Mathematics

17 pages, 369 KiB

Open AccessArticle

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

by Freek Verdonck, Herwig Bruneel and Sabine Wittevrongel

Mathematics 2021, 9(14), 1709; https://doi.org/10.3390/math9141709 - 20 Jul 2021

Viewed by 1873

Abstract

In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and [...] Read more.

In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay. Full article

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

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10 pages, 596 KiB

Open AccessArticle

Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

by Melike Bildirici, Nilgun Guler Bayazit and Yasemen Ucan

Mathematics 2021, 9(14), 1708; https://doi.org/10.3390/math9141708 - 20 Jul 2021

Cited by 4 | Viewed by 2250

Abstract

In this paper, we propose hybrid models for modelling the daily oil price during the period from 2 January 1986 to 5 April 2021. The models on

S^{2}

manifolds that we consider, including the reference ones, employ matrix representations rather than differential [...] Read more.

In this paper, we propose hybrid models for modelling the daily oil price during the period from 2 January 1986 to 5 April 2021. The models on

S^{2}

manifolds that we consider, including the reference ones, employ matrix representations rather than differential operator representations of Lie algebras. Firstly, the performance of Lie_NLS model is examined in comparison to the Lie-OLS model. Then, both of these reference models are improved by integrating them with a recurrent neural network model used in deep learning. Thirdly, the forecasting performance of these two proposed hybrid models on the

S^{2}

manifold, namely Lie-LSTM_OLS and Lie-LSTM_NLS, are compared with those of the reference Lie_OLS and Lie_NLS models. The in-sample and out-of-sample results show that our proposed methods can achieve improved performance over Lie_OLS and Lie_NLS models in terms of RMSE and MAE metrics and hence can be more reliably used to assess volatility of time-series data. Full article

(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)

29 pages, 16690 KiB

Open AccessArticle

A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

by Tomaž Kos and Damir Vrančić

Mathematics 2021, 9(14), 1707; https://doi.org/10.3390/math9141707 - 20 Jul 2021

Cited by 3 | Viewed by 2350

Abstract

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides [...] Read more.

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides a good model and requires a relatively simple experiment. This is the advantage of the method of moments. In this paper, an analytical method based on the measurement of the process moments (characteristic areas) is proposed, to identify the five-parameter model (second-order process with zero plus time delay) from either the closed-loop or open-loop time responses of the process (in the time-domain), or the general-order transfer function with time delay (in the frequency-domain). The only parameter required by the user is the type of process (minimum phase or non-minimum phase process), which in practice can be easily determined from the time response of the process. The method can also be used to reduce the higher-order process model. The proposed identification method was tested on several illustrative examples, and compared to other identification methods. The comparison with existing methods showed the superiority of the proposed method. Moreover, the tests confirmed that the algorithm of the proposed method works properly for a wide family of process models, even in the presence of moderate process noise. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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16 pages, 297 KiB

Open AccessArticle

A Certain Subclass of Multivalent Analytic Functions Defined by the q-Difference Operator Related to the Janowski Functions

by Bo Wang, Rekha Srivastava and Jin-Lin Liu

Mathematics 2021, 9(14), 1706; https://doi.org/10.3390/math9141706 - 20 Jul 2021

Cited by 11 | Viewed by 1769

Abstract

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of [...] Read more.

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper. Full article

(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)

12 pages, 648 KiB

Open AccessArticle

A Mathematical Program for Scheduling Preventive Maintenance of Cogeneration Plants with Production

by Khaled Alhamad, Rym M’Hallah and Cormac Lucas

Mathematics 2021, 9(14), 1705; https://doi.org/10.3390/math9141705 - 20 Jul 2021

Cited by 4 | Viewed by 2010

Abstract

This paper considers the scheduling of preventive maintenance for the boilers, turbines, and distillers of power plants that produce electricity and desalinated water. It models the problem as a mathematical program (MP) that maximizes the sum of the minimal ratios of production to [...] Read more.

This paper considers the scheduling of preventive maintenance for the boilers, turbines, and distillers of power plants that produce electricity and desalinated water. It models the problem as a mathematical program (MP) that maximizes the sum of the minimal ratios of production to the demand of electricity and water during a planning time horizon. This objective encourages the plants’ production and enhances the chances of meeting consumers’ needs. It reduces the chance of power cuts and water shortages that may be caused by emergency disruptions of equipment on the network. To assess its performance and effectiveness, we test the MP on a real system consisting of 32 units and generate a preventive maintenance schedule for a time horizon of 52 weeks (one year). The generated schedule outperforms the schedule established by experts of the water plant; it induces, respectively, 16% and 12% increases in the surpluses while either matching or surpassing the total production. The sensitivity analysis further indicates that the generated schedule can handle unforeseen longer maintenance periods as well as a 120% increase in demand—a sizable realization in a country that heavily relies on electricity to acclimate to the harsh weather conditions. In addition, it suggests the robustness of the schedules with respect to increased demand. In summary, the MP model yields optimal systematic sustainable schedules. Full article

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10 pages, 283 KiB

Open AccessArticle

Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure

by Hristo Manev and Mancho Manev

Mathematics 2021, 9(14), 1704; https://doi.org/10.3390/math9141704 - 20 Jul 2021

Cited by 8 | Viewed by 1487

Abstract

We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were [...] Read more.

