Mathematics

26 pages, 748 KiB

Open AccessArticle

Study of a Modified Kumaraswamy Distribution

by Rashad A. R. Bantan, Christophe Chesneau, Farrukh Jamal, Mohammed Elgarhy, Waleed Almutiry and Amani Abdullah Alahmadi

Mathematics 2021, 9(21), 2836; https://doi.org/10.3390/math9212836 - 8 Nov 2021

Cited by 4 | Viewed by 2392

Abstract

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on

(0, 1)

, called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and [...] Read more.

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on

(0, 1)

, called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed. Full article

(This article belongs to the Special Issue Analysis and Comparison of Probabilistic Models)

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15 pages, 3985 KiB

Open AccessArticle

Optimized Unidirectional and Bidirectional Stiffened Objects for Minimum Material Consumption of 3D Printing

by Anzong Zheng, Zaiping Zhu, Shaojun Bian, Jian Chang, Habibollah Haron, Andres Iglesias, Lihua You and Jianjun Zhang

Mathematics 2021, 9(21), 2835; https://doi.org/10.3390/math9212835 - 8 Nov 2021

Cited by 1 | Viewed by 2147

Abstract

3D printing, regarded as the most popular additive manufacturing technology, is finding many applications in various industrial sectors. Along with the increasing number of its industrial applications, reducing its material consumption and increasing the strength of 3D printed objects have become an important [...] Read more.

3D printing, regarded as the most popular additive manufacturing technology, is finding many applications in various industrial sectors. Along with the increasing number of its industrial applications, reducing its material consumption and increasing the strength of 3D printed objects have become an important topic. In this paper, we introduce unidirectionally and bidirectionally stiffened structures into 3D printing to increase the strength and stiffness of 3D printed objects and reduce their material consumption. To maximize the advantages of such stiffened structures, we investigated finite element analysis, especially for general cases of stiffeners in arbitrary positions and directions, and performed optimization design to minimize the total volume of stiffened structures. Many examples are presented to demonstrate the effectiveness of the proposed finite element analysis and optimization design as well as significant reductions in the material costs and stresses in 3D printed objects stiffened with unidirectional and bidirectional stiffeners. Full article

(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)

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24 pages, 1340 KiB

Open AccessArticle

Comparison of the Average Kappa Coefficients of Two Binary Diagnostic Tests with Missing Data

by José Antonio Roldán-Nofuentes and Saad Bouh Regad

Mathematics 2021, 9(21), 2834; https://doi.org/10.3390/math9212834 - 8 Nov 2021

Cited by 2 | Viewed by 1834

Abstract

The average kappa coefficient of a binary diagnostic test is a parameter that measures the average beyond-chance agreement between the diagnostic test and the gold standard. This parameter depends on the accuracy of the diagnostic test and also on the disease prevalence. This [...] Read more.

The average kappa coefficient of a binary diagnostic test is a parameter that measures the average beyond-chance agreement between the diagnostic test and the gold standard. This parameter depends on the accuracy of the diagnostic test and also on the disease prevalence. This article studies the comparison of the average kappa coefficients of two binary diagnostic tests when the gold standard is not applied to all individuals in a random sample. In this situation, known as partial disease verification, the disease status of some individuals is a missing piece of data. Assuming that the missing data mechanism is missing at random, the comparison of the average kappa coefficients is solved by applying two computational methods: the EM algorithm and the SEM algorithm. With the EM algorithm the parameters are estimated and with the SEM algorithm their variances-covariances are estimated. Simulation experiments have been carried out to study the sizes and powers of the hypothesis tests studied, obtaining that the proposed method has good asymptotic behavior. A function has been written in R to solve the proposed problem, and the results obtained have been applied to the diagnosis of Alzheimer's disease. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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24 pages, 3816 KiB

Open AccessArticle

Deciphering Genomic Heterogeneity and the Internal Composition of Tumour Activities through a Hierarchical Factorisation Model

by José Carbonell-Caballero, Antonio López-Quílez, David Conesa and Joaquín Dopazo

Mathematics 2021, 9(21), 2833; https://doi.org/10.3390/math9212833 - 8 Nov 2021

Viewed by 1827

Abstract

Genomic heterogeneity constitutes one of the most distinctive features of cancer diseases, limiting the efficacy and availability of medical treatments. Tumorigenesis emerges as a strongly stochastic process, producing a variable landscape of genomic configurations. In this context, matrix factorisation techniques represent a suitable [...] Read more.

