Editor(s)

Dr. Narayan Thapa
Associate Professor,Department of Mathematical Sciences, Cameron University, Lawton, OK, USA.

ISBN 978-93-90768-07-3 (Print)
ISBN 978-93-90768-08-0 (eBook)
DOI: 10.9734/bpi/tpmcs/v8

This book covers key areas of mathematics and computer science. The contributions by the authors include collaborative information retrieval, algorithms, logistic regression, multicollinearity, variance inflation factor, condition index, variance proportions, system reliability, multi-state system, multiple-valued logic, multi-valued Karnaugh Map, Capacitated networks, map method, reduction rule, max-flow min-cut theorem, star-delta transformation, pseudo-switching function, prime implicant, probability-ready expression, cyclic codes, quaternion algebra, muffin ideal, mannheim distance, etinal pigment epithelium, subretinal space, choriocapillaris, vitreous humor, Dirichlet problem, fictitious domain, Daubechies wavelet function, finite difference, heat transfer, isomorphism, indexing variables, optimization, algorithms performance, quarterly disaggregation. This book contains various materials suitable for students, researchers and academicians in the field of mathematics and computer sciences.

 

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Chapters


Opportunities for Remote Collaboration in a Social Web Search Model That Integrates Parents and Children: A Recent Advancement

Sandra Regina Rocha Silva, Geraldo Bonorino Xexéo, Moacir Florentino da Silva Jr

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 1-10
https://doi.org/10.9734/bpi/tpmcs/v6/6401D

Traditionally, search engines are designed to support a single user working alone. However, the construction of knowledge is enriched when one adds collaboration to search tasks. We identified opportunities for remote collaboration in a Social Web search model that integrates parents and children guided by 5W + 1H (who, what, where, when, why, how) dimensions. There are many good techniques in information retrieval for adults, but still not much scientific insight on how to design search engines for children in terms of both user interfaces and underlying algorithms. Our social search model aims at improving the search process for children. We found 7 opportunities for remote collaboration on the search process, based on implicit-explicit interactions. We propose to adapt the form of evaluation applied in Search Together to evaluate the prototype.

Multicollinearity in Binary Logistic Regression Model

N. A. M. R. Senaviratna, T. M. J. A. Cooray

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 11-19
https://doi.org/10.9734/bpi/tpmcs/v6/2417E

One of the key problems arises in binary logistic regression model is that explanatory variables being considered for the logistic regression model are highly correlated among themselves. Multicollinearity will cause unstable estimates and inaccurate variances that affects confidence intervals and hypothesis tests. Aim of this was to discuss some diagnostic measurements to detect multicollinearity namely tolerance, Variance Inflation Factor (VIF), condition index and variance proportions. The adapted diagnostics are illustrated with data based on a study of road accidents. Secondary data used from 2014 to 2016 in this study were acquired from the Traffic Police headquarters, Colombo in Sri Lanka. The response variable is accident severity that consists of two levels particularly grievous and non-grievous. Multicollinearity is identified by correlation matrix, tolerance and VIF values and confirmed by condition index and variance proportions. The range of solutions available for logistic regression such as increasing sample size, dropping one of the correlated variables and combining variables into an index. It is safely concluded that without increasing sample size, to omit one of the correlated variables can reduce multicollinearity considerably. Hence, reliable and valid predictive logistic regression model can be built based on the adequate inspection and measures of remedy taken against multicollinearity.

Karnaugh-Map Analysis of a Commodity-Supply Multi-State Reliability System

Ali Muhammad Ali Rushdi, Abdulghani Bakur Alsayegh

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 20-37
https://doi.org/10.9734/bpi/tpmcs/v6/2410E

