Comparative Analysis Of Mathematical Models Research Articles

Comparative analysis of mathematical models describing radiobiological processes in radiotherapy

Comparative analysis of mathematical models describing radiobiological processes in radiotherapy

Comparative analysis of mathematical models for assessing damage to critical organs during radiation therapy

Comparative analysis of mathematical models for assessing damage to critical organs during radiation therapy

Comparative Analysis of Mathematical Models of Tracking Radio Altimeters

Introduction. Tracking radio altimeters of low altitudes are widely used in civil aviation. These devises use periodic frequency modulated continuous wave (FMCW) signals, while altitude measurements are based on processing the beat signal processing. For this purpose, a closed automatic control loop is arranged to maintain the frequency of the beat signal at a fixed level by changing parameters of the transmitted signal (the frequency deviation or the modulation period). An alternative approach to arranging the tracking loop for altitude variations is based on the use of a phase locked loop (PLL), which adjusts the reference signal – a copy of the emitted signal – to obtain the maximum cross-correlation of the beat and reference signals. А comparative analysis of short-range radio altimeters with other currently known tracking radio altimeters for various types of frequency modulation of the transmitted signal seems to be a relevant research task.Aim. An analysis of the influence of the type of frequency modulation on the accuracy of altitude estimation in a PLL-based radar altimeter, as well as a comparative analysis of this altimeter with other known tracking altimeters.Materials and methods. Mathematical models of tracking radio altimeters are proposed, and a computer simulation of their performance is carried out for the case of altitude estimation over a smooth flat surface.Results. The conducted comparative analysis of tracking radio altimeters confirmed the effectiveness of the PLL when processing signals of different frequency modulation type (sawtooth, triangular, and harmonic FM). Altitude estimates produced by PLL-based radar altimeters are unbiased, with their standard deviation not exceeding 3 cm for the signalto-noise ratio of greater than 10 dB and under the scenario parameters adopted in the work. The conducted comparison with other tracking altimeters showed that estimation errors of this radar altimeter are an order of magnitude smaller.Conclusion. A PLL-based tracking radar altimeter can be used to estimate the height of the aircraft flight. The quality of altitude estimates produced by this device is higher than those produced by other known tracking radio altimeters. Further research and field tests will investigate the accuracy of altitude estimation when working over a rough surface.

Verification of subclinical carotid atherosclerosis as part of risk stratification in overweight and obesity: the role of machine learning in the development of a diagnostic algorithm

Aim. Comparative analysis of mathematical models obtained using multivariate logistic regression (MLR) with stepwise inclusion of predictors and machine learning (ML) for assessing the probability of subclinical carotid atherosclerosis in normotensive overweight and obese patients without cardiovascular diseases and/or diabetes.Material and methods. We received data on patients from the Webiomed platform database. The inclusion criteria were age ≥18 years, body mass index ≥25 kg/m2, extracranial artery ultrasound results, while the exclusion criteria included diabetes and/or cardiovascular disease. MLR analysis was carried out with stepwise inclusion of predictors. ML algorithms were used to create an alternative model.Results. The overall percentage of true results for MLR model was 73,2%, while the proportion of true negative and positive predictions was 80,1% and 63,4%, respectively. Mathematical models created using ML methods are characterized by a predictive value from 75 to 97% with a sensitivity of 77 to 92% and a specificity of 80 to 98%.Conclusion. A significant superiority of ML models was revealed in the study of available clinical and paraclinical parameters. Integration of ML mathematical models into a diagnostic algorithm for making a decision to refer a low-risk patient for extracranial artery ultrasound will significantly improve its accuracy and cost efficiency.

Models of projects portfolio formation in construction business

The paper presents models and methods of projects portfolio formation in the construction business. The company’s strategy success depends on the projects which an organization includes in its portfolio to achieve strategic goals. Nowadays companies often use methods of individual project estimation and selection to include in their portfolio of projects. However, such approach does not consider the effect from an individual project on the whole portfolio financial result and the total risk as well as the specificities of the construction industry portfolio formation. There is usually a set of projects for evaluation and selection and, as a consequence, there are several potential portfolio combinations for a company to choose. Construction business is project-oriented and a correct choice of a certain project and a portfolio with the best combination of projects is a strategically important management element. Models and methods of portfolio formation and management will help to make a choice. The paper presents specific features of portfolio in the construction area which should be considered in the portfolio methodology formation. The comparative analysis of mathematical models for project evaluation and portfolio selection in the construction business was provided. The profiles of companies to implement different models were determined. The results of the research will be useful for scientists and practitioners to choose a model for application or adaption to a company’s needs.

