Mathematical and Computational Applications doi: 10.3390/mca29050076

Authors: Isidro Vargas-Moreno Héctor Gabriel Acosta-Mesa Juan Francisco Rodríguez-Landa Martha Lorena Avendaño-Garrido Rafael Fernández-Demeneghi Socorro Herrera-Meza

Behavioral neuropharmacology, a branch of neuroscience, uses behavioral analysis to demonstrate treatment effects on animal models, which is fundamental for pre-clinical evaluation. Typically, this determination is univariate, neglecting the relevant associations for understanding treatment effects in animals and humans. This study implements regression trees and Bayesian networks from a multivariate perspective by using variables obtained from behavioral tests to predict the time spent in the open arms of the elevated arm maze, a key variable to assess anxiety. Three doses of allopregnanolone were analyzed and compared to a vehicle group and a diazepam-positive control. Regression trees identified cut-off points between the anxiolytic and anxiogenic effects, with the anxiety index standing out as a robust predictor, combined with the percentage of open-arm entries and the number of entries. Bayesian networks facilitated the visualization and understanding of the interactions between multiple behavioral and biological variables, demonstrating that treatment with allopregnanolone (2 mg) emulates the effects of diazepam, validating the multivariate approach. The results highlight the relevance of integrating advanced methods, such as Bayesian networks, into preclinical research to enrich the interpretation of complex behavioral data in animal models, which can hardly be observed with univariate statistics.

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Authors: Saima Noor Albandari W. Alrowaily Mohammad Alqudah Rasool Shah Samir A. El-Tantawy

This study explores the application of advanced mathematical techniques to solve fractional differential equations, focusing particularly on the fractional diffusion equation. The fractional diffusion equation, used to simulate a range of physical and engineering phenomena, poses considerable difficulties when applied to fractional orders. Thus, by utilizing the mighty powers of fractional calculus, we employ the variational iteration method (VIM) with the Elzaki transform to produce highly accurate approximations for these specific differential equations. The VIM provides an iterative framework for refining solutions progressively, while the Elzaki transform simplifies the complex integral transforms involved. By integrating these methodologies, we achieve accurate and efficient solutions to the fractional diffusion equation. Our findings demonstrate the robustness and effectiveness of combining the VIM and the Elzaki transform in handling fractional differential equations, offering explicit functional expressions that are beneficial for theoretical analysis and practical applications. This research contributes to the expanding field of fractional calculus, providing valuable insights and useful tools for solving complex, nonlinear fractional differential equations across various scientific and engineering disciplines.

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Authors: Matthew Pugh Jo Grundy Corina Cirstea Nick Harris

Recent research has suggested that category theory can provide useful insights into the field of machine learning (ML). One example is improving the connection between an ML problem and the design of a corresponding ML algorithm. A tool from category theory called a Kan extension is used to derive the design of an unsupervised anomaly detection algorithm for a commonly used benchmark, the Occupancy dataset. Achieving an accuracy of 93.5% and an ROCAUC of 0.98, the performance of this algorithm is compared to state-of-the-art anomaly detection algorithms tested on the Occupancy dataset. These initial results demonstrate that category theory can offer new perspectives with which to attack problems, particularly in making more direct connections between the solutions and the problem&rsquo;s structure.

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Authors: Jenny Betsabé Vázquez-Aguirre Guadalupe Carmona-Arroyo Marcela Quiroz-Castellanos Nicandro Cruz-Ramírez

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study for the causal analysis of the performance of two state-of-the-art algorithms for the one-dimensional Bin Packing Problem (BPP). We meticulously selected the set of features associated with the parameters that define the instances of the problem. Subsequently, we evaluated the algorithmic performance on instances with distinct features. Our analysis scrutinizes both instance features and algorithm performance, aiming to identify causes influencing the performance of the algorithms. The proposed study successfully identifies specific values affecting algorithmic effectiveness and efficiency, revealing shared causes within some value ranges across both algorithms. The knowledge generated establishes a robust foundation for future research, enabling predictions of algorithmic performance, as well as the selection and design of heuristic strategies for improving the performance in the most difficult instances. The causal analysis employed in this study did not require specific configurations, making it an invaluable tool for analyzing the performance of different algorithms in other COPs.

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Authors: Weam G. Alharbi

This paper analyzes the first-order delay equation y&prime;(t)=&alpha;y(t)+&beta;y(t&minus;&tau;) subject to a history function in addition to an initial condition that assumes discontinuity at t=0. The method of steps is successfully applied to derive the exact solution in an explicit form. In addition, a unified formula is provided to describe the solution in any finite sub-interval of the problem&rsquo;s domain. The characteristics and properties of the solution are theoretically investigated and then confirmed through several plots. The behavior of the solution and its derivative are examined and interpreted. The results show that the method of steps is an effective method of solution to treat the current delay model. The present successful analysis can be used to investigate other delay models with complex initial conditions. Furthermore, the present approach can be generalized to include the inhomogeneous version of the current model without using numerical methods.

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Authors: Vincent Milimo Masilokwa Punabantu Malebogo Ngoepe Amit Kumar Mishra Thomas Aldersley John Lawrenson Liesl Zühlke

Patient-specific computational fluid dynamics (CFD) studies on coarctation of the aorta (CoA) in resource-constrained settings are limited by the available imaging modalities for geometry and velocity data acquisition. Doppler echocardiography is considered a suitable velocity acquisition modality due to its low cost and safety. This study aims to investigate the application of classical machine learning (ML) methods to create an adequate and robust approach to obtain boundary conditions (BCs) from Doppler echocardiography images for haemodynamic modelling using CFD. Our proposed approach combines ML and CFD to model haemodynamic flow within the region of interest. The key feature of the approach is the use of ML models to calibrate the inlet and outlet BCs of the CFD model. In the ML model, patient heart rate served as the crucial input variable due to its temporal variation across the measured vessels. ANSYS Fluent was used for the CFD component of the study, whilst the Scikit-learn Python library was used for the ML component. We validated our approach against a real clinical case of severe CoA before intervention. The maximum coarctation velocity of our simulations was compared to the measured maximum coarctation velocity obtained from the patient whose geometry was used within the study. Of the 5 mL models used to obtain BCs, the top model was within 5% of the maximum measured coarctation velocity. The framework demonstrated that it was capable of taking into account variations in the patient&rsquo;s heart rate between measurements. Therefore, it allowed for the calculation of BCs that were physiologically realistic when the measurements across each vessel were scaled to the same heart rate while providing a reasonably accurate solution.

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Authors: Rhoda Ngira Aduke Martin P. Venter Corné J. Coetzee

Numerical modelling of corrugated paperboard is quite challenging due to its waved geometry and material non-linearity which is affected by the material properties of the individual paper sheets. Because of the complex geometry and material behaviour of the board, there is still scope to enhance the accuracy of current modelling techniques as well as gain a better understanding of the structural performance of corrugated paperboard packaging for improved packaging design. In this study, four-point bending tests were carried out to determine the bending stiffness of un-creased samples in the machine direction (MD) and cross direction (CD). Bending tests were also carried out on creased samples with the fluting oriented in the CD with the crease at the centre. Inverse analysis was applied using the results from the bending tests to determine the material properties that accurately predict the bending stiffness of the horizontal creases, vertical creases, and panels of a box under compression loading. The finite element model of the box was divided into three sections, the horizontal creases, vertical creases, and the box panels. Each of these sections is described using different material properties. The box edges/corners are described using the optimal material properties from bending and compression tests conducted on creased samples, while the box panels are described using the optimal material properties obtained from four-point bending tests conducted on samples without creases. A homogenised finite element (FE) model of a box was simulated using the obtained material properties and validated using experimental results. The developed FE model accurately predicted the failure load of a corrugated paperboard box under compression with a variation of 0.1% when compared to the experimental results.

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Authors: Mohamed Cherif Belili Mohamed Lamine Sahari Omar Kebiri Halim Zeghdoudi

This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin&rsquo;s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic&rsquo;s spread.

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Authors: José-Luis Morales-Reyes Elia-Nora Aquino-Bolaños Héctor-Gabriel Acosta-Mesa Aldo Márquez-Grajales

The concentration of anthocyanins in common beans indicates their nutritional value. Understanding this concentration makes it possible to identify the functional compounds present. Previous studies have presented color characterization as two-dimensional histograms, based on the probability mass function. In this work, we proposed a new type of color characterization represented by three two-dimensional histograms that consider chromaticity and luminosity channels in order to verify the robustness of the information. Using a neuroevolutionary approach, we also found a convolutional neural network (CNN) for the regression task. The results demonstrate that using three two-dimensional histograms increases the accuracy compared to the color characterization represented by one two-dimensional histogram. As a result, the precision was 93.00 &plusmn; 5.26 for the HSI color space and 94.30 &plusmn; 8.61 for CIE L*a*b*. Our procedure is suitable for estimating anthocyanins in homogeneous and heterogeneous colored bean landraces.

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Authors: Martha Pulido Patricia Melin Oscar Castillo Juan R. Castro

In this work, interval type-2 and type-3 fuzzy systems were designed, of Mamdani and Sugeno types, for time series prediction. The aggregation performed by the type-2 and type-3 fuzzy systems was carried out by using the results of an optimized ensemble neural network (ENN) obtained with the particle swarm optimization algorithm. The time series data that were used were of the Mexican stock exchange. The method finds the best prediction error. This method consists of the aggregation of the responses of the ENN with type-2 and type-3 fuzzy systems. In this case, the systems consist of five inputs and one output. Each input is made up of two membership functions and there are 32 possible fuzzy if-then rules. The simulation results show that the approach with type-2 and type-3 fuzzy systems provides a good prediction of the Mexican stock exchange. Statistical tests of the comparison of type-1, type-2, and type-3 fuzzy systems are also presented.

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Authors: Mohammed K. Ibrahim Taha Rabeh Elbaz I. Abouelmagd

In this work, some dynamical properties of Hill&rsquo;s system are studied under the effect of continued fraction perturbation. The locations and kinds of equilibrium points are identified, and it is demonstrated that these points are saddle points and the general motion in their proximity is unstable. Furthermore, the curves of zero velocity and the regions of possible motion are defined at different Jacobian constant values. It is shown that the regions of forbidden motion increase with increasing Jacobian constant values and there is a noticeable decrease in the permissible regions of motion, leading to the possibility that the body takes a path far away from the primary body and escapes to take an unknown trajectory. Furthermore, the stability of perturbed motion is analyzed from the perspective of a linear sense, and it is observed that the linear motion is also unstable.

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Authors: Jesse Stevens Daniel N. Wilke Isaac I. Setshedi

The Latent Space Perspicacity and Interpretation Enhancement (LS-PIE) framework enhances dimensionality reduction methods for linear latent variable models (LVMs). This paper extends LS-PIE by introducing an optimal latent discovery strategy to automate identifying optimal latent dimensions and projections based on user-defined metrics. The latent condensing (LCON) method clusters and condenses an extensive latent space into a compact form. A new approach, latent expansion (LEXP), incrementally increases latent dimensions using a linear LVM to find an optimal compact space. This study compares these methods across multiple datasets, including a simple toy problem, mixed signals, ECG data, and simulated vibrational data. LEXP can accelerate the discovery of optimal latent spaces and may yield different compact spaces from LCON, depending on the LVM. This paper highlights the LS-PIE algorithm&rsquo;s applications and compares LCON and LEXP in organising, ranking, and scoring latent components akin to principal component analysis or singular value decomposition. This paper shows clear improvements in the interpretability of the resulting latent representations allowing for clearer and more focused analysis.

