Statistical Mathematical Modeling Research Articles

Określanie szacowanego czasu pracy maszyn i wydajności sprzętu w przedsiębiorstwie naftowo-gazowym w warunkach niepewności

One of the main conditions for long-term forecasting of equipment requirements is to ensure the maximum level of equipment utilization, which characterizes production efficiency. In line with this condition, production in drilling departments must be organized to achieve an optimal volume that maximizes equipment productivity. In other words, it is necessary to determine the functional relationship between changes in the amount of equipment involved in the production process and its productivity. Following this, it is necessary to determine the optimal amount of equipment for the enterprise to maximize its productivity. The primary goal is to identify the negative and positive consequences of changes in the production scale. This article examines the solution to the above issues using the example of SOCAR (State Oil Company of the Azerbaijan Republic). To adequately address this problem, a procedure for determining the estimated machine time for each drilling equipment at the enterprise level is proposed, using the “Annual drilling calendar balance” report from the SOCAR enterprise, Azerbaijan. It is known that as the drilling depth of a well increases, so do the labor costs associated with drilling. To solve this problem, the research examines the functional dependency of the amount of drilling equipment on its productivity. This study led to the development of a mathematical-statistical model to predict productive time based on drilling depth. The scientific innovations proposed in this article are presented with calculations, based on the example of the SOCAR drilling enterprise, offering practical insights. The results of the study can be applied when justifying production plans and forecasting future equipment and spare parts requirements for drilling enterprises.

Profitability of dairy goat farms in Bulgaria

Abstract. The purpose of the present study was to establish the economic performance of dairy goat farms in Bulgaria by using the indicator profitability and the related indicators – total production, total revenues, total costs and profit per doe (before and after subsidy). Data for 2022 were provided by the owners of 8 farms within the survey and processed using a mathematical-statistical model and Excel program. The adopted production system was semi-intensive with indoor winter period and grazing (supplemented with cereals and hay) during most of the year. Profit before subsidies was found positive only for farm 5, and all other holdings were unprofitable based on the results of their own production. When subsidies were added, some of them reported a positive financial result, while others remained loss-making. Based on the results found within the study, it could be summarized that in the dairy sector the level of milk production is the leading factor for farm income. Оf great importance are also the sale of value-added dairy products, own feed production and optimization of labour costs. In most farms, subsidies (incl. for pastures) are extremely important for the viability of the farms. In addition, when analyzing the economic efficiency of dairy goats, an individual approach to farms is necessary. All elements of the production system, both biological and economic, should be taken into account in order to improve production and profits.

Beijing Symbiotic Courtyard Model’s Post Evaluation from the Perspective of Stock Renewal

Stock renewal is one of the important methods of urban renewal, which focuses on optimizing and reusing existing urban spaces. With the increasing land pressure in present-day China and the need for land to be reclassified, the thinking mode of stock updating has become increasingly important. Beijing symbiotic courtyard is a representative urban renewal model that combines the characteristics of traditional quadrangle dwelling and modern architecture, aiming to achieve the symbiosis of history and modernity. After several years of implementation, the effectiveness of this model has become a matter of concern for all parties involved. Therefore, this paper takes stock renewal as the observation perspective, describing an evaluation for the Beijing symbiotic courtyard model, which contains different types of residents living in particular historical districts. It attempts to propose corresponding strategies, aiming to provide a more comprehensive thinking angle and planning method for the sustainability of stock renewal. In contrast to earlier studies, the proposed methods involve a specific mathematical statistical model called the IPA-KANO model, in addition to other traditional urban renewal methods. For a wide range of problems including historical district evaluation and renewal, the approach leads to potentially less errors than caused by manual operation. This comes from the fact that all the data are collected through survey questionnaires and big data, so the technical restriction of using mathematical model is to some extent ruled out in this new approach. Moreover, the approach offers new potential problems that cannot be handled using earlier techniques. After the calculation, although there are still defects, local residents are generally satisfied with the Beijing symbiotic courtyard model. The result suggests that it is of importance to reference this model for urban renewal so that can be widely promoted in historical district vitality regeneration.