Genomic heterogeneity constitutes one of the most distinctive features of cancer diseases, limiting the efficacy and availability of medical treatments. Tumorigenesis emerges as a strongly stochastic process, producing a variable landscape of genomic configurations. In this context, matrix factorisation techniques represent a suitable approach for modelling such complex patterns of variability. In this work, we present a hierarchical factorisation model conceived from a systems biology point of view. The model integrates the topology of molecular pathways, allowing to simultaneously factorise genes and pathways activity matrices. The protocol was evaluated by using simulations, showing a high degree of accuracy. Furthermore, the analysis with a real cohort of breast cancer patients depicted the internal composition of some of the most relevant altered biological processes in the disease, describing gene and pathway level strategies and their observed combinations in the population of patients. We envision that this kind of approaches will be essential to better understand the hallmarks of cancer. Full article

(This article belongs to the Special Issue Models and Methods in Bioinformatics: Theory and Applications)

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26 pages, 26423 KiB

Open AccessArticle

Snow Leopard Optimization Algorithm: A New Nature-Based Optimization Algorithm for Solving Optimization Problems

by Petr Coufal, Štěpán Hubálovský, Marie Hubálovská and Zoltan Balogh

Mathematics 2021, 9(21), 2832; https://doi.org/10.3390/math9212832 - 8 Nov 2021

Cited by 19 | Viewed by 2921

Abstract

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this [...] Read more.

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this paper, a new nature-based optimization algorithm called Snow Leopard Optimization Algorithm (SLOA) is designed that mimics the natural behaviors of snow leopards. SLOA is simulated in four phases including travel routes, hunting, reproduction, and mortality. The different phases of the proposed algorithm are described and then the mathematical modeling of the SLOA is presented in order to implement it on different optimization problems. A standard set of objective functions, including twenty-three functions, is used to evaluate the ability of the proposed algorithm to optimize and provide appropriate solutions for optimization problems. Also, the optimization results obtained from the proposed SLOA are compared with eight other well-known optimization algorithms. The optimization results show that the proposed SLOA has a high ability to solve various optimization problems. Also, the analysis and comparison of the optimization results obtained from the SLOA with the other eight algorithms shows that the SLOA is able to provide more appropriate quasi-optimal solutions and closer to the global optimal, and with better performance, it is much more competitive than similar algorithms. Full article

(This article belongs to the Special Issue Optimization Theory and Applications)

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15 pages, 268 KiB

Open AccessArticle

The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

by Vladimir Rusev and Alexander Skorikov

Mathematics 2021, 9(21), 2831; https://doi.org/10.3390/math9212831 - 8 Nov 2021

Viewed by 1774

Abstract

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a [...] Read more.

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given. Full article

(This article belongs to the Special Issue Stochastic Modeling and Applied Probability)

22 pages, 356 KiB

Open AccessArticle

Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

by Aigerim Kalybay, Ryskul Oinarov and Yaudat Sultanaev

Mathematics 2021, 9(21), 2830; https://doi.org/10.3390/math9212830 - 8 Nov 2021

Cited by 4 | Viewed by 1535

Abstract

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality [...] Read more.

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest. Full article

(This article belongs to the Special Issue Nonlocal Linearization and Nonlocal Symmetries of Differential Equations)

28 pages, 16294 KiB

Open AccessReview

A Review on Text Steganography Techniques

by Mohammed Abdul Majeed, Rossilawati Sulaiman, Zarina Shukur and Mohammad Kamrul Hasan

Mathematics 2021, 9(21), 2829; https://doi.org/10.3390/math9212829 - 8 Nov 2021

Cited by 48 | Viewed by 19865

Abstract

There has been a persistent requirement for safeguarding documents and the data they contain, either in printed or electronic form. This is because the fabrication and faking of documents is prevalent globally, resulting in significant losses for individuals, societies, and industrial sectors, in [...] Read more.

There has been a persistent requirement for safeguarding documents and the data they contain, either in printed or electronic form. This is because the fabrication and faking of documents is prevalent globally, resulting in significant losses for individuals, societies, and industrial sectors, in addition to national security. Therefore, individuals are concerned about protecting their work and avoiding these unlawful actions. Different techniques, such as steganography, cryptography, and coding, have been deployed to protect valuable information. Steganography is an appropriate method, in which the user is able to conceal a message inside another message (cover media). Most of the research on steganography utilizes cover media, such as videos, images, and sounds. Notably, text steganography is usually not given priority because of the difficulties in identifying redundant bits in a text file. To embed information within a document, its attributes must be changed. These attributes may be non-displayed characters, spaces, resized fonts, or purposeful misspellings scattered throughout the text. However, this would be detectable by an attacker or other third party because of the minor change in the document. To address this issue, it is necessary to change the document in such a manner that the change would not be visible to the eye, but could still be decoded using a computer. In this paper, an overview of existing research in this area is provided. First, we provide basic information about text steganography and its general procedure. Next, three classes of text steganography are explained: statistical and random generation, format-based methodologies, and linguistics. The techniques related to each class are analyzed, and particularly the manner in which a unique strategy is provided for hiding secret data. Furthermore, we review the existing works in the development of approaches and algorithms related to text steganography; this review is not exhaustive, and covers research published from 2016 to 2021. This paper aims to assist fellow researchers by compiling the current methods, challenges, and future directions in this field. Full article

(This article belongs to the Special Issue Mathematical Mitigation Techniques for Network and Cyber Security)

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11 pages, 1100 KiB

Open AccessArticle

Mathematics Model for 6-DOF Joints Manipulation Robots

by Oleg Krakhmalev, Nikita Krakhmalev, Sergey Gataullin, Irina Makarenko, Petr Nikitin, Denis Serdechnyy, Kang Liang and Sergey Korchagin

Mathematics 2021, 9(21), 2828; https://doi.org/10.3390/math9212828 - 8 Nov 2021

Cited by 14 | Viewed by 9341

Abstract

A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, [...] Read more.

