Mathematics

33 pages, 15084 KiB

Open AccessArticle

Optimal Control of Dengue Transmission with Vaccination

by Anusit Chamnan, Puntani Pongsumpun, I-Ming Tang and Napasool Wongvanich

Mathematics 2021, 9(15), 1833; https://doi.org/10.3390/math9151833 - 03 Aug 2021

Cited by 6 | Viewed by 2719

Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals [...] Read more.

Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals having documented past dengue infection history are vaccinated. This is the present practice in Thailand and is the latest recommendation of the WHO. The model used is the Susceptible-Infected-Recovered (SIR) model in series configuration for the human population and the Susceptible-Infected (SI) model for the vector population. Both dynamical models for the two populations were recast as optimal control problems with two optimal control parameters. The analysis showed that the equilibrium states were locally asymptotically stable. The numerical solution of the control systems and conclusions are presented. Full article

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12 pages, 1761 KiB

Open AccessArticle

Marketing Mix Modeling Using PLS-SEM, Bootstrapping the Model Coefficients

by Mariano Méndez-Suárez

Mathematics 2021, 9(15), 1832; https://doi.org/10.3390/math9151832 - 03 Aug 2021

Cited by 8 | Viewed by 5244

Abstract

Partial least squares structural equations modeling (PLS-SEM) uses sampling bootstrapping to calculate the significance of the model parameter estimates (e.g., path coefficients and outer loadings). However, when data are time series, as in marketing mix modeling, sampling bootstrapping shows inconsistencies that arise because [...] Read more.

Partial least squares structural equations modeling (PLS-SEM) uses sampling bootstrapping to calculate the significance of the model parameter estimates (e.g., path coefficients and outer loadings). However, when data are time series, as in marketing mix modeling, sampling bootstrapping shows inconsistencies that arise because the series has an autocorrelation structure and contains seasonal events, such as Christmas or Black Friday, especially in multichannel retailing, making the significance analysis of the PLS-SEM model unreliable. The alternative proposed in this research uses maximum entropy bootstrapping (meboot), a technique specifically designed for time series, which maintains the autocorrelation structure and preserves the occurrence over time of seasonal events or structural changes that occurred in the original series in the bootstrapped series. The results showed that meboot had superior performance than sampling bootstrapping in terms of the coherence of the bootstrapped data and the quality of the significance analysis. Full article

(This article belongs to the Special Issue Partial Least Squares Structural Equation Modeling (PLS-SEM) Applications in Economics and Finance)

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20 pages, 45632 KiB

Open AccessArticle

Style Transformation Method of Stage Background Images by Emotion Words of Lyrics

by Hyewon Yoon, Shuyu Li and Yunsick Sung

Mathematics 2021, 9(15), 1831; https://doi.org/10.3390/math9151831 - 03 Aug 2021

Cited by 1 | Viewed by 2223

Abstract

Recently, with the development of computer technology, deep learning has expanded to the field of art, which requires creativity, which is a unique ability of humans, and an understanding of the human emotions expressed in art to process them as data. The field [...] Read more.

Recently, with the development of computer technology, deep learning has expanded to the field of art, which requires creativity, which is a unique ability of humans, and an understanding of the human emotions expressed in art to process them as data. The field of art is integrating with various industrial fields, among which artificial intelligence (AI) is being used in stage art, to create visual images. As it is difficult for a computer to process emotions expressed in songs as data, existing stage background images for song performances are human designed. Recently, research has been conducted to enable AI to design stage background images on behalf of humans. However, there is no research on reflecting emotions contained in song lyrics to stage background images. This paper proposes a style transformation method to reflect emotions in stage background images. First, multiple verses and choruses are derived from song lyrics, one at a time, and emotion words included in each verse and chorus are extracted. Second, the probability distribution of the emotion words is calculated for each verse and chorus, and the image with the most similar probability distribution from an image dataset with emotion word tags in advance is selected for each verse and chorus. Finally, for each verse and chorus, the stage background images with the transferred style are outputted. Through an experiment, the similarity between the stage background and the image transferred to the style of the image with similar emotion words probability distribution was 38%, and the similarity between the stage background image and the image transferred to the style of the image with completely different emotion word probability distribution was 8%. The proposed method reduced the total variation loss of change from 1.0777 to 0.1597. The total variation loss is the sum of content loss and style loss based on weights. This shows that the style transferred image is close to edge information about the content of the input image, and the style is close to the target style image. Full article

(This article belongs to the Special Issue Mathematical Methods and Applications for Artificial Intelligence and Computer Vision)

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14 pages, 336 KiB

Open AccessArticle

Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

by Ekaterina Gromova, Anastasiia Zaremba and Shimai Su

Mathematics 2021, 9(15), 1830; https://doi.org/10.3390/math9151830 - 03 Aug 2021

Cited by 2 | Viewed by 1338

Abstract

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with [...] Read more.

