We apply the light-cone QCD sum rules with chiral currents to compute transition form factors of the semileptonic decay of the charmed and bottom scalar mesons $D/B$ to $a_{0}(980)l^{+}ν_{l}$ $(l=e$, $μ)$, where the scalar meson $a_{0}(980)$ are firstly regarded as two quark states, and contributions from the tetraquark component are then added via proper modulation of four distribution amplitudes considered. The obtained transition form factors and branching fraction are free of the contribution from the light-cone distribution amplitudes at the level of twist-three and two simple relations connecting their form factors are obtained. Our computations indicates that the decay branch fractions are on the margin of the measurements reported by Beijing Spectrometer \uppercase\expandafter{\romannumeral3} in the pure two-quark scenario and are in good agreement with observations when tetraquark component is considered.

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

It is shown that a generalization of the Painlevé-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at different infinities via an asymptotically exact WKB approach. The analysis relies on an exact solution of the quantum mechanical Demkov-Osherov model (DOM). An application to the problem of unstable vacuum decay during a second order phase transition provides precise scaling of the number of excitations, including subdominant contributions.

We introduce FA-matrices for computing ranks of vector bundles of coinvariants and conformal blocks associated with modules over vertex operator algebras on the moduli space of stable pointed curves, unifying the notions of fusion and averaging matrices and generalizing Ueno's work. To illustrate, we compute ranks of vector bundles determined by pointed VOAs and the tensor product of certain VOAs, as well as other examples. As an application, positivity properties of their first Chern classes are analyzed.

The constancy of the speed of light (the maximum velocity of interaction) is the second postulate of Albert Einstein's special theory of relativity. Currently, there is no correct theoretical proof of this constancy in all inertial frames of reference. This paper presents such a proof, demonstrating that quantum mechanics (quantum field theory) can only be formulated under the condition of the constancy of the speed of light in a vacuum. It has been established that this constancy is determined by the minimum energy of the particles. When this minimum is reached, two identical solutions emerge -- one with positive and one with negative energies. Thus, within the framework of classical physics, the existence of particles and antiparticles is demonstrated. It is shown that matter dominates over antimatter.

Ride-hailing platforms increasingly rely on non-exclusive notifications-broadcasting a single request to multiple drivers simultaneously-to mitigate inefficiencies caused by uncertain driver acceptance. In this paper, the first in a two-part collaboration with Lyft, we formally model the 'Notification Set Selection Problem' for a single decision cycle, where the platform determines the optimal subset of drivers to notify for each incoming ride request. We analyze this combinatorial optimization problem under two contention-resolution protocols: 'First Acceptance (FA)', which prioritizes speed by assigning the ride to the first responder, and 'Best Acceptance (BA)', which prioritizes match quality by selecting the highest-valued accepting driver. We show that welfare maximization under both mechanisms is strongly NP-hard, ruling out a Fully Polynomial Time Approximation Scheme (FPTAS). Despite this, we derive several positive algorithmic results. For FA, we present a Polynomial Time Approximation Scheme (PTAS) for the single-rider case and a constant-factor approximation (factor 4) for the general matching setting. We highlight that the FA valuation function can be viewed as a novel discrete choice model with theoretical properties of independent interest. For BA, we prove that the objective is monotone and submodular, admitting a standard $(1 - 1/e)$-approximation. Moreover, using a polynomial-time demand oracle that we design for this problem, we show it is possible to surpass the $(1 - 1/e)$ barrier. Finally, in the special case of homogeneous acceptance probabilities, we show that the BA problem can be solved exactly in polynomial time via a linear programming formulation. We validate the empirical performance our algorithms through numerical experiments on synthetic data and on instances calibrated using real ride-sharing data from Lyft.

