Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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45 pages, 4025 KiB  
Article
Mathematics of Epidemics: On the General Solution of SIRVD, SIRV, SIRD, and SIR Compartment Models
by Reinhard Schlickeiser and Martin Kröger
Mathematics 2024, 12(7), 941; https://doi.org/10.3390/math12070941 - 22 Mar 2024
Cited by 5 | Viewed by 1559
Abstract
The susceptible–infected–recovered–vaccinated–deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between [...] Read more.
The susceptible–infected–recovered–vaccinated–deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest, not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using an a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave. Full article
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12 pages, 262 KiB  
Article
A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem
by Wen-Xiu Ma
Mathematics 2024, 12(6), 927; https://doi.org/10.3390/math12060927 - 21 Mar 2024
Cited by 7 | Viewed by 945
Abstract
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, [...] Read more.
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters. Full article
14 pages, 297 KiB  
Article
Cohen–Macaulayness of Vertex Splittable Monomial Ideals
by Marilena Crupi and Antonino Ficarra
Mathematics 2024, 12(6), 912; https://doi.org/10.3390/math12060912 - 20 Mar 2024
Viewed by 962
Abstract
In this paper, we give a new criterion for the Cohen–Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of checking [...] Read more.
In this paper, we give a new criterion for the Cohen–Macaulayness of vertex splittable ideals, a family of monomial ideals recently introduced by Moradi and Khosh-Ahang. Our result relies on a Betti splitting of the ideal and provides an inductive way of checking the Cohen–Macaulay property. As a result, we obtain characterizations for Gorenstein, level and pseudo-Gorenstein vertex splittable ideals. Furthermore, we provide new and simpler combinatorial proofs of known Cohen–Macaulay criteria for several families of monomial ideals, such as (vector-spread) strongly stable ideals and (componentwise) polymatroidals. Finally, we characterize the family of bi-Cohen–Macaulay graphs by the novel criterion for the Cohen–Macaulayness of vertex splittable ideals. Full article
(This article belongs to the Special Issue Combinatorics and Computation in Commutative Algebra)
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14 pages, 340 KiB  
Article
Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data
by Kalanka P. Jayalath
Mathematics 2024, 12(6), 874; https://doi.org/10.3390/math12060874 - 16 Mar 2024
Viewed by 1364
Abstract
This work focuses on making Bayesian inferences for the two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. A flexible Gibbs sampler is employed to handle the censored BS data in this Bayesian work that relies on Jeffrey’s and Achcar’s reference priors. [...] Read more.
This work focuses on making Bayesian inferences for the two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. A flexible Gibbs sampler is employed to handle the censored BS data in this Bayesian work that relies on Jeffrey’s and Achcar’s reference priors. A comprehensive simulation study is conducted to compare estimates under various parameter settings, sample sizes, and levels of censoring. Further comparisons are drawn with real-world examples involving Type-II, progressively Type-II, and randomly right-censored data. The study concludes that the suggested Gibbs sampler enhances the accuracy of Bayesian inferences, and both the amount of censoring and the sample size are identified as influential factors in such analyses. Full article
(This article belongs to the Special Issue New Trends in Stochastic Processes, Probability and Statistics)
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28 pages, 844 KiB  
Article
Sparse Bayesian Neural Networks: Bridging Model and Parameter Uncertainty through Scalable Variational Inference
by Aliaksandr Hubin and Geir Storvik
Mathematics 2024, 12(6), 788; https://doi.org/10.3390/math12060788 - 7 Mar 2024
Cited by 1 | Viewed by 2556
Abstract
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, [...] Read more.
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, facilitating more rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, the construction of scalable techniques that combine both structural and parameter uncertainty remains a challenge. In this paper, we apply the concept of model uncertainty as a framework for structural learning in BNNs and, hence, make inferences in the joint space of structures/models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark datasets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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13 pages, 1556 KiB  
Review
Potential Applications of Explainable Artificial Intelligence to Actuarial Problems
by Catalina Lozano-Murcia, Francisco P. Romero, Jesus Serrano-Guerrero, Arturo Peralta and Jose A. Olivas
Mathematics 2024, 12(5), 635; https://doi.org/10.3390/math12050635 - 21 Feb 2024
Cited by 1 | Viewed by 1838
Abstract
Explainable artificial intelligence (XAI) is a group of techniques and evaluations that allows users to understand artificial intelligence knowledge and increase the reliability of the results produced using artificial intelligence. XAI can assist actuaries in achieving better estimations and decisions. This study reviews [...] Read more.
Explainable artificial intelligence (XAI) is a group of techniques and evaluations that allows users to understand artificial intelligence knowledge and increase the reliability of the results produced using artificial intelligence. XAI can assist actuaries in achieving better estimations and decisions. This study reviews the current literature to summarize XAI in common actuarial problems. We proposed a research process based on understanding the type of AI used in actuarial practice in the financial industry and insurance pricing and then researched XAI implementation. This study systematically reviews the literature on the need for implementation options and the current use of explanatory artificial intelligence (XAI) techniques for actuarial problems. The study begins with a contextual introduction outlining the use of artificial intelligence techniques and their potential limitations, followed by the definition of the search equations used in the research process, the analysis of the results, and the identification of the main potential fields for exploitation in actuarial problems, as well as pointers for potential future work in this area. Full article
(This article belongs to the Special Issue Mathematical Economics and Insurance)
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12 pages, 271 KiB  
Article
Novel Robust Stability Criteria for Lur’e Systems with Time-Varying Delay
by Wei Wang, Jinming Liang, Mihan Liu, Liming Ding and Hongbing Zeng
Mathematics 2024, 12(4), 583; https://doi.org/10.3390/math12040583 - 15 Feb 2024
Cited by 21 | Viewed by 1025
Abstract
This paper focuses on addressing the issue of absolute stability for uncertain Lur’e systems with time-varying delay using a delay-segmentation approach. The approach involves decomposing the delay interval into two distinct subintervals of unequal lengths. This allows for the introduction of a delay-segmentation-based [...] Read more.
This paper focuses on addressing the issue of absolute stability for uncertain Lur’e systems with time-varying delay using a delay-segmentation approach. The approach involves decomposing the delay interval into two distinct subintervals of unequal lengths. This allows for the introduction of a delay-segmentation-based augmented Lyapunov–Krasovskii functional that ensures piecewise continuity at the partition points. By selecting two sets of Lyapunov matrices for the time-varying delay in each interval, the obtained results are less conservative, providing a more accurate assessment of absolute stability. Finally, a numerical example is given to demonstrate the superiority of the delay-segmentation approach. Full article
20 pages, 1639 KiB  
Article
Apriorics: Information and Graphs in the Description of the Fundamental Particles—A Mathematical Proof
by Yakir Shoshani and Asher Yahalom
Mathematics 2024, 12(4), 579; https://doi.org/10.3390/math12040579 - 15 Feb 2024
Viewed by 1467
Abstract
In our earlier work, we suggested an axiomatic framework for deducing the fundamental entities which constitute the building block of the elementary particles in physics. The basic concept of this theory, named apriorics, is the ontological structure (OS)—an undirected simple graph satisfying specified [...] Read more.
In our earlier work, we suggested an axiomatic framework for deducing the fundamental entities which constitute the building block of the elementary particles in physics. The basic concept of this theory, named apriorics, is the ontological structure (OS)—an undirected simple graph satisfying specified conditions. The vertices of this graph represent the fundamental entities (FEs), its edges are binary compounds of the FEs (which are the fundamental bosons and fermions), and the structures constituting more than two connected vertices are composite particles. The objective of this paper is to focus the attention on several mathematical theorems and ideas associated with such graphs of order n, including their enumeration, showing what is the information content of apriorics. Full article
(This article belongs to the Section Mathematical Physics)
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23 pages, 845 KiB  
Article
The Beddington–DeAngelis Competitive Response: Intra-Species Interference Enhances Coexistence in Species Competition
by María Carmen Vera, Marcos Marvá, Víctor José García-Garrido and René Escalante
Mathematics 2024, 12(4), 562; https://doi.org/10.3390/math12040562 - 13 Feb 2024
Cited by 2 | Viewed by 1325
Abstract
Species coexistence is a major issue in ecology. We disentangled the role of individual interference when competing in the classical interference competition model. For the first time, we considered simultaneously intra- and inter-species interference by introducing the Beddington–DeAngelis competitive response into the classical [...] Read more.