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations. Full article

(This article belongs to the Special Issue Application of Optimal Control and Game Theory to the Problem of Resource Management)

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16 pages, 2255 KiB

Open AccessArticle

Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay

by Ardak Kashkynbayev and Fathalla A. Rihan

Mathematics 2021, 9(15), 1829; https://doi.org/10.3390/math9151829 - 03 Aug 2021

Cited by 11 | Viewed by 2176

Abstract

In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if [...] Read more.

In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if

R_{0} < 1

, the disease-free steady-state is locally and globally asymptotically stable. However, for

R_{0} > 1

, there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical results. Full article

(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)

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31 pages, 3259 KiB

Open AccessArticle

On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations

by Christos G. Massouros and Naveed Yaqoob

Mathematics 2021, 9(15), 1828; https://doi.org/10.3390/math9151828 - 03 Aug 2021

Cited by 4 | Viewed by 2004

Abstract

This paper presents the study of algebraic structures equipped with the inverted associativity axiom. Initially, the definition of the left and the right almost-groups is introduced and afterwards, the study is focused on the more general structures, which are the left and the [...] Read more.

This paper presents the study of algebraic structures equipped with the inverted associativity axiom. Initially, the definition of the left and the right almost-groups is introduced and afterwards, the study is focused on the more general structures, which are the left and the right almost-hypergroups and on their enumeration in the cases of order 2 and 3. The outcomes of these enumerations compared with the corresponding in the hypergroups reveal interesting results. Next, fundamental properties of the left and right almost-hypergroups are proved. Subsequently, the almost hypergroups are enriched with more axioms, like the transposition axiom and the weak commutativity. This creates new hypercompositional structures, such as the transposition left/right almost-hypergroups, the left/right almost commutative hypergroups, the join left/right almost hypergroups, etc. The algebraic properties of these new structures are analyzed and studied as well. Especially, the existence of neutral elements leads to the separation of their elements into attractive and non-attractive ones. If the existence of the neutral element is accompanied with the existence of symmetric elements as well, then the fortified transposition left/right almost-hypergroups and the transposition polysymmetrical left/right almost-hypergroups come into being. Full article

(This article belongs to the Special Issue Hypercompositional Algebra and Applications)

14 pages, 308 KiB

Open AccessArticle

A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

by Pablo Manuel Berná and Diego Mondéjar

Mathematics 2021, 9(15), 1827; https://doi.org/10.3390/math9151827 - 02 Aug 2021

Viewed by 1275

Abstract

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new [...] Read more.

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco. Full article

(This article belongs to the Section Mathematics and Computer Science)

15 pages, 310 KiB

Open AccessArticle

Bipolar Hypersoft Sets

by Sagvan Y. Musa and Baravan A. Asaad

Mathematics 2021, 9(15), 1826; https://doi.org/10.3390/math9151826 - 02 Aug 2021

Cited by 34 | Viewed by 2447

Abstract

Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more, a new mixed mathematical model [...] Read more.

Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more, a new mixed mathematical model called the bipolar hypersoft set is created by merging hypersoft sets and bipolarity. It is characterized by two hypersoft sets, one of which provides positive information and the other provides negative information. Moreover, some fundamental properties relative to it such as subset, superset, equal set, complement, difference, relative (absolute) null set and relative (absolute) whole set are defined. Furthermore, some set-theoretic operations such as the extended intersection, the restricted union, intersection, union, AND-operation and OR-operation of two bipolar hypersoft sets with their properties are discussed and supported by examples. Finally, tabular representations for the purposes of storing bipolar hypersoft sets in computer memory are used. Full article

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

13 pages, 6726 KiB

Open AccessArticle

Teaching Combinatorial Principles Using Relations through the Placemat Method

by Viliam Ďuriš, Gabriela Pavlovičová, Dalibor Gonda and Anna Tirpáková

Mathematics 2021, 9(15), 1825; https://doi.org/10.3390/math9151825 - 02 Aug 2021

Cited by 2 | Viewed by 2774

Abstract

The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. [...] Read more.

