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Mathematics, Volume 12, Issue 8 (April-2 2024) – 148 articles

Cover Story (view full-size image): The two graphs illustrate the evolution of population and wealth near two steady points discussed in our study. These graphs focus on two key variables, population and wealth, plotting their trajectories in a two-dimensional space. The first graph depicts a stable point, where the dynamics gradually guide the system towards equilibrium. Conversely, the second graph shows an unstable point, with dynamics indicating a divergence from this state. The starting points are marked by small circles, while the steady states are indicated by a small star. View this paper
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14 pages, 2548 KiB  
Article
Applying a Mathematical Model for Calculating the Ideal Nutrition for Sheep
by Kristina Pavlova, Elisaveta Trichkova-Kashamova and Stanislav Dimitrov
Mathematics 2024, 12(8), 1270; https://doi.org/10.3390/math12081270 - 22 Apr 2024
Viewed by 601
Abstract
The principal economic sector devoted to the breeding, raising, and production of farm animals is known as the livestock industry. There are precise standards for making high-quality feed in animal husbandry. Precision livestock feeding is a crucial component, with the potential to significantly [...] Read more.
The principal economic sector devoted to the breeding, raising, and production of farm animals is known as the livestock industry. There are precise standards for making high-quality feed in animal husbandry. Precision livestock feeding is a crucial component, with the potential to significantly impact the profitability of livestock; it permits the provision of diets to animals that are precisely tailored to their specific daily nutritional needs. Through simulation modeling, a single model can be created for automated systems to determine daily rations for farm animals. For the purposes of this document, precision livestock feeding refers to the practice of tailoring feed to individual animals or groups of animals, taking into account their changing nutritional needs over time and individual differences in terms of nutritional requirements. The practice aims to optimize animal health and performance while reducing feed waste. This paper presents a formal model for determining the quantities of components needed to achieve a minimum cost mixture that satisfies compositional and quantitative criteria. The present research calculates the amount of hay and silage required to feed an animal per day at the most economical cost by applying an optimization approach that involves defining and solving an optimization problem. The problem is solved using a well-known software package, which is necessary for the practical application of the resulting model. Real data from livestock production in Bulgaria are used to numerically test the model. Full article
(This article belongs to the Special Issue Mathematical Methods and Models in Software Engineering, 2nd Edition)
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16 pages, 1839 KiB  
Article
Link Prediction and Graph Structure Estimation for Community Detection
by Dongming Chen, Mingshuo Nie, Fei Xie, Dongqi Wang and Huilin Chen
Mathematics 2024, 12(8), 1269; https://doi.org/10.3390/math12081269 - 22 Apr 2024
Viewed by 467
Abstract
In real-world scenarios, obtaining the relationships between nodes is often challenging, resulting in incomplete network topology. This limitation significantly reduces the applicability of community detection methods, particularly neighborhood aggregation-based approaches, on structurally incomplete networks. Therefore, in this situation, it is crucial to obtain [...] Read more.
In real-world scenarios, obtaining the relationships between nodes is often challenging, resulting in incomplete network topology. This limitation significantly reduces the applicability of community detection methods, particularly neighborhood aggregation-based approaches, on structurally incomplete networks. Therefore, in this situation, it is crucial to obtain meaningful community information from the limited network structure. To address this challenge, the LPGSE algorithm was designed and implemented, which includes four parts: link prediction, structure observation, network estimation, and community partitioning. LPGSE demonstrated its performance in community detection in structurally incomplete networks with 10% missing edges on multiple datasets. Compared with traditional community detection algorithms, LPGSE achieved improvements in NMI and ARI metrics of 1.5781% to 29.0780% and 0.4332% to 31.9820%, respectively. Compared with similar community detection algorithms for structurally incomplete networks, LPGSE also outperformed other algorithms on all datasets. In addition, different edge-missing ratio settings were also attempted, and the performance of different algorithms in these situations was compared and analyzed. The results showed that the algorithm can still maintain high accuracy and stability in community detection across different edge-missing ratios. Full article
(This article belongs to the Special Issue Theory and Application of Neural Networks and Complex Networks)
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18 pages, 317 KiB  
Article
New Results on the Solvability of Abstract Sequential Caputo Fractional Differential Equations with a Resolvent-Operator Approach and Applications
by Abdelhamid Mohammed Djaouti, Khellaf Ould Melha and Muhammad Amer Latif
Mathematics 2024, 12(8), 1268; https://doi.org/10.3390/math12081268 - 22 Apr 2024
Viewed by 394
Abstract
This paper aims to establish the existence and uniqueness of mild solutions to abstract sequential fractional differential equations. The approach employed involves the utilization of resolvent operators and the fixed-point theorem. Additionally, we investigate a specific example concerning a partial differential equation incorporating [...] Read more.
This paper aims to establish the existence and uniqueness of mild solutions to abstract sequential fractional differential equations. The approach employed involves the utilization of resolvent operators and the fixed-point theorem. Additionally, we investigate a specific example concerning a partial differential equation incorporating the Caputo fractional derivative. Full article
(This article belongs to the Special Issue Theory and Applications of Fractional Equations and Calculus)
24 pages, 5099 KiB  
Article
Predicting Compressive Strength of High-Performance Concrete Using Hybridization of Nature-Inspired Metaheuristic and Gradient Boosting Machine
by Nhat-Duc Hoang, Van-Duc Tran and Xuan-Linh Tran
Mathematics 2024, 12(8), 1267; https://doi.org/10.3390/math12081267 - 22 Apr 2024
Viewed by 513
Abstract
This study proposes a novel integration of the Extreme Gradient Boosting Machine (XGBoost) and Differential Flower Pollination (DFP) for constructing an intelligent method to predict the compressive strength (CS) of high-performance concrete (HPC) mixes. The former is employed to generalize a mapping function [...] Read more.