A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots. Full article

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10 pages, 246 KiB

Open AccessArticle

Framelet Sets and Associated Scaling Sets

by Zhihua Zhang

Mathematics 2021, 9(21), 2824; https://doi.org/10.3390/math9212824 - 8 Nov 2021

Cited by 1 | Viewed by 1527

Abstract

In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets [...] Read more.

In time–frequency analysis, an increasing interest is to develop various tools to split a signal into a set of non-overlapping frequency regions without the influence of their adjacent regions. Although the framelet is an ideal tool for time–frequency analysis, most of the framelets only give an overlapping partition of the frequency domain. In order to obtain a non-overlapping partition of the frequency domain, framelet sets and associated scaling sets are introduced. In this study, we will investigate the relation between framelet (or scaling) sets and the frequency domain of framelets (or frame scaling functions). We find that the frequency domain of any frame scaling function always contains a scaling set and the frequency domain of any FMRA framelet always contains a framelet set. Moreover, we give a simple approach to construct various framelet/scaling sets from band-limited framelets and frame scaling functions. Full article

14 pages, 267 KiB

Open AccessArticle

Functional Form of Nonmanipulable Social Choice Functions with Two Alternatives

by Anna De Simone and Ciro Tarantino

Mathematics 2021, 9(21), 2827; https://doi.org/10.3390/math9212827 - 7 Nov 2021

Cited by 1 | Viewed by 1450

Abstract

We propose a new functional form characterization of binary nonmanipulable social choice functions on a universal domain and an arbitrary, possibly infinite, set of agents. In order to achieve this, we considered the more general case of two-valued social choice functions and describe [...] Read more.

We propose a new functional form characterization of binary nonmanipulable social choice functions on a universal domain and an arbitrary, possibly infinite, set of agents. In order to achieve this, we considered the more general case of two-valued social choice functions and describe the structure of the family consisting of groups of agents having no power to determine the values of a nonmanipulable social choice function. With the help of such a structure, we introduce a class of functions that we call powerless revealing social choice functions and show that the binary nonmanipulable social choice functions are the powerless revealing ones. Full article

20 pages, 617 KiB

Open AccessArticle

Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity

by Manuel Franco and Juana-María Vivo

Mathematics 2021, 9(21), 2826; https://doi.org/10.3390/math9212826 - 7 Nov 2021

Cited by 2 | Viewed by 3841

Abstract

The burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the

R O C

( [...] Read more.

The burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the

R O C

(

p A U C

) indexes exhibit limitations to analysing genomic data. Among other issues, the inability to differentiate between biomarkers whose

R O C

curves cross each other with the same

p A U C

value, the inappropriate expression of non-concave

R O C

curves, and the lack of a convenient interpretation, restrict their use in practice. Here, we have proposed the fitted partial area index (

F p A U C

), which is computable through an algorithm valid for any

R O C

curve shape, as an alternative performance summary for the evaluation of highly sensitive biomarkers. The proposed approach is based on fitter upper and lower bounds of the

p A U C

in a high-sensitivity region. Through variance estimates, simulations, and case studies for diagnosing leukaemia, and ovarian and colon cancers, we have proven the usefulness of the proposed metric in terms of restoring the interpretation and improving diagnostic accuracy. It is robust and feasible even when the

R O C

curve shows hooks, and solves performance ties between competitive biomarkers. Full article

(This article belongs to the Special Issue Models and Methods in Bioinformatics: Theory and Applications)

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27 pages, 425 KiB

Open AccessArticle

Doss ρ-Almost Periodic Type Functions in

R

ⁿ

by Marko Kostić, Wei-Shih Du and Vladimir E. Fedorov

Mathematics 2021, 9(21), 2825; https://doi.org/10.3390/math9212825 - 7 Nov 2021

Cited by 4 | Viewed by 1448

Abstract

In this paper, we investigate various classes of multi-dimensional Doss

ρ

-almost periodic type functions of the form

F : Λ \times X \to Y,

where

n \in N,

\emptyset \neq Λ \subseteq R^{n},

X and Y are complex [...] Read more.

In this paper, we investigate various classes of multi-dimensional Doss

ρ

-almost periodic type functions of the form

F : Λ \times X \to Y,

where

n \in N,

\emptyset \neq Λ \subseteq R^{n},

X and Y are complex Banach spaces, and

ρ

is a binary relation on

Y .

