Mathematics

3 pages, 173 KiB

Open AccessEditorial

Preface to the Special Issue on “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”

by Vilém Novák and Antonín Dvořák

Mathematics 2022, 10(22), 4393; https://doi.org/10.3390/math10224393 - 21 Nov 2022

Viewed by 889

Abstract

In [...] Full article

(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)

18 pages, 354 KiB

Open AccessArticle

Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators

by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Velmurugan Subramanian, Ghada AlNemer and Ahmed M. Elshenhab

Mathematics 2022, 10(22), 4392; https://doi.org/10.3390/math10224392 - 21 Nov 2022

Cited by 6 | Viewed by 1313

Abstract

In this article, we examine the existence of Hilfer fractional

(HF)

stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the

M \ddot{o} n c h

[...] Read more.

In this article, we examine the existence of Hilfer fractional

(HF)

stochastic differential systems with nonlocal conditions and delay via almost sectorial operators. The major methods depend on the semigroup of operators method and the

M \ddot{o} n c h

fixed-point technique via the measure of noncompactness, and the fundamental theory of fractional calculus. Finally, to clarify our key points, we provide an application. Full article

(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)

17 pages, 382 KiB

Open AccessArticle

A Preserving Precision Mixed Finite Element Dimensionality Reduction Method for Unsaturated Flow Problem

by Zhendong Luo and Yuejie Li

Mathematics 2022, 10(22), 4391; https://doi.org/10.3390/math10224391 - 21 Nov 2022

Viewed by 944

Abstract

The unsaturated flow problem is of important applied background and its mixed finite element (MFE) method can be used to simultaneously calculate both water content and flux in soil, which is the most ideal calculation method. Nonetheless, it includes many unknowns. Thereby, herein [...] Read more.

The unsaturated flow problem is of important applied background and its mixed finite element (MFE) method can be used to simultaneously calculate both water content and flux in soil, which is the most ideal calculation method. Nonetheless, it includes many unknowns. Thereby, herein we will employ the proper orthogonal decomposition (POD) to lower the dimension of unknown solution coefficient vectors in the MFE method for the unsaturated flow problem. Thus, we first examine the MFE method for the unsaturated flow problem and the existence and convergence of the classical MFE solutions. We then take advantage of the initial L MFE solution coefficient vectors to generate a set of POD basis vectors and utilize the most POD basis vectors to create the preserving precision MFE reduced-dimension (PPMFERD) format. Under the circumstances, the PPMFERD format has the same basis functions as the classical MFE format so that it can maintain the same accuracy as the classical MFE format, but it only includes a few unknowns, so it greatly lightens the calculating load, retards the accumulation of computing errors, saves CPU runtime, and improves the accuracy of the real-time calculation in the computational process. Next, we employ the analysis of matrices to demonstrate the existence and convergence of the PPMFERD solutions such that the theoretical analysis becomes very simple and elegant. Finally, we take advantage of some numerical simulations to check on the correctness of the PPMFERD method. It shows that the PPMFERD method is effective and feasible for simulating both water content and flux in unsaturated flow soil. Full article

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

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31 pages, 2788 KiB

Open AccessArticle

Global Stability of a Reaction–Diffusion Malaria/COVID-19 Coinfection Dynamics Model

by Ahmed M. Elaiw and Afnan D. Al Agha

Mathematics 2022, 10(22), 4390; https://doi.org/10.3390/math10224390 - 21 Nov 2022

Cited by 11 | Viewed by 1824

Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand [...] Read more.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand the dynamics of coinfection. In this paper, we construct a reaction–diffusion in-host malaria/COVID-19 model. The model includes seven-dimensional partial differential equations that explore the interactions between seven compartments, healthy red blood cells (RBCs), infected RBCs, free merozoites, healthy epithelial cells (ECs), infected ECs, free SARS-CoV-2 particles, and antibodies. The biological validation of the model is confirmed by establishing the nonnegativity and boundedness of the model’s solutions. All equilibrium points with the corresponding existence conditions are calculated. The global stability of all equilibria is proved by picking up appropriate Lyapunov functionals. Numerical simulations are used to enhance and visualize the theoretical results. We found that the equilibrium points show the different cases when malaria and SARS-CoV-2 infections occur as mono-infection or coinfection. The shared antibody immune response decreases the concentrations of SARS-CoV-2 and malaria merozoites. This can have an important role in reducing the severity of SARS-CoV-2 if the immune response works effectively. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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17 pages, 1206 KiB

Open AccessArticle

Key Success Factors of Sustainable Organization for Traditional Manufacturing Industries: A Case Study in Taiwan

by Shih-Hsien Tseng, Hsiu-Chuan Chen and Tien Son Nguyen

Mathematics 2022, 10(22), 4389; https://doi.org/10.3390/math10224389 - 21 Nov 2022

Cited by 3 | Viewed by 1512

Abstract

Even sustainable organizations have received overwhelming attention, but there is a lack of studies to explore the key success factors for sustainable traditional manufacturing based on expert opinions. The purpose of this study was to explore the key success factors for sustainable development [...] Read more.

