Mesoscopic traffic flow models combines the merits of both macroscopic and microscopic models by capturing individual vehicle behavior in great detail and remaining the computational efficiency. At the time of this study, the mesoscopic model proposed by Eissfeldt (2004) is used in Simulation of Urban MObility (SUMO). The movement of vehicles is governed by dynamic headways between edges. However, the model does not fully comply with the principle of the Lighthill-Whitham-Richards (LWR) model. Several problems are identified, including the incomplete consideration of queue dynamics and the limited implementation of backward traveling spaces. Two case study scenarios demonstrate that the problems lead to unrealistic onset and recovery pattern of congestion. The magnitude of congestion is generally underestimated with this model. To address these drawbacks, a proper mesoscopic discrete-time implementation of link transmission model, which follows the LWR principle, is proposed. By explicitly incorporating backward traveling spaces to capture queue spillback phenomena, the proposed model provides a more precise representation of congestion dynamics. The link density outputs are consistent with the kinematic wave theory and the microscopic traffic simulation in SUMO, thus verifying its theoretical accuracy.

We present a combined X-ray diffraction and transmission electron microscopy study of superconducting FeSe/FeTe multilayers grown by molecular beam epitaxy on SrTiO$_3$(001) substrates. While X-ray diffraction confirms perfect in-plane epitaxial alignment between FeSe, FeTe, and the substrate, scanning transmission electron microscopy reveals a surprising lack of atomic registry at the FeSe/SrTiO$_3$ interface. Instead of adapting to the substrate lattice, FeSe retains its own in-plane lattice spacing. A periodic lateral shift between the atomic positions of FeSe and SrTiO$_3$ is observed, with a registry recurrence length that matches the lattice mismatch determined by X-ray diffraction. No misfit dislocations or other relaxation features are detected at the interface. This coexistence of directional alignment and registry-free growth suggests an unconventional regime of epitaxy in which crystallographic orientation is maintained without atomic matching. The findings offer insight into strain accommodation in layered systems and may have implications for interface engineering in Fe-based superconductors.

We classify the long-time decay rate in dispersive estimates for the Schrödinger and wave equations on non-trapping asymptotically conic manifolds and exact metric cones in terms of the intensity of geometric focusing. Letting $X_0$ be a metric cone, one of our main results demonstrates that each multiplicity of conjugate points within distance $π$ on $Y=\partial X_0$ leads to a $|t|^{1/2}$-loss in the long-time decay order and a half-order shift in the regularity index in the dispersive estimate for the Schrödinger equation. Unexpectedly, conjugate point pairs on $Y$ at distance $π$ do not cause loss when the Legendre submanifold carrying the wave propagation satisfies a natural admissible condition that we propose. In sum, we give a robust framework for proving dispersive estimates that is stable under geometric perturbations and also accommodates perturbations by potentials.

Accurate prediction of the material behavior of polymer nanocomposites under various thermomechanical loading conditions is increasingly demanded for engineering applications. This study proposes an integrated framework combining coarse-grained (CG) molecular simulations and experimental testing to develop predictive constitutive models for nanoparticle/epoxy nanocomposites. The key contribution of this work lies in characterizing the influence of nanoparticle content and agglomerate size on the rate- and temperature-dependent behavior of nanocomposites, enabled by large-scale CG simulations. The proposed framework successfully captures the material response, including nonlinear hyperelasticity, softening behavior, and rate- and temperature-dependent properties, across a broad range of strain rates, temperatures, and nanoparticle sizes and weight fractions. The predictive capability of the CG simulation-informed constitutive model is validated using additional experimental data that were not included in the parameter identification process. By reducing reliance on extensive experimental testing while maintaining high accuracy, this simulation-driven approach offers an efficient pathway for developing robust, predictive constitutive models for designing and optimizing advanced nanocomposites.