A common practice in empirical finance is to construct calendar-aligned panels that implicitly treat all instruments as having existed for the full observation period. When securities with different listing histories are combined without explicit coverage constraints, price histories can be inadvertently extended before valid trading ever began. This paper formalizes this problem and proposes a coverage-aware structuring framework built around instrument-level observation windows encoded through structured metadata and an availability matrix. Applied to end-of-day data from the Dhaka Stock Exchange spanning October 2012 to January 2026 and covering 486 instruments, the framework reveals substantial distortions from naive temporal alignment. ARIMA-based experiments establish the mechanism through which padded observations corrupt return dynamics, and volatility analysis across 53 instruments shows that forward-filling alone suppresses return volatility by roughly 20% on average, with GARCH unconditional variance distortions exceeding 26% in over 90% of instruments - a lower bound, as backward extension to the panel start produces 36.6% suppression and causes GARCH non-convergence in 41% of instruments. The distortion affects any method requiring calendar alignment of heterogeneous histories, including dynamic time warping, covariance-based portfolio construction, factor model regression, and temporal foundation model fine-tuning. Although demonstrated on financial data, the framework applies to any panel combining entities with heterogeneous entry dates, including sensor networks, clinical cohorts, and country-level economic panels. Listing coverage is not a minor preprocessing detail but a first-order variable in panel construction.

The $Δ$SCF DFT approach defines the system energy as a function of orbital occupancy. Inspired by Landau Fermi liquid theory, we develop an occupancy extrapolation (OE) method that captures excited-state energies via a Taylor expansion of the energy with respect to occupation fluctuation from a reference state. OE retains the physics of $Δ$SCF while offering a physical interpretation of excitation energies as sums of quasiparticle energies and their generalized screened interactions. It yields accurate valence, Rydberg, and charge-transfer excitation energies at $O(N^3)$ cost, avoids separate SCF calculations for each excited state, and enables efficient large-scale excited-state simulations from ground-state calculations.

We characterize and phenomenologically model the merger-ringdown of gravitational waves emitted by a small compact object that plunges and merges into a Kerr black hole from equatorial-eccentric inspirals. The waveforms are generated employing a time-domain Teukolsky code sourced with trajectories computed using the effective-one-body framework. We span values of the Kerr spin $a\in[-0.9, 0.9] $, eccentricity at the last stable orbit (LSO) $ e_{\rm LSO} \in [0,0.9] $, and relativistic anomaly $ ξ_{\rm LSO} \in [0 , 2 π]$. We characterize the last peak of the waveform and ringdown features across the parameter space, finding that the eccentricity mainly affects the last peak features, while it has a smaller impact on the ringdown signal. In contrast, the relativistic anomaly measured at the LSO influences the morphology of the last peak in a restricted portion of the parameter space and has no impact on the ringdown part. We perform the analysis for all the spin-weighted spherical harmonic modes normally included in the $\texttt{SEOBNR}$ family of models, $(\ell,m)\in\{ (2,2), (3,3), (4,4), (5,5), (2,1), (3,2), (4,3)\}$. Finally, we introduce a merger-ringdown model for $\texttt{SEOB-TMLE}$, a forthcoming inspiral-merger-ringdown waveform model for eccentric spin-aligned binary black holes in the test-mass limit, whose features can be extended to comparable-mass regimes. The model also accounts for quasinormal mode mixing during the ringdown. It provides a first step toward incorporating the impact of residual eccentricity close to merger into spin-aligned effective-one-body merger-ringdown models for binary black holes.

Space-filling experimental designs are widely used in engineering computer experiments, where only a limited number of expensive model evaluations can be afforded. Distance-based designs such as Maximin or Minimax ensure global space-filling, while Latin hypercube sampling enforces uniform one-dimensional projections, yet neither guarantees uniformity in lowdimensional subspaces. Maximum Projection (MaxPro) designs were introduced to improve uniformity in low-dimensional subspaces, yet their original formulation relies on the Euclidean distance and may induce systematic density distortions in bounded domains. We demonstrate that the standard MaxPro criterion leads to statistically non-uniform sampling, resulting in undersampling of corner regions and biased Monte Carlo estimates. To remedy this issue, we introduce a periodic variant of the criterion, termed Uniform Maximum Projection (uMaxPro), in which the Euclidean metric is replaced by a periodic distance based on the minimum image convention. The proposed uMaxPro designs preserve the projection-aware structure of MaxPro while achieving statistical uniformity of the design-generation mechanism. Numerical experiments show unbiased Monte Carlo integration with reduced variance, excellent subspace projection performance, and competitive discrepancy properties. The methodology is further validated on benchmark engineering problems, including a meso-scale finite element model of concrete, demonstrating improved accuracy in surrogate modeling and probabilistic estimation. The resulting criterion provides a simple and computationally efficient modification of MaxPro that enhances its robustness for nonadaptive computer experiments. The construction algorithm, open-source implementation, and reproducible optimized designs are provided to facilitate practical adoption of the method.