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Authors: Lebohang Reginald Masheane Willie du Preez Jacques Combrinck

It is costly and time-consuming to design and manufacture functional polyurethane heart valve prototypes, to evaluate and comprehend their hemodynamic behaviour. To enhance the rapid and effective design of replacement heart valves, to meet the minimum criteria of FDA and ISO regulations and specifications, and to reduce the length of required clinical testing, computational fluid dynamics (CFD) and finite element analysis (FEA) were used. The results revealed that when the flexibility of the stent was taken into consideration with a uniform leaflet thickness, stress concentration regions that were present close to the commissural attachment were greatly diminished. Furthermore, it was found that the stress on the leaflets was directly impacted by the effect of reducing the post height on both rigid and flexible stents. When varying the leaflet thickness was considered, the high-stress distribution close to the commissures appeared to reduce at thicker leaflet regions. However, thicker leaflets may result in a stiffer valve with a corresponding increase in pressure drop. It was concluded that a leaflet with predefined varying thickness may be a better option.

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Authors: Pablo Martin Juan Pablo Ramos-Andrade Fabián Caro-Pérez Freddy Lastra

We obtain an accurate analytic approximation for the Bessel function J2(x) using an improved multipoint quasirational approximation technique (MPQA). This new approximation is valid for all real values of the variable x, with a maximum absolute error of approximately 0.009. These errors have been analyzed in the interval from x=0 to x=1000, and we have found that the absolute errors for large x decrease logarithmically. The values of x at which the zeros of the exact function J2(x) and the approximated function J&tilde;2(x) occur are also provided, exhibiting very small relative errors. The largest relative error is for the second zero, with &epsilon;rel=0.0004, and the relative errors continuously decrease, reaching 0.0001 for the eleventh zero. The procedure to obtain this analytic approximation involves constructing a bridge function that connects the power series with the asymptotic approximation. This is achieved by using rational functions combined with other elementary functions, such as trigonometric and fractional power functions.

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Authors: Toshihito Umegaki Naoya Hatanaka Takashi Suzuki

This study analyzed the non-canonical NF-&kappa;B pathway, which controls functions distinct from those of the canonical pathway. Although oscillations of NF-&kappa;B have been observed in the non-canonical pathway, a detailed mechanism explaining the observed behavior remains elusive, owing to the different behaviors observed across cell types. This study demonstrated that oscillations cannot be produced by the experimentally observed pathway alone, thereby suggesting the existence of an unknown reaction pathway. Assuming this pathway, it became evident that the oscillatory structure of the non-canonical pathway was caused by stable periodic orbits. In addition, we demonstrated that altering the expression levels of specific proteins reproduced various behaviors. By fitting 14 parameters, excluding those measured in previous studies, this study successfully reproduce nuclear retention (saturation), oscillation, and singular events that had been experimentally confirmed. The analysis also provided a comprehensive understanding of the dynamics of the RelB protein and suggested a potential inhibitory role for the unknown factor. These findings indicate that the unknown factor may be an isoform of I&kappa;B, contributing to the regulation of NF-&kappa;B signaling. Based on these models, we gained invaluable understanding of biological systems, paving the way for the development of new strategies to manipulate specific biological processes.

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Authors: Jacques Terblanche Johan van der Merwe Ryno Laubscher

Accurate assessment and prediction of mandible shape are fundamental prerequisites for successful orthognathic surgery. Previous studies have predominantly used linear models to predict lower facial structures from facial landmarks or measurements; the prediction errors for this did not meet clinical tolerances. This paper compared non-linear models, namely a Multilayer Perceptron (MLP), a Mixture Density Network (MDN), and a Random Forest (RF) model, with a Linear Regression (LR) model in an attempt to improve prediction accuracy. The models were fitted to a dataset of measurements from 155 subjects. The test-set mean absolute errors (MAEs) for distance-based target features for the MLP, MDN, RF, and LR models were respectively 2.77 mm, 2.79 mm, 2.95 mm, and 2.91 mm. Similarly, the MAEs for angle-based features were 3.09&deg;, 3.11&deg;, 3.07&deg;, and 3.12&deg; for each model, respectively. All models had comparable performance, with neural network-based methods having marginally fewer errors outside of clinical specifications. Therefore, while non-linear methods have the potential to outperform linear models in the prediction of lower facial measurements from upper facial measurements, current results suggest that further refinement is necessary prior to clinical use.

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Authors: Ugur Camci

In this paper, Lie symmetries and Noether symmetries along with the corresponding conservation laws are derived for weakly nonlinear dispersive magnetohydrodynamic wave equations, also known as the triple degenerate derivative nonlinear Schr&ouml;dinger equations. The main goal of this study is to obtain Noether symmetries of the second-order Lagrangian density for these equations using the Noether symmetry approach with a gauge term. For this Lagrangian density, we compute the conserved densities and fluxes corresponding to the Noether symmetries with a gauge term, which differ from the conserved densities obtained using Lie symmetries in Webb et al. (J. Plasma Phys.&nbsp;1995, 54, 201&ndash;244; J. Phys. A Math. Gen.&nbsp;1996, 29, 5209&ndash;5240). Furthermore, we find some new Lie symmetries of the dispersive triple degenerate derivative nonlinear Schr&ouml;dinger equations for non-vanishing integration functions Ki(t) (i=1,2,3).

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Authors: Maha A. Thafar Mashael M. Alsulami Somayah Albaradei

The growth in academic and scientific publications has increased very rapidly. Researchers must choose a representative and significant literature for their research, which has become challenging worldwide. Usually, the paper citation number indicates this paper&rsquo;s potential influence and importance. However, this standard metric of citation numbers is not suitable to assess the popularity and significance of recently published papers. To address this challenge, this study presents an effective prediction method called FutureCite to predict the future citation level of research articles. FutureCite integrates machine learning with text and graph mining techniques, leveraging their abilities in classification, datasets in-depth analysis, and feature extraction. FutureCite aims to predict future citation levels of research articles applying a multilabel classification approach. FutureCite can extract significant semantic features and capture the interconnection relationships found in scientific articles during feature extraction using textual content, citation networks, and metadata as feature resources. This study&rsquo;s objective is to contribute to the advancement of effective approaches impacting the citation counts in scientific publications by enhancing the precision of future citations. We conducted several experiments using a comprehensive publication dataset to evaluate our method and determine the impact of using a variety of machine learning algorithms. FutureCite demonstrated its robustness and efficiency and showed promising results based on different evaluation metrics. Using the FutureCite model has significant implications for improving the researchers&rsquo; ability to determine targeted literature for their research and better understand the potential impact of research publications.

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Authors: Hossein Hassani Leila Marvian Masoud Yarmohammadi Mohammad Reza Yeganegi

The objective of this paper is to assess the distribution of the Partial Autocorrelation Function (PACF), both theoretically and empirically, emphasizing its crucial role in modeling and forecasting time series data. Additionally, it evaluates the deviation of the sum of sample PACF from normality: identifying the lag at which departure occurs. Our investigation reveals that the sum of the sample PACF, and consequently its components, diverges from the expected normal distribution beyond a certain lag. This observation challenges conventional assumptions in time series modeling and forecasting, indicating a necessity for reassessment of existing methodologies. Through our analysis, we illustrate the practical implications of our findings using real-world scenarios, highlighting their significance in unraveling complex data patterns. This study delves into 185 years of monthly Bank of England Rate data, utilizing this extensive dataset to conduct an empirical analysis. Furthermore, our research paves the way for future exploration, offering insights into the complexities and potential revisions in time series analysis, modeling, and forecasting.

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Authors: Dulce A. Serrano-Cruz Latifa Boutat-Baddas Mohamed Darouach Carlos M. Astorga-Zaragoza Gerardo V. Guerrero Ramírez

This paper presents a mathematical model of the cardiovascular system (CVS) designed to simulate both normal and pathological conditions within the systemic circulation. The model introduces a novel representation of the CVS through a change of coordinates, transforming it into the &ldquo;quadratic normal form&rdquo;. This model facilitates the implementation of a sliding mode observer (SMO), allowing for the estimation of system states and the detection of anomalies, even though the system is linearly unobservable. The primary focus is on identifying valvular heart diseases, which are significant risk factors for cardiovascular diseases. The model&rsquo;s validity is confirmed through simulations that replicate hemodynamic parameters, aligning with existing literature and experimental data.

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Authors: Jesús-Arnulfo Barradas-Palmeros Efrén Mezura-Montes Rafael Rivera-López Hector-Gabriel Acosta-Mesa Aldo Márquez-Grajales

Feature selection is a preprocessing step in machine learning that aims to reduce dimensionality and improve performance. The approaches for feature selection are often classified according to the evaluation of a subset of features as filter, wrapper, and embedded approaches. The high performance of wrapper approaches for feature selection is associated at the same time with the disadvantage of high computational cost. Cost-reduction mechanisms for feature selection have been proposed in the literature, where competitive performance is achieved more efficiently. This work applies the simple and effective resource-saving mechanisms of the fixed and incremental sampling fraction strategies with memory to avoid repeated evaluations in multi-objective permutational-based differential evolution for feature selection. The selected multi-objective approach is an extension of the DE-FSPM algorithm with the selection mechanism of the GDE3 algorithm. The results showed high resource savings, especially in computational time and the number of evaluations required for the search process. Nonetheless, it was also detected that the algorithm&rsquo;s performance was diminished. Therefore, the results reported in the literature on the effectiveness of the strategies for cost reduction in single-objective feature selection were only partially sustained in multi-objective feature selection.

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Authors: Toni Škugor Lana Virag Gerhard Sommer Igor Karšaj

Finite element modeling has become one of the main tools necessary for understanding cardiovascular homeostasis and lesion progression. The accuracy of such simulations significantly depends on the precision of material parameters, which are obtained via the mechanical characterization process, i.e., experimental testing and material parameter estimation using the optimization process. The process of mounting specimens on the machine often introduces slight preloading to avoid sagging and to ensure perpendicular orientation with respect to the loading axes. As such, the reference configuration proposes non-zero forces at zero-state displacements. This error further extends to the material parameters&rsquo; estimation where initial loading is usually manually annulled. In this work, we have developed a new computational procedure that includes prestretches during mechanical characterization. The verification of the procedure was performed on the series of simulated virtual planar biaxial experiments using the Gasser&ndash;Ogden&ndash;Holzapfel material model where the exact material parameters could be set and compared to the obtained ones. Furthermore, we have applied our procedure to the data gathered from biaxial experiments on aortic tissue and compared it with the results obtained through standard optimization procedure. The analysis has shown a significant difference between the material parameters obtained. The rate of error increases with the prestretches and decreases with an increase in maximal experimental stretches.

]]>Mathematical and Computational Applications doi: 10.3390/mca29040054

Authors: Francisco Martínez Mohammed K. A. Kaabar Inmaculada Martínez

In this article, new results are investigated in the context of the recently introduced Abu-Shady&ndash;Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation. As in the classical case, the generalized Legendre polynomials constitute notable solutions to the aforementioned fractional differential equation. In the sense of the fractional derivative of Abu-Shady&ndash;Kaabar, we establish important properties of the generalized Legendre polynomials such as Rodrigues formula and recurrence relations. Special attention is also devoted to another very important property of Legendre polynomials and their orthogonal character. Finally, the representation of a function f&isin;L&alpha;2([&minus;1,1]) in a series of generalized Legendre polynomials is addressed.