The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach. Full article

(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)

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9 pages, 434 KiB

Open AccessArticle

Critical Examination Using Business Intelligence on the Gender Gap in Information Technology in Brazil

by Erica L. Gallindo, Hobson A. Cruz and Mário W. L. Moreira

Mathematics 2021, 9(15), 1824; https://doi.org/10.3390/math9151824 - 02 Aug 2021

Cited by 5 | Viewed by 1919

Abstract

In the early 1990s, cyberfeminism emerged as an area of knowledge to discuss the connection between gender and technology. According to UNESCO, women are underrepresented in the field of science, technology, engineering, and mathematics and less than a third of women worldwide work [...] Read more.

In the early 1990s, cyberfeminism emerged as an area of knowledge to discuss the connection between gender and technology. According to UNESCO, women are underrepresented in the field of science, technology, engineering, and mathematics and less than a third of women worldwide work in scientific research and development. However, this number has grown and this reality is constantly changing. In this context, using business intelligence techniques, this study analyzes data from the computer and information and communication technology market to characterize the impact of the performance of women in these areas. It is expected to show that this performance in the highlighted fields is still a challenge in Brazil. Based on this hypothesis, results indicates that public policies must be focused on the base, i.e., to encourage young women to work in STEM areas. This study could encourage policymakers to find solutions to the challenges presented in this research. Full article

(This article belongs to the Special Issue Recent Advances in STEM Education)

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22 pages, 838 KiB

Open AccessArticle

Reset Control of Parallel MISO Systems

by José Francisco Sáez and Alfonso Baños

Mathematics 2021, 9(15), 1823; https://doi.org/10.3390/math9151823 - 02 Aug 2021

Cited by 2 | Viewed by 1549

Abstract

The proportional–integral plus Clegg integrator (PI + CI) controller is a hybrid extension of the proportional–integral (PI) controller that is able to overcome fundamental limitations of the linear and time-invariant control systems, potentially obtaining faster responses without increasing overshooting. This work focused on [...] Read more.

The proportional–integral plus Clegg integrator (PI + CI) controller is a hybrid extension of the proportional–integral (PI) controller that is able to overcome fundamental limitations of the linear and time-invariant control systems, potentially obtaining faster responses without increasing overshooting. This work focused on the analysis and design of PI + CI controllers and reset controllers in general, for the case of parallel multiple-input single-output (MISO) systems, extending previous design methods developed for the single-input single-output (SISO) case. Several design strategies were developed: one for first-order MISO plants achieving a flat response with a finite settling time, and for second-order MISO plants obtaining a fast response with a reduced overshoot and settling time in comparison with non-hybrid strategies. Several case studies were also developed to illustrate the potential of the proposed methods. Full article

(This article belongs to the Section Engineering Mathematics)

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16 pages, 18461 KiB

Open AccessArticle

Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

by Lazaros Moysis, Karthikeyan Rajagopal, Aleksandra V. Tutueva, Christos Volos, Beteley Teka and Denis N. Butusov

Mathematics 2021, 9(15), 1821; https://doi.org/10.3390/math9151821 - 02 Aug 2021

Cited by 13 | Viewed by 2022

Abstract

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of [...] Read more.

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves. Full article

(This article belongs to the Special Issue Chaos Based Computer Security and Functions)

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15 pages, 1018 KiB

Open AccessArticle

A Predictive Control Strategy for Aerial Payload Transportation with an Unmanned Aerial Vehicle

by Norberto Urbina-Brito, María-Eusebia Guerrero-Sánchez, Guillermo Valencia-Palomo, Omar Hernández-González, Francisco-Ronay López-Estrada and José Antonio Hoyo-Montaño

Mathematics 2021, 9(15), 1822; https://doi.org/10.3390/math9151822 - 01 Aug 2021

Cited by 15 | Viewed by 2758

Abstract

This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving [...] Read more.

