Editor(s)
Dr. Xingting Wang,
Assistant Professor, Department of Mathematics, Howard University, Washington, USA.

ISBN 978-93-5547-772-9 (Print)
ISBN 978-93-5547-773-6 (eBook)
DOI: 10.9734/bpi/nramcs/v7

This book covers key areas of Mathematical and Computer Science. The contributions by the authors include Risk measures, Backtesting, weighted distribution, normal mixture, EM-algorithm, Log-Logistic distribution, parathyroid hormone, fuzzy reliability function, Smart cities, remote health systems, IoT cloud integration, IoT security, Convection-diffusion equation, control volume method, moved node. richardson extrapolation, difference scheme, peclet number, Quadrilateral snake graphs, triangular snake graph, independent domination, path coefficient, Authentic assessment, students’ mathematical problem solving, Markov model, land transportation, expectation-maximization, EM algorithm, Bayesian regression, gaussian process, maximum likelihood, Random matrix theory, Wigner’s law, multivariate distribution, superheat map, eigenvalue distribution, Linear regression model, and triangular decomposition. This book contains various materials suitable for students, researchers and academicians in the field of Mathematical and Computer Science.

Media Promotion:


Chapters


Estimating Value at Risk (VaR) and Expected Shortfall Using Normal Weighted Inverse Gaussian Distributions

Calvin B. Maina, Patrick G. O. Weke, Carolyne A. Ogutu, Joseph A. M. Ottieno

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 1-29
https://doi.org/10.9734/bpi/nramcs/v7/6817F

This study calculates the VaR for Normal Weighted Inverse Gaussian (NWIG) distributions. Value at Risk (VaR) and Expected Shortfall (ES) is commonly used measures of potential risk for losses in financial markets. The Normal Inverse Gaussian (NIG) distribution, a particular instance of the Generalized Hyperbolic Distribution (GHD), is widely utilised in literature when discussing VaR and ES. However, there are additional specific situations of GHD called Normal Inverse Gaussian Related Distributions that can be used. The Basel Committee [1] proposed to replace Value at Risk with Expected Shortfall but concluded that the backtesting will still be done on VaR even though the capital would be based on Expected Shortfall. Therefore the two measures of risk still remain the most popular and useful in financial management. The Maximum Likelihood (ML) estimates of the suggested models for the financial data from Range Resource Corporation (RRC) have been obtained using the Expectation Maximization (EM) technique. To backtest VaR, we employed the Kupiec likelihood ratio (LR). The goodness of fit test has been conducted using the Kolmogorov-Smirnov and Anderson-Darling tests. For model selection, the Akaike Information Creterion (AIC), Bayesian Information Creterion (BIC), and Log-likelihood have all been utilized. The outcomes unequivocally demonstrate that the NWIG distributions are good substitutes for NIG for calculating VaR and ES.

Effect of Parathyroid Hormone of Young Men: Mathematical Modelling by using Fuzzy Logic

S. Prakasam

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 30-36
https://doi.org/10.9734/bpi/nramcs/v7/3261A

Mathematical models are used in medical, physics, chemistry, engineering, geology, geography, computer and many other fields. The reason for use of mathematical models is because we get the easy answers. I have find out the Fuzzy survival and Fuzzy Hazard values in mathematical model of binary parameter Log-Logistic Distribution of PTH stages that arise in the body when taking Serum iPTH for young men.

Iot Technologies: Remote Health Monitoring Systems, Security Risks and Recommendations

Basant Kumar, Sulaiman Al Rawahi, Abdullah Al Kharusi

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 37-50
https://doi.org/10.9734/bpi/nramcs/v7/3484A

IoT technologies have been catching the headlines in the last recent years. Smart devices such as smart phones, IoT wearables and automation systems are unforgettable. The new wave of technology (IoT) has led to unexpected enchantments globally. Today all sectors in the world including healthcare industry are looking forward to implementing IoT technologies for the purpose of improving the quality in order to reach the balance of efficient workability. IoT has extended widely effectiveness outset from smart cities, supply chain, power saving, healthcare, etc. Between all mentioned industries, healthcare takes the priority that needs to improve to save human lives. IoT technologies have also declared several challenges that did not exist earlier. This paper discusses IoT functionality, integration of IoT with cloud computing, the way IoT can be used in healthcare as well as challenges caused by IoT.

