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Mathematical and Computational Applications
Number of Followers: 3  Open Access journalISSN (Print) 1300-686X - ISSN (Online) 2297-8747 Published by MDPI  [258 journals]
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- MCA, Vol. 29, Pages 47: Partitioning Uncertainty in Model Predictions from
Compartmental Modeling of Global Carbon Cycle
Authors: Suzan Gazioğlu
First page: 47
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-22
DOI: 10.3390/mca29040047
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 48: Induction of Convolutional Decision Trees with
Success-History-Based Adaptive Differential Evolution for Semantic
Segmentation
Authors: Adriana-Laura López-Lobato, Héctor-Gabriel Acosta-Mesa, Efrén Mezura-Montes
First page: 48
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-27
DOI: 10.3390/mca29040048
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 49: IoT-Driven Transformation of Circular Economy
Efficiency: An Overview
Authors: Zenonas Turskis, Violeta Šniokienė
First page: 49
Abstract: 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’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’s promise.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-28
DOI: 10.3390/mca29040049
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 50: Fuzzy Bipolar Hypersoft Sets: A Novel Approach for
Decision-Making Applications
Authors: Baravan A. Asaad, Sagvan Y. Musa, Zanyar A. Ameen
First page: 50
Abstract: 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’ 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-02
DOI: 10.3390/mca29040050
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 51: H∞ State and Parameter Estimation for
Lipschitz Nonlinear Systems
Authors: Pedro Eusebio Alvarado-Méndez, Carlos M. Astorga-Zaragoza, Gloria L. Osorio-Gordillo, Adriana Aguilera-González, Rodolfo Vargas-Méndez, Juan Reyes-Reyes
First page: 51
Abstract: A H∞ 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∞ 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-04
DOI: 10.3390/mca29040051
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 52: A Condition-Monitoring Methodology Using Deep
Learning-Based Surrogate Models and Parameter Identification Applied to
Heat Pumps
Authors: Pieter Rousseau, Ryno Laubscher
First page: 52
Abstract: 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 “forward” 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 “backward” 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-05
DOI: 10.3390/mca29040052
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 53: Correction: Angelova et al. Estimating Surface EMG
Activity of Human Upper Arm Muscles Using InterCriteria Analysis. Math.
Comput. Appl. 2024, 29, 8
Authors: Silvija Angelova, Maria Angelova, Rositsa Raikova
First page: 53
Abstract: Due to imprecise meaning in the original publication [...]
Citation: Mathematical and Computational Applications
PubDate: 2024-07-11
DOI: 10.3390/mca29040053
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 54: Novel Results on Legendre Polynomials in the Sense
of a Generalized Fractional Derivative
Authors: Francisco Martínez, Mohammed K. A. Kaabar, Inmaculada Martínez
First page: 54
Abstract: In this article, new results are investigated in the context of the recently introduced Abu-Shady–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–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∈Lα2([−1,1]) in a series of generalized Legendre polynomials is addressed.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-12
DOI: 10.3390/mca29040054
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 55: Improved Mechanical Characterization of Soft
Tissues including Mounting Stretches
Authors: Toni Škugor, Lana Virag, Gerhard Sommer, Igor Karšaj
First page: 55
Abstract: 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’ 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–Ogden–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-12
DOI: 10.3390/mca29040055
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 56: Computational Cost Reduction in Multi-Objective
Feature Selection Using Permutational-Based Differential Evolution
Authors: Jesús-Arnulfo Barradas-Palmeros, Efrén Mezura-Montes, Rafael Rivera-López, Hector-Gabriel Acosta-Mesa, Aldo Márquez-Grajales
First page: 56
Abstract: 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’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-13
DOI: 10.3390/mca29040056
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 57: Modeling of the Human Cardiovascular System:
Implementing a Sliding Mode Observer for Fault Detection and Isolation
Authors: Dulce A. Serrano-Cruz, Latifa Boutat-Baddas, Mohamed Darouach, Carlos M. Astorga-Zaragoza, Gerardo V. Guerrero Ramírez
First page: 57
Abstract: 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 “quadratic normal form”. 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’s validity is confirmed through simulations that replicate hemodynamic parameters, aligning with existing literature and experimental data.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-17
DOI: 10.3390/mca29040057
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 58: Unraveling Time Series Dynamics: Evaluating
Partial Autocorrelation Function Distribution and Its Implications
Authors: Hossein Hassani, Leila Marvian, Masoud Yarmohammadi, Mohammad Reza Yeganegi
First page: 58
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-19
DOI: 10.3390/mca29040058
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 59: FutureCite: Predicting Research Articles’
Impact Using Machine Learning and Text and Graph Mining Techniques
Authors: Maha A. Thafar, Mashael M. Alsulami, Somayah Albaradei
First page: 59
Abstract: 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’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’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’ ability to determine targeted literature for their research and better understand the potential impact of research publications.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-21
DOI: 10.3390/mca29040059
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 60: Noether Symmetries of the Triple Degenerate DNLS
Equations
Authors: Ugur Camci
First page: 60
Abstract: 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 Schrödinger 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. 1995, 54, 201–244; J. Phys. A Math. Gen. 1996, 29, 5209–5240). Furthermore, we find some new Lie symmetries of the dispersive triple degenerate derivative nonlinear Schrödinger equations for non-vanishing integration functions Ki(t) (i=1,2,3).
