Dr. Shi-Hai Dong
Professor, Department of Physics, School of Physics and Mathematics, National Polytechnic Institute, Building 9, Unit Professional Adolfo Lopez Mateos, A. P. 07738, Mexico D. F., Mexico.

ISBN 978-93-91215-40-8 (Print)
ISBN 978-93-91215-41-5 (eBook)
DOI: 10.9734/bpi/tpmcs/v11

This book covers key areas of mathematics and computer science. The contributions by the authors include guard channel, dynamic channel, fixed channel, spectrum, joint entropy estimation, conditional entropy estimation, mutual information estimation, concomitants of order statistics, best linear unbiased estimator, Lindley distribution, morgenstern type bivariate Lindley distribution, axisymmetry, graph invariant, shifts of feature locations, mental rotation, microcontroller, leaf sensor, phase sensor, multipath routing, single shortest path, load balancing, multiple paths, path selection, traffic distribution, Bioequivalence test, Three-arm four-step clinical trial, Z-Chi Square method, biological algorithms, data mining and clustering techniques, ant colony optimization clustering algorithm, K-Harmonic Means Clustering algorithm, matrix multiplication, ST-coloring, ST-chromatic number, ST-span, ST-edge span, global positioning system, geocoding engine, location listener, location intelligence, Tikhonov method, constrained linear equations, closed ranges, real Hilbert spaces, Randic spread, Randic matrix, Riemann's hypothesis, positive integers, Möbius's function, finite exponential functional series, finite exponential functional progressions, Lindelof's hypothesis, Filtered Derivative, False Discovery Rate, semi supervised clustering, PSO algorithm, image segmentation. This book contains various materials suitable for students, researchers and academicians in the field of mathematics and computer science.


Media Promotion:


Studies on Dynamic Channel Allocation Scheme to Handle Handoff in Wireless Mobile Network

S. Alagu, T. Meyyappan

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 1-14

Because of the significant development in demand for mobile communications, there has been a lot of study into making optimal use of the limited spectrum available for cellular communications. The authors propose a novel call admission control mechanism, DCAS (Dynamic Channel Allocation Scheme), in this work. The number of guard channel(s) is automatically modified in this new method based on the average handoff blocking rate observed over a given period of time. The handoff blocking rate is kept below the set limit, and the new call blocking rate is kept to a minimum. Simulation of nodes is used to evaluate the DCAS's performance. The DCAS method surpasses the Static Channel Allocation Scheme by setting a strict limitation on the likelihood of handoff rejection. The suggested approach provides the best results by optimizing resource consumption and dynamically adapting to changing traffic circumstances.

Joint-Conditional Entropy and Mutual Information Estimation Involving Three Random Variables and asymptotic Normality

Amadou Diadie Ba, Gane Samb Lo

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 15-38

A method of estimating the joint probability mass function of a triplet of discrete random variables is described. This estimator is used to construct the joint-conditional entropies and mutual information estimates involving three random variables. From there almost sure rates of convergence and asymptotic normality are established. The theorical results are validated by simulations.

Concomitants of Order Statistics Arising from the Morgenstern Type Bivariate Lindley Distribution

M. R. Irshad, R. Maya, S. P. Arun

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 39-47

In this work, we developed the distribution theory of concomitants of order statistics arising from the Morgenstern type bivariate Lindley distribution (MTBLDD) and derived the best linear unbiased estimator (BLUE) of the parameter associated with the study variate  when the dependence parameter  is known. The efficiency comparison of the BLUE with respect to the unbiased estimator is also evaluated in this work.

The present experiment investigates whether patterns of shifts of feature locations could affect the same/different decisions of simultaneously presented pairs of geometrical figures. A shift of locations was defined as the angular distance from the location of a feature in one figure to the location of the same feature in another figure. It was hypothesized that the difficulty in discriminating mirror-reflected (or axisymmetric) pairs from disoriented identical pairs was caused by complex shifting patterns inherent in axisymmetric pairs. According to the shifts of the locations of the four structural features, five pair types were prepared. They could be ordered from completely identical to completely different in their shifts: identical 0/4 pairs, non-identical 1/4 pairs, non-identical 2/4 pairs, axisymmetric 2/4 pairs and non-identical 4/4 pairs. The latencies for non-identical pairs decreased with the increase of difference in the shifts of feature locations, indicating that serial, self-terminating comparisons of the shifts were applied to the discrimination of non-identical pairs from identical pairs. However, the longer latencies in axisymmetric 2/4 pairs than in non-identical 2/4 pairs suggested that the difficulty for axisymmetric pairs was not caused by the complex shifting patterns, and the difficulty was not satisfactorily explained by the comparisons of feature locations. The latencies obtained for Nonid pairs decreased with the increase of the difference in the shifts of feature locations, indicating that serial, self-terminating comparisons of the shifts were applied to the discrimination of Nonid pairs from Id pairs.

India is the agriculture based country.  Our ancient people completely depended on the agricultural harvesting. Agricultural sector is playing vital role in Indian economy, in which irrigation mechanism is of key concern. Our work aim is to control the wastage of water in the field by using the drip irrigation and also to provide exact controlling of field by atomizing the agricultural environment by using the components and building the necessary hardware. Irrigation by help of freshwater resources in agricultural areas has a crucial importance. Because of highly increasing demand for freshwater, optimal usage of water resources has been provided with greater extent by automation technology and its apparatus such as drip irrigation, sensors and remote control.

The humidity and temperature of plants are precisely monitored and controlled more efficiently, which is a real time feedback control system. By using drip irrigation the water will be maintained at the constant level i.e. the water will reach the roots by going drop by drop. Irrigation system controls valves by using automated controller to turn ON & OFF. This allows the farmer to apply the right amount of water at the right time, regardless of the availability of the labor to turn valves or motor ON & OFF. This reduces runoff over watering saturated soils avoid irrigating at the wrong time of the day. It improves crop performances and help in time saving in all the aspects.  

For the precisely monitoring and controlling of the agriculture filed, different types of sensors were used. To implement the proposed system ARM LPC2148 Microcontroller is used. In this work an ARM LPC2148 Microcontroller based drip irrigation mechanism is proposed, which is a real time feedback control system for monitoring and controlling all the activities of drip irrigation system more efficiently.

The information is given on user request in form of SMS. Eg. GSM modem can be controlled by standard set of AT (Attention) commands. These commands can be used to control majority of the functions of GSM modem. GSM serves as an important part as it is responsible for controlling the irrigation on field and sends them to the receiver through coded signals. GSM operates through SMS’s and is the link between ARM processor and centralized unit. GSM technology is used to inform the end user about the exact field condition. The drip method of irrigation has been found to have a significant impact on resources saving, cost of cultivation, yield of crops and farm profitability.

The Perspective of Multipath Routing

Gaytri Devi, Shuchita Upadhyaya

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 71-76

Multipath routing means using multiple paths instead of using single path to forward the traffic, through the network between source node to destination node. Multipath routing provides better overall network performance by allowing maximum utilization of available network resources. If multiple paths are being used for the transmission of the traffic then the traffic will be redirected to the backup path if active path fails or in the case of congestion. Moreover, the multiple paths can be used simultaneously by distributing the traffic. Thus Multipath routing can be more efficient than the single path routing for improving network utilization and for providing load balancing. It can significantly reduce congestion and gives more network throughput and hence increases the reliability in the network. The two main concerns to implement multipath routing scheme are the calculation of multiple paths and traffic distribution among multiple paths. There are various algorithms presented in literature for effectively calculating the multiple paths. In this chapter, we have discussed some multipath routing approaches considering path construction and path selection to distribute the flow.

A clinical endpoint bioequivalence (BE) study aims to establish BE between a generic drug (TEST) and an innovator drug (REF). A placebo (PLB) is usually included to demonstrate the sensitivity of the study. BE is established if TEST is shown to be superior to PLB, REF superior to PLB, and TEST equivalent to REF. Therefore, an overall BE test for a clinical endpoint BE study is composed of two superiority tests (TEST vs. PLB and REF vs. PLB) and one equivalence test(TEST vs. REF).
Chang et al. [1] calculated the sample size and power for an overall BE test based on one superiority test (TEST vs. PLB) and an equivalence test (TEST vs. REF) using the joint distribution of sample means and sample variances (we call this a Z-ChiSquare method). Previously, we proposed an exact method to calculate the power and sample size for an overall BE test based on two superiority tests (TEST vs. PLB, REF vs. PLB) and one equivalence test (TEST vs. REF) using a multivariate non-central t distribution directly (we call this an Exact-t method) for a clinical endpoint BE study with two superiority tests and one equivalence test. Yang and Sun showed that the Exact-t method is computationally more efficient and more accurate when sample size is small as compared to the Z-ChiSquare method. These methods, however, were generally verified by simulation under the
normality assumption. In reality, data can deviate from normality (e.g., be skewed). In this paper, we test the robustness of the Exact-t method and the Z-ChiSquare method when data is mildly or severely skewed. It turns out that both methods remain accurate even when data is severely skewed as long as the mean and variance of the data are correctly specified. One thing to note is that when data is more skewed, the required sample size to attain a desired power is larger. Therefore, the Exact-t method is recommended when calculating power and determining sample size for a three-arm clinical endpoint study.

Clustering Efficiency of ACO and K-Harmonic Means Techniques: A Comparative Study

M. Divyavani, T. Amudha

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 93-107

In the last two decades, many advances on the computer sciences have been based on the observation and emulation of processes of the natural world. The nature inspired methods like ant based clustering techniques have found success in solving clustering problems. They have received special attention from the research community over the recent years because these methods are particularly suitable to perform exploratory data analysis. The clustering is an important technique that has been studied in various fields with many applications such as image processing, marketing, data mining and information retrieval. Recently, the various algorithms inspired by nature are used for clustering. Data clustering is a useful process to extract meaning from sets of unlabeled data or to perform data exploration for pattern recognition. This paper focuses on the behavior of clustering procedures in two approaches, ant based clustering algorithm and K-harmonic means clustering algorithm. The two algorithms were evaluated in two of well- known benchmark data sets. Empirical results clearly show that ant clustering algorithm performs well compared to another technique called K-Harmonic means clustering algorithm.

Classical Algebra: Matrix Multiplication (The Rule of Vacancies)

Surajit Bhattacharyya

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 108-111

In this paper I have described a new and simpler method for matrix multiplication which is the result of my long teaching experience. This method “The Rule of Vacancies” is very effective for the beginners. Hope, this enthusiastic research work will create lots of interests in the students mind.

A Note on St-Coloring of Some Non Perfect Graphs

Rubul Moran, Aditya Pegu, I. J. Gogoi, A. Bharali

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 112-119

For a graph G = (V,E) and a finite set T of positive integers containing zero, ST-coloring of a graph G is a coloring of the vertices with non negative integers such that for any two vertices of an edge, the absolute differences between the colors of the vertices does not belong to a fixed set T of non negative integers containing zero and for any two distinct edges their absolute differences between the colors of their vertices are distinct. The minimum number of colors needed for an efficient Strong T coloring of a graph is known as ST-Chromatic number. This communication is concerned with the ST-coloring of some non perfect graphs viz. Petersen graph, Double Wheel graph, Helm graph, Flower graph, Sun Flower graph. We compute ST-chromatic number of these non perfect graphs.

Study on Microaddress Recorder for Location Tracking

Shaveta Bhatia

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 120-130

When we think about location-based services, the first thing that comes to mind is a physical location. Location Intelligence with tracking has expanded on mobile networks during this time period, thanks to apps operating on smart phones with GPS. Location-based services are expanding to meet the needs of a wider user base while also addressing a number of basic issues. This article covers the Micro Address Recorder location tracking application, which is used to monitor a person at minute locations in defined areas. This application is built on combining a person's current position with distances from two adjacent locations to determine their precise position. The study also includes a thorough analysis of the data in several areas, as well as recommendations for further study.

Advanced Studies on Rate of Convergence of Tikhonov Method of Regularization for Constrained Linear Equations with Operators Having Closed Ranges

Milojica Ja´cimovi´c, Izedin Krni´c, Oleg Obradovi´c

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 131-142

We derive the estimates of the rate of convergence of the Tikhonov method of regularization for the constrained operator linear equation. In the case that the range of the corresponding operator is closed, the estimate is of the same order as the estimates for a linear equation without constraints.

A Preliminary Study of Randic Spread of Graphs

Aditya Pegu, I. J. Gogoi, Rubul Moran, A. Bharali

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 143-153

For a simple undirected graph  spread is defined as the difference between the largest and the smallest eigenvalue of the graph. As 1 is the largest eigenvalue of the Randic matrix therefore disregarding the spectral radius, the Randic spread  is the difference between the second largest and the smallest eigenvalue of the Randic matrix. In this communication we have studied the bounds for Randic spread. Moreover we have introduced a new upper and lower bound for this spread.

Multiple Change Points by Filtered Derivative and False Discovery Rate

Mohamed Elmi

Theory and Practice of Mathematics and Computer Science Vol. 11, 24 May 2021, Page 171-186

Let X = (X1; X2; : : : ; Xn) be a time series, that is a sequence of random variable indexed by the time t = 1; 2; : : : ; n. We assume the existence of a segmentation T = (t1; t2; : : : ; tn) such that Xi is a family of independent identically distributed (i.i.d) random variable for i E (tk; tk + 1]; and k = 0; : : : ; K where by convention to and tK+1 = N. In the literature, it exist two main kinds of change points detection : The change points on-line and the change points off-line. In this work, we consider only the change point analysis ( off-line), when number of change points is unknown. The result obtained is based on Filtered Derivative method where we use a second step based on False Discovery Rate. We compare numerically this new method with the Filtered Derivative with p-Value. We also give a real application of the method of Filtered Derivative with False Discovery Rate (FDqV).

The initial stage in image processing, pattern recognition, and feature extraction is picture segmentation. This segmentation may be done using a variety of approaches. This is a crucial yet fundamental part of image analysis as it is the single factor that affects the characteristics of the finished image analysis output. The semi-supervised picture segmentation using the hierarchical clustering technique is discussed in this study. The prior information for the clustering process is given as an interested area selection from image using mouse. The picture qualities of intensity, colour, and texture are discussed here. The suggested technique provides more clarity of segmented regions than previous semi-supervised approaches.