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Authors: Silvija Angelova Maria Angelova Rositsa Raikova

Due to imprecise meaning in the original publication [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca29040052

Authors: Pieter Rousseau Ryno Laubscher

Online condition-monitoring techniques that are used to reveal incipient faults before breakdowns occur are typically data-driven or model-based. We propose the use of a fundamental physics-based thermofluid model of a heat pump cycle combined with deep learning-based surrogate models and parameter identification in order to simultaneously detect, locate, and quantify degradation occurring in the different components. The methodology is demonstrated with the aid of synthetically generated data, which include the effect of measurement uncertainty. A &ldquo;forward&rdquo; neural network surrogate model is trained and then combined with parameter identification which minimizes the residuals between the surrogate model results and the measured plant data. For the forward approach using four measured performance parameters with 100 or more measured data points, very good prediction accuracy is achieved, even with as much as 20% noise imposed on the measured data. Very good accuracy is also achieved with as few as 10 measured data points with noise up to 5%. However, prediction accuracy is reduced with less data points and more measurement uncertainty. A &ldquo;backward&rdquo; neural network surrogate model can also be applied directly without parameter identification and is therefore much faster. However, it is more challenging to train and produce less accurate predictions. The forward approach is fast enough so that the calculation time does not impede its application in practice, and it can still be applied if some of the measured performance parameters are no longer available, due to sensor failure for instance, albeit with reduced accuracy.

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Authors: Pedro Eusebio Alvarado-Méndez Carlos M. Astorga-Zaragoza Gloria L. Osorio-Gordillo Adriana Aguilera-González Rodolfo Vargas-Méndez Juan Reyes-Reyes

A H&infin; robust adaptive nonlinear observer for state and parameter estimation of a class of Lipschitz nonlinear systems with disturbances is presented in this work. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer in the presence of disturbances is analyzed using Lyapunov stability theory and by considering an H&infin; performance criterion. Numerical simulations were carried out to demonstrate the applicability of this observer for a semi-active car suspension. The adaptive observer performed well in estimating the tire rigidity (as an unknown parameter) and induced disturbances representing damage to the damper. The main contribution is the proposal of an alternative methodology for simultaneous parameter and actuator disturbance estimation for a more general class of nonlinear systems.

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Authors: Baravan A. Asaad Sagvan Y. Musa Zanyar A. Ameen

This article presents a pioneering mathematical model, fuzzy bipolar hypersoft (FBHS) sets, which combines the bipolarity of parameters with the fuzziness of data. Motivated by the need for a comprehensive framework capable of addressing uncertainty and variability in complex phenomena, our approach introduces a novel method for representing both the presence and absence of parameters through FBHS sets. By employing two mappings to estimate positive and negative fuzziness levels, we bridge the gap between bipolarity, fuzziness, and parameterization, allowing for more realistic simulations of multifaceted scenarios. Compared to existing models like bipolar fuzzy hypersoft (BFHS) sets, FBHS sets offer a more intuitive and user-friendly approach to modeling phenomena involving bipolarity, fuzziness, and parameterization. This advantage is underscored by a detailed comparison and a practical example illustrating FBHS sets&rsquo; superiority in modeling such phenomena. Additionally, this paper provides an in-depth exploration of fundamental FBHS set operations, highlighting their robustness and applicability in various contexts. Finally, we demonstrate the practical utility of FBHS sets in problem-solving and introduce an algorithm for optimal object selection based on available information sets, further emphasizing the advantages of our proposed framework.

]]>Mathematical and Computational Applications doi: 10.3390/mca29040049

Authors: Zenonas Turskis Violeta Šniokienė

The intersection of the Internet of Things (IoT) and the circular economy (CE) creates a revolutionary opportunity to redefine economic sustainability and resilience. This review article explores the intricate interplay between IoT technologies and CE economics, investigating how the IoT transforms supply chain management, optimises resources, and revolutionises business models. IoT applications boost efficiency, reduce waste, and prolong product lifecycles through data analytics, real-time tracking, and automation. The integration of the IoT also fosters the emergence of inventive circular business models, such as product-as-a-service and sharing economies, offering economic benefits and novel market opportunities. This amalgamation with the IoT holds substantial implications for sustainability, advancing environmental stewardship and propelling economic growth within emerging CE marketplaces. This comprehensive review unfolds a roadmap for comprehending and implementing the pivotal components propelling the IoT&rsquo;s transformation toward CE economics, nurturing a sustainable and resilient future. Embracing IoT technologies, the authors embark on a journey transcending mere efficiency, heralding an era where economic progress harmonises with full environmental responsibility and the CE&rsquo;s promise.

]]>Mathematical and Computational Applications doi: 10.3390/mca29040048

Authors: Adriana-Laura López-Lobato Héctor-Gabriel Acosta-Mesa Efrén Mezura-Montes

Semantic segmentation is an essential process in computer vision that allows users to differentiate objects of interest from the background of an image by assigning labels to the image pixels. While Convolutional Neural Networks have been widely used to solve the image segmentation problem, simpler approaches have recently been explored, especially in fields where explainability is essential, such as medicine. A Convolutional Decision Tree (CDT) is a machine learning model for image segmentation. Its graphical structure and simplicity make it easy to interpret, as it clearly shows how pixels in an image are classified in an image segmentation task. This paper proposes new approaches for inducing a CDT to solve the image segmentation problem using SHADE. This adaptive differential evolution algorithm uses a historical memory of successful parameters to guide the optimization process. Experiments were performed using the Weizmann Horse dataset and Blood detection in dark-field microscopy images to compare the proposals in this article with previous results obtained through the traditional differential evolution process.

]]>Mathematical and Computational Applications doi: 10.3390/mca29040047

Authors: Suzan Gazioğlu

Our comprehension of the real world remains perpetually incomplete, compelling us to rely on models to decipher intricate real-world phenomena. However, these models, at their pinnacle, serve merely as close approximations of the systems they seek to emulate, inherently laden with uncertainty. Therefore, investigating the disparities between observed system behaviors and model-derived predictions is of paramount importance. Although achieving absolute quantification of uncertainty in the model-building process remains challenging, there are avenues for both mitigating and highlighting areas of uncertainty. Central to this study are three key sources of uncertainty, each exerting significant influence: (i) structural uncertainty arising from inadequacies in mathematical formulations within the conceptual models; (ii) scenario uncertainty stemming from our limited foresight or inability to forecast future conditions; and (iii) input factor uncertainty resulting from vaguely defined or estimated input factors. Through uncertainty analysis, this research endeavors to understand these uncertainty domains within compartmental models, which are instrumental in depicting the complexities of the global carbon cycle. The results indicate that parameter uncertainty has the most significant impact on model outputs, followed by structural and scenario uncertainties. Evident deviations between the observed atmospheric CO2 content and simulated data underscore the substantial contribution of certain uncertainties to the overall estimated uncertainty. The conclusions emphasize the need for comprehensive uncertainty quantification to enhance model reliability and the importance of addressing these uncertainties to improve predictions related to global carbon dynamics and inform policy decisions. This paper employs partitioning techniques to discern the contributions of the aforementioned primary sources of uncertainty to the overarching prediction uncertainty.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030046

Authors: Julio B. Clempner

This paper introduces a dynamic mechanism design tailored for uncertain environments where incentive schemes are challenged by the inability to observe players&rsquo; actions, known as moral hazard. In these scenarios, the system operates as a Markov game where outcomes depend on both the state of payouts and players&rsquo; actions. Moral hazard and adverse selection further complicate decision-making. The proposed mechanism aims to incentivize players to truthfully reveal their states while maximizing their expected payoffs. This is achieved through players&rsquo; best-reply strategies, ensuring truthful state revelation despite moral hazard. The revelation principle, a core concept in mechanism design, is applied to models with both moral hazard and adverse selection, facilitating optimal reward structure identification. The research holds significant practical implications, addressing the challenge of designing reward structures for multiplayer Markov games with hidden actions. By utilizing dynamic mechanism design, researchers and practitioners can optimize incentive schemes in complex, uncertain environments affected by moral hazard. To demonstrate the approach, the paper includes a numerical example of solving an oligopoly problem. Oligopolies, with a few dominant market players, exhibit complex dynamics where individual actions impact market outcomes significantly. Using the dynamic mechanism design framework, the paper shows how to construct optimal reward structures that align players&rsquo; incentives with desirable market outcomes, mitigating moral hazard and adverse selection effects. This framework is crucial for optimizing incentive schemes in multiplayer Markov games, providing a robust approach to handling the intricacies of moral hazard and adverse selection. By leveraging this design, the research contributes to the literature by offering a method to construct effective reward structures even in complex and uncertain environments. The numerical example of oligopolies illustrates the practical application and effectiveness of this dynamic mechanism design.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030045

Authors: Payal Bose Samir Bandyopadhyay

Leukemia is a form of blood cancer that results in an increase in the number of white blood cells in the body. The correct identification of leukemia at any stage is essential. The current traditional approaches rely mainly on field experts&rsquo; knowledge, which is time consuming. A lengthy testing interval combined with inadequate comprehension could harm a person&rsquo;s health. In this situation, an automated leukemia identification delivers more reliable and accurate diagnostic information. To effectively diagnose acute lymphoblastic leukemia from blood smear pictures, a new strategy based on traditional image analysis techniques with machine learning techniques and a composite learning approach were constructed in this experiment. The diagnostic process is separated into two parts: detection and identification. The traditional image analysis approach was utilized to identify leukemia cells from smear images. Finally, four widely recognized machine learning algorithms were used to identify the specific type of acute leukemia. It was discovered that Support Vector Machine (SVM) provides the highest accuracy in this scenario. To boost the performance, a deep learning model Resnet50 was hybridized with this model. Finally, it was revealed that this composite approach achieved 99.9% accuracy.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030044

Authors: Aubain Nzokem Daniel Maposa

The S&amp;P 500 Index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past few years, Bitcoin has grown in popularity and adoption. This study analyzes the daily return distribution of Bitcoin and the S&amp;P 500 Index and assesses their tail probabilities using two financial risk measures. As a methodology, we use Bitcoin and S&amp;P 500 Index daily return data to fit the seven-parameter General Tempered Stable (GTS) distribution using the advanced fast fractional Fourier transform (FRFT) scheme developed by combining the fast fractional Fourier transform algorithm and the 12-point composite Newton&ndash;Cotes rule. The findings show that peakedness is the main characteristic of the S&amp;P 500 Index return distribution, whereas heavy-tailedness is the main characteristic of Bitcoin return distribution. The GTS distribution shows that 80.05% of S&amp;P 500 returns are within &minus;1.06% and 1.23% against only 40.32% of Bitcoin returns. At a risk level (&alpha;), the severity of the loss (AVaR&alpha;(X)) on the left side of the distribution is larger than the severity of the profit (AVaR1&minus;&alpha;(X)) on the right side of the distribution. Compared to the S&amp;P 500 Index, Bitcoin has 39.73% more prevalence to produce high daily returns (more than 1.23% or less than &minus;1.06%). The severity analysis shows that, at &alpha; risk level, the average value-at-risk (AVaR(X)) of Bitcoin returns at one significant figure is four times larger than that of the S&amp;P 500 Index returns at the same risk.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030043

Authors: Roman Cherniha Vasyl’ Davydovych Alla Vorobyova

A one-dimensional model for fluid and solute transport in poroelastic materials (PEMs) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary cases, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated, and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030042

