Mathematical and Computational Applications

20 pages, 6490 KiB

Open AccessArticle

Inducing Perceptual Dominance with Binocular Rivalry in a Virtual Reality Head-Mounted Display

by Julianne Blignaut, Martin Venter, David van den Heever, Mark Solms and Ivan Crockart

Math. Comput. Appl. 2023, 28(3), 77; https://doi.org/10.3390/mca28030077 - 17 Jun 2023

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Binocular rivalry is the perceptual dominance of one visual stimulus over another. Conventionally, binocular rivalry is induced using a mirror-stereoscope—a setup involving mirrors oriented at an angle to a display. The respective mirror planes fuse competing visual stimuli in the observer’s visual field [...] Read more.

Binocular rivalry is the perceptual dominance of one visual stimulus over another. Conventionally, binocular rivalry is induced using a mirror-stereoscope—a setup involving mirrors oriented at an angle to a display. The respective mirror planes fuse competing visual stimuli in the observer’s visual field by projecting the stimuli through the stereoscope to the observed visual field. Since virtual-reality head-mounted displays fuse dichoptic vision in a similar way, and since virtual-reality head-mounted displays are more versatile and more readily available than mirror stereoscopes, this study investigated the efficacy of using a virtual-reality headset (Oculus Rift-S) as an alternative to using a mirror stereoscope to study binocular rivalry. To evaluate the validity of using virtual-reality headsets to induce visual dominance/suppression, two identical experimental sequences—one using a conventional mirror stereoscope and one using a virtual-reality headset—were compared and evaluated. The study used Gabor patches at different orientations to induce binocular rivalry and to evaluate the efficacy of the two experiments. Participants were asked to record all instances of perceptual dominance (complete suppression) and non-dominance (incomplete suppression). Independent sample t-tests confirmed that binocular rivalry with stable vergence was successfully induced for the mirror-stereoscope experiment (t = −4.86; p ≤ 0.0001) and the virtual-reality experiment (t = −9.41; p ≤ 0.0001). Using ANOVA to compare Gabor patch pairs of gratings at +45°/−45° orientations presented in both visual fields, gratings at 0°/90° orientations presented in both visual fields, and mixed gratings (i.e., unconventional grating pairs) presented in both visual fields, the performance of the two experiments was evaluated by comparing observation duration in seconds (F = 0.12; p = 0.91) and the alternation rate per trial (F = 8.1; p = 0.0005). The differences between the stimulus groups were not statistically significant for the observation duration but were significantly different based on the alternation rates per trial. Moreover, ANOVA also showed that the dominance durations (F = 114.1; p < 0.0001) and the alternation rates (F = 91.6; p < 0.0001) per trial were significantly different between the mirror-stereoscope and the virtual-reality experiments, with the virtual-reality experiment showing an increase in alternation rate and a decrease in observation duration. The study was able to show that a virtual-reality head-mounted display can be used as an effective and novel alternative to induce binocular rivalry, but there were some differences in visual bi-stability between the two methods. This paper discusses the experimental measures taken to minimise piecemeal rivalry and to evaluate perceptual dominance between the two experimental designs. Full article

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

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13 pages, 760 KiB

Open AccessArticle

Developing a Robust Bioventing Model

by Mohammad Khodabakhshi Soureshjani and Richard G. Zytner

Math. Comput. Appl. 2023, 28(3), 76; https://doi.org/10.3390/mca28030076 - 16 Jun 2023

Cited by 2 | Viewed by 1186

Abstract

Bioventing is a widely recognized technique for the remediation of petroleum hydrocarbon-contaminated soil. In this study, the objective was to identify an optimal mathematical model that balances accuracy and ease of implementation. A comprehensive review of various models developed for bioventing was conducted [...] Read more.

