Statistical Mathematical Modeling Research Articles

A Study on the Interaction Between Population Mobility and High-Quality Development of Manufacturing Industry in China —Based on the Data of Fujian Province

This paper uses relevant mathematical statistical models to verify the interactive effect between population mobility and the high-quality development of the manufacturing industry based on the panel data of 43 counties in the Fujian province from 2007 to 2021. The results show that (1) the inflow areas of population flow in the Fujian province are mainly concentrated in the southeast region; (2) there is mutual promotion between population mobility and the high-quality development of the manufacturing industry in the Fujian province, and the population mobility in adjacent areas has a significant promotion effect on the high-quality development of the local manufacturing industry; and (3) heterogeneity results show that after 2011, the interaction effect between population mobility and the high-quality development of the manufacturing industry has declined, and population inflow has a stronger role in promoting the high-quality development of the manufacturing industry than population outflow. The conclusions of this study are of great significance to the Fujian province for implementing a reasonable population policy and promoting the coordinated development of manufacturing enterprises.

The Way to Construct Innovative Methods for Solving Initial-Value Problem of the Volterra Integro-Differential Equation

Mathematical models for many problems in the natural sciences are often simplified to solving initial-value problems (IVPs) for the Volterra integro-differential equations (VIDE). Numerical methods of a multistep type are typically used to solve these problems. It is known that in some cases, the multi-step method (MSM) is applied to solving the IVPs of both ordinary differential equations (ODEs) and VIDE encountered in solving some problems in mathematical biology. Here, to solve such problems by combining different methods, some modifications of established methods were developed, and it was demonstrated that these methods outperform the existing ones. As is known, one of the main issues in solving the aforementioned problems is determining the reliability of calculating values using the known mathematicalstatistical models (MSMs). In this regard, some experts utilize the predictor-corrector method. Having highlighted the disadvantages of this method, the proposal is to develop an innovative approach and assess the errors that may arise when applying this method to solve various problems. Here, the IVPs for the VIDE of the first order are primarily investigated. To illustrate the benefits of the innovative methods proposed here, we discuss the use of simple numerical methods to solve some common examples.

Analysis of Land Use/Cover Characteristics and Dynamic of Changes in Huai River Basin from 2000 to 2020

Globally, land use is considered as one of the most closely related link between human being and nature. But land use/cover change (LULC) is regarded as the main cause for global environmental change with possible serious impact on human livelihoods and many parts of social and physical environmental aspects. Huai River Basin (HRB) is among the global river-land ecosystems that has been intensively altered by land use change. Unfortunately, the increasing land use change in HRB is not well scientifically addressed and still, related existing problems are not solved putting the basin ecological status and its basic grain production agricultural capacity at risks. This study adopted data image processing software and various mathematical statistical models to analyze the current LULC characteristics and dynamics of change in the study basin. From the analysis that adopted combined scientific techniques of CA-Markov, InVEST models with ArcGIS and IDRISI software, the results indicate that in 20 years of study, area of cultivated land in HRB declined by -4.34%, grassland declined by -21.28%, forest land declined by -3.22% and unused land declined by -18.84% while area of construction land increased by 26.38% and water area increased by 11.62%. Cultivated land was the major land use type in the basin while unused land was the minor land use type. Land use projection trend of HRB in 2035 predicts decline of areas coverage on cultivated land by -6.92%, on forestland by -9.20% and on grassland by -12.29%. But the basin is expected to have area increase on construction land by 30.07%, on water area by 15.03% and on unused land by 18.45%. Pictorial summary for the analysis of land use/cover characteristics and dynamic of changes in HRB is shown below.

