Mathematical and Computational Applications

16 pages, 2663 KiB

Open AccessArticle

Bag of Feature-Based Ensemble Subspace KNN Classifier in Muscle Ultrasound Diagnosis of Diabetic Peripheral Neuropathy

by Kadhim K. Al-Barazanchi, Ali H. Al-Timemy and Zahid M. Kadhim

Math. Comput. Appl. 2024, 29(5), 95; https://doi.org/10.3390/mca29050095 - 20 Oct 2024

Viewed by 627

Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD) [...] Read more.

Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD) system based on muscle ultrasound that integrates the bag of features (BOF) and an ensemble subspace k-nearest neighbor (KNN) algorithm for DPN detection. The BOF creates a histogram of visual word occurrences to represent the muscle ultrasound images and trains an ensemble classifier through cross-validation, determining optimal parameters to improve classification accuracy for the ensemble diagnosis system. The dataset includes ultrasound images of six muscles from 53 subjects, consisting of 27 control and 26 patient cases. An empirical analysis was conducted for each binary classifier based on muscle type to select the best vocabulary tree properties or K values for BOF. The result indicates that ensemble subspace KNN classification, based on the bag of features, achieved an accuracy of 97.23%. CAD systems can effectively diagnose muscle pathology, thereby addressing limitations and identifying issues in individuals with diabetes. This research underscores muscle ultrasound as a promising diagnostic tool to aid physicians in making accurate diagnoses, streamlining workflow, and uncovering muscle-related complications in DPN patients. Full article

(This article belongs to the Section Engineering)

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16 pages, 1037 KiB

Open AccessArticle

Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization

by Ikram Ullah, Imtiaz Ahmad, Nigar Ali, Ihtisham Ul Haq, Mohammad Idrees, Mohammed Daher Albalwi and Mehmet Yavuz

Math. Comput. Appl. 2024, 29(5), 94; https://doi.org/10.3390/mca29050094 - 12 Oct 2024

Viewed by 861

Abstract

This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public [...] Read more.

This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public knowledge. The findings might improve healthcare budget apportionment, public health policy, and contest Ebola and related infections. In this study, we fully observe the new model

S E I H R

that we have constructed. We start by outlining the essential concepts of the model and confirming its mathematical reliability. Next, we calculate the fundamental reproductive number

(R_{0})

, which is critical for appreciating how the infection spreads and how effective treatments might be. We also study stability analysis, which looks at when the disease may decline or become chronic. Furthermore, we exhibit the occurrence of bifurcation in the EVD Epidemic Model and perform a sensitivity analysis of

(R_{0})

. The main findings of this study show that for

R_{0} < 1

, the disease-free equilibrium, is globally stable, meaning the disease will die out, whereas for

R_{0} > 1

, the endemic equilibrium is stable, meaning the disease persists. Additionally, the sensitivity analysis reveals that the most influential parameters in controlling

R_{0}

are the transmission rate and the recovery rate, which could guide effective intervention strategies. Finally, we use numerical simulations so that out outcomes are more significant. Full article

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13 pages, 4030 KiB

Open AccessArticle

Application of Bispectral Analysis to Assess the Effect of Drought on the Photosynthetic Activity of Lettuce Plants Lactuca sativa L.

by Maxim E. Astashev, Dmitriy E. Burmistrov, Denis V. Yanykin, Andrey A. Grishin, Inna V. Knyazeva, Alexey S. Dorokhov and Sergey V. Gudkov

Math. Comput. Appl. 2024, 29(5), 93; https://doi.org/10.3390/mca29050093 - 11 Oct 2024

Viewed by 592

Abstract

This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of L. sativa plants and analyzing the resulting time series [...] Read more.