Bioventing is a widely recognized technique for the remediation of petroleum hydrocarbon-contaminated soil. In this study, the objective was to identify an optimal mathematical model that balances accuracy and ease of implementation. A comprehensive review of various models developed for bioventing was conducted wherein the advantages and disadvantages of each model were evaluated and compared regarding the different numerical methods used to solve relevant bioventing equations. After investigating the various assumptions and methods from the literature, an improved foundational bioventing model was developed that characterizes gas flow in unsaturated zones where water and non-aqueous phase liquid (NAPL) are present and immobile, accounting for interphase mass transfer and biodegradation, incorporating soil properties through a rate constant correlation. The proposed model was solved using the finite volume method in OpenFOAM, an independent dimensional open-source coding toolbox. The preliminary simulation results of a simple case indicate good agreement with the exact analytical solution of the same equations. This improved bioventing model has the potential to enhance predictions of the remediation process and support the development of efficient remediation strategies for petroleum hydrocarbon-contaminated soil. Full article

(This article belongs to the Topic Mathematical Modeling)

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13 pages, 530 KiB

Open AccessArticle

Evolutionary Selection of a Set of Association Rules Considering Biological Constraints Describing the Prevalent Elements in Bacterial Vaginosis

by María Concepción Salvador-González, Juana Canul-Reich, Rafael Rivera-López, Efrén Mezura-Montes and Erick de la Cruz-Hernandez

Math. Comput. Appl. 2023, 28(3), 75; https://doi.org/10.3390/mca28030075 - 14 Jun 2023

Viewed by 1059

Abstract

Bacterial Vaginosis is a common disease and recurring public health problem. Additionally, this infection can trigger other sexually transmitted diseases. In the medical field, not all possible combinations among the pathogens of a possible case of Bacterial Vaginosis are known to allow a [...] Read more.

Bacterial Vaginosis is a common disease and recurring public health problem. Additionally, this infection can trigger other sexually transmitted diseases. In the medical field, not all possible combinations among the pathogens of a possible case of Bacterial Vaginosis are known to allow a diagnosis at the onset of the disease. It is important to contribute to this line of research, so this study uses a dataset with information from sexually active women between 18 and 50 years old, including 17 numerical attributes of microorganisms and bacteria with positive and negative results for BV. These values were semantically categorized for the Apriori algorithm to create the association rules, using support, confidence, and lift as statistical metrics to evaluate the quality of the rules, and incorporate those results in the objective function of the DE algorithm. To guide the evolutionary process we also incorporated the knowledge of a human expert represented as a set of biologically meaningful constraints. Thus, we were able to compare the performance of the rand/1/bin and best/1/bin versions from Differential Evolution to analyze the results of 30 independent executions. Therefore the experimental results allowed a reduced subset of biologically meaningful association rules by their executions, dimension, and DE version to be selected. Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2023)

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20 pages, 3841 KiB

Open AccessArticle

Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

by Vijay and Arya Kumar Bedabrata Chand

Math. Comput. Appl. 2023, 28(3), 74; https://doi.org/10.3390/mca28030074 - 10 Jun 2023

Cited by 1 | Viewed by 1051

Abstract

A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature. A zipper fractal function constructed through a zipper iterated function system (IFS) allows one to use negative and [...] Read more.

A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature. A zipper fractal function constructed through a zipper iterated function system (IFS) allows one to use negative and positive horizontal scalings. In contrast, a fractal function constructed with an IFS uses positive horizontal scalings only. This article introduces some novel classes of continuously differentiable convexity-preserving zipper fractal interpolation curves and surfaces. First, we construct zipper fractal interpolation curves for the given univariate Hermite interpolation data. Then, we generate zipper fractal interpolation surfaces over a rectangular grid without using any additional knots. These surface interpolants converge uniformly to a continuously differentiable bivariate data-generating function. For a given Hermite bivariate dataset and a fixed choice of scaling and shape parameters, one can obtain a wide variety of zipper fractal surfaces by varying signature vectors in both the x direction and y direction. Some numerical illustrations are given to verify the theoretical convexity results. Full article

(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)

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13 pages, 4774 KiB

Open AccessArticle

On the Fluctuations of Internal DLA on the Sierpinski Gasket Graph

by Nico Heizmann

Math. Comput. Appl. 2023, 28(3), 73; https://doi.org/10.3390/mca28030073 - 07 Jun 2023

Viewed by 764

Abstract

Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph G, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the Sierpinski gasket graph, the [...] Read more.

