Mathematics

18 pages, 8241 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 924

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 2507

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 2 | Viewed by 1017

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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20 pages, 1888 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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

Viewed by 1002

Abstract

We investigate the divisibility properties of the tensor products

Λ_{t}^{(1)} \otimes Λ_{t}^{(2)}

of open quantum dynamics

Λ_{t}^{(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

Λ_{t}^{(1)} \otimes Λ_{t}^{(2)}

of open quantum dynamics

Λ_{t}^{(1, 2)}

with time-dependent generators. These dynamical maps emerge from a compound open system

S_{1} + S_{2}

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

S_{1} + S_{2}

without the same phenomenon occurring for either

S_{1}

and

S_{2}

. 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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42 pages, 9281 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1361

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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18 pages, 358 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 739

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 2 | Viewed by 974

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

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

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17 pages, 2459 KiB

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 702

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 4 | Viewed by 1518

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

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1340

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 4 | Viewed by 2730

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

(This article belongs to the Special Issue Artificial Intelligence and Algorithms in Intelligent Systems for Augmented Human)

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19 pages, 329 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 2 | Viewed by 1079

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

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1118

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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

Viewed by 1226

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

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 946

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 877

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

(This article belongs to the Special Issue New Trends in Graph and Complexity Based Data Analysis and Processing, 2nd Edition)

26 pages, 6683 KiB

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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 5 | Viewed by 2171

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

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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

Viewed by 738

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

a_{2} > 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

a_{2} > 0

and without imposing any restrictive growth assumption on the damping term

f_{1},

using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function

ψ

, namely

ψ^{'} (t) \leq - 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

f_{0}

, which characterizes the growth behavior of

f_{1}

at the origin. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations)

16 pages, 398 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1382

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1058

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1007

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 901

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

(This article belongs to the Special Issue Recent Advances in Numerical Methods for Scientific and Engineering Applications, 2nd Edition)

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45 pages, 5204 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1218

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1494

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

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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 794

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 3 | Viewed by 1331

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 771

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 4 | Viewed by 1039

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

(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)

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15 pages, 321 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 928

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

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

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 1 | Viewed by 973

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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15 pages, 4185 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control

by Yi Liang, Yunyun Deng and Chuan Zhang

Mathematics 2023, 11(16), 3543; https://doi.org/10.3390/math11163543 - 16 Aug 2023

Cited by 4 | Viewed by 903

Abstract

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response [...] Read more.

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes. Full article

(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)

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13 pages, 295 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Fuzzy Metrics in Terms of Fuzzy Relations

by Olga Grigorenko and Alexander Šostak

Mathematics 2023, 11(16), 3528; https://doi.org/10.3390/math11163528 - 15 Aug 2023

Cited by 1 | Viewed by 1036

Abstract

In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order relations. Further, we [...] Read more.

In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order relations. Further, we explore the criteria that crisp relations must satisfy in order to determine a crisp metric. Subsequently, we extend these conditions to obtain a fuzzy metric and investigate the additional axioms involved. Additionally, we introduce the definition of an extensional fuzzy metric or E-d-metric, which is a fuzzification of the expression

d (x, y) = t

. Thus, we examine fuzzy metrics from both the linear order and from the equivalence relation perspectives, where one argument is a value

d (x, y)

and the other is a number within the range

[0, + \infty)

. Full article

(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures, 2nd Edition)

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21 pages, 386 KiB

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Optimization Models for the Vehicle Routing Problem under Disruptions

by Kai Huang and Michael Xu

Mathematics 2023, 11(16), 3521; https://doi.org/10.3390/math11163521 - 15 Aug 2023

Cited by 2 | Viewed by 1494

Abstract

In this paper, we study the role of disruptions in the multi-period vehicle routing problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that at any time during the delivery phase, each vehicle could have chance to be disrupted. [...] Read more.

In this paper, we study the role of disruptions in the multi-period vehicle routing problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that at any time during the delivery phase, each vehicle could have chance to be disrupted. When a disruption happens, vehicles will be unable to continue their journeys and supplies will be unable to be delivered. We model the occurrence of disruption as a given probability and consider the multi-period expected delivery. Our objective is to either minimize the total travel cost or maximize the demand fulfillment, depending on the supply quantity. This problem is denoted as the multi-period vehicle routing problem with disruption (VRPMD). VRPMD does not deal with disruptions in real-time and is more focused on the long-term performance of a single routing plan. We first prove that the proposed VRPMD problems are NP-hard. We then present some analytical properties related to the optimal solutions to these problems. We show that Dror and Trudeau’s property does not apply in our problem setting. Nevertheless, a generalization of Dror and Trudeau’s property holds. Finally, we present efficient heuristic algorithms to solve these problems and show the effectiveness of the proposed models and algorithms through numerical studies. Full article

(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)

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23 pages, 544 KiB

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A Binary Black Widow Optimization Algorithm for Addressing the Cell Formation Problem Involving Alternative Routes and Machine Reliability

by Paulo Figueroa-Torrez, Orlando Durán, Broderick Crawford and Felipe Cisternas-Caneo

Mathematics 2023, 11(16), 3475; https://doi.org/10.3390/math11163475 - 11 Aug 2023

Cited by 5 | Viewed by 1115

Abstract

The Cell Formation Problem (CFP) involves the clustering of machines to enhance productivity and capitalize on various benefits. This study addresses a variant of the problem where alternative routes and machine reliability are included, which we call a Generalized Cell Formation Problem with [...] Read more.

The Cell Formation Problem (CFP) involves the clustering of machines to enhance productivity and capitalize on various benefits. This study addresses a variant of the problem where alternative routes and machine reliability are included, which we call a Generalized Cell Formation Problem with Machine Reliability (GCFP-MR). This problem is known to be NP-Hard, and finding efficient solutions is of utmost importance. Metaheuristics have been recognized as effective optimization techniques due to their adaptability and ability to generate high-quality solutions in a short time. Since BWO was originally designed for continuous optimization problems, its adaptation involves binarization. Accordingly, our proposal focuses on adapting the Black Widow Optimization (BWO) metaheuristic to tackle GCFP-MR, leading to a new approach named Binary Black Widow Optimization (B-BWO). We compare our proposal in two ways. Firstly, it is benchmarked against a previous Clonal Selection Algorithm approach. Secondly, we evaluate B-BWO with various parameter configurations. The experimental results indicate that the best configuration of parameters includes a population size

(P o p)

set to 100, and the number of iterations

(M a x_{i} t e r)

defined as 75. Procreating Rate

(P R)

is set at 0.8, Cannibalism Rate

(C R)

is set at 0.4, and the Mutation Rate

(P M)

is also set at 0.4. Significantly, the proposed B-BWO outperforms the state-of-the-art literature’s best result, achieving a noteworthy improvement of 1.40%. This finding reveals the efficacy of B-BWO in solving GCFP-MR and its potential to produce superior solutions compared to alternative methods. Full article

(This article belongs to the Special Issue Recent Advances in Computational Intelligence Methodologies for Industries)

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29 pages, 618 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing

by Kevin Wils and Boyang Chen

Mathematics 2023, 11(16), 3451; https://doi.org/10.3390/math11163451 - 9 Aug 2023

Cited by 5 | Viewed by 1149

Abstract

With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem [...] Read more.

With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem is the discrete truss sizing problem—the goal is to select the best size for each truss member so as to minimize a stress-based objective function. To make the problem compatible with quantum annealing devices, the objective function must be translated into a quadratic unconstrained binary optimization (QUBO) form. This work focuses on exploring the feasibility of making this translation. The practicality of using a quantum annealer for such optimization problems is also assessed. A method is eventually established to translate the objective function into a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger problems faces some challenges that would require further research to address. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

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26 pages, 424 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

A New Instrumental-Type Estimator for Quantile Regression Models

by Li Tao, Lingnan Tai, Manling Qian and Maozai Tian

Mathematics 2023, 11(15), 3412; https://doi.org/10.3390/math11153412 - 4 Aug 2023

Cited by 1 | Viewed by 954

Abstract

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The [...] Read more.

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures. Full article

(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)

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27 pages, 872 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Machine Learning Alternatives to Response Surface Models

by Badih Ghattas and Diane Manzon

Mathematics 2023, 11(15), 3406; https://doi.org/10.3390/math11153406 - 4 Aug 2023

Cited by 5 | Viewed by 2022

Abstract

In the Design of Experiments, we seek to relate response variables to explanatory factors. Response Surface methodology (RSM) approximates the relation between output variables and a polynomial transform of the explanatory variables using a linear model. Some researchers have tried to adjust other [...] Read more.