Architectural construction using technologies based on knowledge about the flow of Bingham plastic fluids in various pipelines

Currently, such types of engineering work as construction of classic buildings and structures, as well as erection of new ones that have an irregular shape, i.e. curved, arched, elliptical, round and similar surfaces, can be performed using complex technological equipment, such as combined external or internal formwork, the use of shotcrete technology together with the off-formwork construction technologies (3D printers). One of the prerequisites for uniform transportation of media by a concrete pump through pipelines, concrete conveying pipes, and most importantly, their homogeneous distribution by an extruder during layering, is a study based on mathematical modeling and comparative analysis of mathematical models of the flow of Shvedov-Bingham fluids in pipelines of various cross-sections, determining the performance, optimal rheological properties of mortars and concrete liquids. This will allow further control of their fluidity and plastic viscosity during the extrusion process.

Intelligent control system for continuous technological process of alkylation

Relevance of intelligent control for complex dynamic objects and processes are shown in this paper. The model of a virtual analyzer based on a neural network is proposed. Comparative analysis of mathematical models implemented in MathLab software showed that the most effective from the point of view of the reproducibility of the result is the model with seven neurons in the hidden layer, the training of which was performed using the method of scaled coupled gradients. Comparison of the data from the laboratory analysis and the theoretical model are showed that the root-mean-square error does not exceed 3.5, and the calculated value of the correlation coefficient corresponds to a "strong" connection between the values.

Сравнительный анализ математических моделей судна с позиций управляемости по отклонениям

Сравнительный анализ математических моделей судна с позиций управляемости по отклонениям

The Rationale for Increasing the Theoretical Understanding on the Basic Concepts of Economic Theory

The issues dealing with the process of making rational decisions in the production and consumption, an accurate assessment of results and costs in the economy have been the focus of attention for many generations of economists. Assessment of results and costs in the economy are always associated with consideration of the prices for different types of resources. However, some underlying aspects of prices still require further comprehensive consideration. By now, the economic essence of such basic concepts of economic theory as money, price, and utility have not been studied thoroughly, on an appropriate theoretical level. Therefore, one cannot provide a monistic theoretical justification for many economic phenomena such economic processes as forecasting prices for economic resources, optimization of the market economy operation according to the theories of economic welfare, social (collective) choice, general equilibrium, etc. This study aims to increase the theoretical understanding of the basic concepts of economic theory, which would enable to eliminate inconsistencies and contradictions in their interpretation at the fundamental and applied levels of research. The methods of scientific abstraction, system and comparative analysis of mathematical models aiming to establish their possible inconsistency and incompatibility, a logical method, as well as economic and mathematical modeling were used as a methodological basis of the research. Upon conducting a comparative analysis of economic and mathematical models that describe the foundations of the economy, we identified their logical inconsistency and discrepancies with the underlying nature of prices, money and utility. Having analyzed utility functions and the “function of social or aggregated utility†, we proved the need for changing the traditional form of these functions, the need to introduce new phenomena, both individual utility functions and social utility functions that consider the system (emergent) characteristics of the economy. The authors propose considering the system (emergent) characteristics of the economy as: the matrix structure of the economy and the limited cyclic-temporal potential of its lifespan. We believe that the focus on the system (emergent) content characteristic of the nature of prices will allow a more accurate prediction and regulation of their future dynamics, and this will also enable to overcome one of the main contradictions of economic theory between the theoretical basis of consumer choices that are made according to utility values and the practical basis of these choices which are always made according to cost parameters.

МЕТОДЫ И УСТРОЙСТВА ДЛЯ ИЗМЕРЕНИЯ УДЕЛЬНОЙ ПОВЕРХНОСТИ ДИСПЕРСНЫХ МАТЕРИАЛОВ

The aim of this work is to systematize the information contained in scientific publications, patents, websites on methods and devices of measuring the specific surface area of dispersed materials, the classification of measurement methods, consideration of their physical bases, comparative analysis of metrological characteristics and mathematical models for specific surface measurements. Comparative analysis of mathematical models of measurement, metrological characteristics and the physical basis of the method is given. A patent search revealed that the described invention is used as adsorbate gas, nitrogen or argon, an inert gas (helium) as the carrier gas. To achieve adsorption temperature the liquid nitrogen is used as the refrigerant. Analysis of commercially available models suggests that a significant portion of analyzers operates on the base of the low-temperature gas adsorption method (BET), and only a small part is made with limited permeability methods measurement range of the specific surface materials. The most used is a laboratory method of low-temperature gas adsorption (BET method or MTD). Despite the many commercially available analyzers are fundamentally common dynamic response - a long analysis time, due to the fact that adsorption processes at low temperatures are slow. Such speed information to the control system is unacceptable because they do not allow the quality control process. Search and development of high-speed analyzer remains relevant for the determination of the specific surface.

