Nothing Special   »   [go: up one dir, main page]
Next Issue
Volume 11, December
Previous Issue
Volume 11, October
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
1.9
Journals
Computation
Volume 11
Issue 11
share announcement

Computation, Volume 11, Issue 11 (November 2023) – 26 articles

Cover Story (view full-size image): This study introduces a novel simulated-annealing-quasi-oppositional teaching–learning-based optimization algorithm for efficient distributed energy resource (DER) allocation method in distribution systems. Focused on wind turbines, photovoltaics, and fuel cells, the algorithm minimizes voltage losses, reduces costs, and mitigates greenhouse gas emissions. Implemented on the IEEE 70-bus test system, it outperforms conventional methods such as genetic algorithms, particle swarm optimization, honey-bee mating optimization, and teaching–learning-based optimization in accuracy and computational speed, as validated by statistical tests (probability < 0.1). View this paper
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
62 pages, 14899 KiB  
Article
Marburg Virus Outbreak and a New Conspiracy Theory: Findings from a Comprehensive Analysis and Forecasting of Web Behavior
by Nirmalya Thakur, Shuqi Cui, Kesha A. Patel, Nazif Azizi, Victoria Knieling, Changhee Han, Audrey Poon and Rishika Shah
Computation 2023, 11(11), 234; https://doi.org/10.3390/computation11110234 - 17 Nov 2023
Cited by 1 | Viewed by 3636
Abstract
During virus outbreaks in the recent past, web behavior mining, modeling, and analysis have served as means to examine, explore, interpret, assess, and forecast the worldwide perception, readiness, reactions, and response linked to these virus outbreaks. The recent outbreak of the Marburg Virus [...] Read more.
During virus outbreaks in the recent past, web behavior mining, modeling, and analysis have served as means to examine, explore, interpret, assess, and forecast the worldwide perception, readiness, reactions, and response linked to these virus outbreaks. The recent outbreak of the Marburg Virus disease (MVD), the high fatality rate of MVD, and the conspiracy theory linking the FEMA alert signal in the United States on 4 October 2023 with MVD and a zombie outbreak, resulted in a diverse range of reactions in the general public which has transpired in a surge in web behavior in this context. This resulted in “Marburg Virus” featuring in the list of the top trending topics on Twitter on 3 October 2023, and “Emergency Alert System” and “Zombie” featuring in the list of top trending topics on Twitter on 4 October 2023. No prior work in this field has mined and analyzed the emerging trends in web behavior in this context. The work presented in this paper aims to address this research gap and makes multiple scientific contributions to this field. First, it presents the results of performing time-series forecasting of the search interests related to MVD emerging from 216 different regions on a global scale using ARIMA, LSTM, and Autocorrelation. The results of this analysis present the optimal model for forecasting web behavior related to MVD in each of these regions. Second, the correlation between search interests related to MVD and search interests related to zombies was investigated. The findings show that there were several regions where there was a statistically significant correlation between MVD-related searches and zombie-related searches on Google on 4 October 2023. Finally, the correlation between zombie-related searches in the United States and other regions was investigated. This analysis helped to identify those regions where this correlation was statistically significant. Full article
(This article belongs to the Special Issue Artificial Intelligence Applications in Public Health)
►▼ Show Figures

Figure 1

Figure 1
<p>A workflow diagram to represent the data collection and the development of the master dataset using Google Trends.</p> Full article ">Figure 2
<p>A flowchart to represent the application of Algorithm 1 (Model 1), Algorithm 2 (Model 2), and Algorithm 3 (Model 3) to the master dataset.</p> Full article ">Figure 3
<p>A flowchart that represents different forms of correlation analysis that was performed on the dataset.</p> Full article ">Figure 4
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Australia using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 5
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Canada using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 6
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Morocco using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 7
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Ukraine using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 8
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in the USA using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 9
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Uruguay using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 10
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Ireland using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 11
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in France using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 12
<p>Representation of the results of Time-Series Forecasting of the Search Interests related to MVD in Denmark using Autocorrelation, ARIMA, and LSTM.</p> Full article ">Figure 13
<p>Trends in zombie-related web searches on 4 October 2023 in Argentina, Bhutan, Burundi, France, Ghana, Lebanon, and Madagascar.</p> Full article ">Figure 14
<p>Trends in zombie-related web searches on 4 October 2023 in Myanmar (Burma), Peru, Romania, South Africa, South Korea, the United States, and Uruguay.</p> Full article ">
12 pages, 4397 KiB  
Article
Correlations of the Electronic, Elastic and Thermo-Electric Properties of Alpha Copper Sulphide and Selenide
by Moshibudi Ramoshaba and Thuto Mosuang
Computation 2023, 11(11), 233; https://doi.org/10.3390/computation11110233 - 17 Nov 2023
Cited by 1 | Viewed by 1837
Abstract
A full potential all-electron density functional method within generalized gradient approximation is used herein to investigate correlations of the electronic, elastic and thermo-electric transport properties of cubic copper sulphide and copper selenide. The electronic band structure and density of states suggest a metallic [...] Read more.
A full potential all-electron density functional method within generalized gradient approximation is used herein to investigate correlations of the electronic, elastic and thermo-electric transport properties of cubic copper sulphide and copper selenide. The electronic band structure and density of states suggest a metallic behaviour with a zero-energy band gap for both materials. Elastic property calculations suggest stiff materials, with bulk to shear modulus ratios of 0.35 and 0.44 for Cu2S and Cu2Se, respectively. Thermo-electric transport properties were estimated using the Boltzmann transport approach. The Seebeck coefficient, electrical conductivity, thermal conductivity and power factor all suggest a potential p-type conductivity for α-Cu2S and n-type conductivity for α-Cu2Se. Full article
(This article belongs to the Topic Advances in Computational Materials Sciences)
►▼ Show Figures

Figure 1

Figure 1
<p>Change in total energy against volume. (<b>a</b>) Cubic copper sulphide (α-Cu<sub>2</sub>S). (<b>b</b>) Cubic copper selenide (α-Cu<sub>2</sub>Se). The red dots signify the actual minimum point values in both curves.</p> Full article ">Figure 2
<p>Calculated electronic band structures. (<b>a</b>) Cubic copper sulphide (α-Cu<sub>2</sub>S). (<b>b</b>) Cubic copper selenide (α-Cu<sub>2</sub>Se).</p> Full article ">Figure 3
<p>Calculated electronic density of states (DOS). (<b>a</b>) Cubic copper sulphide (α-Cu<sub>2</sub>S). (<b>b</b>) Cubic copper selenide (α-Cu<sub>2</sub>Se).</p> Full article ">Figure 4
<p>Thermo-electric transport properties of cubic α-Cu<sub>2</sub>S and α-Cu<sub>2</sub>Se, all at 300 K. (<b>a</b>) Variations in the Seebeck coefficient (<span class="html-italic">S</span>) against the chemical potential (μ). (<b>b</b>) Variations in electrical conductivity per relaxation time (σ/τ) against the chemical potential (μ). (<b>c</b>) Variations in thermal conductivity per relaxation time (κ/τ) against the chemical potential (μ). (<b>d</b>) Variations in the power factor per relaxation time (σS<sup>2</sup>/τ) against the chemical potential (μ).</p> Full article ">Figure 4 Cont.
<p>Thermo-electric transport properties of cubic α-Cu<sub>2</sub>S and α-Cu<sub>2</sub>Se, all at 300 K. (<b>a</b>) Variations in the Seebeck coefficient (<span class="html-italic">S</span>) against the chemical potential (μ). (<b>b</b>) Variations in electrical conductivity per relaxation time (σ/τ) against the chemical potential (μ). (<b>c</b>) Variations in thermal conductivity per relaxation time (κ/τ) against the chemical potential (μ). (<b>d</b>) Variations in the power factor per relaxation time (σS<sup>2</sup>/τ) against the chemical potential (μ).</p> Full article ">Figure 5
<p>Variations in the Seebeck coefficient (<span class="html-italic">S</span>) with respect to temperature (<span class="html-italic">T</span>). (<b>a</b>) Cubic α-Cu<sub>2</sub>S. (<b>b</b>) Cubic α-Cu<sub>2</sub>Se.</p> Full article ">Figure 6
<p>Variations in electrical conductivity per relaxation time (σ/τ) with temperature (<span class="html-italic">T</span>). (<b>a</b>) Cubic α-Cu<sub>2</sub>S. (<b>b</b>) Cubic α-Cu<sub>2</sub>Se.</p> Full article ">Figure 7
<p>Variations in the thermal conductivity per relaxation time (κ/τ) with temperature (<span class="html-italic">T</span>). (<b>a</b>) Cubic α-Cu<sub>2</sub>S. (<b>b</b>) Cubic α-Cu<sub>2</sub>Se.</p> Full article ">Figure 8
<p>Variations in the power factor per relaxation time (<span class="html-italic">σS</span><sup>2</sup>/τ) with respect to temperature (<span class="html-italic">T</span>). (<b>a</b>) Cubic α-Cu<sub>2</sub>S. (<b>b</b>) Cubic α-Cu<sub>2</sub>Se.</p> Full article ">
15 pages, 585 KiB  
Article
Development of AI-Based Tools for Power Generation Prediction
by Ana Paula Aravena-Cifuentes, Jose David Nuñez-Gonzalez, Andoni Elola and Malinka Ivanova
Computation 2023, 11(11), 232; https://doi.org/10.3390/computation11110232 - 16 Nov 2023
Cited by 1 | Viewed by 2158
Abstract
This study presents a model for predicting photovoltaic power generation based on meteorological, temporal and geographical variables, without using irradiance values, which have traditionally posed challenges and difficulties for accurate predictions. Validation methods and evaluation metrics are used to analyse four different approaches [...] Read more.
This study presents a model for predicting photovoltaic power generation based on meteorological, temporal and geographical variables, without using irradiance values, which have traditionally posed challenges and difficulties for accurate predictions. Validation methods and evaluation metrics are used to analyse four different approaches that vary in the distribution of the training and test database, and whether or not location-independent modelling is performed. The coefficient of determination, R2, is used to measure the proportion of variation in photovoltaic power generation that can be explained by the model’s variables, while gCO2eq represents the amount of CO2 emissions equivalent to each unit of power generation. Both are used to compare model performance and environmental impact. The results show significant differences between the locations, with substantial improvements in some cases, while in others improvements are limited. The importance of customising the predictive model for each specific location is emphasised. Furthermore, it is concluded that environmental impact studies in model production are an additional step towards the creation of more sustainable and efficient models. Likewise, this research considers both the accuracy of solar energy predictions and the environmental impact of the computational resources used in the process, thereby promoting the responsible and sustainable progress of data science. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Engineering)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Geographic locations of the studied sites (This map was generated using the Python package plotly.io).</p> Full article ">Figure 2
<p>Distribution of power generation.</p> Full article ">Figure 3
<p>Correlation matrix of all numerical variables within the database.</p> Full article ">Figure 4
<p>Correlation of all numerical variables in the database with the variable PolyPwr.</p> Full article ">Figure 5
<p>Comparative graph of the models proposed by Pasion et al.</p> Full article ">Figure 6
<p>Results obtained from location modelling using the parametrisation proposed by Pasion et al.</p> Full article ">Figure 7
<p>Comparison between results obtained from modelling using the parametrisation proposed by this study and by Pasion et al.</p> Full article ">Figure 8
<p>Results obtained from location modelling using the parametrisation proposed by this study.</p> Full article ">Figure 9
<p>Results from location modelling excluding a location using our proposed model.</p> Full article ">Figure 10
<p>Results from location modelling excluding a location and providing 1-week data context using our proposed model.</p> Full article ">
32 pages, 2003 KiB  
Article
Enhancing Algorithm Selection through Comprehensive Performance Evaluation: Statistical Analysis of Stochastic Algorithms
by Azad Arif Hama Amin, Aso M. Aladdin, Dler O. Hasan, Soran R. Mohammed-Taha and Tarik A. Rashid
Computation 2023, 11(11), 231; https://doi.org/10.3390/computation11110231 - 16 Nov 2023
Cited by 2 | Viewed by 2884
Abstract
Analyzing stochastic algorithms for comprehensive performance and comparison across diverse contexts is essential. By evaluating and adjusting algorithm effectiveness across a wide spectrum of test functions, including both classical benchmarks and CEC-C06 2019 conference functions, distinct patterns of performance emerge. In specific situations, [...] Read more.
Analyzing stochastic algorithms for comprehensive performance and comparison across diverse contexts is essential. By evaluating and adjusting algorithm effectiveness across a wide spectrum of test functions, including both classical benchmarks and CEC-C06 2019 conference functions, distinct patterns of performance emerge. In specific situations, underscoring the importance of choosing algorithms contextually. Additionally, researchers have encountered a critical issue by employing a statistical model randomly to determine significance values without conducting other studies to select a specific model for evaluating performance outcomes. To address this concern, this study employs rigorous statistical testing to underscore substantial performance variations between pairs of algorithms, thereby emphasizing the pivotal role of statistical significance in comparative analysis. It also yields valuable insights into the suitability of algorithms for various optimization challenges, providing professionals with information to make informed decisions. This is achieved by pinpointing algorithm pairs with favorable statistical distributions, facilitating practical algorithm selection. The study encompasses multiple nonparametric statistical hypothesis models, such as the Wilcoxon rank-sum test, single-factor analysis, and two-factor ANOVA tests. This thorough evaluation enhances our grasp of algorithm performance across various evaluation criteria. Notably, the research addresses discrepancies in previous statistical test findings in algorithm comparisons, enhancing result reliability in the later research. The results proved that there are differences in significance results, as seen in examples like Leo versus the FDO, the DA versus the WOA, and so on. It highlights the need to tailor test models to specific scenarios, as p-value outcomes differ among various tests within the same algorithm pair. Full article
(This article belongs to the Special Issue Applications of Evolutionary Computation: Past Success and Future Challenges)
►▼ Show Figures