In the Design of Experiments, we seek to relate response variables to explanatory factors. Response Surface methodology (RSM) approximates the relation between output variables and a polynomial transform of the explanatory variables using a linear model. Some researchers have tried to adjust other types of models, mainly nonlinear and nonparametric. We present a large panel of Machine Learning approaches that may be good alternatives to the classical RSM approximation. The state of the art of such approaches is given, including classification and regression trees, ensemble methods, support vector machines, neural networks and also direct multi-output approaches. We survey the subject and illustrate the use of ten such approaches using simulations and a real use case. In our simulations, the underlying model is linear in the explanatory factors for one response and nonlinear for the others. We focus on the advantages and disadvantages of the different approaches and show how their hyperparameters may be tuned. Our simulations show that even when the underlying relation between the response and the explanatory variables is linear, the RSM approach is outperformed by the direct neural network multivariate model, for any sample size (<50) and much more for very small samples (15 or 20). When the underlying relation is nonlinear, the RSM approach is outperformed by most of the machine learning approaches for small samples (n ≤ 30). Full article

(This article belongs to the Section Probability and Statistics)

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21 pages, 3355 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceReview

Advancements in Phase-Field Modeling for Fracture in Nonlinear Elastic Solids under Finite Deformations

by Gang Zhang, Cheng Tang, Peng Chen, Gongbo Long, Jiyin Cao and Shan Tang

Mathematics 2023, 11(15), 3366; https://doi.org/10.3390/math11153366 - 1 Aug 2023

Cited by 3 | Viewed by 1926

Abstract

The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the [...] Read more.

The prediction of failure mechanisms in nonlinear elastic materials holds significant importance in engineering applications. In recent years, the phase-field model has emerged as an effective approach for addressing fracture problems. Compared with other discontinuous fracture methods, the phase-field method allows for the easy simulation of complex fracture paths, including crack initiation, propagation, coalescence, and branching phenomena, through a scalar field known as the phase field. This method offers distinct advantages in tackling complex fracture problems in nonlinear elastic materials and exhibits substantial potential in material design and manufacturing. The current research has indicated that the energy distribution method employed in phase-field approaches significantly influences the simulated results of material fracture, such as crack initiation load, crack propagation path, crack branching, and so forth. This impact is particularly pronounced when simulating the fracture of nonlinear materials under finite deformation. Therefore, this review outlines various strain energy decomposition methods proposed by researchers for phase-field models of fracture in tension–compression symmetric nonlinear elastic materials. Additionally, the energy decomposition model for tension–compression asymmetric nonlinear elastic materials is also presented. Moreover, the fracture behavior of hydrogels is investigated through the application of the phase-field model with energy decomposition. In addition to summarizing the research on these types of nonlinear elastic body fractures, this review presents numerical benchmark examples from relevant studies to assess and validate the accuracy and effectiveness of the methods presented. Full article

(This article belongs to the Special Issue Recent Development and Application of Methods in Computational Mechanics)

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25 pages, 1124 KiB

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

An Inhomogeneous Model for Laser Welding of Industrial Interest

by Carmelo Filippo Munafò, Annunziata Palumbo and Mario Versaci

Mathematics 2023, 11(15), 3357; https://doi.org/10.3390/math11153357 - 31 Jul 2023

Cited by 9 | Viewed by 1415

Abstract

An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si

5 %

alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is [...] Read more.

An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si

5 %

alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer. Full article

(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)

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21 pages, 2650 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

A Methodology for Planning City Logistics Concepts Based on City-Dry Port Micro-Consolidation Centres

by Milovan Kovač, Snežana Tadić, Mladen Krstić and Miloš Veljović

Mathematics 2023, 11(15), 3347; https://doi.org/10.3390/math11153347 - 31 Jul 2023

Cited by 8 | Viewed by 1257

Abstract

The purpose of this study is to conceptualize a novel idea of potentially sustainable city logistics concepts—the development of urban consolidation centers (UCCs) on riverbanks and the establishment of city-dry port (DP) micro-consolidation centers (MCCs) as their displaced subsystems within the delivery zone. [...] Read more.

The purpose of this study is to conceptualize a novel idea of potentially sustainable city logistics concepts—the development of urban consolidation centers (UCCs) on riverbanks and the establishment of city-dry port (DP) micro-consolidation centers (MCCs) as their displaced subsystems within the delivery zone. The concept enables the application of river transportation in delivering goods to the UCC, where the modal shift to electric delivery vehicles takes place for delivering goods to city-DP MCCs. In the final delivery phase (from city-DP MCCs to flow generators), smaller eco-vehicles are utilized. An innovative methodology for the planning and selection of the most sustainable concept variant is developed. The methodology combines mathematical programming and the axial-distance-based aggregated measurement (ADAM) multi-criteria decision-making (MCDM) method. The application of the defined approach is demonstrated in a case study inspired by Belgrade, Serbia. The theoretical contribution of this study is in demonstrating how a wide set of potentially viable city logistics concepts can be defined, starting from an initial idea (city-DP MCC). The practical contribution lies in developing a robust methodology that considers all relevant tactical and operational-level planning questions and takes into account qualitative and quantitative criteria in evaluating different concept variants. Full article