Comparative analysis of mathematical models of the matrix photodetector used in digital holography

It is established, that in modern works on digital holography, three fundamentally different mathematical models of a matrix photodetector are used. Comparative analysis of these models, including analysis of the formula of each model and test calculations, has been conducted. The possibility of using these models to account for the influence of geometrical parameters of a matrix photodetector on the properties of recorded digital holograms is considered.

Comparative analysis of mathematical models for estimate of radiation net in grasslands

O saldo de radiacao e um parâmetro fundamental para diversos processos fisicos, quimicos e biologicos. Apesar de ser um parâmetro de grande importância, muitas das estacoes meteorologicas do Brasil ainda nao dispoem de equipamentos para medir o saldo de radiacao. Uma alternativa e a utilizacao de metodos matematicos para estimar o saldo de radiacao, todavia ha poucos estudos com relacao ao saldo de radiacao no Nordeste do Brasil. O objetivo deste trabalho foi avaliar a estimativa de quatro modelos (um proposto por Iziomon, dois por Fietz e Fisch e um pela FAO) propostos na literatura em areas de pastagens. Primeiramente determinou-se os parâmetros de ajustes, utilizando os dados referentes ao ano de 2011, e, depois a estimativa para os anos de 2012 a 2015, utilizando os parâmetros obtidos para o ano de 2011. De forma geral, os quatro modelos apresentaram desempenho satisfatorios durante a fase de calibragem dos parâmetros. Na fase de validacao, o modelo proposto por Iziomon conseguiu apenas o quarto desempenho, os modelos propostos por Fietz e Fisch obtiveram resultados bastante semelhantes, ficando na segunda e terceira posicao. O modelo proposto pela FAO obteve o melhor desempenho no periodo de validacao dos modelos. A B S T R A C T The net radiation is a fundamental parameter for various physical, chemical and biological processes. Although it is a parameter of great importance many of the weather stations in Brazil not yet have equipment to measure the net radiation. An alternative is to estimate the net radiation using mathematical models, however, few studies have evaluated the estimation of the net radiation in the Northeast of Brazil. The objective of this study was to evaluate four models (One proposed by Iziomon, two by Fietz and Fisch and one by FAO) proposed to estimate Rn in grasslands. Initially the parameters of adjustments were determined using data for the year 2011, and then for the estimation data for the years 2012 to 2015, using the parameters obtained for the year 2011. Overall, the four models presented satisfactory performance during the calibration phase of the parameters. In the validation phase, the model proposed by Iziomon achieved only the fourth performance, the models proposed by Fietz and Fisch obtained very similar results, being in second and third position. The model proposed by the FAO achieved the best performance in the validation period of the models. Keywords: net radiation, estimate, net radiometer.

Comparative Analysis of Mathematical Models in Epidemiology- There Adaptation to Explain Herding in Financial Markets

There are different approaches in the use of mathematical model to explain the spread of infectious disease. In epidemiological study the models like Cox,B Spline, SIR and Transmission probability are used to explain herding effect. Bulk of the studies shows the use of these models in Epidemiological research. This paper tries to find the rational of choosing particular models. The collected data sample could be left truncated, right truncated, interval censured and similarly the approximation required to fit the dataset in models could be different. This paper tries to find out the appropriate model which can be used to describe herding phenomena in case of financial market. One of the key finding is that it is better to use B spline model due to the present of left truncated data in a stock market crash or in a bank run.

