Mathematics

15 pages, 2065 KiB

Open AccessArticle

Electricity Load and Internet Traffic Forecasting Using Vector Autoregressive Models

by Yunsun Kim and Sahm Kim

Mathematics 2021, 9(18), 2347; https://doi.org/10.3390/math9182347 - 21 Sep 2021

Cited by 1 | Viewed by 1820

This study was conducted to investigate the applicability of measuring internet traffic as an input of short-term electricity demand forecasts. We believe our study makes a significant contribution to the literature, especially in short-term load prediction techniques, as we found that Internet traffic [...] Read more.

This study was conducted to investigate the applicability of measuring internet traffic as an input of short-term electricity demand forecasts. We believe our study makes a significant contribution to the literature, especially in short-term load prediction techniques, as we found that Internet traffic can be a useful variable in certain models and can increase prediction accuracy when compared to models in which it is not a variable. In addition, we found that the prediction error could be further reduced by applying a new multivariate model called VARX, which added exogenous variables to the univariate model called VAR. The VAR model showed excellent forecasting performance in the univariate model, rather than using the artificial neural network model, which had high prediction accuracy in the previous study. Full article

(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech)

► Show Figures

Figure 1

28 pages, 555 KiB

Open AccessArticle

Geometric Invariants of Surjective Isometries between Unit Spheres

by Almudena Campos-Jiménez and Francisco Javier García-Pacheco

Mathematics 2021, 9(18), 2346; https://doi.org/10.3390/math9182346 - 21 Sep 2021

Cited by 5 | Viewed by 1726

Abstract

In this paper we provide new geometric invariants of surjective isometries between unit spheres of Banach spaces. Let

X, Y

be Banach spaces and let

T : S_{X} \to S_{Y}

be a surjective isometry. The most relevant geometric invariants under [...] Read more.

In this paper we provide new geometric invariants of surjective isometries between unit spheres of Banach spaces. Let

X, Y

be Banach spaces and let

T : S_{X} \to S_{Y}

be a surjective isometry. The most relevant geometric invariants under surjective isometries such as T are known to be the starlike sets, the maximal faces of the unit ball, and the antipodal points (in the finite-dimensional case). Here, new geometric invariants are found, such as almost flat sets, flat sets, starlike compatible sets, and starlike generated sets. Also, in this work, it is proved that if F is a maximal face of the unit ball containing inner points, then

T (- F) = - T (F)

. We also show that if

[x, y]

is a non-trivial segment contained in the unit sphere such that

T ([x, y])

is convex, then T is affine on

[x, y]

. As a consequence, T is affine on every segment that is a maximal face. On the other hand, we introduce a new geometric property called property P, which states that every face of the unit ball is the intersection of all maximal faces containing it. This property has turned out to be, in a implicit way, a very useful tool to show that many Banach spaces enjoy the Mazur-Ulam property. Following this line, in this manuscript it is proved that every reflexive or separable Banach space with dimension greater than or equal to 2 can be equivalently renormed to fail property P. Full article

(This article belongs to the Special Issue Ordered Topological Vector Spaces, Operators Acting on Them and Related Applications)

11 pages, 4711 KiB

Open AccessArticle

Numerical Simulation of Higher-Order Nonlinearity of Human Brain Functional Connectivity Using Hypergraph p-Laplacian

by Jichao Ma, Chunyu Du, Weifeng Liu and Yanjiang Wang

Mathematics 2021, 9(18), 2345; https://doi.org/10.3390/math9182345 - 21 Sep 2021

Cited by 1 | Viewed by 1776

Abstract

Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of [...] Read more.

Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian. Full article

(This article belongs to the Section Engineering Mathematics)

► Show Figures

Figure 1

9 pages, 314 KiB

Open AccessArticle

Composition Vector Spaces as a New Type of Tri-Operational Algebras

by Omid Reza Dehghan, Morteza Norouzi and Irina Cristea

Mathematics 2021, 9(18), 2344; https://doi.org/10.3390/math9182344 - 21 Sep 2021

Viewed by 1477

Abstract

The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can [...] Read more.

The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations. Full article

(This article belongs to the Special Issue Ordered Topological Vector Spaces, Operators Acting on Them and Related Applications)

► Show Figures

Figure 1

14 pages, 1102 KiB

Open AccessArticle

Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

by Xijian Hu, Yaori Lu, Huiguo Zhang, Haijun Jiang and Qingdong Shi

Mathematics 2021, 9(18), 2343; https://doi.org/10.3390/math9182343 - 21 Sep 2021

Cited by 3 | Viewed by 1640

Abstract

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually [...] Read more.