The intrinsic symmetry breaking in the breathing kagome lattice of layered Nb$_3$Cl$_8$ provides a unique mechanism for realizing electrically polar surfaces. In each monolayer, the trimerization of Nb atoms breaks inversion and mirror symmetries, generating an out-of-plane electric dipole. The AB-stacked $α$ phase arranges adjacent layer dipoles antiferroelectrically, leaving the uncompensated surface polarization strictly governed by layer parity. Here, using atomic force microscopy operated in Kelvin probe force microscopy mode, we directly visualize layer-dependent polarization states in exfoliated Nb$_3$Cl$_8$ flakes and resolve a pronounced odd-even oscillation of the surface electrostatic potential. Beyond this parity-locked antiferroelectric order, we further identify intralayer polar domains in which local atomic reconstructions of the breathing kagome network reverse the out-of-plane dipole of the surface layer, producing ferroelectric-like stacking configurations. By interfacing monolayer MoSe$_2$ with Nb$_3$Cl$_8$, we demonstrate that these surface-polarization textures effectively modulate adjacent excitonic emission through domain-dependent interfacial band alignment and charge transfer. Our findings establish Nb$_3$Cl$_8$ as an intrinsic layer-polarized van der Waals platform and show that layer parity provides powerful structural degree of freedom for programming excitonic and optoelectronic responses at van der Waals interfaces.

The Material Point Method provides an effective approach for modelling the large deformations that often arise from contact interactions between rigid structures and surrounding continua. However, solving these problems requires accurate representation of the continuum-structure interface, which necessitates high resolution background mesh and material point discretisations. This requirement, combined with evolving continuum-structure interfaces and the fact that most Material Point Method implementations are dependent on structured meshes, can result in large numerical systems and long run times especially when modelling problems in three-dimensions. Motivated by this issue, this paper provides the first octree-based implicit Material Point Method for efficient solution of large deformation continuum-structure interaction problems. The octree background mesh provides a natural way to automatically adapt both the computational mesh and the material point discretisation based on the position of the interaction between the structure and continuum. The new approach is demonstrated on a number of large deformation benchmark and continuum-structure interaction problems, where up to a 5.5-times speed up and a consequent 21-times CO2 saving is achieved when running on a HPC compared to results obtained using a conforming mesh.

This paper develops a methodological framework for reverse stress testing (RST) in which a multivariate stress scenario, coherent with the empirical dependence structure of a market, is reconstructed from a single exogenous shock prescribed on one asset class. The problem is formulated as the maximisation of the conditional density given the imposed shock, and is solved under three progressively weaker distributional assumptions. In the parametric setting, joint Gaussianity of the returns yields a closed-form modal scenario coinciding with the conditional mean of the non-shocked components. In the semiparametric setting, the modal scenario is estimated nonparametrically through the empirical likelihood methodology and the surrounding stressed trajectories are generated via a Gaussian or Student-t local sampling scheme. In the fully nonparametric setting, stressed trajectories are obtained by inverse-distance resampling of the historical observations within a Mahalanobis neighbourhood of the estimated scenario. The three variants are validated on real market data. The simulated scenarios prove to be economically coherent and capable of reproducing the standard risk-reward asymmetry observed in stressed market regimes.

These pedagogical notes provide an introduction to nonlinear filtering for diffusion processes. The objective of nonlinear filtering is to estimate an unobserved stochastic state from partial and noisy observations, and thereby characterize the conditional distribution of the state given the observation history. After introducing the state-observation model, we develop the main tools of the theory, including Markov semigroups, infinitesimal generators, and change-of-measure methods. This leads naturally to the Kallianpur-Striebel formula, the Zakai equation for the unnormalized filter, and the Kushner-Stratonovich equation for the normalized filter. The presentation follows, to a large extent, the classical exposition of Bain and Crisan's "Fundamentals of Stochastic Filtering", while placing particular emphasis on intuition, motivation, and the interpretation of the main concepts and equations. Many technical arguments are revisited, with additional details and comments intended to facilitate a first reading of the subject. These notes are not intended to be an exhaustive account of stochastic filtering. Their aim is instead to provide a guided tour of some of its central ideas, methods, and equations.