Moving Node Method for the Approximate Analytical Solution One-dimensional Convection-Diffusion Problems

Dalabaev Umurdin, Ikramova Malika, Umarova Shoira

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 51-71
https://doi.org/10.9734/bpi/nramcs/v7/3456A

Methods for solving problems of mathematical physics can be divided into the following four classes.
Analytical methods (the method of separation of variables, the method of characteristics, the method of Green's functions, etc.) methods have a relatively low degree of universality, i.e. focused on solving rather narrow classes of problems.
Approximate analytical methods (projection, variational methods, small parameter method, operational methods, various iterative methods) are more universal than analytical ones.
Numerical methods (finite difference method, method of lines, control volume method, finite element method, etc.) are very universal methods.
Probabilistic methods (Monte Carlo methods) are highly versatile. Can be used to calculate discontinuous solutions. However, they require large amounts of calculations and, as a rule, lose with the computational complexity of the above methods when solving such problems to which these methods are applicable.
This chapter contains information about new approaches to solving boundary value problems for differential equations. It introduces a new method of moving nodes. Based on the approximation of differential equations (by the finite difference method or the control volume method), introducing the concept of a moving node, approximately analytical solutions are obtained. To increase the accuracy of the obtained analytical solutions, multipoint moving nodes are used. The moving node method is used to construct compact circuits. The moving node method allows you to investigate the diskette equation for monotonicity, as well as the approximation error of the differential equation. Various test problems are considered.
Subject Areas: Mathematics.

Independent Domination for Some Special Types of Snake Graphs

N. Senthurpriya, S. Meenakshi

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 72-99
https://doi.org/10.9734/bpi/nramcs/v7/2959A

In this chapter, we discussed about a particular types of snake graphs i.e., Triangular and Quadrilateral Snake graphs. We determined the Independent Domination and Independent Domination Number for various forms of Triangular Snake graph (Tn), Quadrilateral Snake graph (Qn), Alternate Triangular Snake graph (A(Tn)), Alternate Quadrilateral Snake graph (A(Qn)). Later, we extended our work to a new form of alternate snake graph (ie.,) n Alternative snake graph. Here, we have figured out the new form of -alternate snake graph in various forms and found the independent domination and independent domination number for 2-Alternate Triangular Snake graph (2A(Tn)), 3-Alternate Triangular Snake graph (3A(Tn)), 4-Alternate Triangular Snake graph (4A(Tn)) , 5-Alternate Triangular Snake graph (5A(Tn)) ,  2-Alternate Quadrilateral Snake graph (2Q(Tn)), 3-Alternate Quadrilateral Snake graph (3Q(Tn)) , 4-Alternate Quadrilateral Snake graph (4Q(Tn)) , 5-Alternate Quadrilateral Snake graph (5Q(Tn)).

Recent Development of Authentic Assessment to Improve Students' Mathematical Problem Solving Ability

. Firdausi, R. Supinah

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 100-108
https://doi.org/10.9734/bpi/nramcs/v7/3506B

This study tries to find out how to develop an authentic assessment based on its principles and characteristics, and how to apply the assessment to improve students' mathematical problem solving abilities. This study uses research and development methods by carrying out the following stages: 1) needs analysis, 2) literature review, 3) pre-test, 4) designing an authentic assessment form, and 5) conducting a post-test to determine the value of mathematical problem solving ability. The research findings reveal that the stages of developing authentic assessment through a limited validation process and wider validation based on the principles and characteristics of authentic assessment are able to produce new products and their application can have an effect on increasing students' mathematical problem solving abilities. The effect of the application of authentic assessment products resulting from the development process is known from the mean pre-test and post-test, as well as the significance value of the t-test results for interconnecting samples of 0.000 which is smaller than 0.05.