Figure 1

Figure 1
<p>The proposed statistical methodology for delineating the data analysis process.</p> Full article ">Figure 2
<p>Demystifying the <span class="html-italic">p</span>-value in the analysis of variance (ANOVA).</p> Full article ">Figure 3
<p>Summation ranking of results for the null hypothesis (acceptance/rejection) in classical benchmarks.</p> Full article ">Figure 4
<p>Summation ranking of null hypothesis results for Leo compared to other algorithms in the CEC-C06 2019 benchmark.</p> Full article ">Figure 5
<p>Summation ranking of null hypothesis results for the FDO compared to other algorithms in the CEC-C06 2019 benchmark.</p> Full article ">Figure 6
<p>Summation ranking of null hypothesis results for the FOX compared to other algorithms in the CEC-C06 2019 benchmark.</p> Full article ">Figure 7
<p>Summation ranking of null hypothesis results for the DA, WOA, and SSA in comparison with the CEC-C06 2019 benchmark.</p> Full article ">
26 pages, 1867 KiB  
Article
Improvement in Sizing Constrained Analog IC via Ts-CPD Algorithm
by Pedro Lagos-Eulogio, Pedro Miranda-Romagnoli, Juan Carlos Seck-Tuoh-Mora and Norberto Hernández-Romero
Computation 2023, 11(11), 230; https://doi.org/10.3390/computation11110230 - 16 Nov 2023
Cited by 1 | Viewed by 1840
Abstract
In this work, we propose a variation of the cellular particle swarm optimization algorithm with differential evolution hybridization (CPSO-DE) to include constrained optimization, named Ts-CPD. It is implemented as a kernel of electronic design automation (EDA) tool capable of sizing circuit components considering [...] Read more.
In this work, we propose a variation of the cellular particle swarm optimization algorithm with differential evolution hybridization (CPSO-DE) to include constrained optimization, named Ts-CPD. It is implemented as a kernel of electronic design automation (EDA) tool capable of sizing circuit components considering a single-objective design with restrictions and constraints. The aim is to improve the optimization solutions in the sizing of analog circuits. To evaluate our proposal’s performance, we present the design of three analog circuits: a differential amplifier, a two-stage operational amplifier (op-amp), and a folded cascode operational transconductance amplifier. Numerical simulation results indicate that Ts-CPD can find better solutions, in terms of the design objective and the accomplishment of constraints, than those reported in previous works. The Ts-CPD implementation was performed in Matlab using Ngspice and can be found on GitHub (see Data Availability Statement). Full article
(This article belongs to the Special Issue Applications of Evolutionary Computation: Past Success and Future Challenges)
►▼ Show Figures

Figure 1

Figure 1
<p>Different ECA evolution rules and the dynamic behavior observed in each of them.</p> Full article ">Figure 2
<p>Neighborhood for CPSO-outer and CPSO-DE.</p> Full article ">Figure 3
<p>Convergence curves of the different algorithms for CEC05 functions in 30 dimensions.</p> Full article ">Figure 3 Cont.
<p>Convergence curves of the different algorithms for CEC05 functions in 30 dimensions.</p> Full article ">Figure 4
<p>Flow chart of Ts-CPD as part of an EDA Tool.</p> Full article ">Figure 5
<p>CMOS differential amplifier.</p> Full article ">Figure 6
<p>CMOS two-stage operational amplifier.</p> Full article ">Figure 7
<p>CMOS folded cascode operational transconductance amplifier.</p> Full article ">Figure 8
<p>Performance of CMOS differential amplifier.</p> Full article ">Figure 9
<p>Ts-CPDtest for CMOS differential amplifier.</p> Full article ">Figure 10
<p>Performance of CMOS two-stage operational amplifier.</p> Full article ">Figure 10 Cont.
<p>Performance of CMOS two-stage operational amplifier.</p> Full article ">Figure 11
<p>Ts-CPD test for CMOS two-stage operational amplifier.</p> Full article ">Figure 12
<p>Performance of CMOS folded cascode operational transconductance amplifier.</p> Full article ">Figure 12 Cont.
<p>Performance of CMOS folded cascode operational transconductance amplifier.</p> Full article ">Figure 13
<p>Ts-CPD test for CMOS folded cascode operational transconductance amplifier.</p> Full article ">
15 pages, 7423 KiB  
Article
Anomalous Solute Transport Using Adsorption Effects and the Degradation of Solute
by B. Kh. Khuzhayorov, K. K. Viswanathan, F. B. Kholliev and A. I. Usmonov
Computation 2023, 11(11), 229; https://doi.org/10.3390/computation11110229 - 16 Nov 2023
Cited by 3 | Viewed by 1560
Abstract
In this work, anomalous solute transport using adsorption effects and the decomposition of solute was studied. During the filtration of inhomogeneous liquids, a number of new phenomena arise, and this is very important for understanding the mechanisms of the filtration process. Recently, issues [...] Read more.
In this work, anomalous solute transport using adsorption effects and the decomposition of solute was studied. During the filtration of inhomogeneous liquids, a number of new phenomena arise, and this is very important for understanding the mechanisms of the filtration process. Recently, issues of mathematical modeling of substance transfer processes have been intensively discussed. Modeling approaches are based on the law of matter balance in a certain control volume using additional phenomenological relationships. The process of anomalous solute transport in a porous medium was modeled by differential equations with a fractional derivative. A new mobile—immobile model is proposed to describe anomalous solute transport with a scale-dependent dispersion in inhomogeneous porous media. The profiles of changes in the concentrations of suspended particles in the macropore and micropore were determined. The influence of the order of the derivative with respect to the coordinate and time, i.e., the fractal dimension of the medium, was estimated based on the characteristics of the solute transport in both zones. The hydrodynamic dispersion was set through various relations: constant, linear, and exponential. Based on the numerical results, the concentration fields were determined for different values of the initial data and different relations of hydrodynamic dispersion. Full article
(This article belongs to the Special Issue Computational Techniques for Fluid Dynamics Problems)
►▼ Show Figures

Figure 1

Figure 1
<p>Scheme of the solute transport in two-zone medium.</p> Full article ">Figure 2
<p>Concentration profile for solute transport at time <span class="html-italic">T</span> = 3600.</p> Full article ">Figure 3
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. Constant: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, Linear: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, Exponential: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 4
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 5
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 6
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 7
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 8
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 9
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 10
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 11
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 12
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 13
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 14
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 15
<p>Concentration profiles (<b>a</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 16
<p>Concentration profiles <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> (<b>a</b>–<b>c</b>), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> (<b>d</b>–<b>f</b>) at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>a</b>,<b>d</b>): Constant, (<b>b</b>,<b>e</b>): Linear, (<b>c</b>,<b>f</b>): Exponential, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 17
<p>Concentration profiles <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> (<b>a</b>–<b>c</b>), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> (<b>d</b>–<b>f</b>) at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>a</b>,<b>d</b>): Constant, (<b>b</b>,<b>e</b>): Linear, (<b>c</b>,<b>f</b>): Exponential, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 17 Cont.
<p>Concentration profiles <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> (<b>a</b>–<b>c</b>), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> (<b>d</b>–<b>f</b>) at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> <mo> </mo> <mi mathvariant="normal">s</mi> </mrow> </semantics></math>. (<b>a</b>,<b>d</b>): Constant, (<b>b</b>,<b>e</b>): Linear, (<b>c</b>,<b>f</b>): Exponential, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 18
<p>Concentration profiles <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> (<b>a</b>–<b>c</b>), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>(<b>d</b>–<b>f</b>) at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. (<b>a</b>,<b>d</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>,<b>e</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>,<b>f</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, Constant: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, Linear: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, Exponential: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">Figure 18 Cont.
<p>Concentration profiles <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>m</mi> </msub> </mrow> </semantics></math> (<b>a</b>–<b>c</b>), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>(<b>d</b>–<b>f</b>) at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>3600</mn> </mrow> </semantics></math>. (<b>a</b>,<b>d</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>,<b>e</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>,<b>f</b>): <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>d</mi> </msub> <mo>=</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, Constant: <span class="html-fig-inline" id="computation-11-00229-i001"><img alt="Computation 11 00229 i001" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i001.png"/></span>, Linear: <span class="html-fig-inline" id="computation-11-00229-i002"><img alt="Computation 11 00229 i002" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i002.png"/></span>, Exponential: <span class="html-fig-inline" id="computation-11-00229-i003"><img alt="Computation 11 00229 i003" src="/computation/computation-11-00229/article_deploy/html/images/computation-11-00229-i003.png"/></span>.</p> Full article ">
16 pages, 668 KiB  
Article
Superconvergence Analysis of Discontinuous Galerkin Methods for Systems of Second-Order Boundary Value Problems
by Helmi Temimi
Computation 2023, 11(11), 228; https://doi.org/10.3390/computation11110228 - 15 Nov 2023
Cited by 1 | Viewed by 1513
Abstract
In this paper, we present an innovative approach to solve a system of boundary value problems (BVPs), using the newly developed discontinuous Galerkin (DG) method, which eliminates the need for auxiliary variables. This work is the first in a series of papers on [...] Read more.
In this paper, we present an innovative approach to solve a system of boundary value problems (BVPs), using the newly developed discontinuous Galerkin (DG) method, which eliminates the need for auxiliary variables. This work is the first in a series of papers on DG methods applied to partial differential equations (PDEs). By consecutively applying the DG method to each space variable of the PDE using the method of lines, we transform the problem into a system of ordinary differential equations (ODEs). We investigate the convergence criteria of the DG method on systems of ODEs and generalize the error analysis to PDEs. Our analysis demonstrates that the DG error’s leading term is determined by a combination of specific Jacobi polynomials in each element. Thus, we prove that DG solutions are superconvergent at the roots of these polynomials, with an order of convergence of O(hp+2). Full article
(This article belongs to the Section Computational Engineering)
►▼ Show Figures