This paper studies O'Neil-type convolution inequalities in local and generalized Morrey spaces on the n-dimensional torus. We extend classical Minkowski and Young inequalities to the Morrey setting and obtain boundedness results for convolution operators. The main result is a generalization of O'Neil's inequality from Lorentz spaces to Morrey-type spaces via dyadic decompositions. We derive norm estimates for convolution operators between Morrey spaces with different parameters and characterize the admissible range of exponents ensuring boundedness. The proof relies on interpolation theory for Morrey spaces, Köthe duality, and real interpolation methods. We also establish embedding relations between local and generalized Morrey spaces. These results extend classical convolution inequalities and unify Lorentz and Morrey frameworks, with applications to partial differential equations and harmonic analysis.

We solve a boundary value problem arising from Maxwell's equations in the quasi-static approximation, which governs the time evolution of the so-called weighting potential $V_{\mathrm{w}}(t,x)$ in resistive solid-state particle detectors. The model reduces to the third-order time-dependent PDE $$ \varepsilon\,\partial_t ΔV_{\mathrm{w}}(t,x) + \mathrm{div}\,\big(σ(x)\nabla V_{\mathrm{w}}(t,x)\big)=0 \quad\text{in } [0,T]\timesΩ,$$ supplemented with mixed Neumann-Dirichlet boundary conditions, possibly degenerate. Our analysis is based on the decomposition of the weighting potential into a static and a dynamic component. The static part solves a uniformly elliptic mixed boundary value problem, while the dynamic part satisfies a degenerate parabolic Cauchy problem. We also establish interior regularity results.

We define a winding number within the Non-Bloch band theory framework that captures the emergence of magnon edge modes in a one-dimensional antiferromagnetic spin chain, even when the conventional Bloch winding number is trivial. Within linear spin-wave theory, magnon excitations are governed by a non-Hermitian dynamic matrix, despite the underlying Hamiltonian being Hermitian. The symmetry classification of this matrix yields a trivial bulk invariant, however, finite systems exhibit boundary-localized modes, signaling a breakdown of the conventional bulk-boundary correspondence. We further show that these edge modes can be controlled via boundary perturbations. By tuning the boundary potential, the modes can be driven into or out of the bulk spectrum. To resolve the bulk-boundary mismatch, we develop a non-Bloch framework based on a generalized Brillouin zone and a winding number that correctly predicts the presence of edge states. Our results establish boundary-controlled topological transitions that are experimentally accessible through local Zeeman fields or modified edge anisotropy in antiferromagnetic van der Waals nanostructures.

In soft condensed matter, curvature does more than simply distort an ordered medium: it helps select defect structures, redistribute elastic stress, bias chirality, and guide self-assembly. This review examines how curved, multiply connected, and knotted boundaries in liquid-crystal colloids and confined nematics generate topological defects and localized solitonic textures, and how these structures mediate interactions between mesoscale building blocks. We introduce a unifying framework based on genus, Euler characteristic, anchoring, and chirality, and use it to discuss spherical, handlebody, and boundary-bearing colloids, together with droplets and polymer-dispersed nematics of nontrivial topology. Particular emphasis is placed on the interplay of geometry and topology in determining boojums, disclination loops, hedgehog charges, and linked and knotted defect structures. We then turn to chiral systems hosting skyrmions, torons, hopfions, and related localized textures, highlighting how chirality and confinement stabilize three-dimensional topological states. Finally, we discuss how these concepts translate into design principles for controlled self-assembly, templating, and functional composite materials. More broadly, we argue that liquid-crystal colloids and confined nematics provide experimentally accessible model systems in which curvature, topology, and chirality can be harnessed as programmable tools for designing organized soft matter.

