In light of Lov & aacute;sz's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, this paper considers a natural variant: what if the vertex-transitivity is relaxed, yet a high degree of symmetry-specifically edge-transitivity-is retained? To investigate this, we focus on the class of semisymmetric graphs, which are regular, edge-transitive, but not vertex-transitive. In this paper, it will be shown that every connected semisymmetric graph of order 2pq, where p and q are two distinct primes contains a Hamilton cycle and that every connected cubic semisymmetric graph of order less than 3000 contains a Hamilton cycle too. Based on these observations, the following question is posed: construct a connected semisymmetric graph which has no Hamilton cycle. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods, often face challenges in generalization and long-time prediction efficiency due to their dependence on full space-time approximations. To address these issues, we propose a novel and scalable framework that significantly enhances the Neural Galerkin Method (NGM) by incorporating the Meta-Auto-Decoder (MAD) paradigm. Our approach leverages space-time decoupling to enable more stable and efficient time integration, while meta-learning-driven adaptation allows rapid generalization to unseen parameter configurations with minimal retraining. Furthermore, randomized sparse updates effectively reduce computational costs without compromising accuracy. Together, these advancements enable our method to achieve physically consistent, long-horizon predictions for complex parameterized evolution equations with significantly lower computational overhead. Numerical experiments on benchmark problems demonstrate that our methods performs comparatively well in terms of accuracy, robustness, and adaptability.
This paper is concerned with the existence and stability of a type of blowing-up positive steady states for a shadow system of the Shigesada-Kawasaki-Teramoto (SKT) two-species competition model and for the perturbed SKT system with a sufficiently large cross-diffusion parameter and bounded random diffusion parameters. The asymptotic behavior of coexistence steady states of the SKT model as one of the cross-diffusion parameters tends to infinity was studied by Lou and Ni [1], who showed that almost all coexistence states can be characterized by one of three shadow systems. In [2], the first author of the present paper studied one of these shadow systems with one cross-diffusion term in one space dimension and proved that one component along a bifurcation branch blows up as the bifurcation parameter approaches the least positive eigenvalue of-Delta under the homogeneous Neumann boundary condition. Using a different approach from that in [2], based on suitable transformations and the Lyapunov-Schmidt reduction, we establish the existence and detailed asymptotic structure of several branches of positive steady states near the blow-up points for shadow systems with one or two cross-diffusion terms in one-and multidimensional domains. We further prove that all the large steady states obtained near the blow-up points are spectrally unstable. Finally, by perturbation arguments, we establish the existence and instability of corresponding branches of positive steady states for the original SKT system when one of the cross-diffusion parameters is sufficiently large.
High-throughput phenotyping platforms enable dense temporal monitoring of plant growth, yet field-based image collection remains labor-intensive with sparse sampling intervals, leading to missing information on intermediate developmental stages. Functional–structural plant models (FSPMs) offer dynamic growth simulation but often lack realistic 3D architecture derived from actual plants. This study proposes a lightweight framework that bridges sparse phenotyping time points by integrating 3D reconstruction with the GreenLab plant growth model, enabling the construction of plant digital twins for rapeseed (Brassica napus L.). Multi-angle smartphone images of four rapeseed cultivars at two key growth stages were used to reconstruct 3D plant architecture via 3D Gaussian Splatting (3DGS). Leaves were segmented from the point cloud to calculate area. GreenLab source and sink parameters were estimated from organ-level fresh weights (leaves, internodes, and roots) measured at two growth stages. The goodness–of–fit was high, with weighted sum of squares (WSS) between 5.63 and 9.33 and Pearson correlation coefficients (r) ranging from 0.93 to 0.95 across the four cultivars. The calibrated model reproduced leaf areas consistent with 3D reconstructed static structures. Reconstructed organ geometries were used for visualization and functional analysis of light interception. The integrated model thus recovered the complete dynamic development and growth trajectory between sparse sampling points. Temporal hold-out validation showed reasonable agreement between reconstructed leaf area and length–width–derived reference estimates, with a single-leaf mean absolute percentage error (MAPE) of 18.42%. Light interception analysis revealed cultivar-specific differences in canopy light use efficiency attributable to contrasting morphological architectures. Simulated and reconstructed canopy light interception showed strong agreement (r=0.98). This framework provides a cost-effective approach to reconstructing plant growth dynamics and evaluating light capture characteristics from minimal field data. It offers practical utility for breeders in cultivar evaluation and for optimizing environmental control strategies in precision agriculture.
Accelerating global climate change has been triggering large-scale vegetation reorganizations, yet our understanding of how mountain ecosystems respond to rapid climatic oscillations is critically constrained. Here, we present a high-resolution palynological record from Erhai Lake, southwestern China that reveals eight episodes of rapid vegetation reorganizations in southern Hengduan Mountains (HMs) over the past 35,200 years. These reorganizations closely tracked the rhythms of rapid climate oscillations, particularly during the Last Glacial Maximum and the Last Deglacial Period. We find that while the timing of rapid vegetation reorganizations was synchronous with Atlantic Meridional Overturning Circulation (AMOC) anomalies that modulated global climate variability, the magnitude of these reorganizations did not exhibit a linear correlation with AMOC strength; instead, they were governed by local heat and moisture availability mediated through teleconnections. Using the Erhai pollen record as a benchmark, we project that rapid reorganizations under the high-emission pathway (SSP585) will possibly surpass the magnitudes documented in the geological record in the coming decades. These findings reveal the high climatic sensitivity and strong natural regulatory capacity of mountain ecosystems in southern HMs, highlighting the critical necessity of climate mitigation actions and nature-based solutions to safeguard subalpine and alpine biodiversity against unprecedented future climate change.