Figure 1

Figure 1
<p>The error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>U</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> </semantics></math> for problem (37) with <span class="html-italic">p</span> = 2, 3, 4 and <span class="html-italic">N</span> = 20 and + denotes the roots of <math display="inline"><semantics> <msub> <mi>Q</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> mapped to each element.</p> Full article ">Figure 2
<p>The error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>U</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> </semantics></math> for problem (37) with <span class="html-italic">p</span> = 2, 3, 4 and <span class="html-italic">N</span> = 20 and + denotes the roots of <math display="inline"><semantics> <msub> <mi>Q</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> mapped to each element.</p> Full article ">Figure 3
<p>The error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>3</mn> </msub> <mo>−</mo> <msub> <mi>U</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> </semantics></math> for problem (37) with <span class="html-italic">p</span> = 2, 3, 4 and <span class="html-italic">N</span> = 20 and + denotes the roots of <math display="inline"><semantics> <msub> <mi>Q</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> mapped to each element.</p> Full article ">Figure 4
<p>The error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>5</mn> </msub> <mo>−</mo> <msub> <mi>U</mi> <mrow> <mn>5</mn> <mo>,</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> </semantics></math> for problem (39) with <span class="html-italic">p</span> = 2, 3, 4 and <span class="html-italic">N</span> = 20 and + denotes the roots of <math display="inline"><semantics> <msub> <mi>Q</mi> <mrow> <mn>5</mn> <mo>,</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> mapped to each element.</p> Full article ">Figure 5
<p>The error <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>−</mo> <msub> <mi>U</mi> <mrow> <mn>10</mn> <mo>,</mo> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> </semantics></math> for problem (39) with <span class="html-italic">p</span> = 2,3,4 and <span class="html-italic">N</span> = 20 and + denotes the roots of <math display="inline"><semantics> <msub> <mi>Q</mi> <mrow> <mn>10</mn> <mo>,</mo> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </semantics></math> mapped to each element.</p> Full article ">
12 pages, 777 KiB  
Article
Buckling Assessment in the Dynamics Mechanisms, Stewart Platform Case Study: In the Context of Loads and Joints, Deflection Positions Gradient
by Reza Hassanian and Morris Riedel
Computation 2023, 11(11), 227; https://doi.org/10.3390/computation11110227 - 15 Nov 2023
Viewed by 2002
Abstract
This study introduces an approach for modeling an arm of a Stewart platform to analyze the location of sections with a high deflection among the arms. Given the dynamic nature of the Stewart platform, its arms experience static and dynamic loads. The static [...] Read more.
This study introduces an approach for modeling an arm of a Stewart platform to analyze the location of sections with a high deflection among the arms. Given the dynamic nature of the Stewart platform, its arms experience static and dynamic loads. The static loads originate from the platform’s own weight components, while the dynamic loads arise from the movement or holding of equipment in a specific position using the end-effector. These loads are distributed among the platform arms. The arm encompasses various design categories, including spring-mass, spring-mass-damper, mass-actuator, and spring-mass-actuator. In accordance with these designs, joint points should be strategically placed away from critical sections where maximum buckling or deformation is prominent. The current study presents a novel model employing Euler’s formula, a fundamental concept in buckling analysis, to propose this approach. The results align with experimental and numerical reports in the literature that prove the internal force of the platform arm is affecting the arm stiffness. The equal stiffness of an arm is related to its internal force and its deflection. The study demonstrates how higher levels of dynamic loading influence the dynamic platform, causing variations in the maximum arm’s buckling deflection, its precise location, and the associated deflection slope. Notably, in platform arms capable of adjusting their tilt angles relative to the vertical axis, the angle of inclination directly correlates with deflection and its gradient. The assumption of linearity in Euler’s formula seems to reveal distinctive behavior in deflection gradients concerning dynamic mechanisms. Full article
(This article belongs to the Special Issue Application of Finite Element Methods)
►▼ Show Figures

Figure 1

Figure 1
<p>Illustrative depiction showcasing the schematic view of a 6-6 type Stewart platform.</p> Full article ">Figure 2
<p>Visualization of Complete Deflection in a Platform Arm: On the left, a load of 2 kPa is applied, while on the right, the load is increased to 4 kPa. The uniform loading is directed onto the top plate, within the computational environment of Ansys Inc. [<a href="#B25-computation-11-00227" class="html-bibr">25</a>].</p> Full article ">Figure 3
<p>The visualization showcases overall deformation patterns within a true scale of the platform arm subjected to three distinct load configurations. Notably, based on Euler’s formula for buckling deflection, it is expected to have the maximum deflection location in the middle of the arm, and it is not a function of the load. However, the result displays that when increasing the load over time, the maximum deflection location tends to be the upper half of the arm, and it is not a fixed location. Moreover, a discernible distinction is observed in the slope of the deflection function on both sides of the maximum displacement point.</p> Full article ">Figure 4
<p>Presented here is an exhibition of the equivalent stress distribution across the true scale of the platform arm. On the left, a load of 2 kPa is applied, while on the right, the load is elevated to 4 kPa. The uniform load is uniformly distributed onto the end-effector within the computational framework of Ansys Inc. [<a href="#B25-computation-11-00227" class="html-bibr">25</a>].</p> Full article ">Figure 5
<p>Illustrating the variation in equivalent stress along the length of a platform arm, this presentation encompasses three different loading scenarios. Notably, with similar behavior to the maximum deflection, the axial load of the arm depends on the tilt angle, and the dynamics load could be changed. It can be seen the critical stress location does not have a fixed location and, with extensive load, tends to the upper half of the arm, and it is not always in the middle of the arm as a buckling column with pinned-pinned boundary condition.</p> Full article ">
17 pages, 1501 KiB  
Article
Global Dynamics of a Within-Host Model for Usutu Virus
by Ibrahim Nali and Attila Dénes
Computation 2023, 11(11), 226; https://doi.org/10.3390/computation11110226 - 14 Nov 2023
Cited by 2 | Viewed by 1646
Abstract
We propose a within-host mathematical model for the dynamics of Usutu virus infection, incorporating Crowley–Martin functional response. The basic reproduction number R0 is found by applying the next-generation matrix approach. Depending on this threshold, parameter, global asymptotic stability of one of the [...] Read more.
We propose a within-host mathematical model for the dynamics of Usutu virus infection, incorporating Crowley–Martin functional response. The basic reproduction number R0 is found by applying the next-generation matrix approach. Depending on this threshold, parameter, global asymptotic stability of one of the two possible equilibria is also established via constructing appropriate Lyapunov functions and using LaSalle’s invariance principle. We present numerical simulations to illustrate the results and a sensitivity analysis of R0 was also completed. Finally, we fit the model to actual data on Usutu virus titers. Our study provides new insights into the dynamics of Usutu virus infection. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Biology)
►▼ Show Figures

Figure 1

Figure 1
<p>Virus transmission cycle: from reservoir host to vector, onward to avian hosts. ’Dead end’ hosts like horses or humans, where the virus transmission is limited are also highlighted.</p> Full article ">Figure 2
<p>Flow chart of the infection dynamics of Usutu virus. <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> (shown in blue) stands for healthy target cells, <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> (shown in orange) denotes exposed cells, <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> (shown in green) stands for infected cells. Virus particles (<math display="inline"><semantics> <mrow> <mi>V</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) are shown in red. The meaning of the parameters is given in <a href="#computation-11-00226-t001" class="html-table">Table 1</a>.</p> Full article ">Figure 3
<p>Solution curves of system (1) illustrating the dynamics for different values of <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.970</mn> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics></math> depicting disease extinction, and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.481</mn> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math> showing disease persistence.</p> Full article ">Figure 4
<p>Partial rank correlation coefficients of parameters of model (1).</p> Full article ">Figure 5
<p>Contour plots of the basic reproduction number <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math> for various parameter values. (<b>a</b>) Contour plot of <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <span class="html-italic">p</span>. (<b>b</b>) Contour plot of <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <span class="html-italic">c</span>. (<b>c</b>) Contour plot of <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math> as a function of <span class="html-italic">c</span> and <span class="html-italic">p</span>. (<b>d</b>) Contour plot of <math display="inline"><semantics> <msub> <mi mathvariant="fraktur">R</mi> <mn>0</mn> </msub> </semantics></math> as a function of <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <span class="html-italic">d</span>.</p> Full article ">Figure 6
<p>Virus curve <math display="inline"><semantics> <mrow> <mi>V</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> (blue line) represents the model (1) prediction, while the red dots indicate the experimental data points, with a <math display="inline"><semantics> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math> confidence interval, which was obtained by letting for all parameters a 5% relative error with respect to the best fitting values. Parameter values are given in <a href="#computation-11-00226-t003" class="html-table">Table 3</a>. For details of the experiments, see [<a href="#B15-computation-11-00226" class="html-bibr">15</a>,<a href="#B41-computation-11-00226" class="html-bibr">41</a>]. Subfigures correspond to the following experiments in [<a href="#B15-computation-11-00226" class="html-bibr">15</a>]: (<b>a</b>) B7 (<b>b</b>) B16 (<b>c</b>) B25 (<b>d</b>) B31.</p> Full article ">
20 pages, 1008 KiB  
Article
EEG-Based Classification of Spoken Words Using Machine Learning Approaches
by Denise Alonso-Vázquez, Omar Mendoza-Montoya, Ricardo Caraza, Hector R. Martinez and Javier M. Antelis
Computation 2023, 11(11), 225; https://doi.org/10.3390/computation11110225 - 10 Nov 2023
Cited by 1 | Viewed by 2384
Abstract
Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease that affects the nerve cells in the brain and spinal cord. This condition leads to the loss of motor skills and, in many cases, the inability to speak. Decoding spoken words from electroencephalography (EEG) signals [...] Read more.
Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease that affects the nerve cells in the brain and spinal cord. This condition leads to the loss of motor skills and, in many cases, the inability to speak. Decoding spoken words from electroencephalography (EEG) signals emerges as an essential tool to enhance the quality of life for these patients. This study compares two classification techniques: (1) the extraction of spectral power features across various frequency bands combined with support vector machines (PSD + SVM) and (2) EEGNet, a convolutional neural network specifically designed for EEG-based brain–computer interfaces. An EEG dataset was acquired from 32 electrodes in 28 healthy participants pronouncing five words in Spanish. Average accuracy rates of 91.04 ± 5.82% for Attention vs. Pronunciation, 73.91 ± 10.04% for Short words vs. Long words, 81.23 ± 10.47% for Word vs. Word, and 54.87 ± 14.51% in the multiclass scenario (All words) were achieved. EEGNet outperformed the PSD + SVM method in three of the four classification scenarios. These findings demonstrate the potential of EEGNet for decoding words from EEG signals, laying the groundwork for future research in ALS patients using non-invasive methods. Full article
(This article belongs to the Special Issue Bioinspiration: The Path from Engineering to Nature II)
►▼ Show Figures