Functional ultrasound (fUS) has emerged as a powerful neuroimaging modality due to its high resolution in both space and time, low cost and potential portability. Nevertheless, fUS signals provide only indirect observations of neuronal activity through the neurovascular coupling, and hence require the blind separation of latent neuronal sources while also deconvolving their hemodynamic responses. In this work, we propose a data-driven convolutive block-term tensor decomposition-based model for multi-trial fUS measurements, where each source has a spatiotemporal representation comprising a low-rank spatial map and a piecewise-constant neuronal activation signal convolved with a trial- and source-dependent hemodynamic response function (HRF) with a physiologically plausible shape. We propose a constrained optimization framework for the model computation, which consists of alternating projected gradient descent iterations. Simulation results are reported that demonstrate accurate recovery of spatial maps and reliable estimation of activation temporal profiles across various noise levels, while confirming that HRF estimation remains the most challenging part of the problem.

Let $π:E\to Q$ be a fibred manifold, with $\dim Q=n$ and rank $m$. We prove that the Cartan distribution $C^r_π$ on $J^rπ$ is an $N^r_π$-contact distribution, where $N^r_π=m\binom{n+r-1}{r-1}$, by giving a natural local construction of an $N^r_π$-contact form. This recovers the canonical structure of $J^rπ$ and the Spencer contractions, among other structures. It also yields a natural local Hamiltonian structure on $J^rπ$, recovering and extending the standard theory of characteristics to general Lie symmetries of the Cartan distribution. We introduce new classes of polarisations for $k$-contact distributions. This leads to our main recognition theorem, which shows that a polarised $k$-contact manifold is locally equivalent to a finite-order jet bundle with its Cartan distribution precisely when its polarisation is of jet type. This characterises finite-order jet geometry as polarised $N_π^r$-contact geometry of jet type. Moreover, the highest-order vertical polarisation, the symbol spaces, the vertical and horizontal differentials, holonomic submanifolds, and initial conditions for differential equations are reconstructed via $k$-contact geometry. For instance, adapted coordinates become $k$-contact Darboux coordinates, solutions of PDEs are treated as polarised Legendrian submanifolds, jet prolongations are recovered as polarised Legendrian prolongations, and so on. The resulting formalism gives a deeper geometric understanding of several parts of jet geometry, provides a uniform intrinsic language for constructions that are awkward in a single fixed jet presentation, such as Bäcklund transformations, and allows jet theory to be extended to new problems. In particular, our techniques provide very general reduction methods for PDEs. The results are applied to PDEs with mathematical and physical relevance.

Ga$_2$O$_3$/GaAs heterojunctions are emerging as promising candidates for next-generation power electronics, photonics, and energy devices, leveraging the high breakdown voltage and thermal stability of Ga$_2$O$_3$ alongside the mature technology, high hole mobility, and higher refractive index of GaAs. The efficiency of these devices depends strongly on the band alignment between the two materials, however both type-I and type-II alignment have been reported in the literature for these heterostructures. To address this ambiguity, we use hybrid density functional theory to systematically investigate the band alignment at GaAs/Ga$_2$O$_3$ interfaces, focusing on the role of interface chemistry. By considering Ga-O-, As-, and As-O-rich interfaces both in amorphous and crystalline Ga$_2$O$_3$ phases, we demonstrate that interface stoichiometry determines the alignment type: Ga-O-rich interfaces exhibit type-II alignment with large valence band offsets (~3.1 eV), while As-rich and As-O-rich interfaces favor type-I alignment with reduced offsets (~2.3-2.6 eV). These trends are attributed to interface dipole formation driven by bonding configuration. Our findings provide insight into the relationship between chemistry and band alignment in GaAs/Ga$_2$O$_3$ heterostructures, enabling targeted optimization for specific device applications.

Recently, topological MV-algebras have been investigated by several mathematicians. In this paper, we find that every topological \(MV\)-algebra is a Mal'tsev space introduced by Mal'tsev in 1954. Hence, applying the theorem of Reznichenko and Uspenskij on pseudocompact Mal'tsev spaces, we show that the product of arbitrary family of pseudocompact topological \(MV\)-algebras are pseudocompact. We also prove that every $σ$-compact topological \(MV\)-algebra is ccc. Secondly, we obtain that the Stone-Čech compactification of a pseudocompact topological \(MV\)-algebra carries a natural compact topological \(MV\)-algebra structure extending the original one. Finally, we prove that: let \(I\) be a closed ideal in a pseudocompact topological \(MV\)-algebra \(A\) and \(ι_1:A\hookrightarrow\bet A\) is the naturally injective; then \(\cl_{βA}ι_1(I)\) is a closed ideal of \(βA\) and \( βA/\cl_{βA}ι_1(I)\cong β(A/I)\).