We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss

ρ

-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss

ρ

-almost periodic type functions with

(ω, c)

-periodic functions and Weyl-

ρ

-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given. Full article

(This article belongs to the Special Issue Abstract Fractional Integro-Differential Equations and Fixed Point Theory with Applications)

11 pages, 280 KiB

Open AccessArticle

On the Quasi-Total Roman Domination Number of Graphs

by Abel Cabrera Martínez, Juan C. Hernández-Gómez and José M. Sigarreta

Mathematics 2021, 9(21), 2823; https://doi.org/10.3390/math9212823 - 6 Nov 2021

Cited by 4 | Viewed by 1911

Abstract

Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems, computer and social networks, [...] Read more.

Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems, computer and social networks, monitoring communication, coding theory, and algorithm design, among others. In the last two decades, the functions defined on graphs have attracted the attention of several researchers. The Roman-dominating functions and their variants are one of the main attractions. This paper is a contribution to the Roman domination theory in graphs. In particular, we provide some interesting properties and relationships between one of its variants: the quasi-total Roman domination in graphs. Full article

(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory)

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71 pages, 10583 KiB

Open AccessArticle

Genetic Algorithm-Based Fuzzy Inference System for Describing Execution Tracing Quality

by Tamas Galli, Francisco Chiclana and Francois Siewe

Mathematics 2021, 9(21), 2822; https://doi.org/10.3390/math9212822 - 6 Nov 2021

Cited by 1 | Viewed by 1839

Abstract

Execution tracing is a tool used in the course of software development and software maintenance to identify the internal routes of execution and state changes while the software operates. Its quality has a high influence on the duration of the analysis required to [...] Read more.

Execution tracing is a tool used in the course of software development and software maintenance to identify the internal routes of execution and state changes while the software operates. Its quality has a high influence on the duration of the analysis required to locate software faults. Nevertheless, execution tracing quality has not been described by a quality model, which is an impediment while measuring software product quality. In addition, such a model needs to consider uncertainty, as the underlying factors involve human analysis and assessment. The goal of this study is to address both issues and to fill the gap by defining a quality model for execution tracing. The data collection was conducted on a defined study population with the inclusion of software professionals to consider their accumulated experiences; moreover, the data were processed by genetic algorithms to identify the linguistic rules of a fuzzy inference system. The linguistic rules constitute a human-interpretable rule set that offers further insights into the problem domain. The study found that the quality properties accuracy, design and implementation have the strongest impact on the quality of execution tracing, while the property legibility is necessary but not completely inevitable. Furthermore, the quality property security shows adverse effects on the quality of execution tracing, but its presence is required to some extent to avoid leaking information and to satisfy legal expectations. The created model is able to describe execution tracing quality appropriately. In future work, the researchers plan to link the constructed quality model to overall software product quality frameworks to consider execution tracing quality with regard to software product quality as a whole. In addition, the simplification of the mathematically complex model is also planned to ensure an easy-to-tailor approach to specific application domains. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

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16 pages, 446 KiB

Open AccessArticle

Performance of Gradient-Based Optimizer on Charging Station Placement Problem

by Essam H. Houssein, Sanchari Deb, Diego Oliva, Hegazy Rezk, Hesham Alhumade and Mokhtar Said

Mathematics 2021, 9(21), 2821; https://doi.org/10.3390/math9212821 - 6 Nov 2021

Cited by 18 | Viewed by 2055

Abstract

The electrification of transportation is necessary due to the expanded fuel cost and change in climate. The management of charging stations and their easy accessibility are the main concerns for receipting and accepting Electric Vehicles (EVs). The distribution network reliability, voltage stability and [...] Read more.

The electrification of transportation is necessary due to the expanded fuel cost and change in climate. The management of charging stations and their easy accessibility are the main concerns for receipting and accepting Electric Vehicles (EVs). The distribution network reliability, voltage stability and power loss are the main factors in designing the optimum placement and management strategy of a charging station. The planning of a charging stations is a complicated problem involving roads and power grids. The Gradient-based optimizer (GBO) used for solving the charger placement problem is tested in this work. A good balance between exploitation and exploration is achieved by the GBO. Furthermore, the likelihood of becoming stuck in premature convergence and local optima is rare in a GBO. Simulation results establish the efficacy and robustness of the GBO in solving the charger placement problem as compared to other metaheuristics such as a genetic algorithm, differential evaluation and practical swarm optimizer. Full article

(This article belongs to the Special Issue Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications)

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12 pages, 308 KiB

Open AccessArticle

A Compound Poisson Perspective of Ewens–Pitman Sampling Model

by Emanuele Dolera and Stefano Favaro

Mathematics 2021, 9(21), 2820; https://doi.org/10.3390/math9212820 - 6 Nov 2021

Cited by 3 | Viewed by 1579

Abstract

The Ewens–Pitman sampling model (EP-SM) is a distribution for random partitions of the set

{1, \dots, n}

, with

n \in N

, which is indexed by real parameters

α

and

θ

such that either [...] Read more.