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix. Full article

► Show Figures

Figure 1

14 pages, 819 KiB

Open AccessArticle

Inverse Problem for an Equation of the Reaction-Diffusion-Advection Type with Data on the Position of a Reaction Front: Features of the Solution in the Case of a Nonlinear Integral Equation in a Reduced Statement

by Raul Argun, Alexandr Gorbachev, Natalia Levashova and Dmitry Lukyanenko

Mathematics 2021, 9(18), 2342; https://doi.org/10.3390/math9182342 - 21 Sep 2021

Cited by 5 | Viewed by 1947

Abstract

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse [...] Read more.

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods. Full article

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

► Show Figures

Figure 1

8 pages, 258 KiB

Open AccessArticle

On a Volterra Integral Equation with Delay, via w-Distances

by Veronica Ilea and Diana Otrocol

Mathematics 2021, 9(18), 2341; https://doi.org/10.3390/math9182341 - 21 Sep 2021

Viewed by 1510

Abstract

The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the [...] Read more.

The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the support of w-distance and the complexity of the delay equation. Gronwall-type theorem and comparison theorem are also discussed using a weak Picard operator technique. In the end, an example is provided to support our results. Full article

(This article belongs to the Section Difference and Differential Equations)

14 pages, 4715 KiB

Open AccessArticle

Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

by Svetoslav G. Nikolov and Vassil M. Vassilev

Mathematics 2021, 9(18), 2340; https://doi.org/10.3390/math9182340 - 21 Sep 2021

Cited by 3 | Viewed by 1414

Abstract

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of [...] Read more.

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations. Full article

(This article belongs to the Section Dynamical Systems)

► Show Figures

Figure 1

11 pages, 343 KiB

Open AccessArticle

Multi-Objective Pharmaceutical Portfolio Optimization under Uncertainty of Cost and Return

by Mahboubeh Farid, Hampus Hallman, Mikael Palmblad and Johannes Vänngård

Mathematics 2021, 9(18), 2339; https://doi.org/10.3390/math9182339 - 21 Sep 2021

Cited by 2 | Viewed by 2458

Abstract

This paper presents the study of multi-objective optimization of a pharmaceutical portfolio when both cost and return values are uncertain. Decision makers in the pharmaceutical industry encounter several challenges in deciding the optimal selection of drug projects for their portfolio since they have [...] Read more.

This paper presents the study of multi-objective optimization of a pharmaceutical portfolio when both cost and return values are uncertain. Decision makers in the pharmaceutical industry encounter several challenges in deciding the optimal selection of drug projects for their portfolio since they have to consider several key aspects such as a long product-development process split into multiple phases, high cost and low probability of success. Additionally, the optimization often involves more than a single objective (goal) with a non-deterministic nature. The aim of the study is to develop a stochastic multi-objective approach in the frame of chance-constrained goal programming. The application of the results of this study allows pharmaceutical decision makers to handle two goals simultaneously, where one objective is to achieve a target return and another is to keep the cost within a finite annual budget. Finally, the numerical results for portfolio optimization are presented and discussed. Full article

(This article belongs to the Special Issue Multiple Criteria Decision Making)

► Show Figures

Figure 1

24 pages, 87297 KiB

Open AccessEditor’s ChoiceArticle

A Comprehensive Analysis of Demand Response Pricing Strategies in a Smart Grid Environment Using Particle Swarm Optimization and the Strawberry Optimization Algorithm

by Emad M. Ahmed, Rajarajeswari Rathinam, Suchitra Dayalan, George S. Fernandez, Ziad M. Ali, Shady H. E. Abdel Aleem and Ahmed I. Omar

Mathematics 2021, 9(18), 2338; https://doi.org/10.3390/math9182338 - 21 Sep 2021

Cited by 29 | Viewed by 3116

Abstract

In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to [...] Read more.

In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to the shortfall in power generation. The abovesaid deficit signifies the explicit need for a strategy that reduces the peak demand by rescheduling the load pattern, as well as reduces the stress on grids. Demand-side management (DSM) uses several algorithms for proper reallocation of loads, collectively known as demand response (DR). DR strategies effectively culminate in monetary benefits for customers and the utilities using dynamic pricing (DP) and incentive-based procedures. This study attempts to analyze the DP schemes of DR such as time-of-use (TOU) and real-time pricing (RTP) for different load scenarios in a smart grid (SG). Centralized and distributed algorithms are used to analyze the price-based DR problem using RTP. A techno-economic analysis was performed by using particle swarm optimization (PSO) and the strawberry (SBY) optimization algorithms used in handling the DP strategies with 109, 1992, and 7807 controllable industrial, commercial, and residential loads. A better optimization algorithm to go along with the pricing scheme to reduce the peak-to-average ratio (PAR) was identified. The results demonstrate that centralized RTP using the SBY optimization algorithm helped to achieve 14.80%, 21.7%, and 21.84% in cost reduction and outperformed the PSO. Full article

► Show Figures

Figure 1

36 pages, 489 KiB

Open AccessArticle

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

by Gia Sirbiladze

Mathematics 2021, 9(18), 2337; https://doi.org/10.3390/math9182337 - 21 Sep 2021

Cited by 15 | Viewed by 1914

Abstract

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many [...] Read more.