(This article belongs to the Special Issue Mathematical Optimization and Decision Making)

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25 pages, 6506 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

An Improved Strength Pareto Evolutionary Algorithm 2 with Adaptive Crossover Operator for Bi-Objective Distributed Unmanned Aerial Vehicle Delivery

by Yu Song and Xi Fang

Mathematics 2023, 11(15), 3327; https://doi.org/10.3390/math11153327 - 28 Jul 2023

Cited by 3 | Viewed by 1123

Abstract

With the development of the e-commerce industry, using UAVs (unmanned aerial vehicles) to deliver goods has become more popular in transportation systems. This delivery method can reduce labor costs and improve the distribution efficiency, and UAVs can reach places that are difficult for [...] Read more.

With the development of the e-commerce industry, using UAVs (unmanned aerial vehicles) to deliver goods has become more popular in transportation systems. This delivery method can reduce labor costs and improve the distribution efficiency, and UAVs can reach places that are difficult for humans to reach. Because some goods are perishable, the quality of the delivery will have an impact on the customer satisfaction. At the same time, the delivery time should also meet the needs of customers as much as possible. Therefore, this paper takes the distribution distance and customer satisfaction as the objective functions, establishes a bi-objective dynamic programming model, and proposes an improved SPEA2 (strength Pareto evolutionary algorithm 2). The improved algorithm introduces the local search strategy, on the basis of the original algorithm. It conducts a local search for the better non-dominated solutions obtained in each iteration. The new dominated solutions and non-dominated solutions are determined, and the crossover operator is improved, so that the local search ability is improved, on the basis of ensuring its global search ability. The numerical experiment results show that the improved algorithm achieves an excellent performance in three aspects: the Pareto front, generation distance, and spacing, and would have a high application value in UAV cargo delivery and other MOPs (multi-objective optimization problems). The average spacing value of the improved algorithm is more than 20% smaller than SPEA2 + SDE (strength Pareto evolution algorithm 2–shift-based density estimation), which is the second-best algorithm. In the comparison of the average generation distance value, this number reaches 30%. Full article

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

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24 pages, 368 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Two-Round Multi-Signatures from Okamoto Signatures

by Kwangsu Lee and Hyoseung Kim

Mathematics 2023, 11(14), 3223; https://doi.org/10.3390/math11143223 - 22 Jul 2023

Cited by 4 | Viewed by 1193

Abstract

Multi-signatures (MS) are a special type of public-key signature (PKS) in which multiple signers participate cooperatively to generate a signature for a single message. Recently, applications that use an MS scheme to strengthen the security of blockchain wallets or to strengthen the security [...] Read more.

Multi-signatures (MS) are a special type of public-key signature (PKS) in which multiple signers participate cooperatively to generate a signature for a single message. Recently, applications that use an MS scheme to strengthen the security of blockchain wallets or to strengthen the security of blockchain consensus protocols are attracting a lot of attention. In this paper, we propose an efficient two-round MS scheme based on Okamoto signatures rather than Schnorr signatures. To this end, we first propose a new PKS scheme by modifying the Okamoto signature scheme and prove the unforgeability of our PKS scheme under the discrete logarithm assumption in the algebraic group model (AGM) and the non-programmable random oracle model (ROM). Next, we propose a two-round MS scheme based on the new PKS scheme and prove the unforgeability of our MS scheme under the discrete logarithm assumption in the AGM and the non-programmable ROM. Our MS scheme is the first one to prove security among two-round MS based on Okamoto signatures. Full article

(This article belongs to the Special Issue Advances in Cryptography and Blockchain: Mathematics for Healthcare Security)

11 pages, 1262 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense

by Zhao Li and Chen Peng

Mathematics 2023, 11(14), 3185; https://doi.org/10.3390/math11143185 - 20 Jul 2023

Cited by 9 | Viewed by 751

Abstract

The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear systems. Firstly, a two-dimensional dynamics system and [...] Read more.