The Ewens–Pitman sampling model (EP-SM) is a distribution for random partitions of the set

{1, \dots, n}

, with

n \in N

, which is indexed by real parameters

α

and

θ

such that either

α \in [0, 1)

and

θ > - α

, or

α < 0

and

θ = - m α

for some

m \in N

. For

α = 0

, the EP-SM is reduced to the Ewens sampling model (E-SM), which admits a well-known compound Poisson perspective in terms of the log-series compound Poisson sampling model (LS-CPSM). In this paper, we consider a generalisation of the LS-CPSM, referred to as the negative Binomial compound Poisson sampling model (NB-CPSM), and we show that it leads to an extension of the compound Poisson perspective of the E-SM to the more general EP-SM for either

α \in (0, 1)

, or

α < 0

. The interplay between the NB-CPSM and the EP-SM is then applied to the study of the large n asymptotic behaviour of the number of blocks in the corresponding random partitions—leading to a new proof of Pitman’s

α

diversity. We discuss the proposed results and conjecture that analogous compound Poisson representations may hold for the class of

α

-stable Poisson–Kingman sampling models—of which the EP-SM is a noteworthy special case. Full article

(This article belongs to the Special Issue Bayesian Predictive Inference and Related Asymptotics—Festschrift for Eugenio Regazzini's 75th Birthday)

6 pages, 203 KiB

Open AccessArticle

Inflection Points in Cubic Structures

by Vladimir Volenec, Zdenka Kolar-Begović and Ružica Kolar-Šuper

Mathematics 2021, 9(21), 2819; https://doi.org/10.3390/math9212819 - 6 Nov 2021

Viewed by 1540

Abstract

In this paper, we introduce and study new geometric concepts in a general cubic structure. We define the concept of the inflection point in a general cubic structure and investigate relationships between inflection points and associated and corresponding points in a general cubic [...] Read more.

In this paper, we introduce and study new geometric concepts in a general cubic structure. We define the concept of the inflection point in a general cubic structure and investigate relationships between inflection points and associated and corresponding points in a general cubic structure. Full article

18 pages, 7166 KiB

Open AccessArticle

GPS Data Correction Based on Fuzzy Logic for Tracking Land Vehicles

by Pedro J. Correa-Caicedo, Horacio Rostro-González, Martin A. Rodriguez-Licea, Óscar Octavio Gutiérrez-Frías, Carlos Alonso Herrera-Ramírez, Iris I. Méndez-Gurrola, Miroslava Cano-Lara and Alejandro I. Barranco-Gutiérrez

Mathematics 2021, 9(21), 2818; https://doi.org/10.3390/math9212818 - 6 Nov 2021

Cited by 7 | Viewed by 3271

Abstract

GPS sensors are widely used to know a vehicle’s location and to track its route. Although GPS sensor technology is advancing, they present systematic failures depending on the environmental conditions to which they are subjected. To tackle this problem, we propose an intelligent [...] Read more.

GPS sensors are widely used to know a vehicle’s location and to track its route. Although GPS sensor technology is advancing, they present systematic failures depending on the environmental conditions to which they are subjected. To tackle this problem, we propose an intelligent system based on fuzzy logic, which takes the information from the sensors and correct the vehicle’s absolute position according to its latitude and longitude. This correction is performed by two fuzzy systems, one to correct the latitude and the other to correct the longitude, which are trained using the MATLAB ANFIS tool. The positioning correction system is trained and tested with two different datasets. One of them collected with a Pmod GPS sensor and the other a public dataset, which was taken from routes in Brazil. To compare our proposal, an unscented Kalman filter (UKF) was implemented. The main finding is that the proposed fuzzy systems achieve a performance of 69.2% higher than the UKF. Furthermore, fuzzy systems are suitable to implement in an embedded system such as the Raspberry Pi 4. Another finding is that the logical operations facilitate the creation of non-linear functions because of the ‘if else’ structure. Finally, the existence justification of each fuzzy system section is easy to understand. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2021)

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33 pages, 7042 KiB

Open AccessArticle

Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights

by Pushpa Dissanayake, Teresa Flock, Johanna Meier and Philipp Sibbertsen

Mathematics 2021, 9(21), 2817; https://doi.org/10.3390/math9212817 - 5 Nov 2021

Cited by 6 | Viewed by 2358

Abstract

The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely [...] Read more.

The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification. Full article

(This article belongs to the Section Probability and Statistics)

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87 pages, 665 KiB

Open AccessEditor’s ChoiceArticle

General Fractional Vector Calculus

by Vasily E. Tarasov

Mathematics 2021, 9(21), 2816; https://doi.org/10.3390/math9212816 - 5 Nov 2021

Cited by 32 | Viewed by 4039

Abstract

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus [...] Read more.