Species coexistence is a major issue in ecology. We disentangled the role of individual interference when competing in the classical interference competition model. For the first time, we considered simultaneously intra- and inter-species interference by introducing the Beddington–DeAngelis competitive response into the classical competition model. We found a trade-off between intra- and inter-species interference that refines in a sense the well-known balance of intra- and inter-species competition coefficients. As a result, we found that (i) global coexistence is possible for a larger range of values of the inter-/intra-species competition coefficients and contributes to explaining the high prevalence of species coexistence in nature. This feature is exclusively due to intra-species interference. (ii) We found multi-stability scenarios previously described in the literature that can be reinterpreted in terms of individuals interference. Full article
(This article belongs to the Section Mathematical Biology)
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16 pages, 3324 KiB  
Article
Rational Involutions and an Application to Planar Systems of ODE
by Ivan Mastev, Valery G. Romanovski and Yun Tian
Mathematics 2024, 12(3), 486; https://doi.org/10.3390/math12030486 - 2 Feb 2024
Viewed by 1033
Abstract
An involution refers to a function that acts as its own inverse. In this paper, our focus lies on exploring two-dimensional involutive maps defined by rational functions. These functions have denominators represented by polynomials of degree one and numerators by polynomials of a [...] Read more.
An involution refers to a function that acts as its own inverse. In this paper, our focus lies on exploring two-dimensional involutive maps defined by rational functions. These functions have denominators represented by polynomials of degree one and numerators by polynomials of a degree of, at most, two, depending on parameters. We identify the sets in the parameter space of the maps that correspond to involutions. The investigation relies on leveraging algorithms from computational commutative algebra based on the Groebner basis theory. To expedite the computations, we employ modular arithmetic. Furthermore, we showcase how involution can serve as a valuable tool for identifying reversible and integrable systems within families of planar polynomial ordinary differential equations. Full article
(This article belongs to the Section Dynamical Systems)
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18 pages, 487 KiB  
Article
A Formulation of Structural Design Optimization Problems for Quantum Annealing
by Fabian Key and Lukas Freinberger
Mathematics 2024, 12(3), 482; https://doi.org/10.3390/math12030482 - 2 Feb 2024
Cited by 1 | Viewed by 1837
Abstract
We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where [...] Read more.
We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems. Full article
(This article belongs to the Special Issue Advances in Quantum Computing and Applications)
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27 pages, 1764 KiB  
Article
Intelligent Vehicle Computation Offloading in Vehicular Ad Hoc Networks: A Multi-Agent LSTM Approach with Deep Reinforcement Learning
by Dingmi Sun, Yimin Chen and Hao Li
Mathematics 2024, 12(3), 424; https://doi.org/10.3390/math12030424 - 28 Jan 2024
Cited by 6 | Viewed by 1451
Abstract
As distributed computing evolves, edge computing has become increasingly important. It decentralizes resources like computation, storage, and bandwidth, making them more accessible to users, particularly in dynamic Telematics environments. However, these environments are marked by high levels of dynamic uncertainty due to frequent [...] Read more.
As distributed computing evolves, edge computing has become increasingly important. It decentralizes resources like computation, storage, and bandwidth, making them more accessible to users, particularly in dynamic Telematics environments. However, these environments are marked by high levels of dynamic uncertainty due to frequent changes in vehicle location, network status, and edge server workload. This complexity poses substantial challenges in rapidly and accurately handling computation offloading, resource allocation, and delivering low-latency services in such a variable environment. To address these challenges, this paper introduces a “Cloud–Edge–End” collaborative model for Telematics edge computing. Building upon this model, we develop a novel distributed service offloading method, LSTM Muti-Agent Deep Reinforcement Learning (L-MADRL), which integrates deep learning with deep reinforcement learning. This method includes a predictive model capable of forecasting the future demands on intelligent vehicles and edge servers. Furthermore, we conceptualize the computational offloading problem as a Markov decision process and employ the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) approach for autonomous, distributed offloading decision-making. Our empirical results demonstrate that the L-MADRL algorithm substantially reduces service latency and energy consumption by 5–20%, compared to existing algorithms, while also maintaining a balanced load across edge servers in diverse Telematics edge computing scenarios. Full article
(This article belongs to the Special Issue Parallel and Distributed Computing: Theory and Applications)
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25 pages, 784 KiB  
Article
Assessing Strategies to Overcome Barriers for Drone Usage in Last-Mile Logistics: A Novel Hybrid Fuzzy MCDM Model
by Snežana Tadić, Mladen Krstić and Ljubica Radovanović
Mathematics 2024, 12(3), 367; https://doi.org/10.3390/math12030367 - 23 Jan 2024
Cited by 6 | Viewed by 2108
Abstract
Effective last-mile (LM) delivery is critical to the efficient functioning of supply chains. In addition to speed and the cost of delivery, environmental and social sustainability are increasingly important factors in last-mile logistics (LML), especially in urban areas. Sustainable solutions such as drones [...] Read more.
Effective last-mile (LM) delivery is critical to the efficient functioning of supply chains. In addition to speed and the cost of delivery, environmental and social sustainability are increasingly important factors in last-mile logistics (LML), especially in urban areas. Sustainable solutions such as drones attract special attention from researchers due to their high potential. The future of drone logistics is uncertain due to many barriers. This study analyzes, evaluates and ranks barriers to identify those that most significantly hinder broader drone adoption in LML, and proposes and ranks strategies to overcome them. This type of issue requires the involvement of multiple stakeholders with conflicting goals and interests. Therefore, the study employs a novel hybrid multi-criteria decision-making (MCDM) model that combines fuzzy Delphi-based fuzzy factor relationship (Fuzzy D-FARE) and fuzzy comprehensive distance-based ranking (Fuzzy COBRA) methods. The results indicate that the main obstacle to drone implementation in LM is the lack of aviation regulations. The risks of unauthorized access, data misuse, privacy breaches, and data security represent significant challenges. They are followed by ambiguously defined or burdensome requirements for insurance and liability for drone owners. The main contributions of this study are the establishment of a novel hybrid model, identification and ranking of barriers for broader application of drones in LML, and strategies for overcoming them. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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39 pages, 570 KiB  
Review
Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey
by Virginia Kiryakova and Jordanka Paneva-Konovska
Mathematics 2024, 12(2), 319; https://doi.org/10.3390/math12020319 - 18 Jan 2024
Cited by 6 | Viewed by 1170
Abstract
In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright generalized hypergeometric functions pΨq [...] Read more.