We present the first systematic calculations of $ϕ$-, $η_c$-, and $J/ψ$-nucleus ground states up to mass number $A{=}12$ based on the HAL QCD meson-nucleon potentials at near-physical point. The $(A{+}1)$-body Schrödinger equation is solved with a neural-network variational Monte Carlo framework, generalized to incorporate mesonic degrees of freedom. Benchmarking on light nuclei from $^2$H to $^{12}$C yields ground-state energies consistent with experiment. Meson-nucleus bound states emerge at $A\ge2$ for $ϕ$, $A\ge4$ for $J/ψ$, and $A\ge6$ for $η_c$. The $ϕ$-nucleus systems exhibit the strongest binding, with binding energies reaching tens of MeV. The $J/ψ$-nucleus and $η_c$-nucleus systems are weakly bound at the few-MeV and sub-MeV scale, respectively. The binding energy per nucleon deepens nearly linearly with $A$ for charmonium systems, whereas the $ϕ$-nucleus system exhibits a non-monotonic behavior peaking at $^4$He -- a distinctive hallmark of the short-range and strongly attractive $ϕN$ interaction. The meson compresses the nucleon distribution relative to the parent nucleus, and evolves from a halo configuration to one embedded inside the nucleus with increasing $A$. Our results provide predictions for future experimental searches, and establish a quantitative bridge between lattice QCD meson-nucleon interactions and the emergent many-body phenomena in meson-nucleus bound states.

We carried out radiometric calibration of the Visible Emission Line Coronagraph (VELC) onboard Aditya-L1 at 5303Å using observations of the Sun itself, a novel approach compared to the calibration using bright stars in the other currently operational space solar coronagraphs. The measured VELC detector count corresponding to the center of Sun's disk is ${\approx}(1.70{\pm}0.12){\times}10^{8}\, \rm sec^{-1}Å^{-1}$, which relates to Sun's flux at 1\,AU in 5303Å, ${\approx}3.0456{\times}10^{6}\, \rm {erg\,sec^{-1} cm^{-2} Å^{-1}}$. We verified the above calibration using observations of the bright star Sirius-A whose estimated flux at 1\,AU in 5303Å is ${\approx}1.44{\times}10^{-8}\,\mathrm{erg\,sec^{-1} cm^{-2} Å^{-1}}$. The expected detector count with VELC in this case is ${\approx}19{\pm}1.4\, \rm sec^{-1}Å^{-1}$, and the measured count is ${\approx}23{\pm}0.4\, \rm sec^{-1}Å^{-1}$. The reasonable agreement between the expected and observed values for Sirius-A in this initial consistency check after two years of observations with VELC, indicates that measurements of coronal brightness at 5303Å with the VELC and its conversion into absolute physical units using observations of the Sun disk light are in order. Using the Sirius-A observations we measured the point spread function (PSF) of the VELC in its 5303Å channel also. Its full width at half maximum (FWHM) is ${\approx}3.8^{\prime\prime}$.

The elastic properties of the neutron-star crust are important for the calculations of crustal modes. In particular, the ability of the crust to support shear stresses has been connected to observations of quasi-periodic oscillations and to crust deformations potentially emitting gravitational waves. In this work, we assess the uncertainties in the shear modulus and shear speed in the neutron-star outer and inner crust. To this aim, we performed a Bayesian analysis of the shear properties of the neutron-star crust at zero temperature starting from both a non-informative and a nuclear-physics-informed prior. For the treatment of inhomogeneous matter in the crust, we relied on the one-component plasma approximation, with a (semi-)classical treatment of the ions. We show that the use of a nuclear-physics-informed prior has a non-negligible impact on the prediction of the elastic properties of the crust. The frequency of the fundamental torsional crustal modes we obtain is compatible with the low-frequency range of observed quasi-periodic oscillations, our estimates lying in the interval $\approx 20 - 50$~Hz. Although the different considered priors lead to compatible results, the inclusion of nuclear-physics experimental information in the prior considerably reduces the uncertainties in the prediction of the elastic properties of the crust, potentially constraining the predicted frequency of the crustal modes.

