Disproof of a conjecture on the minimum spectral radius and the domination number

Let $G_{n,\gamma}$ be the set of all connected graphs on $n$ vertices with domination number $\gamma$. A graph is called a minimizer graph if it attains the minimum spectral radius among $G_{n,\gamma}$. Very recently, Liu, Li and Xie [Linear Algebra and its Applications 673 (2023) 233--258] proved that the minimizer graph over all graphs in $\mathbb{G}_{n,\gamma}$ must be a tree. Moreover, they determined the minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for even $n$, and posed the conjecture on the minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$. In this paper, we disprove the conjecture and completely determine the unique minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$

Quadratic Embedding Constants of Graph Joins

The quadratic embedding constant (QE constant) of a graph is a new characteristic value of a graph defined through the distance matrix. We derive formulae for the QE constants of the join of two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite graphs, wheel graphs, friendship graphs, completely split graph, and some graphs associated to strongly regular graphs.Comment: 20 page

DEVELOPMENT OF MINIATURIZED EXTRACTION METHODS WITH ADVANCES OF NOVEL SORBENT MATERIALS FOR ENVIRONMENTAL ANALYSIS

Ph.DDOCTOR OF PHILOSOPH

Belowground Rhizomes in Paleosols: The Hidden Half of an Early Devonian Vascular Plant

The colonization of terrestrial environments by rooted vascular plants had far-reaching impacts on the Earth system. However, the belowground structures of early vascular plants are rarely documented, and thus the plant−soil interactions in early terrestrial ecosystems are poorly understood. Here we report the earliest rooted paleosols (fossil soils) in Asia from Early Devonian deposits of Yunnan, China. Plant traces are extensive within the soil and occur as complex network-like structures, which are interpreted as representing long-lived, belowground rhizomes of the basal lycopsid Drepanophycus. The rhizomes produced large clones and helped the plant survive frequent sediment burial in well-drained soils within a seasonal wet−dry climate zone. Rhizome networks contributed to the accumulation and pedogenesis of floodplain sediments and increased the soil stabilizing effects of early plants. Predating the appearance of trees with deep roots in the Middle Devonian, plant rhizomes have long functioned in the belowground soil ecosystem. This study presents strong, direct evidence for plant−soil interactions at an early stage of vascular plant radiation. Soil stabilization by complex rhizome systems was apparently widespread, and contributed to landscape modification at an earlier time than had been appreciated

A Slice Escape Detection Model Based on Full Flow Adaptive Detection

The 5G power trading private network increases network flexibility and lowers building costs with the aid of 5G and Access Point Name (APN) technology. However, the private network is facing a series of security problems, such as the lack of effective isolation between slices and malicious terminal damage in slices, which result in a large consumption of slice resource failures and even slice escape attacks. To solve this problem, we propose a slice escape detection model based on full flow adaptive detection. Firstly, we improve the "six-tuple" flow table features detection technology, and creatively proposed a set of "eleven-tuple" features scheme, so as to realize the adaptive detection of intra-slice and inter-slice escape attacks. Secondly, we construct a two-level detection model based on long short-term memory network and self-attention mechanism to improve detection efficiency and reduce false alarm rate. Thirdly, we design an exception handling module to handle the abnormally detected traffic. Our model has a high detection accuracy and a low false alarm rate for the slice escape assault, according to a large number of experiments on the CIC-DDoS2019 dataset, and the detection delay complies with the requirements for online detection

DualToken-ViT: Position-aware Efficient Vision Transformer with Dual Token Fusion

Self-attention-based vision transformers (ViTs) have emerged as a highly competitive architecture in computer vision. Unlike convolutional neural networks (CNNs), ViTs are capable of global information sharing. With the development of various structures of ViTs, ViTs are increasingly advantageous for many vision tasks. However, the quadratic complexity of self-attention renders ViTs computationally intensive, and their lack of inductive biases of locality and translation equivariance demands larger model sizes compared to CNNs to effectively learn visual features. In this paper, we propose a light-weight and efficient vision transformer model called DualToken-ViT that leverages the advantages of CNNs and ViTs. DualToken-ViT effectively fuses the token with local information obtained by convolution-based structure and the token with global information obtained by self-attention-based structure to achieve an efficient attention structure. In addition, we use position-aware global tokens throughout all stages to enrich the global information, which further strengthening the effect of DualToken-ViT. Position-aware global tokens also contain the position information of the image, which makes our model better for vision tasks. We conducted extensive experiments on image classification, object detection and semantic segmentation tasks to demonstrate the effectiveness of DualToken-ViT. On the ImageNet-1K dataset, our models of different scales achieve accuracies of 75.4% and 79.4% with only 0.5G and 1.0G FLOPs, respectively, and our model with 1.0G FLOPs outperforms LightViT-T using global tokens by 0.7%