This study proposes a novel integration of the Extreme Gradient Boosting Machine (XGBoost) and Differential Flower Pollination (DFP) for constructing an intelligent method to predict the compressive strength (CS) of high-performance concrete (HPC) mixes. The former is employed to generalize a mapping function between the mechanical property of concrete and its influencing factors. DFP, as a metaheuristic algorithm, is employed to optimize the learning phase of XGBoost and reach a fine balance between the two goals of model building: reducing the prediction error and maximizing the generalization capability. To construct the proposed method, a historical dataset consisting of 400 samples was collected from previous studies. The model’s performance is reliably assessed via multiple experiments and Wilcoxon signed-rank tests. The hybrid DFP-XGBoost is able to achieve good predictive outcomes with a root mean square error of 5.27, a mean absolute percentage error of 6.74%, and a coefficient of determination of 0.94. Additionally, quantile regression based on XGBoost is performed to construct interval predictions of the CS of HPC. Notably, an asymmetric error loss is used to diminish overestimations committed by the model. It was found that this loss function successfully reduced the percentage of overestimated CS values from 47.1% to 27.5%. Hence, DFP-XGBoost can be a promising approach for accurately and reliably estimating the CS of untested HPC mixes. Full article
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31 pages, 8410 KiB  
Article
Robust Consensus Modeling: Concerning Consensus Fairness and Efficiency with Uncertain Costs
by Xuyuan Zhang, Hailin Liang and Shaojian Qu
Mathematics 2024, 12(8), 1266; https://doi.org/10.3390/math12081266 - 22 Apr 2024
Viewed by 339
Abstract
Extensive uncertainty can affect the efficiency and fairness of consensus in the consensus reaching process (CRP), but few scholars have studied consensus modeling that focuses on fairness and efficiency in uncertain environments. Additionally, the weight of the decision maker (DM) in the CRP [...] Read more.
Extensive uncertainty can affect the efficiency and fairness of consensus in the consensus reaching process (CRP), but few scholars have studied consensus modeling that focuses on fairness and efficiency in uncertain environments. Additionally, the weight of the decision maker (DM) in the CRP is influenced by multiple factors. Therefore, this paper proposes robust consensus models (EFCMs) focusing on fairness and efficiency under uncertain costs to address these issues. Firstly, this paper constructs multiple uncertainty sets to describe the uncertainty of the unit adjustment cost. Secondly, the fair utility level and opinion adjustment distance are used to measure the fairness and efficiency of reaching consensus, respectively. Furthermore, this paper uses a data-driven method based on the KDE method combined with trust propagation in social networks to determine the DMs’ weights jointly. Finally, this paper also applies the proposed models to the carbon emission reduction negotiation process between the government and enterprises. The experimental results and sensitivity analysis show that the consensus cost budget and the DMs’ jealous preference behavior particularly affects the efficiency of reaching consensus, which provides a theoretical basis for solving practical decision making problems. Full article
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23 pages, 1168 KiB  
Article
Numerical Analysis for Sturm–Liouville Problems with Nonlocal Generalized Boundary Conditions
by Chein-Shan Liu, Chih-Wen Chang and Chung-Lun Kuo
Mathematics 2024, 12(8), 1265; https://doi.org/10.3390/math12081265 - 22 Apr 2024
Viewed by 456
Abstract
For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such [...] Read more.
For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such that the GSLP becomes an initial value problem for a new variable. For the uniqueness of eigenfunction an extra condition is imposed, which renders the right-end value of the new variable available; a derived implicit nonlinear equation is solved by an iterative method without using the differential; we can achieve highly precise eigenvalues. For the nonlocal Sturm–Liouville problem (NSLP), we consider two types of integral boundary conditions on the right end. For the first type of NSLP we can prove sufficient conditions for the positiveness of the eigenvalue. Negative eigenvalues and multiple solutions may exist for the second type of NSLP. We propose a boundary shape function method, a two-dimensional fixed-quasi-Newton method and a combination of them to solve the NSLP with fast convergence and high accuracy. From the aspect of numerical analysis the initial value problem of ordinary differential equations and scalar nonlinear equations are more easily treated than the original GSLP and NSLP, which is the main novelty of the paper to provide the mathematically equivalent and simpler mediums to determine the eigenvalues and eigenfunctions. Full article
(This article belongs to the Special Issue Numerical Analysis in Computational Mathematics)
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17 pages, 762 KiB  
Article
An Efficient Lightweight Authentication Scheme for Smart Meter
by Jingqi Du, Chengjing Dai, Pinshang Mao, Wenlong Dong, Xiujun Wang and Zhongwei Li
Mathematics 2024, 12(8), 1264; https://doi.org/10.3390/math12081264 - 22 Apr 2024
Viewed by 377
Abstract
With the rapid development of the information age, smart meters play an important role in the smart grid. However, there are more and more attacks on smart meters, which mainly focus on the identity authentication of smart meters and the security protection of [...] Read more.
