Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Real-Time EtherCAT-Based Control Architecture for Electro-Hydraulic Humanoid
Mathematics 2024, 12(9), 1405; https://doi.org/10.3390/math12091405 - 03 May 2024
Abstract
Electro-hydraulic actuators have witnessed significant development over recent years due to their remarkable abilities to perform complex and dynamic movements. Integrating such an actuator in humanoids is highly beneficial, leading to a humanoid capable of performing complex tasks requiring high force. This highlights
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Electro-hydraulic actuators have witnessed significant development over recent years due to their remarkable abilities to perform complex and dynamic movements. Integrating such an actuator in humanoids is highly beneficial, leading to a humanoid capable of performing complex tasks requiring high force. This highlights the importance of safety, especially since high power output and safe interaction seem to be contradictory; the greater the robot’s ability to generate high dynamic movements, the more difficult it is to achieve safety, as this requires managing a large amount of motor energy before, during, and after the collision. No matter what technology or algorithm is used to achieve safety, none can be implemented without a stable control system. Hence, one of the main parameters remains the quality and reliability of the robot’s control architecture through handling a huge amount of data without system failure. This paper addresses the development of a stable control architecture that ensures, in later stages, that the safety algorithm is implemented correctly. The optimum control architecture to utilize and ensure the maximum benefit of electro-hydraulic actuators in humanoid robots is one of the important subjects in this field. For a stable and safe functioning of the humanoid, the development of the control architecture and the communication between the different components should adhere to some requirements such as stability, robustness, speed, and reduced complexity, ensuring the easy addition of numerous components. This paper presents the developed control architecture for an underdeveloped electro-hydraulic actuated humanoid. The proposed solution has the advantage of being a distributed, real-time, open-source, modular, and adaptable control architecture, enabling simple integration of numerous sensors and actuators to emulate human actions and safely interact with them. The contribution of this paper is an enhancement of the updated rate compared to other humanoids by 20% and by 40 % in the latency of the master. The results demonstrate the potential of using EtherCAT fieldbus and open-source software to develop a stable robot control architecture capable of integrating safety and security algorithms in later stages.
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(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 2nd Edition)
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Cooperative Vehicle Infrastructure System or Autonomous Driving System? From the Perspective of Evolutionary Game Theory
by
Wei Bai, Xuguang Wen, Jiayan Zhang and Linheng Li
Mathematics 2024, 12(9), 1404; https://doi.org/10.3390/math12091404 - 03 May 2024
Abstract
In this paper, we explore the trade-offs between public and private investment in autonomous driving technologies. Utilizing an evolutionary game model, we delve into the complex interaction mechanisms between governments and auto manufacturers, focusing on how strategic decisions impact overall outcomes. Specifically, we
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In this paper, we explore the trade-offs between public and private investment in autonomous driving technologies. Utilizing an evolutionary game model, we delve into the complex interaction mechanisms between governments and auto manufacturers, focusing on how strategic decisions impact overall outcomes. Specifically, we predict that governments may opt for strategies such as constructing and maintaining infrastructure for Roadside Infrastructure-based Vehicles (RIVs) or subsidizing high-level Autonomous Driving Vehicles (ADVs) without additional road infrastructure. Manufacturers’ choices involve deciding whether to invest in RIVs or ADVs, depending on governmental policies and market conditions. Our simulation results, based on scenarios derived from existing economic data and forecasts on technology development costs, suggest that government subsidy policies need to dynamically adjust in response to manufacturers’ shifting strategies and market behavior. This dynamic adjustment is crucial as it addresses the evolving economic environment and technological advancements, ensuring that subsidies effectively incentivize the desired outcomes in autonomous vehicle development. The findings of this paper could serve as valuable decision-making tools for governments and auto manufacturers, guiding investment strategies that align with the dynamic landscape of autonomous driving technology.