The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities in the Itô sense, which can further help researchers understand the propagation of soliton nonlinear systems. Firstly, a two-dimensional dynamics system and its perturbation system are obtained by using a traveling wave transformation. Secondly, the phase portraits of the two-dimensional dynamics system are plotted. Furthermore, the chaotic behavior, two-dimensional phase portraits, three-dimensional phase portraits and sensitivity of the perturbation system are analyzed via Maple software. Finally, the embedded solitons of stochastic quadratic and cubic nonlinear susceptibilities are obtained. Moreover, three-dimensional and two-dimensional solitons of stochastic quadratic and cubic nonlinear susceptibilities are plotted. Full article

(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering, 2nd Edition)

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21 pages, 9043 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science

by Sondos M. Syam, Z. Siri, Sami H. Altoum and R. Md. Kasmani

Mathematics 2023, 11(14), 3132; https://doi.org/10.3390/math11143132 - 16 Jul 2023

Cited by 8 | Viewed by 1165

Abstract

In this article, we present a new numerical approach for solving a class of systems of fractional initial value problems based on the operational matrix method. We derive the method and provide a convergence analysis. To reduce computational cost, we transform the algebraic [...] Read more.

In this article, we present a new numerical approach for solving a class of systems of fractional initial value problems based on the operational matrix method. We derive the method and provide a convergence analysis. To reduce computational cost, we transform the algebraic problem produced by this approach into a set of

2 \times 2

nonlinear equations, instead of solving a system of 2 m × 2 m equations. We apply our approach to three main applications in science: optimal control problems, Riccati equations, and clock reactions. We compare our results with those of other researchers, considering computational time, cost, and absolute errors. Additionally, we validate our numerical method by comparing our results with the integer model when the fractional order approaches one. We present numerous figures and tables to illustrate our findings. The results demonstrate the effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Recent Advances in Theoretical and Numerical Analysis for Fractional and Integral Differential Equations)

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29 pages, 13241 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

by Zhixuan Xu and Minghui Qian

Mathematics 2023, 11(14), 3059; https://doi.org/10.3390/math11143059 - 11 Jul 2023

Cited by 5 | Viewed by 2836

Abstract

The viral spread of online content can lead to unexpected consequences such as extreme opinions about a brand or consumers’ enthusiasm for a product. This makes the prediction of viral content’s future popularity an important problem, especially for digital marketers, as well as [...] Read more.

The viral spread of online content can lead to unexpected consequences such as extreme opinions about a brand or consumers’ enthusiasm for a product. This makes the prediction of viral content’s future popularity an important problem, especially for digital marketers, as well as for managers of social platforms. It is not surprising that conventional methods, which heavily rely on either hand-crafted features or unrealistic assumptions, are insufficient in dealing with this challenging problem. Even state-of-art graph-based approaches are either inefficient to work with large-scale cascades or unable to explain what spread mechanisms are learned by the model. This paper presents a temporal-spatial cascade convolutional learning framework called ViralGCN, not only to address the challenges of existing approaches but also to try to provide some insights into actual mechanisms of viral spread from the perspective of artificial intelligence. We conduct experiments on the real-world dataset (i.e., to predict the retweet popularity of micro-blogs on Weibo). Compared to the existing approaches, ViralGCN possesses the following advantages: the flexible size of the input cascade graph, a coherent method for processing both structural and temporal information, and an intuitive and interpretable deep learning architecture. Moreover, the exploration of the learned features also provides valuable clues for managers to understand the elusive mechanisms of viral spread as well as to devise appropriate strategies at early stages. By using the visualization method, our approach finds that both broadcast and structural virality contribute to online content going viral; the cascade with a gradual descent or ascent-then-descent evolving pattern at the early stage is more likely to gain significant eventual popularity, and even the timing of users participating in the cascade has an effect on future popularity growth. Full article

(This article belongs to the Special Issue Artificial Intelligence and Data Science)

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20 pages, 331 KiB

Open AccessFeature PaperMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes

by Emel Savku

Mathematics 2023, 11(14), 3043; https://doi.org/10.3390/math11143043 - 9 Jul 2023

Cited by 8 | Viewed by 1407

Abstract

We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context, we prove corresponding theorems [...] Read more.

We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal control setting and a Lagrangian method. In this context, we prove corresponding theorems for two different types of constraints, which lead us to find real-valued and stochastic Lagrange multipliers, respectively. Then, we illustrate our results for a nonzero-sum game problem with the stochastic maximum principle technique. Our application is an example of cooperation between a bank and an insurance company, which is a popular, well-known business agreement type called Bancassurance. Full article

(This article belongs to the Special Issue Stochastic Analysis and Applications in Financial Mathematics)

19 pages, 4540 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Numerical Solution of Thermal Phenomena in Welding Problems

by Mario Freire-Torres, Manuel Colera and Jaime Carpio

Mathematics 2023, 11(13), 3009; https://doi.org/10.3390/math11133009 - 6 Jul 2023

Viewed by 1293

Abstract

We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and [...] Read more.