In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright generalized hypergeometric functions pΨq and a large number of their representatives. Among these, the Mittag-Leffler-type functions are the most popular and frequently used in fractional calculus. Naturally, these also include all “Classical Special Functions” of the class of the Meijer’s G- and pFq-functions, orthogonal polynomials and many elementary functions. However, it so happened that almost simultaneously with the appearance of the Mittag-Leffler function, another “fractionalized” variant of the exponential function was introduced by Le Roy, and in recent years, several authors have extended this special function and mentioned its applications. Then, we introduced a general class of so-called (multi-index) Le Roy-type functions, and observed that they fall in an “Extended Class of SF of FC”. This includes the I-functions of Rathie and, in particular, the H¯-functions of Inayat-Hussain, studied also by Buschman and Srivastava and by other authors. These functions initially arose in the theory of the Feynman integrals in statistical physics, but also include some important special functions that are well known in math, like the polylogarithms, Riemann Zeta functions, some famous polynomials and number sequences, etc. The I- and H¯-functions are introduced by Mellin–Barnes-type integral representations involving multi-valued fractional order powers of Γ-functions with a lot of singularities that are branch points. Here, we present briefly some preliminaries on the theory of these functions, and then our ideas and results as to how the considered Le Roy-type functions can be presented in their terms. Next, we also introduce Gelfond–Leontiev generalized operators of differentiation and integration for which the Le Roy-type functions are eigenfunctions. As shown, these “generalized integrations” can be extended as kinds of generalized operators of fractional integration, and are also compositions of “Le Roy type” Erdélyi–Kober integrals. A close analogy appears with the Generalized Fractional Calculus with H- and G-kernel functions, thus leading the way to its further development. Since the theory of the I- and H¯-functions still needs clarification of some details, we consider this work as a “Discussion Survey” and also provide a list of open problems. Full article
(This article belongs to the Special Issue Integral Transforms and Special Functions in Applied Mathematics)
39 pages, 727 KiB  
Article
Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics
by Felipe Cisternas-Caneo, Broderick Crawford, Ricardo Soto, Giovanni Giachetti, Álex Paz and Alvaro Peña Fritz
Mathematics 2024, 12(2), 262; https://doi.org/10.3390/math12020262 - 12 Jan 2024
Cited by 5 | Viewed by 1170
Abstract
Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present [...] Read more.
Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map. Full article
(This article belongs to the Special Issue Mathematical Optimization and Decision Making Analysis)
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24 pages, 1715 KiB  
Article
Dynamic Malware Mitigation Strategies for IoT Networks: A Mathematical Epidemiology Approach
by Roberto Casado-Vara, Marcos Severt, Antonio Díaz-Longueira, Ángel Martín del Rey and Jose Luis Calvo-Rolle
Mathematics 2024, 12(2), 250; https://doi.org/10.3390/math12020250 - 12 Jan 2024
Cited by 2 | Viewed by 1400
Abstract
With the progress and evolution of the IoT, which has resulted in a rise in both the number of devices and their applications, there is a growing number of malware attacks with higher complexity. Countering the spread of malware in IoT networks is [...] Read more.
With the progress and evolution of the IoT, which has resulted in a rise in both the number of devices and their applications, there is a growing number of malware attacks with higher complexity. Countering the spread of malware in IoT networks is a vital aspect of cybersecurity, where mathematical modeling has proven to be a potent tool. In this study, we suggest an approach to enhance IoT security by installing security updates on IoT nodes. The proposed method employs a physically informed neural network to estimate parameters related to malware propagation. A numerical case study is conducted to evaluate the effectiveness of the mitigation strategy, and novel metrics are presented to test its efficacy. The findings suggest that the mitigation tactic involving the selection of nodes based on network characteristics is more effective than random node selection. Full article
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12 pages, 270 KiB  
Article
Coupon Collector Problem with Reset Button
by Jelena Jocković and Bojana Todić
Mathematics 2024, 12(2), 239; https://doi.org/10.3390/math12020239 - 11 Jan 2024
Viewed by 1377
Abstract
We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection [...] Read more.
We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection that has already been drawn. For the case where standard coupons have unequal probabilities of being drawn, we obtain the distribution of the waiting time until the end of the collection process. For the case where standard coupons have equal probabilities, we derive a simple formula for the expected waiting time in terms of the beta function, and discuss the asymptotic properties of this expected waiting time, when the number of standard coupons tends toward infinity. Full article
(This article belongs to the Section Probability and Statistics)
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14 pages, 527 KiB  
Article
Bounds on the Clique and the Independence Number for Certain Classes of Graphs
by Valentin E. Brimkov and Reneta P. Barneva
Mathematics 2024, 12(2), 170; https://doi.org/10.3390/math12020170 - 5 Jan 2024
Viewed by 1264
Abstract
In this paper, we study the class of graphs Gm,n that have the same degree sequence as two disjoint cliques Km and Kn, as well as the class G¯m,n of the complements of [...] Read more.
In this paper, we study the class of graphs Gm,n that have the same degree sequence as two disjoint cliques Km and Kn, as well as the class G¯m,n of the complements of such graphs. The problems of finding a maximum clique and a maximum independent set are NP-hard on Gm,n. Therefore, looking for upper and lower bounds for the clique and independence numbers of such graphs is a challenging task. In this article, we obtain such bounds, as well as other related results. In particular, we consider the class of regular graphs, which are degree-equivalent to arbitrarily many identical cliques, as well as such graphs of bounded degree. Full article
(This article belongs to the Section Mathematics and Computer Science)
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11 pages, 935 KiB  
Article
On the Bessel Solution of Kepler’s Equation
by Riccardo Borghi
Mathematics 2024, 12(1), 154; https://doi.org/10.3390/math12010154 - 3 Jan 2024
Cited by 2 | Viewed by 2829
Abstract
Since its introduction in 1650, Kepler’s equation has never ceased to fascinate mathematicians, scientists, and engineers. Over the course of five centuries, a large number of different solution strategies have been devised and implemented. Among them, the one originally proposed by J. L. [...] Read more.
Since its introduction in 1650, Kepler’s equation has never ceased to fascinate mathematicians, scientists, and engineers. Over the course of five centuries, a large number of different solution strategies have been devised and implemented. Among them, the one originally proposed by J. L. Lagrange and later by F. W. Bessel still continue to be a source of mathematical treasures. Here, the Bessel solution of the elliptic Kepler equation is explored from a new perspective offered by the theory of the Stieltjes series. In particular, it has been proven that a complex Kapteyn series obtained directly by the Bessel expansion is a Stieltjes series. This mathematical result, to the best of our knowledge, is a new integral representation of the KE solution. Some considerations on possible extensions of our results to more general classes of the Kapteyn series are also presented. Full article
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33 pages, 9935 KiB  
Article
Computer Model for an Intelligent Adjustment of Weather Conditions Based on Spatial Features for Soil Moisture Estimation
by Luis Pastor Sánchez-Fernández, Diego Alberto Flores-Carrillo and Luis Alejandro Sánchez-Pérez
Mathematics 2024, 12(1), 152; https://doi.org/10.3390/math12010152 - 2 Jan 2024
Cited by 3 | Viewed by 1236
Abstract
In this paper, an intelligent weather conditions fuzzy adjustment based on spatial features (IWeCASF) is developed. It is indispensable for our regional soil moisture estimation approach, complementing a point estimation model of soil moisture from the literature. The point estimation model requires the [...] Read more.
In this paper, an intelligent weather conditions fuzzy adjustment based on spatial features (IWeCASF) is developed. It is indispensable for our regional soil moisture estimation approach, complementing a point estimation model of soil moisture from the literature. The point estimation model requires the weather conditions at the point where an estimate is made. Therefore, IWeCASF’s aim is to determine these weather conditions. The procedure begins measuring them at only one checkpoint, called the primary checkpoint. The model determines the weather conditions anywhere within a region through image processing algorithms and fuzzy inference systems. The results are compared with the measurement records and with a spatial interpolation method. The performance is similar to or better than interpolation, especially in the rain, where the model developed is more accurate due to the certainty of replication. Additionally, IWeCASF does not require more than one measurement point. Therefore, it is a more appropriate approach to complement the point estimation model for enabling a regional soil moisture estimation. Full article
(This article belongs to the Special Issue Data Analytics in Intelligent Systems)
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18 pages, 8241 KiB  
Article
Adaptive Neural Consensus of Unknown Non-Linear Multi-Agent Systems with Communication Noises under Markov Switching Topologies
by Shaoyan Guo and Longhan Xie
Mathematics 2024, 12(1), 133; https://doi.org/10.3390/math12010133 - 31 Dec 2023
Cited by 3 | Viewed by 1197
Abstract
In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the [...] Read more.