Internal diffusion limited aggregation (IDLA) is a random aggregation model on a graph G, whose clusters are formed by random walks started in the origin (some fixed vertex) and stopped upon visiting a previously unvisited site. On the Sierpinski gasket graph, the asymptotic shape is known to be a ball in the graph metric. In this paper, we improve the sublinear bounds for the fluctuations known from its known asymptotic shape result by establishing bounds for the odometer function for a divisible sandpile model. Full article

(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)

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11 pages, 1084 KiB

Open AccessArticle

Neuroevolution of Convolutional Neural Networks for Breast Cancer Diagnosis Using Western Blot Strips

by José-Luis Llaguno-Roque, Rocio-Erandi Barrientos-Martínez, Héctor-Gabriel Acosta-Mesa, Tania Romo-González and Efrén Mezura-Montes

Math. Comput. Appl. 2023, 28(3), 72; https://doi.org/10.3390/mca28030072 - 24 May 2023

Viewed by 1523

Abstract

Breast cancer has become a global health problem, ranking first in incidences and fifth in mortality in women around the world. In Mexico, the first cause of death in women is breast cancer. This work uses deep learning techniques to discriminate between healthy [...] Read more.

Breast cancer has become a global health problem, ranking first in incidences and fifth in mortality in women around the world. In Mexico, the first cause of death in women is breast cancer. This work uses deep learning techniques to discriminate between healthy and breast cancer patients, based on the banding patterns obtained from the Western Blot strip images of the autoantibody response to antigens of the T47D tumor line. The reaction of antibodies to tumor antigens occurs early in the process of tumorigenesis, years before clinical symptoms. One of the main challenges in deep learning is the design of the architecture of the convolutional neural network. Neuroevolution has been used to support this and has produced highly competitive results. It is proposed that neuroevolve convolutional neural networks (CNN) find an optimal architecture to achieve competitive ranking, taking Western Blot images as input. The CNN obtained reached 90.67% accuracy, 90.71% recall, 95.34% specificity, and 90.69% precision in classifying three different classes (healthy, benign breast pathology, and breast cancer). Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2023)

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3 pages, 170 KiB

Open AccessEditorial

Numerical and Evolutionary Optimization 2021

by Marcela Quiroz-Castellanos, Luis Gerardo de la Fraga, Adriana Lara, Leonardo Trujillo and Oliver Schütze

Math. Comput. Appl. 2023, 28(3), 71; https://doi.org/10.3390/mca28030071 - 23 May 2023

Viewed by 1028

Abstract

This Special Issue was inspired by the 9th International Workshop on Numerical and Evolutionary Optimization (NEO 2021) held—due to the COVID-19 pandemic—as an online-only event from 8 to 10 September 2021 [...] Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)

16 pages, 770 KiB

Open AccessArticle

Sierpiński Fractals and the Dimension of Their Laplacian Spectrum

by Mark Pollicott and Julia Slipantschuk

Math. Comput. Appl. 2023, 28(3), 70; https://doi.org/10.3390/mca28030070 - 17 May 2023

Cited by 1 | Viewed by 1211

Abstract

We establish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated with Sierpiński lattices and infinite Sierpiński gaskets and other post-critically finite self-similar sets. Full article

(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)

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15 pages, 508 KiB

Open AccessArticle

Numerical Aspects of a Continuum Sintering Model Formulated in the Standard Dissipative Framework

by Sebastian Stark

Math. Comput. Appl. 2023, 28(3), 69; https://doi.org/10.3390/mca28030069 - 17 May 2023

Cited by 1 | Viewed by 818

Abstract

Robust and computationally efficient numeric algorithms are required to simulate the sintering process of complex ceramic components by means of the finite element method. This work focuses on a thermodynamically consistent sintering model capturing the effects of both, viscosity and elasticity, within the [...] Read more.

Robust and computationally efficient numeric algorithms are required to simulate the sintering process of complex ceramic components by means of the finite element method. This work focuses on a thermodynamically consistent sintering model capturing the effects of both, viscosity and elasticity, within the standard dissipative framework. In particular, the temporal integration of the model by means of several implicit first and second order accurate one step time integration methods is discussed. It is shown in terms of numerical experiments on the material point level that the first order schemes exhibit poor performance when compared to second order schemes. Further numerical experiments indicate that the results translate directly to finite element simulations. Full article

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

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18 pages, 9233 KiB

Open AccessArticle

Intermediate Encoding Layers for the Generative Design of 2D Soft Robot Actuators: A Comparison of CPPN’s, L-Systems and Random Generation

by Martin Philip Venter and Naudé Thomas Conradie

Math. Comput. Appl. 2023, 28(3), 68; https://doi.org/10.3390/mca28030068 - 15 May 2023

Viewed by 1214

Abstract

This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding [...] Read more.