Ferroelectricity, typically arising from ionic displacements in noncentrosymmetric lattices, enabling applications in memory devices and sensors. Recent advances in two-dimensional materials and van der Waals heterostructures have revealed novel ferroelectric phenomena, including sliding ferroelectricity and correlation-driven ferroelectricity in moire superlattices. In this work, we fabricate and study a MoS2/WSe2 moire superlattice device exhibiting a high field-effect mobility of 17,650 $cm^2V^{-1}s^{-1}$. Electrical transport measurements reveal correlated insulating states accompanied by a prominent and reproducible resistance hysteresis near half filling. Temperature and displacement field dependence further confirms the correlation-enhanced nature of the hysteresis. Our analysis suggests that displacement field-induced metal-to-insulator transition at correlated insulating state coupled with interfacial dipoles enables the observed resistance hysteresis. These results establish correlation enhanced resistance hysteresis near half filling in a MoS2/WSe2 heterobilayer, offering opportunities for exploring emergent quantum phases and device functionalities.

The rapid diffusion of generative artificial intelligence (genAI) systems reshapes how individuals engage with information systems, requiring users to monitor, assess, and adapt their interaction with non-deterministic systems. Existing constructs capture elements of this engagement but do not account for the situated dynamics of the entire evaluative process in genAI use. This research-in-progress, situated in a larger endeavour towards a scale development, derives an initial conceptualisation of reflective use: a behavioural-knowledge capability that unfolds across pre-use, in-use, and post-use phases, reinforced through situated reflective knowledge gained in practice. Drawing on expert interviews and a focus group, we identify four core components of reflective use and show how they form an iterative capability cycle anchored within the motivational needs outlined in self-determination theory. Understanding reflective use is essential to ensure appropriate reliance and high decision quality, and thus provides a foundation for promoting responsible and effective human-AI interaction.

We investigate the implications of the behavior of geodesics in static, cylindrically symmetric spacetimes with a non-zero cosmological constant. We consider the symmetries of these spacetimes to restrict admissible ranges of the metric parameters and to formulate an intuitively plausible interpretation of the coordinates.

Extreme mass ratio inspirals (EMRIs) are among the primary targets for space-based gravitational-wave (GW) detectors, providing valuable opportunities to study stellar-mass compact objects orbiting supermassive black holes (SMBHs) and to probe gravity in the strong-field regime. As the LISA, TAIJI, and TianQin missions are expected to operate around 2035, joint observations by multiple detectors may provide enhanced measurement capabilities compared to individual missions. In this work, we investigate the detectability and parameter-constraint prospects for EMRIs using global detector networks composed of LISA, TianQin, and two alternative TAIJI orbital configurations. Employing Fisher information matrix analysis, we find that joint observations improve source localization relative to a standalone LISA mission, with sky-localization uncertainties reduced by up to two orders of magnitude for a one-month observation period. We further find that a three-detector network (LISA-TAIJI-TianQin) operating for one month yields parameter constraints comparable to, and in some cases tighter than, those obtained from a one-year observation by LISA alone. This result indicates that network observations can partially compensate for shorter observation durations in parameter inference. Furthermore, we evaluate measurement uncertainties in concurrent dual-signal scenarios: (i) two EMRIs orbiting the same SMBH and (ii) two EMRIs with identical intrinsic parameters but different sky locations and orientations. The results indicate that differences in the detector responses associated with the source geometries reduce correlations between overlapping signals, allowing the sources to remain distinguishable even for a standalone mission. The inclusion of multiple detector constellations further improves source localization and tightens parameter constraints in these concurrent-source scenarios.