Citation: Mathematical and Computational Applications
PubDate: 2024-07-30
DOI: 10.3390/mca29040060
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 61: Linear and Non-Linear Regression Methods for the
Prediction of Lower Facial Measurements from Upper Facial Measurements
Authors: Jacques Terblanche, Johan van der Merwe, Ryno Laubscher
First page: 61
Abstract: 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°, 3.11°, 3.07°, and 3.12° 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-07-31
DOI: 10.3390/mca29040061
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 62: Mathematical Structure of RelB Dynamics in the
NF-κB Non-Canonical Pathway
Authors: Toshihito Umegaki, Naoya Hatanaka, Takashi Suzuki
First page: 62
Abstract: This study analyzed the non-canonical NF-κB pathway, which controls functions distinct from those of the canonical pathway. Although oscillations of NF-κB 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 IκB, contributing to the regulation of NF-κB 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-08-05
DOI: 10.3390/mca29040062
Issue No: Vol. 29, No. 4 (2024)
- MCA, Vol. 29, Pages 30: Simulation of Temperature Field in Steel Billets
during Reheating in Pusher-Type Furnace by Meshless Method
Authors: Qingguo Liu, Umut Hanoglu, Zlatko Rek, Božidar Šarler
First page: 30
Abstract: 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' 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’s productivity, energy consumption, and the billet’s quality. For the first time, the LRBFCM is successfully demonstrated for solving such a complex industrial problem.
Citation: Mathematical and Computational Applications
PubDate: 2024-04-24
DOI: 10.3390/mca29030030
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 31: A New Generalized Definition of
Fractal–Fractional Derivative with Some Applications
Authors: Martínez, Kaabar
First page: 31
Abstract: In this study, a new generalized fractal–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’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’s rule. Finally, we analytically solve interesting FF ordinary differential equations by applying our proposed definition.
Citation: Mathematical and Computational Applications
PubDate: 2024-04-25
DOI: 10.3390/mca29030031
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 32: Recognizable Languages of k-Forcing Automata
Authors: Marzieh Shamsizadeh, Mohammad Mehdi Zahedi, Khadijeh Abolpour, Manuel De la Sen
First page: 32
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-04-25
DOI: 10.3390/mca29030032
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 33: Evaluation of Aortic Valve Pressure Gradients for
Increasing Severities of Rheumatic and Calcific Stenosis Using Empirical
and Numerical Approaches
Authors: Lindi Grobler, Ryno Laubscher, Johan van der Merwe, Philip G. Herbst
First page: 33
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-04-28
DOI: 10.3390/mca29030033
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 34: New Model for Hill’s Problem in the
Framework of Continuation Fractional Potential
Authors: Elbaz I. Abouelmagd
First page: 34
Abstract: In this work, we derived a new type model for spatial Hill’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’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’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-02
DOI: 10.3390/mca29030034
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 35: Clustering of Wind Speed Time Series as a Tool for
Wind Farm Diagnosis
Authors: Ana Alexandra Martins, Daniel C. Vaz, Tiago A. N. Silva, Margarida Cardoso, Alda Carvalho
First page: 35
Abstract: 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’ 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—the COMB distance matrix plot—provides a quick way to compare pairs of time bands (turbines) regarding various features.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-09
DOI: 10.3390/mca29030035
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 36: Periodic Solutions in a Simple Delay Differential
Equation
Authors: Anatoli Ivanov, Sergiy Shelyag
First page: 36
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-12
DOI: 10.3390/mca29030036
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 37: Exploring Trust Dynamics in Online Social
Networks: A Social Network Analysis Perspective
Authors: Stavroula Kridera, Andreas Kanavos
First page: 37
Abstract: This study explores trust dynamics within online social networks, blending social science theories with advanced machine-learning (ML) techniques. We examine trust’s multifaceted nature—definitions, types, and mechanisms for its establishment and maintenance—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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-15
DOI: 10.3390/mca29030037
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 38: Detailed Investigation of the Eddy Current and
Core Losses in Coaxial Magnetic Gears through a Two-Dimensional Analytical
Model
Authors: Nikolina Nikolarea, Panteleimon Tzouganakis, Vasilios Gakos, Christos Papalexis, Antonios Tsolakis, Vasilios Spitas
First page: 38
Abstract: 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–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-18
DOI: 10.3390/mca29030038