This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving a good balance between fast stabilization times and small swing angles. The mathematical model is based on the Euler–Lagrange formulation and considers the dynamics of the vehicle, the cable, and the load. Then, the mathematical model is represented as an input-affine system to obtain the linear model for the control design. A constrained MPC strategy was designed and compared with an unconstrained MPC and an algorithm from the literature for the case of study. The constraints to be considered include the limits on the swing angles and the quadrotor position. The constrained control algorithm was constructed to stabilize the aerial vehicle. It aims to track a trajectory reference while attenuating the load swing, considering a maximum swing range of

\pm 10^{\circ}

. Numerical simulations were carried out to validate the control strategy. Full article

(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering)

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28 pages, 18161 KiB

Open AccessArticle

Methodology and Models for Individuals’ Creditworthiness Management Using Digital Footprint Data and Machine Learning Methods

by Ekaterina V. Orlova

Mathematics 2021, 9(15), 1820; https://doi.org/10.3390/math9151820 - 01 Aug 2021

Cited by 17 | Viewed by 5378

Abstract

This research deals with the challenge of reducing banks’ credit risks associated with the insolvency of borrowing individuals. To solve this challenge, we propose a new approach, methodology and models for assessing individual creditworthiness, with additional data about borrowers’ digital footprints to implement [...] Read more.

This research deals with the challenge of reducing banks’ credit risks associated with the insolvency of borrowing individuals. To solve this challenge, we propose a new approach, methodology and models for assessing individual creditworthiness, with additional data about borrowers’ digital footprints to implement comprehensive analysis and prediction of a borrower’s credit profile. We suggest a model for borrowers’ clustering based on the method of hierarchical clustering and the k-means method, which groups actual borrowers having similar creditworthiness and similar credit risks into homogeneous clusters. We also design the model for borrowers’ classification based on the stochastic gradient boosting (SGB) method, which reliably determines the cluster number and therefore the risk level for a new borrower. The developed models are the basis for decision making regarding the decision about lending value, interest rates and lending terms for each risk-homogeneous borrower’s group. The modified version of the methodology for assessing individual creditworthiness is presented, which is to reduce the credit risks and to increase the stability and profitability of financial organizations. Full article

(This article belongs to the Special Issue Application of Mathematical Methods to Economics, Management, Finance and Social Problems)

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16 pages, 18824 KiB

Open AccessArticle

Geological Modeling Method Based on the Normal Dynamic Estimation of Sparse Point Clouds

by Tiandong Shi, Deyun Zhong and Liguan Wang

Mathematics 2021, 9(15), 1819; https://doi.org/10.3390/math9151819 - 31 Jul 2021

Cited by 5 | Viewed by 1939

Abstract

The effect of geological modeling largely depends on the normal estimation results of geological sampling points. However, due to the sparse and uneven characteristics of geological sampling points, the results of normal estimation have great uncertainty. This paper proposes a geological modeling method [...] Read more.

The effect of geological modeling largely depends on the normal estimation results of geological sampling points. However, due to the sparse and uneven characteristics of geological sampling points, the results of normal estimation have great uncertainty. This paper proposes a geological modeling method based on the dynamic normal estimation of sparse point clouds. The improved method consists of three stages: (1) using an improved local plane fitting method to estimate the normals of the point clouds; (2) using an improved minimum spanning tree method to redirect the normals of the point clouds; (3) using an implicit function to construct a geological model. The innovation of this method is an iterative estimation of the point cloud normal. The geological engineer adjusts the normal direction of some point clouds according to the geological law, and then the method uses these correct point cloud normals as a reference to estimate the normals of all point clouds. By continuously repeating the iterative process, the normal estimation result will be more accurate. Experimental results show that compared with the original method, the improved method is more suitable for the normal estimation of sparse point clouds by adjusting normals, according to prior knowledge, dynamically. Full article

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10 pages, 1510 KiB

Open AccessArticle

Revealing Driver’s Natural Behavior—A GUHA Data Mining Approach

by Esko Turunen and Klara Dolos

Mathematics 2021, 9(15), 1818; https://doi.org/10.3390/math9151818 - 31 Jul 2021

Cited by 3 | Viewed by 1623

Abstract

We investigate the applicability and usefulness of the GUHA data mining method and its computer implementation LISp-Miner for driver characterization based on digital vehicle data on gas pedal position, vehicle speed, and others. Three analytical questions are assessed: (1) Which measured features, also [...] Read more.