Even sustainable organizations have received overwhelming attention, but there is a lack of studies to explore the key success factors for sustainable traditional manufacturing based on expert opinions. The purpose of this study was to explore the key success factors for sustainable development in traditional industries through expert knowledge. In this study, the Delphi method was applied to construct the research framework with the most appropriate criteria. Moreover, we proposed an effective solution based on the Decision-Making Trial and Evaluation Laboratory (DEMATEL)-based Analytic Network Process (ANP) to determine the correlation and causality of these factors based on the decision laboratory method for multi-criteria decision-making. We also integrated the importance–performance analysis to illustrate the attributes improvement priorities. Our results show that managers and policy-makers should concentrate more on knowledge management to enhance the sustainability of organizations. Moreover, managers should keep teamwork and employee engagement at a high level to achieve the goal of organizations. Additionally, the theoretical and practical implications provide five priority indicators for the success of a sustainable organization. Full article

(This article belongs to the Special Issue Multiple Criteria Decision Making, 2nd Edition)

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17 pages, 10256 KiB

Open AccessArticle

An Energy Efficient Specializing DAG Federated Learning Based on Event-Triggered Communication

by Xiaofeng Xue, Haokun Mao, Qiong Li, Furong Huang and Ahmed A. Abd El-Latif

Mathematics 2022, 10(22), 4388; https://doi.org/10.3390/math10224388 - 21 Nov 2022

Cited by 2 | Viewed by 1600

Abstract

Specializing Directed Acyclic Graph Federated Learning (SDAGFL) is a new federated learning framework with the advantages of decentralization, personalization, resisting a single point of failure, and poisoning attack. Instead of training a single global model, the clients in SDAGFL update their models asynchronously [...] Read more.

Specializing Directed Acyclic Graph Federated Learning (SDAGFL) is a new federated learning framework with the advantages of decentralization, personalization, resisting a single point of failure, and poisoning attack. Instead of training a single global model, the clients in SDAGFL update their models asynchronously from the devices with similar data distribution through Directed Acyclic Graph Distributed Ledger Technology (DAG-DLT), which is designed for IoT scenarios. Because of many the features inherited from DAG-DLT, SDAGFL is suitable for IoT scenarios in many aspects. However, the training process of SDAGFL is quite energy consuming, in which each client needs to compute the confidence and rating of the nodes selected by multiple random walks by traveling the ledger with 15–25 depth to obtain the “reference model” to judge whether or not to broadcast the newly trained model. As we know, the energy consumption is an important issue for IoT scenarios, as most devices are battery-powered with strict energy restrictions. To optimize SDAGFL for IoT, an energy-efficient SDAGFL based on an event-triggered communication mechanism, i.e., ESDAGFL, is proposed in this paper. In ESDAGFL, the new model is broadcasted only in the event that the new model is significantly different from the previous one, instead of traveling the ledger to search for the “reference model”. We evaluate the ESDAGFL on the FMNIST-clustered and Poets dataset. The simulation is performed on a platform with Intel

^{®}

Core

^{TM}

i7-10700 CPU (CA, USA). The simulation results demonstrate that ESDAGFL can reach a balance between training accuracy and specialization as good as SDAGFL. What is more, ESDAGFL can reduce the energy consumption by 42.5% and 51.7% for the FMNIST-clustered and Poets datasets, respectively. Full article

(This article belongs to the Special Issue Applied Statistical Modeling and Data Mining)

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20 pages, 3855 KiB

Open AccessArticle

A Method Combining Multi-Feature Fusion and Optimized Deep Belief Network for EMG-Based Human Gait Classification

by Jie He, Farong Gao, Jian Wang, Qiuxuan Wu, Qizhong Zhang and Weijie Lin

Mathematics 2022, 10(22), 4387; https://doi.org/10.3390/math10224387 - 21 Nov 2022

Cited by 6 | Viewed by 1219

Abstract

In this paper, a gait classification method based on the deep belief network (DBN) optimized by the sparrow search algorithm (SSA) is proposed. The multiple features obtained based on surface electromyography (sEMG) are fused. These functions are used to train the model. First, [...] Read more.

In this paper, a gait classification method based on the deep belief network (DBN) optimized by the sparrow search algorithm (SSA) is proposed. The multiple features obtained based on surface electromyography (sEMG) are fused. These functions are used to train the model. First, the sample features, such as the time domain and frequency domain features of the denoised sEMG are extracted and then the fused features are obtained by feature combination. Second, the SSA is utilized to optimize the architecture of DBN and its weight parameters. Finally, the optimized DBN classifier is trained and used for gait recognition. The classification results are obtained by varying different factors and the recognition rate is compared with the previous classification algorithms. The results show that the recognition rate of SSA-DBN is higher than other classifiers, and the recognition accuracy is improved by about 2% compared with the unoptimized DBN. This indicates that for the application in gait recognition, SSA can optimize the network performance of DBN, thus improving the classification accuracy. Full article

(This article belongs to the Special Issue Machine Learning and Data Mining: Techniques and Tasks)

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26 pages, 11303 KiB

Open AccessArticle

Fault-Tolerant Control for Quadrotor Based on Fixed-Time ESO

by Lei Liu, Junjie Liu, Junfang Li, Yuehui Ji, Yu Song, Liang Xu and Wenxing Niu

Mathematics 2022, 10(22), 4386; https://doi.org/10.3390/math10224386 - 21 Nov 2022

Cited by 1 | Viewed by 1148

Abstract

Focusing on the actuator fault of the quadrotor unmanned aerial vehicle (QUAV), an active fault-tolerant control scheme based on fixed-time linear active disturbance rejection control is proposed. Firstly, in order to simplify the complex dynamic model, the virtual control quantity is introduced to [...] Read more.