We prove that the asymptotics of the Hermitian-Yang-Mills flow on a slope semistable holomorphic vector bundle over a compact Kähler manifold are determined algebro-geometrically, via the iterated filtration defined by Haiden-Katzarkov-Kontsevich-Pandit. This proves a conjecture of Haiden-Katzarkov-Kontsevich-Pandit in this setting. Moreover, we prove a non-linear analogue, relating the asymptotics of the Calabi flow near a cscK manifold to the iterated balancing filtration of the deformation space. In both settings, we reduce the infinite-dimensional flow to a finite-dimensional flow, following the foundational work of Chen-Sun. In finite dimensions, we prove that the asymptotics of the moment map flow are determined by the iterated balancing filtration, proving a conjecture of Ibáñez Núñez.

MRI simulation often separates two descriptions that are both essential for realistic sequence analysis: Bloch dynamics for waveform-resolved radiofrequency (RF) excitation, and phase-graph methods for coherence-pathway evolution. Extended Phase Graph (EPG) models provide pathway tracking, and Phase--Distribution Graphs (PDG) extend this idea to spatially resolved $k$-space simulation, but existing PDG formulations rely on hard-pulse RF mixing that is \emph{order-local}: the RF pulse mixes $F_n^+$, $F_n^-$, and $Z_n$ at a fixed coherence order $n$, without coupling different $k_z$ orders. This work introduces a unified Bloch-resolved PDG framework for slice-profile-aware MRI simulation. A scanner-rasterized sequence is partitioned into RF-sensitive Bloch spans and non-RF phase-graph spans. For each unique RF span, Bloch dynamics are solved on a slice grid to obtain a spatially varying propagator $R(z)$. Its Fourier coefficients $\mathcal{R}_Δ$, indexed by slice-order offset $Δ$, are compiled into the PDG state graph as sparse cross-order coupling in $k_z$. Graph growth is controlled by retaining the dominant Fourier coefficients and pruning low-contribution PDG states. This retains PDG pathway history and voxel-wise image formation while incorporating shaped slice-selective and off-resonant RF behavior. Experiments show close agreement with direct one-dimensional Bloch slice-profile evolution through repeated excitations, while retaining only a few hundred active PDG states. Image simulations further illustrate slice-position dependence, fat-suppression behavior, measured three-dimensional $B_0$ field maps, and comparison with scanner data. The proposed framework enables sequence-consistent simulation and signal formation understanding in regimes where RF physics, spatial encoding, object heterogeneity, and echo-pathway formation interact.

Based on the tight-binding model and the semiconductor Bloch equations, this work systematically reveals the microscopic mechanism of strain engineering in turning of third-harmonic generation (THG) in monolayer black phosphorene (BP). % The results show that under strain-free conditions, monolayer BP exhibits significant in-plane anisotropy, and its dominant susceptibility component reaches a maximum of $χ^{(3);xxxx} = 1.8 \times 10^{-17} \, \text{m}^2/\text{V}^2$, agreeing well with the experimental results. % By applying uniaxial and biaxial strains along the armchair ($x$), zigzag ($y$), and out-of-plane ($z$) directions, we find that the THG response presents strong direction dependence and unique spectral shifting behaviors: in-plane compressive strain and out-of-plane tensile strain both significantly enhance the THG conductivity and induce a redshift, whereas in-plane tensile strain and out-of-plane compression lead to suppression and a blueshift, with the tuning efficiency following the order of $z > y > x$. The microscopic origin of these phenomena is identified as the synergistic modulation of the bandgap and Berry connection by strain. % Furthermore, the synergistic or competitive effects of biaxial strain further enrich the manipulation of THG signals. % Strain engineering can serve as an effective strategy for dynamically controlling nonlinear optical processes in two-dimensional materials, and it also lays a theoretical foundation for the development of high-performance reconfigurable infrared photonic devices.