With the rapid development of the information age, smart meters play an important role in the smart grid. However, there are more and more attacks on smart meters, which mainly focus on the identity authentication of smart meters and the security protection of electricity consumption data. In this paper, an efficient lightweight smart meter authentication scheme is proposed based on the Chinese Remainder Theorem (CRT), which can realize the revocation of a single smart meter user by publishing a secret random value bound to the smart meter identity. The proposed scheme not only protects the security of smart meter electricity consumption data by using encryption, but also resists identity attacks from both internal and external adversaries by using hash functions and timestamps. Experiment shows that the proposed scheme has lower computation overhead and communication overhead than other authentication schemes and is more suitable for smart meter authentication. Full article
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12 pages, 1925 KiB  
Article
Multidimensional Model of Information Struggle with Impulse Perturbation in Terms of Levy Approximation
by Anatolii Nikitin, Svajonė Bekešienė, Šárka Hošková-Mayerová and Bohdan Krasiuk
Mathematics 2024, 12(8), 1263; https://doi.org/10.3390/math12081263 - 22 Apr 2024
Viewed by 415
Abstract
The focus of this research was on building a decision support system for a model that characterizes the conflict interaction of n-dimensional complex systems with non-trivial internal structures. The interpretation of the new model was focused on information warfare as the impact of [...] Read more.
The focus of this research was on building a decision support system for a model that characterizes the conflict interaction of n-dimensional complex systems with non-trivial internal structures. The interpretation of the new model was focused on information warfare as the impact of rare events that quickly change certain perceptions of a large number of people. Consequently, the support for various ideas experiences stochastic jumps, a phenomenon observable through a non-classical Levy approximation scheme. The essence of our decision support system lies in its ability to navigate the complex dynamics of conflict interaction among multifaceted systems. Through the utilization of advanced modeling techniques, our aim is to illuminate the complicated interplay of factors influencing information warfare and its cascading effects on societal perceptions and behaviors. Key components of our decision support system encompass model development, simulation capabilities, data integration, and visualization tools. The significance of our work lies in its potential to inform policy formulation, conflict resolution strategies, and societal resilience in the face of information warfare. By providing decision-makers with actionable intelligence and foresight into emerging threats and opportunities, our decision support system serves as a valuable tool for navigating the complexities of modern conflict dynamics. In conclusion, developing a decision support system for modeling conflict interaction in complex systems represents an essential step toward enhancing our understanding of information warfare and its consequences. Through interdisciplinary collaboration and innovative modeling techniques, we aim to provide stakeholders with the insights and capabilities needed to navigate the developing landscape of conflict and ensure the stability and resilience of society. Full article
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13 pages, 641 KiB  
Article
Computational Characterization of the Multiplication Operation of Octonions via Algebraic Approaches
by Ray-Ming Chen
Mathematics 2024, 12(8), 1262; https://doi.org/10.3390/math12081262 - 22 Apr 2024
Viewed by 372
Abstract
A succinct and systematic form of multiplication for any arbitrary pairs of octonions is devised. A typical expression of multiplication for any pair of octonions involves 64 terms, which, from the computational and theoretical aspect, is too cumbersome. In addition, its internal relation [...] Read more.
A succinct and systematic form of multiplication for any arbitrary pairs of octonions is devised. A typical expression of multiplication for any pair of octonions involves 64 terms, which, from the computational and theoretical aspect, is too cumbersome. In addition, its internal relation could not be directly visualized via the expression per se. In this article, we study the internal structures of the indexes between imaginary unit octonions. It is then revealed by various copies of isomorphic structures for the multiplication. We isolate one copy and define a multiplicative structure on this. By doing so, we could keep track of all relations between indexes and the signs for cyclic permutations. The final form of our device is expressed in the form of a series of determinants, which shall offer some direct intuition about octonion multiplication and facilitate the further computational aspect of applications. Full article
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17 pages, 1409 KiB  
Article
The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution
by Hanan Haj Ahmad
Mathematics 2024, 12(8), 1261; https://doi.org/10.3390/math12081261 - 22 Apr 2024
Viewed by 395
Abstract
In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed, symmetric, and monotonic datasets. Statistical analyses [...] Read more.
In this study, we introduce two novel discrete counterparts for the Rayleigh–Lindley mixture, constructed through the application of survival and hazard rate preservation techniques. These two-parameter discrete models demonstrate exceptional adaptability across various data types, including skewed, symmetric, and monotonic datasets. Statistical analyses were conducted using maximum likelihood estimation and Bayesian approaches to assess these models. The Bayesian analysis, in particular, was implemented with the squared error and LINEX loss functions, incorporating a modified Lwin Prior distribution for parameter estimation. Through simulation studies and numerical methods, we evaluated the estimators’ performance and compared the effectiveness of the two discrete adaptations of the Rayleigh–Lindley distribution. The simulations reveal that Bayesian methods are especially effective in this setting due to their flexibility and adaptability. They provide more precise and dependable estimates for the discrete Rayleigh–Lindley model, especially when using the hazard rate preservation method. This method is a compelling alternative to the traditional survival discretization approach, showcasing its significant potential in enhancing model accuracy and applicability. Furthermore, two real data sets are analyzed to assess the performance of each analog. Full article
(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling)
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12 pages, 387 KiB  
Article
On a Family of Hamilton–Poisson Jerk Systems
by Cristian Lăzureanu and Jinyoung Cho
Mathematics 2024, 12(8), 1260; https://doi.org/10.3390/math12081260 - 22 Apr 2024
Viewed by 371
Abstract
In this paper, we construct a family of Hamilton–Poisson jerk systems. We show that such a system has infinitely many Hamilton–Poisson realizations. In addition, we discuss the stability and we prove the existence of periodic orbits around nonlinearly stable equilibrium points. Particularly, we [...] Read more.
In this paper, we construct a family of Hamilton–Poisson jerk systems. We show that such a system has infinitely many Hamilton–Poisson realizations. In addition, we discuss the stability and we prove the existence of periodic orbits around nonlinearly stable equilibrium points. Particularly, we deduce conditions for the existence of homoclinic and heteroclinic orbits. We apply the obtained results to a family of anharmonic oscillators. Full article
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19 pages, 431 KiB  
Article
Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index
by Akbar Ali, Sadia Noureen, Abdul Moeed, Naveed Iqbal and Taher S. Hassan
Mathematics 2024, 12(8), 1259; https://doi.org/10.3390/math12081259 - 21 Apr 2024
Viewed by 414
Abstract
Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set [...] Read more.
Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set E={e1,e2,,em}, its multiplicative sum Zagreb index is defined as the product of the numbers D(e1),D(e2),,D(em), where D(ei) is the sum of the degrees of the end vertices of ei. A chemical tree is a tree of maximum degree at most 4. In this research work, graphs possessing the maximum multiplicative sum Zagreb index are determined from the class of chemical trees with a given order and fixed number of segments. The values of the multiplicative sum Zagreb index of the obtained extremal trees are also obtained. Full article
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17 pages, 315 KiB  
Article
Functional Solutions of Stochastic Differential Equations
by Imme van den Berg
Mathematics 2024, 12(8), 1258; https://doi.org/10.3390/math12081258 - 21 Apr 2024
Viewed by 341
Abstract
We present an integration condition ensuring that a stochastic differential equation dXt=μ(t,Xt)dt+σ(t,Xt)dBt, where μ and σ are sufficiently regular, [...] Read more.
We present an integration condition ensuring that a stochastic differential equation dXt=μ(t,Xt)dt+σ(t,Xt)dBt, where μ and σ are sufficiently regular, has a solution of the form Xt=Z(t,Bt). By generalizing the integration condition we obtain a class of stochastic differential equations that again have a functional solution, now of the form Xt=Z(t,Yt), with Yt an Ito process. These integration conditions, which seem to be new, provide an a priori test for the existence of functional solutions. Then path-independence holds for the trajectories of the process. By Green’s Theorem, it holds also when integrating along any piece-wise differentiable path in the plane. To determine Z at any point (t,x), we may start at the initial condition and follow a path that is first horizontal and then vertical. Then the value of Z can be determined by successively solving two ordinary differential equations. Due to a Lipschitz condition, this value is unique. The differential equations relate to an earlier path-dependent approach by H. Doss, which enables the expression of a stochastic integral in terms of a differential process. Full article
(This article belongs to the Special Issue First SDE: New Advances in Stochastic Differential Equations)
12 pages, 750 KiB  
Article
Performance Analysis of RIS-Assisted SatComs Based on a ZFBF and Co-Phasing Scheme
by Minchae Jung, Taehyoung Kim and Hyukmin Son
Mathematics 2024, 12(8), 1257; https://doi.org/10.3390/math12081257 - 21 Apr 2024
Viewed by 426
Abstract
In recent high-throughput satellite communication (SatCom) systems, the use of reconfigurable intelligent surfaces (RISs) has emerged as a promising solution to improve spectral efficiency and extend coverage in areas with limited terrestrial network access. However, the RIS may amplify the inter-beam interference (IBI) [...] Read more.
In recent high-throughput satellite communication (SatCom) systems, the use of reconfigurable intelligent surfaces (RISs) has emerged as a promising solution to improve spectral efficiency and extend coverage in areas with limited terrestrial network access. However, the RIS may amplify the inter-beam interference (IBI) caused by multibeam transmission at the satellite, and multiple RISs can also cause inter-RIS interference (IRI) to terrestrial users. In this paper, the performance of the RIS-assisted SatCom system is asymptotically analyzed for both full and partial channel state information (CSI) scenarios. In particular, zero-forcing beamforming is considered as the active beamforming for data transmission, while the co-phasing scheme is considered as the passive beamforming for RIS reflection. Based on the asymptotic analyses, deterministic active and passive beamforming techniques using partial CSI are proposed that can gradually eliminate both IBI and IRI, ultimately achieving ideal performance. Simulation results validate the accuracy of asymptotic analyses and demonstrate the superiority of deterministic active and passive beamforming techniques using partial CSI. The simulation results also confirm that the proposed beamforming can achieve approximately 92.8% of the ideal performance, even though it only requires partial CSI. Full article
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17 pages, 1440 KiB  
Article
A Probabilistic Structural Damage Identification Method with a Generic Non-Convex Penalty
by Rongpeng Li, Wen Yi, Fengdan Wang, Yuzhu Xiao, Qingtian Deng, Xinbo Li and Xueli Song
Mathematics 2024, 12(8), 1256; https://doi.org/10.3390/math12081256 - 21 Apr 2024
Viewed by 406
Abstract
Due to the advantage that the non-convex penalty accurately characterizes the sparsity of structural damage, various models based on non-convex penalties have been effectively utilized to the field of structural damage identification. However, these models generally ignore the influence of the uncertainty on [...] Read more.