In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the local interfered relative information and the estimation of the unknown dynamic. The Radial Basis Function networks (RBFNNs) approximate the nonlinear dynamic, and the estimated weight matrix is updated by utilizing the measurable state information. Then, using the stochastic Lyapunov analysis method, conditions for attaining consensus are derived on the consensus gain and the weight of RBFNNs. The main findings of this paper are as follows: the consensus control of multi-agent systems under more complicated and practical circumstances, including unknown nonlinear dynamic, Markov switching topologies and communication noises, is discussed; the nonlinear dynamic is approximated based on the RBFNNs and the local interfered relative information; the consensus gain k must to be small to guarantee the consensus performance; and the proposed algorithm is validated by the numerical simulations finally. Full article
(This article belongs to the Section Engineering Mathematics)
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39 pages, 1044 KiB  
Article
Option Pricing under a Generalized Black–Scholes Model with Stochastic Interest Rates, Stochastic Strings, and Lévy Jumps
by Alberto Bueno-Guerrero and Steven P. Clark
Mathematics 2024, 12(1), 82; https://doi.org/10.3390/math12010082 - 26 Dec 2023
Viewed by 3078
Abstract
We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to [...] Read more.
We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. Full article
(This article belongs to the Special Issue Financial Mathematics and Applications)
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14 pages, 311 KiB  
Article
New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One
by Muhammed Rasheed Irshad, Sreedeviamma Aswathy, Radhakumari Maya and Saralees Nadarajah
Mathematics 2024, 12(1), 81; https://doi.org/10.3390/math12010081 - 26 Dec 2023
Cited by 3 | Viewed by 1201
Abstract
Count data arise in inference, modeling, prediction, anomaly detection, monitoring, resource allocation, evaluation, and performance measurement. This paper focuses on a one-parameter discrete distribution obtained by compounding the Poisson and new X-Lindley distributions. The probability-generating function, moments, skewness, kurtosis, and other properties are [...] Read more.
Count data arise in inference, modeling, prediction, anomaly detection, monitoring, resource allocation, evaluation, and performance measurement. This paper focuses on a one-parameter discrete distribution obtained by compounding the Poisson and new X-Lindley distributions. The probability-generating function, moments, skewness, kurtosis, and other properties are derived in the closed form. The maximum likelihood method, method of moments, least squares method, and weighted least squares method are used for parameter estimation. A simulation study is carried out. The proposed distribution is applied as the innovation in an INAR(1) process. The importance of the proposed model is confirmed through the analysis of two real datasets. Full article
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42 pages, 9281 KiB  
Article
A Dynamic CGE Model for Optimization in Business Analytics: Simulating the Impact of Investment Shocks
by Ana Medina-López, Montserrat Jiménez-Partearroyo and Ángeles Cámara
Mathematics 2024, 12(1), 41; https://doi.org/10.3390/math12010041 - 22 Dec 2023
Cited by 1 | Viewed by 1860
Abstract
This study formulates a mathematical dynamic Computable General Equilibrium (CGE) model within a rational expectations framework, adhering to neo-classical principles. It emphasizes the significant role of agents’ expectations in determining the broader economic trajectory over time. The model combines microeconomic and macroeconomic perspectives [...] Read more.
This study formulates a mathematical dynamic Computable General Equilibrium (CGE) model within a rational expectations framework, adhering to neo-classical principles. It emphasizes the significant role of agents’ expectations in determining the broader economic trajectory over time. The model combines microeconomic and macroeconomic perspectives by merging the concept of intertemporal choice with savings behavior. Its mathematical foundations are derived and calibrated using data from a social accounting matrix to enhance its simulation capabilities. The paper presents a practical simulation investigating the economic implications of a strategic investment impact within an specific European region, Madrid as the case of study. Such demand shock affects sectors such as electronics, food, pharmaceuticals, and education. The study models the long-term effects of heightened investment and persistent demand-side shocks. The research demonstrates the CGE model’s ability to forecast economic shifts toward a new equilibrium after an investment shock, proving its utility for assessing the impacts of extensive environmental policies within a European context. The work’s originality lies in its detailed mathematical formulation, contributing to theoretical discourse and practical application in business analytics. Full article
(This article belongs to the Special Issue Simulation-Based Optimisation in Business Analytics)
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20 pages, 1888 KiB  
Article
Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information
by Fabio Benatti and Giovanni Nichele
Mathematics 2024, 12(1), 37; https://doi.org/10.3390/math12010037 - 22 Dec 2023
Cited by 1 | Viewed by 1191
Abstract
We investigate the divisibility properties of the tensor products Λt(1)Λt(2) of open quantum dynamics Λt(1,2) with time-dependent generators. These dynamical maps emerge from a compound open system [...] Read more.
We investigate the divisibility properties of the tensor products Λt(1)Λt(2) of open quantum dynamics Λt(1,2) with time-dependent generators. These dynamical maps emerge from a compound open system S1+S2 that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to S1+S2 without the same phenomenon occurring for either S1 and S2. We shall refer to this effect as the Superactivation of BFI (SBFI). Full article
(This article belongs to the Special Issue Recent Advances in Quantum Theory and Its Applications)
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18 pages, 358 KiB  
Article
A Fuzzy Entropy-Based Group Consensus Measure for Financial Investments
by József Dombi, Jenő Fáró and Tamás Jónás
Mathematics 2024, 12(1), 4; https://doi.org/10.3390/math12010004 - 19 Dec 2023
Viewed by 886
Abstract
This study presents a novel, fuzzy entropy-based approach to the measurement of consensus in group decision making. Here, the basic assumption is that the decision inputs are the ‘yes’ or ‘no’ votes of group members on a financial investment that has a particular [...] Read more.
This study presents a novel, fuzzy entropy-based approach to the measurement of consensus in group decision making. Here, the basic assumption is that the decision inputs are the ‘yes’ or ‘no’ votes of group members on a financial investment that has a particular expected rate of return. In this paper, using a class of fuzzy entropies, a novel consensus measure satisfying reasonable requirements is introduced for a case where the decision inputs are dichotomous variables. It is also shown here that some existing consensus measures are just special cases of the proposed fuzzy entropy-based consensus measure when the input variables are dichotomous. Next, the so-called group consensus map for financial investments is presented. It is demonstrated that this construction can be used to characterize the level of consensus among the members of a group concerning financial investments as a function of the expected rate of return. Moreover, it is described how a consensus map can be constructed from empirical data and how this map is connected with behavioral economics. Full article
(This article belongs to the Special Issue Applications of Fuzzy Modeling in Risk Management)
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18 pages, 3975 KiB  
Article
Demand Prediction of Shared Bicycles Based on Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism
by Jian-You Xu, Yan Qian, Shuo Zhang and Chin-Chia Wu
Mathematics 2023, 11(24), 4994; https://doi.org/10.3390/math11244994 - 18 Dec 2023
Cited by 3 | Viewed by 1267
Abstract
Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, [...] Read more.
Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, which makes it necessary to predict bicycle demand. In this paper, we propose a novel shared-bicycle demand prediction method based on station clustering. First, to address the challenge of capturing patterns in station-level bicycle demand, which exhibits significant fluctuations, we employ a clustering method that combines graph information from the bicycle transfer graph and potential energy. This method aggregates closely related stations into corresponding prediction regions. Second, we use the GCN-CRU-AM (Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism) model to predict bicycle demand in each region. This model extracts the spatial information and correlation between regions, integrates time feature data and local weather data, and assigns weights to the input features. Finally, experimental results based on the data from Citi Bike System in New York City demonstrate that the proposed model achieves a more accurate demand prediction. Full article
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17 pages, 2459 KiB  
Article
Characterization of the Mean First-Passage Time Function Subject to Advection in Annular-like Domains
by Hélia Serrano and Ramón F. Álvarez-Estrada
Mathematics 2023, 11(24), 4998; https://doi.org/10.3390/math11244998 - 18 Dec 2023
Cited by 1 | Viewed by 839
Abstract
Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by [...] Read more.
Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations. Full article
(This article belongs to the Section Mathematical Biology)
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17 pages, 2134 KiB  
Article
A Bidirectional Long Short-Term Memory Autoencoder Transformer for Remaining Useful Life Estimation
by Zhengyang Fan, Wanru Li and Kuo-Chu Chang
Mathematics 2023, 11(24), 4972; https://doi.org/10.3390/math11244972 - 16 Dec 2023
Cited by 6 | Viewed by 2132
Abstract
Estimating the remaining useful life (RUL) of aircraft engines holds a pivotal role in enhancing safety, optimizing operations, and promoting sustainability, thus being a crucial component of modern aviation management. Precise RUL predictions offer valuable insights into an engine’s condition, enabling informed decisions [...] Read more.
Estimating the remaining useful life (RUL) of aircraft engines holds a pivotal role in enhancing safety, optimizing operations, and promoting sustainability, thus being a crucial component of modern aviation management. Precise RUL predictions offer valuable insights into an engine’s condition, enabling informed decisions regarding maintenance and crew scheduling. In this context, we propose a novel RUL prediction approach in this paper, harnessing the power of bi-directional LSTM and Transformer architectures, known for their success in sequence modeling, such as natural languages. We adopt the encoder part of the full Transformer as the backbone of our framework, integrating it with a self-supervised denoising autoencoder that utilizes bidirectional LSTM for improved feature extraction. Within our framework, a sequence of multivariate time-series sensor measurements serves as the input, initially processed by the bidirectional LSTM autoencoder to extract essential features. Subsequently, these feature values are fed into our Transformer encoder backbone for RUL prediction. Notably, our approach simultaneously trains the autoencoder and Transformer encoder, different from the naive sequential training method. Through a series of numerical experiments carried out on the C-MAPSS datasets, we demonstrate that the efficacy of our proposed models either surpasses or stands on par with that of other existing methods. Full article
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21 pages, 1467 KiB  
Article
Asymptotic Properties for Cumulative Probability Models for Continuous Outcomes
by Chun Li, Yuqi Tian, Donglin Zeng and Bryan E. Shepherd
Mathematics 2023, 11(24), 4896; https://doi.org/10.3390/math11244896 - 7 Dec 2023
Cited by 1 | Viewed by 1698
Abstract
Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordered categorically. [...] Read more.
Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordered categorically. They thus represent a flexible analysis approach for continuous outcomes. However, it is difficult to establish asymptotic properties for CPMs due to the potentially unbounded range of the transformation. Here we show asymptotic properties for CPMs when applied to slightly modified data where bounds, one lower and one upper, are chosen and the outcomes outside the bounds are set as two ordinal categories. We prove the uniform consistency of the estimated regression coefficients and of the estimated transformation function between the bounds. We also describe their joint asymptotic distribution, and show that the estimated regression coefficients attain the semiparametric efficiency bound. We show with simulations that results from this approach and those from using the CPM on the original data are very similar when a small fraction of the data are modified. We reanalyze a dataset of HIV-positive patients with CPMs to illustrate and compare the approaches. Full article
(This article belongs to the Special Issue Nonparametric Regression Models: Theory and Applications)
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37 pages, 2323 KiB  
Article
Smart Lithium-Ion Battery Monitoring in Electric Vehicles: An AI-Empowered Digital Twin Approach
by Mitra Pooyandeh and Insoo Sohn
Mathematics 2023, 11(23), 4865; https://doi.org/10.3390/math11234865 - 4 Dec 2023
Cited by 7 | Viewed by 4410
Abstract
This paper presents a transformative methodology that harnesses the power of digital twin (DT) technology for the advanced condition monitoring of lithium-ion batteries (LIBs) in electric vehicles (EVs). In contrast to conventional solutions, our approach eliminates the need to calibrate sensors or add [...] Read more.
This paper presents a transformative methodology that harnesses the power of digital twin (DT) technology for the advanced condition monitoring of lithium-ion batteries (LIBs) in electric vehicles (EVs). In contrast to conventional solutions, our approach eliminates the need to calibrate sensors or add additional hardware circuits. The digital replica works seamlessly alongside the embedded battery management system (BMS) in an EV, delivering real-time signals for monitoring. Our system is a significant step forward in ensuring the efficiency and sustainability of EVs, which play an essential role in reducing carbon emissions. A core innovation lies in the integration of the digital twin into the battery monitoring process, reshaping the landscape of energy storage and alternative power sources such as lithium-ion batteries. Our comprehensive system leverages a cloud-based IoT network and combines both physical and digital components to provide a holistic solution. The physical side encompasses offline modeling, where a long short-term memory (LSTM) algorithm trained with various learning rates (LRs) and optimized by three types of optimizers ensures precise state-of-charge (SOC) predictions. On the digital side, the digital twin takes center stage, enabling the real-time monitoring and prediction of battery activity. A particularly innovative aspect of our approach is the utilization of a time-series generative adversarial network (TS-GAN) to generate synthetic data that seamlessly complement the monitoring process. This pioneering use of a TS-GAN offers an effective solution to the challenge of limited real-time data availability, thus enhancing the system’s predictive capabilities. By seamlessly integrating these physical and digital elements, our system enables the precise analysis and prediction of battery behavior. This innovation—particularly the application of a TS-GAN for data generation—significantly contributes to optimizing battery performance, enhancing safety, and extending the longevity of lithium-ion batteries in EVs. Furthermore, the model developed in this research serves as a benchmark for future digital energy storage in lithium-ion batteries and comprehensive energy utilization. According to statistical tests, the model has a high level of precision. Its exceptional safety performance and reduced energy consumption offer promising prospects for sustainable and efficient energy solutions. This paper signifies a pivotal step towards realizing a cleaner and more sustainable future through advanced EV battery management. Full article
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19 pages, 329 KiB  
Article
An Improved Inverse DEA for Assessing Economic Growth and Environmental Sustainability in OPEC Member Nations
by Kelvin K. Orisaremi, Felix T. S. Chan and Xiaowen Fu
Mathematics 2023, 11(23), 4861; https://doi.org/10.3390/math11234861 - 4 Dec 2023
Cited by 4 | Viewed by 1387
Abstract
Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may [...] Read more.
Economic growth is essential for nations endowed with natural resources as it reflects how well those resources are utilized in an efficient and sustainable way. For instance, OPEC member nations, which hold a large proportion of the world’s oil and gas reserves, may require a frequent evaluation of economic growth patterns to ensure that the natural resources are best used. For this purpose, this study proposes an inverse data envelopment analysis model for assessing the optimal increase in input resources required for economic growth among OPEC member nations. In this context, economic growth is reflected in the GDP per capita, taking into account possible environmental degradation. Such a model is applied to the selected OPEC member nations, which suggests that in terms of increasing the GDP per capita, only one member was able to achieve the best efficiency (i.e., reaching the efficiency frontier), resulting in a hierarchy or dominance within the sample countries. The analysis results further identify the economic growth potential for each member country. For the case of Indonesia, the analysis suggests that further economic growth may be achieved for Indonesia without additional input resources. This calls for diversification of the nation’s economy or investment in other input resources. In addition, the overall results indicated that each member nation could increase its GDP per capita while experiencing minimal environmental degradation. Our analysis not only benchmarks the growth efficiency of countries, but also identifies opportunities for more efficient and sustainable growth. Full article
(This article belongs to the Special Issue Data Envelopment Analysis for Decision Making)
16 pages, 1969 KiB  
Article
Representation of Fractional Operators Using the Theory of Functional Connections
by Daniele Mortari
Mathematics 2023, 11(23), 4772; https://doi.org/10.3390/math11234772 - 26 Nov 2023
Cited by 1 | Viewed by 1243
Abstract
This work considers fractional operators (derivatives and integrals) as surfaces f(x,α) subject to the function constraints defined by integer operators, which is a mandatory requirement of any fractional operator definition. In this respect, the problem can be seen [...] Read more.