We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

20 pages, 4849 KiB

Open AccessArticle

Reversible Data Hiding Based on Pixel-Value-Ordering and Prediction-Error Triplet Expansion

by Heng-Xiao Chi, Ji-Hwei Horng and Chin-Chen Chang

Mathematics 2021, 9(14), 1703; https://doi.org/10.3390/math9141703 - 20 Jul 2021

Cited by 4 | Viewed by 2369

Abstract

Pixel value ordering and prediction error expansion (PVO+PEE) is a very successful reversible data hiding (RDH) scheme. A series of studies were proposed to improve the performance of the PVO-based scheme. However, the embedding capacity of those schemes is quite limited. We propose [...] Read more.

Pixel value ordering and prediction error expansion (PVO+PEE) is a very successful reversible data hiding (RDH) scheme. A series of studies were proposed to improve the performance of the PVO-based scheme. However, the embedding capacity of those schemes is quite limited. We propose a two-step prediction-error-triplet expansion RDH scheme based on PVO. A three-dimensional state transition map for the prediction-error triplet is also proposed to guide the embedding of the two-step scheme. By properly designing the state transitions, the proposed scheme can embed secret data or expand without embedding by modifying just a single entry of the triplet. The experimental results show that the proposed scheme significantly enlarges the embedding capacity of the PVO-based scheme and further reduces the distortion due to embedding. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods in Intelligent Multimedia: Security and Applications)

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31 pages, 1106 KiB

Open AccessArticle

Corruption Shock in Mexico: fsQCA Analysis of Entrepreneurial Intention in University Students

by Fernando Castelló-Sirvent and Pablo Pinazo-Dallenbach

Mathematics 2021, 9(14), 1702; https://doi.org/10.3390/math9141702 - 20 Jul 2021

Cited by 10 | Viewed by 3004

Abstract

Entrepreneurship is the basis of the production network, and thus a key to territorial development. In this line, entrepreneurial intention has been pointed out as an indicator of latent entrepreneurship. In this article, the entrepreneurial intention of university students is studied from a [...] Read more.

Entrepreneurship is the basis of the production network, and thus a key to territorial development. In this line, entrepreneurial intention has been pointed out as an indicator of latent entrepreneurship. In this article, the entrepreneurial intention of university students is studied from a configurational approach, allowing the study of the combined effect of corruption perception, corruption normalization, gender, university career area, and family entrepreneurial background to explain high levels of entrepreneurial intention. The model was tested with the fsQCA methodology according to two samples of students grouped according to their household income (medium and high level: N = 180; low level: N = 200). Stress tests were run to confirm the robustness of the results. This study highlights the negative impact produced by corruption among university students’ entrepreneurial intention. Furthermore, the importance of family entrepreneurial background for specific archetypes like female, STEM, and low household income students is pointed out, as well as the importance of implementing education programs for entrepreneurship in higher education, and more specifically in STEM areas. Policies focused on facilitating the access to financial resources for female students and low household income students, and specific programs to foster female entrepreneurship, are also recommended. Full article

(This article belongs to the Special Issue Fuzzy Sets in Business Management, Finance, and Economics)

11 pages, 369 KiB

Open AccessReview

Soft Computing for Decision-Making in Fuzzy Environments: A Tribute to Professor Ioan Dzitac

by Simona Dzitac and Sorin Nădăban

Mathematics 2021, 9(14), 1701; https://doi.org/10.3390/math9141701 - 20 Jul 2021

Cited by 17 | Viewed by 3436

Abstract

This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a [...] Read more.

This paper is dedicated to Professor Ioan Dzitac (1953–2021). Therefore, his life has been briefly presented as well as a comprehensive overview of his major contributions in the domain of soft computing methods in a fuzzy environment. This paper is part of a special reverential volume, dedicated to the Centenary of the Birth of Lotfi A. Zadeh, whom Ioan Dzitac considered to be is his mentor, and to whom he showed his gratitude many times and in innumerable ways, including by being the Guest Editor of this Special Issue. Professor Ioan Dzitac had many important achievements throughout his career: he was co-founder and Editor-in-Chief of an ISI Expanded quoted journal, International Journal of Computers Communications & Control; together with L.A. Zadeh, D. Tufis and F.G. Filip he edited the volume “From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence”; his scientific interest focused on different sub-fields: fuzzy logic applications, soft computing in a fuzzy environment, artificial intelligence, learning platform, distributed systems in internet. He had the most important contributions in soft computing in a fuzzy environment. Some of them will be presented in this paper. Finally, some future trends are discussed. Full article

(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))

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16 pages, 781 KiB

Open AccessArticle

Multiple Criteria Decision-Making for Developing an International Game Participation Strategy: A Novel Application of the Data Envelopment Analysis (DEA) Two-Stage Efficiency Process

by Yi-Chieh Chen, Lin-Huan Hu, Wan Chen Lu, Jei-Zheng Wu and Jiun-Jen Yang

Mathematics 2021, 9(14), 1700; https://doi.org/10.3390/math9141700 - 20 Jul 2021

Cited by 4 | Viewed by 2315

Abstract

Background: This study aims to develop an efficient future game participation strategy for teenaged athletes based on an analysis of the 2019 International Table Tennis Federation (ITTF) World Tour game expenditure efficiency and prize-winning efficiency. Methods: In this research, Chinese Taipei (TPE) players [...] Read more.