Authors: Majid Hojati Steven Roberts Colin Robertson

The widespread availability of tools to collect and share spatial data enables us to produce a large amount of geographic information on a daily basis. This enormous production of spatial data requires scalable data management systems. Geospatial architectures have changed from clusters to cloud architectures and more parallel and distributed processing platforms to be able to tackle these challenges. Peer-to-peer (P2P) systems as a backbone of distributed systems have been established in several application areas such as web3, blockchains, and crypto-currencies. Unlike centralized systems, data storage in P2P networks is distributed across network nodes, providing scalability and no single point of failure. However, managing and processing queries on these networks has always been challenging. In this work, we propose a spatio-temporal indexing data structure, DSTree. DSTree does not require additional Distributed Hash Trees (DHTs) to perform multi-dimensional range queries. Inserting a piece of new geographic information updates only a portion of the tree structure and does not impact the entire graph of the data. For example, for time-series data, such as storing sensor data, the DSTree performs around 40% faster in spatio-temporal queries for small and medium datasets. Despite the advantages of our proposed framework, challenges such as 20% slower insertion speed or semantic query capabilities remain. We conclude that more significant research effort from GIScience and related fields in developing decentralized applications is needed. The need for the standardization of different geographic information when sharing data on the IPFS network is one of the requirements.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030041

Authors: Martín G. Frixione Facundo Roffet Miguel A. Adami Marcelo Bertellotti Verónica L. D’Amico Claudio Delrieux Débora Pollicelli

Recently, nuclear abnormalities in avian erythrocytes have been used as biomarkers of genotoxicity in several species. Anomalous shapes are usually detected in the nuclei by means of microscopy inspection. However, due to inter- and intra-observer variability, the classification of these blood cell abnormalities could be problematic for replicating research. Deep learning, as a powerful image analysis technique, can be used in this context to improve standardization in identifying the biological configurations of medical and veterinary importance. In this study, we present a standardized deep learning model for identifying and classifying abnormal shapes in erythrocyte nuclei in blood smears of the hemispheric and synanthropic Kelp Gull (Larus dominicanus). We trained three convolutional backbones (ResNet34 and ResNet50 architectures) to obtain models capable of detecting and classifying these abnormalities in blood cells. The analysis was performed at three discrimination levels of classification, with broad categories subdivided into increasingly specific subcategories (level 1: &ldquo;normal&rdquo;, &ldquo;abnormal&rdquo;, &ldquo;other&rdquo;; level 2: &ldquo;normal&rdquo;, &ldquo;ENAs&rdquo;, &ldquo;micronucleus&rdquo;, &ldquo;other&rdquo;; level 3: &ldquo;normal&rdquo;, &ldquo;irregular&rdquo;, &ldquo;displaced&rdquo;, &ldquo;enucleated&rdquo;, &ldquo;micronucleus&rdquo;, &ldquo;other&rdquo;). The results were more than adequate and very similar in levels 1 and 2 (F1-score 84.6% and 83.6%, and accuracy 83.9% and 82.6%). In level 3, performance was lower (F1-score 65.9% and accuracy 80.8%). It can be concluded that the level 2 analysis should be considered the most appropriate as it is more specific than level 1, with similar quality of performance. This method has proven to be a fast, efficient, and standardized approach that reduces the dependence on human supervision in the classification of nuclear abnormalities in avian erythrocytes, and can be adapted to be used in similar contexts with reduced effort.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030040

Authors: Elkin Gelvez-Almeida Marco Mora Ricardo J. Barrientos Ruber Hernández-García Karina Vilches-Ponce Miguel Vera

The randomization-based feedforward neural network has raised great interest in the scientific community due to its simplicity, training speed, and accuracy comparable to traditional learning algorithms. The basic algorithm consists of randomly determining the weights and biases of the hidden layer and analytically calculating the weights of the output layer by solving a linear overdetermined system using the Moore&ndash;Penrose generalized inverse. When processing large volumes of data, randomization-based feedforward neural network models consume large amounts of memory and drastically increase training time. To efficiently solve the above problems, parallel and distributed models have recently been proposed. Previous reviews of randomization-based feedforward neural network models have mainly focused on categorizing and describing the evolution of the algorithms presented in the literature. The main contribution of this paper is to approach the topic from the perspective of the handling of large volumes of data. In this sense, we present a current and extensive review of the parallel and distributed models of randomized feedforward neural networks, focusing on extreme learning machine. In particular, we review the mathematical foundations (Moore&ndash;Penrose generalized inverse and solution of linear systems using parallel and distributed methods) and hardware and software technologies considered in current implementations.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030039

Authors: Pranowo Albertus Joko Santoso Agung Tri Wijayanta

A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The technique couples the pressure with the velocity components using an artificial compressibility model. The RPIM is used to discretize the spatial terms of the governing equation. We solve the semi-algebraic system implicitly in backward Euler pseudo-time. The proposed method solves two test problems&mdash;natural convection in the annulus of concentric circular cylinders and trapezoidal cavity. Additionally, the results are validated using experimental and numerical data available in the literature. Excellent agreement was seen between the numerical results acquired with the suggested method and those obtained through the standard techniques found in the literature.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030038

Authors: Nikolina Nikolarea Panteleimon Tzouganakis Vasilios Gakos Christos Papalexis Antonios Tsolakis Vasilios Spitas

This work introduces a 2D model that calculates power losses in coaxial magnetic gears (CMGs). The eddy current losses of the magnets are computed analytically, whereas the core losses of the ferromagnetic segments are computed using an analytical&ndash;finite element hybrid model. The results were within 1.51% and 3.18% of those obtained from an FEA for the eddy current and core losses in the CMG for an indicative inner rotor speed of 2500 rpm. In addition, the significance of the circumferential magnet segmentation is demonstrated in the CMGs. Furthermore, a parametric investigation of the efficiency of the system for different applied external loads is carried out. Finally, a mesh sensitivity analysis is performed, along with the computation of the average power losses throughout one full period, resulting in an at least 80% reduction in computational costs with a negligible effect on accuracy. The developed model could be a valuable tool for the minimization of power losses in CMGs since it combines high accuracy with a low computational cost.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030037

Authors: Stavroula Kridera Andreas Kanavos

This study explores trust dynamics within online social networks, blending social science theories with advanced machine-learning (ML) techniques. We examine trust&rsquo;s multifaceted nature&mdash;definitions, types, and mechanisms for its establishment and maintenance&mdash;and analyze social network structures through graph theory. Employing a diverse array of ML models (e.g., KNN, SVM, Naive Bayes, Gradient Boosting, and Neural Networks), we predict connection strengths on Facebook, focusing on model performance metrics such as accuracy, precision, recall, and F1-score. Our methodology, executed in Python using the Anaconda distribution, unveils insights into trust formation and sustainability on social media, highlighting the potent application of ML in understanding these dynamics. Challenges, including the complexity of modeling social behaviors and ethical data use concerns, are discussed, emphasizing the need for continued innovation. Our findings contribute to the discourse on trust in social networks and suggest future research directions, including the application of our methodologies to other platforms and the study of online trust over time. This work not only advances the academic understanding of digital social interactions but also offers practical implications for developers, policymakers, and online communities.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030036

Authors: Anatoli Ivanov Sergiy Shelyag

A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case with piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation, which make it smooth. The theoretical results are verified through extensive numerical simulations.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030035

Authors: Ana Alexandra Martins Daniel C. Vaz Tiago A. N. Silva Margarida Cardoso Alda Carvalho

In several industrial fields, environmental and operational data are acquired with numerous purposes, potentially generating a huge quantity of data containing valuable information for management actions. This work proposes a methodology for clustering time series based on the K-medoids algorithm using a convex combination of different time series correlation metrics, the COMB distance. The multidimensional scaling procedure is used to enhance the visualization of the clustering results, and a matrix plot display is proposed as an efficient visualization tool to interpret the COMB distance components. This is a general-purpose methodology that is intended to ease time series interpretation; however, due to the relevance of the field, this study explores the clustering of time series judiciously collected from data of a wind farm located on a complex terrain. Using the COMB distance for wind speed time bands, clustering exposes operational similarities and dissimilarities among neighboring turbines which are influenced by the turbines&rsquo; relative positions and terrain features and regarding the direction of oncoming wind. In a significant number of cases, clustering does not coincide with the natural geographic grouping of the turbines. A novel representation of the contributing distances&mdash;the COMB distance matrix plot&mdash;provides a quick way to compare pairs of time bands (turbines) regarding various features.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030034

Authors: Elbaz I. Abouelmagd

In this work, we derived a new type model for spatial Hill&rsquo;s system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect for describing Hill&rsquo;s problem. We identified the associated Lagrangian and Hamiltonian functions of the new system, and used them to verify the existence of the new equations of motion. We also proved that the new model has different six valid solutions under different six symmetries transformations as well as the original solution, where the new model is an invariant under these transformations. The several symmetries of Hill&rsquo;s model can extremely simplify the calculation and analysis of preparatory studies for the dynamical behavior of the system. Finally, we confirm that these symmetries also authorize us to explore the similarities and differences among many classes of paths that otherwise differ from the obtained trajectories by restricted three-body problem.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030033

Authors: Lindi Grobler Ryno Laubscher Johan van der Merwe Philip G. Herbst

The evaluation and accurate diagnosis of the type and severity of aortic stenosis relies on the precision of medical imaging technology and clinical correlations and the expertise of medical professionals. The application of the clinical correlation to different aortic stenosis morphologies and severities is investigated. The manner in which numerical techniques can be used to simulate the blood flow through pathological aortic valves was analysed and compared to the ground-truth CFD model. Larger pressure gradients are estimated in all severities of rheumatic aortic valves compared to calcific aortic valves. The zero-dimensional morphology-insensitive model underpredicted the transvalvular pressure gradient with the greatest error. The 1D model underestimated the pressure gradient in rheumatic cases and overestimated the pressure gradient in calcific cases. The pressure gradients estimated by the clinical approach depends on the location of the flow vena contracta and is sensitive to the severity and type of valve lesion. Through the analysis of entropy generation within the flow domain, the dominant parameters and regions driving adverse pressure gradients were identified. It is concluded that sudden expansion is the dominant parameter leading to higher pressure gradients in rheumatic heart valves compared to calcific ones.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030032

Authors: Marzieh Shamsizadeh Mohammad Mehdi Zahedi Khadijeh Abolpour Manuel De la Sen

In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030031

Authors: Francisco Martínez Mohammed K. A. Kaabar

In this study, a new generalized fractal&ndash;fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function&rsquo;s derivative. We complete the theory of generalized FF calculus by proposing a notion of integration and presenting two important results of integral calculus: the fundamental theorem and Barrow&rsquo;s rule. Finally, we analytically solve interesting FF ordinary differential equations by applying our proposed definition.

]]>Mathematical and Computational Applications doi: 10.3390/mca29030030

Authors: Qingguo Liu Umut Hanoglu Zlatko Rek Božidar Šarler

Using a meshless method, a simulation of steel billets in a pusher-type reheating furnace is carried out for the first time. The simulation represents an affordable way to replace the measurements. The heat transfer from the billets with convection and radiation is considered. Inside each of the billets, the heat diffusion equation is solved on a two-dimensional central slice of the billet. The diffusion equation is solved in a strong form by the Local Radial Basis Function Collocation Method (LRBFCM) with explicit time-stepping. The ray tracing procedure solves the radiation, where the view factors are computed with the Monte Carlo method. The changing number of billets in the furnace at the start and the end of the loading and unloading of the furnace is considered. A sensitivity study on billets&rsquo; temperature evolution is performed as a function of a different number of rays used in the Monte Carlo method, different stopping times of the billets in the furnace, and different spacing between the billets. The temperature field simulation is also essential for automatically optimizing the furnace&rsquo;s productivity, energy consumption, and the billet&rsquo;s quality. For the first time, the LRBFCM is successfully demonstrated for solving such a complex industrial problem.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020029

Authors: Yuan-Jay Wang

This study aims to synthesize and implement a robust fractional order PD (RFOPD) controller to increase the speed at which defects in automated touch panel inspection systems (ATPISs) are detected. A three-dimensional orthogonal stage (TDOS) driven by BLDC servo motors moves the inspection pen (IP) vertically and horizontally. The dynamic equation relating the BLDC servo motor input to the tip motion is established. A touch position identification (TPI) system is used to locate the touch point rapidly. An RFOPD controller is used to actuate the BLDC servo motors and move the TDOS rapidly and accurately in three dimensions. This method displaces the IP to any specified position and shows user-defined inspection trajectories on the touch screens. The gain-phase margin tester (GPMT) and stability equation methods are exploited to schedule the RFOPD controller gain settings and to maintain the specific safety margins for the controlled system. The simulation studies show that the proposed RFOPD controller exhibits better tracking and disturbance rejection responses than a conventional PID controller. The robustness of the RFOPD-controlled ATPIS, considering unmodeled uncertainties and friction-induced disturbances, is verified through simulation and experimental studies. Several user-defined inspection patterns are used to verify performance, and the experimental results show that the proposed RFOPD controller is effective.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020028

Authors: Messaoud Berkal Juan Francisco Navarro Raafat Abo-Zeid

In this paper, we derive the well-defined solutions to a &theta;-dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences. Moreover, we study the global stability of the solutions to that system. Finally, we give some numerical examples which confirm our theoretical results.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020026

Authors: Wanqing Tian Changxing Ma

Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to satisfy different research proposed in randomized clinical trials. In this article, we propose three test statistics (the likelihood ratio test, score test, and Wald-type test statistics) to evaluate the homogeneity of proportion ratios for stratified bilateral correlated data under an equal correlation assumption. Monte Carlo simulations of Type I error and power are performed, and the score test yields a robust outcome based on empirical Type I error and power. Lastly, two real data examples are conducted to illustrate the proposed three tests.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020027

Authors: Patrick Mahoney Alex Povitsky

In this study, the Method of Fundamental Solutions (MFSs) is adopted to model Chemical Vapor Infiltration (CVI) in a fibrous preform. The preparation of dense fiber-reinforced silicon carbide composites is considered. The reaction flux at the solid surface is equal to the diffusion flux towards the surface. The Robin or third-type boundary condition is implemented into the MFS. From the fibers&rsquo; surface concentrations obtained by MFS, deposition rates are calculated, and the geometry is updated at each time step, modeling the pore filling over time. The MFS solution is verified by comparing the results to a known analytical solution for a simplified geometry of concentric cylinders with a concentration set at the outer cylinder and a reaction at the inner cylinder. MFS solutions are compared to published experimental data. Porosity transients are obtained by a combination of MFSs with surface deposition to show the relation between the initial and final porosities.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020025

Authors: Luis Cárdenas Florido Leonardo Trujillo Daniel E. Hernandez Jose Manuel Muñoz Contreras

Machine learning and artificial intelligence are growing in popularity thanks to their ability to produce models that exhibit unprecedented performance in domains that include computer vision, natural language processing and code generation. However, such models tend to be very large and complex and impossible to understand using traditional analysis or human scrutiny. Conversely, Symbolic Regression methods attempt to produce models that are relatively small and (potentially) human-readable. In this domain, Genetic Programming (GP) has proven to be a powerful search strategy that achieves state-of-the-art performance. This paper presents a new GP-based feature transformation method called M5GP, which is hybridized with multiple linear regression to produce linear models, implemented to exploit parallel processing on graphical processing units for efficient computation. M5GP is the most recent variant from a family of feature transformation methods (M2GP, M3GP and M4GP) that have proven to be powerful tools for both classification and regression tasks applied to tabular data. The proposed method was evaluated on SRBench v2.0, the current standard benchmarking suite for Symbolic Regression. Results show that M5GP achieves performance that is competitive with the state-of-the-art, achieving a top-three rank on the most difficult subset of black-box problems. Moreover, it achieves the lowest computation time when compared to other GP-based methods that have similar accuracy scores.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020024

Authors: Parham Azhir Jafar Asgari Marnani Mehdi Panji Mohammad Sadegh Rohanimanesh

This paper introduces an innovative approach to numerically model Structure&ndash;Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM&ndash;FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020023

Authors: Izaz Ali Umut Hanoglu Robert Vertnik Božidar Šarler

This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020022

Authors: Alda Carvalho Ana Martins Ana F. Mota Maria A. R. Loja

Carbon nanotubes are widely used as material reinforcement in diverse fields of engineering. Being that their contribution is significant to improving the mean properties of the resulting materials, it is important to assess the influence of the variability on carbon nanotubes&rsquo; material and geometrical properties to structures&rsquo; responses. This work considers functionally graded plates constituted by an aluminum continuous phase reinforced with single-walled or multi-walled carbon. The nanotubes' weight fraction evolution through the thickness is responsible for the plates&rsquo; functional gradient. The plates&rsquo; samples are simulated considering that only the nanotubes&rsquo; material and geometrical characteristics are affected by uncertainty. The results obtained from the multiple regression models developed allow us to conclude that the length of the nanotubes has no impact on the maximum transverse displacement of the plates in opposition to the carbon nanotubes&rsquo; weight fraction evolution, their internal and external diameters, and the Young&rsquo;s modulus. The multiple regression models developed can be used as alternative prediction tools within the domain of the study.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020021

Authors: Faroque Ahmed Mrittika Shamsuddin Tanzila Sultana Rittika Shamsuddin

Risk and uncertainty play a vital role in almost every significant economic decision, and an individual&rsquo;s propensity to make riskier decisions also depends on various circumstances. This article aims to investigate the effects of social and economic covariates on an individual&rsquo;s willingness to take general risks and extends the scope of existing works by using quantitative measures of risk-taking from the GPS and Gallup datasets (in addition to the qualitative measures used in the literature). Based on the available observed risk-taking data for one year, this article proposes a semi-supervised machine learning-based approach that can efficiently predict the observed risk index for those countries/individuals for years when the observed risk-taking index was not collected. We find that linear models are insufficient to capture certain patterns among risk-taking factors, and non-linear models, such as random forest regression, can obtain better root mean squared values than those reported in past literature. In addition to finding factors that agree with past studies, we also find that subjective well-being influences risk-taking behavior.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020020

Authors: Rabab A. Alghanmi Rawan H. Aljaghthami

This study is centered on examining the static bending behavior of sandwich plates featuring functionally graded materials, specifically addressing distinct representations of porosity distribution across their thickness. The composition of the sandwich plate involves a ceramic core and two face sheets with functionally graded properties. Mechanical loads with a sinusoidal distribution are applied to the sandwich plate, and a four-variable shear deformation theory is employed to establish the displacement field. Notably, this theory involves only four unknowns, distinguishing it from alternative shear deformation theories. Equilibrium equations are derived using the virtual work concept, and Navier&rsquo;s method is applied to obtain the solution. The study addresses the impact of varying porosities, inhomogeneity parameters, aspect ratios, and side-to-thickness ratios on the static bending behavior of the sandwich plates. The influence of various porosities, inhomogeneity parameter, aspect ratio, and side-to-thickness ratio of the sandwich plates are explored and compared in the context of static bending behavior. The three porosity distributions are compared in terms of their influence on the bending behavior of the sandwich plate. The findings indicate that a higher porosity causes larger deflections and Model A has the highest central deflection. Adopting the four-variable shear deformation theory demonstrated its validity since the results were similar to those obtained in the literature. Several important findings have been found, which could be useful in the construction and application of FG sandwich structures. Examples of comparison will be discussed to support the existing theory&rsquo;s accuracy. Further findings are presented to serve as benchmarks for comparison.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020019

Authors: Juan Frausto-Solís José Christian de Jesús Galicia-González Juan Javier González-Barbosa Guadalupe Castilla-Valdez Juan Paulo Sánchez-Hernández

Accurate forecasting remains a challenge, even with advanced techniques like deep learning (DL), ARIMA, and Holt&ndash;Winters (H&amp;W), particularly for chaotic phenomena such as those observed in several areas, such as COVID-19, energy, and financial time series. Addressing this, we introduce a Forecasting Method with Filters and Residual Analysis (FMFRA), a hybrid methodology specifically applied to datasets of COVID-19 time series, which we selected for their complexity and exemplification of current forecasting challenges. FMFFRA consists of the following two approaches: FMFRA-DL, employing deep learning, and FMFRA-SSA, using singular spectrum analysis. This proposed method applies the following three phases: filtering, forecasting, and residual analysis. Initially, each time series is split into filtered and residual components. The second phase involves a simple fine-tuning for the filtered time series, while the third phase refines the forecasts and mitigates noise. FMFRA-DL is adept at forecasting complex series by distinguishing primary trends from insufficient relevant information. FMFRA-SSA is effective in data-scarce scenarios, enhancing forecasts through automated parameter search and residual analysis. Chosen for their geographical and substantial populations and chaotic dynamics, time series for Mexico, the United States, Colombia, and Brazil permitted a comparative perspective. FMFRA demonstrates its efficacy by improving the common forecasting performance measures of MAPE by 22.91%, DA by 13.19%, and RMSE by 25.24% compared to the second-best method, showcasing its potential for providing essential insights into various rapidly evolving domains.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020018

Authors: Gerardo J. Riveros-Rojas Pedro P. Cespedes-Sanchez Diego P. Pinto-Roa Horacio Legal-Ayala

Internet energy consumption has increased rapidly, and energy conservation has become a significant issue that requires focused research efforts. The most promising solution is to identify the minimum power subsets within the network and shut down unnecessary network devices and links to satisfy traffic loads. Due to their distributed network control, implementing a centralized and coordinated strategy in traditional networks is challenging. Software-Defined Networking (SDN) is an emerging technology with dynamic, manageable, cost-effective, and adaptable solutions. SDN decouples network control and forwarding functions, allowing network control to be directly programmable, centralizing control with a global network view to manage power states. Nevertheless, it is crucial to develop efficient algorithms that leverage the centralized control of SDN to achieve maximum energy savings and consider peak traffic times. Traffic demand usually cannot be satisfied, even when all network devices are active. This work jointly addresses the routing of traffic flows and the assignment of SDN devices to these flows, called the Routing and Device Assignment (RDA) problem. It simultaneously seeks to minimize the network&rsquo;s energy consumption and blocked traffic flows. For this approach, we develop an exact solution based on Mixed-Integer Linear Programming (MILP) as well as a metaheuristic based on a Genetic Algorithm (GA) that seeks to optimize both criteria by routing flows efficiently and suspending devices not used by the flows. Conducted simulations on traffic environment scenarios show up to 34% savings in overall energy consumption for the MILP and 33% savings achieved by the GA. These values are better than those obtained using competitive state-of-the-art strategies.