A multi-state k-out-of-n: G system is a multi-state system whose multi-valued success is greater than or equal to a certain value j (lying between 1 (the lowest non-zero output level) and M (the highest output level)) whenever at least km components are in state m or above for all m such that 1 ? m ? j. This paper is devoted to the analysis of a commodity-supply system that serves as a standard gold example of a non-repairable multi-state k-out-of-n: G system with independent non-identical components. We express each instance of the multi-state system output as an explicit function of the multi-valued inputs of the system. The ultimate outcome of our analysis is a Multi-Valued Karnaugh Map (MVKM), which serves as a natural, unique, and complete representation of the multi-state system. To construct this MVKM, we use “binary” entities to relate each of the instances of the output to the multi-valued inputs. These binary entities are represented via an eight-variable Conventional Karnaugh Map (CKM) that is adapted to a map representing four variables that are four-valued each. Despite the relatively large size of the maps used, they are still very convenient, thanks to their regular structure. No attempt was made to draw loops on the maps or to seek minimal formulas. The maps just served as handy tools for combinatorial representation and for collectively implementing the operations of ANDing, ORing, and complementation. The MVKM obtained serves as a means for symbolic analysis yielding results that agree numerically with those obtained earlier. The map is a useful tool for visualizing many system properties, and is a valuable resource for computing a plethora of Importance Measures for the components of the system.

Techniques for Analyzing Capacitated Networks: A Tutorial Review

Ali Muhammad Ali Rushdi, Omar Mutab Alsalami

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 38-67
https://doi.org/10.9734/bpi/tpmcs/v6/2411E

This chapter reviews various types of techniques utilized for analyzing capacitated networks, with an eye on assessing the performance indexes of practical systems having fixed channel capacities, such as telecommunication networks, power transmission systems or commodity pipeline systems. The techniques reviewed include Karnaugh maps, capacity-preserving network reduction rules associated with delta-star transformations, and a generalization of the max-flow min-cut theorem. All methods rely on recognizing the network capacity function as a random pseudo-Boolean function of link successes; a fact that allows the expected value of this function to be easily obtainable from its sum-of-products expression. This network capacity has certain advantages for representation of nonbinary discrete random functions, mostly employed in the analysis of flow networks. Five tutorial examples demonstrate the afore-mentioned methods and illustrate their computational advantages over the exhaustive state enumeration method. The chapter is supplemented with an appendix, which introduces the concept of a “probability-ready expression” for a Boolean-based coherent pseudo-Boolean function.

Utilization of Eight-Variable Karnaugh Maps in the Digital Design of n-bit Comparators

Ali Muhammad Ali Rushdi, Sultan Sameer Zagzoog

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 68-96
https://doi.org/10.9734/bpi/tpmcs/v6/2409E

An -bit comparator is a celebrated combinational circuit that compares two -bit inputs  and  and produces three orthonormal outputs: G (indicating that  is strictly greater than ), E (indicating that  and  are equal or equivalent), and L (indicating that  is strictly less than ). The symbols ‘G’, ‘E’, and ‘L’ are deliberately chosen to convey the notions of ‘Greater than,’ ‘Equal to,’ and ‘Less than,’ respectively. This paper analyzes an -bit comparator in the general case of arbitrary  and visualizes the analysis for  on a regular and modular version of the 8-variable Karnaugh-map. The cases  3, 2 and 1 appear as special cases on 6-variable, 4-variable, and 2-variable submaps of the original map. The analysis is a tutorial exposition of many important concepts in switching theory including those of implicants, prime implicants, essential prime implicants, irredundant disjunctive forms, minimal sums, the complete sum and disjoint sums of products (or probability-ready expressions).

Advanced Study on Cyclic Codes Associated to Muffin Ideals over Quaternion Integer Ring ((-1,-1)/z_p )

Shaikh Javed Shafee, Arunkumar R. Patil

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 97-105
https://doi.org/10.9734/bpi/tpmcs/v6/1455D

In this paper, we construct cyclic codes associated with Muffin ideals over quaternion integer rings-  where  is the finite field integers modulo odd prime p. We also find a generator matrix in standard form for these cyclic codes. Further we determine the Mannheim distance of these cyclic codes. In future we would like to determine the Grobner basis of the cyclic codes associated with muffin ideals.