Analysis of the Effect of Digital Financial Inclusion in Promoting Inclusive Growth: Mechanism and Statistical Verification

Abstract As the main goal of economic development, inclusive growth (IG) is an important strategic measure to achieve common prosperity. Whether digital inclusive finance can make use of the advantages of scientific and technological innovation to promote IG is of great significance to promote the fairness, effectiveness, and inclusiveness of global development. Based on the panel data of 30 provinces in China from 2011 to 2021 (excluding Tibet, Hong Kong, Macao and Taiwan), this article first measures the IG index of China from three dimensions: sustainable economic growth, income distribution, and social equity. Subsequently, the article uses a series of mathematical statistical models to verify the transmission path and mechanism of the influence of digital inclusive finance on IG. The findings are as follows: (1) The level of IG in China shows a decreasing trend from east to middle to west, while the average annual growth rate of IG in the eastern region is obviously lower than that in the central and western regions; (2) digital inclusive finance has a significant promotion effect on IG, and digital inclusive finance in the central and western regions has a more obvious promotion effect on IG; (3) digital inclusive finance can achieve IG by increasing innovation activity and improving the level of human capital. Finally, based on the research conclusions, the article puts forward relevant policy suggestions, which provide reference value for formulating high-quality national development strategies and promoting high-quality economic development.

Systematic approach to the study of working surfaces wear of automotive and tractor equipment parts

The paper uses the principles of the system approach to establish the relationship between wear of individual surfaces on the example of a gear drive of the GP type pump. The hierarchical structure of the part is considered, its individual functional parts are classified as subsystems, and the working surfaces are classified as system elements. A systematic approach to the study of part wear condition included, in addition to identifying the relationships between the wear of individual elements of the part, the creation of a mathematical statistical model of the worn part as a whole, as a system. The main types of wear of the gear working surfaces were determined. The laws of wear distribution of gear working surfaces and their main numerical characteristics were found. The established relationship between the wear of individual gear elements has become the basis for the system quality of the technical system "gear drive of the GP pump" in relation to the wear of its elements. A mathematical statistical wear model was obtained in the form of linear regression equations system of gear elements wear dependence on their outer diameter wear. This makes it possible, using the principles of a systematic approach based on the data of a single defect – gear wear along the outer diameter, to create a complete statistical image of the worn part, i.e., to determine the wear of other elements of the drive gear. The results obtained allow us to reasonably approach the issue of choosing a method for restoring parts and forming routes for the technological process of restoring a part.

Sparse optical flow outliers elimination method based on Borda stochastic neighborhood graph

During the tracking of moving targets in dynamic scenes, efficiently handling outliers in the optical flow and maintaining robustness across various motion amplitudes represents a critical challenge. So far, studies have used thresholding and local consistency based approaches to deal with optical outliers. However, there is subjectivity through expert-defined thresholds or delineated regions, and therefore these methods do not perform consistently enough under different target motion amplitudes. Other studies have focused on complex statistical-mathematical modeling which, although theoretically valid, requires significant computational resources. Aiming at the above problems this paper proposes a new method to calculate the optical outliers by using stochastic neighborhood graph combined with the Borda counting method, which reduces the computation amount on the basis of objectively eliminating the outliers. Sparse optical flow (SOF) values are used as the overall population and the outlier and inlier SOF values are used as samples. Analyze the dissimilarity between SOF data points, obtaining the dissimilarity matrix, introducing the Gaussian function to smooth and reduce the dimensionality of the dissimilarity matrix, and then normalizing the smoothing matrix to generate the binding matrix, where the probability sum of each node to other nodes in the matrix is equal to 1. Stochastic neighborhood graphs are then generated based on a binding matrix to obtain the outlier probabilities of data points in different neighborhood graphs, and outlier samples are obtained based on the probability. To avoid the subjectivity of the expert thresholds, the outlier probabilities are weighted and ranked to calculate the data point Borda scores to obtain accurate optical outliers. The experimental results show that the method in this paper is robust to different amplitude motions and real scenarios, and the accuracy, precision and recall of outliers elimination are better than the current mainstream algorithms.