Recent advancements and widespread adoption of Large Language Models (LLMs) in both industry and academia have catalyzed significant demand for LLM serving. However, traditional cloud services incur high costs, while on-device inference alone faces challenges due to limited resources. Edge-cloud collaboration emerges as a key research direction to combine the strengths of both paradigms, yet efficiently utilizing limited network bandwidth while fully leveraging and balancing the computational capabilities of edge devices and the cloud remains an open problem. To address these challenges, we propose Pipelined Collaborative Speculative Decoding Framework (PicoSpec), a novel, general-purpose, and training-free speculative decoding framework for LLM edge-cloud collaborative inference. We design an asynchronous pipeline that resolves the mutual waiting problem inherent in vanilla speculative decoding within edge collaboration scenarios, which concurrently executes a Small Language Model (SLM) on the edge device and a LLM in the cloud. Meanwhile, to mitigate the significant communication latency caused by transmitting vocabulary distributions, we introduce separate rejection sampling with sparse compression, which completes the rejection sampling with only a one-time cost of transmitting the compressed vocabulary. Experimental results demonstrate that our solution outperforms baseline and existing methods, achieving up to 2.9 speedup.

In this work, we derive novel exact solutions describing Schwarzschild-like black holes (BHs) embedded in a Dehnen-type dark matter (DM) halo density profile and investigate their geometric, dynamical, and observational signatures arising from such geometries. We begin by analyzing the horizon structure and spacetime curvature invariants, as well as examining the energy conditions associated with the DM halo. Subsequently, we study the influence of the DM halo on both timelike and null geodesics in the resulting geometry. Finally, we obtain observational constraints on the DM halo parameters by comparing the model predictions with weak-field data from Mercury and the S2 star orbit, as well as strong-field observations from the Event Horizon Telescope (EHT), GRAVITY, and combined (EHT+GRAVITY) datasets for M87* and Sgr A*, employing Bayesian inference and Markov Chain Monte Carlo (MCMC) methods to determine the best-fit values and corresponding upper limits of the model parameters. Our analysis provides valuable insight into probing the potential influence of DM halo environments on spacetime geometry and observable properties of astrophysical BHs, offering an alternative perspective on BH-DM interactions.

Field emission from metals underpinned early vacuum-tube technology, and recent nanoscale engineering made field-emission devices compatible with modern silicon platforms. However, the limited tunability of electron transport in metals has restricted their applicability. Here, we show that noble metals coated with graphene exhibit clean non-monotonic $I-V$ characteristics arising from resonant tunneling through graphene's electronic states, enabled by graphene's atomic thinness and weak electronic hybridization with noble metals. Our approach combines ab-initio interface parameters with exact solutions of the Schrödinger equation for electron transmission across the interface. We analyze two experimentally relevant geometries: a vertical configuration with a flat suspended emitter and a coplanar configuration with sharp electrodes allowing for strong field enhancement and gating. These results establish a practical route to tunable electron transport in metal heterostructures, positioning them as competitive components for air-channel field-emission nanoelectronics.

