Mathematics

Journal Information
EISSN: 22277390
Published by: MDPI
Total articles ≅ 11,874

Latest articles in this journal

Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234589

Abstract:
Determining the author of a text is a difficult task. Here, we compare multiple Artificial Intelligence techniques for classifying literary texts written by multiple authors by taking into account a limited number of speech parts (prepositions, adverbs, and conjunctions). We also introduce a new dataset composed of texts written in the Romanian language on which we have run the algorithms. The compared methods are artificial neural networks, multi-expression programming, k-nearest neighbour, support vector machines, and decision trees with C5.0. Numerical experiments show, first of all, that the problem is difficult, but some algorithms are able to generate acceptable error rates on the test set.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234588

Abstract:
Bounds for the parameters of codes are very important in coding theory. The Grey–Rankin bound refers to the cardinality of a self-complementary binary code. Codes meeting this bound are associated with families of two-weight codes and other combinatorial structures. We study the relations among six infinite families of binary linear codes with two and three nonzero weights that are closely connected to the self-complementary linear codes meeting the Grey–Rankin bound. We give a construction method and partial classification results for such codes. The properties of the codes in the studied families and their relations help us in constructing codes of a higher dimension from codes with a given dimension.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234586

Abstract:
Nowadays, graph representation learning methods, in particular graph neural network methods, have attracted great attention and performed well in many downstream tasks. However, most graph neural network methods have a single perspective since they start from the edges (or adjacency matrix) of graphs, ignoring the mesoscopic structure (high-order local structure). In this paper, we introduce HS-GCN (High-order Node Similarity Graph Convolutional Network), which can mine the potential structural features of graphs from different perspectives by combining multiple high-order node similarity methods. We analyze HS-GCN theoretically and show that it is a generalization of the convolution-based graph neural network methods from different normalization perspectives. A series of experiments have shown that by combining high-order node similarities, our method can capture and utilize the high-order structural information of the graph more effectively, resulting in better results.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234587

Abstract:
This is a work about football. In it, we depart from two well-known approaches to forecast the outcome of a football match (or even a full tournament) and take advantage of their strengths to develop a new method of prediction. We illustrate the Élö–Runyan rating system and the Poisson technique in the English Premier League and we analyze their accuracies with respect to the actual results. We obtained an accuracy of 84.37% for the former, and 79.99% for the latter in this first exercise. Then, we present a criticism of these methods and use it to complement the aforementioned procedures, and hence, introduce the so-called Élö–Runyan–Poisson–Pearson method, which consists of adopting the distribution that best fits the historical distribution of goals to simulate the score of each match. Finally, we obtain a Monte Carlo-based forecast of the result. We test our mechanism to backcast the World Cup of Russia 2018, obtaining an accuracy of 87.09%; and forecast the results of the World Cup of Qatar 2022.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234585

Abstract:
The performance of a gearbox is sensitive to failures, especially in the long-term high speed and heavy load field. However, the multi-fault diagnosis in gearboxes is a challenging problem because of the complex and non-stationary measured signal. To obtain fault information more fully and improve the accuracy of gearbox fault diagnosis, this paper proposes a feature extraction method, hierarchical refined composite multiscale fluctuation dispersion entropy (HRCMFDE) to extract the fault features of rolling bearing and the gear vibration signals at different layers and scales. On this basis, a novel fault diagnosis scheme for the gearbox based on HRCMFDE, ReliefF and grey wolf optimizer regularized extreme learning machine is proposed. Firstly, HRCMFDE is employed to extract the original features, the multi-frequency time information can be evaluated simultaneously, and the fault feature information can be extracted more fully. After that, ReliefF is used to screen the sensitive features from the high-dimensional fault features. Finally, the sensitive features are inputted into the optimized regularized extreme learning machine to identify the fault states of the gearbox. Through three different types of gearbox experiments, the experimental results confirm that the proposed method has better diagnostic performance and generalization, which can effectively and accurately identify the different fault categories of the gearbox and outperforms other contrastive methods.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234584