Modelación de crecimiento de frutos de tangor murcott e incidencia de factores medioambientales sobre los parámetros estimados

Fruit production forecasts are a tool to plan the harvest and improve market strategies. To carry it out, it is essential to have information about the behavior of fruit development over time. The objective of this work was to find the mathematical-statistical model that best describes the growth pattern of tangor murcott fruit (Citrus reticulata x C. sinensis 'Murcott') and analyze how it is affected by environmental conditions. For this, in nine orchards, located in four locations in the province of Corrientes, Argentina, the equatorial diameter of 2,053 fruit from 82 days after full flowering to harvest were periodically registered during five seasons. The nonlinear models were compared: Logistic, Gompertz, Brody, Von Bertalanffy, Weibull, Morgan Mercer Flodin (MMF), Richards, and their respective re-parameterizations. The magnitudes of nonlinearity measures, coefficient of determination and estimates of residual deviation were considered as the main goodness-of-fit criteria. The selected model-parameterization combination was the fifth parameterization of the Logistic model with random effects on its three parameters. An Analysis of Variance model on the estimates of these parameters for each fruit showed that orchard and season factors were an important source of variability, mainly in those related to the initial size of the fruit and their growth rate. These results will allow the construction of growth tables, which in addition to making yield predictions, can be used to estimate fruit size distribution at harvest and improve the cultural practice of manual fruit thinning.

Geological hazard susceptibility assessment based on different mathematical statistical models: a case study of Zhejiang province

Geological disaster is a great threat to people's life and property safety, how to predict it reliably and divide it according to the susceptibility of geological disaster is of great significance. Based on the historical collapse data of Zhejiang Province, this paper selects the evaluation indexes of water flow intensity index (SPI), terrain wetness index (TWI), land use type, slope aspect, slope, annual rainfall, river network density, elevation, road density, plane curvature, normalized difference vegetation index (NDVI) and other factors. Based on the frequency ratio model (FR), random forest model (RF) and logistic regression model (LR), the susceptibility zoning of geological disasters in Zhejiang Province is carried out. The results show that: (1) The high and extremely high risk areas in Zhejiang province are mainly distributed near the river system and road network in the high altitude area; (2) In terms of the evaluation effect of comprehensive PR curve, the random forest model has a better evaluation effect than other models; (3) With the increase of the vulnerability level, the proportion of disasters under each model zoning is gradually increasing, indicating that the zoning effect of each model is good; 4) Quzhou city, Jinhua City, Wenzhou city and Shaoxing city in Zhejiang Province account for a large proportion of the high susceptibility areas and above. The results of vulnerability zoning can provide reference for geological hazard prevention and land planning in Zhejiang province.

Experimental Analysis of Effect of Machined Material on Cutting Forces during Drilling.

Current research studies devoted to cutting forces in drilling are oriented toward predictive model development, however, in the case of mechanistic models, the material effect on the drilling process itself is mostly not considered. This research study aims to experimentally analyze how the machined material affects the feed force (Ff) during drilling, alongside developing predictive mathematical-statistical models to understand the main effects and interactions of the considered technological and tool factors on Ff. By conducting experiments involving six factors (feed, cutting speed, drill diameter, point angle, lip relief angle, and helix angle) at five levels, the drilling process of stainless steel AISI1045 and case-hardened steel 16MnCr5 is executed to validate the numerical accuracy of the established prediction models (AdjR = 99.600% for C45 and AdjR = 97.912% for 16MnCr5). The statistical evaluation (ANOVA, RSM, and Lack of Fit) of the data proves that the drilled material affects the Ff value at the level of 17.600% (p < 0.000). The effect of feed represents 44.867% in C45 and 34.087% in 16MnCr5; the cutting speed is significant when machining C45 steel only (9.109%). When machining 16MnCr5 compared to C45 steel, the influence of the point angle (lip relief angle) is lower by 49.198% (by 22.509%). The effect of the helix angle is 163.060% higher when machining 16MnCr5.

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.

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.

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.