Rendering fair prices for financial, credit, and insurance products is of ethical and regulatory interest. In many jurisdictions, discriminatory covariates, such as gender and ethnicity, are prohibited from use in pricing such instruments. In this work, we propose a discrimination-insensitive pricing framework, where we require the pricing principle to be insensitive to the (exogenously determined) protected covariates, that is the sensitivity of the pricing principle to the protected covariate is zero. We formulate and solve the optimisation problem that finds the nearest (in Kullback-Leibler (KL) divergence) "pricing" measure to the real world probability, such that under this pricing measure the principle is discrimination-insensitive. We call the solution the discrimination-insensitive measure and provide conditions for its existence and uniqueness. In situations when there are more than one protected covariates, the discrimination-insensitive pricing measure might not exist, and we propose a two-step procedure. First, for each protected covariate separately, we find the measure under which the pricing principle becomes insensitivity to that covariate. Second we reconcile these measures through a constrained barycentre model. We provide a close-form solution to this problem and give conditions for existence and uniqueness of the constrained barycentre pricing measure. As an intermediary result, we prove the representation, existence, and uniqueness of the KL barycentre of general probability measures, which may be of independent interest. Finally, in a numerical illustration, we compare our discrimination-insensitive premia and the constrained barycentre pricing measure with recently proposed fair premia from the actuarial literature.

Scientific visualization pipelines encode domain-specific procedural knowledge with strict execution dependencies, making their construction sensitive to missing stages, incorrect operator usage, or improper ordering. Thus, generating executable scientific visualization pipelines from natural-language descriptions remains challenging for large language models, particularly in web-based environments where visualization authoring relies on explicit code-level pipeline assembly. In this work, we investigate the reliability of LLM-based scientific visualization pipeline generation, focusing on vtk.js as a representative web-based visualization library. We propose a structure-aware retrieval-augmented generation workflow that provides pipeline-aligned vtk.js code examples as contextual guidance, supporting correct module selection, parameter configuration, and execution order. We evaluate the proposed workflow across multiple multi-stage scientific visualization tasks and LLMs, measuring reliability in terms of pipeline executability and human correction effort. To this end, we introduce correction cost as metric for the amount of manual intervention required to obtain a valid pipeline. Our results show that structured, domain-specific context substantially improves pipeline executability and reduces correction cost. We additionally provide an interactive analysis interface to support human-in-the-loop inspection and systematic evaluation of generated visualization pipelines.

Bouncing geodesics have been used as valuable probes of black hole singularities. In the dual boundary theory, the presence of bouncing geodesics is encoded in the analytic structure of correlation functions. Thus, when their existence is related to the presence of a black hole singularity, this presents a practical holographic framework to analyse, diagnose, and classify spacetimes with curvature singularities. To make this intuition precise, we use the Hadamard theory of hyperbolic differential equations to prove that both bulk and boundary retarded propagators diverge whenever two points can be connected by a null geodesic. We clarify why this statement remains valid beyond the geodesic regime (for operators of any dimension) and examine how holographic renormalisation modifies the structure of the dual propagator. We also present a general characterisation of bouncing geodesics and the associated singularities in correlation functions for arbitrary spacetimes. Furthermore, we compare the analytic structure of the correlators in position and momentum space and discuss explicit examples. Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities. In particular, we show an explicit example of a black hole in the self-dual linear axion model, which has a curvature singularity despite the absence of bouncing geodesics.

We report on the cosmic ray mass composition measured by the Telescope Array Low-energy Extension (TALE) hybrid detector. The TALE detector consists of a fluorescence detector (FD) station with 10 FD telescopes located at the Telescope Array (TA) Middle Drum FD Station (itself made up of 14 FD telescopes), and a surface detector (SD) array of scintillators. The array consists of 40 SDs with 400 m spacing and 40 SDs with 600 m spacing. In this paper, we present results on the measurement of the depth of shower maxima ($X_\mathrm{max}$) in the energy range from $10^{16.5}$ eV to $10^{18.5}$ eV collected over five years of the TALE hybrid detector. The $X_\mathrm{max}$ distributions were analyzed and compared with Monte Carlo simulations of proton, helium, nitrogen, and iron primaries, using the QGSJet II-04 hadronic interaction model. Our results indicate that the elongation rate of the mean $X_\mathrm{max}$, which is defined as the slope of $\langle X_\mathrm{max} \rangle$ versus cosmic ray energy, exhibits a break around $10^{17}$ eV. Up to this energy, the composition becomes increasingly heavy, characterized by a growing dominance of heavy nuclei and a steadily decreasing fraction of light primaries. Beyond this energy, the proton fraction increases significantly with energy. These findings suggest a transition from Galactic to extra-Galactic cosmic ray sources around the so-called second knee.