This work considers fractional operators (derivatives and integrals) as surfaces f(x,α) subject to the function constraints defined by integer operators, which is a mandatory requirement of any fractional operator definition. In this respect, the problem can be seen as the problem of generating a surface constrained at some positive integer values of α for fractional derivatives and at some negative integer values for fractional integrals. This paper shows that by using the Theory of Functional Connections, all (past, present, and future) fractional operators can be approximated at a high level of accuracy by smooth surfaces and with no continuity issues. This practical approach provides a simple and unified tool to simulate nonlocal fractional operators that are usually defined by infinite series and/or complicated integrals. Full article
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25 pages, 26532 KiB  
Article
Statistical Image Watermark Algorithm for FAPHFMs Domain Based on BKF–Rayleigh Distribution
by Siyu Yang, Ansheng Deng and Hui Cui
Mathematics 2023, 11(23), 4720; https://doi.org/10.3390/math11234720 - 21 Nov 2023
Cited by 1 | Viewed by 1419
Abstract
In the field of image watermarking, imperceptibility, robustness, and watermarking capacity are key indicators for evaluating the performance of watermarking techniques. However, these three factors are often mutually constrained, posing a challenge in achieving a balance among them. To address this issue, this [...] Read more.
In the field of image watermarking, imperceptibility, robustness, and watermarking capacity are key indicators for evaluating the performance of watermarking techniques. However, these three factors are often mutually constrained, posing a challenge in achieving a balance among them. To address this issue, this paper presents a novel image watermark detection algorithm based on local fast and accurate polar harmonic Fourier moments (FAPHFMs) and the BKF–Rayleigh distribution model. Firstly, the original image is chunked without overlapping, the entropy value is calculated, the high-entropy chunks are selected in descending order, and the local FAPHFM magnitudes are calculated. Secondly, the watermarking signals are embedded into the robust local FAPHFM magnitudes by the multiplication function, and then MMLE based on the RSS method is utilized to estimate the statistical parameters of the BKF–Rayleigh distribution model. Finally, a blind image watermarking detector is designed using BKF–Rayleigh distribution and LO decision criteria. In addition, we derive the closed expression of the watermark detector using the BKF–Rayleigh model. The experiments proved that the algorithm in this paper outperforms the existing methods in terms of performance, maintains robustness well under a large watermarking capacity, and has excellent imperceptibility at the same time. The algorithm maintains a well-balanced relationship between robustness, imperceptibility, and watermarking capacity. Full article
(This article belongs to the Special Issue Advanced Research in Data-Centric AI)
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22 pages, 408 KiB  
Article
On Some Weingarten Surfaces in the Special Linear Group SL(2,R)
by Marian Ioan Munteanu
Mathematics 2023, 11(22), 4636; https://doi.org/10.3390/math11224636 - 13 Nov 2023
Viewed by 1145
Abstract
We classify Weingarten conoids in the real special linear group SL(2,R). In particular, there is no linear Weingarten nontrivial conoids in SL(2,R). We also prove that the only conoids in [...] Read more.
We classify Weingarten conoids in the real special linear group SL(2,R). In particular, there is no linear Weingarten nontrivial conoids in SL(2,R). We also prove that the only conoids in SL(2,R) with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup N is a Weingarten surface. Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
13 pages, 302 KiB  
Article
The Measurement Problem in Statistical Signal Processing
by Miloš Milovanović
Mathematics 2023, 11(22), 4623; https://doi.org/10.3390/math11224623 - 12 Nov 2023
Cited by 2 | Viewed by 1054
Abstract
Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for their claim is the insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes [...] Read more.
Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for their claim is the insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is an adequate framework to elaborate the measurement problem. It considers signals to be stochastic processes, regardless of whether they correspond to variables or distribution densities. Signal processing that utilizes statistical properties to perform tasks is statistical signal processing. The hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has been generalized to an open system by the use of duality in frame theory. Full article
26 pages, 6683 KiB  
Article
Modeling and Control of a DC-DC Buck–Boost Converter with Non-Linear Power Inductor Operating in Saturation Region Considering Electrical Losses
by Ernesto Molina-Santana, Felipe Gonzalez-Montañez, Jesus Ulises Liceaga-Castro, Victor Manuel Jimenez-Mondragon and Irma Siller-Alcala
Mathematics 2023, 11(22), 4617; https://doi.org/10.3390/math11224617 - 11 Nov 2023
Cited by 6 | Viewed by 2583
Abstract
The present work proposes a nonlinear model of a buck–boost DC-DC power converter considering the nonlinear magnetic characteristics of the power inductor and electrical losses of the system. The Euler–Lagrange formalism is used for formulating the proposed model. Previous research works have reported [...] Read more.
The present work proposes a nonlinear model of a buck–boost DC-DC power converter considering the nonlinear magnetic characteristics of the power inductor and electrical losses of the system. The Euler–Lagrange formalism is used for formulating the proposed model. Previous research works have reported mathematical models to describe power inductor dynamics. However, a gap in the literature remains regarding modeling this kind of element when it operates within power converters. Also, a linear-based controller scheme is proposed to regulate a non-ideal buck–boost DC-DC power converter. A methodology for tuning the proposed controller is presented, which considers the nonlinear model structure of the power converter, the linearization procedure based on an identification process, and a frequency domain analysis based on the approximated linear model. Finally, the tuned control scheme is tested on the nonlinear model of the power converter under several operational conditions showing excellent performance by effectively regulating the output voltage. The results are compared with those derived from alternative control strategies, and a better performance is generally obtained. Full article
(This article belongs to the Special Issue Dynamics and Control Theory with Applications)
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21 pages, 353 KiB  
Article
General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions
by Mi Jin Lee and Jum-Ran Kang
Mathematics 2023, 11(22), 4593; https://doi.org/10.3390/math11224593 - 9 Nov 2023
Cited by 2 | Viewed by 904
Abstract
This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a2>0 and without [...] Read more.
This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a2>0 and without imposing any restrictive growth assumption on the damping term f1, using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function ψ, namely ψ(t)μ(t)G(ψ(t)), where G is a convex and increasing function near the origin, and μ is a positive nonincreasing function. Moreover, the energy decay rates depend on the functions μ and G, as well as the function F defined by f0, which characterizes the growth behavior of f1 at the origin. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations)
16 pages, 398 KiB  
Article
Exploring Spatial-Based Position Encoding for Image Captioning
by Xiaobao Yang, Shuai He, Junsheng Wu, Yang Yang, Zhiqiang Hou and Sugang Ma
Mathematics 2023, 11(21), 4550; https://doi.org/10.3390/math11214550 - 4 Nov 2023
Cited by 2 | Viewed by 1767
Abstract
Image captioning has become a hot topic in artificial intelligence research and sits at the intersection of computer vision and natural language processing. Most recent imaging captioning models have adopted an “encoder + decoder” architecture, in which the encoder is employed generally to [...] Read more.