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of operators. In the generalization of FVC from power-law nonlocality to the general form of nonlocality in space, we use the general fractional calculus (GFC) in the Luchko approach, which was published in 2021. This paper proposed the following: (I) Self-consistent definitions of general fractional differential vector operators: the regional and line general fractional gradients, the regional and surface general fractional curl operators, the general fractional divergence are proposed. (II) Self-consistent definitions of general fractional integral vector operators: the general fractional circulation, general fractional flux and general fractional volume integral are proposed. (III) The general fractional gradient, Green’s, Stokes’ and Gauss’s theorems as fundamental theorems of general fractional vector calculus are proved for simple and complex regions. The fundamental theorems (Gradient, Green, Stokes, Gauss theorems) of the proposed general FVC are proved for a wider class of domains, surfaces and curves. All these three parts allow us to state that we proposed a calculus, which is a general fractional vector calculus (General FVC). The difficulties and problems of defining general fractional integral and differential vector operators are discussed to the nonlocal case, caused by the violation of standard product rule (Leibniz rule), chain rule (rule of differentiation of function composition) and semigroup property. General FVC for orthogonal curvilinear coordinates, which includes general fractional vector operators for the spherical and cylindrical coordinates, is also proposed. Full article

(This article belongs to the Special Issue Fractals, Fractional Calculus and Applied Statistics)

22 pages, 25356 KiB

Open AccessArticle

RFaNet: Receptive Field-Aware Network with Finger Attention for Fingerspelling Recognition Using a Depth Sensor

by Shih-Hung Yang, Yao-Mao Cheng, Jyun-We Huang and Yon-Ping Chen

Mathematics 2021, 9(21), 2815; https://doi.org/10.3390/math9212815 - 5 Nov 2021

Cited by 4 | Viewed by 1905

Abstract

Automatic fingerspelling recognition tackles the communication barrier between deaf and hearing individuals. However, the accuracy of fingerspelling recognition is reduced by high intra-class variability and low inter-class variability. In the existing methods, regular convolutional kernels, which have limited receptive fields (RFs) and often [...] Read more.

Automatic fingerspelling recognition tackles the communication barrier between deaf and hearing individuals. However, the accuracy of fingerspelling recognition is reduced by high intra-class variability and low inter-class variability. In the existing methods, regular convolutional kernels, which have limited receptive fields (RFs) and often cannot detect subtle discriminative details, are applied to learn features. In this study, we propose a receptive field-aware network with finger attention (RFaNet) that highlights the finger regions and builds inter-finger relations. To highlight the discriminative details of these fingers, RFaNet reweights the low-level features of the hand depth image with those of the non-forearm image and improves finger localization, even when the wrist is occluded. RFaNet captures neighboring and inter-region dependencies between fingers in high-level features. An atrous convolution procedure enlarges the RFs at multiple scales and a non-local operation computes the interactions between multi-scale feature maps, thereby facilitating the building of inter-finger relations. Thus, the representation of a sign is invariant to viewpoint changes, which are primarily responsible for intra-class variability. On an American Sign Language fingerspelling dataset, RFaNet achieved 1.77% higher classification accuracy than state-of-the-art methods. RFaNet achieved effective transfer learning when the number of labeled depth images was insufficient. The fingerspelling representation of a depth image can be effectively transferred from large- to small-scale datasets via highlighting the finger regions and building inter-finger relations, thereby reducing the requirement for expensive fingerspelling annotations. Full article

(This article belongs to the Special Issue Computational Intelligence and Human–Computer Interaction: Modern Methods and Applications)

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27 pages, 9351 KiB

Open AccessArticle

Real-World Data-Driven Machine-Learning-Based Optimal Sensor Selection Approach for Equipment Fault Detection in a Thermal Power Plant

by Salman Khalid, Hyunho Hwang and Heung Soo Kim

Mathematics 2021, 9(21), 2814; https://doi.org/10.3390/math9212814 - 5 Nov 2021

Cited by 17 | Viewed by 4387

Abstract

Due to growing electricity demand, developing an efficient fault-detection system in thermal power plants (TPPs) has become a demanding issue. The most probable reason for failure in TPPs is equipment (boiler and turbine) fault. Advance detection of equipment fault can help secure maintenance [...] Read more.

Due to growing electricity demand, developing an efficient fault-detection system in thermal power plants (TPPs) has become a demanding issue. The most probable reason for failure in TPPs is equipment (boiler and turbine) fault. Advance detection of equipment fault can help secure maintenance shutdowns and enhance the capacity utilization rates of the equipment. Recently, an intelligent fault diagnosis based on multivariate algorithms has been introduced in TPPs. In TPPs, a huge number of sensors are used for process maintenance. However, not all of these sensors are sensitive to fault detection. The previous studies just relied on the experts’ provided data for equipment fault detection in TPPs. However, the performance of multivariate algorithms for fault detection is heavily dependent on the number of input sensors. The redundant and irrelevant sensors may reduce the performance of these algorithms, thus creating a need to determine the optimal sensor arrangement for efficient fault detection in TPPs. Therefore, this study proposes a novel machine-learning-based optimal sensor selection approach to analyze the boiler and turbine faults. Finally, real-world power plant equipment fault scenarios (boiler water wall tube leakage and turbine electric motor failure) are employed to verify the performance of the proposed model. The computational results indicate that the proposed approach enhanced the computational efficiency of machine-learning models by reducing the number of sensors up to 44% in the water wall tube leakage case scenario and 55% in the turbine motor fault case scenario. Further, the machine-learning performance is improved up to 97.6% and 92.6% in the water wall tube leakage and turbine motor fault case scenarios, respectively. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Modeling with Applications in Real-World Data and Artificial Intelligence)

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20 pages, 546 KiB

Open AccessArticle

Android Malware Detection Using Machine Learning with Feature Selection Based on the Genetic Algorithm

by Jaehyeong Lee, Hyuk Jang, Sungmin Ha and Yourim Yoon

Mathematics 2021, 9(21), 2813; https://doi.org/10.3390/math9212813 - 5 Nov 2021

Cited by 30 | Viewed by 7600

Abstract

Since the discovery that machine learning can be used to effectively detect Android malware, many studies on machine learning-based malware detection techniques have been conducted. Several methods based on feature selection, particularly genetic algorithms, have been proposed to increase the performance and reduce [...] Read more.