Background: This study aims to develop an efficient future game participation strategy for teenaged athletes based on an analysis of the 2019 International Table Tennis Federation (ITTF) World Tour game expenditure efficiency and prize-winning efficiency. Methods: In this research, Chinese Taipei (TPE) players served as the main research subjects. The input and output categories were determined through a literature analysis. A two-stage efficiency process of data envelopment analysis (DEA) and Boston consulting group (BCG) matrix were applied in this study to facilitate the calculation. Results: Based on a slack variable analysis, local travel expenses are the key elements impacting efficiency. The game recommendation order was based on a BCG matrix. The top seven recommended games were the Japan Open, Czech Open, Australian Open, Bulgarian Open, Austrian Open, China Open, and German Open. Conclusion: The results of this current study provide efficient game participation recommendations for teenaged athletes. Long-term follow-up records of game participation information should be developed to provide teenaged athletes with a precise efficiency analysis. Full article

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15 pages, 2186 KiB

Open AccessArticle

Nonlinear Differential Braking Control for Collision Avoidance During Lane Change

by Young Seop Son and Wonhee Kim

Mathematics 2021, 9(14), 1699; https://doi.org/10.3390/math9141699 - 19 Jul 2021

Cited by 3 | Viewed by 1982

Abstract

In this paper, a nonlinear differential braking control method is developed to avoid collision during lane change under driver torque. The lateral dynamics consist of lateral offset error and yaw error dynamics and can be interpreted as a semi-strict feedback form. In the [...] Read more.

In this paper, a nonlinear differential braking control method is developed to avoid collision during lane change under driver torque. The lateral dynamics consist of lateral offset error and yaw error dynamics and can be interpreted as a semi-strict feedback form. In the differential braking control problem under the driver torque, a matching condition does not satisfy, and the system is not in the form of, the strict feedback form. Thus, a general backstepping control method cannot be applied. To overcome this problem, the proposed method is designed via the combination of the sliding mode control and backstepping. Two sliding surfaces are designed for differential braking control. One of the surfaces is designed considering the lateral offset error, and the other sliding surface is designed using the combination of the yaw and yaw rate errors as the virtual input of the lateral offset error dynamics. A brake steer force input is developed to regulate the two sliding surfaces using a backstepping procedure under the driver torque. Integral action and a super twisting algorithm are used in the lateral controller to ensure the robustness of the system. The proposed method, which is designed via the combination of the sliding mode control and backstepping, can improve the lateral control performance using differential braking. The proposed method is validated through simulations. Full article

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22 pages, 2637 KiB

Open AccessArticle

Theoretical Efficiency Study of Output Lubricant Flow Rate Regulating Principle on the Example of a Two-Row Aerostatic Journal Bearing with Longitudinal Microgrooves and a System of External Combined Throttling

by Vladimir Kodnyanko, Stanislav Shatokhin, Andrey Kurzakov, Yuri Pikalov, Lilia Strok, Iakov Pikalov, Olga Grigorieva and Maxim Brungardt

Mathematics 2021, 9(14), 1698; https://doi.org/10.3390/math9141698 - 19 Jul 2021

Cited by 4 | Viewed by 1752

Abstract

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance [...] Read more.

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance and an increased tendency for instability. In radial bearings, it is possible to use longitudinal microgrooves, which practically exclude circumferential air leakage, and contributes to a significant increase in load-bearing capacity. To reduce compliance to zero and negative values, inlet diaphragm and elastic airflow regulators are used. Active flow compensation is inextricably linked to the problem of ensuring the stability of bearings due to the presence of relatively large volumes of gas in the regulator, which have a destabilizing effect. This problem was solved by using an external combined throttling system. Bearings with input flow regulators have a number of disadvantages-they are very energy-intensive and have an insufficiently stable load capacity. A more promising way to reduce compliance is the use of displacement compensators for the movable element. Such bearings also allow for a decrease in compliance to zero and negative values, which makes it possible to use them not only as supports, but also as active deformation compensators of the technological system of machine tools in order to reduce the time and increase the accuracy of metalworking. The new idea of using active flow compensators is to regulate the flow rate not at the inlet, but at the outlet of the air flow. This design has the energy efficiency that is inherent to a conventional bearing, but the regulation of the lubricant output flow allows the compliance to be reduced to zero and negative values. This article discusses the results of a theoretical study of the static and dynamic characteristics of a two-row radial aerostatic bearing with longitudinal microgrooves and an output flow regulator. Mathematical modeling and theoretical study of stationary modes have been carried out. Formulas for determining static compliance and load capacity are obtained. Iterative finite-difference methods for determining the dynamic characteristics of a structure are proposed. The calculation of dynamic quality criteria was carried out on the basis of the method of rational interpolation of the bearing transfer function, as a system with distributed parameters, developed by the authors. It was found that the volumes of the microgrooves do not have a noticeable effect on the bearing dynamics. It is shown that, in this design, the external combined throttling system is an effective means of maintaining stability and high dynamic quality of the design operating in the modes of low, zero and negative compliance. Full article

(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)

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16 pages, 347 KiB

Open AccessArticle

Mathematics Preservice Trainee Teachers’ Perceptions of Attention to Diversity in Initial Training as Secondary Education Teachers

by María Jesús Caurcel Cara, Emilio Crisol Moya and Carmen del Pilar Gallardo-Montes

Mathematics 2021, 9(14), 1697; https://doi.org/10.3390/math9141697 - 19 Jul 2021

Cited by 3 | Viewed by 2368

Abstract

Research on teachers’ perceptions about diversity is key to understanding the different approaches to be implemented to build inclusive education. Within this framework, the perceptions and attitudes of 73 students in the Mathematics specialization of the University Master’s Degree in Teacher Training for [...] Read more.