We study partial orders induced by constrained variants of finite graph homomorphisms: monomorphisms, embeddings, full homomorphisms, vertex-surjective, edge-surjective and surjective homomorphisms, and locally injective, locally surjective and locally bijective homomorphisms. For each order we ask for analogues of the standard structural properties of the graph homomorphism order: canonical cores, past- or future-finiteness, universality, gaps and finite dualities. The comparison shows which phenomena are specific to ordinary homomorphisms and which are consequences of simpler order-theoretic mechanisms. We identify cores for full and surjective homomorphisms, relate full-homomorphism cores to point-determining graphs, characterize gaps in the full homomorphism order, and give finite obstruction bounds for several one-sided finite orders. We also analyze locally constrained homomorphisms on connected graphs. In particular, locally injective homomorphisms have all connected graphs as cores, admit infinite-chain density under natural degree-refinement assumptions, have explicit gap witnesses, and are universal already on finite connected bipartite subcubic cactus graphs. The paper reorganizes and extends several earlier arguments into a single framework for constrained homomorphism orders.

Fallback accretion in collapsar models is often associated with underluminous gamma-ray bursts (GRBs), leading to the widespread view that fallback-fed engines may be intrinsically inefficient at producing high-luminosity events. In this Letter, we present GRB 250706B/C, a luminous long GRB observed by \textit{Insight}-HXMT that exhibits an unusual combination of extreme short-timescale variability and coherent large-scale temporal evolution. The prompt emission contains at least 79 resolved pulses and a minimum variability timescale of $\sim11$ ms. The pulse widths are nearly independent of photon energy and span a broad distribution with a median FWHM of $\sim0.30$ s, while the waiting times between adjacent pulses have a median of $\sim0.38$ s. The prompt-emission envelope exhibits a prolonged rise described by $F(t)\propto (t-t_0)^{0.47\pm0.01}$ followed by a rapid decline. Despite substantial pulse-to-pulse fluctuations, neither the pulse widths nor the waiting times show significant secular evolution during the main emission episode. These features indicate the coexistence of two distinct temporal components, including a slow evolving rising luminosity envelope and rapid stochastic variability. Such behavior is consistent with scenarios in which a time-dependent engine-feeding history regulates the large-scale emission while internal dissipation within the relativistic outflow produces the pulse structure. Within this context, GRB~250706B/C may represent a fallback-fed collapsar operating on a high-luminosity branch, suggesting that fallback itself does not necessarily limit the luminosity scale of GRBs.

We consider the asymptotic behaviour of topological indices of random caterpillar graphs, such as the Zagreb, $α$-Randić, Wiener, Gini and level indices, as the size of the graph grows. Our simple, general framework, which is based on a multivariate central limit theorem, the continuous mapping theorem and Slutsky's theorem, can also be used to cover other topological indices. We derive limit laws for these indices and provide exact and asymptotic results on their means and variances. The $α$-Randić index exhibits a discontinuity in its limit distribution at $α=\frac{1}{2}$.

We examined the applicability of observational data-driven magnetohydrodynamic (MHD) simulations to flare prediction. The target event was the X1.6 flare that occurred in NOAA AR 13663 at 02:22 UT on 3 May 2024. We employed a velocity-driven model, in which the photospheric velocity field was derived from the time-series magnetograms to use as the boundary input. The simulation showed a rapid increase in both thermal and kinetic energy density around the actual onset time and location of the X1.6 flare. We revealed that the flare was triggered by two-step reconnection, in which the initial tether-cutting reconnection facilitated the subsequent breakout reconnection. We further examined whether the flare could be reproduced when the boundary input was stopped prior to the actual flare onset time, assuming the situation in which the flare must be predicted using the data before it actually occurs. When the photospheric magnetic field was fixed more than 1 hour before the actual flare onset time, the flare was not reproduced in the simulations. In contrast, when the photospheric velocity field at the final observation time was incorporated to infer the subsequent magnetic evolution, the prediction lead time could be extended beyond 1 hour. On the other hand, quantitative prediction of the magnitude of flares remains a subject for future study.