We establish the phase transition and universality for the partition function of time inhomogeneous branching random walks (BRWs) with decreasing variance increment,a model related to two dimensional directed polymers. By modifying Berestycki's GMC framework (removing martingale property dependency) and adapting it to discrete BRWs, we prove that the critical value of time inhomogeneous BRWs coincides with that of time homogeneous ones, and the partition functions converge in L1 in the subcritical regime. We also extend the universality at the critical parameter, showing the same decay rate of partition functions. Our approach reveals the potential for such framework in GMC, which provides a new technical path for martingale free processes and random fields beyond log correlated. Finally, we raise some open problems related to GMC beyond log correlations, branching Brownian motions and directed polymers.

We develop a simulation framework for electrostatic and transport modeling of 2D Topological insulator field-effect transistor (2D TIFETs), based solely on first-principles calculations using density functional theory (DFT). We find that careful consideration of basis set and symmetry constraints in DFT calculations is crucial for determining critical electric field ($E_c$), defined as the electric field intensity at which the topological phase transition occurs. Using ballistic Landauer-B$ü$ttiker formula and local potential profile, the drain current-gate bias voltage ($I_D$-$V_G$) characteristics were obtained and switching behavior was studied. A comparison with the $\mathbf{k}\cdot\mathbf{p}$ model reveals the necessity of DFT calculations for investigating realistic edge dispersions. Our approach provides an efficient and rigorous simulation methodology for mesoscopic transport in 2D TIFETs.

We propose an exotic geometric M-theory dual for the weak coupling Type 0A string: compactification on a sub-Planckian $S^1\vee S^1$ (two circles connected at a point), where strong quantum effects lead to fields living on distinct resolutions of that space. Moreover we argue that tachyon condensation of the 0A theory corresponds to shrinking of one of the two circles leading to the IIA supersymmetric string. We use this and other dualities to provide an F-theoretic description of the axio-dilaton and the tachyonic field of Type 0B and argue for the existence of a strong coupling critical point of the potential using the resulting duality symmetry $Γ_0(2)\subset SL(2,\mathbb{Z})$ when tachyon field vanishes. The existence of this critical point can also be argued using conventional M-theory dualities. If this critical point is unique it is an unstable dS vacuum. Using this we propose a strong coupling conformal fixed point for a non-supersymmetric gauge theory in four dimensions living on coincident $D3^+-D3^-$branes of 0B. More generally we conjecture that the tachyon field can be identified with a pair of points on the torus parameterized by $z$ leading to the full duality group $SL(2,\mathbb{Z})$ acting on $(z,τ)$. We find tantalizing hints that for both 0A and 0B the tachyon fields can be identified with the holonomy of a flat $SU(2)$ gauge field suggesting that we have two copies of the universe interacting with one another as if they are D-branes!

Nuclear spins in $4f$ single-molecule magnets (SMMs) are promising qubits or qudits candidates for quantum information processing due to their relative isolation and reduced susceptibility to environmental disturbances, while hyperfine coupling with the $4f$ moments enables readout and control. So far, the nuclear spin states of individual TbPc$_2$ SMMs have been detected in transport measurements via the spin-cascade effect, in which transitions of the Tb$^{3+}$ magnetic moment coupled to the unpaired ligand electron manifest as conductance jumps in spin-polarized transport. The ligand electron also gives rise to a Kondo effect through its interaction with the metallic contacts. By sweeping a magnetic field along the easy axis of the Tb$^{3+}$ moment, the system is tuned to avoided crossings of the hyperfine levels, such that the magnetic field at which the conductance jumps occur indicates the nuclear spin state. Here, we present a method to read the nuclear spin of $^{163}$DyPc$_2$ ($I=5/2$) using millikelvin spin-polarized scanning tunneling microscopy without the need for magnetic-field sweeps. Instead, hyperfine interactions modify the statistics of the telegraph noise generated by reversals of the Dy$^{3+}$ moment, thereby revealing the nuclear spin state. We observe nuclear spin relaxation times $T_1$ in excess of minutes at \SI{35}{mK}. Furthermore, we drive nuclear spin transitions using a radio-frequency field and detect the resulting nuclear magnetic resonance directly in the tunneling current, as the conductance near the split Kondo peaks depends on the nuclear spin state.

