $m \ge 1$, where $K_n$ and $P_m$ denote the complete graph on $n$ vertices and the path on $m$ vertices, respectively.

This article has two parts. In the first part we introduce two positivity conditions for the modified $χ_y$-genus on almost-complex manifolds and show that each of them implies a family of optimal Chern number inequalities. It turns out that many important Kähler and symplectic manifolds satisfy either of the two positivity conditions, and hence these Chern number inequalities hold true on them. In the second part we focus on the signature, a special value of the $χ_y$-genus, of symplectic manifolds equipped with symplectic circle actions and give applications. Our results in this part unify and generalize various related results in the existing literature.

Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules. Since these random frameworks have much more complicated algebraic, topological and geometric structures than their prototypes, the development of fixed point theory in random functional analysis had been almost stagnant before 2010. Unexpectedly, with the deep development of stable set theory fixed point theory in random functional analysis, including both its metric and topological fixed point theory, has made considerable progress in the recent 15 years. The purpose of this paper is to survey the important progress in metric fixed point theory in random functional analysis, including the random Banach contraction mapping principle and Caristi fixed point theorem on complete random metric spaces, and fixed point theorems for random nonexpansive and asymptotically nonexpansive mappings in complete random normed modules. Besides, the connections among the topics surveyed, random equations and random fixed point theorems for random operators are also briefly mentioned.

We present a radar sensing framework based on a low-complexity, quantized reconfigurable intelligent surface (RIS) that enables programmable manipulation of electromagnetic wavefronts for enhanced detection in non-specular and shadowed regions. We develop closed-form expressions for the scattered field and radar cross section (RCS) of phase-quantized RIS apertures based on aperture field theory, accurately capturing the effects of quantized phase, periodicity, and grating lobes on radar detection performance. The theory enables us to analyze the RIS's RCS along both the forward and backward paths from the radar to the target. The theory is benchmarked against full-wave electromagnetic simulations incorporating realistic unit-cell amplitude and phase responses. To validate practical feasibility, a $[16\times10]$ 1-bit RIS operating at 5.5 GHz is fabricated and experimentally characterized inside an anechoic chamber. Measurements of steering angles, beam-squint errors, and peak-to-specular ratios of the RCS patterns exhibit strong agreement with analytical and simulated results. Further experiments demonstrate that the RIS can redirect the beam in a non-specular direction and recover micro-Doppler signatures that remain undetectable with a conventional radar deployment.

Chance-constrained programs (CCPs) provide a powerful modeling framework for decision-making under uncertainty, but their nonconvex feasible regions make them computationally challenging. A widely used convex inner approximation replaces chance constraints with Conditional Value-at-Risk (CVaR) constraints; however, the resulting solutions can be overly conservative and suboptimal. We propose a scenario-wise scaling approach that strengthens CVaR approximations for CCPs with finitely supported uncertainty. The method introduces scaling factors that reweight individual scenarios within the CVaR constraint, yielding a family of potentially tighter inner approximations. We establish sufficient conditions under which, for a suitable choice of scaling factors, the scaled CVaR approximation attains the same optimal value as the original CCP and admits a (near-)optimal solution of the CCP. We show that these conditions are tight and further relax them in the convex setting. We also show that optimizing over scenario-wise scaling factors is NP-hard. To address this computational challenge, we develop efficient heuristic and sequential convex approximation algorithms that iteratively update the scaling factors and generate improved feasible solutions. Numerical experiments demonstrate that the proposed methods consistently improve upon standard CVaR and state-of-the-art convex approximations, often reducing conservativeness while maintaining tractability.

Investment in artificial intelligence (AI) has grown rapidly, yet its returns to scientific research remain poorly understood. We study how AI reshapes the production of science using a comprehensive dataset of research proposals submitted to a large international funding agency, including both funded and unfunded projects. Combining keyword extraction with large language model classification, we identify the presence, type, and functional role of AI within each proposal and link these measures to detailed budget allocations, team structure, and subsequent publication outcomes. We find that, in the short run, AI adoption is associated with modest improvements in scientific outcomes concentrated in the upper tail. Instead, its primary effects arise in the organization of research: AI-enabled projects reallocate resources toward human capital, involve larger teams, and undertake a broader set of tasks. These patterns are consistent with a reorganization of the scientific production process rather than immediate efficiency gains, in line with theories of general-purpose technologies. Task-level analyses further show that activities expanded in AI-enabled projects, particularly ideation and experimentation, are increasingly compatible with large language model capabilities, suggesting potential for future productivity gains as these technologies mature.