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms

(T_{p}, S_{p}^{q})

and

(T_{\min}, S_{\max})

are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes. Full article

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

26 pages, 7563 KiB

Open AccessArticle

Synthetic Data Augmentation and Deep Learning for the Fault Diagnosis of Rotating Machines

by Asif Khan, Hyunho Hwang and Heung Soo Kim

Mathematics 2021, 9(18), 2336; https://doi.org/10.3390/math9182336 - 21 Sep 2021

Cited by 19 | Viewed by 3874

Abstract

As failures in rotating machines can have serious implications, the timely detection and diagnosis of faults in these machines is imperative for their smooth and safe operation. Although deep learning offers the advantage of autonomously learning the fault characteristics from the data, the [...] Read more.

As failures in rotating machines can have serious implications, the timely detection and diagnosis of faults in these machines is imperative for their smooth and safe operation. Although deep learning offers the advantage of autonomously learning the fault characteristics from the data, the data scarcity from different health states often limits its applicability to only binary classification (healthy or faulty). This work proposes synthetic data augmentation through virtual sensors for the deep learning-based fault diagnosis of a rotating machine with 42 different classes. The original and augmented data were processed in a transfer learning framework and through a deep learning model from scratch. The two-dimensional visualization of the feature space from the original and augmented data showed that the latter’s data clusters are more distinct than the former’s. The proposed data augmentation showed a 6–15% improvement in training accuracy, a 44–49% improvement in validation accuracy, an 86–98% decline in training loss, and a 91–98% decline in validation loss. The improved generalization through data augmentation was verified by a 39–58% improvement in the test accuracy. Full article

(This article belongs to the Special Issue Deep Learning and Machine Learning Mathematical Models for Computer Assisted Diagnostic Systems)

► Show Figures

Graphical abstract

52 pages, 1788 KiB

Open AccessReview

Review of Metaheuristics Inspired from the Animal Kingdom

by Elena Niculina Dragoi and Vlad Dafinescu

Mathematics 2021, 9(18), 2335; https://doi.org/10.3390/math9182335 - 21 Sep 2021

Cited by 26 | Viewed by 5625

Abstract

The search for powerful optimizers has led to the development of a multitude of metaheuristic algorithms inspired from all areas. This work focuses on the animal kingdom as a source of inspiration and performs an extensive, yet not exhaustive, review of the animal [...] Read more.

The search for powerful optimizers has led to the development of a multitude of metaheuristic algorithms inspired from all areas. This work focuses on the animal kingdom as a source of inspiration and performs an extensive, yet not exhaustive, review of the animal inspired metaheuristics proposed in the 2006–2021 period. The review is organized considering the biological classification of living things, with a breakdown of the simulated behavior mechanisms. The centralized data indicated that 61.6% of the animal-based algorithms are inspired from vertebrates and 38.4% from invertebrates. In addition, an analysis of the mechanisms used to ensure diversity was performed. The results obtained showed that the most frequently used mechanisms belong to the niching category. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning)

► Show Figures

Figure 1

52 pages, 10360 KiB

Open AccessArticle

RHOASo: An Early Stop Hyper-Parameter Optimization Algorithm

by Ángel Luis Muñoz Castañeda, Noemí DeCastro-García and David Escudero García

Mathematics 2021, 9(18), 2334; https://doi.org/10.3390/math9182334 - 20 Sep 2021

Cited by 4 | Viewed by 1923

Abstract

This work proposes a new algorithm for optimizing hyper-parameters of a machine learning algorithm, RHOASo, based on conditional optimization of concave asymptotic functions. A comparative analysis of the algorithm is presented, giving particular emphasis to two important properties: the capability of the algorithm [...] Read more.