Research on Temporal and Spatial Distribution Pattern of the Night-Time Economy Supported by Multi-Source Data—A Case Study of Xiamen City, Fujian Province, China

The increasing proportion of night consumption in the total daily consumption means the night economy has become an indispensable part of national economic development. However, early social science research on alcohol in the night economy and social science research on the night leisure industry dominated our understanding of the night city. Few researchers have built effective mathematical statistical models to explore the spatio-temporal distribution and regional interactions of the night economy. This paper presents a method to analyze the spatial and temporal distribution pattern of the night economy based on multi-source data. Firstly, K-Means++ and DBSCAN were used to cluster OD points to identify the gathering areas of night activities. Then, the local L-function in “flow space” was used to extract the aggregated flow of each aggregation area and analyze the regional interactions. Finally, the correlation between night activity and night service facilities was calculated by using geographic detector, and night activity and lighting were coupled by the profit and loss value. The research shows that this method can identify the main areas of night activity, dig out the interrelationships at the community level, and find the new night activity gathering points and night economic growth areas in the future. This study extends the current situation that the night economy is limited to theoretical research and research in central urban areas, provides the temporal and spatial distribution of night activities and night lighting supplies from the perspective of big data, and provides a basis for future night economy research, urban planning, and relevant policy issuance.

Mathematical modeling of basal body temperature influence on menstrual cycle, length of sleep, and stress levels as detection of fertile period (ovulation) in women

Basal body temperature is the temperature when the body reaches the resting phase or does not perform any activity. Basal body temperature is influenced by factors such as the quality of a person's length of sleep, stress, and menstrual cycle patterns. The benefit of checking and monitoring basal body temperature for a woman is to determine when a woman starts to enter the ovulation period, making it easier for couples who want a target pregnancy. The measurement method was carried out in the morning right after waking up using a thermometer flanked in the armpit area by applying three repetitions of measurements within a period of two months with the number of sample participants of 10 cadet students of military biology study program with an age range of 19-21 years. This type of research is carried out observationally and analytically using longitudinal data. The analysis used in this study was by conducting a statistical mathematical model trial by analyzing the p-value. The results showed that in the paired test there was a significant influence of the relationship of basal body temperature on the menstrual cycle at the time before menstruation and when menstruation. The researcher's suggestion is to conduct further research with larger participants of samples and the presence of sample variations in observations because not all biologists do significant research with the statistical method.

Valorization of chicken feather waste using recombinant bacillus subtilis cells by solid-state fermentation for soluble proteins and serine alkaline protease production

Feather waste, a by-product of the poultry industry, is rich in proteins, peptides, and amino acids. Improper disposal of feathers can cause environmental pollution. Solid-state fermentation (SSF) is a viable alternative to submerged fermentation due to its simplicity, productivity, and lower cost. The study goal is a biorefinery of chicken feather waste supplemented with wheat bran using a recombinant Bacillus subtilis strain to produce soluble proteins and a serine alkaline protease. Plackett-Burman Design and Central Composite Design were utilized in a statistical-mathematical model to optimize the process. Multi-factorial design optimization resulted in 80 % substrate degradation efficiency, an alkaline protease with dual activities (1423 proteolytic units and 190 keratinolytic units), 214 mg soluble proteins/g substrate, and 87 % model validation. Scaling up the SSF process to 50 g of substrate significantly enhanced the end products of feather biodegradation to 1616 proteolytic units, 2844 keratinolytic units, and 127 mg soluble proteins/g substrate. Aim and scope of the manuscriptThe aim of the present study is to utilize chicken feather waste (alone or supplemented with other materials) through recombinant Bacillus subtilis cells using solid state fermentation (SSF) at a laboratory scale. The plan study provides a promising waste management in the environmental field concerning biodegradation of such recalcitrant keratinous wastes supplemented with agricultural residues via recombinant microorganism. On semi-pilot scale, high production and quality of soluble protein, protease, and keratinase activity were produced according to the statistically optimised first stage fermentation in the laboratory scale. The bioconversion process took place as a major goal to obtain valuable products, with low utilities and energy requirements. Therefore, this will consider as an economically feasible and environmentally friendly alternative. Moreover, this study is considered as first step fermentation for feather waste to pave the road for directing it to a second step fermentation for biogas production and bioenergy generation through bio-electrochemical systems (Manuscript under publication).

Comparison of two statistical methodologies for a binary classification problem of two-dimensional images

The present work intends to compare two statistical classification methods using images as covariates and under the comparison criterion of the ROC curve. The first implemented procedure is based on exploring a mathematical-statistical model using multidimensional arrangements, frequently known as tensors. It is based on the theoretical framework of the high-dimensional generalized linear model. The second methodology is situated in the field of functional data analysis, particularly in the space of functions that have a finite measure of the total variation. A simulation study is carried out to compare both classification methodologies using the area under the ROC curve (AUC). The model based on functional data had better performance than the tensor model. A real data application using medical images is presented.