]]>Mathematical and Computational Applications doi: 10.3390/mca29020017

Authors: Sanjar M. Abrarov Rehan Siddiqui Rajinder Kumar Jagpal Brendan M. Quine

In this work, we develop a new iterative method for computing the digits of &pi; by argument reduction of the tangent function. This method combines a modified version of the iterative formula for &pi; with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of &pi; per increment. Mathematica codes, showing the convergence rate for computing the digits of &pi;, are presented.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010016

Authors: Mohammad Khodabakhshi Soureshjani Hermann J. Eberl Richard G. Zytner

Bioventing is an established technique extensively employed in the remediation of soil contaminated with petroleum hydrocarbons. In this study, the objective was to develop an improved foundational bioventing model that characterizes gas flow in vadose zones where aqueous and non-aqueous phase liquid (NAPL) are present and immobile, accounting for interphase mass transfer and first order biodegradation kinetics. By incorporating a correlation for the biodegradation rate constant, which is a function of soil properties including initial population of petroleum degrader microorganisms in soil, sand content, clay content, water content, and soil organic matter content, this model offers the ability to integrate a specific biodegradation rate constant tailored to the soil properties for each site. The governing equations were solved using the finite volume method in OpenFOAM employing the &ldquo;porousMultiphaseFoam v2107&rdquo; (PMF) toolbox. The equation describing gas flow in unsaturated soil was solved using a mixed pressure-saturation method, where calculated values were employed to solve the component transport equations. Calibration was done against a set of experimental data for a meso-scale reactor considering contaminant volatilization rate as the pre-calibration parameter and the mass transfer coefficient between aqueous and NAPL phase as the main calibration parameter. The calibrated model then was validated by simulating a large-scale reactor. The modelling results showed an error of 2.9% for calibrated case and 4.7% error for validation case which present the fitness to the experimental data, proving that the enhanced bioventing model holds the potential to improve predictions of bioventing and facilitate the development of efficient strategies to remediate soil contaminated with petroleum hydrocarbons.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010015

Authors: Asghar Qadir

In this paper, it is noted that three apparently disparate areas of mathematics&mdash;singularity analysis, complex symmetry analysis and the distributional representation of special functions&mdash;have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010014

Authors: Jorge Chávez-Saab Odalis Ortega Amalia Pizarro-Madariaga

A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies. This computation traditionally relied on V&eacute;lu&rsquo;s formulas, an approach with time complexity linear in the degree but which was further enhanced by Bernstein, De Feo, Leroux, and Smith to a square-root complexity. The improved square-root V&eacute;lu&rsquo;s formulas exhibit a degree of parallelizability that has not been exploited in major implementations. In this study, we introduce a theoretical framework for parallelizing isogeny computations and provide a proof-of-concept implementation in C with OpenMP. While the parallelization effectiveness exhibits diminishing returns with the number of cores, we still obtain strong results when using a small number of cores. Concretely, our implementation shows that for large degrees it is easy to achieve speedup factors of up to 1.74, 2.54, and 3.44 for two, four, and eight cores, respectively.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010013

Authors: Pritha Dutta Anita T. Layton

Calcium (Ca2+) and magnesium (Mg2+) are essential for cellular function. The kidneys play an important role in maintaining the homeostasis of these cations. Their reabsorption along the nephron is dependent on distinct trans- and paracellular pathways and is coupled to the transport of other electrolytes. Notably, sodium (Na+) transport establishes an electrochemical gradient to drive Ca2+ and Mg2+ reabsorption. Consequently, alterations in renal Na+ handling, under pathophysiological conditions or pharmacological manipulations, can have major effects on Ca2+ and Mg2+ transport. One such condition is the administration of diuretics, which are used to treat a large range of clinical conditions, but most commonly for the management of blood pressure and fluid balance. While the pharmacological targets of diuretics typically directly mediate Na+ transport, they also indirectly affect renal Ca2+ and Mg2+ handling through alterations in the electrochemical gradient. To investigate renal Ca2+ and Mg2 handling and how those processes are affected by diuretic treatment, we have developed computational models of electrolyte transport along the nephrons. Model simulations indicate that along the proximal tubule and thick ascending limb, the transport of Ca2+ and Mg2+ occurs in parallel with Na+, but those processes are dissociated along the distal convoluted tubule. We also simulated the effects of acute administration of loop, thiazide, and K-sparing diuretics. The model predicted significantly increased Ca2+ and Mg2+ excretions and significantly decreased Ca2+ and Mg2+ excretions on treatment with loop and K-sparing diuretics, respectively. Treatment with thiazide diuretics significantly decreased Ca2+ excretion, but there was no significant alteration in Mg2+ excretion. The present models can be used to conduct in silico studies on how the kidney adapts to alterations in Ca2+ and Mg2+ homeostasis during various physiological and pathophysiological conditions, such as pregnancy, diabetes, and chronic kidney disease.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010012

Authors: Pranowo Djoko Budiyanto Setyohadi Agung Tri Wijayanta

This paper proposes the D2Q5 Lattice Boltzmann method (LBM) method, in two dimensions with five discrete lattice velocities, for simulating linear sound wave propagation in closed rooms. A second-order linear acoustic equation obtained from the LBM method was used as the model equation. Boundary conditions at the domain boundary use the bounce-back scheme. The LBM numerical calculation algorithm in this paper is relatively simpler and easy to implement. Parallelization with the GPU CUDA was implemented to speed up the execution time. The calculation results show that the use of parallel GPU CUDA programming can accelerate the proposed simulation 27.47 times faster than serial CPU programming. The simulation results are validated with analytical solutions for acoustic pulse reflected by the flat and oblique walls, the comparisons show very good concordance, and the D2Q5 LBM has second-order accuracy. In addition, the simulation results in the form of wavefront propagation images in complicated shaped rooms are also compared with experimental photographs, and the comparison also shows excellent concordance. The numerical results of the D2Q5 LBM are promising and also demonstrate the great capability of the D2Q5 LBM for investigating room acoustics in various complexities.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010011

Authors: Gilbert Kerr Nehemiah Lopez Gilberto González-Parra

In this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theorem. The obtained solutions have the form of infinite non-harmonic Fourier series. The main advantage of the proposed approach is the closed-form of the solutions, which are capable of accurately evaluating the solution at any time. Moreover, it allows one to study the asymptotic behavior of the solutions. A remarkable discovery, which to the best of our knowledge has never been presented in the literature, is that there are some particular linear systems of both retarded and neutral delay differential equations for which the solution asymptotically approaches a limit cycle. The well-known method of steps in many cases is unable to obtain the asymptotic behavior of the solution and would most likely fail to detect such cycles. Examples illustrating the Laplace transform method for linear systems of DDEs are presented and discussed. These examples are designed to facilitate a discussion on how the spectral properties of the matrices determine the manner in which one proceeds and how they impact the behavior of the solution. Comparisons with the exact solution provided by the method of steps are presented. Finally, we should mention that the solutions generated by the Laplace transform are, in most instances, extremely accurate even when the truncated series is limited to only a handful of terms and in many cases become more accurate as the independent variable increases.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010010

Authors: Lidiya Kurpa Francesco Pellicano Tetyana Shmatko Antonio Zippo

Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz&rsquo;s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010009

Authors: Saakaar Bhatnagar

Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the generalization accuracy of a CTESN surrogate is the method of projecting the reservoir state to the output. This paper shows that of the two common projection methods (linear and nonlinear), the surrogates developed via the nonlinear projection consistently outperform those developed via the linear method. CTESN surrogates are developed for several challenging benchmark cases governed by stiff ODEs, and for each case, the performance of the linear and nonlinear projections is compared. The results of this paper demonstrate the applicability of CTESNs to a variety of problems while serving as a reference for important algorithmic and hyper-parameter choices for CTESNs.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010008

Authors: Silvija Angelova Maria Angelova Rositsa Raikova

Electromyography (EMG) is a widely used method for estimating muscle activity and could help in understanding how muscles interact with each other and affect human movement control. To detect muscle interactions during elbow flexion and extension, a recently developed InterCriteria Analysis (ICrA) based on the mathematical formalisms of index matrices and intuitionistic fuzzy sets is applied. ICrA has had numerous implementations in different fields, including biomedicine and quality of life; however, this is the first time the approach has been used for establishing muscle interactions. Six human upper arm large surface muscles or parts of muscles responsible for flexion and extension in shoulder and elbow joints were selected. Surface EMG signals were recorded from four one-joint (pars clavicularis and pars spinata of m. deltoideus [DELcla and DELspi, respectively], m. brachialis [BRA], and m. anconeus [ANC]) and two two-joint (m. biceps brachii [BIC] and m. triceps brachii-caput longum [TRI]) muscles. The outcomes from ten healthy subjects performing flexion and extension movements in the sagittal plane at four speeds with and without additional load are implemented in this study. When ICrA was applied to examine the two different movements, the BIC&ndash;BRA muscle interaction was distinguished during flexion. On the other hand, when the ten subjects were observed, four interacting muscle pairs, namely DELcla-DELspi, BIC-TRI, BIC-BRA, and TRI-BRA, were detected. The results obtained after the ICrA application confirmed the expectations that the investigated muscles contribute differently to the human upper arm movements when the flexion and extension velocities are changed, or a load is added.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010007

Authors: Yang Lin Jin Liang

In this paper, we propose an extended credit migration model with asymmetric fixed boundaries and multiple ratings, for a more precise depiction of credit changes in the real world. A model with three ratings is established and analyzed as an example, and then the results are generalized to a general multirating form model. We prepare the model meaningfully by arranging the asymmetric boundaries in a suitable order. A PDE system problem is deduced, and the existence and uniqueness of the solution for the problem are obtained using PDE techniques, which further ensure the rationality of the model. Due to the flexible configuration of asymmetric boundaries, the multirating model has various types of structures in the buffer zones where the credit rating keeps its original state. For instance, the two buffers in the three-rating model may be separated, connected, or intersected, as presented in the numerical results for different boundary parameters.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010006

Authors: Mengli Yao Zhifeng Weng

In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schr&ouml;dinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank&ndash;Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010005

Authors: Yang-Yih Chen Hsien-Kuo Chang

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010004

Authors: Lorentz Jäntschi Mohamed Louzazni

Small-scale photovoltaic (PV) systems are essential for the local energy supply. The most commonly known PV cell is configured as a large-area p&ndash;n junction made from silicon, but PV systems today include PV cells of various manufactures and origins. The dependence relationship between current and voltage is nonlinear, known as the current&ndash;voltage characteristic. The values of the characteristic equation&rsquo;s parameters define the working regime of the PV cell. In the present work, the parameter values are iteratively obtained by nonlinear regression for an explicit model. The acceleration of the convergence of these values is studied for an approximation simplifying the iterative calculation in the case of perpendicular offsets. The new estimations of parameters allow for a much faster estimate of the maximum power point of the PV system.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010003

Authors: Sk Golam Mortoja Ayan Paul Prabir Panja Sabyasachi Bhattacharya Shyamal Kumar Mondal

It is frequently observed that adult members of prey species sometimes use their predation mechanism on juvenile members of predator species. Ecological literature describes this phenomenon as prey&ndash;predator role reversal dynamics.Numerous authors have observed and described the biological development behind this feeding behaviour. However, the dynamics of this role reversal have hardly been illustrated in the literature in a precise way. In this regard, we formulated an ecological model using the standard prey&ndash;predator interactions, allowing for a reverse feeding mechanism. The mathematical model consisted of a three-species food-web structure comprising the common prey, intermediate predator, and top predator. Note that a role-reversal mechanism was observed between the intermediate and top predators based on the scarcity of the prey population. However, we observed the most critical parameters had a significant effect on this reverse feeding behaviour. The bifurcation analysis is the primary criterion for this identification. The proposed deterministic model is then extended to its stochastic analogue by allowing for environmental influences on the tri-trophic food web structure. The conditional moment approach is applied to obtain the equilibrium distribution of populations and their conditional moments in the system. The stochastic setup analysis also supports the stability of this food chain structure, with some restricted conditions. Finally, to facilitate the interpretation of our mathematical results, we investigated it using numerical simulations.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010002

Authors: Manruo Cui Cui-Cui Ji Weizhong Dai

In this paper, we develop a finite difference method for solving the wave equation with fractional damping in 1D and 2D cases, where the fractional damping is given based on the Caputo fractional derivative. Firstly, based on the weighted method, we propose a new numerical approximation for the Caputo fractional derivative and apply it for the 1D case to obtain a time-stepping method. We then develop an alternating direction implicit (ADI) scheme for the 2D case. Using the discrete energy method, we prove that the proposed difference schemes are unconditionally stable and convergent in both 1D and 2D cases. Finally, several numerical examples are given to verify the theoretical results.