Due to the advantage that the non-convex penalty accurately characterizes the sparsity of structural damage, various models based on non-convex penalties have been effectively utilized to the field of structural damage identification. However, these models generally ignore the influence of the uncertainty on the damage identification, which inevitably reduces the accuracy of damage identification. To improve the damage identification accuracy, a probabilistic structural damage identification method with a generic non-convex penalty is proposed, where the uncertainty corresponding to each mode is quantified using the separate Gaussian distribution. The proposed model is estimated via the iteratively reweighted least squares optimization algorithm according to the maximum likelihood principle. The numerical and experimental results illustrate that the proposed method improves the damage identification accuracy by 3.98% and 7.25% compared to the original model, respectively. Full article
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18 pages, 2337 KiB  
Article
Urban Origin–Destination Travel Time Estimation Using K-Nearest-Neighbor-Based Methods
by Felipe Lagos, Sebastián Moreno, Wilfredo F. Yushimito and Tomás Brstilo
Mathematics 2024, 12(8), 1255; https://doi.org/10.3390/math12081255 - 20 Apr 2024
Viewed by 481
Abstract
Improving the estimation of origin–destination (O-D) travel times poses a formidable challenge due to the intricate nature of transportation dynamics. Current deep learning models often require an overwhelming amount of data, both in terms of data points and variables, thereby limiting their applicability. [...] Read more.
Improving the estimation of origin–destination (O-D) travel times poses a formidable challenge due to the intricate nature of transportation dynamics. Current deep learning models often require an overwhelming amount of data, both in terms of data points and variables, thereby limiting their applicability. Furthermore, there is a scarcity of models capable of predicting travel times with basic trip information such as origin, destination, and starting time. This paper introduces novel models rooted in the k-nearest neighbor (KNN) algorithm to tackle O-D travel time estimation with limited data. These models represent innovative adaptations of weighted KNN techniques, integrating the haversine distance of neighboring trips and incorporating correction factors to mitigate prediction biases, thereby enhancing the accuracy of travel time estimations for a given trip. Moreover, our models incorporate an adaptive heuristic to partition the time of day, identifying time blocks characterized by similar travel-time observations. These time blocks facilitate a more nuanced understanding of traffic patterns, enabling more precise predictions. To validate the effectiveness of our proposed models, extensive testing was conducted utilizing a comprehensive taxi trip dataset sourced from Santiago, Chile. The results demonstrate substantial improvements over existing state-of-the-art models (e.g., MAPE between 35 to 37% compared to 49 to 60% in other methods), underscoring the efficacy of our approach. Additionally, our models unveil previously unrecognized patterns in city traffic across various time blocks, shedding light on the underlying dynamics of urban mobility. Full article
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24 pages, 9831 KiB  
Article
A Novel Computational Instrument Based on a Universal Mixture Density Network with a Gaussian Mixture Model as a Backbone for Predicting COVID-19 Variants’ Distributions
by Yas Al-Hadeethi, Intesar F. El Ramley, Hiba Mohammed, Nada M. Bedaiwi and Abeer Z. Barasheed
Mathematics 2024, 12(8), 1254; https://doi.org/10.3390/math12081254 - 20 Apr 2024
Viewed by 518
Abstract
Various published COVID-19 models have been used in epidemiological studies and healthcare planning to model and predict the spread of the disease and appropriately realign health measures and priorities given the resource limitations in the field of healthcare. However, a significant issue arises [...] Read more.
Various published COVID-19 models have been used in epidemiological studies and healthcare planning to model and predict the spread of the disease and appropriately realign health measures and priorities given the resource limitations in the field of healthcare. However, a significant issue arises when these models need help identifying the distribution of the constituent variants of COVID-19 infections. The emergence of such a challenge means that, given limited healthcare resources, health planning would be ineffective and cost lives. This work presents a universal neural network (NN) computational instrument for predicting the mainstream symptomatic infection rate of COVID-19 and models of the distribution of its associated variants. The NN is based on a mixture density network (MDN) with a Gaussian mixture model (GMM) object as a backbone. Twelve use cases were used to demonstrate the validity and reliability of the proposed MDN. The use cases included COVID-19 data for Canada and Saudi Arabia, two date ranges (300 and 500 days), two input data modes, and three activation functions, each with different implementations of the batch size and epoch value. This array of scenarios provided an opportunity to investigate the impacts of epistemic uncertainty (EU) and aleatoric uncertainty (AU) on the prediction model’s fitting. The model accuracy readings were in the high nineties based on a tolerance margin of 0.0125. The primary outcome of this work indicates that this easy-to-use universal MDN helps provide reliable predictions of COVID-19 variant distributions and the corresponding synthesized profile of the mainstream infection rate. Full article
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27 pages, 858 KiB  
Article
A Nonlinear ODE Model for a Consumeristic Society
by Marino Badiale and Isabella Cravero
Mathematics 2024, 12(8), 1253; https://doi.org/10.3390/math12081253 - 20 Apr 2024
Viewed by 818
Abstract
In this paper, we introduce an ODE system to model the interaction between natural resources and human exploitation in a rich consumeristic society. In this model, the rate of change in population depends on wealth per capita, and the rate of consumption has [...] Read more.
In this paper, we introduce an ODE system to model the interaction between natural resources and human exploitation in a rich consumeristic society. In this model, the rate of change in population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. We distinguish between renewable and non-renewable resources, and we introduce a replenishment term for non-renewable resources. We first obtain some information on the asymptotic behavior of wealth and population, then we compute all system equilibria and study their stability when the resource exploitation parameter is low. Some numerical simulations confirm the theoretical results and suggest directions for future research. Full article
(This article belongs to the Special Issue Problems and Methods in Nonlinear Analysis)
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20 pages, 1095 KiB  
Article
When Optimization Meets AI: An Intelligent Approach for Network Disintegration with Discrete Resource Allocation
by Ruozhe Li, Hao Yuan, Bangbang Ren, Xiaoxue Zhang, Tao Chen and Xueshan Luo
Mathematics 2024, 12(8), 1252; https://doi.org/10.3390/math12081252 - 20 Apr 2024
Viewed by 377
Abstract
Network disintegration is a fundamental issue in the field of complex networks, with its core in identifying critical nodes or sets and removing them to weaken network functionality. The research on this problem has significant strategic value and has increasingly attracted attention, including [...] Read more.