Measuring the competitiveness of commodity markets using price signals and information theory

Technological advancements, abrupt changes in market conditions, and political reforms, among other things, necessitate strong regulatory oversight, and accurate measurement of performance related indicators. The more accurate, information rich, and transparent these measurements/signals, the lower the level of uncertainty felt by value chain participants, who are thus able to recognize and observe whether the market’s state is efficient. Its lack, may lead to indecisiveness, translating into false interpretations that could lead to wrong policy directions. This paper provides an ex-post evaluation tool intending to deliver additional insights or quality information that would aid the regulator in assessing the state of the market. The tool is applied to the UK wholesale natural gas market for the period between 2011 and 2020, assessing and testing the market’s weak-form efficiency. It claims that today’s gas prices reflect a specific type of information, primarily past gas prices, and that only new information can help predict future prices. In this manuscript, based solely on a limited and available untapped dataset (day-ahead price time series), and working under the assumption that gas prices are the result of market processes, a variety of information metrics (gas price randomness, distribution of extreme prices, ability to predict prices - based on historical sets) is extracted with the use of suitable mathematical statistical models. A weighted entropy index is then computed, and measures the state of the commodity market. The results indicate that the analysis has helped gain information, thus reducing uncertainty (relative to a pre-analysis) by 86.5 %. Additionally, there is sufficient evidence that the UK natural gas prices are weak-form efficient.

Incorporating Interventions to an Extended SEIRD Model with Vaccination: Application to COVID-19 in Qatar

The COVID-19 outbreak of 2020 has required many governments to develop and adopt mathematical-statistical models of the pandemic for policy and planning purposes. To this end, this work provides a tutorial on building a compartmental model using Susceptible, Exposed, Infected, Recovered, Deaths and Vaccinated (SEIRDV) status through time. The proposed model uses interventions to quantify the impact of various government attempts made to slow the spread of the virus. Furthermore, a vaccination parameter is also incorporated in the model, which is inactive until the time the vaccine is deployed. A Bayesian framework is utilized to perform both parameter estimation and prediction. Predictions are made to determine when the peak Active Infections occur. We provide inferential frameworks for assessing the effects of government interventions on the dynamic progression of the pandemic, including the impact of vaccination. The proposed model also allows for quantification of number of excess deaths averted over the study period due to vaccination.

Experimental investigation on the impact properties and microstructure of recycled steel fiber and silica fume reinforced recycled aggregate concrete

With the continuous development of the economy and society, the production of solid waste is increasing. Construction and demolition waste (CDW), used tires and silica fume are the main components of solid waste. Recycling these materials will reduce resource pressure, decrease carbon emissions and protect the environment, while bringing certain economic benefits. This study focused on the influence of the synergistic effect of recycled steel fibers (RSF) and silica fume on the mechanical properties and impact resistance of recycled aggregate concrete (RAC). The mathematical statistical model of Weibull distribution was adopted to depict the impact results. In addition, the microstructure of the interfacial transition zone (ITZ) between the cement paste and the aggregate/fiber was researched by scanning electron microscopy (SEM). Results revealed that the synergistic effect of RSF and silica fume significantly improved the impact resistance of RAC. Especially the specimen containing 10% silica fume and 0.75% RSF performed the best properties, the first crack impact and failure impact energy increased by 421.9% and 461.3%, the net-gain in them by the synergistic action of silica fume and RSF with values of 102.7% and 115.3%. The distribution law of the impact life for RSF reinforced RAC can better describe by the two-parameter Weibull distribution function. Impact resistance life was predicted corresponding to reliability levels. SEM investigations revealed that the ITZ between cement and aggregate/RSF significantly improved by mixing silica fume.