This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of L. sativa plants and analyzing the resulting time series using bispectral analysis based on the wavelet transform. The article theoretically shows a possible mechanism for the appearance of a peak on the map of bispectrum indexes during nonlinear analog conversion of a physiological signal in a biological object. The phenomenon of increasing the degree of nonlinearity in the transmission of an external periodic signal in plant signaling systems has been experimentally demonstrated. Full article

(This article belongs to the Section Natural Sciences)

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17 pages, 293 KiB

Open AccessArticle

Lie Symmetry Analysis, Closed-Form Solutions, and Conservation Laws for the Camassa–Holm Type Equation

by Jonathan Lebogang Bodibe and Chaudry Masood Khalique

Math. Comput. Appl. 2024, 29(5), 92; https://doi.org/10.3390/mca29050092 - 10 Oct 2024

Viewed by 573

Abstract

In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim [...] Read more.

In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim is to construct closed-form solutions of the equation using a powerful technique, namely the Lie group analysis method. Firstly, we derive the Lie point symmetries of the equation. Thereafter, the equation is reduced to non-linear ordinary differential equations using symmetry reductions. Furthermore, the solutions of the equation are derived using the extended Jacobi elliptic function technique, the simplest equation method, and the power series method. In conclusion, we construct conservation laws for the equation using Noether’s theorem and the multiplier approach, which plays a crucial role in understanding the behavior of non-linear equations, especially in physics and engineering, and these laws are derived from fundamental principles such as the conservation of mass, energy, momentum, and angular momentum. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

35 pages, 970 KiB

Open AccessArticle

Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation

by Willy Hereman and Ünal Göktaş

Math. Comput. Appl. 2024, 29(5), 91; https://doi.org/10.3390/mca29050091 - 3 Oct 2024

Viewed by 601

Abstract

In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the [...] Read more.

In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica, but can be adapted for major computer algebra systems. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

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19 pages, 2708 KiB

Open AccessArticle

Modeling of Sedimentation of Particles near Corrugated Surfaces by the Meshless Method of Fundamental Solutions

by Alex Povitsky

Math. Comput. Appl. 2024, 29(5), 90; https://doi.org/10.3390/mca29050090 - 3 Oct 2024

Viewed by 543

Abstract

The velocity and trajectory of particles moving along the corrugated (rough) surface under the action of gravity is obtained by a modified Method of Fundamental Solutions (MFS). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with [...] Read more.

The velocity and trajectory of particles moving along the corrugated (rough) surface under the action of gravity is obtained by a modified Method of Fundamental Solutions (MFS). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green’s function for Stokeslets. In the present study, the velocity of a moving particle under the action of the gravity force is not known and becomes a part of the MFS solution. This requires an adjustment of the matrix of the MFS linear system to include the unknown particle velocity and incorporate in the MFS the balance of hydrodynamic and gravity forces acting on the particle. The study explores the combination of the regularization of Stokeslets and placement of Stokeslets outside the flow domain to ensure the accuracy and stability of computations for particles moving in proximity to the wall. The MFS results are compared to prior published approximate analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particles, including their deviation from the vertical trajectory, and select the optimal set of computational parameters. The developed MFS methodology is then applied to the sedimentation of a pair of two spherical particles in proximity to the corrugated wall, in which case, the analytical solution is not available. The MFS results show that particles in the pair deviate from the trajectory of a single particle: the particle located below moves farther away from vertical wall, and the particle located above shifts closer to the wall. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

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18 pages, 328 KiB

Open AccessArticle

Loss of the Sturm–Liouville Property of Time-Varying Second-Order Differential Equations in the Presence of Delayed Dynamics

by Manuel De la Sen

Math. Comput. Appl. 2024, 29(5), 89; https://doi.org/10.3390/mca29050089 - 3 Oct 2024

Viewed by 510

Abstract

This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system [...] Read more.

This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to prescribed two-point boundary conditions. However, the perturbed differential system is not a Sturm–Liouville system, in general, due to the presence of delayed dynamics. The main objective of the paper is to investigate the loss of the boundary values of the Sturm–Liouville nominal undelayed system in the presence of the delayed dynamics. Such a delayed dynamics is considered a perturbation of the nominal dynamics related to the Sturm–Liouville system with given two-point boundary values. In particular, this loss of the Sturm–Liouville exact tracking of the prescribed two-point boundary values might happen because the nominal boundary values may become lost by the state trajectory solution in the presence of delays, related to the undelayed case, due to the presence of the delayed dynamics. The worst-case error description of the deviation of the two-point boundary values of the current perturbed differential with respect to those of the nominal Sturm–Liouville system is characterized in terms of error norms related to the nominal system. Under sufficiently small deviations of the parameterization of the perturbed system with respect to the nominal one, such a worst-error characterization makes the current perturbed system an approximate Sturm–Liouville system of the nominal undelayed one. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