Automated standard cell library extension is crucial for maximizing Quality of Results (QoR) in modern VLSI design. We introduce CellE, a novel framework that leverages formal methods to achieve exhaustive discovery of functionally equivalent subcircuits. CellE applies equality saturation to the post-mapping netlist, generating an e-graph to cluster all functionally equivalent implementations. This canonical representation enables an efficient pattern mining algorithm to select the most area-optimal standard cells. Experimental results show a 15.41% average area reduction (up to 23.64% over prior work). Furthermore, characterization in a commercial flow demonstrates an 8.00% average delay reduction, confirming CellE's superior QoR optimization capabilities.

We compute the vacuum expectation value of the stress-energy tensor of a scalar field on a product spacetime composed of an FLRW background times a compact dimension ($\mathcal{M}^{1, \,d-1} \times \mathcal{S}^1$), where the size of the latter is allowed to vary with time. We modify the standard adiabatic regularization prescription to obtain analytic expressions for both $d=3$ and $d=4$. In the massless and conformally coupled limit, the leading order time-dependent results are consistent with known time-independent Casimir contributions. Furthermore, in this limit the higher-order time-dependent corrections, when the FLRW and compact-dimension scale factors coincide, match known results for ($1+d$)-dimensional FLRW spacetime.

We study multi-variable integrals, that we name Sklyanin-Whittaker integrals, and prove their determinantal formulas. We also discuss a $q$-deformation, a determinantal point process, and associated Mellin--Barnes integrals.

We present a variant of the s-step Preconditioned Conjugate Gradient (PCG) method that combines a Chebyshev-stabilized Krylov basis with a Forward Gauss-Seidel (FGS) iteration for the solution of the reduced Gram systems. In s-step Conjugate Gradient, multiple search directions are generated per outer iteration, reducing global synchronization costs but requiring the solution of small dense Gram systems whose conditioning is critical for stability. We analyze the structure of the Chebyshev Gram matrix and show that its moment-based representation is associated with favorable conditioning properties for moderate step sizes. Building on inexact Krylov theory and on the classical equivalence between FGS and Modified Gram-Schmidt (MGS), we provide a structural analysis and theoretical rationale supporting the use of a small number of FGS sweeps, while preserving the convergence behavior observed in practical regimes. Large-scale experiments on modern NVIDIA GPU architectures demonstrate that the proposed Chebyshev-stabilized, Gauss-Seidel-enhanced s-step PCG achieves convergence comparable to classical CG while reducing synchronization overhead, making it a stable and scalable alternative for current and next-generation accelerator systems.

Smart contracts are fundamental components of blockchain ecosystems; however, their security remains a critical concern due to inherent vulnerabilities. While existing detection methodologies are predominantly syntax-oriented, targeting reentrancy and arithmetic errors, they often overlook logical flaws arising from defective business logic. This paper introduces SmartGraphical, a novel security framework specifically engineered to identify logical attack surfaces. By synthesizing automated static analysis with an interactive graphical representation of contract architectures, SmartGraphical facilitates a comprehensive inspection of a contract's functional control flow. To mitigate the context-dependent nature of logical bugs, the tool adopts a human-in-the-loop approach, empowering developers to interpret heuristic warnings within a visualized structural context. The efficacy of SmartGraphical was validated through a rigorous empirical evaluation involving a large dataset of real-world contracts and a large-scale user study with 100 developers of varying expertise. Furthermore, the framework's performance was demonstrated through case studies on high-profile exploits, such as the SYFI rebase failure and farming protocol flash swap attacks, proving that SmartGraphical identifies intricate vulnerabilities that elude state-of-the-art automated detectors. Our findings indicate that this hybrid methodology significantly enhances the interpretability and detection rate of non-trivial logical security threats in smart contracts.