Trees are key roughness elements in urban environments, shaping airflow, microclimates, and pollutant dispersion. Yet the aerodynamic drag of complex tree-like structures at high Reynolds numbers remains poorly characterized compared with the well-studied drag crisis of simple bluff bodies. We combine large-scale lattice Boltzmann simulations with an analytical branch-wise drag model to examine fractal trees over a wide range of height-based Reynolds numbers, $Re_H$. Direct numerical simulations using a cumulant lattice Boltzmann method with adaptive mesh refinement cover $2.5\times10^3 \le Re_H \le 1.2\times10^5$, and the analytical model extends predictions to $Re_H \sim 10^9$. Under uniform inflow, the analysis indicates a drag-crisis transition near $Re_H \approx 3\times10^6$, with increasing structural complexity smoothing this transition because smaller branches remain subcritical. Introducing inflow turbulence with streamwise intensity $I_u \approx 8\%$, representative of atmospheric-boundary-layer winds, shifts the apparent onset to $Re_H \approx 1.5\times10^5$ and further moderates the drag reduction. Interpreted at full scale, this suggests that urban trees of order $10$--$30$ m exposed to winds of $1$--$10~\mathrm{m/s}$ generally operate in the crisis or post-crisis regime. In both uniform and turbulent inflow, the framework predicts a reversal in drag-coefficient ordering across geometries: simplified trees show lower drag in the subcritical regime but may exhibit higher drag in the supercritical regime, whereas more complex trees undergo a smoother, moderated crisis. These results challenge the common assumption that pruning always reduces aerodynamic loading and highlight the need to reassess vegetation-drag parameterizations and pruning strategies in high-$Re_H$ conditions.

Binary black hole (BBH) systems residing in the centers of galaxies evolve within complex astrophysical environments. These environments, comprising dark matter (DM) halos and baryonic accretion disks, can significantly alter the orbital dynamics of the binaries and their resulting gravitational wave (GW) emission. In this study, we investigate the dynamical evolution and GW waveforms of BBH systems embedded in the centers of the Large Magellanic Cloud (LMC) and the Andromeda Galaxy (M31). We construct a comprehensive analytical framework that jointly incorporates GW radiation reaction, DM spike effects (including dynamical friction and accretion, derived from the Navarro-Frenk-White profile), and accretion disk perturbations. Using this framework, we track the long-term evolution of the binary's semi-latus rectum $p$ and orbital eccentricity $e$. Our simulations reveal that the coexistence of a DM spike and an accretion disk significantly accelerates the inspiral process compared to pure DM or vacuum scenarios. Crucially, to assess the observability of these environmental effects, we calculate the Signal-to-Noise Ratio (SNR) and waveform Mismatch for future Pulsar Timing Arrays (PTAs). Our analysis demonstrates that these systems can achieve robust detectability thresholds ($\text{SNR} \ge 8$) within specific parameter spaces. Furthermore, the substantial Mismatch (reaching $\sim 0.7$ over a 20-year observation in the LMC scenario) indicates that the phase deviations induced by these environmental effects are highly distinguishable from vacuum templates. These findings predict the prospect of using future GW detections to probe complex galactic environments.

Frequency combs are a spectrum of equally spaced frequency components with very high time-frequency accuracy, which have been widely used in the optical and microwave frequency ranges. We propose the realization of a frequency comb operating at the terahertz regime in terms of the nonlinear dynamics of electric-polarization waves, or ferrons as their quanta, in the ferroelectric materials. The efficiency of the frequency comb of the electric-polarization waves is exactly proportional to the static electric polarization carried by the ferron modes, which thereby offers new opportunities for the direct observation and application of the intrinsic properties of ferrons.

As industry and academia continue to advance spaceborne computing and communication capabilities, the formation of cloud-native space clusters (CNSCs) has become an increasingly evident trend. This evolution progressively exposes the resource management challenges associated with coordinating fragmented and heterogeneous onboard resources while supporting large-scale and diverse space applications. However, directly transplanting mature terrestrial cloud-native cluster operating system paradigms into space is ineffective due to the fragmentation of spaceborne computing resources and satellite mobility, which collectively impose substantial challenges on resource awareness and orchestration. This article presents YUHENG-OS, a cloud-native space cluster operating system tailored for CNSCs. YUHENG-OS provides unified abstraction, awareness, and orchestration of heterogeneous spaceborne infrastructure, enabling cluster-wide task deployment and scheduling across distributed satellites. We introduce a four-layer system architecture and three key enabling technologies: modeling of heterogeneous resource demands for space tasks, fragmented heterogeneous resource awareness under network constraints, and matching of differentiated tasks with multidimensional heterogeneous resources under temporal dependency constraints. Evaluation results show that, compared with representative terrestrial cloud-native cluster operating systems exemplified by Kubernetes, YUHENG-OS achieves a substantially higher task completion ratio, with improvements of up to 98%. This advantage is primarily attributed to its ability to reduce resource awareness delay by 71%.