14 pages, 3165 KiB

Open AccessArticle

Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization

by Maeva Cybelle Zoleko Zambou, Alain Soup Tewa Kammogne, Martin Siewe Siewe, Ahmad Taher Azar, Saim Ahmed and Ibrahim A. Hameed

Math. Comput. Appl. 2024, 29(5), 88; https://doi.org/10.3390/mca29050088 - 2 Oct 2024

Cited by 1 | Viewed by 797

Abstract

This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by [...] Read more.

This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by a metaheuristic algorithm called Particle Swarm Optimization (PSO). The proposed methods appear to present adequate solutions to overcome the drawbacks of existing methods despite various weather conditions considered in the analysis, providing a robust solution for dynamic environmental conditions. The results showed better performance and accuracy compared to those encountered in the literature. We also recall that this technique provides a systematic design procedure in the search for the MPPT in photovoltaic (PV) systems that has not yet been documented in the literature to the best of our knowledge. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

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25 pages, 20472 KiB

Open AccessArticle

Meshless Error Recovery Parametric Investigation in Incompressible Elastic Finite Element Analysis

by Essam Althaqafi, Devinder Singh and Mohd Ahmed

Math. Comput. Appl. 2024, 29(5), 87; https://doi.org/10.3390/mca29050087 - 30 Sep 2024

Viewed by 534

Abstract

The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and [...] Read more.

The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and global), convergence rates, and adaptive mesh improvement for triangular/quadrilateral discretization schemes. It uses meshless moving least squares (MLS) interpolation with rectangular and circular support regions and solves benchmark plate and cylinder problems. It is observed that a circular influence region, a cubic spline weight function, and regular mesh patterns yield a better performance of than an MLS-based error recovery method. The study also concludes that lower dilation index values with rectangular influence regions are preferable for regular meshes, while higher dilation index values with radial influence regions are suitable for preferable meshes to enhance MLS error recovery. Full article

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22 pages, 1643 KiB

Open AccessArticle

Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation

by Naveed Iqbal, Wael W. Mohammed, Mohammad Alqudah, Amjad E. Hamza and Shah Hussain

Math. Comput. Appl. 2024, 29(5), 86; https://doi.org/10.3390/mca29050086 - 30 Sep 2024

Viewed by 613

Abstract

This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems [...] Read more.

This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems that produce patterns. We have found that there exist numerous chaotic soliton solutions with periodic and axial perturbations to the intended CQSHE, provided that the coefficients are constrained by certain conditions. Furthermore, by applying a sophisticated transformation, the provided transformative approach RMESEM transforms CQSHE into a set of Nonlinear Ordinary Differential Equations (NODEs). The resulting set of NODEs is then transformed into an algebraic system of equations by incorporating the extended Riccati NODE to assume a series form solution. The soliton solutions to this system of equations can be found as periodic, hyperbolic, exponential, rational-hyperbolic, and rational families of functions. A variety of 3D and contour visuals are also provided to graphically illustrate the axially and periodically perturbed dynamics of these chaotic soliton solutions and the formation of fractals. Our findings are noteworthy because they shed light on the chaotic nature of the framework we are examining, enabling us to better understand the dynamics that underlie it. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

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22 pages, 6500 KiB

Open AccessArticle

Latent Space Perspicacity and Interpretation Enhancement (LS-PIE) Framework

by Jesse Stevens, Daniel N. Wilke and Isaac I. Setshedi

Math. Comput. Appl. 2024, 29(5), 85; https://doi.org/10.3390/mca29050085 - 25 Sep 2024

Viewed by 687

Abstract

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or unordered. These data are then projected onto the latent directions to obtain their [...] Read more.