Research on teachers’ perceptions about diversity is key to understanding the different approaches to be implemented to build inclusive education. Within this framework, the perceptions and attitudes of 73 students in the Mathematics specialization of the University Master’s Degree in Teacher Training for Secondary Education, Bachillerato, Vocational Training and Language Teaching (Máster Universitario en Profesorado de Educación Secundaria Obligatoria, Formación Profesional y Enseñanza de Idiomas (MAES) at the University of Granada (Spain) were analyzed to determine their views about the initial training they received on attention to diversity during the Master’s program. The study is a descriptive and correlational-predictive transversal examination of the responses obtained from the “Questionnaire for preservice secondary education teachers on perceptions about attention to diversity” (Colmenero Ruiz and Pegalajar Palomino, 2015). The findings demonstrate that the students—preservice secondary education teachers—held favorable attitudes toward diversity and the principle of inclusion. The findings also show that contact with persons with disability influences perception of this population. The authors conclude that better training and knowledge of the elements that condition the teaching–learning process for high-quality attention to diversity predict better pedagogical preparation in matters of attention to diversity. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

24 pages, 7253 KiB

Open AccessArticle

Design and Numerical Implementation of V2X Control Architecture for Autonomous Driving Vehicles

by Piyush Dhawankar, Prashant Agrawal, Bilal Abderezzak, Omprakash Kaiwartya, Krishna Busawon and Maria Simona Raboacă

Mathematics 2021, 9(14), 1696; https://doi.org/10.3390/math9141696 - 19 Jul 2021

Cited by 8 | Viewed by 4002

Abstract

This paper is concerned with designing and numerically implementing a V2X (Vehicle-to-Vehicle and Vehicle-to-Infrastructure) control system architecture for a platoon of autonomous vehicles. The V2X control architecture integrates the well-known Intelligent Driver Model (IDM) for a platoon of Autonomous Driving Vehicles (ADVs) with [...] Read more.

This paper is concerned with designing and numerically implementing a V2X (Vehicle-to-Vehicle and Vehicle-to-Infrastructure) control system architecture for a platoon of autonomous vehicles. The V2X control architecture integrates the well-known Intelligent Driver Model (IDM) for a platoon of Autonomous Driving Vehicles (ADVs) with Vehicle-to-Infrastructure (V2I) Communication. The main aim is to address practical implementation issues of such a system as well as the safety and security concerns for traffic environments. To this end, we first investigated a channel estimation model for V2I communication. We employed the IEEE 802.11p vehicular standard and calculated path loss, Packet Error Rate (PER), Signal-to-Noise Ratio (SNR), and throughput between transmitter and receiver end. Next, we carried out several case studies to evaluate the performance of the proposed control system with respect to its response to: (i) the communication infrastructure; (ii) its sensitivity to an emergency, inter-vehicular gap, and significant perturbation; and (iii) its performance under the loss of communication and changing driving environment. Simulation results show the effectiveness of the proposed control model. The model is collision-free for an infinite length of platoon string on a single lane road-driving environment. It also shows that it can work during a lack of communication, where the platoon vehicles can make their decision with the help of their own sensors. V2X Enabled Intelligent Driver Model (VX-IDM) performance is assessed and compared with the state-of-the-art models considering standard parameter settings and metrics. Full article

(This article belongs to the Special Issue Advanced Modeling, Control, and Optimization Methods in Power Hybrid Systems - 2021)

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14 pages, 5073 KiB

Open AccessArticle

Determination of Optimal Diffusion Coefficients in Lake Zirahuén through a Local Inverse Problem

by Tzitlali Gasca-Ortiz, Francisco J. Domínguez-Mota and Diego A. Pantoja

Mathematics 2021, 9(14), 1695; https://doi.org/10.3390/math9141695 - 19 Jul 2021

Cited by 2 | Viewed by 2985

Abstract

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated [...] Read more.

In this study, optimal diffusion coefficients for Lake Zirahuén, Mexico, were found under particular conditions based on images taken with a drone of a dye release experiment. First, the dye patch concentration was discretized using image processing tools, and it was then approximated by an ellipse, finding the optimal major and minor axes. The inverse problem was implemented by comparing these observational data with the concentration obtained numerically from the 2D advection–diffusion equation, varying the diffusion tensor. When the tensor was isotropic, values of

K_{11} = K_{22} \approx 0.003 m^{2} / s

were found; when nonequal coefficients were considered, it was found that

K_{11} \approx 0.005 m^{2} / s

and

K_{22} \approx 0.002 m^{2} / s

, and the cross-term

K_{12}

influenced the results of the orientation of the ellipse. It is important to mention that, with this simple technique, the parameter estimation had consequences of great importance as the value for the diffusion coefficient was bounded significantly under particular conditions for this site of study. Full article

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17 pages, 371 KiB

Open AccessArticle

Estimation of the Average Kappa Coefficient of a Binary Diagnostic Test in the Presence of Partial Verification

by José Antonio Roldán-Nofuentes and Saad Bouh Regad

Mathematics 2021, 9(14), 1694; https://doi.org/10.3390/math9141694 - 19 Jul 2021

Cited by 5 | Viewed by 2085

Abstract

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In [...] Read more.