Figure 1

Figure 1
<p>Photograph of the experimental setup. The participant is seated in front of the monitor with the EEG cap. The monitor shows the word <span class="html-italic">comida</span>, corresponding to the pronunciation stage.</p> Full article ">Figure 2
<p>Graphical illustration of the temporal sequence of a trial. The trial starts with 3 s of attention (fixation cross), then for 3 s, the participant is shown one of the five words that will have to be pronounced only once, and finally 3 s of rest (palm). In addition, the lower part of the image shows the data segment from −1.5 s to 1.5 s, corresponding to the time window of interest.</p> Full article ">Figure 3
<p>Architecture of the convolutional neural network EEGNet.</p> Full article ">Figure 4
<p>Distribution of classification accuracy, recall per class, and precision per class obtained with the PSD + SVM and EEGNet methods in the classification scenario <span class="html-italic">Attention</span> vs. <span class="html-italic">Pronunciation</span>. The diamonds represent outliers. In all performance metrics, no significant differences were found between the two classification methods (Wilcoxon signed-rank test, <span class="html-italic">p</span> &gt; 0.01).</p> Full article ">Figure 5
<p>Distribution of classification accuracy, recall per class, and precision per class obtained with the PSD + SVM and EEGNet methods in the classification scenario <span class="html-italic">Short words</span> vs. <span class="html-italic">Long words</span>. In all performance metrics, significant differences were found between the two classification methods (Wilcoxon signed-rank test, <span class="html-italic">p</span> &lt; 0.01).</p> Full article ">Figure 6
<p>Distribution of classification accuracy for each word pair obtained with the PSD + SVM and EEGNet methods in the classification scenario <span class="html-italic">Word</span> vs. <span class="html-italic">Word</span>. The diamonds represent outliers. In eight out of the ten word pair classifications, significant differences were found between the two classification methods (Wilcoxon signed-rank test, <span class="html-italic">p</span> &lt; 0.01).</p> Full article ">Figure 7
<p>Distribution of classification accuracy, recall per class, and precision per class obtained with the PSD + SVM and EEGNet methods in the classification scenario <span class="html-italic">multiclass</span>. The diamonds represent outliers. In nine of the eleven computed performance metrics, significant differences were found between the two classification methods (Wilcoxon signed-rank test, <span class="html-italic">p</span> &lt; 0.01): <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>l</mi> <mi>a</mi> <mi>s</mi> <msub> <mi>s</mi> <mn>1</mn> </msub> </mrow> </semantics></math> = <span class="html-italic">si</span>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>l</mi> <mi>a</mi> <mi>s</mi> <msub> <mi>s</mi> <mn>2</mn> </msub> </mrow> </semantics></math> = <span class="html-italic">no</span>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>l</mi> <mi>a</mi> <mi>s</mi> <msub> <mi>s</mi> <mn>3</mn> </msub> </mrow> </semantics></math> = <span class="html-italic">agua</span>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>l</mi> <mi>a</mi> <mi>s</mi> <msub> <mi>s</mi> <mn>4</mn> </msub> </mrow> </semantics></math> = <span class="html-italic">comida</span>, and <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>l</mi> <mi>a</mi> <mi>s</mi> <msub> <mi>s</mi> <mn>5</mn> </msub> </mrow> </semantics></math> = <span class="html-italic">dormir</span>.</p> Full article ">Figure A1
<p>Accuracy results per participant by each method in classifying the attention vs. speech segment. The dotted black line corresponds to the level of chance (50%).</p> Full article ">Figure A2
<p>Accuracy results per participant by each method in classifying short words vs. long words. The dotted black line corresponds to the level of chance (50%).</p> Full article ">Figure A3
<p>Accuracy results per participant by each method in multiclass classification. The dotted black line corresponds to the level of chance (20%).</p> Full article ">
18 pages, 5308 KiB  
Article
A Novel Methodology Analyzing the Influence of Micro-Stresses on Human-Centric Environments
by Nataliya Shakhovska, Roman Kaminskyy, Bohdan Khudoba, Vladyslav Mykhailyshyn and Ihor Helzhynskyi
Computation 2023, 11(11), 224; https://doi.org/10.3390/computation11110224 - 6 Nov 2023
Viewed by 1798
Abstract
This article offers experimental studies and a new methodology for analyzing the influence of micro-stresses on human operator activity in man–machine information and search interfaces. Human-centered design is a problem-solving technique that puts real people at the center of the design process. Therefore, [...] Read more.
This article offers experimental studies and a new methodology for analyzing the influence of micro-stresses on human operator activity in man–machine information and search interfaces. Human-centered design is a problem-solving technique that puts real people at the center of the design process. Therefore, mindfulness is one of the most important aspects in various fields such as medicine, industry, and decision-making. The human-operator activity model can be used to create a database of specialized test images and a computer for its implementation. The peculiarity of the tests is that they represent images of real work situations obtained as a result of texture stylization and allow the use of an appropriate search difficulty scale. A mathematical model of a person who makes a decision is built. The requirements for creating a switch to solve the given problem are discussed. This work summarizes the accumulated experience of such studies. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
►▼ Show Figures

Figure 1

Figure 1
<p>Sequential merging of pixels using the method of the average (ascending).</p> Full article ">Figure 2
<p>Sequential merging of pixels using the method of median smoothing.</p> Full article ">Figure 3
<p>View of search objects on test images. Objects are rectangular. In the upper circle, there is one object; in the middle, there are two objects, and in the lower circle, there is one large object.</p> Full article ">Figure 4
<p>The appearance of the simulator interface.</p> Full article ">Figure 5
<p>A regular stream of test images. Where <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> </mrow> </semantics></math> is the starting point and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> </mrow> </semantics></math> are the moments of exposure termination; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>τ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>τ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> </mrow> </semantics></math> are moments of decision-making by the operator.</p> Full article ">Figure 6
<p>Irregular flow of test images.</p> Full article ">Figure 7
<p>Irregular flow of decision-driven test images.</p> Full article ">
16 pages, 938 KiB  
Article
The Accuracy of Computational Results from Wolfram Mathematica in the Context of Summation in Trigonometry
by David Nocar, George Grossman, Jiří Vaško and Tomáš Zdráhal
Computation 2023, 11(11), 222; https://doi.org/10.3390/computation11110222 - 6 Nov 2023
Viewed by 1709
Abstract
This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation [...] Read more.
This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation in trigonometry. In particular, the key issue addressed here is the calculated sum ∑n=044tan⁡1+4n°. This paper utilizes Wolfram Mathematica to handle the irrational numbers in the sum more accurately, which it achieves by representing them symbolically rather than using numerical approximations. Can we rely on the calculated result from Wolfram, especially if almost all the addends are irrational, or must the students eventually prove it mathematically? It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics. Full article
(This article belongs to the Special Issue Computations in Mathematics, Mathematical Education, and Science)
►▼ Show Figures

Figure 1

Figure 1
<p>Individual addends.</p> Full article ">Figure 2
<p>Partial sums.</p> Full article ">
13 pages, 1916 KiB  
Article
Grey Systems Model to Assess Water Quality in Mantaro River in Peru
by Alexi Delgado, Joshis Culqui, Marisabel Lazo, Valeria Guerrero and Isabel Delgado
Computation 2023, 11(11), 223; https://doi.org/10.3390/computation11110223 - 4 Nov 2023
Viewed by 1743
Abstract
The section of the Mantaro River that flows through the department of Huancavelica, Peru, has been affected by toxic wastes and mineral residues from industrial and mining activities, which have directly impacted the water quality. In this work, a grey system model, based [...] Read more.
The section of the Mantaro River that flows through the department of Huancavelica, Peru, has been affected by toxic wastes and mineral residues from industrial and mining activities, which have directly impacted the water quality. In this work, a grey system model, based on the grey clustering method, was used to assess water quality. The grey clustering method was applied using the central point of triangular whitening weight functions (CTWF). In addition, the Prati index and the Environmental Quality Standards for water from the Peru government were revised and used for this study. In the case study, six physicochemical parameters, pH, DO, BOD, Cd, As, and Pb, at nine monitoring points were assessed along the Mantaro River. The results showed that the sixth monitoring point (P6), which is influenced by mining activity, was highly contaminated, while the other points were classified as noncontaminated. Finally, the results obtained by applying the grey clustering method can be useful to competent authorities, for decision making on water management in this watershed. Full article
(This article belongs to the Section Computational Engineering)
►▼ Show Figures