One efficient mechanism for generating a charge supercurrent is Andreev reflection, in which the electric current injected from a normal metal into a conventional superconductor is converted into a supercurrent, thereby preserving charge conservation. We here propose a general principle for generating spin supercurrents in triplet superconductors by analogy with such charge transport, i.e., assuming spin conservation. We find a spin torque that is proportional to the triplet superconducting order parameter and, in the spin-conservation scenario, converts the particle spin to that of Cooper pairs. Based on this general principle, we propose an implementation to efficiently generate a spin supercurrent in unitary triplet superconductors, even though Cooper pairs carry no spin polarization at equilibrium, by the magnetization dynamics ${\bf M}(t)$ of a proximity magnetic nanostructure. The efficiency of this spin pumping is not solely limited to the $d{\bf M}/dt\times {\bf M}$ due to the emergent particle-hole symmetry, thereby going beyond the conventional spin pumping of electrons. This general principle provides an efficient approach to generating and manipulating dissipationless spin currents in many unconventional superconductors.

A marine vessel is a nonlinear system subject to irregular disturbances such as wind and waves, which cause tracking errors between the nominal and actual trajectories. In this study, a nonlinear vessel maneuvering model that includes a tracking controller is formulated and then controlled using a linear approximation around the nominal trajectory. The resulting stochastic linearized system is analyzed using a stochastic zeroing control barrier function (ZCBF). A stochastic safety compensator is designed to ensure probabilistic safety, and its effectiveness is verified through numerical simulations.

We analytically derive the secular changes of the orbital parameters, i.e., energy, angular momentum, and Carter constant, for general bound orbits in Kerr spacetime, at leading order in the mass ratio, through the 6th post-Newtonian (6PN) order and the 16th order in orbital eccentricity. We validate the formulas against high-precision numerical Teukolsky results and quantify how eccentricity affects both the achievable accuracy and the PN convergence. We then construct and test a simple ``hybrid'' approximation that combines different PN and eccentricity truncations to retain accuracy at reduced computational cost. We also assess the performance of exponential resummation at higher PN orders. These results provide building blocks for fast, (analytic) adiabatic inspiral and waveform models for extreme mass ratio inspirals relevant to space-based detectors such as the Laser Interferometer Space Antenna (LISA).

We investigate stability properties of weak supermartingale optimal transport (WSOT) problems on $\mathbb{R}$. For probability measures $μ,ν\in\mathcal{P}_r$ satisfying $μ\leq_{cd} ν$ (equivalently, $Π_S(μ,ν)\neq\emptyset$), we consider supermartingale couplings $π=μ(d x)π_x(d y)$ and the weak transport functional \[ V_S^C(μ,ν) := \inf_{π\inΠ_S(μ,ν)} \int_\mathbb{R} C(x,π_x)\,μ(d x), \] for some appropriate cost function $C:\mathbb{R}\times\mathcal{P}_r\to\mathbb{R}$. Our first main contribution is an approximation result in adapted Wasserstein distance: under $W_r$-convergence of marginals $(μ^k,ν^k)\to(μ,ν)$ with $μ^k\leq_{cd} ν^k$, any $π\inΠ_S(μ,ν)$ can be approximated by $π^k\inΠ_S(μ^k,ν^k)$ such that $A\mathcal{W}_r(π^k,π)\to0$. As a consequence, we obtain the continuity of the functional $(μ,ν) \mapsto V_S^C(μ,ν)$, and the monotonicity principle for WSOT.

The characteristics of high-speed node movement and dynamic topology changes pose great challenges to the design of internet of vehicles (IoV) routing protocols. Existing schemes suffer from common problems such as insufficient adaptability and lack of global consideration, making it difficult to achieve a globally optimal balance between routing reliability, real-time performance and transmission efficiency. This paper proposes an adaptive multi-dimensional coordinated comprehensive routing scheme for IoV environments. A complete IoV system model including network topology, communication links, hierarchical congestion and transmission delay is first constructed, the routing problem is abstracted into a single-objective optimization model with multiple constraints, and a single-hop link comprehensive routing metric integrating link reliability, node local load, network global congestion and link stability is defined. Second, an intelligent transmission switching mechanism is designed: candidate nodes are screened through dual criteria of connectivity and progressiveness, a dual decision-making of primary and backup paths and a threshold switching strategy are introduced to avoid link interruption and congestion, and an adaptive update function is constructed to dynamically adjust weight coefficients and switching thresholds to adapt to changes in network status. Simulation results show that the proposed scheme can effectively adapt to the high dynamic topology and network congestion characteristics of IoV, perform excellently in key indicators such as routing interruption times, packet delivery rate and end-to-end delay, and its comprehensive performance is significantly superior to traditional routing schemes.