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(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)
Open AccessArticle
Characterization of Nonlinear Mixed Bi-Skew Lie Triple Derivations on ∗-Algebras
by
Turki Alsuraiheed, Junaid Nisar and Nadeem ur Rehman
Mathematics 2024, 12(9), 1403; https://doi.org/10.3390/math12091403 - 03 May 2024
Abstract
This paper concentrates on examining the characterization of nonlinear mixed bi-skew Lie triple *- derivations within an *-algebra denoted by which contains a nontrivial projection with a unit I. Additionally, we expand this investigation to applications by describing these derivations within
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This paper concentrates on examining the characterization of nonlinear mixed bi-skew Lie triple *- derivations within an *-algebra denoted by which contains a nontrivial projection with a unit I. Additionally, we expand this investigation to applications by describing these derivations within prime *-algebras, von Neumann algebras, and standard operator algebras.
Full article
(This article belongs to the Special Issue Algebraic Analysis and Its Applications)
Open AccessArticle
Power Load Forecast Based on CS-LSTM Neural Network
by
Lijia Han, Xiaohong Wang, Yin Yu and Duan Wang
Mathematics 2024, 12(9), 1402; https://doi.org/10.3390/math12091402 - 03 May 2024
Abstract
Load forecast is the foundation of power system operation and planning. The forecast results can guide the power system economic dispatch and security analysis. In order to improve the accuracy of load forecast, this paper proposes a forecasting model based on the combination
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Load forecast is the foundation of power system operation and planning. The forecast results can guide the power system economic dispatch and security analysis. In order to improve the accuracy of load forecast, this paper proposes a forecasting model based on the combination of the cuckoo search (CS) algorithm and the long short-term memory (LSTM) neural network. Load data are specific data with time series characteristics and periodicity, and the LSTM algorithm can control the information added or discarded through the forgetting gate, so as to realize the function of forgetting or memorizing. Therefore, the use of the LSTM algorithm for load forecast is more effective. The CS algorithm can perform global search better and does not easily fall into local optima. The CS-LSTM forecasting model, where CS algorithm is used to optimize the hyper-parameters of the LSTM model, has a better forecasting effect and is more feasible. Simulation results show that the CS-LSTM model has higher forecasting accuracy than the standard LSTM model, the PSO-LSTM model, and the GA-LSTM model.
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Open AccessArticle
Mixture Differential Cryptanalysis on Round-Reduced SIMON32/64 Using Machine Learning
by
Zehan Wu, Kexin Qiao, Zhaoyang Wang , Junjie Cheng and Liehuang Zhu
Mathematics 2024, 12(9), 1401; https://doi.org/10.3390/math12091401 - 03 May 2024
Abstract
With the development of artificial intelligence (AI), deep learning is widely used in various industries. At CRYPTO 2019, researchers used deep learning to analyze the block cipher for the first time and constructed a differential neural network distinguisher to meet a certain accuracy.
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With the development of artificial intelligence (AI), deep learning is widely used in various industries. At CRYPTO 2019, researchers used deep learning to analyze the block cipher for the first time and constructed a differential neural network distinguisher to meet a certain accuracy. In this paper, a mixture differential neural network distinguisher using ResNet is proposed to further improve the accuracy by exploring the mixture differential properties. Experiments are conducted on SIMON32/64, and the accuracy of the 8-round mixture differential neural network distinguisher is improved from 74.7% to 92.3%, compared with that of the previous differential neural network distinguisher. The prediction accuracy of the differential neural network distinguisher is susceptible to the choice of the specified input differentials, whereas the mixture differential neural network distinguisher is less affected by the input difference and has greater robustness. Furthermore, by combining the probabilistic expansion of rounds and the neutral bit, the obtained mixture differential neural network distinguisher is extended to 11 rounds, which can realize the 12-round actual key recovery attack on SIMON32/64. With an appropriate increase in the time complexity and data complexity, the key recovery accuracy of the mixture differential neural network distinguisher can be improved to 55% as compared to 52% of the differential neural network distinguisher. The mixture differential neural network distinguisher proposed in this paper can also be applied to other lightweight block ciphers.