Focusing on the actuator fault of the quadrotor unmanned aerial vehicle (QUAV), an active fault-tolerant control scheme based on fixed-time linear active disturbance rejection control is proposed. Firstly, in order to simplify the complex dynamic model, the virtual control quantity is introduced to decouple the flight control system of the QUAV. Secondly, the fixed-time extended state observer (ESO) is utilized to estimate and compensate the internal uncertainty, external disturbance and actuator fault of the QUAV in fixed time. Thirdly, a continuous output feedback controller based on fixed-time ESO is designed to keep the stability of the flight control system with actuator fault and external disturbance. Finally, the closed-loop stability of the flight control system is demonstrated by Lyapunov function. The numerical simulation is carried and the results also verify the effectiveness of the proposed control scheme. Full article

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16 pages, 348 KiB

Open AccessArticle

Fixed Points on Covariant and Contravariant Maps with an Application

by Rajagopalan Ramaswamy, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Ola A. Ashour Abdelnaby, Vuk Stojiljković, Slobodan Radojevic and Stojan Radenović

Mathematics 2022, 10(22), 4385; https://doi.org/10.3390/math10224385 - 21 Nov 2022

Cited by 7 | Viewed by 1215

Abstract

Fixed-point results on covariant maps and contravariant maps in a

C^{★}

-algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We [...] Read more.

Fixed-point results on covariant maps and contravariant maps in a

C^{★}

-algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation. Full article

(This article belongs to the Special Issue Advances in Abstract Inequalities, Partial Functional Differential Equations and Their Applications)

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20 pages, 1172 KiB

Open AccessArticle

Fixed/Predefined-Time Synchronization of Complex-Valued Stochastic BAM Neural Networks with Stabilizing and Destabilizing Impulse

by Jingjing You, Abdujelil Abdurahman and Hayrengul Sadik

Mathematics 2022, 10(22), 4384; https://doi.org/10.3390/math10224384 - 21 Nov 2022

Cited by 4 | Viewed by 1215

Abstract

This article is mainly concerned with the fixed-time and predefined-time synchronization problem for a type of complex-valued BAM neural networks with stochastic perturbations and impulse effect. First, some previous fixed-time stability results on nonlinear impulsive systems in which stabilizing and destabilizing impulses were [...] Read more.

This article is mainly concerned with the fixed-time and predefined-time synchronization problem for a type of complex-valued BAM neural networks with stochastic perturbations and impulse effect. First, some previous fixed-time stability results on nonlinear impulsive systems in which stabilizing and destabilizing impulses were separately analyzed are extended to a general case in which the stabilizing and destabilizing impulses can be handled simultaneously. Additionally, using the same logic, a new predefined-time stability lemma for stochastic nonlinear systems with a general impulsive effect is obtained by using the inequality technique. Then, based on these novel results, two novel controllers are implemented to derive some simple fixed/predefined-time synchronization criteria for the considered complex-valued impulsive BAM neural networks with stochastic perturbations using the non-separation method. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results. Full article

(This article belongs to the Section Dynamical Systems)

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33 pages, 9836 KiB

Open AccessArticle

An Enhanced Northern Goshawk Optimization Algorithm and Its Application in Practical Optimization Problems

by Yan Liang, Xianzhi Hu, Gang Hu and Wanting Dou

Mathematics 2022, 10(22), 4383; https://doi.org/10.3390/math10224383 - 21 Nov 2022

Cited by 4 | Viewed by 1947

Abstract

As a kind of effective tool in solving complex optimization problems, intelligent optimization algorithms are paid more attention to their advantages of being easy to implement and their wide applicability. This paper proposes an enhanced northern goshawk optimization algorithm to further improve the [...] Read more.

As a kind of effective tool in solving complex optimization problems, intelligent optimization algorithms are paid more attention to their advantages of being easy to implement and their wide applicability. This paper proposes an enhanced northern goshawk optimization algorithm to further improve the ability to solve challenging tasks. Firstly, by applying the polynomial interpolation strategy to the whole population, the quality of the solutions can be enhanced to keep a fast convergence to the better individual. Then, to avoid falling into lots of local optimums, especially late in the whole search, different kinds of opposite learning methods are used to help the algorithm to search the space more fully, including opposite learning, quasi-opposite learning, and quasi-reflected learning, to keep the diversity of the population, which is noted as a multi-strategy opposite learning method in this paper. Following the construction of the enhanced algorithm, its performance is analyzed by solving the CEC2017 test suite, and five practical optimization problems. Results show that the enhanced algorithm ranks first on 23 test functions, accounting for 79.31% among 29 functions, and keeps a faster convergence speed and a better stability on most functions, compared with the original northern goshawk optimization algorithm and other popular algorithms. For practical problems, the enhanced algorithm is still effective. When the complexity of the TSP is increased, the performance of the improved algorithm is much better than others on all measure indexes. Thus, the enhanced algorithm can keep the balance between exploitation and exploration and obtain better solutions with a faster speed for problems of high complexity. Full article

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36 pages, 1529 KiB

Open AccessFeature PaperArticle

Modeling and Stability Analysis of Within-Host IAV/SARS-CoV-2 Coinfection with Antibody Immunity

by Ahmed M. Elaiw, Raghad S. Alsulami and Aatef D. Hobiny

Mathematics 2022, 10(22), 4382; https://doi.org/10.3390/math10224382 - 21 Nov 2022

Cited by 11 | Viewed by 1569

Abstract

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to [...] Read more.