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In this manuscript the estimation of the average kappa coefficient of a diagnostic test in the presence of verification bias is studied. Confidence intervals for the average kappa coefficient are studied applying the methods of maximum likelihood and multiple imputation by chained equations. Simulation experiments have been carried out to study the asymptotic behaviors of the proposed intervals, given some application rules. The results obtained in our simulation experiments have shown that the multiple imputation by chained equations method provides better results than the maximum likelihood method. A function has been written in R to estimate the average kappa coefficient by applying multiple imputation. The results have been applied to the diagnosis of liver disease. Full article

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

17 pages, 813 KiB

Open AccessArticle

Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

by Mohammed K. A. Kaabar, Ahmed Refice, Mohammed Said Souid, Francisco Martínez, Sina Etemad, Zailan Siri and Shahram Rezapour

Mathematics 2021, 9(14), 1693; https://doi.org/10.3390/math9141693 - 19 Jul 2021

Cited by 19 | Viewed by 1939

Abstract

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via [...] Read more.

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings. Full article

(This article belongs to the Special Issue Nonlinear Differential Equations and Functional Analysis: Theory and Applications)

8 pages, 254 KiB

Open AccessArticle

Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces

by Izhar Uddin, Sajan Aggarwal and Afrah A. N. Abdou

Mathematics 2021, 9(14), 1692; https://doi.org/10.3390/math9141692 - 19 Jul 2021

Cited by 5 | Viewed by 1911

Abstract

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving

α

—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong [...] Read more.

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving

α

—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and

Δ

—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results. Full article

(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)

20 pages, 2215 KiB

Open AccessArticle

Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

by Shaohong Wang and Zhan Zhou

Mathematics 2021, 9(14), 1691; https://doi.org/10.3390/math9141691 - 19 Jul 2021

Cited by 2 | Viewed by 1676

Abstract

Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical [...] Read more.

Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results. Full article

(This article belongs to the Special Issue Functional Differential Equations and Epidemiological Modelling)

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38 pages, 4857 KiB

Open AccessArticle

Efficient Space–Time Reduced Order Model for Linear Dynamical Systems in Python Using Less than 120 Lines of Code

by Youngkyu Kim, Karen Wang and Youngsoo Choi

Mathematics 2021, 9(14), 1690; https://doi.org/10.3390/math9141690 - 19 Jul 2021

Cited by 18 | Viewed by 5914

Abstract

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems [...] Read more.

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than

10^{- 5}

for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve

O (10^{- 3})

to

O (10^{- 4})

relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve

O (10)

online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods. Full article

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16 pages, 9213 KiB

Open AccessArticle

On the Geometric Description of Nonlinear Elasticity via an Energy Approach Using Barycentric Coordinates

by Odysseas Kosmas, Pieter Boom and Andrey P. Jivkov

Mathematics 2021, 9(14), 1689; https://doi.org/10.3390/math9141689 - 19 Jul 2021

Viewed by 2020

Abstract

The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential (elastic) energy, a function of [...] Read more.

The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential (elastic) energy, a function of the deformation gradient invariants. Based on this, in the present work we built a “discrete energy model” that uses maps between nodal positions of a discrete mesh linked with the invariants of the deformation gradient via standard barycentric coordinates. A special derivation is provided for domains tessellated by tetrahedrons, where the energy functionals are constrained by prescribed boundary conditions via Lagrange multipliers. The analysis of these domains is performed via energy minimisation, where the constraints are eliminated via pre-multiplication of the discrete equations by a discrete null-space matrix of the constraint gradients. Numerical examples are provided to verify the accuracy of the proposed technique. The standard barycentric coordinate system in this work is restricted to three-dimensional (3-D) convex polytopes. We show that for an explicit energy expression, applicable also to non-convex polytopes, the general barycentric coordinates constitute fundamental tools. We define, in addition, the discrete energy via a gradient for general polytopes, which is a natural extension of the definition for discrete domains tessellated by tetrahedra. We, finally, prove that the resulting expressions can consistently describe the deformation of solids. Full article

(This article belongs to the Special Issue Dynamical Systems in Engineering)

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Initial <math display="inline"><mi>ℬ</mi></math> and current S configurations of a domain related by map <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mi>t</mi> </msub> <mo>≡</mo> <mi>φ</mi> </mrow> </semantics></math>. Full article ">Figure 2
Examples of partitioned volumes <math display="inline"><semantics> <msub> <mi>V</mi> <mi>I</mi> </msub> </semantics></math> associated with point <math display="inline"><semantics> <mi mathvariant="double-struck">X</mi> </semantics></math>: (top) two figures illustrate two volumes for point inside the tetrahedron; (bottom) two figures illustrate two volumes for a point outside the tetrahedron. Full article ">Figure 3
The deformation of a 3D tetrahedral element. Full article ">Figure 4
3d cantilever beam. Full article ">Figure 5
The deflection of the geometrically nonlinear case of a cantilever beam subjected to a regular distributed load calculated using finite element method with tetrahedral elements (FEM-tet) and the proposed scheme. Full article ">Figure 6
Cube with a spherical hole. Full article ">Figure 7
Stress distribution around the hole for distance <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>></mo> <mn>1</mn> </mrow> </semantics></math> from the centre of the hole (size does not corresponds to example). Full article ">Figure 8
Two-dimensional triangle formed from points with nodal positions <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="double-struck">X</mi> <mi>a</mi> </msub> <mo>,</mo> <msub> <mi mathvariant="double-struck">X</mi> <mi>b</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="double-struck">X</mi> <mi>c</mi> </msub> </semantics></math>. Full article ">