Consider a viscoelastic fluid of Oldroyd-B type. It is shown that its stress tensor $τ$ and its Newtonian deformation tensor $D(u)$ decay at the same rate, while the elastic part $\varepsilon=τ-2ωD(u)$ decays faster. As a consequence, the stress tensor of a viscoelastic fluid exhibits an almost Newtonian behaviour for large times.

This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of displacement interpolation for data augmentation in handling nonlinear dynamics, we extend its application to more complex and practical scenarios. The framework is designed to correct a computationally inexpensive low-fidelity (LF) model to match an accurate high-fidelity (HF) one by capturing its temporal evolution via displacement interpolation while preserving the problem's physical consistency. The framework is further extended to address systems dependent on a physical parameter, for which we construct a surrogate model using a hierarchical, two-level interpolation strategy. First, it creates synthetic HF checkpoints via displacement interpolation in the parameter space. Second, the residual between these synthetic HF checkpoints and a true LF solution is interpolated in the time domain using the multi-fidelity OT-based methodology. This strategy provides a robust and efficient way to explore the parameter space and to obtain a refined description of the dynamical system. The potential of the method is discussed in the context of complex and computationally expensive diffuse-interface methods for two-phase flow simulations, which are characterized by moving interfaces and nonlinear evolution, and challenging to be dealt with traditional ROM techniques.

Active topological photonic systems enable robust light control and new pathways for semiconductor lasing. However, their intrinsically non-Hermitian nature, combining gain, radiation leakage, and material loss, makes the underlying physics more complex, and prior studies have mostly focused on gain competition while the influence of loss channels is less examined. Here, we experimentally demonstrate radiative-channel-driven topological lasing in a valley photonic crystal consisting of isolated InP nanorods on an insulator, achieving room-temperature single-mode operation within an about 4 lambda scale cavity. Loss-included simulations show that material absorption and radiative leakage can be exploited to establish the lasing pathway. Local off-edge pumping provides spatial evidence of topological edge-guided lasing. Berry-curvature calculations, reflecting unit-cell symmetry breaking, verify the valley-Hall interface in a triangular lattice. Geometry and temperature tuning identify a narrow spectral window where the above-light-line edge branch matches the gain-loss balance and remains decoupled from bulk bands. These results clarify how the loss landscape governs topological lasing and establish a radiative-edge design framework for active topological photonics. The substrate-supported nanorod architecture additionally offers a scalable route for on-chip implementation.

Semantic maps are increasingly utilized in areas such as robotics, autonomous systems, and extended reality, motivating the investigation of efficient compression methods that preserve structured semantic information. This paper studies lossless compression of semantic maps through a novel chain-coding-based framework that explicitly exploits contour topology and shared boundaries between adjacent semantic regions. We propose an extended chain code (ECC) to represent long-range contour transitions more compactly, while retaining a legacy three-orthogonal chain code (3OT) as a fallback mode for further efficiency. To efficiently encode sequences of ECC symbols, a context-adaptive entropy coding scheme based on Markov modeling is employed. Furthermore, a skip-coding mechanism is introduced to eliminate redundant representations of shared contours between adjacent semantic regions, supporting both complete and partial skips via run-length signaling. Experimental results demonstrate that the proposed method achieves an average bitrate reduction of 18\% compared with a state-of-the-art benchmark on semantic map datasets. In addition, the proposed encoder and decoder achieve up to 98\% and 50\% runtime reduction, respectively, relative to a modern generic lossless codec. Extended evaluations on occupancy maps further confirm consistent compression gains across the majority of tested scenarios. The source code is made publicly available at \url{https://github.com/InterDigitalInc/LosslessSegmentationMapCompression}.