Microscopic characterization of residual particles from filtered drinking water and determination of statistical indicators regarding identified deposits

The study shows the findings of a microscopic examination of samples of filtered water obtained using five different types of filters. The novelty of the approach to the research carried out in this paper consisted in using of a statistical mathematical model that confers increased accuracy on the resulting values, with the aim of characterizing the efficiency and quality of drinking water filters intended for the general public for domestic consumption at the national level. Atomic force microscopy was used to carry out the analysis, and particular mathematical models were used to statistically evaluate the findings. The paper explains the methodology used, including details on the laboratory setup, the steps finished, and the tools used to accomplish the suggested goals. With an emphasis on the three dimensions of the particles—height, diameter, and arithmetic roughness—the findings from the microscopic analysis of the particle deposits on the filtered water samples are given and tabular indexed. As a result, it was feasible to use a computational mathematical model to identify the statistical indicators of the values recorded in the samples that underwent microscopical analysis. Following the application of the mathematical model, the findings were centralized, and their correlation was analyzed using graphical representations. The results led to the concrete identification of the impurity degree of drinking water filtered by consumer means.

Studies Advanced in Image Super-resolution Reconstruction based on Deep Learning

Image super-resolution reconstruction (SR) has always been a research hotspot in the computer vision community, whose purpose is to convert low-resolution (LR) images into high-resolution (HR) images by algorithms without changing the hardware. Early SR works were mainly based on manual features and mathematical statistical models, relying on interpolation to achieve high-resolution image reconstruction. Thanks to the rapid development of convolutional neural networks, SR based on deep learning has achieved breakthroughs in both accuracy and speed. This paper first introduces the basic principles of image super-resolution reconstruction, including the basic framework and loss function of SR. Then, we introduce the representative super-resolution reconstruction methods such as SRCNN, SRGAN, and TTSR. We also introduce the common public datasets and evaluation indexes, and compare the performance of several SR methods to analyze their advantages and disadvantages. Finally, we summarize the existing challenges in the image super-resolution reconstruction, and give a look out for the future development direction of SR.

Consumers’ Behavior in the Field of Organic Agriculture and Food Products during the COVID-19 Pandemic in the Czech Republic: Focus on a Comparison of Hyper-, Super- and Farmers’ Markets and Direct Purchases from Producers

The aim of this paper is to assess Czech food consumers’ behavior when buying organic products during the COVID-19 pandemic, with an emphasis on the place of purchase of organic agriculture and food products—especially those purchases with the shortest logistics value chain, i.e., purchase at farmers’ markets, or directly from the producer—and a comparison with the current most common places of purchase of organic products in the Czech Republic, supermarkets and hypermarkets. Categorical data analysis methods were used to create a profile of the consumer according to the most frequent purchase locations. To create mathematical–statistical models and interpretations, the methods of logistic regression, correspondence analysis and contingency table analysis were chosen. According to the results of the survey, respondents under 25 years of age are the least likely to make purchases at farmers’ markets or directly from the producer. Consumers aged 26–35 and with a university degree are the most likely to buy organic agriculture and food products at this location, followed closely by older respondents in the categories 36–45 and 46+ and with a secondary education. It is important for manufacturers to have an overview of where, in what quantities, and for what reasons consumers buy their products, especially for reasons of production optimization and planning, ecological concerns, rural development, and the impact on local areas and the value chain.

Analysis of machined surface topography of AISI M2 in hard turning based on Box-Behnken Design

The surface topography of the workpiece directly affects its service performance. In this study, CLSM and SEM are used to analyze the effects of turning speed, turning feed, and turning depth on the three dimensional topography and surface defects of the machined surface. Amplitude parameters are used to characterize the machined surface topography of hard turning. Twelve groups of single factor experiments are used to analyze the influence of turning parameters on surface topography. Based on analysis of variance (ANOVA) and 15 groups of Box-Behnken Design (BBD), whether cutting parameters have significant influence on arithmetic mean deviation ( Sa) is analyzed. A mathematical statistical model of Sa is established by Response Surface Methodology, and the effectiveness of the model is verified by 10 groups of experiments. By analyzing the research results, it can be concluded that: (1) The consistency of the surface topography of hard turning is good; (2) In the turning feed direction, the surface defects of the machined surface by hard turning include turning grooves, material side flow, adhering chips, and material surface tearing; (3) In hard turning, the most significant factor affecting the three dimensional roughness ( Sa) is the turning feed.