13 pages, 3967 KiB

Open AccessArticle

Diffusion in Sephadex Gel Structures: Time Dependency Revealed by Multi-Sequence Acquisition over a Broad Diffusion Time Range

by Guangyu Dan, Weiguo Li, Zheng Zhong, Kaibao Sun, Qingfei Luo, Richard L. Magin, Xiaohong Joe Zhou and M. Muge Karaman

Mathematics 2021, 9(14), 1688; https://doi.org/10.3390/math9141688 - 19 Jul 2021

Cited by 5 | Viewed by 2415

Abstract

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time [...] Read more.

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time random-walk (CTRW) model, which introduces two new parameters: a fractional order time derivative α and a fractional order spatial derivative β. These new parameters have been linked to intravoxel diffusion heterogeneities in time and space, respectively, and are believed to depend on diffusion times. Studies on this time dependency are limited, largely because the diffusion time cannot vary over a board range in a conventional spin-echo echo-planar imaging sequence due to the accompanying T2 decays. In this study, we investigated the time-dependency of the CTRW model in Sephadex gel phantoms across a broad diffusion time range by employing oscillating-gradient spin-echo, pulsed-gradient spin-echo, and pulsed-gradient stimulated echo sequences. We also performed Monte Carlo simulations to help understand our experimental results. It was observed that the diffusion process fell into the Gaussian regime at extremely short diffusion times whereas it exhibited a strong time dependency in the CTRW parameters at longer diffusion times. Full article

(This article belongs to the Special Issue Fractional Calculus in Magnetic Resonance)

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10 pages, 256 KiB

Open AccessArticle

Bounds for the Energy of Graphs

by Slobodan Filipovski and Robert Jajcay

Mathematics 2021, 9(14), 1687; https://doi.org/10.3390/math9141687 - 18 Jul 2021

Cited by 18 | Viewed by 3782

Abstract

Let G be a graph on n vertices and m edges, with maximum degree

Δ (G)

and minimum degree

δ (G) .

Let A be the adjacency matrix of G, and let [...] Read more.

Let G be a graph on n vertices and m edges, with maximum degree

Δ (G)

and minimum degree

δ (G) .

Let A be the adjacency matrix of G, and let

λ_{1} \geq λ_{2} \geq \dots \geq λ_{n}

be the eigenvalues of G. The energy of G, denoted by

E (G)

, is defined as the sum of the absolute values of the eigenvalues of G, that is

E (G) = | λ_{1} | + \dots + | λ_{n} |

. The energy of G is known to be at least twice the minimum degree of G,

E (G) \geq 2 δ (G) .

Akbari and Hosseinzadeh conjectured that the energy of a graph G whose adjacency matrix is nonsingular is in fact greater than or equal to the sum of the maximum and the minimum degrees of G, i.e.,

E (G) \geq Δ (G) + δ (G) .

In this paper, we present a proof of this conjecture for hyperenergetic graphs, and we prove an inequality that appears to support the conjectured inequality. Additionally, we derive various lower and upper bounds for

E (G)

. The results rely on elementary inequalities and their application. Full article

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

21 pages, 7098 KiB

Open AccessProtocol

A Comparison of Regional Classification Strategies Implemented for the Population Based Approach to Modelling Atrial Fibrillation

by Jordan Elliott, Maria Kristina Belen, Luca Mainardi and Josè Felix Rodriguez Matas

Mathematics 2021, 9(14), 1686; https://doi.org/10.3390/math9141686 - 17 Jul 2021

Cited by 4 | Viewed by 1906

Abstract

(1) Background: in silico models are increasingly relied upon to study the mechanisms of atrial fibrillation. Due to the complexity associated with atrial models, cellular variability is often ignored. Recent studies have shown that cellular variability may have a larger impact on electrophysiological [...] Read more.

(1) Background: in silico models are increasingly relied upon to study the mechanisms of atrial fibrillation. Due to the complexity associated with atrial models, cellular variability is often ignored. Recent studies have shown that cellular variability may have a larger impact on electrophysiological behaviour than previously expected. This paper compares two methods for AF remodelling using regional populations. (2) Methods: using 200,000 action potentials, experimental data was used to calibrate healthy atrial regional populations with two cellular models. AF remodelling was applied by directly adjusting maximum channel conductances. AF remodelling was also applied through adjusting biomarkers. The methods were compared upon replication of experimental data. (3) Results: compared to the percentage method, the biomarker approach resulted in smaller changes. RMP, APD20, APD50, and APD90 were changed in the percentage method by up to 11%, 500%, 50%, and 60%, respectively. In the biomarker approach, RMP, APD20, APD50, and APD90 were changed by up to 4.5%, 132%, 50%, and 35%, respectively. (4) Conclusion: applying AF remodelling through biomarker-based clustering resulted in channel conductance changes that were consistent with experimental data, while maintaining the highly non-linear relationships between channel conductances and biomarkers. Directly changing conductances in the healthy regional populations impacted the non-linear relationships and resulted in non-physiological APD20 and APD50 values. Full article