Abstract:
The large-margin technique has served as the foundation of several successful theoretical and empirical results in multi-label image classification. However, most large-margin techniques are only suitable to shallow multi-label models with preset feature representations and a few large-margin techniques of neural networks only enforce margins at the output layer, which are not well suitable for deep networks. Based on the large-margin technique, a deep large-margin rank loss function suitable for any network structure is proposed, which is able to impose a margin on any chosen set of layers of a deep network, allows choosing any p norm (p1) on the metric measuring the margin between labels and is applicable to any network architecture. Although the complete computation of deep large-margin rank loss function has the O(C2) time complexity, where C denotes the size of the label set, which would cause scalability issues when C is large, a negative sampling technique was proposed to make the loss function scale linearly to C. Experimental results on two large-scale datasets, VOC2007 and MS-COCO, show that the deep large-margin ranking function improves the robustness of the model in multi-label image classification tasks while enhancing the model’s anti-noise performance.
Published: 3 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234583

Abstract:
The bike rebalancing problem is one of the major operational challenges in the urban bike-sharing system, which involves the redistribution of bikes among stations to prevent stations from being empty or overloaded. This paper investigates a new bike rebalancing problem, which considers the collection of broken bikes in the multi-depot system. The proposed problem can be classified as a two-commodity vehicle routing problem with pick-up and delivery. An integer programming model is formulated to find the optimal vehicle assignment and visiting sequences with the minimum total working time and fixed cost of vehicles. A hybrid heuristic algorithm integrating variable neighborhood search and dynamic programming is proposed to solve the problem. The computational results show that the proposed method can find 26 best solutions out of 36 instances, while the CPLEX obtains 16 best solutions. Impact of broken bikes collection and distribution of depots is examined. Comparison of different practical strategies indicates that the number of vehicles can be significantly reduced by allowing multiple visits to depots. Allowing vehicles to return to different depots can help reduce the total working time.
Published: 2 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234573

Abstract:
The present work considers the initial problem (IP) for a linear neutral system with derivatives in Caputo’s sense of incommensurate order, distributed delay and various kinds of initial functions. For the considered IP, the studied problem of existence and uniqueness of a resolvent kernel under some natural assumptions of boundedness type. In the case when, in the system, the term which describes the outer forces is a locally Lebesgue integrable function and the initial function is continuous, it is proved that the studied IP has a unique solution, which has an integral representation via the corresponding resolvent kernel. Applying the obtained results, we establish that, from the existence and uniqueness of a resolvent kernel, the existence and uniqueness of a fundamental matrix of the homogeneous system and vice versa follows. An explicit formula describing the relationship between the resolvent kernel and the fundamental matrix is proved as well.
Published: 2 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234582

Abstract:
In this paper, we adopt the choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Luh’s choice theory, based on harmonic analysis, is mathematically complicated and applies only to function interpolation. Here, we aim at presenting an easily accessible approach to solving differential equations with the choice theory which proves to be very successful, not only by its easy accessibility but also by its striking accuracy and efficiency. Our emphases are on the highly reliable prediction of the optimal value of the shape parameter and the extremely small approximation errors of the numerical solutions to the differential equations. We hope that our approach can be accepted by both mathematicians and non-mathematicians.
Published: 2 December 2022
by MDPI
Journal: Mathematics
Mathematics, Volume 10; https://doi.org/10.3390/math10234581

Abstract:
In this article, an approach to achieve the anti-disturbance fault-tolerant constrained consensus is proposed for time-delay faulty multi-agent systems under semi-Markov switching topology. Firstly, an observer based on the coupled disturbance and fault information is designed to estimate the disturbance and failure at the same time. Next, because of the conservatism of the traditional H control method, a new performance index is constructed to replace the zero initial condition by making use of initial conditions. Then, the time-varying transfer rate is expressed as a convex combination by using the boundedness of transfer rate, so as to solve the numerical solution problem of time-varying transfer rate. On this basis, according to the performance requirements, an anti-disturbance fault-tolerant constrained consensus strategy is proposed. Finally, simulation results are given to verify the feasibility of the approach.
Back to Top Top