This paper introduced a comparison method for three explicitly defined intermediate encoding methods in generative design for two-dimensional soft robotic units. This study evaluates a conventional genetic algorithm with full access to removing elements from the design domain using an implicit random encoding layer, a Lindenmayer system encoding mimicking biological growth patterns and a compositional pattern producing network encoding for 2D pattern generation. The objective of the optimisation problem is to match the deformation of a single actuator unit with a desired target shape, specifically uni-axial elongation, under internal pressure. The study results suggest that the Lindenmayer system encoding generates candidate units with fewer function evaluations than the traditional implicitly encoded genetic algorithm. However, the distribution of constraint and internal energy is similar to that of the random encoding, and the Lindenmayer system encoding produces a less diverse population of candidate units. In contrast, despite requiring more function evaluations than the Lindenmayer System encoding, the Compositional Pattern Producing Network encoding produces a similar diversity of candidate units. Overall, the Compositional Pattern Producing Network encoding results in a proportionally higher number of high-performing units than the random or Lindenmayer system encoding, making it a viable alternative to a conventional monolithic approach. The results suggest that the compositional pattern producing network encoding may be a promising approach for designing soft robotic actuators with desirable performance characteristics. Full article

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

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31 pages, 1620 KiB

Open AccessArticle

Routing, Modulation Level, and Spectrum Assignment in Elastic Optical Networks—A Serial Stage Approach with Multiple Sub-Sets of Requests Based on Integer Linear Programming

by Luis Víctor Maidana Benítez, Melisa María Rosa Villamayor Paredes, José Colbes, César F. Bogado-Martínez, Benjamin Barán and Diego P. Pinto-Roa

Math. Comput. Appl. 2023, 28(3), 67; https://doi.org/10.3390/mca28030067 - 10 May 2023

Viewed by 1807

Abstract

This paper addresses serialized approaches of the routing, modulation level, and spectrum assignment (RMLSA) problem in elastic optical networks, using multiple sequential sub-sets of requests, under Integer Linear Programming (ILP). The literature has reported two-stage serial optimization methods referred to as RML+SA, which [...] Read more.

This paper addresses serialized approaches of the routing, modulation level, and spectrum assignment (RMLSA) problem in elastic optical networks, using multiple sequential sub-sets of requests, under Integer Linear Programming (ILP). The literature has reported two-stage serial optimization methods referred to as RML+SA, which retain computational efficiency when the problem grows, compared to the classical one-stage RMLSA optimization approach. However, there still remain numerous issues in terms of the spectrum used that can be improved when compared to the RMLSA solution. Consequently, this paper proposes RML+SA solutions considering multiple sequential sub-sets of requests, split traffic flow, as well as path-oriented and link-oriented routing models. Simulation results on different test scenarios determine that: (a) the multiple sequential sub-sets of request-based models improve computation time without worsening the spectrum usage when compared to just one set of requests optimization approaches, (b) divisible traffic flow approaches show promise in cases where the number of request sub-sets is low compared to the non-divisible counterpart, and (c) path-oriented routing succeeds in improving the used spectrum by increasing the number of candidate routes compared to link-oriented routing. Full article

(This article belongs to the Topic Mathematical Modeling)

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10 pages, 42149 KiB

Open AccessArticle

Applying Quaternions to Recognize Hidden Details in Images: Rothko as a Case Study

by Adam Aharony, Ron Hindi, Maor Valdman and Shai Gul

Math. Comput. Appl. 2023, 28(3), 66; https://doi.org/10.3390/mca28030066 - 09 May 2023

Viewed by 1232

Abstract

Images or paintings with homogeneous colors may appear dull to the naked eye; however, there may be numerous details in the image that are expressed through subtle changes in color. This manuscript introduces a novel approach that can uncover these concealed details via [...] Read more.