This work proposes a new algorithm for optimizing hyper-parameters of a machine learning algorithm, RHOASo, based on conditional optimization of concave asymptotic functions. A comparative analysis of the algorithm is presented, giving particular emphasis to two important properties: the capability of the algorithm to work efficiently with a small part of a dataset and to finish the tuning process automatically, that is, without making explicit, by the user, the number of iterations that the algorithm must perform. Statistical analyses over 16 public benchmark datasets comparing the performance of seven hyper-parameter optimization algorithms with RHOASo were carried out. The efficiency of RHOASo presents the positive statistically significant differences concerning the other hyper-parameter optimization algorithms considered in the experiments. Furthermore, it is shown that, on average, the algorithm needs around

70 %

of the iterations needed by other algorithms to achieve competitive performance. The results show that the algorithm presents significant stability regarding the size of the used dataset partition. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning)

► Show Figures

Figure 1

12 pages, 1342 KiB

Open AccessArticle

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

by Ruslan Yanbarisov, Yuri Efremov, Nastasia Kosheleva, Peter Timashev and Yuri Vassilevski

Mathematics 2021, 9(18), 2333; https://doi.org/10.3390/math9182333 - 20 Sep 2021

Cited by 3 | Viewed by 1893

Abstract

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first [...] Read more.

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine II)

► Show Figures

Figure 1

13 pages, 273 KiB

Open AccessArticle

Application of Exploratory Factor Analysis in the Construction of a Self-Perception Model of Informational Competences in Higher Education

by Belén Quintero Ordóñez, Ignacio González López, Eloísa Reche Urbano and Juan Antonio Fuentes Esparrell

Mathematics 2021, 9(18), 2332; https://doi.org/10.3390/math9182332 - 20 Sep 2021

Cited by 4 | Viewed by 1909

Abstract

The progress experienced by society resulting from the ready availability of information through the use of technology highlights the need to develop specific learning related to informational competences (IC) in educational settings where future professionals are trained to educate others, specifically in university [...] Read more.

The progress experienced by society resulting from the ready availability of information through the use of technology highlights the need to develop specific learning related to informational competences (IC) in educational settings where future professionals are trained to educate others, specifically in university degrees in social sciences. This study seeks to ascertain the opinions of students enrolled in these degrees at the Universidad de Córdoba (Spain) with regard to the knowledge they consider that they possess about IC for their future professional development, through the practical application of exploratory factor analysis. The methodology designed is based on a descriptive, non-experimental, correlational survey. The results show that factor analysis is a fundamental tool for obtaining results in terms of students’ perception of their knowledge of IC because its psychometric value has confirmed construct validity and enabled us to break down the items that made up the four initial dimensions of IC into eight factors to improve the understanding and explanation of these IC. Full article

(This article belongs to the Special Issue Applied Data Analytics)

20 pages, 2460 KiB

Open AccessArticle

Markov Models for Economic Evaluation in Osteoporosis Treatment

by Marta Osca-Guadalajara, Javier Díaz-Carnicero, Silvia González-de-Julián and David Vivas-Consuelo

Mathematics 2021, 9(18), 2331; https://doi.org/10.3390/math9182331 - 20 Sep 2021

Viewed by 2038

Abstract

Osteoporosis is frequent in elderly people, causing bone fractures and lowering their quality of life. The costs incurred by these fractures constitute a problem for public health. Markov chains were used to carry out an incremental cost-utility analysis of the four main drugs [...] Read more.

Osteoporosis is frequent in elderly people, causing bone fractures and lowering their quality of life. The costs incurred by these fractures constitute a problem for public health. Markov chains were used to carry out an incremental cost-utility analysis of the four main drugs used in Spain to treat osteoporosis (alendronate, risedronate, denosumab and teriparatide). We considered 14 clinical transition states, from starting osteoporotic treatment at the age of 50 until death or the age of 100. Cost-effectiveness was measured by quality adjusted life years (QALYs). The values used in the Markov model were obtained from the literature. Teriparatide is the cost-effective alternative in the treatment of osteoporosis in patients with fractures from the age of 50, establishing a payment threshold of 20,000 EUR/QALY. However, it is the most expensive therapy, not appearing cost-effective in cases that do not present fracture and in ages over 80 years with fracture. Alendronate and denosumab therapies are presented as cost-effective osteoporosis treatment alternatives depending on the age of onset and duration of treatment. From the perspective of cost-effectiveness, establishing a payment threshold of 20,000 EUR/QALY, teriparatide is the cost-effective alternative in patients with fracture from the age of 50 to 70 years old in Spain. Full article

► Show Figures

Figure 1

13 pages, 1863 KiB

Open AccessArticle

Flow towards a Stagnation Region of a Curved Surface in a Hybrid Nanofluid with Buoyancy Effects

by Iskandar Waini, Anuar Ishak and Ioan Pop

Mathematics 2021, 9(18), 2330; https://doi.org/10.3390/math9182330 - 20 Sep 2021

Cited by 13 | Viewed by 1668

Abstract

This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO₂) and alumina (Al₂O₃) nanoparticles are added into water to form SiO₂-Al₂O₃/water hybrid [...] Read more.

