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Modelling and Simulation of Natural Phenomena of Current Interest

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 26458

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Prof. Dr. Yongwimon Lenbury

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Guest Editor

Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Interests: nonlinear systems; differential equations; modelling of natural phenomena
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Prof. Dr. Ravi P. Agarwal

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Emeritus Research Professor of Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Interests: boundary value problems; nonlinear analysis; differential and difference equations; fixed point theory; general inequalities
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Dr. Elvin Moore

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Guest Editor

Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Interests: delay differential equations; mathematical modelling; stability; bifurcation analysis; nonlinear analysis

Special Issue Information

Dear Colleagues,

This Issue will be devoted to the publication of significant advances in mathematical and computer modelling, including the simulation of systems that are of current interest.

Numerous issues of critical and current concern are emerging every day that need the aid of simulation and modelling, with the help of fast-paced advances in the development of related techniques and tools, so that real-world problems may be safely and efficiently solved. Apart from providing important methods of analysis which are easily verified, communicated, and understood, modelling and simulation provide valuable solutions by giving clear insights into complex systems across industries and disciplines.

The aim of this Issue is to provide a medium of exchange for the diverse disciplines utilizing mathematical or computer modelling as either a theoretical or working tool. Equal attention will be given to the particulars, methodology, theory, and applications of modelling, focusing on either mathematical or computer modelling, or the integration of the two. While the unifying aspect of the journal is symmetry and complexity, diversity is welcome and this Special Issue is open to a variety of disciplines, including biological, chemical, physical, engineering, medical, environmental, social, behavioral, and other sciences in which theoretical and applied works employ mathematical or computer modelling. Papers dealing with experiments will be considered where the results are presented as an integral part of the modelling process.

Prof. Dr. Yongwimon Lenbury
Prof. Dr. Ravi P. Agarwal
Dr. Elvin Moore
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Mathematical modelling
Simulation modelling
Numerical modelling
Computational techniques and applications
Statistical and stochastic models
Operations research and optimization.

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Published Papers (9 papers)

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Research

15 pages, 4047 KiB

Open AccessArticle

Effects of Depth-Based Object Isolation in Simulated Retinal Prosthetic Vision

by David Avraham and Yitzhak Yitzhaky

Symmetry 2021, 13(10), 1763; https://doi.org/10.3390/sym13101763 - 22 Sep 2021

Cited by 6 | Viewed by 3249

Abstract

Visual retinal prostheses aim to restore vision for blind individuals who suffer from outer retinal degenerative diseases, such as retinitis pigmentosa and age-related macular degeneration. Perception through retinal prostheses is very limited, but it can be improved by applying object isolation. We used an object isolation algorithm based on integral imaging to isolate objects of interest according to their depth from the camera and applied image processing manipulation to the isolated-object images. Subsequently, we applied a spatial prosthetic vision simulation that converted the isolated-object images to phosphene images. We compared the phosphene images for two types of input images, the original image (before applying object isolation), and the isolated-object image to illustrate the effects of object isolation on simulated prosthetic vision without and with multiple spatial variations of phosphenes, such as size and shape variations, spatial shifts, and dropout rate. The results show an improvement in the perceived shape, contrast, and dynamic range (number of gray levels) of objects in the phosphene image. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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19 pages, 11585 KiB

Open AccessArticle

Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management

by Jianhong Chen, Chaoqun Chen, Qinghua Song, Yifei Zhao, Longxin Deng, Raoqing Xie and Shan Yang

Symmetry 2021, 13(9), 1694; https://doi.org/10.3390/sym13091694 - 14 Sep 2021

Cited by 17 | Viewed by 2984

Abstract

The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R₀ = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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17 pages, 384 KiB

Open AccessArticle

Optimization Models for Efficient (t, r) Broadcast Domination in Graphs

by Poompol Buathong and Tipaluck Krityakierne

Symmetry 2021, 13(6), 1028; https://doi.org/10.3390/sym13061028 - 8 Jun 2021

Cited by 1 | Viewed by 2074

Abstract

Known to be NP-complete, domination number problems in graphs and networks arise in many real-life applications, ranging from the design of wireless sensor networks and biological networks to social networks. Initially introduced by Blessing et al., the

(t, r)

broadcast [...] Read more.