We investigate the applicability and usefulness of the GUHA data mining method and its computer implementation LISp-Miner for driver characterization based on digital vehicle data on gas pedal position, vehicle speed, and others. Three analytical questions are assessed: (1) Which measured features, also called attributes, distinguish each driver from all other drivers? (2) Comparing one driver separately in pairs with each of the other drivers, which are the most distinguishing attributes? (3) Comparing one driver separately in pairs with each of the other drivers, which attributes values show significant differences between drivers? The analyzed data consist of 94,380 measurements and contain clear and understandable patterns to be found by LISp-Miner. In conclusion, we find that the GUHA method is well suited for such tasks. Full article

(This article belongs to the Special Issue Data Analysis and Domain Knowledge)

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21 pages, 1046 KiB

Open AccessArticle

Classification of Diseases Using Machine Learning Algorithms: A Comparative Study

by Marco-Antonio Moreno-Ibarra, Yenny Villuendas-Rey, Miltiadis D. Lytras, Cornelio Yáñez-Márquez and Julio-César Salgado-Ramírez

Mathematics 2021, 9(15), 1817; https://doi.org/10.3390/math9151817 - 31 Jul 2021

Cited by 23 | Viewed by 11398

Abstract

Machine learning in the medical area has become a very important requirement. The healthcare professional needs useful tools to diagnose medical illnesses. Classifiers are important to provide tools that can be useful to the health professional for this purpose. However, questions arise: which [...] Read more.

Machine learning in the medical area has become a very important requirement. The healthcare professional needs useful tools to diagnose medical illnesses. Classifiers are important to provide tools that can be useful to the health professional for this purpose. However, questions arise: which classifier to use? What metrics are appropriate to measure the performance of the classifier? How to determine a good distribution of the data so that the classifier does not bias the medical patterns to be classified in a particular class? Then most important question: does a classifier perform well for a particular disease? This paper will present some answers to the questions mentioned above, making use of classification algorithms widely used in machine learning research with datasets relating to medical illnesses under the supervised learning scheme. In addition to state-of-the-art algorithms in pattern classification, we introduce a novelty: the use of meta-learning to determine, a priori, which classifier would be the ideal for a specific dataset. The results obtained show numerically and statistically that there are reliable classifiers to suggest medical diagnoses. In addition, we provide some insights about the expected performance of classifiers for such a task. Full article

(This article belongs to the Special Issue Classification, Diagnosis and Prognosis of Diseases Using Machine Learning Algorithms)

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13 pages, 842 KiB

Open AccessArticle

Comparing COSTATIS and Generalized Procrustes Analysis with Multi-Way Public Education Expenditure Data

by María Concepción Vega-Hernández and Carmen Patino-Alonso

Mathematics 2021, 9(15), 1816; https://doi.org/10.3390/math9151816 - 31 Jul 2021

Cited by 1 | Viewed by 1931

Abstract

Governments serve a variety of purposes, and where governments spend their money has always been of concern to society. In particular, spending on public education is of great interest. However, the volume of this information can be difficult to manage. Therefore, the purpose [...] Read more.

Governments serve a variety of purposes, and where governments spend their money has always been of concern to society. In particular, spending on public education is of great interest. However, the volume of this information can be difficult to manage. Therefore, the purpose of this work is to compare the COSTATIS method and generalized Procrustes analysis (GPA) when working with multi-way data. Despite the particular characteristics of each of them, they present similarities and differences that, when analyzed together, can provide complementary results to researchers. The COSTATIS consists of a co-inertia analysis of the compromise of two k-table analyses. The GPA method provides an optimal superimposed representation of individual configurations, and a common consensus configuration is constructed as the mean of all transformed configurations. In addition, the GPA method includes the translation, rotation and scaling of coordinates. In this study, both methods were applied, and the advantages and disadvantages of each are presented. The treated data are a sequence of tables from various countries where different public expenditures on education have been measured over time. Full article

(This article belongs to the Special Issue Multivariate Statistics: Theory and Its Applications)

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14 pages, 399 KiB

Open AccessArticle

An Alternative Promotion Time Cure Model with Overdispersed Number of Competing Causes: An Application to Melanoma Data

by Diego I. Gallardo, Mário de Castro and Héctor W. Gómez

Mathematics 2021, 9(15), 1815; https://doi.org/10.3390/math9151815 - 31 Jul 2021

Cited by 5 | Viewed by 1753

Abstract

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure [...] Read more.