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria and investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa. Full article

(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)

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39 pages, 766 KiB

Open AccessArticle

A Class of Semilinear Parabolic Problems and Analytic Semigroups

by Kazuaki Taira

Mathematics 2022, 10(22), 4381; https://doi.org/10.3390/math10224381 - 21 Nov 2022

Viewed by 1081

Abstract

(1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operators due to Lions–Peetre. [...] Read more.

(1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operators due to Lions–Peetre. (3) Results: We give a functional analytic proof of the

C^{2}

compactness of a bounded regular solution orbit for semilinear parabolic problems with Dirichlet, Neumann and Robin boundary conditions. (4) Conclusions: As an application, we study the dynamics of a population inhabiting a strongly heterogeneous environment that is modeled by a class of diffusive logistic equations with Dirichlet and Neumann boundary conditions. Full article

(This article belongs to the Special Issue Feature Papers in Functional Analysis and Applications)

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15 pages, 523 KiB

Open AccessArticle

Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

by Jing Jia Zhou, Kok Haur Ng, Kooi Huat Ng, Shelton Peiris and You Beng Koh

Mathematics 2022, 10(22), 4380; https://doi.org/10.3390/math10224380 - 21 Nov 2022

Viewed by 1090

Abstract

Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean [...] Read more.

Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean charts are developed and their population standard deviation is estimated using the three subgroup scale estimators, namely the standard deviation, median absolute deviation and standard deviation of trimmed mean for monitoring Weibull distributed data with different coefficients of skewness. This study aims to compare the out-of-control average run length of these charts with the pre-determined fixed value of the in-control ARL in terms of different scale estimators, coefficients of skewness and sample sizes via extensive simulation studies. The results indicate that as the coefficients of skewness increase, the charts tend to detect the out-of-control signal more rapidly under identical magnitude of shift. Meanwhile, as the size of the shift increases under the same coefficient of skewness, the proposed charts are able to locate the shifts quicker and the similar scenarios arise as a sample size raised from 5 to 10. A real data set from survival analysis domain which, possessing Weibull distribution, was to demonstrate the usefulness and applicability of the proposed chart in practice. Full article

(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control, 2nd Edition)

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20 pages, 780 KiB

Open AccessArticle

Accelerated Randomized Coordinate Descent for Solving Linear Systems

by Qin Wang, Weiguo Li, Wendi Bao and Feiyu Zhang

Mathematics 2022, 10(22), 4379; https://doi.org/10.3390/math10224379 - 21 Nov 2022

Cited by 1 | Viewed by 1093

Abstract

The randomized coordinate descent (RCD) method is a simple but powerful approach to solving inconsistent linear systems. In order to accelerate this approach, the Nesterov accelerated randomized coordinate descent method (NARCD) is proposed. The randomized coordinate descent with the momentum method (RCDm) is [...] Read more.

The randomized coordinate descent (RCD) method is a simple but powerful approach to solving inconsistent linear systems. In order to accelerate this approach, the Nesterov accelerated randomized coordinate descent method (NARCD) is proposed. The randomized coordinate descent with the momentum method (RCDm) is proposed by Nicolas Loizou, we will provide a new convergence boundary. The global convergence rates of the two methods are established in our paper. In addition, we show that the RCDm method has an accelerated convergence rate by choosing a proper momentum parameter. Finally, in numerical experiments, both the RCDm and the NARCD are faster than the RCD for uniformly distributed data. Moreover, the NARCD has a better acceleration effect than the RCDm and the Nesterov accelerated stochastic gradient descent method. When the linear correlation of matrix A is stronger, the NARCD acceleration is better. Full article

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

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16 pages, 622 KiB

Open AccessArticle

Taxonomy-Aware Prototypical Network for Few-Shot Relation Extraction

by Mengru Wang, Jianming Zheng and Honghui Chen

Mathematics 2022, 10(22), 4378; https://doi.org/10.3390/math10224378 - 21 Nov 2022

Cited by 1 | Viewed by 1266

Abstract

Relation extraction aims to predict the relation triple between the tail entity and head entity in a given text. A large body of works adopt meta-learning to address the few-shot issue faced by relation extraction, where each relation category only contains few labeled [...] Read more.

Relation extraction aims to predict the relation triple between the tail entity and head entity in a given text. A large body of works adopt meta-learning to address the few-shot issue faced by relation extraction, where each relation category only contains few labeled data for demonstration. Despite promising results achieved by existing meta-learning methods, these methods still struggle to distinguish the subtle differences between different relations with similar expressions. We argue this is largely owing to that these methods cannot capture unbiased and discriminative features in the very few-shot scenario. For alleviating the above problems, we propose a taxonomy-aware prototype network, which consists of a category-aware calibration module and a task-aware training strategy module. The former implicitly and explicitly calibrates the representation of prototype to become sufficiently unbiased and discriminative. The latter balances the weight between easy and hard instances, which enables our proposal to focus on data with more information during the training stage. Finally, comprehensive experiments are conducted on four typical meta tasks. Furthermore, our proposal presents superiority over the competitive baselines with an improvement of 3.30% in terms of average accuracy. Full article

(This article belongs to the Topic Machine and Deep Learning)

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24 pages, 1293 KiB

Open AccessArticle

Mathematical Properties of a Novel Graph-Theoretic Irregularity Index with Potential Applicability in QSPR Modeling

by Sakander Hayat, Amina Arif, Laiq Zada, Asad Khan and Yubin Zhong

Mathematics 2022, 10(22), 4377; https://doi.org/10.3390/math10224377 - 21 Nov 2022

Cited by 4 | Viewed by 1202

Abstract

Irregularity indices are graph-theoretic parameters designed to quantify the irregularity in a graph. In this paper, we study the practical applicability of irregularity indices in QSPR modeling of the physicochemical and quantum-theoretic properties of compounds. Our comparative testing shows that the recently introduced [...] Read more.