(This article belongs to the Special Issue Development and Applications of Multi-Scale Mathematical Models in Cardiology)

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14 pages, 288 KiB

Open AccessArticle

A Theoretical Model for Global Optimization of Parallel Algorithms

by Julian Miller, Lukas Trümper, Christian Terboven and Matthias S. Müller

Mathematics 2021, 9(14), 1685; https://doi.org/10.3390/math9141685 - 17 Jul 2021

Cited by 6 | Viewed by 2333

Abstract

With the quickly evolving hardware landscape of high-performance computing (HPC) and its increasing specialization, the implementation of efficient software applications becomes more challenging. This is especially prevalent for domain scientists and may hinder the advances in large-scale simulation software. One idea to overcome [...] Read more.

With the quickly evolving hardware landscape of high-performance computing (HPC) and its increasing specialization, the implementation of efficient software applications becomes more challenging. This is especially prevalent for domain scientists and may hinder the advances in large-scale simulation software. One idea to overcome these challenges is through software abstraction. We present a parallel algorithm model that allows for global optimization of their synchronization and dataflow and optimal mapping to complex and heterogeneous architectures. The presented model strictly separates the structure of an algorithm from its executed functions. It utilizes a hierarchical decomposition of parallel design patterns as well-established building blocks for algorithmic structures and captures them in an abstract pattern tree (APT). A data-centric flow graph is constructed based on the APT, which acts as an intermediate representation for rich and automated structural transformations. We demonstrate the applicability of this model to three representative algorithms and show runtime speedups between 1.83 and 2.45 on a typical heterogeneous CPU/GPU architecture. Full article

(This article belongs to the Special Issue Current Trends in Computer Architecture and High Performance Computing (HPC) with Their Mathematical Foundations)

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17 pages, 721 KiB

Open AccessArticle

Statistical Analysis for Contract Cheating in Chinese Universities

by Yuexia Wang and Zhihuo Xu

Mathematics 2021, 9(14), 1684; https://doi.org/10.3390/math9141684 - 17 Jul 2021

Cited by 8 | Viewed by 3461

Abstract

Contract cheating refers to students using third-party online resources to complete their coursework. It is not only a unilateral result of the student, but also has a relationship with educators, as well as social resources. However, little work has been performed to analyze [...] Read more.

Contract cheating refers to students using third-party online resources to complete their coursework. It is not only a unilateral result of the student, but also has a relationship with educators, as well as social resources. However, little work has been performed to analyze the complex behavioral aspects behind contract cheating in Chinese universities. To this end, this article presents a statistical analysis of contract cheating in Chinese universities. First, a unique parallel survey of educators and students was conducted to collect data from August 2018 to August 2020. Next, statistical analyses were performed to explore students’ experiences and attitudes toward contract cheating and the contextual factors that relate to these behaviors. Additionally, Pearson correlation tests were conducted on the survey data to find potential factors for contract cheating. Finally, a multivariate statistical technique, partial-least-squares regression (PLSR), was applied to interpret the results. The results of the statistical analysis showed that the main motivation for contract cheating is to receive good grades (the correlation coefficient

ρ

is 0.1309) from the perspective of students’ personal learning; from the side of university management, clear regulations (

ρ = - 0.1378

), penalties for cheating (

ρ = - 0.1275

), and the use of cheating-detection software (

ρ = - 0.1186

) can directly reduce cheating; from the perspective of teachers’ teaching, lecturers’ feedback on cheating on assignments (

ρ = - 0.1510

) can effectively reduce students’ cheating behavior; in addition, increasing students’ sense of achievement in course learning (

ρ = - 0.2619

) also helps to reduce the probability of cheating. Full article

(This article belongs to the Special Issue Quantitative Methods for Social Sciences)