Hidden Markov Model Applied for Vehicles Density Prediction

N. I. Asrori, N. Iriawan

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 109-122
https://doi.org/10.9734/bpi/nramcs/v7/6243F

The Gempol-Pandaan toll is a strategic center for regional growth. Number of vehicles passing through this toll has increased in 2017. Because of the passing of numerous cars, particularly trucks carrying loads above their capacity, this condition may result in traffic congestion and road damage. As a result, it is essential to predict the number of vehicles coming from not only the Gempol toll gate but also the Kejapanan, Bangil, and Rembang toll gates that will exit through the Pandaan toll gate. The probability and quantity of each vehicle category—I, II, III, IV, and V—are used in this study to analyse vehicle density. The origin gate and vehicle category cannot be observed directly, but the car must pass the toll gate in order to tap the e-toll card, so the Hidden Markov Model (HMM) method was used in this study. The Expectation-Maximization (EM) algorithm and the Bayesian approach are the two estimation techniques used in this study for HMM parameters. The outcome demonstrates that Bayesian parameter estimation for HMM is superior to the EM algorithm. The model is more representative to explain the predicted vehicle density because the Bayesian estimated parameter values are nearer to the input parameters.

Study on Bayesian Regression Model and Applications

Yijun Yu

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 123-133
https://doi.org/10.9734/bpi/nramcs/v7/3569A

A sparse vector regression model is introduced. The algorithm is established by employing Gaussian process and Bayesian formulation. By using a special prior hyperparameter setting in the developing process, the number of parameters in the algorithm is reduced, and generating a relatively simple algorithm compared with similar type of Bayesian vector regression models. The algorithm is done by using computational iterative approach. The examples of applications to the function approximations and the inverse scattering problem are presented.

Maximum Local Overlapping Semicircles for Comorbidity Analysis

O. Nolasco-Jáuregui, L. A. Quezada-Téllez, Y. Salazar-Flores, Adán Díaz-Hernández

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 134-158
https://doi.org/10.9734/bpi/nramcs/v7/16995D

This chapter presents a regional analysis of COVID-19 in Mexico. Because of comorbidities in Mexican society, this new pandemic puts the population at greater risk.  The research period runs from April 12 to October 5, 2020 (761, 665 Patients). The main objective of this research is a description of the method with a unique methodology of random matrix theory in the moments of a probability measure that appears as the limit of the empirical spectral distribution by Wigner’s semicircle law, which enabled analyzing the behavior of patients who tested positive for COVID-19 and their comorbidities, with the conclusion that the most sensitive comorbidities in hospitalized patients  in the study period are the following three: COPD, Other Diseases, and Renal Diseases.

Another objective is the daily behavior pandemic analysis; in this chapter, we have provided the graphical presentation of the results with Machine Learning methods employing Super Heat maps as a visual tool.

The Selective Regularization of a Linear Regression Model: A Recent Study

V. N. Lutay, N. S. Khusainov

Novel Research Aspects in Mathematical and Computer Science Vol. 7, 5 August 2022, Page 159-169
https://doi.org/10.9734/bpi/nramcs/v7/7591F

The construction of a linear regression model incorporating regularisation of the system matrix of normal equations is covered in this article. Only the matrix diagonal entries that correspond to the data with a high correlation are increased, as opposed to the conventional ridge regression, which adds positive parameters to all of a matrix's diagonal terms. This causes the matrix conditioning to decrease, which in turn causes the corresponding regression equation coefficients to decrease. Based on the triangular decomposition of the correlation matrix of the original dataset, selection of the entries to be increased. On a known dataset, the method's efficacy is evaluated using not only ridge regression but also the outcomes of applying the well-known algorithms LARS and Lasso.