Figure 1

Figure 1
<p>CTWF method flow chart.</p> Full article ">Figure 2
<p>Triangular functions (a color for each function).</p> Full article ">Figure 3
<p>Location map of the monitoring points (1, 2, 3, …, 9).</p> Full article ">
26 pages, 3568 KiB  
Article
Epidemiological Implications of War: Machine Learning Estimations of the Russian Invasion’s Effect on Italy’s COVID-19 Dynamics
by Dmytro Chumachenko, Tetiana Dudkina, Tetyana Chumachenko and Plinio Pelegrini Morita
Computation 2023, 11(11), 221; https://doi.org/10.3390/computation11110221 - 4 Nov 2023
Viewed by 2084
Abstract
Background: The COVID-19 pandemic has profoundly transformed the global scenario, marked by overwhelming infections, fatalities, overburdened healthcare infrastructures, economic upheavals, and significant lifestyle modifications. Concurrently, the Russian full-scale invasion of Ukraine on 24 February 2022, triggered a severe humanitarian and public health crisis, [...] Read more.
Background: The COVID-19 pandemic has profoundly transformed the global scenario, marked by overwhelming infections, fatalities, overburdened healthcare infrastructures, economic upheavals, and significant lifestyle modifications. Concurrently, the Russian full-scale invasion of Ukraine on 24 February 2022, triggered a severe humanitarian and public health crisis, leading to healthcare disruptions, medical resource shortages, and heightened emergency care needs. Italy emerged as a significant refuge for displaced Ukrainians during this period. Aim: This research aims to discern the impact of the Russian full-scale invasion of Ukraine on the COVID-19 transmission dynamics in Italy. Materials and Methods: The study employed advanced simulation methodologies, particularly those integrating machine learning, to model the pandemic’s trajectory. The XGBoost algorithm was adopted to construct a predictive model for the COVID-19 epidemic trajectory in Italy. Results: The model demonstrated a commendable accuracy of 86.03% in forecasting new COVID-19 cases in Italy over 30 days and an impressive 96.29% accuracy in estimating fatalities. When applied to the initial 30 days following the escalation of the conflict (24 February 2022, to 25 March 2022), the model’s projections suggested that the influx of Ukrainian refugees into Italy did not significantly alter the country’s COVID-19 epidemic course. Discussion: While simulation methodologies have been pivotal in the pandemic response, their accuracy is intrinsically linked to data quality, assumptions, and modeling techniques. Enhancing these methodologies can further their applicability in future public health emergencies. The findings from the model underscore that external geopolitical events, such as the mass migration from Ukraine, did not play a determinative role in Italy’s COVID-19 epidemic dynamics during the study period. Conclusion: The research provides empirical evidence negating a substantial influence of the Ukrainian refugee influx due to the Russian full-scale invasion on the COVID-19 epidemic trajectory in Italy. The robust performance of the developed model affirms its potential value in public health analyses. Full article
(This article belongs to the Special Issue Artificial Intelligence Applications in Public Health)
►▼ Show Figures

Figure 1

Figure 1
<p>The framework for assessing the impact of the Russian war in Ukraine on the dynamics of the epidemic process of infectious diseases.</p> Full article ">Figure 2
<p>Retrospective forecast of confirmed COVID-19 cases in Italy (25 January 2022–23 February 2022).</p> Full article ">Figure 3
<p>Retrospective forecast of fatal COVID-19 cases in Italy (25 January 2022–23 February 2022).</p> Full article ">Figure 4
<p>Retrospective forecast of daily COVID-19 cases in Italy (24 February 2022–25 March 2022).</p> Full article ">Figure 5
<p>Retrospective forecast of fatal COVID-19 cases in Italy (24 February 2022–25 March 2022).</p> Full article ">Figure 6
<p>Deviation of COVID-19 daily new cases from forecasted values in Italy (24 February 2022–25 March 2022).</p> Full article ">Figure 7
<p>Deviation of COVID-19 fatal new cases from forecasted values in Italy (24 February 2022–25 March 2022).</p> Full article ">
12 pages, 1364 KiB  
Article
How Sn(IV) Influences on the Reaction Mechanism of 11, tri-Butyl p-Coumarate and Its tri-Butyl-tin p-Coumarate Considering the Solvent Effect: A DFT Level Study
by Rogelio A. Delgado-Alfaro and Zeferino Gómez-Sandoval
Computation 2023, 11(11), 220; https://doi.org/10.3390/computation11110220 - 3 Nov 2023
Viewed by 1440
Abstract
Antioxidants are molecules that neutralize free radicals. In general, the reaction mechanisms of antioxidants are well known. The main reaction mechanisms of antioxidants are electron transfer (ET), hydrogen transfer (HT), and radical adduction formation (RAF). The study of these mechanisms is helpful in [...] Read more.
Antioxidants are molecules that neutralize free radicals. In general, the reaction mechanisms of antioxidants are well known. The main reaction mechanisms of antioxidants are electron transfer (ET), hydrogen transfer (HT), and radical adduction formation (RAF). The study of these mechanisms is helpful in understanding how antioxidants control high free radical levels in the cell. There are many studies focused on determining the main mechanism of an antioxidant to neutralize a wide spectrum of radicals, mainly reactive oxygen species (ROS)-type radicals. Most of these antioxidants are polyphenol-type compounds. Some esters, amides, and metal antioxidants have shown antioxidant activity, but there are few experimental and theoretical studies about the antioxidant reaction mechanism of these compounds. In this work, we show the reaction mechanism proposed for two esters, 11, tri-butyl p-coumarate and its tri-butyl-tin p-coumarate counterpart, using Sn(IV). We show how Sn(IV) increases the electron transfer in polar media and the H transfer in non-polar media. Even though the nature of esters could be polar or non-polar compounds, the antioxidant activity is good for the Sn(IV)-p-coumarate complex in non-polar media. Full article
(This article belongs to the Special Issue Calculations in Solution)
►▼ Show Figures

Figure 1

Figure 1
<p>The 11, <span class="html-italic">tri</span>-butyl <span class="html-italic">p</span>-coumarate (<b>A1</b>) and <span class="html-italic">tri</span>-butyl-tin <span class="html-italic">p</span>-coumarate (<b>A2</b>) structures (Rn = n-butyl, n= 1, 2, 3), where reaction channel <b>4a</b> is shown on the left for both molecules.</p> Full article ">Figure 2
<p>(<b>a</b>) SET-1 and SET-2 mechanism illustration for <b>A1</b>, (<b>b</b>) SET-1 and SET-2 mechanism illustration for <b>A2</b>.</p> Full article ">Figure 3
<p>(<b>a</b>) HT mechanism illustration for <b>A1</b>, (<b>b</b>) HT mechanism illustration for <b>A2</b>.</p> Full article ">Figure 4
<p>Optimized transition state geometry of <b>A1</b> and <b>A2</b> with radical ˙OOH in water (I) and pentylethanoate (II) and their imaginary frequencies (I.F.).</p> Full article ">
18 pages, 2931 KiB  
Article
Determination of the Characteristics of Non-Stationary Random Processes by Non-Parametric Methods of Decision Theory
by Bulat-Batyr Yesmagambetov
Computation 2023, 11(11), 219; https://doi.org/10.3390/computation11110219 - 3 Nov 2023
Viewed by 1358
Abstract
This article is devoted to methods of processing random processes. This task becomes particularly relevant in cases where the random process is broadband and non-stationary; then, the measurement of a random process can be associated with an assessment of its probabilistic characteristics. Very [...] Read more.
This article is devoted to methods of processing random processes. This task becomes particularly relevant in cases where the random process is broadband and non-stationary; then, the measurement of a random process can be associated with an assessment of its probabilistic characteristics. Very often, a non-stationary broadband random process is represented by a single implementation with a priori uncertainty about the type of distribution function. Such random processes occur in information and measuring communication systems in which information is transmitted at a real-time pace (for example, radio telemetry systems in spacecraft). The use of methods of traditional mathematical statistics, for example, maximum likelihood methods, to determine probability characteristics in this case is not possible. In addition, the on-board computing systems of spacecraft operate under conditions of restrictions on mass-dimensional characteristics and energy consumption. Therefore, there is a need to apply accelerated methods of processing measured random processes. This article discusses a method of processing non-stationary broadband random processes based on the use of non-parametric methods of decision theory. An algorithm for dividing the observation interval into stationary intervals using non-parametric Kendall’s statistics is considered, as are methods for estimating probabilistic characteristics on the stationary interval using ordinal statistics. This article presents the results of statistical modeling using the Mathcad program. Full article
(This article belongs to the Section Computational Engineering)
►▼ Show Figures