(t, r)

broadcast domination number is a generalization of the distance domination number. While some theoretical approaches have been addressed for small values of

t, r

in the literature; in this work, we propose an approach from an optimization point of view. First, the

(t, r)

broadcast domination number is formulated and solved using linear programming. The efficient broadcast, whose wasted signals are minimized, is then found by a genetic algorithm modified for a binary encoding. The developed method is illustrated with several grid graphs: regular, slant, and king’s grid graphs. The obtained computational results show that the method is able to find the exact

(t, r)

broadcast domination number, and locate an efficient broadcasting configuration for larger values of

t, r

than what can be provided from a theoretical basis. The proposed optimization approach thus helps overcome the limitations of existing theoretical approaches in graph theory. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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21 pages, 2298 KiB

Open AccessArticle

Identifying the Locations of Atmospheric Pollution Point Source by Using a Hybrid Particle Swarm Optimization

by Wipawinee Chaiwino, Panasun Manorot, Kanyuta Poochinapan and Thanasak Mouktonglang

Symmetry 2021, 13(6), 985; https://doi.org/10.3390/sym13060985 - 1 Jun 2021

Cited by 4 | Viewed by 2318

Abstract

This research aims to improve the particle swarm optimization (PSO) algorithm by combining a multidimensional search with a line search to determine the location of the air pollution point sources and their respective emission rates. Both multidimensional search and line search do not require the derivative of the cost function. By exploring a symmetric property of search domain, this innovative search tool incorporating a multidimensional search and line search in the PSO is referred to as the hybrid PSO (HPSO). Measuring the pollutant concentration emanating from the pollution point sources through the aid of sensors represents the first stage in the process of evaluating the efficiency of HPSO. The summation of the square of the differences between the observed concentration and the concentration that is theoretically expected (inverse Gaussian plume model or numerical estimations) is used as a cost function. All experiments in this research are therefore conducted using the HPSO sensing technique. To effectively identify air pollution point sources as well as calculate emission rates, optimum positioning of sensors must also be determined. Moreover, the frame of discussion of this research also involves a detailed comparison of the results obtained by the PSO algorithm, the GA (genetic algorithm) and the HPSO algorithm in terms of single pollutant location detection, respectively. In the case of multiple sources, only the findings based on PSO and HPSO algorithms are taken into consideration. This research eventually verifies and confirms that the HPSO does offer substantially better performance in the measuring of pollutant locations as well as emission rates of the air pollution point sources than the original PSO. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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16 pages, 275 KiB

Open AccessArticle

Asymptotic Properties of Discrete Minimal s,log^t-Energy Constants and Configurations

by Nichakan Loesatapornpipit and Nattapong Bosuwan

Symmetry 2021, 13(6), 932; https://doi.org/10.3390/sym13060932 - 24 May 2021

Viewed by 1819

Abstract

We investigated the energy of N points on an infinite compact metric space

(A, d)

of a diameter less than 1 that interact through the potential

(1 / d^{s}) {(log 1 / d)}^{t},

[...] Read more.

We investigated the energy of N points on an infinite compact metric space

(A, d)

of a diameter less than 1 that interact through the potential

(1 / d^{s}) {(log 1 / d)}^{t},

where

s, t \geq 0

and d is the metric distance. With

E_{{log}^{t}}^{s} (A, N)

denoting the minimal energy for such N-point configurations, we studied certain continuity and differentiability properties of

E_{{log}^{t}}^{s} (A, N)

in the variable

s .

Then, we showed that in the limits, as

s \to \infty

and as

s \to s_{0} > 0,

N-point configurations that minimize the

s, {log}^{t}

-energy tends to an N-point best-packing configuration and an N-point configuration that minimizes the

s_{0}, {log}^{t}

-energy, respectively. Furthermore, we considered when A are circles in the Euclidean space

R^{2} .

