SidAhmed Benchiha, L. Sapkota, Aned Al Mutairi, Vijay Kumar, Rana H. Khashab, Ahmed M. Gemeay, M. Elgarhy, S. G. Nassr
In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study.
{"title":"A New Sine Family of Generalized Distributions: Statistical Inference with Applications","authors":"SidAhmed Benchiha, L. Sapkota, Aned Al Mutairi, Vijay Kumar, Rana H. Khashab, Ahmed M. Gemeay, M. Elgarhy, S. G. Nassr","doi":"10.3390/mca28040083","DOIUrl":"https://doi.org/10.3390/mca28040083","url":null,"abstract":"In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48224764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al2O3-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated.
{"title":"Thermal Stress Formation in a Functionally Graded Al2O3-Adhesive Single Lap Joint Subjected to a Uniform Temperature Field","authors":"M. Apalak, J. Reddy","doi":"10.3390/mca28040082","DOIUrl":"https://doi.org/10.3390/mca28040082","url":null,"abstract":"This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al2O3-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43171300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Diana-Itzel Vázquez-Santiago, H. Acosta-Mesa, E. Mezura-Montes
One of the main limitations of traditional neural-network-based classifiers is the assumption that all query data are well represented within their training set. Unfortunately, in real-life scenarios, this is often not the case, and unknown class data may appear during testing, which drastically weakens the robustness of the algorithms. For this type of problem, open-set recognition (OSR) proposes a new approach where it is assumed that the world knowledge of algorithms is incomplete, so they must be prepared to detect and reject objects of unknown classes. However, the goal of this approach does not include the detection of new classes hidden within the rejected instances, which would be beneficial to increase the model’s knowledge and classification capability, even after training. This paper proposes an OSR strategy with an extension for new class discovery aimed at vehicle make and model recognition. We use a neuroevolution technique and the contrastive loss function to design a domain-specific CNN that generates a consistent distribution of feature vectors belonging to the same class within the embedded space in terms of cosine similarity, maintaining this behavior in unknown classes, which serves as the main guide for a probabilistic model and a clustering algorithm to simultaneously detect objects of new classes and discover their classes. The results show that the presented strategy works effectively to address the VMMR problem as an OSR problem and furthermore is able to simultaneously recognize the new classes hidden within the rejected objects. OSR is focused on demonstrating its effectiveness with benchmark databases that are not domain-specific. VMMR is focused on improving its classification accuracy; however, since it is a real-world recognition problem, it should have strategies to deal with unknown data, which has not been extensively addressed and, to the best of our knowledge, has never been considered from an OSR perspective, so this work also contributes as a benchmark for future domain-specific OSR.
{"title":"Vehicle Make and Model Recognition as an Open-Set Recognition Problem and New Class Discovery","authors":"Diana-Itzel Vázquez-Santiago, H. Acosta-Mesa, E. Mezura-Montes","doi":"10.3390/mca28040080","DOIUrl":"https://doi.org/10.3390/mca28040080","url":null,"abstract":"One of the main limitations of traditional neural-network-based classifiers is the assumption that all query data are well represented within their training set. Unfortunately, in real-life scenarios, this is often not the case, and unknown class data may appear during testing, which drastically weakens the robustness of the algorithms. For this type of problem, open-set recognition (OSR) proposes a new approach where it is assumed that the world knowledge of algorithms is incomplete, so they must be prepared to detect and reject objects of unknown classes. However, the goal of this approach does not include the detection of new classes hidden within the rejected instances, which would be beneficial to increase the model’s knowledge and classification capability, even after training. This paper proposes an OSR strategy with an extension for new class discovery aimed at vehicle make and model recognition. We use a neuroevolution technique and the contrastive loss function to design a domain-specific CNN that generates a consistent distribution of feature vectors belonging to the same class within the embedded space in terms of cosine