]]>Mathematical and Computational Applications doi: 10.3390/mca29010001

Authors: Francisco Zdanowski Isabel Malico Paulo Canhoto Rui Pedro Lima

Simulation and modeling of thermal recuperative incinerators may play an important role in enhancing efficiency and ensuring compliance with environmental regulations. In this context, the primary objective of this study is to simulate and comprehensively understand the operation of a geometrically complex thermal recuperative incinerator with an integrated preheater featuring varying levels of heat recovery. To achieve this objective, a simple yet effective 0D model was developed. This modeling approach allows for a holistic evaluation of the performance of the incinerator, enabling the assessment of key parameters, such as temperatures and heat transfer rates, under varying operating conditions. Successful validation of the model is established by comparing its results with measurements from an industrial thermal recuperative incinerator in operation at a vehicle assembly plant, with maximum relative differences of around 9%. Simulations for different percentages of flue gases bypassing the preheater were conducted, indicating a good compromise between heat transfer and pressure drop and a 22% heat recovery at around 50%. The model presented in this paper provides a robust foundation for comprehensively assessing and optimizing the performance of thermal recuperative incinerators and systems that comprise thermal recuperative incinerators, with implications for waste management and sustainable energy recovery systems.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060113

Authors: Mario Annunziato Alfio Borzì

A method for the analysis of super-resolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this membrane. Thus, the purpose of this method is to recover the structural properties of the membrane by solving an inverse problem governed by the Fokker&ndash;Planck equation related to the stochastic trajectories. Results of numerical experiments demonstrate the ability of the proposed method to reconstruct the potential of a cell membrane by using synthetic data similar those captured by super-resolution microscopy of luminescent activated proteins.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060112

Authors: Himel Barua Alex Povitsky

Chemical vapor deposition (CVD) is a common industrial process that incorporates a complex combination of fluid flow, chemical reactions, and surface deposition. Understanding CVD processes requires rigorous and costly experimentation involving multiple spatial scales, from meters to nanometers. The numerical modeling of deposition over macro-scale substrates has been conducted in the literature and results show compliance with experimental data. For smaller-scale substrates, where the corresponding Knudsen number is larger than zero, continuum modeling does not provide accurate results, which calls for the implementation of molecular-level modeling techniques. In the current study, the finite-volume method (FVM) and Direct Simulation Monte Carlo (DSMC) method were combined to model the reactor-scale flow with CVD around micro- and nano-scale fibers. CVD at fibers with round cross-sections was modeled in the reactor, where fibers were oriented perpendicularly with respect to the feedstock gas flow. The DSMC method was applied to modeling flow around the matrix of nano-scale circular individual fibers. Results show that for smaller diameters of individual fibers with the same filling ratio, the residence time of gas particles inside the fibrous media reduces, and, consequently, the amount of material surface deposition decreases. The sticking coefficient on the fibers&rsquo; surface plays an important role; for instance, increasing the sticking coefficient from 20% to 80% will double the deposition rate.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060111

Authors: Elio Chiodo Fabio De Angelis Bassel Diban Giovanni Mazzanti

In the present paper, the process of estimating the important statistical properties of extreme wind loads on structures is investigated by considering the effect of large variability. In fact, for the safety design and operating conditions of structures such as the ones characterizing tall buildings, wind towers, and offshore structures, it is of interest to obtain the best possible estimates of extreme wind loads on structures, the recurrence frequency, the return periods, and other stochastic properties, given the available statistical data. In this paper, a Bayes estimation of extreme load values is investigated in the framework of structural safety analysis. The evaluation of extreme values of the wind loads on the structures is performed via a combined employment of a Poisson process model for the peak-over-threshold characterization and an adequate characterization of the parent distribution which generates the base wind load values. In particular, the present investigation is based upon a key parameter for assessing the safety of structures, i.e., a proper safety index referred to a given extreme value of wind speed. The attention is focused upon the estimation process, for which the presented procedure proposes an adequate Bayesian approach based upon prior assumptions regarding (1) the Weibull probability that wind speed is higher than a prefixed threshold value, and (2) the frequency of the Poisson process of gusts. In the last part of the investigation, a large set of numerical simulations is analyzed to evaluate the feasibility and efficiency of the above estimation method and with the objective to analyze and compare the presented approach with the classical Maximum Likelihood method. Moreover, the robustness of the proposed Bayes estimation is also investigated with successful results, both with respect to the assumed parameter prior distributions and with respect to the Weibull distribution of the wind speed values.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060110

Authors: Yanan Wang Shuying Zhai

The extended Fisher&ndash;Kolmogorov (EFK) equation is an important model for phase transitions and bistable phenomena. This paper presents some fast explicit numerical schemes based on the integrating factor Runge&ndash;Kutta method and the Fourier spectral method to solve the EFK equation. The discrete global convergence of these new schemes is analyzed rigorously. Three numerical examples are presented to verify the theoretical analysis and the efficiency of the proposed schemes.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060109

Authors: Ali M. Mubaraki

This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation. In addition, perfect continuity conditions are imposed between the coating layer and the substrate, while suitable decaying conditions are slated along the infinite depth of the half-space. The effect of the thin layer is modeled using appropriate effective boundary conditions within the long-wave limit. By applying the Radon transform and using the perturbation method, the derived model successfully captures the physical characteristics of elastic surface waves in coated half-spaces. The model consists of a pesudo-static elliptic equation decaying over the interior of the half-space and a singularly perturbed hyperbolic equation with a pseudo-differential operator. The pseudo-differential equation gives the approximate dispersion of surface waves on the coated half-space structure and is analyzed numerically at the end.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060108

Authors: Muhammad Tariq Hijaz Ahmad Asif Ali Shaikh Sotiris K. Ntouyas Evren Hınçal Sania Qureshi

The theory of convexity pertaining to fractional calculus is a well-established concept that has attracted significant attention in mathematics and various scientific disciplines for over a century. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we establish new fractional identities. Employing these identities, some extensions of the fractional H-H type inequality via generalized preinvexities are explored. Finally, we discuss some applications to the q-digamma and Bessel functions via the established results. We believe that the methodologies and approaches presented in this work will intrigue and spark the researcher&rsquo;s interest even more.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060107

Authors: Patricia Melin Daniela Sánchez Martha Pulido Oscar Castillo

The preventive measures taken to curb the spread of COVID-19 have emphasized the importance of wearing face masks to prevent potential infection with serious diseases during daily activities or for medical professionals working in hospitals. Due to the mandatory use of face masks, various methods employing artificial intelligence and deep learning have emerged to detect whether individuals are wearing masks. In this paper, we utilized convolutional neural networks (CNNs) to classify the use of face masks into three categories: no mask, incorrect mask, and proper mask. Establishing the appropriate CNN architecture can be a demanding task. This study compares four swarm intelligent metaheuristics: particle swarm optimization (PSO), grey wolf optimizer (GWO), bat algorithm (BA), and whale optimization algorithm (WOA). The CNN architecture design involves determining the essential hyperparameters of the CNNs. The results indicate the effectiveness of the PSO and BA in achieving an accuracy of 100% when using 10% of the images for testing. Meanwhile, when 90% of the images were used for testing, the results were as follows: PSO 97.15%, WOA 97.14%, BA 97.23%, and GWO 97.18%. These statistically significant differences demonstrate that the BA allows better results than the other metaheuristics analyzed in this study.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060106

Authors: Mary A. Familusi Sebastian Skatulla Jagir R. Hussan Olukayode O. Aremu Daniel Mutithu Evelyn N. Lumngwena Freedom N. Gumedze Ntobeko A. B. Ntusi

Non-invasive measurements are important for the development of new treatments for heart failure, which is one of the leading causes of death worldwide. This study aimed to develop realistic subject-specific computational models of human biventricles using clinical data. Three-dimensional finite element models of the human ventricles were created using cardiovascular magnetic resonance images of rheumatic heart disease (RHD) patients and healthy subjects. The material parameter optimization uses inverse modeling based on the finite element method combined with the Levenberg&ndash;Marquardt method (LVM) by targeting subject-specific hemodynamics. The study of elastic myocardial parameters between healthy subjects and RHD patients showed an elevated stiffness in diseased hearts. In particular, the anisotropic material behavior of the healthy and diseased cardiac tissue significantly differed from one another. Furthermore, as the LVEF decreased, the stiffness and its orientation-dependent parameters increased. The simulation-derived LV myocardial circumferential and longitudinal stresses were negatively associated with the LVEF. The sensitivity analysis result demonstrated that the observed significant difference between the elastic material parameters of diseased and healthy myocardium was not exclusively attributable to an increased LVEDP in the diseased heart. These results could be applied to future computational studies for developing heart failure treatment.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060105

Authors: Marta M. Sánchez-García Gonzalo Barderas Pilar Romero

The aim of this paper is to analyze the determination of interplanetary trajectories from Earth to Mars to evaluate the cost of the required impulse magnitudes for an areostationary orbiter mission design. Such analysis is first conducted by solving the Lambert orbital boundary value problem and studying the launch and arrival conditions for various date combinations. Then, genetic algorithms are applied to investigate the minimum-energy transfer orbit. Afterwards, an iterative procedure is used to determine the heliocentric elliptic transfer orbit that matches at the entry point of Mars&rsquo;s sphere of influence with an areocentric hyperbolic orbit imposing specific conditions on inclination and periapsis radius. Finally, the maneuvers needed to obtain an areostationary orbit are numerically computed for different objective condition values at the Mars entry point to evaluate an areostationary preliminary mission cost for further study and characterization. Results show that, for the dates of the minimum-energy Earth&ndash;Mars transfer trajectory, a low value for the maneuvers to achieve an areostationary orbit is obtained for an arrival hyperbola with the minimum possible inclination and a capture into an elliptical trajectory with a low periapsis radius and an apoapsis at the stationary orbit. For a 2026 mission with a TOF of 304 for the minimum-energy Earth&ndash;Mars transfer trajectory, for a capture with a periapsis of 300 km above the Mars surface the value achieved will be 2.083 km/s.