Figure 1

Figure 1
<p>Non-stationary random process model.</p> Full article ">Figure 2
<p>Testing the distribution symmetry hypothesis.</p> Full article ">Figure 3
<p>Division of observation interval into stationarity intervals.</p> Full article ">Figure 4
<p>Comparative analysis of computing costs of an estimation. <math display="inline"><semantics> <mrow> <mi>S</mi> </mrow> </semantics></math>—memory size; <math display="inline"><semantics> <mrow> <mi>T</mi> </mrow> </semantics></math>—average calculation time; <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <msub> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>(</mo> <msub> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo stretchy="false">~</mo> </mover> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math>—the memory size and the average calculation time when using the maximum likelihood estimate.</p> Full article ">Figure 5
<p>Modeling a random process with a Gaussian distribution.</p> Full article ">Figure 6
<p>Estimation of distribution function.</p> Full article ">Figure 7
<p>Estimation of correlation function.</p> Full article ">
22 pages, 6759 KiB  
Article
Deep Learning Enriched Automation in Damage Detection for Sustainable Operation in Pipelines with Welding Defects under Varying Embedment Conditions
by Li Shang, Zi Zhang, Fujian Tang, Qi Cao, Nita Yodo, Hong Pan and Zhibin Lin
Computation 2023, 11(11), 218; https://doi.org/10.3390/computation11110218 - 2 Nov 2023
Cited by 6 | Viewed by 2049
Abstract
Welded joints in metallic pipelines and other structures are used to connect metallic structures. Welding defects, such as cracks and lack of fusion, are vulnerable to initiating early-age cracking and corrosion. The present damage identification techniques use ultrasonic-guided wave procedures, which depend on [...] Read more.
Welded joints in metallic pipelines and other structures are used to connect metallic structures. Welding defects, such as cracks and lack of fusion, are vulnerable to initiating early-age cracking and corrosion. The present damage identification techniques use ultrasonic-guided wave procedures, which depend on the change in the physical characteristics of waveforms as they propagate to determine damage states. However, the complexity of geometry and material discontinuity (e.g., the roughness of a weldment with or without defects) could lead to complicated wave reflection and scatters, thus increasing the difficulty in the signal processing. Artificial intelligence and machine learning exhibit their capability for data fusion, including processing signals originally from ultrasonic-guided waves. This study aims to utilize deep learning approaches, including a convolutional neural network (CNN), Long-short term memory network (LSTM), or hybrid CNN-LSTM model, to demonstrate the capability in automation for damage detection for pipes with welded joints embedded in soil. The damage features in terms of welding defect types and severity as well as multiple defects are used to understand the effectiveness of the hybrid CNN-LSTM model, which is further compared to the two commonly used deep learning approaches, CNN and LSTM. The results showed the hybrid CNN-LSTM model has much higher classification accuracy for damage states under all scenarios in comparison with the CNN and LSTM models. Furthermore, the impacts of the pipelines embedded in different types of materials, ranging from loose sand to stiff soil, on signal processing and data classification were further calibrated. The results demonstrated these deep learning approaches can still perform well to detect various pipeline damage under varying embedment conditions. However, the results demonstrate when concrete is used as an embedding material, high attention to absorbing the signal energy of concrete could pose a challenge for the signal processing, particularly under high noise levels. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Engineering)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the research methodology.</p> Full article ">Figure 2
<p>The structure of the CNN-LSTM hybrid model.</p> Full article ">Figure 3
<p>COMSOL model of pipeline under soil embedment.</p> Full article ">Figure 4
<p>Four kinds of welding defects.</p> Full article ">Figure 5
<p>Excited guided wave.</p> Full article ">Figure 6
<p>Pipeline waveforms under soil embedment.</p> Full article ">Figure 7
<p>The signals with varying degrees of noise disturbance.</p> Full article ">Figure 7 Cont.
<p>The signals with varying degrees of noise disturbance.</p> Full article ">Figure 8
<p>Accuracy of three deep learning models with different features.</p> Full article ">Figure 9
<p>The confusion matrix of the CNN-LSTM model with time- and frequency-domain features on different noise levels.</p> Full article ">Figure 10
<p>The confusion matrix showing the CNN-LSTM model with different noise levels.</p> Full article ">Figure 10 Cont.
<p>The confusion matrix showing the CNN-LSTM model with different noise levels.</p> Full article ">Figure 11
<p>ROC curve for three models on different noise levels.</p> Full article ">Figure 12
<p>Pipeline waveforms of four kind of defects with 10% severity under different kinds of embedment (Case 1).</p> Full article ">Figure 12 Cont.
<p>Pipeline waveforms of four kind of defects with 10% severity under different kinds of embedment (Case 1).</p> Full article ">Figure 13
<p>Accuracy of three deep learning models with different pipeline embedment.</p> Full article ">Figure 13 Cont.
<p>Accuracy of three deep learning models with different pipeline embedment.</p> Full article ">
36 pages, 970 KiB  
Article
Global Properties of Cytokine-Enhanced HIV-1 Dynamics Model with Adaptive Immunity and Distributed Delays
by Elsayed Dahy, Ahmed M. Elaiw, Aeshah A. Raezah, Hamdy Z. Zidan and Abd Elsattar A. Abdellatif
Computation 2023, 11(11), 217; https://doi.org/10.3390/computation11110217 - 2 Nov 2023
Cited by 3 | Viewed by 1676
Abstract
In this paper, we study a model that enhances our understanding of cytokine-influenced HIV-1 infection. The impact of adaptive immune response (cytotoxic T lymphocytes (CTLs) and antibodies) and time delay on HIV-1 infection is included. The model takes into account two types of [...] Read more.
In this paper, we study a model that enhances our understanding of cytokine-influenced HIV-1 infection. The impact of adaptive immune response (cytotoxic T lymphocytes (CTLs) and antibodies) and time delay on HIV-1 infection is included. The model takes into account two types of distributional delays, (i) the delay in the HIV-1 infection of CD4+T cells and (ii) the maturation delay of new virions. We first investigated the fundamental characteristics of the system, then found the system’s equilibria. We derived five threshold parameters, ℜi, i = 0, 1,…, 4, which completely determine the existence and stability of the equilibria. The Lyapunov method was used to prove the global asymptotic stability for all equilibria. We illustrate the theoretical results by performing numerical simulations. We also performed a sensitivity analysis on the basic reproduction number ℜ0 and identified the most-sensitive parameters. We found that pyroptosis contributes to the number ℜ0, and then, neglecting it will make ℜ0 underevaluated. Necrosulfonamide and highly active antiretroviral drug therapy (HAART) can be effective in preventing pyroptosis and at reducing viral replication. Further, it was also found that increasing time delays can effectively decrease ℜ0 and, then, inhibit HIV-1 replication. Furthermore, it is shown that both CTLs and antibody immune responses have no effect on ℜ0, while this can result in less HIV-1 infection. Full article
(This article belongs to the Special Issue Mathematical Modeling and Study of Nonlinear Dynamic Processes)
►▼ Show Figures

Figure 1

Figure 1
<p>Forward sensitivity analysis to assess the influence of the system’s (<a href="#FD62-computation-11-00217" class="html-disp-formula">62</a>)–(67) parameters on <math display="inline"><semantics> <msub> <mo>ℜ</mo> <mn>0</mn> </msub> </semantics></math>.</p> Full article ">Figure 2
<p>The equilibrium point <math display="inline"><semantics> <mrow> <mi>E</mi> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>1000</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> </mfenced> </mrow> </semantics></math> is G.A.S. whenever <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>0</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 3
<p>The equilibrium point <math display="inline"><semantics> <mrow> <mi>E</mi> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>112.64</mn> <mo>,</mo> <mn>7.73</mn> <mo>,</mo> <mn>7.73</mn> <mo>,</mo> <mn>274.39</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> </mfenced> </mrow> </semantics></math> is G.A.S. whenever <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>1</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>2</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 4
<p>The equilibrium point <math display="inline"><semantics> <mrow> <mi>E</mi> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>165.78</mn> <mo>,</mo> <mn>6.66</mn> <mo>,</mo> <mn>6.66</mn> <mo>,</mo> <mn>236.51</mn> <mo>,</mo> <mn>77.003</mn> <mo>,</mo> <mn>0</mn> </mfenced> </mrow> </semantics></math> is G.A.S. whenever <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>2</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>3</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 5
<p>The equilibrium point <math display="inline"><semantics> <mrow> <mi>E</mi> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>277.65</mn> <mo>,</mo> <mn>6.29</mn> <mo>,</mo> <mn>6.29</mn> <mo>,</mo> <mn>8.34</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>9.67</mn> </mfenced> </mrow> </semantics></math> is G.A.S. whenever <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>3</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>4</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 6
<p>The equilibrium point <math display="inline"><semantics> <mrow> <mi>E</mi> <msub> <mi>P</mi> <mn>4</mn> </msub> <mo>=</mo> </mrow> </semantics></math><math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>124.35</mn> <mo>,</mo> <mn>6.66</mn> <mo>,</mo> <mn>6.66</mn> <mo>,</mo> <mn>62.5</mn> <mo>,</mo> <mn>123.04</mn> <mo>,</mo> <mn>1.0441</mn> </mfenced> </semantics></math> is G.A.S. whenever <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>3</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>ℜ</mo> <mn>4</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 7
<p>Influence of the delay parameter <math display="inline"><semantics> <mi>ν</mi> </semantics></math> on the solutions of System (<a href="#FD62-computation-11-00217" class="html-disp-formula">62</a>)–(67). (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">Figure 8
<p>Influence of the immune response parameters <math display="inline"><semantics> <mi>σ</mi> </semantics></math> and <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> on the solutions of System (<a href="#FD62-computation-11-00217" class="html-disp-formula">62</a>)–(67). (<b>a</b>) Uninfected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>b</b>) infected CD4<math display="inline"><semantics> <msup> <mrow/> <mo>+</mo> </msup> </semantics></math>T cells; (<b>c</b>) inflammatory cytokines; (<b>d</b>) free HIV-1; (<b>e</b>) CTLs; (<b>f</b>) antibodies.</p> Full article ">
22 pages, 6601 KiB  
Article
Learning Trajectory Tracking for an Autonomous Surface Vehicle in Urban Waterways
by Toma Sikora, Jonathan Klein Schiphorst and Riccardo Scattolini
Computation 2023, 11(11), 216; https://doi.org/10.3390/computation11110216 - 2 Nov 2023
Viewed by 1628
Abstract
Roboat is an autonomous surface vessel (ASV) for urban waterways, developed as a research project by the AMS Institute and MIT. The platform can provide numerous functions to a city, such as transport, dynamic infrastructure, and an autonomous waste management system. This paper [...] Read more.
Roboat is an autonomous surface vessel (ASV) for urban waterways, developed as a research project by the AMS Institute and MIT. The platform can provide numerous functions to a city, such as transport, dynamic infrastructure, and an autonomous waste management system. This paper presents the development of a learning-based controller for the Roboat platform with the goal of achieving robustness and generalization properties. Specifically, when subject to uncertainty in the model or external disturbances, the proposed controller should be able to track set trajectories with less tracking error than the current nonlinear model predictive controller (NMPC) used on the ASV. To achieve this, a simulation of the system dynamics was developed as part of this work, based on the research presented in the literature and on the previous research performed on the Roboat platform. The simulation process also included the modeling of the necessary uncertainties and disturbances. In this simulation, a trajectory tracking agent was trained using the proximal policy optimization (PPO) algorithm. The trajectory tracking of the trained agent was then validated and compared to the current control strategy both in simulations and in the real world. Full article
(This article belongs to the Special Issue Applications of Statistics and Machine Learning in Electronics)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Roboat platform “+” thruster configuration.</p> Full article ">Figure 2
<p>Structure of the Roboat platform architecture.</p> Full article ">Figure 3
<p>Visualization of Gaussian terms in the reward function in a 3D plot.</p> Full article ">Figure 4
<p>A contour plot of Gaussian terms in the reward function.</p> Full article ">Figure 5
<p>Plot of the episodic reward throughout one million steps of training. Orange line presents the moving average with a window size 50; light orange presents the standard deviation of the value.</p> Full article ">Figure 6
<p>Visualization of intermediate trajectory tracking training results for the RL controller upon initialization: 100,000, 200,000, 500,000, and 1,000,000 training steps.</p> Full article ">Figure 7
<p>Scenario 1—baseline. Comparison between the NMPC and RL algorithm trajectory tracking performance. Trajectories of NMPC, RL, and reference sine wave on the top graph. Tracking errors of NMPC and RL on the bottom graph.</p> Full article ">Figure 8
<p>Scenario 1—baseline. Comparison between the NMPC and RL algorithm trajectory tracking performance. Force allocation of NMPC (<b>top graph</b>) and RL (<b>bottom graph</b>) for tracking the sine wave trajectory.</p> Full article ">Figure 9
<p>Scenario 2—payload. Comparison between the NMPC and RL algorithm trajectory tracking performance with payload equal to 50% of vessel’s mass. Trajectories of NMPC, RL, and reference sine wave on the top graph. Tracking errors of NMPC and RL on the bottom graph.</p> Full article ">Figure 10
<p>Scenario 2—payload. Comparison between the NMPC and RL algorithm trajectory tracking performance with payload equal to 50% of vessel’s mass. Force allocation of NMPC (<b>top graph</b>) and RL (<b>bottom graph</b>) for tracking the sine wave trajectory.</p> Full article ">Figure 11
<p>Scenario 3—current. Comparison between the NMPC and RL algorithm trajectory tracking performance with a current of 0.5 m/s acting on the system. Trajectories of NMPC, RL, and reference sine wave on the top graph. Tracking errors of NMPC and RL on the bottom graph.</p> Full article ">Figure 12
<p>Scenario 3—current.Comparison between the NMPC and RL algorithm trajectory tracking performance with a current of 0.5 m/s acting on the system. Force allocation of NMPC (<b>top graph</b>) and RL (<b>bottom graph</b>) for tracking the sine wave trajectory.</p> Full article ">Figure 13
<p>Scenario 4—wind. Comparison between the NMPC and RL algorithm trajectory tracking performance with a wind of speed 9 m/s acting on the system. Trajectories of NMPC, RL, and reference sine wave on the top graph. Tracking errors of NMPC and RL on the bottom graph.</p> Full article ">Figure 14
<p>Scenario 4—wind. Comparison between the NMPC and RL algorithm trajectory tracking performance with a wind of speed 9 m/s acting on the system. Force allocation of NMPC (<b>top graph</b>) and RL (<b>bottom graph</b>) for tracking the sine wave trajectory.</p> Full article ">Figure 15
<p>Scenario 5—real world. Comparison between the NMPC and RL algorithm trajectory tracking performance on the real Roboat vessel. Trajectories of NMPC, RL, and reference sine wave on the top; tracking errors of NMPC and RL on the bottom.</p> Full article ">Figure 16
<p>Scenario 5—real world. Comparison between the NMPC and RL algorithm trajectory tracking performance on the real Roboat vessel. Force allocation of NMPC (<b>top graph</b>) and RL (<b>bottom graph</b>).</p> Full article ">
14 pages, 3531 KiB  
Article
Numerical Approximations of Diblock Copolymer Model Using a Modified Leapfrog Time-Marching Scheme
by Lizhen Chen, Ying Ma, Bo Ren and Guohui Zhang
Computation 2023, 11(11), 215; https://doi.org/10.3390/computation11110215 - 2 Nov 2023
Viewed by 1847
Abstract
An efficient modified leapfrog time-marching scheme for the diblock copolymer model is investigated in this paper. The proposed scheme offers three main advantages. Firstly, it is linear in time, requiring only a linear algebra system to be solved at each time-marching step. This [...] Read more.
An efficient modified leapfrog time-marching scheme for the diblock copolymer model is investigated in this paper. The proposed scheme offers three main advantages. Firstly, it is linear in time, requiring only a linear algebra system to be solved at each time-marching step. This leads to a significant reduction in computational cost compared to other methods. Secondly, the scheme ensures unconditional energy stability, allowing for a large time step to be used without compromising solution stability. Thirdly, the existence and uniqueness of the numerical solution at each time step is rigorously proven, ensuring the reliability and accuracy of the method. A numerical example is also included to demonstrate and validate the proposed algorithm, showing its accuracy and efficiency in practical applications. Full article
►▼ Show Figures