Irregularity indices are graph-theoretic parameters designed to quantify the irregularity in a graph. In this paper, we study the practical applicability of irregularity indices in QSPR modeling of the physicochemical and quantum-theoretic properties of compounds. Our comparative testing shows that the recently introduced

I R A

index has significant priority in applicability over other irregularity indices. In particular, we show that the correlation potential of the

I R A

index with certain physicochemical and quantum-theoretic properties such as the enthalpy of formation, boiling point, and

π

-electron energies is significant. Our QSPR modeling suggests that the regression models with the aforementioned characteristics such as strong curve fitting are, in fact, linear. Considering this the motivation, the

I R A

index was studied further, and we provide analytically explicit expressions of the

I R A

index for certain graph operations and compositions. We conclude the paper by reporting the conclusions, implications, limitations, and future scope of the current study. Full article

(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory, 2nd Edition)

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15 pages, 1341 KiB

Open AccessArticle

Land Plots Evaluation for Agriculture and Green Energy Projects: How to Overcome the Conflict Using Mathematics

by Igor Ilin, Mikhail Laskin, Irina Logacheva, Askar Sarygulov and Andrea Tick

Mathematics 2022, 10(22), 4376; https://doi.org/10.3390/math10224376 - 20 Nov 2022

Viewed by 1676

Abstract

Seventeen sustainable development goals were formulated to create a harmonious world order for the benefit of different nations and peoples. At the same time, economic practice provides a lot of examples of conflicts of an economic nature between individual sustainable development goals. One [...] Read more.

Seventeen sustainable development goals were formulated to create a harmonious world order for the benefit of different nations and peoples. At the same time, economic practice provides a lot of examples of conflicts of an economic nature between individual sustainable development goals. One of these conflicts is the need for environmental imperatives and economic growth when a massive assessment of land used for crop production and green energy projects is needed. The present paper considers a non-traditional approach to the mass evaluation of land plots on the condition that geographic information systems provide the main source of information, such as the case of land allocation for green energy facilities and evaluation of agricultural plots. The novelty of the proposed approach firstly means the development of a comparative approach, which receives much less attention in the valuation literature than cost and income approaches, as it can give an adequate picture of the current state of the market. The model includes the study of the entire dataset, the selection of model distributions and the construction of estimates based on model distributions. The methodology of multivariate lognormal distribution of factors and prices of analogues is used. The peculiarity of the market evaluation of land plots in such cases is, as a rule, the absence of rank predictors and sufficient number of continuous predictors, which provides a base for the application of a novel approach. The method of express testing of hypotheses about joint normality of logarithms of values of pricing factors and prices is proposed. The market value is estimated as an estimate of the modal value of conditional lognormal price distribution. Secondly, the problem of market valuation is solved in case of the almost complete absence of information about price-forming factors in the areas being assessed, and thirdly, the factors are determined based on geoinformation databases (distance to the nearest large city, regional center, federal highway, large rivers, lakes, and solid waste landfills), which allow for market assessment in the absence of information on pricing factors for land plots, except for the offer price and the plot area. The research was necessitated by the claim to determine on a specific date the cadastral value of agricultural land for the purposes of taxation, corresponding to the market value, in the almost complete absence of information on pricing factors in the assessed areas. The value of land reflects a complex combination of factors, so the use of the proposed mathematical toolkit allows for building a consistent model for the evaluation of land where improvements are absent or have no value in terms of land acquisition purposes. Full article

(This article belongs to the Special Issue Advances in Mathematical Methods for Economy and Sustainable Development Goals)

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16 pages, 300 KiB

Open AccessArticle

Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

by Ismat Beg, Mujahid Abbas and Muhammad Waseem Asghar

Mathematics 2022, 10(22), 4375; https://doi.org/10.3390/math10224375 - 20 Nov 2022

Cited by 3 | Viewed by 1297

Abstract

The aim of this paper is to approximate the fixed points of generalized

α

-nonexpansive mappings using

A A

-iterative algorithm. We establish some weak and strong convergence results for generalized

α

-nonexpansive mappings in uniformly convex Banach spaces. A numerical example is [...] Read more.

The aim of this paper is to approximate the fixed points of generalized

α

-nonexpansive mappings using

A A

-iterative algorithm. We establish some weak and strong convergence results for generalized

α

-nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the

A A

-iterative algorithm converges faster than some others algorithms for generalized

α

-nonexpansive mappings. Lastly, using the

A A

-iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type. Full article

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17 pages, 5033 KiB

Open AccessArticle

A New Simple Chaotic System with One Nonlinear Term

by Yassine Bouteraa, Javad Mostafaee, Mourad Kchaou, Rabeh Abbassi, Houssem Jerbi and Saleh Mobayen

Mathematics 2022, 10(22), 4374; https://doi.org/10.3390/math10224374 - 20 Nov 2022

Cited by 1 | Viewed by 1598

Abstract

In this research article, a simple four-dimensional (4D) chaotic dynamic system with uncomplicated structure and only one nonlinear term is introduced. The features of the proposed design have been conducted with some standard nonlinear dynamic analysis and mathematical tools which show the chaotic [...] Read more.