Prediction of regional carbon emissions using deep learning and mathematical–statistical model

Detecting carbon emissions is the key to carbon peaking and carbon neutrality goals. Existing research has focused on utilizing data-driven method to study carbon emissions off a single object. This study proposes a regional carbon emissions prediction method. The area objects are divided into dynamic objects for vehicles and static objects for buildings. For the dynamic object, carbon emissions is modeled using the vehicle location provided by the BeiDou satellite navigation system (BDS). For the static object, the neural network R3det (rotation remote sensing target detection) is used to identify the buildings in remote sensing images, and then the trained ARIMA time series model is used to predict the carbon emissions. The model is tested in an industrial park in Tangshan, Hebei Province in China. The result of the regional three-dimensional emission map shows that the method provided a novel and feasible idea for carbon emissions prediction.

ФАКТОРЫ РИСКА НЕУДАЧИ ЛЕЧЕНИЯ ТУБЕРКУЛЕЗА ОРГАНОВ ДЫХАНИЯ У ДЕТЕЙ И ПОДРОСТКОВ

Objective: to identify the major risk factors for treatment failure among children and adolescents with pulmonary TB. Materials and methods: aretrospective comparative study enrolled 141 patients aged 2–17 years with different forms of pulmonary TB. Upon completion of the main chemotherapy course consisting of the intensive and continuation phases, the patients were divided into two groups: group 1 – patients with treatment failure, group 2 – patients with treatment success. We compared the patients’ gender and age, social status of the families, the presence of medical or biological risk factors (the absence of anti-TB vaccination, concomitant chronic diseases, acute infectious diseases during the treatment, TB process at detection, drug resistance patterns in the patients and infection sources, the time of drug resistance development, the information about chemotherapy regimens and treatment administration, the occurrence and duration of treatment interruptions) in the groups. The obtained data were processed using binary logistic regression carried out by the SPSS 21.0 software. Results: we built a mathematical statistical model of the individual risk for treatment failure among children and adolescents with pulmonary TB. Conclusion: the major risk factors for treatment failure among children andadolescents with pulmonary TB were associated with inadequate chemotherapy: ignorance of drug resistance patterns on the initial treatment phase, defective use of chemotherapy potentials, wrong choice of treatment administration form. Late detection of TB (lung destruction, advanced TB process) was a more frequent factor in group 2 than group 1 but did not significantly influence treatment outcome.

Дослідження впливу параметрів глибокорозпушувача та комбінації робочих органів на ефективність обробітку ґрунту

The paper proves the expediency of deep subsurface tillage with combined chisel deep tillers and raises the question of the expediency of studying the influence of tillage unit parameters and a combination of operating parts on the efficiency of tillage. Existing research addresses the issues of soil monolith destruction, interaction of certain elements and operating parts with soil particles, construction of statistical models of the operation of certain elements of tillage units, search for rational forms of surfaces of operating parts and the ways to reduce overall traction resistance of different deep tillers, but the assessment of the quality of operation of such tillage units depending on their design, combination of operating parts and parameters has not been sufficiently studied. To study the parameters of a deep tiller, a prototype was made, which is actually a full-fledged tillage unit with three chisel tines with a straight riser, a chisel, a tooth and wings. The design of the experimental deep tiller is made in such a way that the position of the chisel tines on the unit frame can be changed on the brackets in a wide range, both between rows and in terms of the working width of the unit. In addition, the deep tiller can be operated with different variants of the toothed roller. After selecting the most significant factors and the interval of their values based on the methodology for planning a multivariate experiment, studies were conducted to obtain a statistical mathematical model and response surfaces for tillage efficiency. The obtained regression equation was tested for reproducibility and adequacy, and the graphical display of the research results allows obtaining the desired design parameters and operating modes of the tillage unit. Experimentally found areas of rational values at which the quality of soil pulverization is equal to 70...75%, which is achieved at the depth of loosening with chisel tines 32...42 cm, the distance between the chisel tines in one row 80... 100 cm, distance between rows of chisel tines 40...55 cm, tillage speed 8...9.5 km/h, depth of wings on the tine riser 24...27 cm and number of additional operating parts (toothed rollers) 2 pcs.