Figure 1

Figure 1
<p>Time accuracy convergence test. The figures show the error versus time step <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> </mrow> </semantics></math> for the diblock copolymer model using second-order Scheme 3. Two different initial parameters, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>5.0</mn> </mrow> </semantics></math> (<b>right</b>), are used.</p> Full article ">Figure 2
<p>Time accuracy convergence test. The figures show the error versus time step <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> </mrow> </semantics></math> for the diblock copolymer model using second-order Scheme 3. (<b>Left</b>): <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math>; (<b>Right</b>): <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>Time evolution of the energy decay for the diblock copolymer model. The time step is set at <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> with different physical parameters <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> (left of the first row), <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> (right of the first row), and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> (second row).</p> Full article ">Figure 4
<p>Time snapshots of coarsening dynamics driven by the phase field diblock copolymer model with random initial conditions. The parameters are set as <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.02</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>. The profiles of <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> at different time slots <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>40</mn> <mo>,</mo> <mn>150</mn> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, are presented.</p> Full article ">Figure 5
<p>Time snapshots of coarsening dynamics driven by the phase field diblock copolymer model with random initial conditions. The parameters are set as <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.02</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>. The profiles of <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> at different time slots <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>40</mn> <mo>,</mo> <mn>150</mn> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, are presented.</p> Full article ">Figure 6
<p>Time snapshots of coarsening dynamics driven by the phase field diblock copolymer model with random initial conditions. The parameters are set as <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>0.02</mn> <mo>,</mo> <mi>ε</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>. The profiles of <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> at different time slots <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>40</mn> <mo>,</mo> <mn>150</mn> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>, are presented.</p> Full article ">Figure 7
<p>Time evolution of the energy decay for the diblock copolymer model. The time step is set at <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> with different parameters <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.0</mn> <mo>,</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.2</mn> <mo>,</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.4</mn> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Time evolution of the energy decay for the diblock copolymer model. The time step is set at <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> with different <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> </mrow> </semantics></math>.</p> Full article ">
28 pages, 9378 KiB  
Article
A Simulated-Annealing-Quasi-Oppositional-Teaching-Learning-Based Optimization Algorithm for Distributed Generation Allocation
by Seyed Iman Taheri, Mohammadreza Davoodi and Mohd. Hasan Ali
Computation 2023, 11(11), 214; https://doi.org/10.3390/computation11110214 - 2 Nov 2023
Cited by 2 | Viewed by 2451
Abstract
Conventional evolutionary optimization techniques often struggle with finding global optima, getting stuck in local optima instead, and can be sensitive to initial conditions and parameter settings. Efficient Distributed Generation (DG) allocation in distribution systems hinges on streamlined optimization algorithms that handle complex energy [...] Read more.
Conventional evolutionary optimization techniques often struggle with finding global optima, getting stuck in local optima instead, and can be sensitive to initial conditions and parameter settings. Efficient Distributed Generation (DG) allocation in distribution systems hinges on streamlined optimization algorithms that handle complex energy operations, support real-time decisions, adapt to dynamics, and improve system performance, considering cost and power quality. This paper proposes the Simulated-Annealing-Quasi-Oppositional-Teaching-Learning-Based Optimization Algorithm to efficiently allocate DGs within a distribution test system. The study focuses on wind turbines, photovoltaic units, and fuel cells as prominent DG due to their growing usage trends. The optimization goals include minimizing voltage losses, reducing costs, and mitigating greenhouse gas emissions in the distribution system. The proposed algorithm is implemented and evaluated on the IEEE 70-bus test system, with a comparative analysis conducted against other evolutionary methods such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Honey Bee Mating Optimization (HBMO), and Teaching-Learning-Based Optimization (TLBO) algorithms. Results indicate that the proposed algorithm is effective in allocating the DGs. Statistical testing confirms significant results (probability < 0.1), indicating superior optimization capabilities for this specific problem. Crucially, the proposed algorithm excels in both accuracy and computational speed compared to other methods studied. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Engineering)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Flowchart of the proposed optimization algorithm.</p> Full article ">Figure 2
<p>Location of 12 Fuel cell units with different objective functions by the single-objective MQOTLBO algorithm in the 70-bus distribution system.</p> Full article ">Figure 3
<p>MQOTLBO convergence curves for (<b>A</b>) the cost, (<b>B</b>) emission, (<b>C</b>) losses, and (<b>D</b>) voltage deviation.</p> Full article ">Figure 4
<p>Pareto front obtained using the MQTLBO algorithm.</p> Full article ">Figure 5
<p>Comparison of various methods by their obtained Pareto fronts.</p> Full article ">Figure 6
<p>Pareto front of three objective functions.</p> Full article ">Figure A1
<p>The illustration of membership functions for the objective function.</p> Full article ">Figure A2
<p>Learners score distribution (<b>a</b>) for classes 1 and 2 (<b>b</b>) for classes A and B.</p> Full article ">Figure A3
<p>Test system.</p> Full article ">
17 pages, 4411 KiB  
Article
Modeling of Wind Turbine Interactions and Wind Farm Losses Using the Velocity-Dependent Actuator Disc Model
by Ziemowit Malecha and Gideon Dsouza
Computation 2023, 11(11), 213; https://doi.org/10.3390/computation11110213 - 1 Nov 2023
Cited by 3 | Viewed by 2077
Abstract
This paper analyzes the interaction of wind turbines and losses in wind farms using computational fluid dynamics (CFD). The mathematical model used consisted of three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations, while the presence of wind turbines in the flow was simulated as additional source [...] Read more.
This paper analyzes the interaction of wind turbines and losses in wind farms using computational fluid dynamics (CFD). The mathematical model used consisted of three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations, while the presence of wind turbines in the flow was simulated as additional source terms. The novelty of the research is the definition of the source term as a velocity-dependent actuator disc model (ADM). This allowed for modeling the operation of a wind farm consisting of real wind turbines, characterized by power coefficients Cp and thrust force coefficients CT, which are a function of atmospheric wind speed. The calculations presented used a real 5 MW Gamesa turbine. Two different turbine spacings, 5D and 10D, where D is the diameter of the turbine, and two different locations corresponding to the offshore and onshore conditions were examined. The proposed model can be used to analyze wind farm losses not only in terms of the geometric distribution of individual turbines but also in terms of a specific type of wind turbine and in the entire wind speed spectrum. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Engineering)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Sketch of the actuator disc model concept. Numbers 1, 2, 3, and 4 show the locations of the characteristic cross-sections used in linear momentum theory.</p> Full article ">Figure 2
<p>Actuator discs simulating two wind turbines placed one behind the other over rugged terrain. The characteristics of the turbines are described by the Equations (<a href="#FD5-computation-11-00213" class="html-disp-formula">5</a>) and (<a href="#FD6-computation-11-00213" class="html-disp-formula">6</a>). Calculation example taken from [<a href="#B42-computation-11-00213" class="html-bibr">42</a>,<a href="#B43-computation-11-00213" class="html-bibr">43</a>].</p> Full article ">Figure 3
<p>Power curve <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>W</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>U</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>U</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>U</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the <span class="html-italic">Gamesa G132-5.0MW</span> turbine considered in the current study [<a href="#B47-computation-11-00213" class="html-bibr">47</a>].</p> Full article ">Figure 4
<p>Front view (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> </semantics></math> plane) of the placement of the actuator disc, dimensions, and boundaries.</p> Full article ">Figure 5
<p>Side view (<math display="inline"><semantics> <mrow> <mi>x</mi> <mo>,</mo> <mi>z</mi> </mrow> </semantics></math> plane) of the placement of the actuator discs, dimensions, and boundaries.</p> Full article ">Figure 6
<p>Numerical mesh detail with visibility of three levels of refinement. The actuator discs are located in the center of the region with the finest mesh.</p> Full article ">Figure 7
<p>Kinematic pressure distribution in the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> plane at <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mi>W</mi> <mo>+</mo> <mn>0.5</mn> <mi>D</mi> </mrow> </semantics></math> for WF number 1.</p> Full article ">Figure 8
<p>Velocity magnitude distribution in the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> plane at <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mi>W</mi> <mo>+</mo> <mn>0.5</mn> <mi>D</mi> </mrow> </semantics></math> for WF number 1.</p> Full article ">Figure 9
<p>Kinematic pressure and <span class="html-italic">x</span> component of velocity distribution along a line parallel to the <span class="html-italic">x</span> axis and passing through the center of the discs for WF number 1.</p> Full article ">Figure 10
<p>Comparison of the velocity profiles in the wake between the single-column wind farm WF1 and multi-column wind farm WF2. The plots are taken in the direction of the width direction <span class="html-italic">y</span> just behind the actuator discs and at the height <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>120</mn> </mrow> </semantics></math> m (the hub height).</p> Full article ">Figure 11
<p>Comparison of <math display="inline"><semantics> <msub> <mi>U</mi> <mi>x</mi> </msub> </semantics></math> velocity between the corresponding onshore and offshore wind farms (see <a href="#computation-11-00213-t002" class="html-table">Table 2</a>). Plots are taken along the line that goes through the centers of the actuator discs.</p> Full article ">Figure 12
<p>Weibull wind velocity probability distribution for the onshore location and modified wind velocity distributions reaching the turbines in subsequent rows. Data for WF1.</p> Full article ">
20 pages, 390 KiB  
Article
Evaluating the Performance of Multiple Sequence Alignment Programs with Application to Genotyping SARS-CoV-2 in the Saudi Population
by Aminah Alqahtani and Meznah Almutairy
Computation 2023, 11(11), 212; https://doi.org/10.3390/computation11110212 - 1 Nov 2023
Cited by 2 | Viewed by 3182
Abstract
This study explores the accuracy and efficiency of multiple sequence alignment (MSA) programs, focusing on ClustalΩ, MAFFT, and MUSCLE in the context of genotyping SARS-CoV-2 for the Saudi population. Our results indicate that MAFFT outperforms the others, making it an ideal [...] Read more.
This study explores the accuracy and efficiency of multiple sequence alignment (MSA) programs, focusing on ClustalΩ, MAFFT, and MUSCLE in the context of genotyping SARS-CoV-2 for the Saudi population. Our results indicate that MAFFT outperforms the others, making it an ideal choice for large-scale genomic analyses. The comparative performance of MSAs assembled using MergeAlign demonstrates that MAFFT and MUSCLE consistently exhibit higher accuracy than ClustalΩ in both reference-based and consensus-based approaches. The evaluation of genotyping effectiveness reveals that the addition of a reference sequence, such as the SARS-CoV-2 Wuhan-Hu-1 isolate, does not significantly affect the alignment process, suggesting that using consensus sequences derived from individual MSA alignments may yield comparable genotyping outcomes. Investigating single-nucleotide polymorphisms (SNPs) and mutations highlights distinctive features of MSA programs. ClustalΩ and MAFFT show similar counts, while MUSCLE displays the highest SNP count. High-frequency SNP analysis identifies MAFFT as the most accurate MSA program, emphasizing its reliability. Comparisons between Saudi and global SARS-CoV-2 populations underscore regional genetic variations. Saudis exhibit consistently higher frequencies of high-frequency SNPs, attributed to genetic similarity within the population. Transmission dynamics analysis reveals a higher frequency of co-mutations in the Saudi dataset, suggesting shared evolutionary patterns. These findings emphasize the importance of considering regional diversity in genetic analyses. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Biology)
►▼ Show Figures