Mathematical Models Of Torque-Velocity Relation

The modeling of torque-velocity relationship in various joints and different muscle groups is analyzed in the literature mainly with polynomial functions. The purpose of this study was to compare the mathematical models with polynomial, cubic spline and Boltzmann function. The torque (Nm) was measured at 10 untrained women with isokinetic dynamometer for flexors and extensors of the elbow of the following range of velocities 30-210 $^o$/s. There was no statistically significant differences in the values of peak torque between flexors and extensors at all velocities (Kruskal-Wallis ANOVA, p$<$ 0.05). However, there differences in the values of the torque, more pronounced of the high velocities were established (Kruskal-Wallis ANOVA). The comparative analysis of mathematical models fitted with a polynomial of 4th order, proved the optimal in our previous study, with a cubic spline and with a Boltzmann function, of torque-velocity relation revealed: (1) Although the modeling with cubic spline, the interpolation curve passes through all points unlike with polynomial curve at 4th order, the curves at both models show nonphysiological behavior especially at flexors in the range 180-210 $^o$/s. and (2) The curves obtained by modeling of the relationship with Boltzmann function, were as close as possible to the classical force-velocity relation of the Hill (Proc. R. Soc. Lond., 1938, 126 (843)) for a single mascle. Further studies are needed to determine how much exponential functions, which are less studied, are optimal for the modeling of such relationships.

Сравнительный анализ математических моделей аппроксимации тока абсорбции

Сравнительный анализ математических моделей аппроксимации тока абсорбции

Mathematical modelling of the within-host HIV quasispecies dynamics in response to antiviral treatment

AbstractThe aim of this work is the construction, calibration, and comparative analysis of mathematical models of the evolution of the human immunodeficiency virus (HIV) in the course of infection when the models are based on deterministic principles of the quasispecies theory (Eigen-Schuster) and on stochastic approaches of genetic algorithms (Holland). The models take into account the replication of viral genomes and selection of descendants according to their fitness, point mutations, multi-infection of target cells and recombination of genomes at the stage of formation of proviral DNA. The processes of diversification of the virus population under the action of the antiviral drug azidothymidine (AZT) that blocks reverse transcription of the virus are simulated. A four-letter alphabet is used in the stochasticmodel for description of nucleotide sequences. The parameters of the model are estimated using original data on the degree of adaptation of the HIV mutants that are partly or completely resistant to this drug. The influence of parameters of infection on the characteristics of viral mutants population diversity is studied

Research of mathematical models in design of experiments by the method of comparative analysis

The method and soft for realization of comparative analysis of mathematical models of processes and effects, which were received by methods of complete factorial and fractional factorial experiments, are developed. In result the most optimal goodness of fit of mathematical models are Fisher’s and Munn-Whitney criterion. Refs.: 11 titles.Keywords: design of experiments; comparative analysis; complete and fractional factorial experiment; soft.

Comparative analysis of mathematical models of cell death and thermal damage processes

The standard method for assessing hyperthermia treatment has been calculation of cumulative equivalent minutes at 43 °C, CEM43 and its variations. This parameter normalises treatment thermal histories rather than predicts treatment results. Arrhenius models have been widely used in analysing higher temperature thermal treatments and successfully employed to predict irreversible thermal alterations in structural proteins. Unfortunately, in many, but not all cases they fail to represent thermally induced damage or cell death at hyperthermic temperatures, 43–50 °C, exhibiting significant over-prediction of the initial ‘shoulder’ region. The failure arises from the simplifying assumptions used to derive the irreversible reaction format that has been used in thermal damage studies. Several successful multi-parameter fit methods have been employed to model cell survival data. The two-state statistical thermodynamic model was derived from basic thermodynamic principles. The three-state model results from relaxing the assumptions under the Arrhenius formulation that result in an irreversible reaction. In other cell processes studied in vitro the irreversible Arrhenius model holds, and is sufficient to provide an accurate and useful estimate of thermal damage and cell death. It is essential in numerical model work to include multiple thermal damage processes operating in parallel to obtain a clear image of the likely outcome in tissues. Arrhenius and other C(t) models have that capability, while a single value for CEM43, does not.

A comparative analysis of mathematical models of the cochlea

The article describes the role of the shape of the cochlea and the role of the Reissner’s membrane, that are relating to formulation of the problem of constructing a mathematical model of human cochlea. For the first time in a three-dimensional model was included the longitudinal coupling in form of elastic stiffness of fibers.Reference 7, figures 2

Comparative analysis of mathematical models for supercritical extraction simulation from industrially valuable lamiaceae herbs

AbstractThe present study was aimed to compare different mathematical models used to simulate process of supercritical extraction from commercially important Lamiaceae herbs. Supercritical extractions with carbon dioxide from rosemary, sage, thyme and lavender originated from the southern Balkan region were performed at 10 MPa and 40°C. Obtained extraction curves were simulated by the model based on the heat transfer analogy, Sovova's model and the model on the micro‐scale. The models were used to analyse mass transfer phenomena and to quantify mass transfer parameters in the fluid and/or solid phase as well as the solubility of the solute in supercritical phase.