This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO₂) and alumina (Al₂O₃) nanoparticles are added into water to form SiO₂-Al₂O₃/water hybrid nanofluid. Both buoyancy-opposing and -assisting flows are considered. The governing partial differential equations are reduced to a set of ordinary differential equations, before being coded in MATLAB software to obtain the numerical solutions. Findings show that the solutions are not unique, where two solutions are obtained, for both buoyancy-assisting and -opposing flow cases. The local Nusselt number increases in the presence of the hybrid nanoparticles. The temporal stability analysis shows that only one of the solutions is stable over time. Full article

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

► Show Figures

Figure 1

28 pages, 5721 KiB

Open AccessArticle

LAE-GAN-Based Face Image Restoration for Low-Light Age Estimation

by Se Hyun Nam, Yu Hwan Kim, Jiho Choi, Seung Baek Hong, Muhammad Owais and Kang Ryoung Park

Mathematics 2021, 9(18), 2329; https://doi.org/10.3390/math9182329 - 19 Sep 2021

Cited by 2 | Viewed by 2382

Abstract

Age estimation is applicable in various fields, and among them, research on age estimation using human facial images, which are the easiest to acquire, is being actively conducted. Since the emergence of deep learning, studies on age estimation using various types of convolutional [...] Read more.

Age estimation is applicable in various fields, and among them, research on age estimation using human facial images, which are the easiest to acquire, is being actively conducted. Since the emergence of deep learning, studies on age estimation using various types of convolutional neural networks (CNN) have been conducted, and they have resulted in good performances, as clear images with high illumination were typically used in these studies. However, human facial images are typically captured in low-light environments. Age information can be lost in facial images captured in low-illumination environments, where noise and blur generated by the camera in the captured image reduce the age estimation performance. No study has yet been conducted on age estimation using facial images captured under low light. In order to overcome this problem, this study proposes a new generative adversarial network for low-light age estimation (LAE-GAN), which compensates for the brightness of human facial images captured in low-light environments, and a CNN-based age estimation method in which compensated images are input. When the experiment was conducted using the MORPH, AFAD, and FG-NET databases—which are open databases—the proposed method exhibited more accurate age estimation performance and brightness compensation in low-light images compared to state-of-the-art methods. Full article

(This article belongs to the Special Issue Artificial Intelligence with Applications of Soft Computing)

► Show Figures

Figure 1

18 pages, 807 KiB

Open AccessEditor’s ChoiceArticle

An Integrated Mathematical Attitude Utilizing Fully Fuzzy BWM and Fuzzy WASPAS for Risk Evaluation in a SOFC

by Zeyu Lin, Hamdi Ayed, Belgacem Bouallegue, Hana Tomaskova, Saeid Jafarzadeh Ghoushchi and Gholamreza Haseli

Mathematics 2021, 9(18), 2328; https://doi.org/10.3390/math9182328 - 19 Sep 2021

Cited by 18 | Viewed by 2153

Abstract

Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, [...] Read more.

Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, failure modes evaluations need an experts team to achieve uncertainties belongs to the risk assessment procedure. To improve the efficiency of the routine FMEA methodology and to represent a suitable hybrid fuzzy MCDM approach for FMEA, in this work, fully fuzzy best-worst method (FF-BWM) is employed to achieve the risk factors weights then fuzzy weighted aggregated sum product assessment (F-WASPAS) approach to detect the failure modes priorities is utilized. Ultimately, the sensitivity analyses demonstrate that the offered framework is verified and can make applicable data in risk management decision-making evaluation. Full article

► Show Figures

Figure 1

12 pages, 273 KiB

Open AccessArticle

Decision-Making with Fuzzy Soft Matrix Using a Revised Method: A Case of Medical Diagnosis of Diseases

by Taiwo Olubunmi Sangodapo, Babatunde Oluwaseun Onasanya and Sarka Mayerova-Hoskova

Mathematics 2021, 9(18), 2327; https://doi.org/10.3390/math9182327 - 19 Sep 2021

Cited by 4 | Viewed by 1752

Abstract

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new method (max-min average) [...] Read more.

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new method (max-min average) based on fuzzy reference function is introduced instead of the max-product method by Lavanya and Akila to extend Sanchez’s technique for decision making problems in medical diagnosis. Using the same data by Lavanya and Akila, the result shows that the new method gives more information about the medical status of the patients being considered in relation to a set of diseases. Full article

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

24 pages, 1542 KiB

Open AccessArticle

Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

by Noufe H. Aljahdaly, Ravi P. Agarwal, Rasool Shah and Thongchai Botmart

Mathematics 2021, 9(18), 2326; https://doi.org/10.3390/math9182326 - 19 Sep 2021

Cited by 40 | Viewed by 2133

Abstract

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed [...] Read more.