Since the discovery that machine learning can be used to effectively detect Android malware, many studies on machine learning-based malware detection techniques have been conducted. Several methods based on feature selection, particularly genetic algorithms, have been proposed to increase the performance and reduce costs. However, because they have yet to be compared with other methods and their many features have not been sufficiently verified, such methods have certain limitations. This study investigates whether genetic algorithm-based feature selection helps Android malware detection. We applied nine machine learning algorithms with genetic algorithm-based feature selection for 1104 static features through 5000 benign applications and 2500 malwares included in the Andro-AutoPsy dataset. Comparative experimental results show that the genetic algorithm performed better than the information gain-based method, which is generally used as a feature selection method. Moreover, machine learning using the proposed genetic algorithm-based feature selection has an absolute advantage in terms of time compared to machine learning without feature selection. The results indicate that incorporating genetic algorithms into Android malware detection is a valuable approach. Furthermore, to improve malware detection performance, it is useful to apply genetic algorithm-based feature selection to machine learning. Full article

(This article belongs to the Special Issue Swarm and Evolutionary Computation—Bridging Theory and Practice)

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33 pages, 6193 KiB

Open AccessArticle

Theory and Practice of Quantitative Assessment of System Harmonicity: Case of Road Safety in Russia before and during the COVID-19 Epidemic

by Artur I. Petrov, Victor I. Kolesov and Daria A. Petrova

Mathematics 2021, 9(21), 2812; https://doi.org/10.3390/math9212812 - 5 Nov 2021

Cited by 6 | Viewed by 2287

Abstract

People have had an interest in harmony issues for thousands of years; however, there is still no elaborated system of views on these questions. Ancient Greeks understood harmony as an agreement of opposites. A surge of interest in the study of the harmonic [...] Read more.

People have had an interest in harmony issues for thousands of years; however, there is still no elaborated system of views on these questions. Ancient Greeks understood harmony as an agreement of opposites. A surge of interest in the study of the harmonic aspects of being occurred in the twentieth century due to the development of systems science, particularly regarding synergetic system effects. At the same time, there are still relatively few applications of synergetics because of the absence of an accurate methodology for the identification of system harmonicity. The aim of this research is to develop the methodology for the quantitative assessment of system harmonicity by considering a practical example: the quantitative assessment of the harmonicity of the road safety provision system (RSS) and its dynamics during the last 15 years (2006–2020). In addition, the impact of the COVID restrictions on population mobility in Russia in 2020, on the change in the harmonicity of the road safety provision system, is considered. During the research it was established that the quality factor g of the Russian road safety provision system changed from g₂₀₀₆ = 1.9565 to g₂₀₂₀ = 2.4646, which promoted the decline of the relative entropy of the Russian road safety provision system from H_{n RSS}₂₀₀₆ = 0.8623 to H_{n RSS}₂₀₂₀ = 0.7553. The deep reason for that change was the modification of relation between “weights” or the significance of the contribution of different elements of the cause-and-effect chain in the formation of the factual level of the road accident rate in Russia in the last 15 years. The main conclusion of this research is that the harmonicity of the Russian road safety provision system, assessed by the normalized functional general utility GU_n_, has been increased, and it has already exceeded the level of harmonious reference systems GU_n = 0.618. In fact, the normalized functional general utility GU_n of the Russian road safety provision system increased from GU_n_RSS₂₀₀₆ = 0.615 to GU_n_RSS₂₀₂₀ = 0.652 (by 6.0%), from 2006 to 2020. Simultaneously, the share of the normalized used resource X_n declined, allowing a conclusion to be drawn about a significant improvement in the balance “efficiency-quality” of the Russian road safety provision system. The COVID lockdown played a positive role in this process. Harmonicity of the Russian road safety provision system, assessed by the normalized general utility GU_n_RSS, increased by 0.46% from 2019 to 2020. Full article

(This article belongs to the Special Issue From COVID-19 to Resilience: Quantitative Methods in Economics and Business)

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24 pages, 1312 KiB

Open AccessArticle

Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

by Sergey Stepanov and Mikhail Stepanov

Mathematics 2021, 9(21), 2811; https://doi.org/10.3390/math9212811 - 5 Nov 2021

Cited by 13 | Viewed by 2061

Abstract

The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted [...] Read more.

