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Feb 27, 2025Open Access
The paper investigated the problem of restoring missing values in time series data analysis. The aim of this study was to advance the imputation of missing values for some autoregressive moving average models (ARMA) with generalized autoregressive conditioned heteroscedastic (GARCH) models. In this work, the novel imputation estimators for ARMA (1, 1) ＋ GARCH (1, 1) and ARMA (2, 2) ＋ GARCH (2, 2) were derived. The study utilized the method of optimal int...
Dec 25, 2024Open Access
With the development of Internet technology, artificial intelligence technology is widely used in the field of education, promoting the development of education. Advanced mathematics, as an important discipline for cultivating logical thinking and innovative abilities, is facing profound changes brought about by artificial intelligence technology. This article aims to analyze the innovation and existing problems brought by artificial intelligence technology to higher mathematics teaching, reform...
Oct 11, 2024Open Access
In this paper we compare track data association purity, accuracy, and timing on a simple, idealized model tracking problem for two data association methods: Global Nearest Neighbor (GNN) and Linear Assignment Problem (LAP). Accurate data association is the central problem of multi-target track assembly. Though simple, the model, a 1d process noise-free Kalman filter, captures the essence of the problem of tracking multiple closely spaced objects: 1) assembly of object sensor measurements into tr...
Sep 30, 2024Open Access
West Lake is renowned worldwide for its picturesque scenery and profound cultural heritage. This paper uses two famous scenic spots, Leifeng Pagoda and Broken Bridge, as examples to explore the mathematical culture embedded in the landscapes of West Lake. We analyze not only the architectural structure and geometric aesthetics of Leifeng Pagoda and Broken Bridge but also employ mathematical knowledge to understand these structures. This includes using the theorem of similar triangles to measure ...
Sep 04, 2024Open Access
This article assesses the unmet needs for family planning among women of childbearing age in the Donga department, Benin, using a mixed method (quantitative and qualitative) based on data from a field survey conducted among 466 women of childbearing age in 280 households and 57 resource people. To this end, multiple correspondence analysis (MCA) and logistic regression were used to identify the profiles of women with unmet needs and their associated factors. The results indicate that 89.6% of un...
Dec 28, 2023Open Access
In this paper, we explore the inverse spectral problem for a kind of pseudo-symmetric matrix A(ε,c,s) that corresponds to a graph of a banana tree when all ε=1. The problem of reconstructing pseudo-symmetric matrices from their spectra was considered. The sufficient and necessary conditions for the existence of these matrices are provided, and an algorithm and numerical example were provided to illustrate their characteristics. In addition, the effectiveness of the solution was v...
Dec 27, 2023Open Access
Group testing is an efficient method for classifying observations and estimating trait prevalence in a population. However, using appropriate group sizes is crucial for maximizing its benefits. Adaptive schemes have been developed to address improper group size selection issues. Existing adaptive schemes are based on a Binomial sampling model, requiring testing of all groups before recording successes. In certain scenarios, like infectious diseases, immediate reporting of estimates upon detectio...
Jan 19, 2023Open Access
Since the start of COVID-19 there have been widely spread notions that men can contract the disease at a higher rate than women and are more likely to die from it. Furthermore, age has been reported as a risk factor in COVID-19 mortality, and a vast majority of COVID-19 deaths have been among elderly people. Therefore, it is interesting to conduct a statistical analysis on COVID-19 deaths to draw conclusions on whether men are more likely to die of COVID-19 than women, and the influence of age g...
Sep 20, 2022Open Access
Vehicular traffic congestion is an extremely dangerous problem in urban areas, where transportation networks are becoming more complicated to design and execute. However, the apparent normal idea to build more roads in order to solve the traffic congestion can be sometimes quite a bad idea. The Braess’ paradox, which is a counter-intuitive phenomenon that can occur in transportation networks, states that under certain circumstances the addition of a new road to a traffic network can increase the...
Jun 23, 2022Open Access
Ridge Regression is an important statistical method in modeling vehicle crash frequency when crash data contains collinear predictors. The term multicollinearity refers to the condition in which two or more predictors are highly correlated with one another. This would make the explanatory variables become very sensitive to small changes in the model. Multicollinearity reduces the precision of the estimated coefficients, which weakens the statistical power of the regression model. Common methods ...
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