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results. Full article

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)

► Show Figures

Figure 1

34 pages, 42145 KiB

Open AccessArticle

A Bi-Level Programming Approach to the Location-Routing Problem with Cargo Splitting under Low-Carbon Policies

by Cong Wang, Zhongxiu Peng and Xijun Xu

Mathematics 2021, 9(18), 2325; https://doi.org/10.3390/math9182325 - 19 Sep 2021

Cited by 5 | Viewed by 2145

Abstract

To identify the impact of low-carbon policies on the location-routing problem (LRP) with cargo splitting (LRPCS), this paper first constructs the bi-level programming model of LRPCS. On this basis, the bi-level programming models of LRPCS under four low-carbon policies are constructed, respectively. The [...] Read more.

To identify the impact of low-carbon policies on the location-routing problem (LRP) with cargo splitting (LRPCS), this paper first constructs the bi-level programming model of LRPCS. On this basis, the bi-level programming models of LRPCS under four low-carbon policies are constructed, respectively. The upper-level model takes the engineering construction department as the decision-maker to decide on the distribution center’s location. The lower-level model takes the logistics and distribution department as the decision-maker to make decisions on the vehicle distribution route’s scheme. Secondly, the hybrid algorithm of Ant Colony Optimization and Tabu Search (ACO-TS) is designed, and an example is introduced to verify the model’s and algorithm’s effectiveness. Finally, multiple sets of experiments are designed to explore the impact of various low-carbon policies on the decision-making of the LRPCS. The experimental results show that the influence of the carbon tax policy is the greatest, the carbon trading and carbon offset policy have a certain impact on the decision-making of the LRPCS, and the influence of the emission cap policy is the least. Based on this, we provide the relevant low-carbon policies advice and management implications. Full article

(This article belongs to the Section Dynamical Systems)

► Show Figures

Figure 1

17 pages, 460 KiB

Open AccessArticle

The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

by Bogdan Căruntu and Mădălina Sofia Paşca

Mathematics 2021, 9(18), 2324; https://doi.org/10.3390/math9182324 - 19 Sep 2021

Viewed by 1908

Abstract

We present a relatively new and very efficient method to find approximate analytical solutions for a very general class of nonlinear fractional Volterra and Fredholm integro-differential equations. The test problems included and the comparison with previous results by other methods clearly illustrate the [...] Read more.

We present a relatively new and very efficient method to find approximate analytical solutions for a very general class of nonlinear fractional Volterra and Fredholm integro-differential equations. The test problems included and the comparison with previous results by other methods clearly illustrate the simplicity and accuracy of the method. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

► Show Figures

Figure 1

18 pages, 1571 KiB

Open AccessArticle

A Fuzzy Delphi Consensus Methodology Based on a Fuzzy Ranking

by Antonio Francisco Roldán López de Hierro, Miguel Sánchez, Daniel Puente-Fernández, Rafael Montoya-Juárez and Concepción Roldán

Mathematics 2021, 9(18), 2323; https://doi.org/10.3390/math9182323 - 19 Sep 2021

Cited by 5 | Viewed by 2868

Abstract

Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown [...] Read more.

Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts’ subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert’s fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts’ answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers. Full article

(This article belongs to the Special Issue General Metric Spaces: Usage and Applications in Statistics and Fixed Point Theory)

► Show Figures

Figure 1

19 pages, 2617 KiB

Open AccessArticle

A Dynamic Model of Cytosolic Calcium Concentration Oscillations in Mast Cells

by Mingzhu Sun, Yingchen Li and Wei Yao

Mathematics 2021, 9(18), 2322; https://doi.org/10.3390/math9182322 - 19 Sep 2021

Cited by 4 | Viewed by 2135

Abstract

In this paper, a dynamic model of cytosolic calcium concentration (

{{[Ca}^{2 +}]}_{Cyt}

) oscillations is established for mast cells (MCs). This model includes the cytoplasm (Cyt), endoplasmic reticulum (ER), mitochondria (Mt), and functional region (μd), formed by the [...] Read more.