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 39: Numerical Solution of Natural Convection Problems
Using Radial Point Interpolation Meshless (RPIM) Method Combined with
Artificial-Compressibility Model
Authors: Pranowo, Albertus Joko Santoso, Agung Tri Wijayanta
First page: 39
Abstract: 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—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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-20
DOI: 10.3390/mca29030039
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 40: A Review on Large-Scale Data Processing with
Parallel and Distributed Randomized Extreme Learning Machine Neural
Networks
Authors: Elkin Gelvez-Almeida, Marco Mora, Ricardo J. Barrientos, Ruber Hernández-García, Karina Vilches-Ponce, Miguel Vera
First page: 40
Abstract: 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–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–Penrose generalized inverse and solution of linear systems using parallel and distributed methods) and hardware and software technologies considered in current implementations.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-27
DOI: 10.3390/mca29030040
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 41: Integrating Deep Learning into Genotoxicity
Biomarker Detection for Avian Erythrocytes: A Case Study in a Hemispheric
Seabird
Authors: Martín G. Frixione, Facundo Roffet, Miguel A. Adami, Marcelo Bertellotti, Verónica L. D’Amico, Claudio Delrieux, Débora Pollicelli
First page: 41
Abstract: 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 gulls (Larus dominicanus). We trained three convolutional backbones (ResNet34, ResNet50, and ResNet101 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: “normal”, “abnormal”, “other”; level 2: “normal”, “ENAs”, “micronucleus”, “other”; level 3: “normal”, “irregular”, “displaced”, “enucleated”, “micronucleus”, “other”). 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-28
DOI: 10.3390/mca29030041
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 42: DSTree: A Spatio-Temporal Indexing Data Structure
for Distributed Networks
Authors: Majid Hojati, Steven Roberts, Colin Robertson
First page: 42
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-05-31
DOI: 10.3390/mca29030042
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 43: New Lie Symmetries and Exact Solutions of a
Mathematical Model Describing Solute Transport in Poroelastic Materials
Authors: Roman Cherniha, Vasyl’ Davydovych, Alla Vorobyova
First page: 43
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-03
DOI: 10.3390/mca29030043
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 44: Bitcoin versus S&P 500 Index: Return and
Risk Analysis
Authors: Aubain Nzokem, Daniel Maposa
First page: 44
Abstract: The S&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&P 500 Index and assesses their tail probabilities using two financial risk measures. As a methodology, we use Bitcoin and S&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–Cotes rule. The findings show that peakedness is the main characteristic of the S&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&P 500 returns are within −1.06% and 1.23% against only 40.32% of Bitcoin returns. At a risk level (α), the severity of the loss (AVaRα(X)) on the left side of the distribution is larger than the severity of the profit (AVaR1−α(X)) on the right side of the distribution. Compared to the S&P 500 Index, Bitcoin has 39.73% more prevalence to produce high daily returns (more than 1.23% or less than −1.06%). The severity analysis shows that, at α 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&P 500 Index returns at the same risk.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-09
DOI: 10.3390/mca29030044
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 45: A Comprehensive Assessment and Classification of
Acute Lymphocytic Leukemia
Authors: Payal Bose, Samir Bandyopadhyay
First page: 45
Abstract: 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’ knowledge, which is time consuming. A lengthy testing interval combined with inadequate comprehension could harm a person’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-09
DOI: 10.3390/mca29030045
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 46: Dynamic Mechanism Design for Repeated Markov Games
with Hidden Actions: Computational Approach
Authors: Julio B. Clempner
First page: 46
Abstract: This paper introduces a dynamic mechanism design tailored for uncertain environments where incentive schemes are challenged by the inability to observe players’ 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’ 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’ 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’ 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-06-10
DOI: 10.3390/mca29030046
Issue No: Vol. 29, No. 3 (2024)
- MCA, Vol. 29, Pages 17: An Iterative Method for Computing π by Argument
Reduction of the Tangent Function
Authors: Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine
First page: 17
Abstract: In this work, we develop a new iterative method for computing the digits of π by argument reduction of the tangent function. This method combines a modified version of the iterative formula for π 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 π per increment. Mathematica codes, showing the convergence rate for computing the digits of π, are presented.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-25