Images or paintings with homogeneous colors may appear dull to the naked eye; however, there may be numerous details in the image that are expressed through subtle changes in color. This manuscript introduces a novel approach that can uncover these concealed details via a transformation that increases the distance between adjacent pixels, ultimately leading to a newly modified version of the input image. We chose the artworks of Mark Rothko—famous for their simplicity and limited color palette—as a case study. Our approach offers a different perspective, leading to the discovery of either accidental or deliberate clusters of colors. Our method is based on the quaternion ring, wherein a suitable multiplication can be used to boost the color difference between neighboring pixels, thereby unveiling new details in the image. The quality of the transformation between the original image and the resultant versions can be measured by the ratio between the number of connected components in the original image (m) and the number of connected components in the output versions (n), which usually satisfies

\frac{n}{m} ≫ 1

. Although this procedure has been employed as a case study for artworks, it can be applied to any type of image with a similar simplicity and limited color palette. Full article

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23 pages, 427 KiB

Open AccessFeature PaperReview

Notes on the Transversality Method for Iterated Function Systems—A Survey

by Boris Solomyak

Math. Comput. Appl. 2023, 28(3), 65; https://doi.org/10.3390/mca28030065 - 04 May 2023

Viewed by 1338

Abstract

This is a brief survey of selected results obtained using the “transversality method” developed for studying parametrized families of fractal sets and measures. We mostly focus on the early development of the theory, restricting ourselves to self-similar and self-conformal iterated function systems. Full article

(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)

15 pages, 6201 KiB

Open AccessArticle

The Use of Computational Fluid Dynamics for Assessing Flow-Induced Acoustics to Diagnose Lung Conditions

by Khanyisani Mhlangano Makhanya, Simon Connell, Muaaz Bhamjee and Neil Martinson

Math. Comput. Appl. 2023, 28(3), 64; https://doi.org/10.3390/mca28030064 - 03 May 2023

Viewed by 1281

Abstract

Pulmonary diseases are a leading cause of illness and disability globally. While having access to hospitals or specialist clinics for investigations is currently the usual way to characterize the patient’s condition, access to medical services is restricted in less resourced settings. We posit [...] Read more.

Pulmonary diseases are a leading cause of illness and disability globally. While having access to hospitals or specialist clinics for investigations is currently the usual way to characterize the patient’s condition, access to medical services is restricted in less resourced settings. We posit that pulmonary disease may impact on vocalization which could aid in characterizing a pulmonary condition. We therefore propose a new method to diagnose pulmonary disease analyzing the vocal and cough changes of a patient. Computational fluid dynamics holds immense potential for assessing the flow-induced acoustics in the lungs. The aim of this study is to investigate the potential of flow-induced vocal-, cough-, and lung-generated acoustics to diagnose lung conditions using computational fluid dynamics methods. In this study, pneumonia is the model disease which is studied. The hypothesis is that using a computational fluid dynamics model for assessing the flow-induced acoustics will accurately represent the flow-induced acoustics for healthy and infected lungs and that possible modeled difference in fluid and acoustic behavior between these pathologies will be tested and described. Computational fluid dynamics and a lung geometry will be used to simulate the flow distribution and obtain the acoustics for the different scenarios. The results suggest that it is possible to determine the difference in vocalization between healthy lungs and those with pneumonia, using computational fluid dynamics, as the flow patterns and acoustics differ. Our results suggest there is potential for computational fluid dynamics to enhance understanding of flow-induced acoustics that could be characteristic of different lung pathologies. Such simulations could be repeated using machine learning with the final objective to use telemedicine to triage or diagnose patients with respiratory illness remotely. Full article

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

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9 pages, 1002 KiB

Open AccessArticle

Computation of the Distribution of the Sum of Independent Negative Binomial Random Variables

by Marc Girondot and Jon Barry

Math. Comput. Appl. 2023, 28(3), 63; https://doi.org/10.3390/mca28030063 - 28 Apr 2023

Cited by 1 | Viewed by 1979

Abstract

The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series expression by convolution. We compare both [...] Read more.

The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series expression by convolution. We compare both methods, as well as a new normalized saddlepoint approximation, and normal and single distribution negative binomial approximations. We show that the exact series expression used lots of memory when the number of random variables was high (>7). The normalized saddlepoint approximation gives an output with a high relative error (around 3–5%), which can be a problem in some situations. The convolution method is a good compromise for applied practitioners, considering the amount of memory used, the computing time, and the precision of the estimates. However, a simplistic implementation of the algorithm could produce incorrect results due to the non-monotony of the convergence rate. The tolerance limit must be chosen depending on the expected magnitude order of the estimate, for which we used the answer generated by the saddlepoint approximation. Finally, the normal and negative binomial approximations should not be used, as they produced outputs with a very low accuracy. Full article

(This article belongs to the Special Issue Statistical Inference in Linear Models)

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Math. Comput. Appl., Volume 28, Issue 3 (June 2023) – 15 articles

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