In this research article, a simple four-dimensional (4D) chaotic dynamic system with uncomplicated structure and only one nonlinear term is introduced. The features of the proposed design have been conducted with some standard nonlinear dynamic analysis and mathematical tools which show the chaotic nature. One of the most important indicators for detecting complexity of the chaotic systems is the Kaplan-York dimension of the system. Moreover, one of the main criteria of chaotic systems is its simplicity due to the reduction of operating costs. Therefore, it seems necessary to design a system as simple as possible and with high complexity. In this research, a comparison has been made between the proposed system and similar chaotic systems, which has given noticeable results. For the practical implementation of the proposed design, the circuit analysis using Multisim software has been employed. The proposed scheme has been used in the application of image encryption to show the efficiency of the proposed chaotic system and standard encryption tests have been performed. The rest of the numerical results have been conducted using MATLAB/Simulink software. Full article

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20 pages, 5280 KiB

Open AccessArticle

Deep Learning-Based Cyber–Physical Feature Fusion for Anomaly Detection in Industrial Control Systems

by Yan Du, Yuanyuan Huang, Guogen Wan and Peilin He

Mathematics 2022, 10(22), 4373; https://doi.org/10.3390/math10224373 - 20 Nov 2022

Cited by 5 | Viewed by 1835

Abstract

In this paper, we propose an unsupervised anomaly detection method based on the Autoencoder with Long Short-Term Memory (LSTM-Autoencoder) network and Generative Adversarial Network (GAN) to detect anomalies in industrial control system (ICS) using cyber–physical fusion features. This method improves the recall of [...] Read more.

In this paper, we propose an unsupervised anomaly detection method based on the Autoencoder with Long Short-Term Memory (LSTM-Autoencoder) network and Generative Adversarial Network (GAN) to detect anomalies in industrial control system (ICS) using cyber–physical fusion features. This method improves the recall of anomaly detection and overcomes the challenges of unbalanced datasets and insufficient labeled samples in ICS. As a first step, additional network features are extracted and fused with physical features to create a cyber–physical dataset. Following this, the model is trained using normal data to ensure that it can properly reconstruct the normal data. In the testing phase, samples with unknown labels are used as inputs to the model. The model will output an anomaly score for each sample, and whether a sample is anomalous depends on whether the anomaly score exceeds the threshold. Whether using supervised or unsupervised algorithms, experimentation has shown that (1) cyber–physical fusion features can significantly improve the performance of anomaly detection algorithms; (2) the proposed method outperforms several other unsupervised anomaly detection methods in terms of accuracy, recall, and F1 score; (3) the proposed method can detect the majority of anomalous events with a low false negative rate. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics)

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16 pages, 4354 KiB

Open AccessArticle

Relaxed Variable Metric Primal-Dual Fixed-Point Algorithm with Applications

by Wenli Huang, Yuchao Tang, Meng Wen and Haiyang Li

Mathematics 2022, 10(22), 4372; https://doi.org/10.3390/math10224372 - 20 Nov 2022

Viewed by 1112

Abstract

In this paper, a relaxed variable metric primal-dual fixed-point algorithm is proposed for solving the convex optimization problem involving the sum of two convex functions where one is differentiable with the Lipschitz continuous gradient while the other is composed of a linear operator. [...] Read more.

In this paper, a relaxed variable metric primal-dual fixed-point algorithm is proposed for solving the convex optimization problem involving the sum of two convex functions where one is differentiable with the Lipschitz continuous gradient while the other is composed of a linear operator. Based on the preconditioned forward–backward splitting algorithm, the convergence of the proposed algorithm is proved. At the same time, we show that some existing algorithms are special cases of the proposed algorithm. Furthermore, the ergodic convergence and linear convergence rates of the proposed algorithm are established under relaxed parameters. Numerical experiments on the image deblurring problems demonstrate that the proposed algorithm outperforms some existing algorithms in terms of the number of iterations. Full article

(This article belongs to the Special Issue Numerical Analysis and Optimization: Methods and Applications)

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14 pages, 298 KiB

Open AccessArticle

On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus

by Ahmed Bakhet, Abd-Allah Hyder, Areej A. Almoneef, Mohamed Niyaz and Ahmed H. Soliman

Mathematics 2022, 10(22), 4371; https://doi.org/10.3390/math10224371 - 20 Nov 2022

Cited by 1 | Viewed by 1000

Abstract

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hypergeometric matrix function and state some integral equations and [...] Read more.

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hypergeometric matrix function and state some integral equations and differential formulas about it. Next, we obtain some results about fractional calculus of these extended incomplete Wright hypergeometric matrix functions. Finally, we discuss an application of the extended incomplete Wright hypergeometric matrix function in the kinetic equations. Full article

(This article belongs to the Special Issue New Trends in Special Functions and Applications)

23 pages, 2872 KiB

Open AccessArticle

Neural Network-Based Bitcoin Pricing Using a New Mutated Climb Monkey Algorithm with TOPSIS Analysis for Sustainable Development

by Samuka Mohanty and Rajashree Dash

Mathematics 2022, 10(22), 4370; https://doi.org/10.3390/math10224370 - 20 Nov 2022

Cited by 3 | Viewed by 1534

Abstract

Bitcoin is yet to be assumed as a worthy cryptocurrency and rewarding asset in the global market. As polynomial-based neural networks (PBNNs) are very robust and more accurate in modeling stock price prediction, their advantage in Bitcoin pricing needs to be analyzed. In [...] Read more.