Image captioning has become a hot topic in artificial intelligence research and sits at the intersection of computer vision and natural language processing. Most recent imaging captioning models have adopted an “encoder + decoder” architecture, in which the encoder is employed generally to extract the visual feature, while the decoder generates the descriptive sentence word by word. However, the visual features need to be flattened into sequence form before being forwarded to the decoder, and this results in the loss of the 2D spatial position information of the image. This limitation is particularly pronounced in the Transformer architecture since it is inherently not position-aware. Therefore, in this paper, we propose a simple coordinate-based spatial position encoding method (CSPE) to remedy this deficiency. CSPE firstly creates the 2D position coordinates for each feature pixel, and then encodes them by row and by column separately via trainable or hard encoding, effectively strengthening the position representation of visual features and enriching the generated description sentences. In addition, in order to reduce the time cost, we also explore a diagonal-based spatial position encoding (DSPE) approach. Compared with CSPE, DSPE is slightly inferior in performance but has a faster calculation speed. Extensive experiments on the MS COCO 2014 dataset demonstrate that CSPE and DSPE can significantly enhance the spatial position representation of visual features. CSPE, in particular, demonstrates BLEU-4 and CIDEr metrics improved by 1.6% and 5.7%, respectively, compared with a baseline model without sequence-based position encoding, and also outperforms current sequence-based position encoding approaches by a significant margin. In addition, the robustness and plug-and-play ability of the proposed method are validated based on a medical captioning generation model. Full article
(This article belongs to the Special Issue Mathematical Methods in Image Processing and Computer Vision)
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31 pages, 1302 KiB  
Article
Time-Inhomogeneous Finite Birth Processes with Applications in Epidemic Models
by Virginia Giorno and Amelia G. Nobile
Mathematics 2023, 11(21), 4521; https://doi.org/10.3390/math11214521 - 2 Nov 2023
Cited by 2 | Viewed by 1284
Abstract
We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of [...] Read more.
We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes, we determine the explicit expressions of the transition probabilities and of the first-passage time densities. For time-homogeneous finite birth processes, the behavior of the mean and the variance of the first-passage time density is also analyzed. Moreover, the approximate duration until the entire population is infected is obtained for a large population size. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory, Simulation and Applications)
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18 pages, 1606 KiB  
Article
A Multi-View Approach for Regional Parking Occupancy Prediction with Attention Mechanisms
by Wei Ye, Haoxuan Kuang, Xinjun Lai and Jun Li
Mathematics 2023, 11(21), 4510; https://doi.org/10.3390/math11214510 - 1 Nov 2023
Cited by 3 | Viewed by 1255
Abstract
The near-future parking space availability is informative for the formulation of parking-related policy in urban areas. Plenty of studies have contributed to the spatial–temporal prediction for parking occupancy by considering the adjacency between parking lots. However, their similarities in properties remain unspecific. For [...] Read more.
The near-future parking space availability is informative for the formulation of parking-related policy in urban areas. Plenty of studies have contributed to the spatial–temporal prediction for parking occupancy by considering the adjacency between parking lots. However, their similarities in properties remain unspecific. For example, parking lots with similar functions, though not adjacent, usually have similar patterns of occupancy changes, which can help with the prediction as well. To fill the gap, this paper proposes a multi-view and attention-based approach for spatial–temporal parking occupancy prediction, namely hybrid graph convolution network with long short-term memory and temporal pattern attention (HGLT). In addition to the local view of adjacency, we construct a similarity matrix using the Pearson correlation coefficient between parking lots as the global view. Then, we design an integrated neural network focusing on graph structure and temporal pattern to assign proper weights to the different spatial features in both views. Comprehensive evaluations on a real-world dataset show that HGLT reduces prediction error by about 30.14% on average compared to other state-of-the-art models. Moreover, it is demonstrated that the global view is effective in predicting parking occupancy. Full article
(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)
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23 pages, 6651 KiB  
Article
A Novel Spacetime Boundary-Type Meshless Method for Estimating Aquifer Hydraulic Properties Using Pumping Tests
by Cheng-Yu Ku and Chih-Yu Liu
Mathematics 2023, 11(21), 4497; https://doi.org/10.3390/math11214497 - 31 Oct 2023
Cited by 2 | Viewed by 1061
Abstract
This article introduces a new boundary-type meshless method designed for solving axisymmetric transient groundwater flow problems, specifically for aquifer tests and estimating hydraulic properties. The method approximates solutions for axisymmetric transient groundwater flow using basis functions that satisfy the governing equation by solving [...] Read more.
This article introduces a new boundary-type meshless method designed for solving axisymmetric transient groundwater flow problems, specifically for aquifer tests and estimating hydraulic properties. The method approximates solutions for axisymmetric transient groundwater flow using basis functions that satisfy the governing equation by solving the inverse boundary value problem in the spacetime domain. The effectiveness of this method was demonstrated through validation with the Theis solution, which involves transient flow to a well in an infinite confined aquifer. The study included numerical examples that predicted drawdown at various radial distances and times near pumping wells. Additionally, an iterative scheme, namely, the fictitious time integration method, was employed to iteratively determine the hydraulic properties during the pumping test. The results indicate that this approach yielded highly accurate solutions without relying on the conventional time-marching scheme. Due to its temporal and spatial discretization within the spacetime domain, this method was found to be advantageous for estimating crucial hydraulic properties, such as the transmissivity and storativity of an aquifer. Full article
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45 pages, 5204 KiB  
Article
An Inventory Model for Growing Items When the Demand Is Price Sensitive with Imperfect Quality, Inspection Errors, Carbon Emissions, and Planned Backorders
by Cynthia Griselle De-la-Cruz-Márquez, Leopoldo Eduardo Cárdenas-Barrón, J. David Porter, Imelda de Jesús Loera-Hernández, Neale R. Smith, Armando Céspedes-Mota, Gerardo Treviño-Garza and Rafael Ernesto Bourguet-Díaz
Mathematics 2023, 11(21), 4421; https://doi.org/10.3390/math11214421 - 25 Oct 2023
Cited by 2 | Viewed by 1585
Abstract
Inventory models that consider environmental and quality concerns have received some attention in the literature, yet no model developed to date has investigated these features in combination with growing items. Therefore, there is a need to incorporate these three relevant aspects together in [...] Read more.
Inventory models that consider environmental and quality concerns have received some attention in the literature, yet no model developed to date has investigated these features in combination with growing items. Therefore, there is a need to incorporate these three relevant aspects together in a single inventory model to support decisions, compare results, and obtain new knowledge for the complexities of the real world. Moreover, current sustainable inventory management practices aim at mitigating the ecological consequences of an industry while preserving its profitability. The present study aligns with this perspective and introduces an economic order quantity (EOQ) model that considers imperfect quality while also accounting for sustainability principles. More specifically, the model addresses growing items, which have a demand dependent on selling price and the unique ability to grow while being stored in inventory. Additionally, the analysis acknowledges the possibility of classification errors during the inspection process, encompassing both Type-I and Type-II inspection errors. Furthermore, the model permits shortages and ensures that any shortage is completely fulfilled through backorders. The optimization model produces an optimal solution for the proposed model that is derived by optimizing three decision variables: order quantity of newborn items, backordering quantity, and the selling price of perfect items. A numerical example is presented, and the results are discussed. Finally, a sensitivity analysis on variations of parameters such as Type-I and Type-II errors shows that it is advantageous to reduce the percentage of good items that are misclassified as defective (i.e., Type-I error). As there is a direct impact of such errors on sales, it is imperative to address and mitigate this issue. When defective items are mistakenly classified as good Type-II errors, adverse consequences ensue, including a heightened rate of product returns. This, in turn, results in additional costs for the company, such as penalties and diminished customer confidence. Hence, the findings clearly suggest that the presence of Type-I and Type-II errors has a negative effect on the ordering policy and on the total expected profit. Moreover, this work provides a model that can be used with any growing item (including plants), so the decision-maker has the opportunity to analyze a wide variety of scenarios. Full article
(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)
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21 pages, 644 KiB  
Article
On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility
by Ana Ezquerro, Brais Cancela and Ana López-Cheda
Mathematics 2023, 11(19), 4150; https://doi.org/10.3390/math11194150 - 2 Oct 2023
Cited by 2 | Viewed by 2053
Abstract
In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should [...] Read more.
In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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6 pages, 231 KiB  
Review
The Problems of Dimension Four, and Some Ramifications
by Valentin Poénaru
Mathematics 2023, 11(18), 3826; https://doi.org/10.3390/math11183826 - 6 Sep 2023
Cited by 1 | Viewed by 971
Abstract
In this short note, I present a very quick review of the peculiarities of dimension four in geometric topology. I consider, in particular, the role of geometric simple connectivity (which means handle decomposition without handles of index one) for both closed manifolds and [...] Read more.