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or unordered. These data are then projected onto the latent directions to obtain their projected representations (or scores). For example, PCA solvers usually rank principal directions by explaining the most variance to the least variance. In contrast, ICA solvers usually return independent directions unordered and often with single sources spread across multiple directions as multiple sub-sources, severely diminishing their usability and interpretability. This paper proposes a general framework to enhance latent space representations to improve the interpretability of linear latent spaces. Although the concepts in this paper are programming language agnostic, the framework is written in Python. This framework simplifies the process of clustering and ranking of latent vectors to enhance latent information per latent vector and the interpretation of latent vectors. Several innovative enhancements are incorporated, including latent ranking (LR), latent scaling (LS), latent clustering (LC), and latent condensing (LCON). LR ranks latent directions according to a specified scalar metric. LS scales latent directions according to a specified metric. LC automatically clusters latent directions into a specified number of clusters. Lastly, LCON automatically determines the appropriate number of clusters to condense the latent directions for a given metric to enable optimal latent discovery. Additional functionality of the framework includes single-channel and multi-channel data sources and data pre-processing strategies such as Hankelisation to seamlessly expand the applicability of linear latent variable models (LLVMs) to a wider variety of data. The effectiveness of LR, LS, LC, and LCON is shown in two foundational problems crafted with two applied latent variable models, namely, PCA and ICA. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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13 pages, 3928 KiB

Open AccessArticle

Computational Modeling of Sodium-Ion-Channel-Based Glucose Sensing Biophysics to Study Cardiac Pacemaker Action Potential

by Chitaranjan Mahapatra, Kirubanandan Shanmugam and Maher Ali Rusho

Math. Comput. Appl. 2024, 29(5), 84; https://doi.org/10.3390/mca29050084 - 21 Sep 2024

Viewed by 756

Abstract

Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate [...] Read more.

Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate the relationship between blood glucose levels and cardiac electrical activity. Our hypothesis suggests that glucose-sensing biophysics mechanisms in cardiac tissue could clarify this connection. To explore this, we adapted a single-compartment computational model of the human pacemaker action potential. We incorporated glucose-sensing mechanisms with voltage-gated sodium ion channels using ordinary differential equations. Parameters for the model were based on existing experimental studies to mimic the impact of glucose levels on pacemaker action potential firing. Simulations using voltage clamp and current clamp techniques showed that elevated glucose levels decreased sodium ion channel currents, leading to a reduction in the pacemaker action potential frequency. In summary, our mathematical model provides a cellular-level understanding of how high glucose levels can lead to bradycardia and sudden cardiac death. Full article

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14 pages, 552 KiB

Open AccessArticle

Design and Implementation of a Discrete-PDC Controller for Stabilization of an Inverted Pendulum on a Self-Balancing Car Using a Convex Approach

by Yasmani González-Cárdenas, Francisco-Ronay López-Estrada, Víctor Estrada-Manzo, Joaquin Dominguez-Zenteno and Manuel López-Pérez

Math. Comput. Appl. 2024, 29(5), 83; https://doi.org/10.3390/mca29050083 - 18 Sep 2024

Viewed by 905

Abstract

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique [...] Read more.

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers the nonlinearities associated with the nonholonomic constraint. The design of a discrete parallel distributed compensation controller is achieved through an alternative method due to the presence of uncontrollable points that avoid finding a solution for the entire polytope. Finally, simulations and experimental results using a prototype illustrate the effectiveness of the proposal. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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4 pages, 144 KiB

Open AccessEditorial

Significance of Mathematical Modeling and Control in Real-World Problems: New Developments and Applications

by Mehmet Yavuz and Ioannis Dassios

Math. Comput. Appl. 2024, 29(5), 82; https://doi.org/10.3390/mca29050082 - 18 Sep 2024

Viewed by 880

Abstract

Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...] Full article

(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)

13 pages, 508 KiB

Open AccessArticle

A Corruption Impunity Model Considering Anticorruption Policies

by Sandra E. Delgadillo-Alemán, Roberto A. Kú-Carrillo and Alejandra Torres-Nájera

Math. Comput. Appl. 2024, 29(5), 81; https://doi.org/10.3390/mca29050081 - 14 Sep 2024

Viewed by 635

Abstract

Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later [...] Read more.

Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later reduce it by proposing strategies, there exist a variety of indices, such as the corruption perception index, and other related issues, such as the global impunity index, the laxness of anticorruption policies, etc., which are computed for different countries worldwide. Based on these indices, we propose a model for corruption using a system of ordinary differential equations, considering anticorruption policies. Those three factors were identified after analyzing the phenomenon and available data, particularly for Mexico. Also, we fit it to the reported data of this country and perform simulations expecting to predict the short term, and performed a sensitivity analysis. The model is capable of reproducing the observed oscillatory behavior of the phenomenon. The model fit can still be improved by including the data for the anticorruption policies, which were only studied for different scenarios. Moreover, the model is susceptible to application in other countries, as long as data are available, and then provides a computational tool to predict and visualize the effect of appropriate public policies to fight corruption. Full article

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20 pages, 3041 KiB

Open AccessArticle

Human Activity Recognition from Accelerometry, Based on a Radius of Curvature Feature

by Elizabeth Cavita-Huerta, Juan Reyes-Reyes, Héctor M. Romero-Ugalde, Gloria L. Osorio-Gordillo, Ricardo F. Escobar-Jiménez and Victor M. Alvarado-Martínez

Math. Comput. Appl. 2024, 29(5), 80; https://doi.org/10.3390/mca29050080 - 13 Sep 2024

Viewed by 641

Abstract

Physical activity recognition using accelerometry is a rapidly advancing field with significant implications for healthcare, sports science, and wearable technology. This research presents an interesting approach for classifying physical activities using solely accelerometry data, signals that were taken from the available “MHEALTH dataset” [...] Read more.

Physical activity recognition using accelerometry is a rapidly advancing field with significant implications for healthcare, sports science, and wearable technology. This research presents an interesting approach for classifying physical activities using solely accelerometry data, signals that were taken from the available “MHEALTH dataset” and processed through artificial neural networks (ANNs). The methodology involves data acquisition, preprocessing, feature extraction, and the application of deep learning algorithms to accurately identify activity patterns. A major innovation in this study is the incorporation of a new feature derived from the radius of curvature. This time-domain feature is computed by segmenting accelerometry signals into windows, conducting double integration to derive positional data, and subsequently estimating a circumference based on the positional data obtained within each window. This characteristic is computed across the three movement planes, providing a robust and comprehensive feature for activity classification. The integration of the radius of curvature into the ANN models significantly enhances their accuracy, achieving over 95%. In comparison with other methodologies, our proposed approach, which utilizes a feedforward neural network (FFNN), demonstrates superior performance. This outperforms previous methods such as logistic regression, which achieved 93%, KNN models with 90%, and the InceptTime model with 88%. The findings demonstrate the potential of this model to improve the precision and reliability of physical activity recognition in wearable health monitoring systems. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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29 pages, 42369 KiB

Open AccessArticle

Analysis and Design for a Wearable Single-Finger-Assistive Soft Robotic Device Allowing Flexion and Extension for Different Finger Sizes

by Sung bok Chung and Martin Philip Venter

Math. Comput. Appl. 2024, 29(5), 79; https://doi.org/10.3390/mca29050079 - 12 Sep 2024

Viewed by 688

Abstract

This paper proposes a design framework to create individualised finger actuators that can be expanded to a generic hand. An actuator design is evaluated to help a finger achieve tendon-gliding exercises (TGEs). We consider musculoskeletal analysis for different finger sizes to determine joint [...] Read more.