Network disintegration is a fundamental issue in the field of complex networks, with its core in identifying critical nodes or sets and removing them to weaken network functionality. The research on this problem has significant strategic value and has increasingly attracted attention, including in controlling the spread of diseases and dismantling terrorist organizations. In this paper, we focus on the problem of network disintegration with discrete entity resources from the attack view, that is, optimizing resource allocation to maximize the effect of network disintegration. Specifically, we model the network disintegration problem with limited entity resources as a nonlinear optimization problem and prove its NP-hardness. Then, we design a method based on deep reinforcement learning (DRL), Net-Cracker, which transforms the two-stage entity resource and network node selection task into a single-stage object selection problem. Extensive experiments demonstrate that compared with the benchmark algorithm, Net-Cracker can improve the solution quality by about 8∼62%, while enabling a 30-to-160-fold speed up. Net-Cracker also exhibits strong generalization ability and can find better results in a near real-time manner even when the network scale is much larger than that in training data. Full article
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16 pages, 289 KiB  
Article
Lie Modules of Banach Space Nest Algebras
by Pedro Capitão and Lina Oliveira
Mathematics 2024, 12(8), 1251; https://doi.org/10.3390/math12081251 - 20 Apr 2024
Viewed by 371
Abstract
In the present work, we extend to Lie modules of Banach space nest algebras a well-known characterisation of Lie ideals of (Hilbert space) nest algebras. Let A be a Banach space nest algebra and L be a weakly closed Lie A-module. We [...] Read more.
In the present work, we extend to Lie modules of Banach space nest algebras a well-known characterisation of Lie ideals of (Hilbert space) nest algebras. Let A be a Banach space nest algebra and L be a weakly closed Lie A-module. We show that there exist a weakly closed A-bimodule K, a weakly closed subalgebra DK of A, and a largest weakly closed A-bimodule J contained in L,such that JLK+DK, with [K,A]L. The first inclusion holds in general, whilst the second is shown to be valid in a class of nest algebras. Full article
(This article belongs to the Special Issue Advances on Nonlinear Functional Analysis)
17 pages, 1507 KiB  
Article
Risk Analysis of the Use of Drones in City Logistics
by Snežana Tadić, Mladen Krstić, Miloš Veljović, Olja Čokorilo and Milica Milovanović
Mathematics 2024, 12(8), 1250; https://doi.org/10.3390/math12081250 - 20 Apr 2024
Viewed by 442
Abstract
Drone delivery in city logistics is gaining attention due to road congestion, environmental threats, etc. However, there are risks associated with using drones which can result in hazardous events, such as conflicts in the air, loss of control, and system failures. It is [...] Read more.
Drone delivery in city logistics is gaining attention due to road congestion, environmental threats, etc. However, there are risks associated with using drones which can result in hazardous events, such as conflicts in the air, loss of control, and system failures. It is crucial to assess the risks involved in using different types of drones and choose the option with the lowest risk. The existence of different criteria important for this decision imposes the need to apply the multi-criteria decision-making (MCDM) method(s). This paper proposes a new hybrid model that combines the fuzzy Factor Relationship (FARE) method for obtaining the criteria weights and the Axial Distance-based Aggregated Measurement (ADAM) method for obtaining the final ranking of the alternatives. A single-rotor microdrone weighing up to 4.4 lb was chosen as the optimal solution, and after that, the most favorable are also the drones of this size (multi-rotor and fixed-wing microdrones). The establishment of a novel hybrid MCDM model, the identified risks, the set of criteria for evaluating the least risky drones, and the framework for prioritizing the drones are the main novelties and contributions of the paper. Full article
(This article belongs to the Special Issue Fuzzy Logic Applications in Traffic and Transportation Engineering)
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29 pages, 749 KiB  
Article
Escaping Stagnation through Improved Orca Predator Algorithm with Deep Reinforcement Learning for Feature Selection
by Rodrigo Olivares, Camilo Ravelo, Ricardo Soto and Broderick Crawford
Mathematics 2024, 12(8), 1249; https://doi.org/10.3390/math12081249 - 20 Apr 2024
Cited by 1 | Viewed by 369
Abstract
Stagnation at local optima represents a significant challenge in bio-inspired optimization algorithms, often leading to suboptimal solutions. This paper addresses this issue by proposing a hybrid model that combines the Orca predator algorithm with deep Q-learning. The Orca predator algorithm is an optimization [...] Read more.
Stagnation at local optima represents a significant challenge in bio-inspired optimization algorithms, often leading to suboptimal solutions. This paper addresses this issue by proposing a hybrid model that combines the Orca predator algorithm with deep Q-learning. The Orca predator algorithm is an optimization technique that mimics the hunting behavior of orcas. It solves complex optimization problems by exploring and exploiting search spaces efficiently. Deep Q-learning is a reinforcement learning technique that combines Q-learning with deep neural networks. This integration aims to turn the stagnation problem into an opportunity for more focused and effective exploitation, enhancing the optimization technique’s performance and accuracy. The proposed hybrid model leverages the biomimetic strengths of the Orca predator algorithm to identify promising regions nearby in the search space, complemented by the fine-tuning capabilities of deep Q-learning to navigate these areas precisely. The practical application of this approach is evaluated using the high-dimensional Heartbeat Categorization Dataset, focusing on the feature selection problem. This dataset, comprising complex electrocardiogram signals, provided a robust platform for testing the feature selection capabilities of our hybrid model. Our experimental results are encouraging, showcasing the hybrid strategy’s capability to identify relevant features without significantly compromising the performance metrics of machine learning models. This analysis was performed by comparing the improved method of the Orca predator algorithm against its native version and a set of state-of-the-art algorithms. Full article
(This article belongs to the Special Issue Evolutionary Computation and Applications)
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25 pages, 934 KiB  
Article
Tampered Random Variable Analysis in Step-Stress Testing: Modeling, Inference, and Applications
by Hanan Haj Ahmad, Dina A. Ramadan and Ehab M. Almetwally
Mathematics 2024, 12(8), 1248; https://doi.org/10.3390/math12081248 - 20 Apr 2024
Viewed by 341
Abstract
This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple [...] Read more.
This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method’s validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis. Full article
(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling)
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26 pages, 2893 KiB  
Article
Fractional-Order Sliding Mode Observer for Actuator Fault Estimation in a Quadrotor UAV
by Vicente Borja-Jaimes, Antonio Coronel-Escamilla, Ricardo Fabricio Escobar-Jiménez, Manuel Adam-Medina, Gerardo Vicente Guerrero-Ramírez, Eduardo Mael Sánchez-Coronado and Jarniel García-Morales
Mathematics 2024, 12(8), 1247; https://doi.org/10.3390/math12081247 - 20 Apr 2024
Viewed by 602
Abstract
In this paper, we present the design of a fractional-order sliding mode observer (FO-SMO) for actuator fault estimation in a quadrotor unmanned aerial vehicle (QUAV) system. Actuator faults can significantly compromise the stability and performance of QUAV systems; therefore, early detection and compensation [...] Read more.
In this paper, we present the design of a fractional-order sliding mode observer (FO-SMO) for actuator fault estimation in a quadrotor unmanned aerial vehicle (QUAV) system. Actuator faults can significantly compromise the stability and performance of QUAV systems; therefore, early detection and compensation are crucial. Sliding mode observers (SMOs) have recently demonstrated their accuracy in estimating faults in QUAV systems under matched uncertainties. However, existing SMOs encounter difficulties associated with chattering and sensitivity to initial conditions and noise. These challenges significantly impact the precision of fault estimation and may even render fault estimation impossible depending on the magnitude of the fault. To address these challenges, we propose a new fractional-order SMO structure based on the Caputo derivative definition. To demonstrate the effectiveness of the proposed FO-SMO in overcoming the limitations associated with classical SMOs, we assess the robustness of the FO-SMO under three distinct scenarios. First, we examined its performance in estimating actuator faults under varying initial conditions. Second, we evaluated its ability to handle significant chattering phenomena during fault estimation. Finally, we analyzed its performance in fault estimation under noisy conditions. For comparison purposes, we assess the performance of both observers using the Normalized Root-Mean-Square Error (NRMSE) criterion. The results demonstrate that our approach enables more accurate actuator fault estimation, particularly in scenarios involving chattering phenomena and noise. In contrast, the performance of classical (non-fractional) SMO suffers significantly under these conditions. We concluded that our FO-SMO is more robust to initial conditions, chattering phenomena, and noise than the classical SMO. Full article
(This article belongs to the Special Issue Control Theory and Computational Intelligence)
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23 pages, 615 KiB  
Article
Comparison of MOEAs in an Optimization-Decision Methodology for a Joint Order Batching and Picking System
by Fabio Maximiliano Miguel, Mariano Frutos, Máximo Méndez, Fernando Tohmé and Begoña González
Mathematics 2024, 12(8), 1246; https://doi.org/10.3390/math12081246 - 19 Apr 2024
Viewed by 410
Abstract
This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve [...] Read more.
This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area. Full article
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26 pages, 7688 KiB  
Article
Bidirectional Tracking Method for Construction Workers in Dealing with Identity Errors
by Yongyue Liu, Yaowu Wang and Zhenzong Zhou
Mathematics 2024, 12(8), 1245; https://doi.org/10.3390/math12081245 - 19 Apr 2024
Viewed by 472
Abstract
Online multi-object tracking (MOT) techniques are instrumental in monitoring workers’ positions and identities in construction settings. Traditional approaches, which employ deep neural networks (DNNs) for detection followed by body similarity matching, often overlook the significance of clear head features and stable head motions. [...] Read more.
Online multi-object tracking (MOT) techniques are instrumental in monitoring workers’ positions and identities in construction settings. Traditional approaches, which employ deep neural networks (DNNs) for detection followed by body similarity matching, often overlook the significance of clear head features and stable head motions. This study presents a novel bidirectional tracking method that integrates intra-frame processing, which combines head and body analysis to minimize false positives and inter-frame matching to control ID assignment. By leveraging head information for enhanced body tracking, the method generates smoother trajectories with reduced ID errors. The proposed method achieved a state-of-the-art (SOTA) performance, with a multiple-object tracking accuracy (MOTA) of 95.191%, higher-order tracking accuracy (HOTA) of 78.884% and an identity switch (IDSW) count of 0, making it a strong baseline for future research. Full article
(This article belongs to the Section Mathematics and Computer Science)
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25 pages, 6916 KiB  
Article
Spatial Constraints on Economic Interactions: A Complexity Approach to the Japanese Inter-Firm Trade Network
by Eduardo Viegas, Orr Levy, Shlomo Havlin, Hideki Takayasu and Misako Takayasu
Mathematics 2024, 12(8), 1244; https://doi.org/10.3390/math12081244 - 19 Apr 2024
Viewed by 464
Abstract
The trade distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. However, agent-based studies supported by the granular analysis of distances are limited. Here, we present a complexity method that places the actual geographical locations [...] Read more.