In this paper, a dynamic model of cytosolic calcium concentration (

{{[Ca}^{2 +}]}_{Cyt}

) oscillations is established for mast cells (MCs). This model includes the cytoplasm (Cyt), endoplasmic reticulum (ER), mitochondria (Mt), and functional region (μd), formed by the ER and Mt, also with

{Ca}^{2 +}

channels in these cellular compartments. By this model, we calculate

{{[Ca}^{2 +}]}_{Cyt}

oscillations that are driven by distinct mechanisms at varying

k_{\deg}

(degradation coefficient of inositol 1,4,5-trisphosphate,

{IP}_{3}

and production coefficient of

{IP}_{3}

), as well as at different distances between the ER and Mt (ER–Mt distance). The model predicts that (i) Mt and μd compartments can reduce the amplitude of

{{[Ca}^{2 +}]}_{Cyt}

oscillations, and cause the ER to release less

{Ca}^{2 +}

during oscillations; (ii) with increasing cytosolic

{IP}_{3}

concentration (

{{[IP}_{3}]}_{Cyt}

), the amplitude of oscillations increases (from 0.1 μM to several μM), but the frequency decreases; (iii) the frequency of

{{[Ca}^{2 +}]}_{Cyt}

oscillations decreases as the ER–Mt distance increases. What is more, when the ER–Mt distance is greater than 65 nm, the μd compartment has less effect on

{{[Ca}^{2 +}]}_{Cyt}

oscillations. These results suggest that Mt, μd, and

{IP}_{3}

can all affect the amplitude and frequency of

{{[Ca}^{2 +}]}_{Cyt}

oscillations, but the mechanism is different. The model provides a comprehensive mechanism for predicting cytosolic

{Ca}^{2 +}

concentration oscillations in mast cells, and a theoretical basis for calcium oscillations observed in mast cells, so as to better understand the regulation mechanism of calcium signaling in mast cells. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine)

► Show Figures

Figure 1

22 pages, 1183 KiB

Open AccessArticle

Boosting Arithmetic Optimization Algorithm with Genetic Algorithm Operators for Feature Selection: Case Study on Cox Proportional Hazards Model

by Ahmed A. Ewees, Mohammed A. A. Al-qaness, Laith Abualigah, Diego Oliva, Zakariya Yahya Algamal, Ahmed M. Anter, Rehab Ali Ibrahim, Rania M. Ghoniem and Mohamed Abd Elaziz

Mathematics 2021, 9(18), 2321; https://doi.org/10.3390/math9182321 - 19 Sep 2021

Cited by 56 | Viewed by 4834

Abstract

Feature selection is a well-known prepossessing procedure, and it is considered a challenging problem in many domains, such as data mining, text mining, medicine, biology, public health, image processing, data clustering, and others. This paper proposes a novel feature selection method, called AOAGA, [...] Read more.

Feature selection is a well-known prepossessing procedure, and it is considered a challenging problem in many domains, such as data mining, text mining, medicine, biology, public health, image processing, data clustering, and others. This paper proposes a novel feature selection method, called AOAGA, using an improved metaheuristic optimization method that combines the conventional Arithmetic Optimization Algorithm (AOA) with the Genetic Algorithm (GA) operators. The AOA is a recently proposed optimizer; it has been employed to solve several benchmark and engineering problems and has shown a promising performance. The main aim behind the modification of the AOA is to enhance its search strategies. The conventional version suffers from weaknesses, the local search strategy, and the trade-off between the search strategies. Therefore, the operators of the GA can overcome the shortcomings of the conventional AOA. The proposed AOAGA was evaluated with several well-known benchmark datasets, using several standard evaluation criteria, namely accuracy, number of selected features, and fitness function. Finally, the results were compared with the state-of-the-art techniques to prove the performance of the proposed AOAGA method. Moreover, to further assess the performance of the proposed AOAGA method, two real-world problems containing gene datasets were used. The findings of this paper illustrated that the proposed AOAGA method finds new best solutions for several test cases, and it got promising results compared to other comparative methods published in the literature. Full article

(This article belongs to the Special Issue Evolutionary Algorithms in Artificial Intelligent Systems)

► Show Figures

Figure 1

18 pages, 2564 KiB

Open AccessArticle

Simulated Annealing with Mutation Strategy for the Share-a-Ride Problem with Flexible Compartments

by Vincent F. Yu, Putu A. Y. Indrakarna, Anak Agung Ngurah Perwira Redi and Shih-Wei Lin

Mathematics 2021, 9(18), 2320; https://doi.org/10.3390/math9182320 - 19 Sep 2021

Cited by 9 | Viewed by 2141

Abstract

The Share-a-Ride Problem with Flexible Compartments (SARPFC) is an extension of the Share-a-Ride Problem (SARP) where both passenger and freight transport are serviced by a single taxi network. The aim of SARPFC is to increase profit by introducing flexible compartments into the SARP [...] Read more.