A cure rate model under the competing risks setup is proposed. For the number of competing causes related to the occurrence of the event of interest, we posit the one-parameter Bell distribution, which accommodates overdispersed counts. The model is parameterized in the cure rate, which is linked to covariates. Parameter estimation is based on the maximum likelihood method. Estimates are computed via the EM algorithm. In order to compare different models, a selection criterion for non-nested models is implemented. Results from simulation studies indicate that the estimation method and the model selection criterion have a good performance. A dataset on melanoma is analyzed using the proposed model as well as some models from the literature. Full article

(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)

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17 pages, 336 KiB

Open AccessArticle

On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study

by Abd El-Raheem M. Abd El-Raheem, Mona Hosny and Mahmoud H. Abu-Moussa

Mathematics 2021, 9(15), 1805; https://doi.org/10.3390/math9151805 - 31 Jul 2021

Cited by 7 | Viewed by 1624

Abstract

Competing risks are frequently overlooked, and the event of interest is analyzed with conventional statistical techniques. In this article, we consider the analysis of bi-causes of failure in the context of competing risk models using the extension of the exponential distribution under progressive [...] Read more.

Competing risks are frequently overlooked, and the event of interest is analyzed with conventional statistical techniques. In this article, we consider the analysis of bi-causes of failure in the context of competing risk models using the extension of the exponential distribution under progressive Type-II censoring. Maximum likelihood estimates for the unknown parameters via the expectation-maximization algorithm are obtained. Moreover, the Bayes estimates of the unknown parameters are approximated using Tierney-Kadane and MCMC techniques. Interval estimates using Bayesian and classical techniques are also considered. Two real data sets are investigated to illustrate the different estimation methods, and to compare the suggested model with Weibull distribution. Furthermore, the estimation methods are compared through a comprehensive simulation study. Full article

(This article belongs to the Section Probability and Statistics)

17 pages, 2839 KiB

Open AccessArticle

Strategies for Solving Addition Problems Using Modified Schema-Based Instruction in Students with Intellectual Disabilities

by Alicia Bruno, Irene Polo-Blanco, María José González-López and Jon González-Sánchez

Mathematics 2021, 9(15), 1814; https://doi.org/10.3390/math9151814 - 30 Jul 2021

Cited by 4 | Viewed by 3893

Abstract

A study is presented on the strategies employed to solve additive change problems by three students with intellectual disabilities (two of them with autism spectrum disorder). The students followed a program involving modified schema-based instruction. The results show an improvement in the problem-solving [...] Read more.

A study is presented on the strategies employed to solve additive change problems by three students with intellectual disabilities (two of them with autism spectrum disorder). The students followed a program involving modified schema-based instruction. The results show an improvement in the problem-solving skills of the three students, who achieved successful formal strategies associated with identifying the operation. We analyze the importance of adapting and/or emphasizing certain steps in the instruction process in order to tailor them to the difficulties of each student. Full article

(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)

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9 pages, 243 KiB

Open AccessArticle

On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

by S. Subburam, Lewis Nkenyereye, N. Anbazhagan, S. Amutha, M. Kameswari, Woong Cho and Gyanendra Prasad Joshi

Mathematics 2021, 9(15), 1813; https://doi.org/10.3390/math9151813 - 30 Jul 2021

Viewed by 1805

Abstract

Consider the Diophantine equation

y^{n} = x + x (x + 1) + \dots + x (x + 1) \dots (x + k)

, where x, y, n, and k are integers. In [...] Read more.

Consider the Diophantine equation

y^{n} = x + x (x + 1) + \dots + x (x + 1) \dots (x + k)

, where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality

n =

19,736 to obtain all solutions

(x, y, n)

of the equation for the fixed positive integers

k \leq 10

. In this paper, we improve the bound as

n \leq

10,000 for the same case

k \leq 10

, and for any fixed general positive integer k, we give an upper bound depending only on k for n. Full article

(This article belongs to the Special Issue Decidability of Logics and Their Theories and Combinations)

14 pages, 315 KiB

Open AccessArticle

A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

by Hari M. Srivastava, Nazar Khan, Shahid Khan, Qazi Zahoor Ahmad and Bilal Khan

Mathematics 2021, 9(15), 1812; https://doi.org/10.3390/math9151812 - 30 Jul 2021

Cited by 18 | Viewed by 1544

Abstract

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, [...] Read more.

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called

(p, q)

-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary. Full article

(This article belongs to the Special Issue Higher Transcendental Functions and Their Multi-Disciplinary Applications)

23 pages, 538 KiB

Open AccessFeature PaperArticle

Prospective Elementary Teachers’ Pedagogical Knowledge for Mathematical Problem Solving

by Juan Luis Piñeiro, Olive Chapman, Elena Castro-Rodríguez and Enrique Castro

Mathematics 2021, 9(15), 1811; https://doi.org/10.3390/math9151811 - 30 Jul 2021

Cited by 3 | Viewed by 2833

Abstract

Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary [...] Read more.

Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS. Full article

(This article belongs to the Special Issue Mathematics Teacher’s Specialised Knowledge)

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18 pages, 3777 KiB

Open AccessArticle

Is Longevity Acceleration Sustainable? An Entropy-Based Trial of the Population of Spain vs. Japan

by Amancio Betzuen Zalbidegoitia and Amaia Jone Betzuen Álvarez

Mathematics 2021, 9(15), 1810; https://doi.org/10.3390/math9151810 - 30 Jul 2021

Cited by 1 | Viewed by 1606

Abstract

Longevity risk is a major concern for governments around the world as they have to address social benefits, whether in the form of pensions, healthcare, or caring for dependents and providing long-term care, and so forth, which directly impact countries’ budgets. This paper [...] Read more.

Longevity risk is a major concern for governments around the world as they have to address social benefits, whether in the form of pensions, healthcare, or caring for dependents and providing long-term care, and so forth, which directly impact countries’ budgets. This paper uses a single entropy index to measure this type of risk. This methodology is clearly different from the one traditionally used in the literature, which is nearly entirely based on measuring the evolution of mathematical life expectancy. The authors used the longest-living populations in the world, Japan and Spain, to create a database in order to analyse the virtue of the indicator. The aim was to establish whether the longevity of those populations is accelerating or decelerating, compared by sex, and whether that occurs at the same intensity at different stages of a person’s life in each case. If the indicator showed differences in intensity, it would be a benchmark for the insurance and financial industry, providing it with information to market different products. Full article

(This article belongs to the Special Issue Business and Economics Mathematics)

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22 pages, 20835 KiB

Open AccessArticle

Modelling Functional Shifts in Two-Species Hypercycles

by Bernat Bassols, Ernest Fontich, Daniel Oro, David Alonso and Josep Sardanyés

Mathematics 2021, 9(15), 1809; https://doi.org/10.3390/math9151809 - 30 Jul 2021

Cited by 1 | Viewed by 2713

Abstract

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural [...] Read more.

Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural shifts due to environmental and ecological changes. Such changes could involve switches from cooperative to antagonistic interactions, in what we call a functional shift. In this article, we investigate a model for a two-member hypercycle model, considering that one species performs a functional shift. First, we introduce the model dynamics without functional shifts to illustrate the dynamics only considering obligate and facultative cooperation. Then, two more cases maintaining cross-catalysis are considered: (i) a model describing the dynamics of ribozymes where a fraction of the population of one replicator degrades the other molecular species while the other fraction still receives catalytic aid; and (ii) a system in which a given fraction of the population predates on the cooperating species while the rest of the population still receives aid. We have characterised the key bifurcation parameters determining extinction, survival, and coexistence of species. We show that predation, regardless of the fraction that benefits from it, does not significantly change dynamics with respect to the degradative case (i), thus conserving dynamics and bifurcations. Their biological significance is interpreted, and their potential implications for the dynamics of early replicators and ecological species are outlined. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

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21 pages, 9582 KiB

Open AccessArticle

From an Optimal Point to an Optimal Region: A Novel Methodology for Optimization of Multimodal Constrained Problems and a Novel Constrained Sliding Particle Swarm Optimization Strategy

by Carine M. Rebello, Márcio A. F. Martins, José M. Loureiro, Alírio E. Rodrigues, Ana M. Ribeiro and Idelfonso B. R. Nogueira

Mathematics 2021, 9(15), 1808; https://doi.org/10.3390/math9151808 - 30 Jul 2021

Cited by 9 | Viewed by 1491

Abstract

The present work proposes a novel methodology for an optimization procedure extending the optimal point to an optimal area based on an uncertainty map of deterministic optimization. To do so, this work proposes the deductions of a likelihood-based test to draw confidence regions [...] Read more.

