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
Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold
Mathematics 2024, 12(9), 1395; https://doi.org/10.3390/math12091395 (registering DOI) - 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.
Full article
(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 (registering DOI) - 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 (registering DOI) - 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 (registering DOI) - 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.
Full article
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 (registering DOI) - 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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Open AccessArticle
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.
Full article
(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.
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(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.
Full article
(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 .
Full article
(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.
Full article
Open AccessArticle
A Modified Depolarization Approach for Efficient Quantum Machine Learning
by
Bikram Khanal and Pablo Rivas
Mathematics 2024, 12(9), 1385; https://doi.org/10.3390/math12091385 - 01 May 2024
Abstract
Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite these progresses, challenges persist due to system noise, errors, and decoherence. These system noises complicate the simulation of quantum systems. The depolarization channel
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Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite these progresses, challenges persist due to system noise, errors, and decoherence. These system noises complicate the simulation of quantum systems. The depolarization channel is a standard tool for simulating a quantum system’s noise. However, modeling such noise for practical applications is computationally expensive when we have limited hardware resources, as is the case in the NISQ era. This work proposes a modified representation for a single-qubit depolarization channel. Our modified channel uses two Kraus operators based only on X and Z Pauli matrices. Our approach reduces the computational complexity from six to four matrix multiplications per channel execution. Experiments on a Quantum Machine Learning (QML) model on the Iris dataset across various circuit depths and depolarization rates validate that our approach maintains the model’s accuracy while improving efficiency. This simplified noise model enables more scalable simulations of quantum circuits under depolarization, advancing capabilities in the NISQ era.
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(This article belongs to the Special Issue Advances in Quantum Computing and Applications)
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Metric Dimension of Circulant Graphs with 5 Consecutive Generators
by
Martin Knor, Riste Škrekovski and Tomáš Vetrík
Mathematics 2024, 12(9), 1384; https://doi.org/10.3390/math12091384 - 01 May 2024
Abstract
The problem of finding the metric dimension of circulant graphs with t generators (and their inverses) has been extensively studied. The problem is solved for , and some exact
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The problem of finding the metric dimension of circulant graphs with t generators (and their inverses) has been extensively studied. The problem is solved for , and some exact values and bounds are known also for . We solve all the open cases for .
Full article
(This article belongs to the Special Issue Graph Theory and Applications, 2nd Edition)
Open AccessArticle
Digital Twin-Based Approach for a Multi-Objective Optimal Design of Wind Turbine Gearboxes
by
Carlos Llopis-Albert, Francisco Rubio, Carlos Devece and Dayanis García-Hurtado
Mathematics 2024, 12(9), 1383; https://doi.org/10.3390/math12091383 - 01 May 2024
Abstract
Wind turbines (WT) are a clean renewable energy source that have gained popularity in recent years. Gearboxes are complex, expensive, and critical components of WT, which are subject to high maintenance costs and several stresses, including high loads and harsh environments, that can
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Wind turbines (WT) are a clean renewable energy source that have gained popularity in recent years. Gearboxes are complex, expensive, and critical components of WT, which are subject to high maintenance costs and several stresses, including high loads and harsh environments, that can lead to failure with significant downtime and financial losses. This paper focuses on the development of a digital twin-based approach for the modelling and simulation of WT gearboxes with the aim to improve their design, diagnosis, operation, and maintenance by providing insights into their behavior under different operating conditions. Powerful commercial computer-aided design tools (CAD) and computer-aided engineering (CAE) software are embedded into a computationally efficient multi-objective optimization framework (modeFrontier) with the purpose of maximizing the power density, compactness, performance, and reliability of the WT gearbox. High-fidelity models are used to minimize the WT weight, volume, and maximum stresses and strains achieved without compromising its efficiency. The 3D CAD model of the WT gearbox is carried out using SolidWorks (version 2023 SP5.0), the Finite Element Analysis (FEA) is used to obtain the stresses and strains, fields are modelled using Ansys Workbench (version 2024R1), while the multibody kinematic and dynamic system is analyzed using Adams Machinery (version 2023.3, Hexagon). The method has been successfully applied to different case studies to find the optimal design and analyze the performance of the WT gearboxes. The simulation results can be used to determine safety factors, predict fatigue life, identify potential failure modes, and extend service life and reliability, thereby ensuring proper operation over its lifetime and reducing maintenance costs.
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(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
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Synchronization in a Three Level Network of All-to-All Periodically Forced Hodgkin–Huxley Reaction–Diffusion Equations
by
B. Ambrosio, M. A. Aziz-Alaoui and A. Oujbara
Mathematics 2024, 12(9), 1382; https://doi.org/10.3390/math12091382 - 01 May 2024
Abstract
This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in
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This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in level 2 receive inputs from one specific neuron in level 1 and all neurons in level 3. The neurons in level 3 (all other neurons) receive inputs from all other neurons in levels 2 and 3. Furthermore, the right-hand side of pre-synaptic neurons is connected to the left-hand side of the post-synaptic neurons. The synchronization phenomenon is observed for neurons in level 3, even though the system is initiated with different functions. As far as we know, it is the first time that evidence of the synchronization phenomenon is provided for spatially extended Hodgkin–Huxley equations, which are periodically forced at three different sites and embedded in such a hierarchical network with space-dependent coupling interactions.
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(This article belongs to the Special Issue Advances in Bio-Dynamics and Applications)
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Gauss’ Second Theorem for 2F1(12)-Series and Novel Harmonic Series Identities
by
Chunli Li and Wenchang Chu
Mathematics 2024, 12(9), 1381; https://doi.org/10.3390/math12091381 - 01 May 2024
Abstract
Two summation theorems concerning the -series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in closed form,
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Two summation theorems concerning the -series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in closed form, including eight conjectured ones made by Z.-W. Sun. The presented comprehensive coverage for the harmonic series of convergence rate “ ” may serve as a reference source for readers.