Bitcoin is yet to be assumed as a worthy cryptocurrency and rewarding asset in the global market. As polynomial-based neural networks (PBNNs) are very robust and more accurate in modeling stock price prediction, their advantage in Bitcoin pricing needs to be analyzed. In this study, the robustness of PBNNs, based on Chebyshev (CPBNN) and Legendre (LPBNN), is blended with the proposed algorithm, coined as the mutated climb monkey algorithm (MCMA), to control the estimation of network parameters to accurately predict the one-day-ahead Bitcoin price. The performance was evaluated by a comparative analysis of the testing of both CPBNN and LPBNN with each of the six algorithms under consideration on three different datasets collected within the same time interval. As the use of a few evaluation criteria will not be able to identify an efficient predictor model, this study also proposes the use of a Multi-Criteria Decision-Making (MCDM) framework to rank all models using 15 different evaluation criteria. The ranking of the models clearly indicates that the proposed MCMA algorithm outperforms all other algorithms under study. The convergence plots of the top two models for the datasets also indicate that the PBNN using MCMA for learning predicts better results. Full article

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

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31 pages, 7916 KiB

Open AccessArticle

A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability

by Sina Etemad, Albert Shikongo, Kolade M. Owolabi, Brahim Tellab, İbrahim Avcı, Shahram Rezapour and Ravi P. Agarwal

Mathematics 2022, 10(22), 4369; https://doi.org/10.3390/math10224369 - 20 Nov 2022

Cited by 12 | Viewed by 1180

Abstract

In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up smoking to analyze its dynamical [...] Read more.

In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up smoking to analyze its dynamical behaviors by considering two parameters of such generalized operators; i.e., fractal dimension and fractional order. We apply a special sub-category of increasing functions to investigate the existence of solutions. Uniqueness property is derived by a standard method based on the Lipschitz rule. After proving stability property, the equilibrium points are obtained and asymptotically stable solutions are studied. Finally, we illustrate all analytical results and findings via numerical algorithms and graphs obtained by Lagrangian piece-wise interpolation, and discuss all behaviors of the relevant solutions in the fractal-fractional system. Full article

(This article belongs to the Special Issue Recent Advances in Theory and Application of Dynamical Systems)

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27 pages, 5785 KiB

Open AccessFeature PaperArticle

Smart Patrolling Based on Spatial-Temporal Information Using Machine Learning

by Cesar Guevara and Matilde Santos

Mathematics 2022, 10(22), 4368; https://doi.org/10.3390/math10224368 - 20 Nov 2022

Viewed by 2121

Abstract

With the aim of improving security in cities and reducing the number of crimes, this research proposes an algorithm that combines artificial intelligence (AI) and machine learning (ML) techniques to generate police patrol routes. Real data on crimes reported in Quito City, Ecuador, [...] Read more.

With the aim of improving security in cities and reducing the number of crimes, this research proposes an algorithm that combines artificial intelligence (AI) and machine learning (ML) techniques to generate police patrol routes. Real data on crimes reported in Quito City, Ecuador, during 2017 are used. The algorithm, which consists of four stages, combines spatial and temporal information. First, crimes are grouped around the points with the highest concentration of felonies, and future hotspots are predicted. Then, the probability of crimes committed in any of those areas at a time slot is studied. This information is combined with the spatial way-points to obtain real surveillance routes through a fuzzy decision system, that considers distance and time (computed with the OpenStreetMap API), and probability. Computing time has been analized and routes have been compared with those proposed by an expert. The results prove that using spatial–temporal information allows the design of patrolling routes in an effective way and thus, improves citizen security and decreases spending on police resources. Full article

(This article belongs to the Special Issue Applied Statistical Modeling and Data Mining)

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6 pages, 257 KiB

Open AccessArticle

A Note on Some Weaker Notions of Cop-Win and Robber-Win Graphs

by Shravan Luckraz, Gafurjan Ibragimov and Bruno Antonio Pansera

Mathematics 2022, 10(22), 4367; https://doi.org/10.3390/math10224367 - 20 Nov 2022

Cited by 2 | Viewed by 1270

Abstract

The game of pursuit and evasion, when played on graphs, is often referred to as the game of cops and robbers. This classical version of the game has been completely solved by Nowakowski and Winkler, who gave the exact class of graphs for [...] Read more.