]]>Mathematical and Computational Applications doi: 10.3390/mca28060104

Authors: Wanlin Wang Jinxiong Chen Zhenkun Huang

An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that individually estimate the state of the neurons at various periods. This new cascade predictor is more useful than the conventional single observer in predicting neural network states when the output delay is arbitrarily large but known. In contrast to examining the stability of error systems solely employing the Lyapunov&ndash;Krasovskii functional (LKF), several new global asymptotic stability standards are obtained by combining the application of the Linear Parameter Varying (LPV) approach, LKF and convex principle. Finally, a series of numerical simulations verify the efficacy of the obtained results.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050103

Authors: Nourddine Azzaoui Tomoko Matsui Daisuke Murakami

We devised a data-driven framework for uncovering hidden control strategies used by an evolutionary system described by an evolutionary probability distribution. This innovative framework enables deciphering of the concealed mechanisms that contribute to the progression or mitigation of such situations as the spread of COVID-19. Novel algorithms are used to estimate the optimal control in tandem with the parameters for evolution in general dynamical systems, thereby extending the concept of model predictive control. This marks a significant departure from conventional control methods, which require knowledge of the system to manipulate its evolution and of the controller&rsquo;s strategy or parameters. We use a generalized additive model, supplemented by extensive statistical testing, to identify a set of predictor covariates closely linked to the control. Using real-world COVID-19 data, we delineate the descriptive behaviors of the COVID-19 epidemics in five prefectures in Japan and nine countries. We compare these nine countries and group them on the basis of shared profiles, providing valuable insights into their pandemic responses. Our findings underscore the potential of our framework as a powerful tool for understanding and managing complex evolutionary processes.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050102

Authors: Beichao Hu Dwayne McDaniel

In recent years, Physics-Informed Neural Networks (PINNs) have drawn great interest among researchers as a tool to solve computational physics problems. Unlike conventional neural networks, which are black-box models that &ldquo;blindly&rdquo; establish a correlation between input and output variables using a large quantity of labeled data, PINNs directly embed physical laws (primarily partial differential equations) within the loss function of neural networks. By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier&ndash;Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the Navier&ndash;Stokes equations for a 2D incompressible laminar flow problem. Flows passing around a 2D circular particle are chosen as the benchmark case, and an elliptical particle is also examined to enrich the research. The velocity and pressure fields are predicted by the PINNs, and the results are compared with those derived from Computational Fluid Dynamics (CFD). Additionally, the particle drag force coefficient is calculated to quantify the discrepancy in the results of the PINNs as compared to CFD outcomes. The drag coefficient maintained an error within 10% across all test scenarios.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050101

Authors: Haojie Lin Xuyang Lou

For positioning and anti-swing control of bridge cranes, the active learning control method can reduce the dependence of controller design on the model and the influence of unmodeled dynamics on the controller&rsquo;s performance. By only using the real-time online input and output data of the bridge crane system, the active learning control method consists of the finite-dimensional approximation of the Koopman operator and the design of an active learning controller based on the linear quadratic optimal tracking control. The effectiveness of the control strategy for positioning and anti-swing of bridge cranes is verified through numerical simulations.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050100

Authors: Kalyanmoy Deb Matthias Ehrgott

Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay out properties of generalized dominance structures which help provide insights for resulting optimal solutions. We introduce the concept of the anti-dominance structure, derived from the chosen dominance structure, to explain how the resulting non-dominated or optimal set can be identified easily compared to using the dominance structure directly. The concept allows a unified explanation of optimal solutions for both single- and multi-objective optimization problems. The anti-dominance structure is applied to analyze respective optimal solutions for most popularly used static and spatially changing dominance structures. The theoretical and deductive results of this study can be utilized to create more meaningful dominance structures for practical problems, understand and identify resulting optimal solutions, and help develop better test problems and algorithms for multi-objective optimization.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050099

Authors: Mohammed Tadj Lakhdar Chaib Abdelghani Choucha Al-Motasem Aldaoudeyeh Ahmed Fathy Hegazy Rezk Mohamed Louzazni Attia El-Fergany

This paper proposes a controller to track the maximum power point (MPP) of a photovoltaic (PV) system using a fractional-order proportional integral derivative (FOPID) controller. The employed MPPT is operated based on a dp/dv feedback approach. The designed FOPID-MPPT method includes a differentiator of order (&mu;) and integrator of order (&lambda;), meaning it is an extension of the conventional PID controller. FOPID has more flexibility and achieves dynamical tuning, which leads to an efficient control system. The contribution of our paper lies is optimizing FOPID-MPPT parameters using Aquila optimizer (AO). The obtained results with the proposed AO-based FOPID-MPPT are contrasted with those acquired with moth flame optimizer (MFO). The performance of our FOPID-MPPT controller with the conventional technique perturb and observe (P&amp;O) and the classical PID controller is analyzed. In addition, a robustness test is used to assess the performance of the FOPID-MPPT controller under load variations, providing valuable insights into its practical applicability and robustness. The simulation results clearly prove the superiority and high performance of the proposed control system to track the MPP of PV systems.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050098

Authors: Bibi Fatima Mehmet Yavuz Mati ur Rahman Ali Althobaiti Saad Althobaiti

The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system&rsquo;s equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050097

Authors: Adel Al-Mahdi

Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point system of equations where the coefficient matrix of this system is dense and ill conditioned (it has a huge condition number). The ill-conditioned property leads to slowing of the convergence of any iterative method, such as Krylov subspace methods. One treatment for the slowness property is to apply the preconditioning technique. In this paper, we propose a block triangular preconditioner because we know that using the exact triangular preconditioner leads to a preconditioned matrix with exactly two distinct eigenvalues. This means that we need at most two iterations to converge to the exact solution. However, we cannot use the exact preconditioner because the Shur complement of our system is of the form S=K*K+λLα which is a huge and dense matrix. The first matrix, K*K, comes from the blurred operator, while the second one is from the TFOV regularization model. To overcome this difficulty, we propose two preconditioners based on the circulant and standard TV matrices. In our algorithm, we use the flexible preconditioned GMRES method for the outer iterations, the preconditioned conjugate gradient (PCG) method for the inner iterations, and the fixed point iteration (FPI) method to handle the nonlinearity. Fast convergence was found in the numerical results by using the proposed preconditioners.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050096

Authors: Fiazuddin D. Zaman Fazal M. Mahomed Faiza Arif

We used the classical Lie symmetry method to study the damped Klein&ndash;Gordon equation (Kge) with power law non-linearity utt+&alpha;(u)ut=(u&beta;ux)x+f(u). We carried out a complete Lie symmetry classification by finding forms for &alpha;(u) and f(u). This led to various cases. Corresponding to each case, we obtained one-dimensional optimal systems of subalgebras. Using the subalgebras, we reduced the Kge to ordinary differential equations and determined some invariant solutions. Furthermore, we obtained conservation laws using the partial Lagrangian approach.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050095

Authors: Guilmer Ferdinand González Flores Pablo Barrera Sánchez

In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. We also define new discrete functionals, which are implemented as objective functions in an optimization-based method for quadrilateral grid generation and improvement. These functionals are linearly combined with a discrete functional whose domain has an infinite barrier at the boundary of the set of unfolded grids to preserve convex grid cells in each step of the optimization process.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050094

Authors: Mohammad M. Kafini Mohammed M. Al-Gharabli Adel M. Al-Mahdi

In this research work, we investigate the asymptotic behavior of a nonlinear swelling (also called expansive) soil system with a time delay and nonlinear damping of variable exponents. We should note here that swelling soils contain clay minerals that absorb water, which may lead to increases in pressure. In architectural and civil engineering, swelling soils are considered sources of problems and harm. The presence of the delay is used to create more realistic models since many processes depend on past history, and the delays are frequently added by sensors, actuators, and field networks that travel through feedback loops. The appearance of variable exponents in the delay and damping terms in this system allows for a more flexible and accurate modeling of this physical phenomenon. This can lead to more realistic and precise descriptions of the behavior of fluids in different media. In fact, with the advancements of science and technology, many physical and engineering models require more sophisticated mathematical tools to study and understand. The Lebesgue and Sobolev spaces with variable exponents proved to be efficient tools for studying such problems. By constructing a suitable Lyapunov functional, we establish exponential and polynomial decay results. We noticed that the energy decay of the system depends on the value of the variable exponent. These results improve on some existing results in the literature.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050093

Authors: Carlos-Iván Páez-Rueda Arturo Fajardo Manuel Pérez German Yamhure Gabriel Perilla

This paper studies and analyzes the approximation of one-dimensional smooth closed-form functions with compact support using a mixed Fourier series (i.e., a combination of partial Fourier series and other forms of partial series). To explore the potential of this approach, we discuss and revise its application in signal processing, especially because it allows us to control the decreasing rate of Fourier coefficients and avoids the Gibbs phenomenon. Therefore, this method improves the signal processing performance in a wide range of scenarios, such as function approximation, interpolation, increased convergence with quasi-spectral accuracy using the time domain or the frequency domain, numerical integration, and solutions of inverse problems such as ordinary differential equations. Moreover, the paper provides comprehensive examples of one-dimensional problems to showcase the advantages of this approach.

]]>Mathematical and Computational Applications doi: 10.3390/mca28050092

Authors: Molahlehi Charles Kakuli Winter Sinkala Phetogo Masemola

This study investigates via Lie symmetry analysis the Hunter&ndash;Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation that arise from first-order multipliers. Conservation laws of the equation, combined with the admitted Lie point symmetries, enable us to perform symmetry reductions by employing the double reduction method. The method exploits the relationship between symmetries and conservation laws to reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter&ndash;Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation. While the double reduction method may be more complex to implement than the classical method, since it involves finding Lie point symmetries and deriving conservation laws, it has some advantages over the classical method of reducing PDEs. Firstly, it is more efficient in that it can reduce the number of variables and order of the equation in a single step. Secondly, by incorporating conservation laws, physically meaningful solutions that satisfy important physical constraints can be obtained.

]]>Mathematical and Computational Applications doi: 10.3390/mca28040091

Authors: Hamidreza Eivazi Jendrik-Alexander Tröger Stefan Wittek Stefan Hartmann Andreas Rausch

Multiscale FE2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE2 simulations with special focus on the errors compared to conventional FE2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations.

]]>Mathematical and Computational Applications doi: 10.3390/mca28040090

Authors: Rohan Singla Shubham Gupta Arnab Chanda

A cerebral aneurysm is a medical condition where a cerebral artery can burst under adverse pressure conditions. A 20% mortality rate and additional 30 to 40% morbidity rate have been reported for patients suffering from the rupture of aneurysms. In addition to wall shear stress, input jets, induced pressure, and complicated and unstable flow patterns are other important parameters associated with a clinical history of aneurysm ruptures. In this study, the anterior cerebral artery (ACA) was modeled using image segmentation and then rebuilt with aneurysms at locations vulnerable to aneurysm growth. To simulate various aneurysm growth stages, five aneurysm sizes and two wall thicknesses were taken into consideration. In order to simulate realistic pressure loading conditions for the anterior cerebral arteries, inlet velocity and outlet pressure were used. The pressure, wall shear stress, and flow velocity distributions were then evaluated in order to predict the risk of rupture. A low-wall shear stress-based rupture scenario was created using a smaller aneurysm and thinner walls, which enhanced pressure, shear stress, and flow velocity. Additionally, aneurysms with a 4 mm diameter and a thin wall had increased rupture risks, particularly at specific boundary conditions. It is believed that the findings of this study will help physicians predict rupture risk according to aneurysm diameters and make early treatment decisions.

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