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This figure shows the results of students’ understanding and perceptions of cheating on coursework. Q1–Q4 represent Questions 1–4 in <a href="#mathematics-09-01684-t001" class="html-table">Table 1</a>. The blue bars represent the percentage of students who understood the definition of cheating in the relevant coursework, university regulations, and teacher requirements for noncheating on assignments, respectively, while the red bars represent the percentage of students who did not understand or agree with the items in question. Full article ">Figure 2
The satisfaction levels with their completed submissions by different frequencies of student engagement in cheating. Full article ">Figure 3
The different accomplishments achieved from the coursework by the different frequencies of student engagement in cheating. Full article ">Figure 4
This figure shows the results of educators’ perceptions of and responses to student engagement in cheating. Q1–Q4 and Q7–Q9 represent Questions 1–4 and 7–9 in <a href="#mathematics-09-01684-t002" class="html-table">Table 2</a>, respectively. The bottom bar represents the percentages of educators who understood the definition of cheating, whose universities had clear regulations and penalization rules, who emphasized cheating rules in the class, whose institutions have cheat-detection software tools, who given feedback to students when there was plagiarism in their coursework submissions, and who designed creative learning environments, respectively, while the top bars indicate the opposite results. Full article ">Figure 5
Percent of variance explained in y with respect to the number of PLS components: (a) The data of the all participant; (b) the data of the student participants from the UCAS, first-class, and national key universities; and (c) the data of the students from the ordinary universities. Full article ">Figure 6
The regression coefficients with respect to the potential factors: (a) The data of the all participant; (b) the data of the student participants from the UCAS, first-class, and national key universities; and (c) the data of the student participants from the ordinary universities. The potential factors are denoted as follows: students understand what plagiarism is (F1), clear regulations on plagiarism in coursework (F2), penalization for plagiarism (F3), lecturers have highlighted plagiarism in their courses (F4), weather teachers make lectures interesting and lively (F5), disinterest in the course assignment (F6), desire to receive a good final course grade (F7), poor time management (F8), fear of failure (F9), coursework is too easy (F10), teachers themselves have committed plagiarism, such as copying lecture notes (F11), lecturers give feedback on plagiarized assignments (F12), use of plagiarism detection tools (F13), lecturers design creative learning environments (F14), lecturers review assignments carefully (F15), satisfaction with teachers’ reviews of submissions (F16), satisfaction with their completed coursework (F17), doing coursework improves learning (F18), doing coursework builds confidence (F19), learn nothing by doing coursework (F20), and doing coursework is a waste of time (F21). Full article ">

18 pages, 1337 KiB

Open AccessArticle

A Cooperative Network Packing Game with Simple Paths

by Sergei Dotsenko and Vladimir Mazalov

Mathematics 2021, 9(14), 1683; https://doi.org/10.3390/math9141683 - 17 Jul 2021

Viewed by 1817

Abstract

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and [...] Read more.

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and its form is obtained. For several particular graphs, the explicit form of the core is presented. Full article

(This article belongs to the Special Issue Mathematical Game Theory 2021)

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20 pages, 1165 KiB

Open AccessArticle

Altruistic Preference Models of Low-Carbon E-Commerce Supply Chain

by Jianfeng Liu, Liguo Zhou and Yuyan Wang

Mathematics 2021, 9(14), 1682; https://doi.org/10.3390/math9141682 - 17 Jul 2021

Cited by 15 | Viewed by 2724

Abstract

With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research [...] Read more.

With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research on the irrational behavior of the e-platform altruistic preference. Therefore, aiming at the LCECSC composed of a single e-platform and a single manufacturer, this paper establishes two basic models with or without altruistic preference. Additionally, this paper combines the characteristics of online sales and assumes that altruistic preference is a proportional function of commission, then establishes a commission-based extended model with altruistic preference to further explore the influence of commission on its altruistic preference. The current literature does not consider this point, nor does it analyze the influence of other parameters on the degree of altruism preference. By comparing the optimal decisions and numerical analysis among the models, the following conclusions can be drawn that: (1) different from the traditional offline supply chain, the profit of the dominator e-platform is lower than the profit of the follower manufacturer; (2) when the consumers’ carbon emission reduction elasticity coefficient increases, service level, sales price, carbon emission reduction, sales, supply chain members profits, and system profit increase, ultimately improving economic and environmental performances; (3) the altruistic preference behavior of the e-platform is a behavior of ‘profit transferring’. The moderate altruistic preference is conducive to the stable operation and long-term development of LCECSC. Full article

(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering)

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13 pages, 308 KiB

Open AccessEditor’s ChoiceArticle

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

by Brecht Verbeken and Marie-Anne Guerry

Mathematics 2021, 9(14), 1681; https://doi.org/10.3390/math9141681 - 16 Jul 2021

Cited by 7 | Viewed by 2845

Abstract

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of [...] Read more.

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria. Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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22 pages, 551 KiB

Open AccessArticle

Self-Expressive Kernel Subspace Clustering Algorithm for Categorical Data with Embedded Feature Selection

by Hui Chen, Kunpeng Xu, Lifei Chen and Qingshan Jiang

Mathematics 2021, 9(14), 1680; https://doi.org/10.3390/math9141680 - 16 Jul 2021

Cited by 5 | Viewed by 1918

Abstract

Kernel clustering of categorical data is a useful tool to process the separable datasets and has been employed in many disciplines. Despite recent efforts, existing methods for kernel clustering remain a significant challenge due to the assumption of feature independence and equal weights. [...] Read more.

Kernel clustering of categorical data is a useful tool to process the separable datasets and has been employed in many disciplines. Despite recent efforts, existing methods for kernel clustering remain a significant challenge due to the assumption of feature independence and equal weights. In this study, we propose a self-expressive kernel subspace clustering algorithm for categorical data (SKSCC) using the self-expressive kernel density estimation (SKDE) scheme, as well as a new feature-weighted non-linear similarity measurement. In the SKSCC algorithm, we propose an effective non-linear optimization method to solve the clustering algorithm’s objective function, which not only considers the relationship between attributes in a non-linear space but also assigns a weight to each attribute in the algorithm to measure the degree of correlation. A series of experiments on some widely used synthetic and real-world datasets demonstrated the better effectiveness and efficiency of the proposed algorithm compared with other state-of-the-art methods, in terms of non-linear relationship exploration among attributes. Full article

(This article belongs to the Special Issue Statistical Data Modeling and Machine Learning with Applications)

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