The game of pursuit and evasion, when played on graphs, is often referred to as the game of cops and robbers. This classical version of the game has been completely solved by Nowakowski and Winkler, who gave the exact class of graphs for which the pursuer can win the game (cop-win). When the graph does not satisfy the dismantlability property, Nowakowski and Winkler’s Theorem does not apply. In this paper, we give some weaker notions of cop-win and robber-win graphs. In particular, we fix the number of cops to be equal to one, and we ask whether there exist sets of initial conditions for which the graph can be cop-win or robber-win. We propose some open questions related to this initial condition problem with the goal of developing both structural characterizations and algorithms that are computable in polynomial time (P) and that can solve weakly cop-win and weakly- robber-win graphs. Full article

(This article belongs to the Special Issue Differential Games and Its Applications)

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20 pages, 4721 KiB

Open AccessArticle

Detection of River Floating Garbage Based on Improved YOLOv5

by Xingshuai Yang, Jingyi Zhao, Li Zhao, Haiyang Zhang, Li Li, Zhanlin Ji and Ivan Ganchev

Mathematics 2022, 10(22), 4366; https://doi.org/10.3390/math10224366 - 20 Nov 2022

Cited by 10 | Viewed by 2921

Abstract

The random dumping of garbage in rivers has led to the continuous deterioration of water quality and affected people’s living environment. The accuracy of detection of garbage floating in rivers is greatly affected by factors such as floating speed, night/daytime natural light, viewing [...] Read more.

The random dumping of garbage in rivers has led to the continuous deterioration of water quality and affected people’s living environment. The accuracy of detection of garbage floating in rivers is greatly affected by factors such as floating speed, night/daytime natural light, viewing angle and position, etc. This paper proposes a novel detection model, called YOLOv5_CBS, for the detection of garbage objects floating in rivers, based on improvements of the YOLOv5 model. Firstly, a coordinate attention (CA) mechanism is added to the original C3 module (without compressing the number of channels in the bottleneck), forming a new C3-CA-Uncompress Bottleneck (CCUB) module for improving the size of the receptive field and allowing the model to pay more attention to important parts of the processed images. Then, the Path Aggregation Network (PAN) in YOLOv5 is replaced with a Bidirectional Feature Pyramid Network (BiFPN), as proposed by other researchers, to enhance the depth of information mining and improve the feature extraction capability and detection performance of the model. In addition, the Complete Intersection over Union (CIoU) loss function, which was originally used in YOLOv5 for the calculation of location score of the compound loss, is replaced with the SCYLLA-IoU (SIoU) loss function, so as to speed up the model convergence and improve its regression precision. The results, obtained through experiments conducted on two datasets, demonstrate that the proposed YOLOv5_CBS model outperforms the original YOLOv5 model, along with three other state-of-the-art models (Faster R-CNN, YOLOv3, and YOLOv4), when used for river floating garbage objects detection, in terms of the recall, average precision, and F1 score achieved by reaching respective values of 0.885, 90.85%, and 0.8669 on the private dataset, and 0.865, 92.18%, and 0.9006 on the Flow-Img public dataset. Full article

(This article belongs to the Special Issue Mathematics: 10th Anniversary)

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13 pages, 311 KiB

Open AccessFeature PaperArticle

On Focal Borel Probability Measures

by Francisco Javier García-Pacheco, Jorge Rivero-Dones and Moisés Villegas-Vallecillos

Mathematics 2022, 10(22), 4365; https://doi.org/10.3390/math10224365 - 20 Nov 2022

Cited by 1 | Viewed by 1183

Abstract

The novel concept of focality is introduced for Borel probability measures on compact Hausdorff topological spaces. We characterize focal Borel probability measures as those Borel probability measures that are strictly positive on every nonempty open subset. We also prove the existence of focal [...] Read more.

The novel concept of focality is introduced for Borel probability measures on compact Hausdorff topological spaces. We characterize focal Borel probability measures as those Borel probability measures that are strictly positive on every nonempty open subset. We also prove the existence of focal Borel probability measures on compact metric spaces. Lastly, we prove that the set of focal (regular) Borel probability measures is convex but not extremal in the set of all (regular) Borel probability measures. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

25 pages, 482 KiB

Open AccessArticle

Probability and Certainty in the Performance of Evolutionary and Swarm Optimization Algorithms

by Nikola Ivković, Robert Kudelić and Matej Črepinšek

Mathematics 2022, 10(22), 4364; https://doi.org/10.3390/math10224364 - 20 Nov 2022

Cited by 4 | Viewed by 1332

Abstract

Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research [...] Read more.

Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research deals with measuring the performance of stochastic optimization algorithms, as well as the confidence intervals of the empirically obtained statistics. Traditionally, the arithmetic mean is used for measuring average performance, but we propose quantiles for measuring average, peak and bad-case performance, and give their interpretations in a relevant context for measuring the performance of the metaheuristics. In order to investigate the differences between arithmetic mean and quantiles, and to confirm possible benefits, we conducted experiments with 7 stochastic algorithms and 20 unconstrained continuous variable optimization problems. The experiments showed that median was a better measure of average performance than arithmetic mean, based on the observed solution quality. Out of 20 problem instances, a discrepancy between the arithmetic mean and median happened in 6 instances, out of which 5 were resolved in favor of median and 1 instance remained unresolved as a near tie. The arithmetic mean was completely inadequate for measuring average performance based on the observed number of function evaluations, while the 0.5 quantile (median) was suitable for that task. The quantiles also showed to be adequate for assessing peak performance and bad-case performance. In this paper, we also proposed a bootstrap method to calculate the confidence intervals of the probability of the empirically obtained quantiles. Considering the many advantages of using quantiles, including the ability to calculate probabilities of success in the case of multiple executions of the algorithm and the practically useful method of calculating confidence intervals, we recommend quantiles as the standard measure of peak, average and bad-case performance of stochastic optimization algorithms. Full article

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

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Mathematics, Volume 10, Issue 22 (November-2 2022) – 229 articles

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