similarity, maintaining this behavior in unknown classes, which serves as the main guide for a probabilistic model and a clustering algorithm to simultaneously detect objects of new classes and discover their classes. The results show that the presented strategy works effectively to address the VMMR problem as an OSR problem and furthermore is able to simultaneously recognize the new classes hidden within the rejected objects. OSR is focused on demonstrating its effectiveness with benchmark databases that are not domain-specific. VMMR is focused on improving its classification accuracy; however, since it is a real-world recognition problem, it should have strategies to deal with unknown data, which has not been extensively addressed and, to the best of our knowledge, has never been considered from an OSR perspective, so this work also contributes as a benchmark for future domain-specific OSR.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49020037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Meicong Li, Zheng Zhang, Yang Li, Qiang Zhao, Mei Huang, Xiaoping Ouyang
Tungsten is a promising material for nuclear fusion reactors, but its performance can be degraded by the accumulation of hydrogen (H) and helium (He) isotopes produced by nuclear reactions. This study investigates the effect of chrome (Cr) and vanadium (V) on the behavior of hydrogen and helium in tungsten (W) using first-principles calculations. The results show W becomes easier to process after adding Cr and V. Stability improves after adding V. Adding Cr negatively impacts H and He diffusion in W, while V promotes it. There is attraction between H and Cr or H and V for distances over 1.769 Å but repulsion below 1.583 Å. There is always attraction between He and Cr or V. The attraction between vacancies and He is stronger than that between He and Cr or V. There is no clear effect on H when vacancies and Cr or V coexist in W. Vacancies can dilute the effects of Cr and V on H and He in W.
{"title":"Effect of Chrome and Vanadium on the Behavior of Hydrogen and Helium in Tungsten","authors":"Meicong Li, Zheng Zhang, Yang Li, Qiang Zhao, Mei Huang, Xiaoping Ouyang","doi":"10.3390/mca28040081","DOIUrl":"https://doi.org/10.3390/mca28040081","url":null,"abstract":"Tungsten is a promising material for nuclear fusion reactors, but its performance can be degraded by the accumulation of hydrogen (H) and helium (He) isotopes produced by nuclear reactions. This study investigates the effect of chrome (Cr) and vanadium (V) on the behavior of hydrogen and helium in tungsten (W) using first-principles calculations. The results show W becomes easier to process after adding Cr and V. Stability improves after adding V. Adding Cr negatively impacts H and He diffusion in W, while V promotes it. There is attraction between H and Cr or H and V for distances over 1.769 Å but repulsion below 1.583 Å. There is always attraction between He and Cr or V. The attraction between vacancies and He is stronger than that between He and Cr or V. There is no clear effect on H when vacancies and Cr or V coexist in W. Vacancies can dilute the effects of Cr and V on H and He in W.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49321935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The inverse finite element method is a technique that can be used for material model parameter characterization. The literature shows that this approach may get caught in the local minima of the design space. These local minimum solutions often fit the material test data with small errors and are often mistaken for the optimal solution. The problem with these sub-optimal solutions becomes apparent when applied to different loading conditions where significant errors can be witnessed. The research of this paper presents a new method that resolves this issue for Mooney–Rivlin and builds on a previous paper that used flat planes, referred to as hyperplanes, to map the error functions, isolating the unique optimal solution. The new method alternatively uses a constrained optimization approach, utilizing equality constraints to evaluate the error functions. As a result, the design space’s curvature is taken into account, which significantly reduces the amount of variation between predicted parameters from a maximum of 1.934% in the previous paper down to 0.1882% in the results presented here. The results of this study demonstrate that the new method not only isolates the unique optimal solution but also drastically reduces the variation in the predicted parameters. The paper concludes that the presented new characterization method significantly contributes to the existing literature.