In this short note, I present a very quick review of the peculiarities of dimension four in geometric topology. I consider, in particular, the role of geometric simple connectivity (which means handle decomposition without handles of index one) for both closed manifolds and open manifolds and for finitely presented groups, together with some of recent developments in geometric group theory. Full article
(This article belongs to the Special Issue Geometry and Topology with Applications)
17 pages, 1714 KiB  
Article
Study of a New Software Reliability Growth Model under Uncertain Operating Environments and Dependent Failures
by Dahye Lee, Inhong Chang and Hoang Pham
Mathematics 2023, 11(18), 3810; https://doi.org/10.3390/math11183810 - 5 Sep 2023
Cited by 4 | Viewed by 1687
Abstract
The coronavirus disease (COVID-19) outbreak has prompted various industries to embark on digital transformation efforts, with software playing a critical role. Ensuring the reliability of software is of the utmost importance given its widespread use across multiple industries. For example, software has extensive [...] Read more.
The coronavirus disease (COVID-19) outbreak has prompted various industries to embark on digital transformation efforts, with software playing a critical role. Ensuring the reliability of software is of the utmost importance given its widespread use across multiple industries. For example, software has extensive applications in areas such as transportation, aviation, and military systems, where reliability problems can result in personal injuries and significant financial losses. Numerous studies have focused on software reliability. In particular, the software reliability growth model has served as a prominent tool for measuring software reliability. Previous studies have often assumed that the testing environment is representative of the operating environment and that software failures occur independently. However, the testing and operating environments can differ, and software failures can sometimes occur dependently. In this study, we propose a new model that assumes uncertain operating environments and dependent failures. In other words, the model proposed in this study takes into account a wider range of environments. The numerical examples in this study demonstrate that the goodness of fit of the new model is significantly better than that of the existing SRGM. Additionally, we show the utilization of the sequential probability ratio test (SPRT) based on the new model to assess the reliability of the dataset. Full article
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13 pages, 317 KiB  
Article
Prabhakar Functions of Le Roy Type: Inequalities and Asymptotic Formulae
by Jordanka Paneva-Konovska
Mathematics 2023, 11(17), 3768; https://doi.org/10.3390/math11173768 - 1 Sep 2023
Cited by 7 | Viewed by 1001
Abstract
In this paper, the four-index generalization of the classical Le Roy function is considered on a wider set of parameters and its order and type are given. Letting one of the parameters take non-negative integer values, a family of functions with such a [...] Read more.
In this paper, the four-index generalization of the classical Le Roy function is considered on a wider set of parameters and its order and type are given. Letting one of the parameters take non-negative integer values, a family of functions with such a type of index is constructed. The behaviour of these functions is studied in the complex plane C and in different domains thereof. First, several inequalities are obtained in C, and then they are modified on its compact subsets as well. Moreover, an asymptotic formula is proved for ‘large’ values of the indices of these functions. Additionally, the multi-index analogue of the abovementioned four-index Le Roy type function is considered and its basic properties are obtained. Finally, several special cases of the two functions under consideration are discussed. Full article
(This article belongs to the Special Issue Recent Trends in Convex Analysis and Mathematical Inequalities)
22 pages, 12443 KiB  
Article
A Novel Prediction Model for Seawall Deformation Based on CPSO-WNN-LSTM
by Sen Zheng, Chongshi Gu, Chenfei Shao, Yating Hu, Yanxin Xu and Xiaoyu Huang
Mathematics 2023, 11(17), 3752; https://doi.org/10.3390/math11173752 - 31 Aug 2023
Cited by 5 | Viewed by 1212
Abstract
Admittedly, deformation prediction plays a vital role in ensuring the safety of seawall during its operation period. However, there still is a lack of systematic study of the seawall deformation prediction model currently. Moreover, the absence of the major influencing factor selection is [...] Read more.
Admittedly, deformation prediction plays a vital role in ensuring the safety of seawall during its operation period. However, there still is a lack of systematic study of the seawall deformation prediction model currently. Moreover, the absence of the major influencing factor selection is generally widespread in the existing model. To overcome this problem, the Chaotic Particle Swarm Optimization (CPSO) algorithm is introduced to optimize the wavelet neural network (WNN) model, and the CPSO-WNN model is utilized to determine the major influencing factors of seawall deformation. Afterward, on the basis of major influencing factor determination results, the CPSO algorithm is applied to optimize the parameters of Long Short-Term Memory (LSTM). Subsequently, the monitoring datasets are divided into training samples and test samples to construct the prediction model and validate the effectiveness, respectively. Ultimately, the CPSO-WNN-LSTM model is employed to fit and predict the long-term settlement monitoring data series of an actual seawall located in China. The prediction performances of LSTM and BPNN prediction models were introduced to be comparisons to verify the merits of the proposed model. The analysis results indicate that the proposed model takes advantage of practicality, high efficiency, stable capability, and high precision in seawall deformation prediction. Full article
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15 pages, 321 KiB  
Article
Novel Roles of Standard Lagrangians in Population Dynamics Modeling and Their Ecological Implications
by Diana T. Pham and Zdzislaw E. Musielak
Mathematics 2023, 11(17), 3653; https://doi.org/10.3390/math11173653 - 24 Aug 2023
Viewed by 1122
Abstract
The Lagrangian formalism based on the standard Lagrangians, which are characterized by the presence of the kinetic and potential energy-like terms, is established for selected population dynamics models. A general method that allows for constructing such Lagrangians is developed, and its specific applications [...] Read more.
The Lagrangian formalism based on the standard Lagrangians, which are characterized by the presence of the kinetic and potential energy-like terms, is established for selected population dynamics models. A general method that allows for constructing such Lagrangians is developed, and its specific applications are presented and discussed. The obtained results are compared with the previously found Lagrangians, whose forms were different as they did not allow for identifying the energy-like terms. It is shown that the derived standard Lagrangians for the population dynamics models can be used to study the oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. Moreover, other physical and biological insights that can be gained from the constructed standard Lagrangians are also discussed. Full article
(This article belongs to the Special Issue Advances in the Mathematics of Ecological Modelling)
17 pages, 5536 KiB  
Article
Autonomous Trajectory Tracking and Collision Avoidance Design for Unmanned Surface Vessels: A Nonlinear Fuzzy Approach
by Yung-Yue Chen and Ming-Zhen Ellis-Tiew
Mathematics 2023, 11(17), 3632; https://doi.org/10.3390/math11173632 - 22 Aug 2023
Cited by 2 | Viewed by 1141
Abstract
An intelligent fuzzy-based control system that consists of several subsystems—a fuzzy collision evaluator, a fuzzy collision avoidance acting timing indicator, a collision-free trajectory generator, and a nonlinear adaptive fuzzy robust control law—is proposed for the collision-free condition and trajectory tracking of unmanned surface [...] Read more.
An intelligent fuzzy-based control system that consists of several subsystems—a fuzzy collision evaluator, a fuzzy collision avoidance acting timing indicator, a collision-free trajectory generator, and a nonlinear adaptive fuzzy robust control law—is proposed for the collision-free condition and trajectory tracking of unmanned surface vessels (USVs). For the purpose of ensuring that controlled USVs are capable of executing tasks in an actual ocean environment that is full of randomly encountered ships under collision-free conditions, the real-time decision making and the desired trajectory arrangements of this proposed control system were developed by following the “Convention on the International Regulations for Preventing Collisions at Sea” (COLREGs). From the simulation results, several promising properties were demonstrated: (1) robustness with respect to modeling uncertainties and ocean environmental disturbances, (2) a precise trajectory tracking ability, and (3) sailing collision avoidance was shown by this proposed system for controlled USVs. Full article
(This article belongs to the Special Issue Fuzzy Logic and Computational Intelligence)
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