Recent studies have shown that there is a profound connection between the existence of H -factors under attack circumstances and the parameters to measure the vulnerability of the network. The disadvantage of the previous theoretical conclusions is that the connectivity is often regarded as fixed, and the relationship between other network parameters and the H -factor is explored. However, in a real situation, as the network structure changes, connectivity becomes a dynamically variational parameter, and its changing will affect other parameters to make corresponding changes. In this study, we treat all parameters as a complex system that restricts each other, consider their mutual constraints from a geometric point of view, and apply high-dimensional surfaces to characterize their relationships. Seven network parameters including toughness and binding number are considered, and the concrete expression form of the surfaces in several specific settings are obtained. Furthermore, the local version for these seven network parameters are introduced.

Graph fractional factor theory plays a crucial role in data transmission and network flow existence analysis, and has become one of the hot research branches of graph theory. This paper introduces fuzzy fractional factor in fuzzy graph setting, and an algorithm-based proof of its necessary and sufficient condition is given. The transformation operation is introduced to show that any two fuzzy fractional f $f$ -factors can be converted between each other, and the characteristic of maximum fuzzy fractional factor through increasing walk is determined. Finally, toughness in fuzzy graph setting is introduced, and preliminary toughness bound for fuzzy fractional ι $\iota $ -factor is presented, where ι = min e ∈ E { μ B ( e ) ∣ μ B ( e ) > 0 } $\iota ={\min }_{e\in E}\{{\mu }_{B}(e)| {\mu }_{B}(e)\gt 0\}$ .

In this paper, an adaptive fuzzy control scheme for strict-feedback nonlinear system with finite-time prescribed performance and actuator fault is studied. First, we consider a prescribed performance function that enables the tracking error to converge within a preset interval in a finite time. Subsequently, the fuzzy logic system and dynamic surface control technology are embedded in the backstepping design process, and the purpose of the dynamic surface control technique is to settle the problem of computational explosion when processing the backstepping design. The fuzzy logic system is used to approximate the unknown functions that appear in the system. Finally, a new controller is designed in combination with an updated law which ensures that all the signals in the closed-loop is bounded. Two simulation examples are taken to illustrate the feasibility of the presented control scheme.

Grayscale image colorization, especially for ethnic costume images, is highly challenging due to its rich and complex color features. The existing image colorization methods usually take the costume image as a whole in practical applications that lead to the ignorance of the semantic information of different parts of the costume. It is known that each part's color distribution of the ethnic costume is different. So, the color mapping of other parts is also diverse, which is determined by distinctive ethnic characteristics. This study introduces fine-grained level semantic information and proposes a high-resolution image colorization model for ethnic costumes targeting enhancement, inspired by semantic-level colorization. The semantic information of different regions of ethnic costumes has a significant impact on the performance of the coloring task. Using Pix2PixHD as the backbone network, we create a new network architecture that maintains color distribution correspondence and spatial consistency of costume images using fine-grained semantic information. In our network, we take the splice result of fine-grained semantic for ethnic costume and grayscale image as the conditions and then feed them into the generative adversarial networks. We also discuss and analyze the influences of the grayscale channel and fine-grained semantics on discriminator. Extensive experiments demonstrate that our method performs well compared with other state-of-the-art automatic colorization methods.

Clothing attribute prediction is a fundamental image classification task in the field of computer vision. Motivated by the human recognition system, we investigate the task relationship and spatial importance where people usually utilize these useful clues to assist in recognizing clothing attributes. In this paper, we propose a novel Holistic Relation Network (HRNet) for clothing attribute recognition, considering the fusion of multiple relations, including spatial and spatial relation via a spatial relation module, spatial and task relation via a task attention module, and task and task relation via a graph context reasoning module. Specifically, we first use the backbone network to extract features from the input image, two types of attention models followed will further learn the features, then the graph context reasoning module will be used to further enhance the features, and finally, a classifier exploited to classify the clothing attributes with the learned representation information. Without using manual image feature filtering methods, this paper aims to achieve clothing attribute recognition by deeply exploring the relationships among different clothing attribute recognition tasks. In this paper, we use double-branches of the attention model to model the relevance of spatial context information and learn more discriminative feature representations from multitask features for clothing attribute prediction. Derived from the prior knowledge learned from the two above-mentioned attention models, we further propose a graph-relation model constructing relationships among different clothing attribute tasks by integrating the spatial association relationships among multitask. The proposed HRNet only uses image-level annotation but it owns a good ability for obtaining distinguishing feature representations. We obtain state-of-the-art performance, which is demonstrated by extensive experiments on three mainstream benchmarks, for example, woman clothing data set, man clothing data set, and shop-domain clothing data set.

Due to the high similarity of fine-grained image subclasses, small inter-class changes and large intra-class changes are caused, which leads to the difficulty of fine-grained image classification task. However, existing convolutional neural networks have been unable to effectively solve this problem. Aiming at the above-mentioned fine-grained image classification problem, this paper proposes a multi-scale and multi-level ViT model. First, through data augmentation techniques, the accuracy of fine-grained image classification can be effectively improved. Secondly, the small-scale input and large-scale input of the model make the input image have more feature ex-pressions. The subsequent multi-layeredness effectively utilizes the results of the previous layer of ViT, so that the data of the previous layer can be more effectively used in the next layer of ViT. Finally, cross-attention allows the results of two scale inputs to be fused in a reasonable way. The proposed model is competitive with current mainstream state-of-the-art methods on multiple datasets.

Isolation toughness is a vital parameter to evaluate the vulnerability of computer networks. In specific network designing stage, it is necessary to find the lower bound of the isolated toughness, and strive to build a network that meets the stability requirements with the least cost. Gao et al.1 conjectured that if a graph G with κ ( G ) ≥ 3 m + 1 2 satisfies I ( G ) > 7 m + 5 4 m + 4 or I ′ ( G ) > 7 m + 5 4 m + 2 , then G is a ( P ≥ 3 , m ) -factor deleted graph. It's proved that this conjecture holds. However, it is found that as the connectivity changes, the tight lower bound of isolated toughness for ( P ≥ 3 , m ) -factor deleted graphs will change as well. Therefore, we propose a new perspective to look into this problem and introduce the concepts of isolated toughness ( P ≥ 3 , m ) factor deleted surface and isolated toughness variant ( P ≥ 3 , m ) factor deleted surface, where the result of the original conjecture is only a cross-section on surfaces. The main contribution in this paper is to determine the concrete expression of these two surfaces.

The issues of ruggedness and vulnerability are cruxes in network security research, which must be considered during the network designing phase. Parameters such as toughness, isolated toughness, and binding number characterize the vulnerable of the network from the structure of networks. The path factor, a special case of the generalized ℋ -factor, measures the feasibility of data transmission in networks. Recent advances have been obtained to show that there is an inevitable connection between the vulnerability parameters of the network and the existence of path factors, while we found that some existing theoretical results are not tight and there is still a long way for further improvement. In view of graph theory approaches, this paper mainly contributes to determine the sharp bounds of toughness, isolated toughness, and binding number for the existence of path factor in different settings, and therefore solve the open problems left unsolved in previous articles.