Figure 1

Figure 1
<p>The pipeline for aligning, genotyping, and analyzing transmission of SARS-CoV-2. In the reference-based approach, the added reference sequence is the Wuhan-Hu-1 reference genome. In the consensus-based approach, the added reference sequence is the consensus sequence from the individual MSA alignment with the best consensus score.</p> Full article ">
13 pages, 433 KiB  
Article
Modeling the Dynamic Effects of Human Mobility and Airborne Particulate Matter on the Spread of COVID-19
by Klot Patanarapeelert, Rossanan Chandumrong and Nichaphat Patanarapeelert
Computation 2023, 11(11), 211; https://doi.org/10.3390/computation11110211 - 30 Oct 2023
Viewed by 1642
Abstract
Identifying the relationship between human mobility, air pollution, and communicable disease poses a challenge for impact evaluation and public health planning. Specifically, Coronavirus disease 2019 (COVID-19) and air pollution from fine particulates (PM2.5), by which human mobility is mediated in a public health [...] Read more.
Identifying the relationship between human mobility, air pollution, and communicable disease poses a challenge for impact evaluation and public health planning. Specifically, Coronavirus disease 2019 (COVID-19) and air pollution from fine particulates (PM2.5), by which human mobility is mediated in a public health emergency. To describe the interplay between human mobility and PM2.5 during the spread of COVID-19, we proposed a nonlinear model of the time-dependent transmission rate as a function of these factors. A compartmental epidemic model, together with daily confirmed case data in Bangkok, Thailand during 2020–2021, was used to estimate the intrinsic parameters that can determine the impact on the transmission dynamic of the two earlier outbreaks. The results suggested a positive association between mobility and transmission, but this was strongly dependent on the context and the temporal characteristics of the data. For the ascending phase of an epidemic, the estimated coefficient of mobility variable in the second wave was greater than in the first wave, but the value of the mobility component in the transmission rate was smaller. Due to the influence of the baseline value and PM2.5, the estimated basic reproduction number of the second wave was higher than that of the first wave, even though mobility had a greater influence. For the descending phase, the value of the mobility component in the second wave was greater, due to the negative value of the estimated mobility coefficient. Despite this scaling effect, the results suggest a negative association between PM2.5 and the transmission rates. Although this conclusion agrees with some previous studies, the true effect of PM2.5 remains inconclusive and requires further investigation. Full article
(This article belongs to the Special Issue Eco-Evolutionary and Computational Epidemiology Modeling of Complex Dynamical Systems)
►▼ Show Figures

Figure 1

Figure 1
<p>Data presentations in Bangkok for (<b>a</b>) the number of daily reported cases, (<b>b</b>) the percentage of mobility changes, and (<b>c</b>) the daily average PM2.5 density.</p> Full article ">Figure 2
<p>Modeling the incidence of COVID-19 driven by mobility and PM2.5.</p> Full article ">Figure 3
<p>Model fitting of the first and second waves of the COVID-19 pandemic in Bangkok.</p> Full article ">Figure 4
<p>Estimated transmission rate for (<b>a</b>) the first wave, and (<b>b</b>) the second wave. Green line shows the estimated transmission rate without the effect of mobility. Vertical line separates the ascending and descending phases.</p> Full article ">Figure A1
<p>Flowchart of parameter estimation process.</p> Full article ">
12 pages, 5127 KiB  
Article
Transformer-Based Model for Predicting Customers’ Next Purchase Day in e-Commerce
by Alexandru Grigoraș and Florin Leon
Computation 2023, 11(11), 210; https://doi.org/10.3390/computation11110210 - 29 Oct 2023
Cited by 2 | Viewed by 4533
Abstract
The paper focuses on predicting the next purchase day (NPD) for customers in e-commerce, a task with applications in marketing, inventory management, and customer retention. A novel transformer-based model for NPD prediction is introduced and compared to traditional methods such as ARIMA, XGBoost, [...] Read more.
The paper focuses on predicting the next purchase day (NPD) for customers in e-commerce, a task with applications in marketing, inventory management, and customer retention. A novel transformer-based model for NPD prediction is introduced and compared to traditional methods such as ARIMA, XGBoost, and LSTM. Transformers offer advantages in capturing long-term dependencies within time series data through self-attention mechanisms. This adaptability to various time series patterns, including trends, seasonality, and irregularities, makes them a promising choice for NPD prediction. The transformer model demonstrates improvements in prediction accuracy compared to the baselines. Additionally, a clustered transformer model is proposed, which further enhances accuracy, emphasizing the potential of this architecture for NPD prediction. Full article
(This article belongs to the Special Issue 10th Anniversary of Computation—Computational Engineering)
►▼ Show Figures

Figure 1

Figure 1
<p>Days between orders feature generation (adapted after [<a href="#B5-computation-11-00210" class="html-bibr">5</a>]).</p> Full article ">Figure 2
<p>Converting the time series data into a supervised learning problem (adapted after [<a href="#B18-computation-11-00210" class="html-bibr">18</a>]).</p> Full article ">Figure 3
<p>The proposed transformer architecture (adapted from [<a href="#B14-computation-11-00210" class="html-bibr">14</a>]).</p> Full article ">Figure 4
<p>Customers’ recency distribution.</p> Full article ">Figure 5
<p>The frequency distribution of customers’ orders.</p> Full article ">Figure 6
<p>The within clusters sum of squared errors (SSE) employed to select the most appropriate number of clusters using the elbow method.</p> Full article ">Figure 7
<p>Time series data with the NPDs for customer 14395.</p> Full article ">Figure 8
<p>Time series data with next purchase days for customer 14911.</p> Full article ">Figure 9
<p>Time series using selected models for customer 14395.</p> Full article ">Figure 10
<p>Time series using selected models for customer 14911.</p> Full article ">Figure 11
<p>The errors obtained by the selected models.</p> Full article ">
21 pages, 4272 KiB  
Article
Exploring the Quotation Inertia in International Currency Markets
by Alexander Musaev, Andrey Makshanov and Dmitry Grigoriev
Computation 2023, 11(11), 209; https://doi.org/10.3390/computation11110209 - 24 Oct 2023
Viewed by 1548
Abstract
The authors suggest a methodology that involves conducting a preliminary analysis of inertia in financial time series. Inertia here means the manifestation of some kind of long-term memory. Such effects may take place in complex processes of a stochastic kind. If the decision [...] Read more.
The authors suggest a methodology that involves conducting a preliminary analysis of inertia in financial time series. Inertia here means the manifestation of some kind of long-term memory. Such effects may take place in complex processes of a stochastic kind. If the decision is negative, they do not recommend using predictive management strategies based on trend analysis. The study uses computational schemes to detect and confirm trends in financial market data. The effectiveness of these schemes is evaluated by analyzing the frequency of trend confirmation over different time intervals and with different levels of trend confirmation. Furthermore, the study highlights the limitations of using smoothed curves for trend analysis due to the lag in the dynamics of the curve, emphasizing the importance of considering real-time data in trend analysis for more accurate predictions. Full article
(This article belongs to the Special Issue Quantitative Finance and Risk Management Research)
►▼ Show Figures

Figure 1

Figure 1
<p>The structure of the basic algorithm for identifying inertia of a stochastic process.</p> Full article ">Figure 2
<p>An example of the dynamics of the EURUSD quotation over a 10-day observation period.</p> Full article ">Figure 3
<p>Positive outcome examples.</p> Full article ">Figure 4
<p>Negative outcome examples.</p> Full article ">Figure 5
<p>An example of an analysis of a simple strategy based on the dynamics of linear trends over an interval of 10 days.</p> Full article ">Figure 6
<p>Examples of incorrect trend detection due to a delay in decision making.</p> Full article ">Figure 7
<p>Example of a decision-making scheme with two trends.</p> Full article ">Figure 8
<p>Detection of an uptrend with first- and second-order approximations.</p> Full article ">Figure 9
<p>Detection of a downtrend with first- and second-order approximations.</p> Full article ">Figure 10
<p>Process, speed, and acceleration estimates.</p> Full article ">Figure 11
<p>Inertia analysis results on a 5-day observation interval.</p> Full article ">
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-26
Previous Issue
Next Issue
Back to TopTop