A Simple Mathematical Model of Exudative Retinal Detachment

Ram Avtar, Swati Srivastava

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 106-117
https://doi.org/10.9734/bpi/tpmcs/v6/5943D

The conditions under which exudative retinal detachment occurs are poorly understood, which hampers the success rate of surgery. Fluid dynamical effects play a major role in the detachment. A simple mathematical model for the exudative retinal detachment in which the sensory retina is separated typically from the underlying retinal pigment epithelium without any retinal hole and tear has been developed to investigate the interaction between the fluid flow and the detached retina. The model takes into consideration a typical retinal blister with unknown shape and the fluid flow caused by its accumulation in the subretinal space through the fluid?leakage into the subretinal space from the choriocapillaris across the outer blood?retina barrier described by Darcy’s law. The theory of bending beams is applied to model the deformation of the retinal blister. The boundary value problem describing the retinal deformation in dimensionless form is solved using the perturbation method. The computational results for the retinal deformation are presented through graphs to illustrate the sensitivity of the deformation to the elastic modulus, the moment of inertia and intraocular pressure and discussed.

Wavelet-Based Method for Solving Linear Elliptic PDE with Dirichlet Boundary Conditions on Irregular Domains

Francis Ohene Boateng, Joseph Ackora-Prah, Benedict Barnes

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 118-132
https://doi.org/10.9734/bpi/tpmcs/v6/2419E

This chapter of the book presents a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) with penalty parameter for solving two dimensional linear elliptic PDE with Dirichlet boundary condition, defined on irregular geometric domains.

MHD Oscillatory Flow of Jeffrey Fluid in an Indented Artery with Heat Source

K. W. Bunonyo, C. Israel-Cookey, E. Amos

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 133-145
https://doi.org/10.9734/bpi/tpmcs/v6/2382E

In this article we studied blood flow through an indented artery and assumed blood to be Jeffrey fluid. The study investigates the influence of heat transfer on the flow profile of Jeffrey fluid in an indented artery. Also, the formulated governing equations are transformed into coupled Bessel differential equation and solved analytically. The effects of various physical parameters such as Prandtl number of blood, , Grashof number, , Darcy number, , Hartmann number M, Reynolds number, , as well as the Jeffrey parameter, and a constant parameter, on the velocity profile and temperature profile. The results are discussed in detail with the graphs obtained using Mathematica version 10.3.

An Innovative 0-Day Attack against ZigBee: Exploitation and Protection System Analysis

Ivan Vaccari, Maurizio Aiello, Enrico Cambiaso

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 146-166
https://doi.org/10.9734/bpi/tpmcs/v6/6969D

Internet of Things networks represent an emerging phenomenon bringing connectivity to common sensors. Due to the limited capabilities and to the sensitive nature of the devices, security assumes a crucial and primary role. In this paper, we report an innovative and extremely dangerous threat targeting  networks. The attack is based on Remote AT Commands exploitation, providing a malicious user the possibility to reconfigure or disconnect  sensors from the network. We present the proposed attack and evaluate its efficiency by executing tests on a real  network. Results demonstrate how the threat can be successfully executed and how it is able to focus on the targeted nodes, without affecting other nodes of the network. Moreover, we developed an innovative protection system able to detect and protect the devices from this innovative threat. Also, the protection system and the attack tool implemented are tested and validated on a real network by using XBee mod? ule, a wireless module adopted to implement and instantiate ZigBee network. The proposed protection system aims to verify if devices are able to communicate on the network when the attack is running. In this case, just before the sensor is ready to communicate on the network, an internal check is accomplished directly by the  device: if needed, an additional reconfiguration is accomplished, in order to restore connectivity of the node in order to mitigate the threat. The results of this work are very interesting since, if executed against a real network, the Remote AT Command attack could create huge damage to companies and networks.

From Two to One Index Isomorphism in Optimization Program for Quarterly Disaggregation of Annual Times Series

Raïmi Aboudou Essessinou, Guy Degla, Babacar Mbaye Ndiaye

Theory and Practice of Mathematics and Computer Science Vol. 8, 27 February 2021, Page 167-181
https://doi.org/10.9734/bpi/tpmcs/v6/2438E

The quarterly disaggregation of an annual economic aggregate, by a mathematical method with a cyclical indicator, gives rise to a problem of minimization to make the quarterly economic aggregate smooth. This involves two indexes for the quarter and the year, which sometimes can make the resolution algorithm less efficient if the problem is large. In this paper we propose a method of indexing quarterly variables based on an isomorphic transformation of a two-index program into a one-index program, in order to minimize the cost of the algorithm of resolution. This method of continuous indexing of variables, applied to national accounts, shows that the algorithm with a single index is more efficient than the algorithm with two indexes when solving the optimization program of the quarterly disaggregation.