Full article
(This article belongs to the Special Issue Privacy-Preserving Techniques in AI, Blockchain and Cloud Systems with Formal Mathematical Analysis)
Open AccessArticle
Average Widths and Optimal Recovery of Multivariate Besov Classes in Orlicz Spaces
by
Xinxin Li and Garidi Wu
Mathematics 2024, 12(9), 1400; https://doi.org/10.3390/math12091400 - 03 May 2024
Abstract
In this paper, we study the average Kolmogorov –widths and the average linear –widths of multivariate isotropic and anisotropic Besov classes in Orlicz spaces and give the weak asymptotic estimates of these two widths. At the same time, we also give
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In this paper, we study the average Kolmogorov –widths and the average linear –widths of multivariate isotropic and anisotropic Besov classes in Orlicz spaces and give the weak asymptotic estimates of these two widths. At the same time, we also give the asymptotic property of the optimal recovery of isotropic Besov classes in Orlicz spaces.
Full article
(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)
Open AccessArticle
Existence Results and Finite-Time Stability of a Fractional (p,q)-Integro-Difference System
by
Mouataz Billah Mesmouli, Loredana Florentina Iambor, Amir Abdel Menaem and Taher S. Hassan
Mathematics 2024, 12(9), 1399; https://doi.org/10.3390/math12091399 - 03 May 2024
Abstract
In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional -difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a
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In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional -difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii’s fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work.
Full article
(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition)
Open AccessArticle
Comparison of Feature Selection Methods—Modelling COPD Outcomes
by
Jorge Cabral, Pedro Macedo, Alda Marques and Vera Afreixo
Mathematics 2024, 12(9), 1398; https://doi.org/10.3390/math12091398 - 03 May 2024
Abstract
Selecting features associated with patient-centered outcomes is of major relevance yet the importance given depends on the method. We aimed to compare stepwise selection, least absolute shrinkage and selection operator, random forest, Boruta, extreme gradient boosting and generalized maximum entropy estimation and suggest
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Selecting features associated with patient-centered outcomes is of major relevance yet the importance given depends on the method. We aimed to compare stepwise selection, least absolute shrinkage and selection operator, random forest, Boruta, extreme gradient boosting and generalized maximum entropy estimation and suggest an aggregated evaluation. We also aimed to describe outcomes in people with chronic obstructive pulmonary disease (COPD). Data from 42 patients were collected at baseline and at 5 months. Acute exacerbations were the aggregated most important feature in predicting the difference in the handgrip muscle strength (dHMS) and the COVID-19 lockdown group had an increased dHMS of 3.08 kg (CI95 ≈ [0.04, 6.11]). Pack-years achieved the highest importance in predicting the difference in the one-minute sit-to-stand test and no clinical change during lockdown was detected. Charlson comorbidity index was the most important feature in predicting the difference in the COPD assessment test (dCAT) and participants with severe values are expected to have a decreased dCAT of 6.51 points (CI95 ≈ [2.52, 10.50]). Feature selection methods yield inconsistent results, particularly extreme gradient boosting and random forest with the remaining. Models with features ordered by median importance had a meaningful clinical interpretation. Lockdown seem to have had a negative impact in the upper-limb muscle strength.
Full article
(This article belongs to the Special Issue Current Research in Biostatistics)
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Scale Mixture of Gleser Distribution with an Application to Insurance Data
by
Neveka M. Olmos, Emilio Gómez-Déniz and Osvaldo Venegas
Mathematics 2024, 12(9), 1397; https://doi.org/10.3390/math12091397 - 03 May 2024
Abstract
In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta distribution. The SMG distribution is an alternative
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In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions.
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(This article belongs to the Special Issue Probabilistic Models in Insurance and Finance)
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High-Precision Quality Prediction Based on Two-Dimensional Extended Windows
by
Luping Zhao and Jiayang Yang
Mathematics 2024, 12(9), 1396; https://doi.org/10.3390/math12091396 - 03 May 2024
Abstract
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A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the directions of sampling time and batch, a newly defined region of support (ROS), called the k-i-back-extended region of
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A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the directions of sampling time and batch, a newly defined region of support (ROS), called the k-i-back-extended region of support (KIBROS), is proposed; it establishes an extended window by adding two regions of data to the traditional ROS to include all possible important data for quality prediction. Based on the new ROS, extended windows are established, and different models are proposed using the extended windows for batch process quality prediction. Furthermore, using the typical injection molding batch process as an example, the proposed quality prediction method is experimentally verified, proving that the proposed methods have higher prediction accuracy than the traditional method and that the prediction stability is also improved.
