Karzan Faidhi Hamad, Bulent Celik, Rizgar Maghded Ahmed
In recent years, there has been a notable increase in interest regarding intelligent classification techniques rooted in Machine Learning within the domain of medical science. Specifically, machine learning, a pivotal area of artificial intelligence, has been extensively utilized to aid medical professionals in predicting and diagnosing various diseases. This study applies two distinct machine learning algorithms to address a medical diagnosis concern related to circular masses in breast cancer. The dataset encompasses 150 cases of breast cancer patients. The primary objective is to assess and compare the effectiveness of artificial neural networks (ANNs) and linear discriminant analysis (LDA) classifiers based on key criteria: accuracy, sensitivity, specificity, and the kappa coefficient in predicting circular masses within breast cancer. Results indicate that the performance of the ANN classifier surpasses that of the LDA model, achieving an accuracy of 97.7%, sensitivity of 95%, specificity of 100%, and a kappa coefficient of 95.31%. Additionally, the final fitted models unveil the pivotal factors significantly influencing circular masses in breast cancer, highlighting Solidity and Entropy as the most critical variables.
Abstract We provide a new, flexible model called the Odd Kappa-Exponential (OK-E) distribution. The shape of its hazard rate function (hrf) might be constant, declining, growing, inverted-J, bathtub, or inverted-bathtub. The probability density function (pdf) and the cumulative distribution function (cdf) have both been expressed as linear expansions. Bonferroni and Lorenz curves, ordinary and incomplete moments, the quantile function, the mean residual life, the mean waiting time, and the entropy are all defined. The maximum likelihood method is used to estimate the values of the model’s unknown parameters. To verify the precision of the estimate, we ran a simulation study. The attractiveness and adaptability of the Odd Kappa-Exponential model were shown using four real-world examples from the fields of economics, engineering, and the environment.
This article studies the problem of conception of a Bayesian single variable sampling plan for Weibull distribution under type II hybrid censoring based on two-sided decision function with a linear random doubt zone. Based on an appropriate loss function, an explicit expression for the Bayes risk is determined. To find the optimal sampling plans, a simple algorithm based on the grid search method is described. Finally, simulation study is given to illustrate the proposed model.
Emmanuel deGraft Johnson Owusu Ansah, Jonathan Ayiku, Simon Kojo Appiah
et al.
The study investigates the existence of long-run equilibrium or mean-reversion using bivariate analysis of paired prices, as well as to test for linear and nonlinear threshold-type mean-reversion of bivariate relationships. The coefficient parameters of (non)linear VECM and threshold parameter value are estimated, and the forecast performance accuracies of the SETAR are compared to linear models of the mean-reversion process.
The two-regime SETAR model gives a much better prediction of cointegration relation than linear AR model. In the test for the two-regime SETAR model for the cointegration relation against a three-regime model, the two-regime model cannot be rejected at any reasonable significance level. The 2-SETAR exhibits significant constant and trending intervention features of the price build-up process. The asymmetric behavior remained the dominant feature of our mean reversion, which was also apparent. Although the MAPE is somewhat higher than the AR and ARMA processes, the threshold models outperformed the AR and ARMA processes. In summary, the mean reversion property is heavily reliant on the events that occurred in the preceding four bi-weekly pricing-periods in the swift unusual directions. In contrast, in the slow usual direction, it relies on the occurrence of the same in the only bi-weekly pricing-periods immediately preceding it.
The primary sourcebook for developments based on the data of the world components "Theory of Intellectualities and Mathematical Statistics" (TIMS) collections of the Department of Mathematics, Physics and Astronomy of Odessky National Maritime University. Presented lecture material on basic axioms, theorems and formulas of statistical divisions and characteristics, which are illustrated by a wealth of butts of the solution specific tasks. Calculations can be made with a calculator or programming environments and electronic table. The basic guide can be used as a guide for astronomers and computer specialties 122, 124, 125, as well as for other technical and economicalspecialties, as well as additional basic material for humanitary students.
I analyse differences in style between traditional prose mathematics writing and computer-formalised mathematics writing, presenting five case studies. I note two aspects where good style seems to differ between the two: in their incorporation of computation and of abstraction. I argue that this reflects a different mathematical aesthetic for formalised mathematics.
Lilis Harianti Hasibuan, Syarto Musthofa, Darvi Mailisa Putri
et al.
Export is the activity of selling goods or services from one country to another. This activity usually occurs in a specific region or country. Export data is a type of data that has a seasonal pattern. This study aims to compare SARIMA and Holt Winter’s methods in forecasting export data. In this study, the SARIMA model ((1,1,1) (0,1,1))12 and Holt Winter's simulation were obtained. The data used is the export data of West Sumatra from 2016 to 2022. The best model is the one with the smallest MAPE or MAD. The SARIMA model yielded a MAPE of 0,437% and MAD of 78,821. Meanwhile, the Holt Winter's method yielded a MAPE of 0,894% and MAD of 163,320 with α=0,2, β=0,5, γ=0,1. Therefore, the SARIMA outperformed the Holt Winter’s method due to its higher accuracy. It can be concluded that the SARIMA is suitable to use as the forecasting model in this case. In this study, forecast have been made for the next 24 periods, from January 2023 to December 2024.