{"title":"A New Method for Improving Inverse Finite Element Method Material Characterization for the Mooney–Rivlin Material Model through Constrained Optimization","authors":"J. V. Van Tonder, M. Venter, G. Venter","doi":"10.3390/mca28040078","DOIUrl":"https://doi.org/10.3390/mca28040078","url":null,"abstract":"The inverse finite element method is a technique that can be used for material model parameter characterization. The literature shows that this approach may get caught in the local minima of the design space. These local minimum solutions often fit the material test data with small errors and are often mistaken for the optimal solution. The problem with these sub-optimal solutions becomes apparent when applied to different loading conditions where significant errors can be witnessed. The research of this paper presents a new method that resolves this issue for Mooney–Rivlin and builds on a previous paper that used flat planes, referred to as hyperplanes, to map the error functions, isolating the unique optimal solution. The new method alternatively uses a constrained optimization approach, utilizing equality constraints to evaluate the error functions. As a result, the design space’s curvature is taken into account, which significantly reduces the amount of variation between predicted parameters from a maximum of 1.934% in the previous paper down to 0.1882% in the results presented here. The results of this study demonstrate that the new method not only isolates the unique optimal solution but also drastically reduces the variation in the predicted parameters. The paper concludes that the presented new characterization method significantly contributes to the existing literature.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45706429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” and approximating the reflection term are challenges. Some numerical algorithms based on neural networks developed recently fail in solving high-dimensional reflected PDEs. To solve these problems, firstly, the reflected PDEs are transformed into reflected backward stochastic differential equations (BSDEs) using the reflected Feyman–Kac formula. Secondly, the reflection term of the reflected BSDEs is approximated using the penalization method. Next, the BSDEs are discretized using a strategy that combines Euler and Crank–Nicolson schemes. Finally, a deep neural network model is employed to simulate the solution of the BSDEs. The effectiveness of the proposed method is tested by two numerical experiments, and the model shows high stability and accuracy in solving reflected PDEs of up to 100 dimensions.
{"title":"Solve High-Dimensional Reflected Partial Differential Equations by Neural Network Method","authors":"Xiaowen Shi, Xiangyu Zhang, Renwu Tang, Juan Yang","doi":"10.3390/mca28040079","DOIUrl":"https://doi.org/10.3390/mca28040079","url":null,"abstract":"Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” and approximating the reflection term are challenges. Some numerical algorithms based on neural networks developed recently fail in solving high-dimensional reflected PDEs. To solve these problems, firstly, the reflected PDEs are transformed into reflected backward stochastic differential equations (BSDEs) using the reflected Feyman–Kac formula. Secondly, the reflection term of the reflected BSDEs is approximated using the penalization method. Next, the BSDEs are discretized using a strategy that combines Euler and Crank–Nicolson schemes. Finally, a deep neural network model is employed to simulate the solution of the BSDEs. The effectiveness of the proposed method is tested by two numerical experiments, and the model shows high stability and accuracy in solving reflected PDEs of up to 100 dimensions.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46800597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Julianne Blignaut, Martin Venter, D.J. van den Heever, M. Solms, Ivan Crockart
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.
{"title":"Inducing Perceptual Dominance with Binocular Rivalry in a Virtual Reality Head-Mounted Display","authors":"Julianne Blignaut, Martin Venter, D.J. van den Heever, M. Solms, Ivan Crockart","doi":"10.3390/mca28030077","DOIUrl":"https://doi.org/10.3390/mca28030077","url":null,"abstract":"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.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44074825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Developing a Robust Bioventing Model","authors":"Mohammad Khodabakhshi Soureshjani, R. Zytner","doi":"10.3390/mca28030076","DOIUrl":"https://doi.org/10.3390/mca28030076","url":null,"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 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.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49338476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
María Concepción Salvador-González, Juana Canul-Reich, Rafael Rivera-López, E. Mezura-Montes, E. de la cruz-Hernandez
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.
{"title":"Evolutionary Selection of a Set of Association Rules Considering Biological Constraints Describing the Prevalent Elements in Bacterial Vaginosis","authors":"María Concepción Salvador-González, Juana Canul-Reich, Rafael Rivera-López, E. Mezura-Montes, E. de la cruz-Hernandez","doi":"10.3390/mca28030075","DOIUrl":"https://doi.org/10.3390/mca28030075","url":null,"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 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.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48463844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces","authors":"Vijay, A. Chand","doi":"10.3390/mca28030074","DOIUrl":"https://doi.org/10.3390/mca28030074","url":null,"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 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.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45272094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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