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Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold
by
Lixu Yan, Yanlin Li, Lokman Bilen and Aydın Gezer
Mathematics 2024, 12(9), 1395; https://doi.org/10.3390/math12091395 - 02 May 2024
Abstract
Let be a statistical manifold and be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of
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Let be a statistical manifold and be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle . The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle according to the twisted Sasaki metric G.
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(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
Open AccessArticle
Interpolation Once Binary Search over a Sorted List
by
Jun-Lin Lin
Mathematics 2024, 12(9), 1394; https://doi.org/10.3390/math12091394 - 02 May 2024
Abstract
Searching over a sorted list is a classical problem in computer science. Binary Search takes at most tries to find an item in a sorted list of size n. Interpolation Search achieves an average time complexity
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Searching over a sorted list is a classical problem in computer science. Binary Search takes at most tries to find an item in a sorted list of size n. Interpolation Search achieves an average time complexity of for uniformly distributed data. Hybrids of Binary Search and Interpolation Search are also available to handle data with unknown distributions. This paper analyzes the computation cost of these methods and shows that interpolation can significantly affect their performance—accordingly, a new method, Interpolation Once Binary Search (IOBS), is proposed. The experimental results show that IOBS outperforms the hybrids of Binary Search and Interpolation Search for nonuniformly distributed data.
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(This article belongs to the Special Issue Advances of Computer Algorithms and Data Structures)
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A Hybrid Image Augmentation Technique for User- and Environment-Independent Hand Gesture Recognition Based on Deep Learning
by
Baiti-Ahmad Awaluddin, Chun-Tang Chao and Juing-Shian Chiou
Mathematics 2024, 12(9), 1393; https://doi.org/10.3390/math12091393 - 02 May 2024
Abstract
This research stems from the increasing use of hand gestures in various applications, such as sign language recognition to electronic device control. The focus is the importance of accuracy and robustness in recognizing hand gestures to avoid misinterpretation and instruction errors. However, many
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This research stems from the increasing use of hand gestures in various applications, such as sign language recognition to electronic device control. The focus is the importance of accuracy and robustness in recognizing hand gestures to avoid misinterpretation and instruction errors. However, many experiments on hand gesture recognition are conducted in limited laboratory environments, which do not fully reflect the everyday use of hand gestures. Therefore, the importance of an ideal background in hand gesture recognition, involving only the signer without any distracting background, is highlighted. In the real world, the use of hand gestures involves various unique environmental conditions, including differences in background colors, varying lighting conditions, and different hand gesture positions. However, the datasets available to train hand gesture recognition models often lack sufficient variability, thereby hindering the development of accurate and adaptable systems. This research aims to develop a robust hand gesture recognition model capable of operating effectively in diverse real-world environments. By leveraging deep learning-based image augmentation techniques, the study seeks to enhance the accuracy of hand gesture recognition by simulating various environmental conditions. Through data duplication and augmentation methods, including background, geometric, and lighting adjustments, the diversity of the primary dataset is expanded to improve the effectiveness of model training. It is important to note that the utilization of the green screen technique, combined with geometric and lighting augmentation, significantly contributes to the model’s ability to recognize hand gestures accurately. The research results show a significant improvement in accuracy, especially with implementing the proposed green screen technique, underscoring its effectiveness in adapting to various environmental contexts. Additionally, the study emphasizes the importance of adjusting augmentation techniques to the dataset’s characteristics for optimal performance. These findings provide valuable insights into the practical application of hand gesture recognition technology and pave the way for further research in tailoring techniques to datasets with varying complexities and environmental variations.