The climatic changes have important role which may lead to huge problems for the health of human and other organisms, therefore it is necessary to study and forecast this type of datasets to reduce .<br /> <br /> the damages through planning and controlling for these changes in the future. The main problem can be summarized in the nonlinearity of climatic dataset and its chaotic changes. The common approach is the integrated autoregressive and moving average model (ARIMA) as traditional univariate time series approach. Therefore, more appropriate model for studying the climatic data has been proposed for obtaining more accurate forecasting, it can be called random forest (RF) model.This model cannot deal with nonlinear data correctly and that may lead to inaccurate forecasting results. In this thesis, climatic datasets are studied represented by minimum air temperature and rational humidity for agricultural meteorological station in Nineveh. This thesis aims to satisfy data homogeneity through different seasons and find suitable model deal with nonlinear data correctly with minimal forecasting error comparing to ARIMA as traditional model. The research found the adequate of the model for this type of data, as it was found that there are some factors that contribute to the increase in the number of deaths in the epidemic, such as the advanced age of the patient, the length of stay in the hospital, the percentage of oxygen in the patient's blood, in addition to the incidence of some chronic diseases such as asthma. The study recommended a more in-depth study of other types of these models, and the use of other estimation methods, in addition to paying attention to the methods of data recording by the city health department.
Fatuh Inayaturohmat, Nursanti Anggriani, Asep K. Supriatna
In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occurs. Endemic equilibrium is a state in which there occurs not only the infection of tuberculosis and COVID-19 but also the coinfection of tuberculosis and COVID-19. We assumed that the parameters follow the uniform distribution, and then, we took 1,000 samples of each parameter using Latin hypercube sampling (LHS). Next, the samples were sorted by ranking. Finally, we used the partial rank correlation coefficient (PRCC) to find the correlation between the parameters with compartments. We analyzed the PRCC for three compartments, namely, individuals infected with COVID-19, individuals infected with tuberculosis, and individuals coinfected with COVID-19 and tuberculosis. The most sensitive parameters are the recovery rate and the infection rate of each COVID-19 and tuberculosis. We performed the optimal control in the form of prevention for COVID-19 and tuberculosis. The numerical simulation shows that these controls effectively reduce the infected population. We also concluded that the effect of isolation has an immediate impact on reducing the number of COVID-19 infections, while the effect of treatment has an impact that tends to take a longer time.
In three-dimensional domain, an identification problem of the source function for Hilfer type partial differential equation of the even order with a condition in an integral form and with a small positive parameter in the mixed derivative is considered. The solution of this fractional differential equation of a higher order is studied in the class of regular functions. The case, when the order of fractional operator is 0 <α< 1, is studied. The Fourier series method is used and a countable system of ordinary differential equations is obtained. The nonlocal boundary value problem is integrated as an ordinary differential equation. By the aid of given additional condition, we obtained the representation for redefinition (source) function. Using the Cauchy-Schwarz inequality and the Bessel inequality, we proved the absolute and uniform convergence of the obtained Fourier series.
This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford’s law, and need to understand general principles clarifying when to expect the appearance of Benford’s law in real-life data and when not to expect it. A second main target audience is students of statistics or mathematics, at all levels, who are curious about the mathematics underlying this surprising and robust phenomenon, and may wish to delve more deeply into the subject. This survey of the fundamental principles behind Benford’s law includes many basic examples and theorems, but does not include the proofs or the most general statements of the theorems; rather it provides precise references where both may be found.
A new family of distributions called the Muth family of distributions is introduced and studied. Five special submodels of the proposed family are discussed. Some mathematical properties of the Muth family are studied. Explicit expressions for the probability weighted, moments, mean deviation and order statistics are investigated. Maximum likelihood procedure is used to estimate the unknown parameters. One real data set is employed to show the usefulness of the new family.
In this article we present the computations of lower bounds of well-known mathematical quantity in control theory known as structured singular value for a family of structured matrices obtained for a DC Motor, that is an electrical machine. The comparison of lower bounds with the well-known MATLAB function mussv is studied. The structured singular values provide an important tool to synthesize robustness as well as analyze performance and stability of feedback systems.
Signalised intersections is deemed amongst complex issues in road safety control system. Due
to the growing number of crashes at signalised intersection every year in Malaysia, this
research aims at understanding driver behaviour at signalised intersection. This paper
discusses the methods to analyse driver behaviour at signalised intersection, which consist of
field data collection using video recording technique and administration of a survey pertaining
to driving behaviour within dilemma zones with selected participants (car driver).The methods
are designed to gain a better understanding of driver behavioursthat influence their decisionmaking
of non-compliance at signalised intersection, within the dilemma zones.The main goal
is to reveal driver responses at dilemma zone during amber signal light, with respect to the
vehicle distance from stop line, signal timing and approaching speed.