DOI: 10.3390/mca29020017
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 18: Energy-and-Blocking-Aware Routing and Device
Assignment in Software-Defined Networking—A MILP and Genetic
Algorithm Approach
Authors: Gerardo J. Riveros-Rojas, Pedro P. Cespedes-Sanchez, Diego P. Pinto-Roa, Horacio Legal-Ayala
First page: 18
Abstract: 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’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-04
DOI: 10.3390/mca29020018
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 19: SSA-Deep Learning Forecasting Methodology with SMA
and KF Filters and Residual Analysis
Authors: Juan Frausto-Solís, José Christian de Jesús Galicia-González, Juan Javier González-Barbosa, Guadalupe Castilla-Valdez, Juan Paulo Sánchez-Hernández
First page: 19
Abstract: Accurate forecasting remains a challenge, even with advanced techniques like deep learning (DL), ARIMA, and Holt–Winters (H&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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-05
DOI: 10.3390/mca29020019
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 20: A Four-Variable Shear Deformation Theory for the
Static Analysis of FG Sandwich Plates with Different Porosity Models
Authors: Rabab A. Alghanmi, Rawan H. Aljaghthami
First page: 20
Abstract: 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’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’s accuracy. Further findings are presented to serve as benchmarks for comparison.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-08
DOI: 10.3390/mca29020020
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 21: Semi-Supervised Machine Learning Method for
Predicting Observed Individual Risk Preference Using Gallup Data
Authors: Faroque Ahmed, Mrittika Shamsuddin, Tanzila Sultana, Rittika Shamsuddin
First page: 21
Abstract: Risk and uncertainty play a vital role in almost every significant economic decision, and an individual’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’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-15
DOI: 10.3390/mca29020021
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 22: Variability on Functionally Graded Plates’
Deflection Due to Uncertainty on Carbon Nanotubes’ Properties
Authors: Alda Carvalho, Ana Martins, Ana F. Mota, Maria A. R. Loja
First page: 22
Abstract: 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’ material and geometrical properties to structures’ 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’ functional gradient. The plates’ samples are simulated considering that only the nanotubes’ 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’ weight fraction evolution, their internal and external diameters, and the Young’s modulus. The multiple regression models developed can be used as alternative prediction tools within the domain of the study.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-16
DOI: 10.3390/mca29020022
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 23: Assessment of Local Radial Basis Function
Collocation Method for Diffusion Problems Structured with Multiquadrics
and Polyharmonic Splines
Authors: Izaz Ali, Umut Hanoglu, Robert Vertnik, Božidar Šarler
First page: 23
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-17
DOI: 10.3390/mca29020023
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 24: A Coupled Finite-Boundary Element Method for
Efficient Dynamic Structure-Soil-Structure Interaction Modeling
Authors: Parham Azhir, Jafar Asgari Marnani, Mehdi Panji, Mohammad Sadegh Rohanimanesh
First page: 24
Abstract: This paper introduces an innovative approach to numerically model Structure–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–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-18
DOI: 10.3390/mca29020024
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 25: M5GP: Parallel Multidimensional Genetic
Programming with Multidimensional Populations for Symbolic Regression
Authors: Luis Cárdenas Florido, Leonardo Trujillo, Daniel E. Hernandez, Jose Manuel Muñoz Contreras
First page: 25
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-18
DOI: 10.3390/mca29020025
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 26: Testing Homogeneity of Proportion Ratios for
Stratified Bilateral Correlated Data
Authors: Wanqing Tian, Changxing Ma
First page: 26
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-22
DOI: 10.3390/mca29020026
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 27: Modeling of Chemical Vapor Infiltration for
Fiber-Reinforced Silicon Carbide Composites Using Meshless Method of
Fundamental Solutions
Authors: Patrick Mahoney, Alex Povitsky
First page: 27
Abstract: 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’ 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-22
DOI: 10.3390/mca29020027
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 28: Global Behavior of Solutions to a
Higher-Dimensional System of Difference Equations with Lucas Numbers
Coefficients
Authors: Messaoud Berkal, Juan Francisco Navarro, Raafat Abo-Zeid
First page: 28
Abstract: In this paper, we derive the well-defined solutions to a θ-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.