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(This article belongs to the Special Issue Deep Learning in Image Processing and Scientific Computing)
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Enhancing Bitcoin Price Volatility Estimator Predictions: A Four-Step Methodological Approach Utilizing Elastic Net Regression
by
Georgia Zournatzidou, Ioannis Mallidis, Dimitrios Farazakis and Christos Floros
Mathematics 2024, 12(9), 1392; https://doi.org/10.3390/math12091392 - 02 May 2024
Abstract
This paper provides a computationally efficient and novel four-step methodological approach for predicting volatility estimators derived from bitcoin prices. In the first step, open, high, low, and close bitcoin prices are transformed into volatility estimators using Brownian motion assumptions and logarithmic transformations. The
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This paper provides a computationally efficient and novel four-step methodological approach for predicting volatility estimators derived from bitcoin prices. In the first step, open, high, low, and close bitcoin prices are transformed into volatility estimators using Brownian motion assumptions and logarithmic transformations. The second step determines the optimal number of time-series lags required for converting the series into an autoregressive model. This selection process utilizes random forest regression, evaluating the importance of each lag using the Mean Decrease in Impurity (MDI) criterion and optimizing the number of lags considering an 85% cumulative importance threshold. The third step of the developed methodological approach fits the Elastic Net Regression (ENR) to the volatility estimator’s dataset, while the final fourth step assesses the predictive accuracy of ENR, compared to decision tree (DTR), random forest (RFR), and support vector regression (SVR). The results reveal that the ENR prevails in its predictive accuracy for open and close prices, as these prices may be linear and less susceptible to sudden, non-linear shifts typically seen during trading hours. On the other hand, SVR prevails for high and low prices as these prices often experience spikes and drops driven by transient news and intra-day market sentiments, forming complex patterns that do not align well with linear modelling.
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Open AccessArticle
Quantum Machine Learning for Credit Scoring
by
Nikolaos Schetakis, Davit Aghamalyan, Michael Boguslavsky, Agnieszka Rees, Marc Rakotomalala and Paul Robert Griffin
Mathematics 2024, 12(9), 1391; https://doi.org/10.3390/math12091391 - 02 May 2024
Abstract
This study investigates the integration of quantum circuits with classical neural networks for enhancing credit scoring for small- and medium-sized enterprises (SMEs). We introduce a hybrid quantum–classical model, focusing on the synergy between quantum and classical rather than comparing the performance of separate
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This study investigates the integration of quantum circuits with classical neural networks for enhancing credit scoring for small- and medium-sized enterprises (SMEs). We introduce a hybrid quantum–classical model, focusing on the synergy between quantum and classical rather than comparing the performance of separate quantum and classical models. Our model incorporates a quantum layer into a traditional neural network, achieving notable reductions in training time. We apply this innovative framework to a binary classification task with a proprietary real-world classical credit default dataset for SMEs in Singapore. The results indicate that our hybrid model achieves efficient training, requiring significantly fewer epochs (350) compared to its classical counterpart (3500) for a similar predictive accuracy. However, we observed a decrease in performance when expanding the model beyond 12 qubits or when adding additional quantum classifier blocks. This paper also considers practical challenges faced when deploying such models on quantum simulators and actual quantum computers. Overall, our quantum–classical hybrid model for credit scoring reveals its potential in industry, despite encountering certain scalability limitations and practical challenges.
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(This article belongs to the Special Issue Quantum Computing Algorithms and Quantum Computing Simulators)
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A New Approach for Modeling Vertical Dynamics of Motorcycles Based on Graph Theory
by
Mouad Garziad, Abdelmjid Saka, Hassane Moustabchir and Maria Luminita Scutaru
Mathematics 2024, 12(9), 1390; https://doi.org/10.3390/math12091390 - 02 May 2024
Abstract
The main objective of this research is to establish a new formulation and mathematical model based on graph theory to create dynamic equations and provide clarity on the fundamental formulation. We have employed graph theory as a new approach to develop a new
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The main objective of this research is to establish a new formulation and mathematical model based on graph theory to create dynamic equations and provide clarity on the fundamental formulation. We have employed graph theory as a new approach to develop a new representation and formulate the vertical dynamics of a motorcycle with four degrees of freedom, including a suspension and tire model. We have outlined the principal procedural steps required to generate the mathematical and dynamic equations. This systematic approach ensures clarity and precision in our formulation process and representation. Subsequently, we implemented the dynamics equations to examine the dynamic behavior of both the sprung and unsprung masses’ vertical displacements, while considering the varying conditions of the road profile.