In particular, we proved the minimality of N distinct equally spaced points on circles in

R^{2}

for some certain s and t. The study on circles shows a possibility for the utilization of N points generated through such new potential to uniformly discretize on objects with very high symmetry. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

18 pages, 2144 KiB

Open AccessArticle

Multinomial Logit Model Building via TreeNet and Association Rules Analysis: An Application via a Thyroid Dataset

by Pannapa Changpetch

Symmetry 2021, 13(2), 287; https://doi.org/10.3390/sym13020287 - 8 Feb 2021

Cited by 2 | Viewed by 2114

Abstract

A model-building framework is proposed that combines two data mining techniques, TreeNet and association rules analysis (ASA) with multinomial logit model building. TreeNet provides plots that play a key role in transforming quantitative variables into better forms for the model fit, whereas ASA is important in finding interactions (low- and high-order) among variables. With the implementation of TreeNet and ASA, new variables and interactions are generated, which serve as candidate predictors in building an optimal multinomial logit model. A real-life example in the context of health care is used to illustrate the major role of these newly generated variables and interactions in advancing multinomial logit modeling to a new level of performance. This method has an explanatory and predictive ability that cannot be achieved using existing methods. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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10 pages, 2284 KiB

Open AccessArticle

Identification Elements Symmetry in Teaching Informatics in Czech Secondary School during the Covid-19 Outbreak from the Perspective of Students

by R. Nemec, A. Jahodova Berkova and S. Hubalovsky

Symmetry 2020, 12(11), 1768; https://doi.org/10.3390/sym12111768 - 26 Oct 2020

Cited by 5 | Viewed by 3142

Abstract

This article describes the research results aimed at distance education during the Covid-19 pandemic and closing schools and its symmetry with the classical state in terms of time, difficulty, and the mental and physical condition of students. An important aspect is therefore to maintain the symmetry of attitudes to teaching in face-to-face form and distance form. In terms of the eight-year gymnasium in the Czech Republic, students’ attitudes to the teaching subject informatics were investigated. The main research questions in our study dealt with whether students felt equally balanced regarding the amount of tasks and time taken for home preparation during the Covid-19 outbreak compared with the time before the quarantine and their condition (both mental and physical) during the Covid-19 outbreak. The research was conducted using an anonymous questionnaire, which was answered by 110 out of 180 students. According to the results, it is evident that students felt that during the distance education, there are more tasks compared to face-to-face ones. Students also claimed to spend more time learning at distance education than at school. On the other hand, they agreed that the self-education schedule is suitable for them. In terms of the questionnaire, their condition (both mental and physical) was also evaluated, which was slightly above the average. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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36 pages, 4068 KiB

Open AccessEditor’s ChoiceArticle

On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic

by Manuel De la Sen, Asier Ibeas and Ravi P. Agarwal

Symmetry 2020, 12(10), 1646; https://doi.org/10.3390/sym12101646 - 7 Oct 2020

Cited by 24 | Viewed by 3643

Abstract

This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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20 pages, 330 KiB

Open AccessArticle

A Comparative Study of Infill Sampling Criteria for Computationally Expensive Constrained Optimization Problems

by Kittisak Chaiyotha and Tipaluck Krityakierne

Symmetry 2020, 12(10), 1631; https://doi.org/10.3390/sym12101631 - 3 Oct 2020

Cited by 9 | Viewed by 2980

Abstract

Engineering optimization problems often involve computationally expensive black-box simulations of underlying physical phenomena. This paper compares the performance of four constrained optimization algorithms relying on a Gaussian process model and an infill sampling criterion under the framework of Bayesian optimization. The four infill sampling criteria include expected feasible improvement (EFI), constrained expected improvement (CEI), stepwise uncertainty reduction (SUR), and augmented Lagrangian (AL). Numerical tests were rigorously performed on a benchmark set consisting of nine constrained optimization problems with features commonly found in engineering, as well as a constrained structural engineering design optimization problem. Based upon several measures including statistical analysis, our results suggest that, overall, the EFI and CEI algorithms are significantly more efficient and robust than the other two methods, in the sense of providing the most improvement within a very limited number of objective and constraint function evaluations, and also in the number of trials for which a feasible solution could be located. Full article

(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)

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