The Share-a-Ride Problem with Flexible Compartments (SARPFC) is an extension of the Share-a-Ride Problem (SARP) where both passenger and freight transport are serviced by a single taxi network. The aim of SARPFC is to increase profit by introducing flexible compartments into the SARP model. SARPFC allows taxis to adjust their compartment size within the lower and upper bounds while maintaining the same total capacity permitting them to service more parcels while simultaneously serving at most one passenger. The main contribution of this study is that we formulated a new mathematical model for the problem and proposed a new variant of the Simulated Annealing (SA) algorithm called Simulated Annealing with Mutation Strategy (SAMS) to solve SARPFC. The mutation strategy is an intensification approach to improve the solution based on slack time, which is activated in the later stage of the algorithm. The proposed SAMS was tested on SARP benchmark instances, and the result shows that it outperforms existing algorithms. Several computational studies have also been conducted on the SARPFC instances. The analysis of the effects of compartment size and the portion of package requests to the total profit showed that, on average, utilizing flexible compartments as in SARPFC brings in more profit than using a fixed-size compartment as in SARP. Full article

(This article belongs to the Section Engineering Mathematics)

► Show Figures

Figure 1

17 pages, 1062 KiB

Open AccessArticle

GDP and Public Expenditure in Education, Health, and Defense. Empirical Research for Greece

by Kyriaki Efthalitsidou, Eleni Zafeiriou, Konstantinos Spinthiropoulos, Ioannis Betsas and Nikolaos Sariannidis

Mathematics 2021, 9(18), 2319; https://doi.org/10.3390/math9182319 - 19 Sep 2021

Cited by 3 | Viewed by 3020

Abstract

Wagner Law and Keynesian approaches are the two fundamental theories of public finance. The aim of this study is to assess empirical evidence for the public spending–national income relationship at a disaggregated level for the time period 1995–2019. The sectoral public expenditures include [...] Read more.

Wagner Law and Keynesian approaches are the two fundamental theories of public finance. The aim of this study is to assess empirical evidence for the public spending–national income relationship at a disaggregated level for the time period 1995–2019. The sectoral public expenditures include education, health, and defense. The data employed were derived by EUROSTAT and OECD. Based on our findings, a sole relationship of the variables was validated, while the causality of the relationship provides conflict results depending on whether two-variate or multivariate methodology is employed. In the case of the multivariate framework that outperforms the two-variate approach in terms of information, the causality is directed from government expenses to the GDP level, validating the Keynesian approach in the long run as well as in the short run. On the other hand, the results validate Wagner Law based on the results of Granger causality pairwise test. A potential interpreatation for the results found is related to the measures imposed by the Memorandum, since the disproportionate cuts of the public expenses in the period of crisis have determined the evolution of national income. The scientific value of the presents study stands on the suggestion of potential effective measures aiming at the limitation of national income shrinkage in periods of severe economic crises worldwide. Full article

(This article belongs to the Special Issue Application of Mathematics in Applied Economic)

► Show Figures

Figure 1

27 pages, 2790 KiB

Open AccessArticle

A Robust Mixed-Integer Linear Programming Model for Sustainable Collaborative Distribution

by Islem Snoussi, Nadia Hamani, Nassim Mrabti and Lyes Kermad

Mathematics 2021, 9(18), 2318; https://doi.org/10.3390/math9182318 - 19 Sep 2021

Cited by 10 | Viewed by 2080

Abstract

In this paper, we propose robust optimisation models for the distribution network design problem (DNDP) to deal with uncertainty cases in a collaborative context. The studied network consists of collaborative suppliers who satisfy their customers’ needs by delivering their products through common platforms. [...] Read more.

In this paper, we propose robust optimisation models for the distribution network design problem (DNDP) to deal with uncertainty cases in a collaborative context. The studied network consists of collaborative suppliers who satisfy their customers’ needs by delivering their products through common platforms. Several parameters—namely, demands, unit transportation costs, the maximum number of vehicles in use, etc.—are subject to interval uncertainty. Mixed-integer linear programming formulations are presented for each of these cases, in which the economic and environmental dimensions of the sustainability are studied and applied to minimise the logistical costs and the CO₂ emissions, respectively. These formulations are solved using CPLEX. In this study, we propose a case study of a distribution network in France to validate our models. The obtained results show the impacts of considering uncertainty by comparing the robust model to the deterministic one. We also address the impacts of the uncertainty level and uncertainty budget on logistical costs and CO₂ emissions. Full article

(This article belongs to the Special Issue Mathematical Models and Exact and Heuristic Algorithms for Solving Complex Optimization Problems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics, Volume 9, Issue 18 (September-2 2021) – 170 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI