Statistical Mathematical Modeling Research Articles

Identifying spatiotemporal traffic patterns in large-scale urban road networks using a modified nonnegative matrix factorization algorithm

The identification and analysis of spatiotemporal traffic patterns in road networks constitute a crucial process for sophisticated traffic management and control. Traditional methods based on mathematical equations and statistical models can hardly be applicable to large-scale urban road networks, where traffic states exhibit high degrees of dynamics and complexity. Recently, advances in data collection and processing have provided new opportunities to effectively understand spatiotemporal traffic patterns in large-scale road networks using data-driven methods. However, limited efforts have been exerted to explore the essential structure of the networks when conducting a spatiotemporal analysis of traffic characteristics. To this end, this study proposes a modified nonnegative matrix factorization algorithm that processes high-dimensional traffic data and provides an improved representation of the global traffic state. After matrix factorization, cluster analysis is conducted based on the obtained low-dimensional representative matrices, which contain different traffic patterns and serve as the basis for exploring the temporal dynamics and spatial structure of network congestion. The applicability and effectiveness of the proposed approach are examined in a road network of Beijing, China. Results show that the methods exhibit considerable potential for identifying and interpreting the spatiotemporal traffic patterns over the entire network and provide a systematic and efficient approach for analyzing the network-level traffic state.

Математико-статистичні методи у моніторингових економетричних дослідженнях

Quality monitoring in modern conditions is carried out using mathematical and statistical methods. With the help of mathematical and statistical methods of research, large amounts of information are processed and causal dependencies are established. The use of statistical techniques contributes to the ability to read reports on statistical studies in the field of education and economics, and teaches techniques for analyzing the data obtained. The article uses a method of multidimensional statistical analysis, defines the identification of the mathematical-statistical model and calculates the coefficients of the influence of the model parameters on the required values of the economic characteristics of a complex system . The main tool for processing incoming information is the theory of random matrices. The construction of mathematical models in modern conditions in the application of a very large number of parameters requires the development of such approaches, which can take into account all the necessary situations, without losing important input information. The development of statistical methods often requires obtaining objective information to select a method for forecasting and assessing the situation. The task is to show the advantages of using some probabilistic approaches in the examples of a complex economic system (assessing the quality of education). Analysis of recent research and publications. Theoretical-probabilistic approach to the solution of applied problems, in which the number of parameters is large, was considered in the works of V.L. Girko [1-4]. The constructed apparatus in the theory of random matrices is tested on dimensionless input data and the research was conducted on examples of complex mathematical models. The aim of the study. There is a lot of applied tasks in the life of a society in which it is almost impossible to calculate the set of indicators without using the construction of models. Assessment of the quality of education and forecasting is an urgent task for which the scientific method of mathematical statistics must be applied. However, looking at the data, it becomes clear that they have time and space restrictions. The multidimensionality of economic and technical indicators of each unit enhances the intuitive assessment of the situation in each case. Many tests are unprofitable, and the characteristics of the parameters come with disabilities. It becomes clear that the use of multivariate statistical analysis allows you to take into account all these complexities. It is proposed to perform a statistical processing of a large number of observations, taking into account probable errors within the constraints assumed. To more accurately identify the proposed mathematical-statistical model, it is necessary to gather all the information at different moments and write it in the corresponding matrix. This information should be taken into account constantly. Keywords : multi-statistical analysis, probability, mathematical model, stochastic matrix

Eurointegration aspects of meat production in agricultural enterprises of Ukraine: problems and prospects

European integration processes have become an indispensable feature and direction of development of meat cattle breeding in Ukraine. To calculate the forecast value of gross production of livestock products, we have chosen a method based on the construction of mathematical statistical models. Forecast indicators of cattle livestock in agricultural enterprises of Ukraine are calculated by constructing a polynomial trend line, since the equation of this model has the highest correlation and determination coefficients (0.980051 and 0.9605 respectively), that is, it describes a number of dynamics most reliably. The polynomial trend model is described by the following equation: y = 35.134x2 – 1704.8x + 20748. According to the results of calculations in 2025, the achievement of the cattle population is projected at 2.243.7 thousand heads. The dynamics of the pig population also reflects the polynomial trend model described by the following equation: y = 19.638x2 – 812.86x + 10803, the correlation and determination coefficients of 0.885268 and 0.77837, respectively. In case of preservation of the current tendency, in 2025 the pig population in agricultural enterprises of Ukraine is expected to grow to 5011.2 thousand head, which is 38% more than in 2017. Based on the calculations (polynominal trend y = 148.43x2 – 2542.8x + 72000, the coefficients of correlation and determination are 0.808084 and 0.653), we forecast that in 2025 in agricultural enterprises of Ukraine, the number of all species of poultry will reach 153019,1 thousand heads. This is 1.4 times more than in 2017. According to our calculations (polynomial trend y = 3.013x2 – 134.03x1489.4, correlation coefficients and determination coefficients (0.95734 and 0.9165 respectively), the production of beef and veal in Ukraine in the coming years will gradually increase, despite decreasing volumes Due to the use of modern technologies and increased production intensification, we predict that in 2025 agricultural enterprises of Ukraine will produce 606.8 tons of pork, which is 50.1% more than in 2017. However, paying attention to the projected volumes of pork production, it should be borne in mind that agrarian production in general and pig production in particular are oriented towards market demand, therefore, its efficiency depends on the competitiveness on the domestic and foreign markets. The increased demand for poultry meat stimulates an increase in its volumes on an industrial basis, first of all, the production of broilers, as speedy and high-yielding poultry. According to our calculations (polynominal trend y = 2.1386x2 – 19.579x + 144.8, correlation coefficients and determination (0.985089 and 0.9704 respectively), using modern means of mechanization and automation of technological processes at low labor costs and facilities per unit of production, commodity producers will be able to produce in 2025 р. 2270,5 thousand. tons of poultry meat. In our opinion, the advantages of integrating meat poultry farming into the European Union are complicated by requirements and restrictions and create additional incentives for the development and improvement of production.

THE CURSE OF COUNTING AND THE DESTINY OF DATA

Writing numbers for counting and record-keeping predates the art of writing by a considerable margin. Never in the history of humankind has the urge to count and to measure everything been so prevalent as today. Numbers were traditionally used to count, measure, and label, but simple numbers have transformed into ‘DATA’, which has become an important, intrinsic, and all invasive part of life. Furthermore, the transformation from data to useful knowledge (and maybe some wisdom) requires, inter alia, the application of statistical analysis and mathematical modelling. Two applications illustrating this process will be presented: The possible existence of an association between some human characteristics — for example, neck circumference and general health — will be investigated, and a model based on nonlinear regression presented. A system dynamics model to investigate the dynamic characteristics of a human sub-system will be developed and discussed. This paper is merely an attempt to investigate the possibility and viability of developing data-dependent models of a medical nature.

Experimental studies of machining parameters on surface roughness, flank wear, cutting forces and work piece vibration in boring of AISI 4340 steels: modelling and optimization approach

The statistical mathematical models are developed to investigate the influence of cutting parameters on surface roughness, tool wear, cutting force, tangential force and the work piece vibration in boring of AISI 4340 steels. A full factorial design of experiments is used to conduct 27 experiments on AISI 4340 as the work piece material and TiCN–Al2O3–TiN multi-layered coated carbide inserts. Online data acquisition of cutting forces on the cutting tool and the work piece vibrations are measured by using piezo-electric dynamometer and laser Doppler vibrometer, respectively. This paper proposes optimization method using grey relational analysis (GRA) and predictive models like support vector machine and response surface method are used to predict the GRG values and optimize the machining parameters. The GRA is used for converting multi response optimization problem into optimization of single objective of grey relational grade (GRG). Finally confirmation test was performed and also optimized the machining parameters to minimize the surface roughness (Ra), tool wear (VB), cutting force (Fx), tangential force (Fz) and work piece vibration (VA).

Hypervolemia Screening for Dialysis Patient Healthcare Using Meta Learning Model-Based Intelligent Scaler

ABSTRACTSodium intake and diet are the main factors controlling fluid volume balance and changes in body weight for dialysis patients. Inadequate dry weight controls will lead to various complications. Sometimes, inadequate fluid volume removal will cause hypotension during dialysis treatment. Therefore, maintaining adequate body weight, water volume balance, and blood pressure are important in the healthcare of dialysis patients. The anthropometric method is a non-invasive and mathematical statistical model to estimate the total body water with the patient characteristics, including gender, age, height, and weight. In the experienced anthropometric methods, Watson standard formula is a well known criterion and has < 2% margin error for estimating TBW in different populations. For multipatient use in hypervolemia and hypovolemia screening, the enrolled dialysis patients will gradually increase, thus, new criterions are required to meet the modified individual standard with varying patient characteristics. This study proposes a meta-learning model-based intelligent scaler. When new subjects or existing subjects update new training patterns in the current active database, an incremental learning scheme is used to retrain the generalized regression neural network, updating new training patterns or adding incremental ones. The meta-learning model also possesses learning-to-optimization capability using the particle swarm optimization algorithm. Through incremental training patterns, this intelligent scaler can gradually enhance optimization that can be applicable to individuals of all gender and age groups. The experimental results indicate that the proposed screening model provides an assistive tool for maintaining an appropriate BMI and dry weight in the healthcare of dialysis patients.

Effect of organic loading rate on the removal of DMF, MC and IPA by a pilot-scale AnMBR for treating chemical synthesis-based antibiotic solvent wastewater

This study focuses on the effects of organic loading rate (OLR) on the removal of N,N-Dimethylformamide(DMF), m-Cresol (MC) and isopropyl alcohol (IPA) by a pilot-scale anaerobic membrane bioreactor (AnMBR) for treating chemical synthesis-based antibiotic solvent wastewater at period of improved influent COD concentration with decreased HRT. The whole process was divided into five stages in terms of the variation of OLR ranging from 3.9 to 12.7 kg COD/(m3·d). During 249 days of operating time, the average DMF, MC, IPA removal efficiency were 96.9%,98.2% and 96.4%, respectively. Cake layer was accumulated on the membrane surface acted as a dynamic secondary biofilm which lead to the increase of physical removal rate. In addition, mathematical statistical models was built on the linear regression techniques for exploring the inner relationship between EPS and the performance of the AnMBR.

Influence of manufacturing parameters on the strength of PLA parts using Layered Manufacturing technique: A statistical approach

A 3D printing was successfully used to fabricate samples of Polylactic Acid (PLA). Processing parameters such as Lay-up speed, Lay-up thickness, and printing nozzle were varied. All samples were tested for flexural strength using three point load test. A statistical mathematical model was developed to correlate the processing parameters with flexural strength. The result clearly demonstrated that the lay-up thickness and nozzle diameter influenced flexural strength significantly, whereas lay-up speed hardly influenced the flexural strength.

Метод пробных заготовок в обеспечении параметров шероховатости поверхности деталей машин

A method for technological support of roughness parameters for machine parts based on an experimental statistical approach is considered. The essence of the method consists in the processing of test blanks (or their test surfaces) according to a pre-planned scheme, in the roughness parameter assessment of test blanks, in the development of mathematical statistical model of the connection of roughness parameters with technological factors and on the basis of the model given a definition of their levels ensuring obtaining the roughness parameter values specified at machining a basic batch blanks. The peculiarities in technological support of relative supporting lengths of a rough surface profile and also a method for the formation of complex functional parameters of a rough surface are touched upon. The necessity for the creation of portable control measuring systems allowing the realization in practice this method is emphasized.

РОЗРОБКА МОДЕЛІ ФУНКЦІОНАЛЬНОГО СТАНУ ОБ'ЄКТА МОНІТОРИНГА ДЛЯ ЗАВДАНЬ ОЦІНКИ РИЗИКІВ ВИНИКНЕННЯ НАДЗВИЧАЙНИХ СИТУАЦІЙ

Here one can find the approach to develop a model of functional state of researched object for the assessment of the risks emergencies appearance. The analysis of the causes of appearance and development of natural and anthropogenic emergencies is conducted and the most indicative causes are defined. Emergency risk analysis is part of a system-wide approach to decision-making in the process of managing territories, procedures and practical measures to address the challenges of managing a security process. The basis of risk analysis is the physical and mathematical modeling of natural and socio-economic systems and processes occurring in them, which involves the interaction of the main components of the system with the environment in regular and extra-ordinary situations. Since dangerous phenomena (emergencies) occur in a certain area with specific coordinates, it is quite clear that geo-information systems (GIS) and geo-information technologies (GIS) are most appropriate for assessing the risk of emergencies. To describe the functioning of the monitoring object it is necessary to construct its mathematical model. The most complete state of the object of the study is characterized by its mathematical functional and statistical model (a system of equations that describes the dependence of the parameters of the monitoring object, its systems and subsystems on external and internal effects in the process of its functioning). Based on the analysis of this model, it becomes possible to formulate the main tasks that are solved by GIS in monitoring of natural or socio-economic systems, and synthesize the optimal structure of GIS.

Investigating Economic Growth, Trade Issues and Future Energy Strategies for Central Asian Countries

We examine the economic growth, energy development policies and strategies for the CAC from various perspectives. We apply statistical data analysis techniques and mathematical modelling methodologies focusing upon regression model analysis in order to deal with the economic and energy related data during the period 1990-2014, and to investigate the relationship among economic growth, energy production, and the trade of energy resources in order to find future desirable policies and strategies for the CAC. Findings show that energy production growth would bring statistically significant positive impact on GDP growth in fossil-fuel rich Kazakhstan, Uzbekistan, and Turkmenistan while we also find negative impact of GDP growth on the trade balance of the CAC except for Turkmenistan. Another finding follows that the foreign direct investment has a significant influence on the trade balance in the cases of Uzbekistan and Turkmenistan, which institute import substitution policies right from their initial years of independence. Based on these quantitative investigations on economy, energy, and trades we propose future energy strategies for the CAC, stressing the importance of diversification of economies.

Improving an Expert-Supported Dynamic Programming Algorithm and Adaptive-Neuro Fuzzy Inference System for Long-Term Load Forecasting

Load forecasting is very important to manage the electrical power systems. Load forecasting can be analyzed in three different ways as short-term, medium-term and long-term. Long-term load forecasting (LTLF) is in need to plan and carry on future energy demand and investment such as size of energy plant. LTLF is affected by energy consumption, national incoming per year, rates of civilization, increasing population rates and moreover economical parameters. Some of the forecasting models use mathematical formulas and statistical models such as correlation and regression analysis. In this study, a new effective expert-supported dynamic programming algorithm (ESDP) has been improved. Additionally, adaptive neuro-fuzzy inference system (ANFIS) and mathematical modeling (MM) are used to forecast long term energy demand. ANFIS is one of the famous artificial intelligence and has widely used to solve forecasting problems in literature. In addition to numerical inputs, ANFIS has linguistics inputs. The results obtained from ESDP, ANFIS and MM are compared to show availability. In order to show error levels mean absolute percentage error (MAPE) and (MAE) are used. The obtained results show that the proposed algorithms are available.

NEW APPROACH TO SOLVING THE PROBLEM OF COMPLEX REGIONAL PAIN SYNDROME

Aim - to improve the results of treatment of patients with complex regional pain syndrome (CRPS) in bone fractures of the lower extremities by applying a new integrated approach. Methods. A new approach to solving the problem of complex regional pain syndrome in fractures of lower limb bones is proposed, including the use of modern minimally invasive methods for surgical treatment of fractures of the lower limb bones, such as blocked osteosynthesis, Fixion technology, use of angular stability plates, metal structures for osteosynthesis of the proximal femur. All these measures help to minimize the negative effect that is produced on the bone by such factors as prolonged immobilization and absence of early movements of the joints, which will make it possible to perform CRPS prophylaxis in bone fractures of the lower limbs more effectively. If it is not possible to prevent the development of CRPS, then it is necessary to administer complex therapy, including psychoemotional correction, adherence to the regime, proper immobilization, rehabilitation exercises, physiotherapy, medical treatment, hyperbaric oxygenation, and gravitational therapy. Results. Clinical tests, radiography, densitometry, method of statistical analysis and mathematical modeling with elements of evidencebased medicine objectively confirmed the activation of the restorative processes in altered tissues of the lower limbs due to the use of the new complex. Conclusion. The analysis of the obtained data of clinical and functional methods of research has proved that the total value of positive results is 80%.

Statistical-mathematical model of the process of extraction of pumpkin seeds by CO2‑extraction

Statistical-mathematical model of the process of extraction of pumpkin seeds by CO2‑extraction

Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients

We examine uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigate mathematical model and statistical model misspecifications in the context of least squares methodology. A difference-based method is directly applied to data to determine the correct statistical model that represents the uncertainty in data. We then carry out an inverse problem with the corresponding iterative weighted least squares technique and use the resulting modified residual plots to detect mathematical model discrepancy. This process is implemented using both clinical and simulated data. Our results demonstrate mathematical model misspecification when both simpler and more complex models are assumed compared to data dynamics.

Epistemological perspectives in business research: an analytical review

Philosophically, positivism adheres to the realistic knowledge acquired through observation, empirical evidences and measurement. In positivism studies the role of the researcher confined to data collection, analysis, and interpretation that are observable and quantifiable within the set objectives. Statistical techniques and mathematical modelling are central to positivist research, which adheres to structured research techniques and pre-determined research designs. Positivist researchers tend to make generalisations with limited observations and data evidences, which have emerged as one of the fundamental weaknesses of the positivist philosophy. They believe positivism is deductive research process in management, which eliminates the possibility of conceptualisation against the evidence based research. This paper aims at critically examining the positivism in management research stemming out of the epistemological growth in management research and contributes to the existing literature by interpreting the convergence of classical school of thoughts with the contemporary ideology on management research.