We survey our works on the locally analytic vectors of completed cohomology of modular curves.

In recent years, many control problems of autonomous mobile robots have been developed. In particular, the robots are required to be safe; that is, they need to be controlled to avoid colliding with people or objects while traveling. In addition, since safety should be ensured even under irregular disturbances, the control for safety is required to be effective for stochastic systems. In this study, we design an almost sure safety-critical control law, which ensures safety with probability one, for a two-wheeled vehicle based on the stochastic control barrier function approach. In the procedure, we also consider a system model using the relative distance measured by a 2D LiDAR. The validity of the proposed control scheme is confirmed by experiments of a collision avoidance problem for a two-wheeled vehicle under vibration.

Autonomous vehicles (AVs) tend to disrupt the atmosphere and pedestrian experience in urban shared spaces, undermining the focus of these spaces on people and placemaking. We investigate how external human-machine interfaces (eHMIs) supporting AV-pedestrian interaction can be extended to consider the characteristics of an urban shared space. Inspired by urban HCI, we devised three place-based eHMI designs that (i) enhance a conventional intent eHMI and (ii) exhibit content and physical integration with the space. In an evaluation study, 25 participants experienced the eHMIs in an immersive simulation of the space via virtual reality and shared their impressions through think-aloud, interviews, and questionnaires. Results showed that the place-based eHMIs had a notable effect on influencing the perception of AV interaction, including aspects like visual aesthetics and sense of reassurance, and on fostering a sense of place, such as social interactivity and the intentionality to coexist. In measuring qualities of pedestrian experience, we found that perceived safety significantly correlated with user experience and affect, including the attractiveness of eHMIs and feelings of pleasantness. The paper opens the avenue for exploring how eHMIs may contribute to the placemaking goals of pedestrian-centric spaces and improve the experience of people encountering AVs within these environments.

Based on an almost Kodaira-type vanishing result in mixed characteristics of Bhatt, we show that, in the locally analytic completed cohomology of a general Shimura variety, sufficiently regular infinitesimal weights can only show up in the middle degree.

We prove an exact finite-volume symmetry formula for two-point functions in the periodic $N$-state superintegrable chiral Potts spin chain. We show that, for every chain length $L$ and every simultaneous eigenvector of the Hamiltonian and the one-site translation operator, the correlations satisfy $\langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle$ for $1\leqslant r\leqslant N-1$. Hence, whenever $L$ is even, the midpoint correlation $\langle Z_0^r Z_{L/2}^{\dagger r}\rangle$ is real. Then we generalise the three-state chain case to arbitrary $N$ and to every translation eigensector. This resolves a conjecture of Fabricius and McCoy.

Social bots increasingly infiltrate online platforms through sophisticated disguises, threatening healthy information ecosystems. Existing detection methods often rely on modality specific cues or local contextual features, making them brittle when modalities are missing or inputs are incomplete. Moreover, most approaches assume similar train test distributions, which limits their robustness to out of distribution (OOD) samples and emerging bot types. To address these challenges, we propose Multi Granularity Summarization and Domain Invariant Learning (MGDIL), a unified framework for robust social bot detection under domain shift. MGDIL first transforms heterogeneous signals into unified textual representations through LLM based multi granularity summarization. Building on these representations, we design a collaborative optimization framework that integrates task oriented LLM instruction tuning with domain invariant representation learning. Specifically, task oriented instruction tuning enhances the LLMs ability to capture subtle semantic cues and implicit camouflage patterns, while domain adversarial learning and cross domain contrastive learning are jointly employed to mitigate distribution shifts across datasets and time periods. Through this joint optimization, MGDIL learns stable and discriminative domain invariant features, improving cross domain social bot detection through better distribution alignment, stronger intra class compactness, and clearer inter class separation.