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(This article belongs to the Section Engineering Mathematics)
Open AccessArticle
Enhancing Portfolio Allocation: A Random Matrix Theory Perspective
by
Fabio Vanni, Asmerilda Hitaj and Elisa Mastrogiacomo
Mathematics 2024, 12(9), 1389; https://doi.org/10.3390/math12091389 - 01 May 2024
Abstract
This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, which are particularly susceptible to instabilities. To address this challenge,
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This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation matrices, which are particularly susceptible to instabilities. To address this challenge, we combine a data preprocessing technique based on the Hilbert transformation of returns with RMT to refine the accuracy and robustness of correlation matrix estimation. By comparing empirical correlations with those generated through RMT, we reveal non-random properties and uncover underlying relationships within financial data. We then utilize this methodology to construct the correlation network dependence structure used in portfolio optimization. The empirical analysis presented in this paper validates the effectiveness of RMT in enhancing portfolio diversification and risk management strategies. This research contributes by offering investors and portfolio managers with methodological insights to construct portfolios that are more stable, robust, and diversified. At the same time, it advances our comprehension of the intricate statistical principles underlying multivariate financial data.
Full article
(This article belongs to the Special Issue Looking at the New Era Challenges in Finance: Forecasting Modeling by Using Artificial Intelligence)
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Lp-Norm for Compositional Data: Exploring the CoDa L1-Norm in Penalised Regression
by
Jordi Saperas-Riera, Glòria Mateu-Figueras and Josep Antoni Martín-Fernández
Mathematics 2024, 12(9), 1388; https://doi.org/10.3390/math12091388 - 01 May 2024
Abstract
The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper
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The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the -norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional -norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach.
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(This article belongs to the Special Issue Multivariate Statistical Analysis and Application)
Open AccessArticle
Ill-Posedness of a Three-Component Novikov System in Besov Spaces
by
Shengqi Yu and Lin Zhou
Mathematics 2024, 12(9), 1387; https://doi.org/10.3390/math12091387 - 01 May 2024
Abstract
In this paper, we consider the Cauchy problem for a three-component Novikov system on the line. We give a construction of the initial data
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In this paper, we consider the Cauchy problem for a three-component Novikov system on the line. We give a construction of the initial data with , such that the corresponding solution to the three-component Novikov system starting from is discontinuous at in the metric of , which implies the ill-posedness for this system in .
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(This article belongs to the Section Difference and Differential Equations)
Open AccessArticle
Experimental Study of Bluetooth Indoor Positioning Using RSS and Deep Learning Algorithms
by
Chunxiang Wu, Ieok-Cheng Wong, Yapeng Wang, Wei Ke and Xu Yang
Mathematics 2024, 12(9), 1386; https://doi.org/10.3390/math12091386 - 01 May 2024
Abstract
Indoor wireless positioning has long been a dynamic field of research due to its broad application range. While many commercial products have been developed, they often are not open source or require substantial and costly infrastructure. Academically, research has extensively explored Bluetooth Low
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Indoor wireless positioning has long been a dynamic field of research due to its broad application range. While many commercial products have been developed, they often are not open source or require substantial and costly infrastructure. Academically, research has extensively explored Bluetooth Low Energy (BLE) for positioning, yet there are a noticeable lack of studies that comprehensively compare traditional algorithms under these conditions. This research aims to fill this gap by evaluating classical positioning algorithms such as K-Nearest Neighbor (KNN), Weighted K-Nearest Neighbor (WKNN), Naïve Bayes (NB), and a Received Signal Strength-based Neural Network (RSS-NN) using BLE technology. We also introduce a novel method using Convolutional Neural Networks (CNN), specifically tailored to process RSS data structured in an image-like format. This approach helps overcome the limitations of traditional RSS fingerprinting by effectively managing the environmental dynamics within indoor settings. In our tests, all algorithms performed well, consistently achieving an average accuracy of less than two meters. Remarkably, the CNN method outperformed others, achieving an accuracy of 1.22 m. These results establish a solid basis for future research, particularly towards enhancing the precision of indoor positioning systems using deep learning for cost-effective, easy to set up applications.
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