The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls. Full article

(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications)

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20 pages, 855 KiB

Open AccessArticle

Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

by Jingjing He, Wei Wang, Min Huang, Shaohua Wang and Xuefei Guan

Mathematics 2021, 9(21), 2810; https://doi.org/10.3390/math9212810 - 5 Nov 2021

Cited by 8 | Viewed by 4160

Abstract

This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as [...] Read more.

This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors and can be derived as the limiting states of normal-inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of different noninformative priors under small sample sizes is compared using the likelihood combining both fitting and prediction performances. Laplace approximation is used to evaluate the likelihood. A realistic fatigue reliability problem was used to illustrate the method. Following that, an actual aeroengine disk lifing application with two test samples is presented, and the results are compared with the existing method. Full article

(This article belongs to the Section Probability and Statistics)

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12 pages, 314 KiB

Open AccessEditor’s ChoiceArticle

Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

by Mart Ratas, Jüri Majak and Andrus Salupere

Mathematics 2021, 9(21), 2809; https://doi.org/10.3390/math9212809 - 5 Nov 2021

Cited by 16 | Viewed by 2688

Abstract

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed [...] Read more.

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed. Full article

(This article belongs to the Special Issue Mathematical Problems in Materials Science)

20 pages, 4723 KiB

Open AccessArticle

A Smart Helmet-Based PLS-BPNN Error Compensation Model for Infrared Body Temperature Measurement of Construction Workers during COVID-19

by Li Li, Jiahui Yu, Hang Cheng and Miaojuan Peng

Mathematics 2021, 9(21), 2808; https://doi.org/10.3390/math9212808 - 5 Nov 2021

Cited by 9 | Viewed by 2854

Abstract

In the context of the long-term coexistence between COVID-19 and human society, the implementation of personnel health monitoring in construction sites has become one of the urgent needs of current construction management. The installation of infrared temperature sensors on the helmets required to [...] Read more.

In the context of the long-term coexistence between COVID-19 and human society, the implementation of personnel health monitoring in construction sites has become one of the urgent needs of current construction management. The installation of infrared temperature sensors on the helmets required to be worn by construction personnel to track and monitor their body temperature has become a relatively inexpensive and reliable means of epidemic prevention and control, but the accuracy of measuring body temperature has always been a problem. This study developed a smart helmet equipped with an infrared temperature sensor and conducted a simulated construction experiment to collect data of temperature and its influencing factors in indoor and outdoor construction operation environments. Then, a Partial Least Square–Back Propagation Neural Network (PLS-BPNN) temperature error compensation model was established to correct the temperature measurement results of the smart helmet. The temperature compensation effects of different models were also compared, including PLS-BPNN with Least Square Regression (LSR), Partial Least Square Regression (PLSR), and single Back Propagation Neural Network (BPNN) models. The results showed that the PLS-BPNN model had higher accuracy and reliability, and the determination coefficient of the model was 0.99377. After using PLS-BPNN model for compensation, the relative average error of infrared body temperature was reduced by 2.745 °C and RMSE was reduced by 0.9849. The relative error range of infrared body temperature detection was only 0.005~0.143 °C. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering)

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13 pages, 3296 KiB

Open AccessArticle

Variable Weight Matter–Element Extension Model for the Stability Classification of Slope Rock Mass

by Shan Yang, Zitong Xu and Kaijun Su

Mathematics 2021, 9(21), 2807; https://doi.org/10.3390/math9212807 - 4 Nov 2021

Cited by 6 | Viewed by 2218

Abstract

The slope stability in an open-pit mine is closely related to the production safety and economic benefit of the mine. As a result of the increase in the number and scale of mine slopes, slope instability is frequently encountered in mines. Therefore, it [...] Read more.

The slope stability in an open-pit mine is closely related to the production safety and economic benefit of the mine. As a result of the increase in the number and scale of mine slopes, slope instability is frequently encountered in mines. Therefore, it is of scientific and social significance to strengthen the study of the stability of the slope rock mass. To accurately classify the stability of the slope rock mass in an open-pit mine, a new stability evaluation model of the slope rock mass was established based on variable weight and matter–element extension theory. First, based on the main evaluation indexes of geology, the environment, and engineering, the stability evaluation index system of the slope rock mass was constructed using the corresponding classification criteria of the evaluation index. Second, the constant weight of the evaluation index value was calculated using extremum entropy theory, and variable weight theory was used to optimize the constant weight to obtain the variable weight of the evaluation index value. Based on matter–element extension theory, the comprehensive correlation between the upper and lower limit indexes in the classification criteria and each classification was calculated, in addition to the comprehensive correlation between the rock mass indexes and the stability grade of each slope. Finally, the grade variable method was used to calculate the grade variable interval corresponding to the classification criteria of the evaluation index and the grade variable value of each slope rock mass, so as to determine the stability grade of the slope rock. The comparison results showed that the classification results of the proposed model are in line with engineering practice, and more accurate than those of the hierarchical-extension model and the multi-level unascertained measure-set pair analysis model. Full article

(This article belongs to the Special Issue Analytical, Numerical and Big-Data-Based Methods in Deep Rock Mechanics)

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