This paper proposes a design framework to create individualised finger actuators that can be expanded to a generic hand. An actuator design is evaluated to help a finger achieve tendon-gliding exercises (TGEs). We consider musculoskeletal analysis for different finger sizes to determine joint forces while considering safety. The simulated Finite Element Analysis (FEA) response of a bi-directional Pneumatic Network Actuator (PNA) is mapped to a reduced-order model, creating a robust design tool to determine the bending angle and moment generated for actuator units. A reduced-order model is considered for both the 2D plane-strain formulation of the actuator and a full 3D model, providing a means to map between the results for a more accurate 3D model and the less computationally expensive 2D model. A setup considering a cascade of reduced-order actuator units interacting with a finger model determined to be able to achieve TGE was validated, and three exercises were successfully achieved. The FEA simulations were validated using the bending response of a manufactured actuator interacting with a dummy finger. The quality of the results shows that the simulated models can be used to predict the behaviour of the physical actuator in achieving TGE. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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27 pages, 1003 KiB

Open AccessFeature PaperArticle

Surrogate-Assisted Symbolic Time-Series Discretization Using Multi-Breakpoints and a Multi-Objective Evolutionary Algorithm

by Aldo Márquez-Grajales, Efrén Mezura-Montes, Héctor-Gabriel Acosta-Mesa and Fernando Salas-Martínez

Math. Comput. Appl. 2024, 29(5), 78; https://doi.org/10.3390/mca29050078 - 11 Sep 2024

Viewed by 653

Abstract

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which incurs a high computational cost for evaluating each objective function. It is essential to mention that each solution [...] Read more.

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which incurs a high computational cost for evaluating each objective function. It is essential to mention that each solution found by eMODiTS is a different-sized vector. Previous work was performed where surrogate models were implemented to reduce the computational cost to solve this problem. However, low-fidelity approximations were obtained concerning the original model. Consequently, our main objective is to propose an improvement to this work, modifying the updating process of the surrogate models to minimize their disadvantages. This improvement was evaluated based on classification, predictive power, and computational cost, comparing it against the original model and ten discretization methods reported in the literature. The results suggest that the proposal achieves a higher fidelity to the original model than previous work. It also achieved a computational cost reduction rate between 15% and 80% concerning the original model. Finally, the classification error of our proposal is similar to eMODiTS and maintains its behavior compared to the other discretization methods. Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2024)

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15 pages, 3843 KiB

Open AccessArticle

A Study of Tennis Tournaments by Means of an Agent-Based Model Calibrated with a Genetic Algorithm

by Salvatore Prestipino and Andrea Rapisarda

Math. Comput. Appl. 2024, 29(5), 77; https://doi.org/10.3390/mca29050077 - 11 Sep 2024

Viewed by 820

Abstract

In this work, we study the sport of tennis, with the aim of understanding competitions and the associated quantities that determine their outcome. We construct an agent-based model that is able to produce data analogous to real data taken from Association of Tennis [...] Read more.

In this work, we study the sport of tennis, with the aim of understanding competitions and the associated quantities that determine their outcome. We construct an agent-based model that is able to produce data analogous to real data taken from Association of Tennis Professionals (ATP) tournaments. This model depends on three parameters: the talent weight, the talent distribution width, and the chance distribution width. Unlike other similar works, we do not fix the values of these parameters and we calibrate the model results with the help of a genetic algorithm, thus exploring all possible combinations of parameters in the parameter space that are able to reproduce real system data. We show that the model fits the real data well only for limited regions of the parameter space. Limiting the region of interest in the parameter space allows us to perform further calibrations of the model that give us more information about the competition under study. Finally, we are able to provide useful information about tennis competitions, obtaining quantitative information about all of the important parameters and quantities related to these competitions with very limited a priori constraints. Through our approach, differing from those of other works, we confirm the importance of chance in the studied competitions, which has a weight of around 80% in determining the outcome of tennis competitions. Full article

(This article belongs to the Topic Mathematical Modeling)

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13 pages, 2327 KiB

Open AccessFeature PaperArticle

An Alternative Analysis of Computational Learning within Behavioral Neuropharmacology in an Experimental Anxiety Model Investigation

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

Math. Comput. Appl. 2024, 29(5), 76; https://doi.org/10.3390/mca29050076 - 9 Sep 2024

Viewed by 866

Abstract

Behavioral neuropharmacology, a branch of neuroscience, uses behavioral analysis to demonstrate treatment effects on animal models, which is fundamental for pre-clinical evaluation. Typically, this determination is univariate, neglecting the relevant associations for understanding treatment effects in animals and humans. This study implements regression [...] Read more.