The trade distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. However, agent-based studies supported by the granular analysis of distances are limited. Here, we present a complexity method that places the actual geographical locations of individual firms in Japan at the epicentre of our research. By combining methods derived from network science together with information theory measures, and by using a comprehensive dataset of Japanese inter-firm business transactions, we evaluate the effects of spatial features on the structural patterns of the economy. We find that the normalised probability distributions of the distances between interacting firms obey a power law like decay concomitant with the sizes of firms and regions. Furthermore, small firms would reach large distances to become customers of large firms, while trading between either only small firms or only large firms tends to be at smaller distances. Furthermore, a time evolution analysis suggests a reduction in the overall average trading distances in last 20 years. Lastly, our analysis concerning the trading dynamics among prefectures indicates that the preference to trade with neighbouring prefectures tends to be more pronounced at rural regions as opposed to the larger central conurbations. Full article
(This article belongs to the Special Issue Modeling Real-World Problems Using Complex Networks)
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19 pages, 4037 KiB  
Article
Blockchain-Enabled Utility Optimization for Supply Chain Finance: An Evolutionary Game and Smart Contract Based Approach
by Shenghua Wang, Mengjie Zhou and Sunan Xiang
Mathematics 2024, 12(8), 1243; https://doi.org/10.3390/math12081243 - 19 Apr 2024
Viewed by 570
Abstract
In recent years, blockchain technology has attracted substantial interest for its capability to transform supply chain management and finance. This paper employs evolutionary game theory to investigate the application of blockchain in mitigating financial risks within supply chains, taking into account the technology’s [...] Read more.
In recent years, blockchain technology has attracted substantial interest for its capability to transform supply chain management and finance. This paper employs evolutionary game theory to investigate the application of blockchain in mitigating financial risks within supply chains, taking into account the technology’s maturity and the risk preferences of financial institutions. By modeling interactions among financial institutions, small and medium enterprises (SMEs), and core enterprises within the accounts receivable financing framework, this study evaluates blockchain’s impact on their decision-making and its efficacy in risk reduction. Our findings suggest the transformative potential of blockchain in mitigating financial risks, solving information asymmetry, and enhancing collaboration between financial entities and SMEs. Additionally, we integrate smart contracts into supply chain finance, proposing pragmatic procedures for their deployment in real-world contexts. Via a detailed examination of blockchain’s maturity and financial institutions’ risk preferences, this research demonstrates the primary determinants of strategic decisions in supply chain finance and underscores how blockchain technology fosters system stability using risk mitigation. Our innovative contribution lies in the design of smart contracts for the ARF process, rooted in blockchain’s core attributes of security, transparency, and immutability, thereby ensuring efficient operation and cost reduction in supply chain finance. Full article
(This article belongs to the Special Issue Modeling and Simulation Analysis of Blockchain System)
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13 pages, 250 KiB  
Article
Bridging the p-Special Functions between the Generalized Hyperbolic and Trigonometric Families
by Ali Hamzah Alibrahim and Saptarshi Das
Mathematics 2024, 12(8), 1242; https://doi.org/10.3390/math12081242 - 19 Apr 2024
Viewed by 495
Abstract
Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We [...] Read more.
Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We show the relationship of these two classes of special functions viz. p-trigonometric and p-hyperbolic functions with imaginary arguments. We also show many properties and identities related to the analogy between these two groups of functions. Further, we extend the research bridging the concepts of hyperbolic and elliptical complex numbers to show the properties of logarithmic functions with complex arguments. Full article
25 pages, 3002 KiB  
Article
Modeling the Propagation of Infectious Diseases across the Air Transport Network: A Bayesian Approach
by Pablo Quirós Corte, Javier Cano, Eduardo Sánchez Ayra, Chaitanya Joshi and Víctor Fernando Gómez Comendador
Mathematics 2024, 12(8), 1241; https://doi.org/10.3390/math12081241 - 19 Apr 2024
Viewed by 539
Abstract
The COVID-19 pandemic, caused by the SARS-CoV-2 virus, continues to impact the world even three years after its outbreak. International border closures and health alerts severely affected the air transport industry, resulting in substantial financial losses. This study analyzes the global data on [...] Read more.
The COVID-19 pandemic, caused by the SARS-CoV-2 virus, continues to impact the world even three years after its outbreak. International border closures and health alerts severely affected the air transport industry, resulting in substantial financial losses. This study analyzes the global data on infected individuals alongside aircraft types, flight durations, and passenger flows. Using a Bayesian framework, we forecast the risk of infection during commercial flights and its potential spread across an air transport network. Our model allows us to explore the effect of mitigation measures, such as closing individual routes or airports, reducing aircraft occupancy, or restricting access for infected passengers, on disease propagation, while allowing the air industry to operate at near-normal levels. Our novel approach combines dynamic network modeling with discrete event simulation. A real-case study at major European hubs illustrates our methodology. Full article
(This article belongs to the Special Issue Statistical and Mathematical Modelling of Infectious Diseases)
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