The maximum-weight perfect matching inverse issue in graph theory and text clustering are the two primary topics of this study. We suggest a novel approach to text clustering that makes use of self-encoders and BERT embeddings for feature extraction in order to increase clustering accuracy. According to experimental results, our technique enhances the clustering results greatly and performs well on numerous short text datasets. In the context of graph theory, we examine the unit paradigm inverse issue of maximum-weight perfect matching with value constraints and provide a robust polynomial-time method for its solution. In addition to effectively solving the maximum-weight perfect matching inverse issue, our technique can also produce the best weight vector configuration scheme for real-world uses. In conclusion, our work has advanced the domains of text clustering and graph theory significantly, offering fresh approaches and theoretical underpinnings for future investigations.

A brief survey on mutually orthogonal resolutions of some combinatorial designs is presented. Some \((2,w)\)-threshold schemes from mutually orthogonal resolutions of these designs are also obtained.

In the era of social media platforms like Douyin, preserving the essence of traditional Chinese culture while adapting it to contemporary trends is crucial for its continued relevance and vitality. This paper delves into the practical implications of leveraging social media for cultural communication, emphasizing communication strategies tailored to platforms like Douyin. It introduces two novel algorithms for generating Douyin information dissemination trees: one based on retweeting relationships and another optimized for rapid dissemination. Comparative experiments assess the performance of these algorithms and analyze the node distribution within dissemination trees, aiming to enhance the dissemination power of traditional culture and foster its inheritance and innovation.

The “Three Rural Issues” has always been the top priority of my country’s economic development, which related to the construction process of modern agriculture, the development effect of agricultural economy and the development speed of the national economy. In recent years, the state and local governments have taken the construction of new countryside as the starting point, seriously discussed many problems faced by the agricultural economy in the process of development, and took targeted measures to effectively solve them, which better promoted the construction of new countryside. Agriculture plays an important role in the national economy and is the foundation of national economic development. Under the background of new rural construction, we must strengthen the management of agricultural economy. This paper analyzes the main contents, characteristics and existing problems of agricultural sustainable development under the background of new rural construction, and puts forward solutions that hope to be discussed by a wide range of partners.

Zhou, Xu and Sun [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional \((a,b,k)\)-critical covered graphs, Information Processing Letters 152(2019)105838] defined the concept of a fractional \((a,b,k)\)-critical covered graph, namely, a graph \(G\) is a fractional \((a,b,k)\)-critical covered graph if after removing any \(k\) vertices of \(G\), the remaining graph of \(G\) is a fractional \([a,b]\)-covered graph. In this paper, we prove that a graph \(G\) with \(\delta(G)\geq2+k\) is fractional \((2,b,k)\)-critical covered if \(bind(G)>\frac{b+k}{b-1}\), where \(k\geq0\) and \(b\geq2+k\) are two integers.

In this paper, we study the submodular hitting set problem (SHSP), which is a variant of the hitting set problem. In the SHSP, we are given a supergraph \(H = (V, \mathcal{C})\) and a nonnegative submodular function on the set \(2^{V}\). The objective is to determine a vertex subset to cover all hyperedges such that the cost of submodular covering is minimized. Our main work is to present a rounding algorithm and a primal-dual algorithm respectively for the SHSP and prove that they both have the approximation ratio \(k\), where \(k\) is the maximum number of vertices in all hyperedges.

In recent years, there is a lot of interest in the topic of conveying the groups of planar graphs with an unvarying metric dimension. A few types of planar graphs have recently had their locating number (or metric dimension) determined, and an outstanding problem concerning these graphs was brought up that: Illustrate the types of planar graphs \(\Upsilon\) that can be generated from a graph \(\Phi\) through the addition of more edges to \(\Phi\), such that \(dim(\Phi)=dim(\Upsilon)\) and \(\mathbb{V}(\Phi)=\mathbb{V}(\Upsilon)\). While proceeding in a similar directives, we identify two families of radially identical planar graphs with unaltered metric dimension in this study: \(\digamma_{n,m}\) and \(\gimel_{n,m}\). We do this by establishing that \(dim(\digamma_{n,m})=dim(\gimel_{n,m})\) and \(\mathbb{V}(\digamma_{n,m})=\mathbb{V}(\gimel_{n,m})\), respectively. We acquire another family of a radially symmetrical plane graph (i.e., \(\daleth_{n,m}\)) with a constant metric dimension. We show that all the vertices of these classes of the plane graphs can potentially be identified with just three well-chosen nodes.

The purpose of this work was to use machine learning classification models and hyperspectral camera technologies to create a model of surface damage to garlic. 140 of the 184 garlic plants of which 44 were used for test validation were pre-treated for surface damage. First, we examined the data in ENVI under various damage scenarios using the normalised vegetation index (NDVI) approach. 579 pixels were then chosen for the training of the logistic regression model. Finally, we used 54 garlic bulbs to practically validate the model. Although tiny regions could not be precisely identified, the mouldy portion of the garlic’s surface could be identified using the NDVI technique. 90% accuracy was attained using the 90% classification model constructed using the logistic regression approach. Garlic’s surface damage, even at first mild ones, was correctly identified. The creation of this model for identifying garlic damage lowers the cost of detecting garlic damage and broadens the use of hyperspectral technologies in garlic detection.

In this paper, the sensor is applied to the collection of rock parameter data. Aiming at the classification and evaluation of stability (i.e. rock quality), an attribute recognition model for the classification and evaluation of surrounding rock quality of underground engineering is established. Using multi-source data fusion and orthogonal numerical simulation test methods, the effects of rock mechanics parameters on the horizontal convergence of the tunnel, the settlement of the vault and the plastic zone coefficient are studied. Six factors (elastic modulus, Poisson’s ratio, internal friction angle, tensile strength, cohesion and density) and three levels of orthogonal experimental solutions were selected. The method of defining similar weight by using similar number to determine the weight of evaluation index, so as to calculate the comprehensive attribute measure, and apply confidence criteria to identify the stability of rock samples. Through the analysis and evaluation of rock mass quality classification of underground engineering, the application of the model and the evaluation method of rock mass quality classification are explained. The test results match the orthogonal test results; Considering the stability of tunnel envelope, the horizontal convergence, vault settlement and plastic zone coefficient after excavation should be comprehensively considered.

This paper proposes a comprehensive framework for testing and evaluating automatic ambulances, crucial for ensuring their reliability and safety in real-world scenarios. The framework includes designing test scenarios with varying complexity, covering environmental factors like road conditions, weather, and obstacles. An evaluation index system is introduced, comprising driving security, ride comfort, intelligence, and efficiency. Methodologies for calculating indicator weights, using the CRITIC and AHP methods, are presented to ensure fair evaluation. Additionally, evaluation methods including qualitative and quantitative techniques, such as grey correlation theory, are discussed. The test results show that the assessment results of the traditional fuzzy comprehensive evaluation method and the grey correlation theory evaluation method are highly consistent. The change in vehicle speed has less of an effect on accuracy during the real-time assessment process when the time interval is set to 0.1s, and the evaluation time of 0.098s can satisfy the requirement that the planning time of autonomous driving vehicles be shorter than 200 ms.