The present work proposes a novel methodology for an optimization procedure extending the optimal point to an optimal area based on an uncertainty map of deterministic optimization. To do so, this work proposes the deductions of a likelihood-based test to draw confidence regions of population-based optimizations. A novel Constrained Sliding Particle Swarm Optimization algorithm is also proposed that can cope with the optimization procedures characterized by multi-local minima. There are two open issues in the optimization literature, uncertainty analysis of the deterministic optimization and application of meta-heuristic algorithms to solve multi-local minima problems. The proposed methodology was evaluated in a series of five benchmark tests. The results demonstrated that the methodology is able to identify all the local minima and the global one, if any. Moreover, it was able to draw the confidence regions of all minima found by the optimization algorithm, hence, extending the optimal point to an optimal region. Moreover, providing the set of decision variables that can give an optimal value, with statistical confidence. Finally, the methodology is evaluated to address a case study from chemical engineering; the optimization of a complex multifunctional process where separation and reaction are processed simultaneously, a true moving bed reactor. The method was able to efficiently identify the two possible optimal operating regions of this process. Therefore, proving the practical application of this methodology. Full article

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12 pages, 274 KiB

Open AccessArticle

Perturbation of Wavelet Frames of Quaternionic-Valued Functions

by Fusheng Xiao and Jianxun He

Mathematics 2021, 9(15), 1807; https://doi.org/10.3390/math9151807 - 30 Jul 2021

Viewed by 1167

Abstract

Let

L^{2} (R, H)

denote the space of all square integrable quaternionic-valued functions. In this article, let

Φ \in L^{2} (R, H)

. We consider the perturbation problems of wavelet frame [...] Read more.

Let

L^{2} (R, H)

denote the space of all square integrable quaternionic-valued functions. In this article, let

Φ \in L^{2} (R, H)

. We consider the perturbation problems of wavelet frame

{Φ_{m, n, a_{0}, b_{0}}, m, n \in Z}

about translation parameter

b_{0}

and dilation parameter

a_{0}

. In particular, we also research the stability of irregular wavelet frame

{\sqrt{S_{m}} Φ (S_{m} x - n b), m, n \in Z}

for perturbation problems of sampling. Full article

(This article belongs to the Section Computational and Applied Mathematics)

16 pages, 419 KiB

Open AccessArticle

Solving High-Dimensional Problems in Statistical Modelling: A Comparative Study

by Stamatis Choudalakis, Marilena Mitrouli, Athanasios Polychronou and Paraskevi Roupa

Mathematics 2021, 9(15), 1806; https://doi.org/10.3390/math9151806 - 30 Jul 2021

Cited by 4 | Viewed by 1244

Abstract

In this work, we present numerical methods appropriate for parameter estimation in high-dimensional statistical modelling. The solution of these problems is not unique and a crucial question arises regarding the way that a solution can be found. A common choice is to keep [...] Read more.

In this work, we present numerical methods appropriate for parameter estimation in high-dimensional statistical modelling. The solution of these problems is not unique and a crucial question arises regarding the way that a solution can be found. A common choice is to keep the corresponding solution with the minimum norm. There are cases in which this solution is not adequate and regularisation techniques have to be considered. We classify specific cases for which regularisation is required or not. We present a thorough comparison among existing methods for both estimating the coefficients of the model which corresponds to design matrices with correlated covariates and for variable selection for supersaturated designs. An extensive analysis for the properties of design matrices with correlated covariates is given. Numerical results for simulated and real data are presented. Full article

(This article belongs to the Special Issue Numerical Linear Algebra and the Applications)

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18 pages, 3041 KiB

Open AccessArticle

Electromagnetic Devices with Moving Parts—Simulation with FEM/BEM Coupling

by Thomas Rüberg, Lars Kielhorn and Jürgen Zechner

Mathematics 2021, 9(15), 1804; https://doi.org/10.3390/math9151804 - 30 Jul 2021

Cited by 2 | Viewed by 1915

Abstract

The numerical analysis of electromagnetic devices by means of finite element methods (FEM) is often hindered by the need to incorporate the surrounding domain. The discretisation of the air may become complex and has to be truncated by artificial boundaries incurring a modelling [...] Read more.

The numerical analysis of electromagnetic devices by means of finite element methods (FEM) is often hindered by the need to incorporate the surrounding domain. The discretisation of the air may become complex and has to be truncated by artificial boundaries incurring a modelling error. Even more problematic are moving parts that require tedious re-meshing and mapping techniques. In this work, we tackle these problems by using the boundary element method (BEM) in conjunction with FEM. Whereas the solid parts of the electrical device are discretised by FEM, which can easily account for material non-linearities, the surrounding domain is represented by BEM, which requires only a surface discretisation. This approach completely avoids an air mesh and its re-meshing during the simulation with moving or deforming parts. Our approach is robust, shows optimal complexity, and provides an accurate calculation of electromagnetic forces that are required to study the mechanical behaviour of the device. Full article

(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)

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Mathematics, Volume 9, Issue 15 (August-1 2021) – 124 articles

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