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(This article belongs to the Special Issue Integral Transforms and Special Functions in Applied Mathematics)
Open AccessArticle
Hierarchical Symmetry-Breaking Model for Stem Cell Differentiation
by
Nikolaos K. Voulgarakis
Mathematics 2024, 12(9), 1380; https://doi.org/10.3390/math12091380 - 01 May 2024
Abstract
Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed
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Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed as a metaphor, Waddington’s hypothesis establishes the fundamental principles for characterizing the differentiation process as a dynamic system: the generated equilibrium points must exhibit hierarchical branching, robustness to perturbations (homeorhesis), and produce the appropriate number of cells for each cell type. This article aims to capture these characteristics using a mathematical model based on two fundamental hypotheses. First, it is assumed that the gene regulatory network consists of hierarchically coupled subnetworks of genes (modules), each modeled as a dynamical system exhibiting supercritical pitchfork or cusp bifurcation. Second, the gene modules are spatiotemporally regulated by feedback mechanisms originating from epigenetic factors. Analytical and numerical results show that the proposed model exhibits self-organized multistability with hierarchical branching. Moreover, these branches of equilibrium points are robust to perturbations, and the number of different cells produced can be determined by the system parameters.
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(This article belongs to the Special Issue Mathematical Modelling in Biology)
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Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales
by
Andrejs Reinfelds and Shraddha Christian
Mathematics 2024, 12(9), 1379; https://doi.org/10.3390/math12091379 (registering DOI) - 30 Apr 2024
Abstract
In this paper, we present sufficient conditions for Hyers–Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem,
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In this paper, we present sufficient conditions for Hyers–Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.
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(This article belongs to the Special Issue Differential and Integro–Differential Equations: Theory and Applications)
Open AccessArticle
Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints
by
Jianhua Zhang and Yinguang Li
Mathematics 2024, 12(9), 1378; https://doi.org/10.3390/math12091378 (registering DOI) - 30 Apr 2024
Abstract
This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the
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This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.
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(This article belongs to the Special Issue Control, Optimisation, and Applications of Stochastic Uncertain Systems)
Open AccessArticle
Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise
by
Almaz T. Abebe, Shenglan Yuan, Daniel Tesfay and James Brannan
Mathematics 2024, 12(9), 1377; https://doi.org/10.3390/math12091377 (registering DOI) - 30 Apr 2024
Abstract
We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case.
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We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling.
Full article
(This article belongs to the Special Issue Stochastic Models in Mathematical Biology, 2nd Edition)
Open AccessArticle
High-Level Process Modeling—An Experimental Investigation of the Cognitive Effectiveness of Process Landscape Diagrams
by
Gregor Polančič and Katja Kous
Mathematics 2024, 12(9), 1376; https://doi.org/10.3390/math12091376 (registering DOI) - 30 Apr 2024
Abstract
Unlike business process diagrams, where ISO/IEC 19510 (BPMN 2.0) prevails, high-level process landscape diagrams are being designed using a variety of standard- or semi-standard-based notations. Consequently, landscape diagrams differ among organizations, domains, and modeling tools. As (process landscape) diagrams need to be understandable
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Unlike business process diagrams, where ISO/IEC 19510 (BPMN 2.0) prevails, high-level process landscape diagrams are being designed using a variety of standard- or semi-standard-based notations. Consequently, landscape diagrams differ among organizations, domains, and modeling tools. As (process landscape) diagrams need to be understandable in order to communicate effectively and thus form the basis for valid business decisions, this study aims to empirically validate the cognitive effectiveness of common landscape designs, including those BPMN-L-based, which represent a standardized extension of BPMN 2.0 specifically aimed at landscape modeling. Empirical research with 298 participants was conducted in which cognitive effectiveness was investigated by observing the speed, ease, accuracy, and efficiency of answering questions related to semantically equivalent process landscape diagrams modeled in three different notations: value chains, ArchiMate, and BPMN-L. The results demonstrate that BPMN-L-based diagrams performed better than value chain- and ArchiMate-based diagrams concerning speed, accuracy, and efficiency; however, subjects perceived BPMN-L-based diagrams as being less easy to use when compared to their counterparts. The results indicate that differences in cognitive effectiveness measures may result from the design principles of the underlying notations, specifically the complexity of the visual vocabulary and semiotic clarity, which states that modeling concepts should have unique visualizations.
Full article
(This article belongs to the Special Issue Industrial Big Data and Process Modelling for Smart Manufacturing)
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Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
Topic Editors: Xiaofeng Wang, Fazlollah SoleymaniDeadline: 30 June 2024
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Algorithms, Computation, Information, Mathematics
Complex Networks and Social Networks
Topic Editors: Jie Meng, Xiaowei Huang, Minghui Qian, Zhixuan XuDeadline: 31 July 2024
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Algorithms, Future Internet, Information, Mathematics, Symmetry
Research on Data Mining of Electronic Health Records Using Deep Learning Methods
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Mathematics
Advances in Linear Recurrence System
Guest Editors: Lorentz Jäntschi, Virginia NiculescuDeadline: 15 May 2024
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New Trends on Boundary Value Problems
Guest Editors: Miklós Rontó, András Rontó, Nino Partsvania, Bedřich Půža, Hriczó KrisztiánDeadline: 31 May 2024
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Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
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Mathematics
Computational Statistical Methods and Extreme Value Theory
Guest Editor: Frederico CaeiroDeadline: 30 June 2024
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Topology and Foundations
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Multiscale Computation and Machine Learning
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Theoretical and Mathematical Ecology
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