This study investigates the characteristics of X-pinch plasmas driven under low current rise rate ($dI/dt$) conditions using soft x-ray spectroscopy combined with the Bennett relation. X-pinch experiments were conducted on the SNU X-pinch device using copper wires at a low $dI/dt$ of 0.2-0.3 kA/ns. The resulting 1-10 keV soft x-ray signals, measured by an x-ray filtered AXUV photodiode array (XFPA), exhibit significant nonlinear effects due to the high intensity of the soft x-ray pulses. This work characterizes the nonlinear behavior of the AXUV-HS5 Si PIN photodiodes under intense pulsed radiation using a pulsed laser. We identified a charge conservation property that the total collected charge remains proportional to the incident pulse energy despite temporal profile distortion. Based on this diagnostic finding, we developed and applied a new framework for plasma parameter estimation. By combining a spherical emission model with the Bennett equilibrium, this approach determines that the soft x-ray source plasma is a 'bright spot', characterized by a plasma density $n_e \sim 10^{21} \text{ cm}^{-3}$, size $d \sim 30-40\ μ\text{m}$, electron temperature $T_e \sim 1 \text{ keV}$, and an emission duration $t_B \sim 1 \text{ ns}$, rather than an extremely compressed 'hot spot'.

This report presents three proofs showing that idealized architectures capable of navigation guided by allocentric maps with landmark structure can be computationally universal. The navigation may occur either online (in the environment) or offline (in the animal's head). The first proof proceeds from a universal two-counter machine by encoding counters as the positions of two movable markers on orthogonal coordinate axes. The second proof directly simulates an ordinary one-tape Turing machine by using a writable tape-path embedded in the map. The third proof strengthens locality by replacing the globally designated path with a two-dimensional field of landmarks that carries only local predecessor/successor information. These constructions are mathematically close to classical graph-based models in computability theory, including Kolmogorov-Uspensky machines, storage-modification machines, graph Turing machines, and related navigation-on-graphs models. Accordingly, the bare universality results are mathematically unsurprising. Nevertheless, the present treatment is, as far as I know, the first self-contained reconstruction of such universality demonstrations in the idiom of allocentric cognitive maps and offline navigation, that is, within an architecture whose core representational and computational primitives are drawn from a body of empirical and theoretical work on spatial navigation. The report therefore reframes known computability-theoretic ideas to show that an allocentric navigation-based architecture can be computationally universal.

We give the explicit formula of the universal $R$-matrix of a double parameter (or two-parameter, or multi-parameter) quantum affine algebra of type ${\mathrm{A}}_1^{(1)}$. For $N$ with $q_{00}q_{01}$ being a primitive $N$-th root of unity, we introduce its $2N$-dimensional representation and explicitly calculate the $R$-matrix associated with it via the universal $R$-matrix.

The bulk-edge correspondence principle, a cornerstone of topological physics, ensures that first-order topological systems host robust chiral edge states in two dimension. This was later extended to higher-order phases, where second-order topological insulators exhibit localized, topologically protected corner states. While the transition between these distinct phases has been demonstrated in periodic systems, its existence in disordered platforms remains an open question. Here, we demonstrate a controllable topological phase transition between a second-order topological phase and a first-order topological phase in a two-dimensional photonic alloy. By tuning the magnetic doping concentration - implemented by attaching permanent magnets randomly to nonmagnetized yttrium iron garnet rods in an alternately magnetized honeycomb lattice with C3 rotational symmetry - we flexibly control the system's topology. At zero doping, we observe higher-order corner states, confirmed by a trivial Chern number and non-zero bulk polarizations of 1/3. As doping concentration increases, these corner states progressively merge with the bulk states, culminating in the closure of the bulk transmission gap. After the bulk transmission gap reopens with further increased doping, the system transitions to a first-order topological phase, characterized by a nontrivial Chern number of -1 and the emergence of a chiral edge state. This transition is reversible, providing a highly tunable and experimentally simple platform for flexibly switching between localized corner states and delocalized chiral edge states within a single photonic system.

This review describes the development and applications of multi-chain coarse-grained simulations for entangled polymer dynamics. The mean-field tube model has long served as the standard paradigm for describing the many-body entanglement problem as the motion of a single chain in a static field; it faces intrinsic limitations when addressing spatial correlations, fluctuations, and complex topological rearrangements. To overcome these limitations, "multi-chain" approaches -- specifically the primitive chain network and multi-chain slip-spring models -- were developed. These simulations explicitly resolve the force balance and topological coupling between multiple chains in three-dimensional space. This review covers the primitive chain network model, which emphasizes real-space force balance, and the multi-chain slip-spring model, which is derived from a well-defined free-energy functional. Linear and nonlinear rheology predictions are discussed, along with molecular mechanisms such as constraint release and stretch/orientation-induced reductions in friction. Extensions to branched polymers, wall-slip phenomena, and network polymers are also mentioned.