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

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2023)

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13 pages, 2526 KiB

Open AccessArticle

Innovative Solutions to the Fractional Diffusion Equation Using the Elzaki Transform

by Saima Noor, Albandari W. Alrowaily, Mohammad Alqudah, Rasool Shah and Samir A. El-Tantawy

Math. Comput. Appl. 2024, 29(5), 75; https://doi.org/10.3390/mca29050075 - 2 Sep 2024

Viewed by 957

Abstract

This study explores the application of advanced mathematical techniques to solve fractional differential equations, focusing particularly on the fractional diffusion equation. The fractional diffusion equation, used to simulate a range of physical and engineering phenomena, poses considerable difficulties when applied to fractional orders. [...] Read more.

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

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15 pages, 1676 KiB

Open AccessArticle

Using Kan Extensions to Motivate the Design of a Surprisingly Effective Unsupervised Linear SVM on the Occupancy Dataset

by Matthew Pugh, Jo Grundy, Corina Cirstea and Nick Harris

Math. Comput. Appl. 2024, 29(5), 74; https://doi.org/10.3390/mca29050074 - 2 Sep 2024

Viewed by 807

Abstract

Recent research has suggested that category theory can provide useful insights into the field of machine learning (ML). One example is improving the connection between an ML problem and the design of a corresponding ML algorithm. A tool from category theory called a [...] Read more.

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

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20 pages, 748 KiB

Open AccessArticle

Causal Analysis to Explain the Performance of Algorithms: A Case Study for the Bin Packing Problem

by Jenny Betsabé Vázquez-Aguirre, Guadalupe Carmona-Arroyo, Marcela Quiroz-Castellanos and Nicandro Cruz-Ramírez

Math. Comput. Appl. 2024, 29(5), 73; https://doi.org/10.3390/mca29050073 - 28 Aug 2024

Viewed by 703

Abstract

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study [...] Read more.

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

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2023)

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10 pages, 669 KiB

Open AccessArticle

Analysis of a First-Order Delay Model under a History Function with Discontinuity

by Weam G. Alharbi

Math. Comput. Appl. 2024, 29(5), 72; https://doi.org/10.3390/mca29050072 - 24 Aug 2024

Viewed by 552

Abstract

This paper analyzes the first-order delay equation

y^{'} (t) = α y (t) + β y (t - τ)

subject to a history function in addition to an initial condition that assumes discontinuity at [...] Read more.

This paper analyzes the first-order delay equation

y^{'} (t) = α y (t) + β y (t - τ)

subject to a history function in addition to an initial condition that assumes discontinuity at

t = 0

. The method of steps is successfully applied to derive the exact solution in an explicit form. In addition, a unified formula is provided to describe the solution in any finite sub-interval of the problem’s domain. The characteristics and properties of the solution are theoretically investigated and then confirmed through several plots. The behavior of the solution and its derivative are examined and interpreted. The results show that the method of steps is an effective method of solution to treat the current delay model. The present successful analysis can be used to investigate other delay models with complex initial conditions. Furthermore, the present approach can be generalized to include the inhomogeneous version of the current model without using numerical methods. Full article

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17 pages, 4513 KiB

Open AccessArticle

Machine Learning Based Extraction of Boundary Conditions from Doppler Echo Images for Patient Specific Coarctation of the Aorta: Computational Fluid Dynamics Study

by Vincent Milimo Masilokwa Punabantu, Malebogo Ngoepe, Amit Kumar Mishra, Thomas Aldersley, John Lawrenson and Liesl Zühlke

Math. Comput. Appl. 2024, 29(5), 71; https://doi.org/10.3390/mca29050071 - 23 Aug 2024

Viewed by 736

Abstract

Patient-specific computational fluid dynamics (CFD) studies on coarctation of the aorta (CoA) in resource-constrained settings are limited by the available imaging modalities for geometry and velocity data acquisition. Doppler echocardiography is considered a suitable velocity acquisition modality due to its low cost and [...] Read more.

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

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))

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Math. Comput. Appl., Volume 29, Issue 5 (October 2024) – 25 articles

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