Modeling of Emissions and Dispersion of Harmful Compounds from Marine Main Propulsion Diesel Engines of Vessels Navigating in Specified Water Basins

Abstract The article presents the results of the first nationwide study of a pro-ecological character, including the problem of the impact of shipping (in a particular basin) on the terrestrial human environment. Shipping in the waters of the Bay of Gdansk is taken as an example of the real system and a detailed identification of the operating conditions for the vessels has been undertaken. Data were obtained from the analysis of information gathered by surveillance systems of vessel traffic (such as Automatic Identification System - AIS) for the complete identification of parameters and characteristics of shipping traffic in the form of deterministic and statistical mathematical models. On the basis of these mathematical models of the emission of harmful exhaust emissions from marine engines have been developed. Models of the spread of exhaust gas are based on the models of Gauss, Euler and Lagrange. Their use has enabled a scientific tool to evaluate the contribution of immission of harmful compounds in the global immission of pollutants in the atmospheric air of the Tri-city agglomeration to be obtained.

Can economics be a physical science?

Economics and other social sciences stem from the same methodological scientific revolution that gave birth to the natural sciences. The natural and social sciences share a commitment to the dialectical process of theory formation on the basis of empirical findings and theory revision to incorporate empirical anomalies. Claims that the subject matter of social and natural sciences differ qualitatively in terms of mathematical formalism, statistical modeling, or reductionism are unconvincing. The notion of a “value-free” character to natural sciences fails historical and critical tests. Natural and social sciences share an ideological component in their representation of the relation between the subject and the external natural and social world. Natural sciences arise from the struggles of human beings with nature in the process of social reproduction, while social sciences arise from the struggles of human beings with each other and with the class divisions social reproduction imposes.

Formulation and Evaluation of Rifampicin Liposomes for Buccal Drug Delivery.

Drug delivery through liposomes offers several advantages, but still challenging to the researchers for the use of liposomes as carriers in drug delivery due to their poor physical stability, unpredictable drug encapsulation and systemic availability of the loaded drug. The present investigation was planned with an objective to prepare Rifampicin loaded liposomes by using response surface methodology of statistical 32 factorial design and further to formulate them into pastilles for deliver through buccal route thereby to enhance systemic absorption. Rifampicin liposomes were prepared by using different ratios of soya lecithin and cholesterol by solvent Injection method. These liposomes were characterized by using optical microscopy, Scanning Electron Microscopy (SEM) and evaluated for particle size, entrapment efficiency (EE), in vitro and ex vivo drug release. Main effects and interaction terms of the formulation variables were evaluated quantitatively using a mathematical statistical model approach showing that both independent variables have significant (P value < 0.05) effects on particle size (P value: 0.0273), percentage entrapment efficiency (P value: 0.0096), percentage drug release through dialysis membrane (P value: 0.0047) and percentage drug release through porcine buccal membrane (P value: 0.0019). The statistical factorial design of liposomal formulations fulfilled all the requirements of the target set and exhibited suitable values for the selected test parameters. Pastilles were prepared for liposomes using glycerol gelatin base and were found to be soft, smooth with uniform drug content and drug release.

Experimental research on the sealing ability of borehole packers

With the use of a full factorial experimental design based on a Box­Hunter rotatable central composite plan for second order response surfaces, it was possible to obtain a statistical mathematical model of the impact of the diametrical tension, the test pressure, and the radial clearance between the thrust bush and the casing as well as the shear modulus of the material on the amount of contact pressure, which is represented by a polynomial of the second order. The research was carried out on the laboratory model of the PJSC “Ukrnafta” (Poltava, Ukraine). The analysis of this model shows that an essential impact on the sealing ability of the self­sealing ring (the value of contact pressure) is made by the following series of factors: the test pressure, the diametrical tension, the radial clearance, and the shear modulus of the compaction material. Moreover, the test pressure factor is characterised by nonlinearity, which manifests itself in intersections of the hypersurface response. The study has experimentally determined the patterns of distributing contact pressure along the length of the conjugate surface between the ring and the casing, characterized by a decreasing contact pressure from the edge of the working bite to the supporting section of the ring. The research has demonstrated that it is possible to manage directly the sealing ability of borehole packers, particularly by changing the geometric parameters of the packer compaction.