Citation: Mathematical and Computational Applications
PubDate: 2024-03-31
DOI: 10.3390/mca29020028
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 29: A Robust FOPD Controller That Allows Faster
Detection of Defects for Touch Panels
Authors: Yuan-Jay Wang
First page: 29
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-04-16
DOI: 10.3390/mca29020029
Issue No: Vol. 29, No. 2 (2024)
- MCA, Vol. 29, Pages 3: Role Reversals in a Tri-Trophic Prey–Predator
Interaction System: A Model-Based Study Using Deterministic and Stochastic
Approaches
Authors: Sk Golam Mortoja, Ayan Paul, Prabir Panja, Sabyasachi Bhattacharya, Shyamal Kumar Mondal
First page: 3
Abstract: 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–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–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-10
DOI: 10.3390/mca29010003
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 4: Accelerating Convergence for the Parameters of PV
Cell Models
Authors: Lorentz Jäntschi, Mohamed Louzazni
First page: 4
Abstract: 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–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–voltage characteristic. The values of the characteristic equation’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-10
DOI: 10.3390/mca29010004
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 5: Accuracy Examination of the Fourier Series
Approximation for Almost Limiting Gravity Waves on Deep Water
Authors: Yang-Yih Chen, Hsien-Kuo Chang
First page: 5
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-11
DOI: 10.3390/mca29010005
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 6: A Numerical Method Based on Operator Splitting
Collocation Scheme for Nonlinear Schrödinger Equation
Authors: Mengli Yao, Zhifeng Weng
First page: 6
Abstract: In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger 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–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-15
DOI: 10.3390/mca29010006
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 7: A Multi-Credit-Rating Migration Model with
Asymmetric Migration Boundaries
Authors: Yang Lin, Jin Liang
First page: 7
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-17
DOI: 10.3390/mca29010007
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 8: Estimating Surface EMG Activity of Human Upper Arm
Muscles Using InterCriteria Analysis
Authors: Silvija Angelova, Maria Angelova, Rositsa Raikova
First page: 8
Abstract: 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–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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-23
DOI: 10.3390/mca29010008
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 9: Investigating the Surrogate Modeling Capabilities
of Continuous Time Echo State Networks
Authors: Saakaar Bhatnagar
First page: 9
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-24
DOI: 10.3390/mca29010009
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 10: Free Vibration Analysis of Porous Functionally
Graded Material Plates with Variable Thickness on an Elastic Foundation
Using the R-Functions Method
Authors: Lidiya Kurpa, Francesco Pellicano, Tetyana Shmatko, Antonio Zippo
First page: 10
Abstract: 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’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-01-29
DOI: 10.3390/mca29010010
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 11: Analytical Solutions of Systems of Linear Delay
Differential Equations by the Laplace Transform: Featuring Limit Cycles
Authors: Gilbert Kerr, Nehemiah Lopez, Gilberto González-Parra
First page: 11
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-04
DOI: 10.3390/mca29010011
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 12: The Lattice Boltzmann Method Using Parallel
Computation: A Great Potential Solution for Various Complicated Acoustic
Problems
Authors: Pranowo, Djoko Budiyanto Setyohadi, Agung Tri Wijayanta
First page: 12
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-04
DOI: 10.3390/mca29010012
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 13: Magnesium and Calcium Transport along the Male Rat
Kidney: Effect of Diuretics
Authors: Pritha Dutta, Anita T. Layton
First page: 13
Abstract: 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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-07
DOI: 10.3390/mca29010013
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 14: On the Parallelization of Square-Root
Vélu’s Formulas
Authors: Jorge Chávez-Saab, Odalis Ortega, Amalia Pizarro-Madariaga
First page: 14
Abstract: 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 Vélu’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 Vélu’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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-16
DOI: 10.3390/mca29010014
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 15: Complex Connections between Symmetry and
Singularity Analysis
Authors: Asghar Qadir
First page: 15
Abstract: In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions—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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-19
DOI: 10.3390/mca29010015
Issue No: Vol. 29, No. 1 (2024)
- MCA, Vol. 29, Pages 16: Three-Dimensional Model for Bioventing:
Mathematical Solution, Calibration and Validation
Authors: Mohammad Khodabakhshi Soureshjani, Hermann J. Eberl, Richard G. Zytner
First page: 16
Abstract: 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 “porousMultiphaseFoam v2107” (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.
Citation: Mathematical and Computational Applications
PubDate: 2024-02-19
DOI: 10.3390/mca29010016
Issue No: Vol. 29, No. 1 (2024)
