Gene regulatory networks characterize directed interactions between transcription factors (TFs) and target genes (TGs), revealing the regulatory logic underlying gene expression. Recent graph neural network approaches have advanced GRN inference from single-cell RNA sequencing (scRNA-seq) data. However, most rely on undirected graphs, overlooking the intrinsic directionality of gene regulation. This paper proposes DGATGRN, a directed graph attention network (DGAT) framework that explicitly models the roles of TFs and TGs through two complementary DGAT branches. A residual network component is further integrated to encode self-feature embeddings. The decoder infers directed regulatory relationships by assessing the consistency between upstream TF embeddings and downstream TG self-embeddings, as well as between downstream TG embeddings and upstream TF self-embeddings. Evaluations across seven scRNA-seq datasets demonstrate that DGATGRN consistently outperforms six state-of-the-art baselines in inference accuracy. A colorectal cancer case study further demonstrates its biological interpretability, highlighting DGATGRN's potential for uncovering meaningful regulatory mechanisms in complex cellular systems.

Knowledge tracing is a core task in intelligent education, aiming to model students’ knowledge states based on their learning behaviors and dynamically predict their mastery of specific concepts. In practical applications, online learning platforms typically provide a large number of questions, but each student can only interact with a small subset. This limited interaction results in extreme data sparsity for certain questions, hindering the model’s ability to build effective representations and make accurate predictions for them. Although recent hypergraph neural network-based knowledge tracing methods can model high-order heterogeneous relationships between questions, improving question representation to some extent, the hypergraph structure often overlooks latent global structural information. This limitation weakens the comprehensive semantic representation of questions, thereby affecting prediction performance. To address these challenges, we propose a Hypergraph Structure-Enhanced for Knowledge Tracing with Gumbel-Softmax sampling (HSEKT-GS). First, we construct a question–concept hypergraph and its dual graph, and incorporate a structural embedding mechanism to capture local high-order relational information between questions and between concepts. Second, to further enhance question representation, we introduce a hypergraph star expansion and use Gumbel-Softmax sampling to generate multiple perturbed embeddings per node to explore structural uncertainty. Finally, the updated representations of all sampled paths are averaged to reveal latent structural links and mitigate the over-smoothing issue in fully connected graphs. In addition, we incorporate a hypergraph structure regularization term as structural supervision to improve the robustness and interpretability of the framework. Experimental results on four publicly available datasets demonstrate that HSEKT-GS outperforms existing baseline methods.

A graph G is a fractional (a,b,n)-critical graph if removing any n vertices from G, the resulting subgraph still admits a fractional [a,b]-factor. In this paper, we determine the exact tight isolated toughness bound for fractional (a,b,n)-critical graphs. To be specific, a graph G is fractional (a,b,n)-critical if δ(G)≥a+n and I(G)>a−1+n+1na,b, where na,b≥2 is an integer satisfies (na,b−1)a≤b≤na,ba−1. Furthermore, the sharpness of bounds is showcased by counterexamples. Our contribution improves a result from [W. Gao, W. Wang, and Y. Chen, Tight isolated toughness bound for fractional (k,n)-critical graphs, Discrete Appl. Math. 322 (2022), 194–202] which established the tight isolated toughness bound for fractional (k,n)-critical graphs.

Nowadays, vehicle-oriented Internet of Things (IoT) is a new generation of IoT networks in which sensors are deployed on electronic hardware modules of vehicles. A secure and feasible IoT-assisted vehicle environment should include a robust data transmission mechanism for transferring and collecting data packets from both onboard and roadside sensors, resulting in the accurate delivery of packages without delay. When designing such Internet of Vehicles (IoV) networks, the vulnerability of the network should be considered to facilitate data transmission in the remaining network under the condition that some nodes (e.g., vehicles) and channels are damaged due to the dynamic environmental factors and unpredicted failures at various nodes. Fractional Critical Deleted Graph (FCDG), which is used in graph theory, can act as Fractional Factor (FF) in the IoV networks to maintain the IoT network stable and provide reliable network connectivity when a part of data transmission network is damaged. Toughness is an important condition to measure the sturdiness of such FF-encoded network. In this work, we study the relationship between toughness and FCDG in IoV networks. Moreover, the graph conditions are considered together with the tight lower bound of the toughness for the existence of path factor. Such feasibility analysis of IoV networks help to find the bound in the effort to recover or realign lost links in networks, which is critical for the next generation of intelligent transportation systems where all vehicles are connected seamlessly.

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.

Abstract Accurate and early detection of the brain tumor region has a great impact on the choice of treatment, its success rate, and the follow‐up of the disease process over time. This study presents a new bioinspired technique for the early detection of the brain tumor area to improve the chance of completely healing. The study presents a multistep technique to detect the brain tumor area. Herein, after image preprocessing and image feature extraction, an artificial neural network is used to determine the tumor area in the image. The method is based on using an improved version of the whale optimization algorithm for optimal selection of the features and optimizing the artificial neural network weights for classification. Simulation results of the proposed method are applied to FLAIR, T1, and T2 datasets and are compared with different algorithms. Three performance indexes including correct detection rate, false acceptance rate, and false rejection rate are selected for the system performance analysis. Final results showed the superiority of the proposed method toward the other similar methods.

Ontology, as a useful tool, is widely applied in lots of fields such as geography science, computer science and medical science. Ontology concept similarity calculation is the key part of the algorithms in these applications. A popular trick is to make use of the similarity between vertices on ontology graphs. It relies on an ontology function that maps the vertex set of an ontology graph to real numbers, and multi-dividing is an effective approach to achieve this goal. In this paper, we report the generalization bounds and uniform bounds for kernel-based multi-dividing ontology algorithms, which are stated as regularization schemes. The ontology loss function is convex and meets Lipschitz assumption. The results are obtained in terms of statistical probability inequality and empirical Rademacher complexity.