We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and non-isothermal melting models are considered to relate the enthalpy with the temperature. Quadratic triangular elements with local anisotropic mesh adaptation are employed for the space discretization of the governing equation, and a second-order backward differentiation formula is employed for the time discretization. The resulting non-linear discretized system is solved with a simple Newton algorithm with two versions: the

θ

-Newton algorithm, which considers the temperature as the main unknown variable, as in most works in the literature, and the h-Newton algorithm, which considers the enthalpy, which is the main novelty of the present work. Then, we show via numerical experiments that the h-Newton method is robust and converges well to the solution, both for isothermal and non-isothermal melting. However, the

θ

-method can only be applied to the case of non-isothermal melting and converges only for a sufficiently large melting temperature range or sufficiently small time step. Numerical experiments also confirm that the method is able to adequately capture the discontinuities or sharp variations in the solution without the need for any kind of numerical dissipation. Full article

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36 pages, 537 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceReview

Set-Based Particle Swarm Optimisation: A Review

by Jean-Pierre van Zyl and Andries Petrus Engelbrecht

Mathematics 2023, 11(13), 2980; https://doi.org/10.3390/math11132980 - 4 Jul 2023

Cited by 14 | Viewed by 1984

Abstract

The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that has gained popularity in recent years. In contrast to the original particle swarm optimisation algorithm, the set-based particle swarm optimisation algorithm is used to solve discrete and combinatorial optimisation problems. The main [...] Read more.

The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that has gained popularity in recent years. In contrast to the original particle swarm optimisation algorithm, the set-based particle swarm optimisation algorithm is used to solve discrete and combinatorial optimisation problems. The main objective of this paper is to review the set-based particle swarm optimisation algorithm and to provide an overview of the problems to which the algorithm has been applied. This paper starts with an examination of previous attempts to create a set-based particle swarm optimisation algorithm and discusses the shortcomings of the existing attempts. The set-based particle swarm optimisation algorithm is established as the only suitable particle swarm variant that is both based on true set theory and does not require problem-specific modifications. In-depth explanations are given regarding the general position and velocity update equations, the mechanisms used to control the exploration–exploitation trade-off, and the quantifiers of swarm diversity. After the various existing applications of set-based particle swarm optimisation are presented, this paper concludes with a discussion on potential future research. Full article

(This article belongs to the Special Issue Combinatorial Optimization: Trends and Applications)

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10 pages, 264 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Some Double q-Series by Telescoping

by Kwang-Wu Chen

Mathematics 2023, 11(13), 2949; https://doi.org/10.3390/math11132949 - 1 Jul 2023

Cited by 1 | Viewed by 733

Abstract

By means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values

ζ (s)

, the Catalan constant G,

\log (2)

,

π

and several other significant mathematical constants. Full article

24 pages, 517 KiB

Open AccessMore Editor’s choice articles in journal Mathematics.">Editor’s ChoiceArticle

Stability and Bifurcations in a Nutrient–Phytoplankton–Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution

by Mihaela Sterpu, Carmen Rocşoreanu, Raluca Efrem and Sue Ann Campbell

Mathematics 2023, 11(13), 2911; https://doi.org/10.3390/math11132911 - 28 Jun 2023

Viewed by 1651

Abstract

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates a delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The models are described by systems of ordinary differential equations of four and [...] Read more.

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates a delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The models are described by systems of ordinary differential equations of four and five dimensions. The purpose of this study is to investigate how the mean delay of the distribution and the total nutrients affect the stability of the equilibrium solutions. Local stability theory and bifurcation theory are used to determine the long-time dynamics of the models. It is found that both models exhibit comparable qualitative dynamics. There are a maximum of three equilibrium points in each of the two models, and at most one of them is locally asymptotically stable. The change of stability from one equilibrium to another takes place through a transcritical bifurcation. In some hypotheses on the functional response, the nutrient–phytoplankton–zooplankton equilibrium loses stability via a supercritical Hopf bifurcation, causing the apparition of a stable limit cycle. The way in which the results are consistent with prior research and how they extend them is discussed. Finally, various application-related consequences of the results of the theoretical study are deduced. Full article

(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 2nd Edition)

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