Special Issue "Mathematical Modelling in Engineering & Human Behaviour 2018"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (30 November 2018).

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A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Lucas Jódar
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Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Tel. +34-963877007 Ext: 79144
Interests: computational methods in finances; boundary value problems; random differential equations
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Prof. Dr. Juan Carlos Cortés
E-Mail Website
Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: random differential equations
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Dr. Luis Acedo Rodríguez
E-Mail Website
Guest Editor
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: gravitation; modified theories of gravity; neural networks; mathematical epidemiology
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Please visit this site http://jornadas.imm.upv.es/jornadas/ for a detailed description of this Special Issue. The Special Issue will mainly consist of selected papers presented at the "Mathematical Modelling in Engineering & Human Behaviour 2018". Papers considered to fit the scope of the journal and of sufficient quality, after evaluation by the reviewers, will be published free of charge. The main topics of this Special Issue are:

  • Financial Mathematics
  • Networks and Applications
  • Mathematical Models in Medicine
  • Internal Combustion Engines
  • Mathematical Models in Engineering and Numerical Simulation
  • Social Addictions and Public Health

Prof. Dr. Lucas Jódar
Prof. Dr. Juan Carlos Cortés
Prof. Dr. Luis Acedo
Guest Editors

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Published Papers (11 papers)

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Research

Open AccessFeature PaperArticle
A Mathematical Model for Intimate Partner Violence
Math. Comput. Appl. 2019, 24(1), 29; https://doi.org/10.3390/mca24010029 - 02 Mar 2019
Cited by 1
Abstract
In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence [...] Read more.
In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence against the woman. We focus on incorporating different key factors reported in the literature as causal or motivational factors to perpetrate IPV. Among the main factors included are the failures in self-regulation, the man’s need to control the woman, the social pressure on the woman to remain married, and empowerment programs. Another aspect that we include is periodic alcohol consumption for the man. The discussion of the model includes a stability analysis of its equilibrium points and the asymptotic behavior of its solutions. Also, the interpretation of results is presented in terms of IPV phenomenon. Finally, a brief review is given on different scales to quantify human behavioral traits and numerical simulations for some IPV scenarios. Full article
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Open AccessArticle
A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript
Math. Comput. Appl. 2019, 24(1), 14; https://doi.org/10.3390/mca24010014 - 23 Jan 2019
Abstract
Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze [...] Read more.
Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the α and β -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript. Full article
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Open AccessArticle
Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems
Math. Comput. Appl. 2019, 24(1), 13; https://doi.org/10.3390/mca24010013 - 18 Jan 2019
Abstract
In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, [...] Read more.
In this paper, we introduce and analyze a family of exponential polynomial discrete dynamical systems that can be considered as functional perturbations of a linear dynamical system. The stability analysis of equilibria of this family is performed by considering three different parametric scenarios, from which we show the intricate and complex dynamical behavior of their orbits. Full article
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Open AccessArticle
Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process
Math. Comput. Appl. 2019, 24(1), 12; https://doi.org/10.3390/mca24010012 - 17 Jan 2019
Abstract
A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, [...] Read more.
A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, and pro- and anti-inflammatory cytokines. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. Numerical simulations are also presented to support the theoretical results, and to monitor the evolution of a broken bone for different types of fractures under various medical interventions. The model can be used to guide clinical experiments and to explore possible medical treatments that accelerate the bone fracture healing process, either by surgical interventions or drug administrations. Full article
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Open AccessFeature PaperArticle
Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation
Math. Comput. Appl. 2019, 24(1), 9; https://doi.org/10.3390/mca24010009 - 15 Jan 2019
Abstract
In nuclear engineering, the λ-modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite [...] Read more.
In nuclear engineering, the λ -modes associated with the neutron diffusion equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied. Full article
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Open AccessArticle
Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia
Math. Comput. Appl. 2019, 24(1), 6; https://doi.org/10.3390/mca24010006 - 03 Jan 2019
Abstract
The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that [...] Read more.
The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia. Full article
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Open AccessArticle
An Approach for Integrating Uncertainty When Selecting an Anti-Torpedo Decoy in Brand New Warships
Math. Comput. Appl. 2019, 24(1), 5; https://doi.org/10.3390/mca24010005 - 03 Jan 2019
Abstract
The Spanish Navy has planned that the F-80 frigates will be replaced by the brand new F-110 frigates in 2022. The F-110 program is in the conceptual design phase and one of the objectives is to provide the new F-110 frigate with a [...] Read more.
The Spanish Navy has planned that the F-80 frigates will be replaced by the brand new F-110 frigates in 2022. The F-110 program is in the conceptual design phase and one of the objectives is to provide the new F-110 frigate with a salient anti-submarine capability. Therefore, it is necessary to choose what anti-torpedo decoy should be installed in the warship. The Joint Chiefs of Navy Staff (EMA) established some guidelines and, considering the Navy guidance’s, the Analytic Hierarchy Process (AHP) method was applied. After applying the AHP method, none of the decoys obtained a better score to the other one to make a decision. This paper addresses the problem of the selection of the best anti-torpedo decoy to be installed in the new frigates. This allowed implementing a new approach, the Graphic Method of Measurement of Uncertainty Beyond Objectivity (GMUBO). This approach considers different scenarios from the AHP, quantifies the uncertainty, and evaluates which is the best alternative. The method integrates the uncertainty in the AHP and allows measuring the robustness of the selected alternative, also providing a useful graphical tool. Furthermore, GMUBO has a great ease of use and it is helpful to make decisions under uncertainty conditions. Full article
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Open AccessArticle
Modified Potra–Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations
Math. Comput. Appl. 2019, 24(1), 3; https://doi.org/10.3390/mca24010003 - 27 Dec 2018
Cited by 1
Abstract
In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra–Pták method and last is weighted-Newton [...] Read more.
In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra–Pták method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods. Full article
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Open AccessFeature PaperArticle
Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling
Math. Comput. Appl. 2018, 23(4), 76; https://doi.org/10.3390/mca23040076 - 27 Nov 2018
Abstract
The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392 [...] Read more.
The objective of this paper is to complete certain issues from our recent contribution (Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ. 2018, 392, 1–29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with the homogeneous case, so that the hypotheses are clearer and also easier to check in applications. Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example. We also prove the uniqueness of mean square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean square calculus. In this manner, the study on general random non-autonomous second order linear differential equations with analytic data processes is completely resolved. Finally, we relate our exposition based on random power series with polynomial chaos expansions and the random differential transform method, the latter being a reformulation of our random Fröbenius method. Full article
Open AccessArticle
Cellular Automata and Artificial Brain Dynamics
Math. Comput. Appl. 2018, 23(4), 75; https://doi.org/10.3390/mca23040075 - 16 Nov 2018
Abstract
Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we [...] Read more.
Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. We have also considered that the model maintains sufficient flexibility. For instance, the timestep is arbitrary, as are the spatial dimensions. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. The way that signals (or life) propagate across the grid was described, along with a discussion on how this model could be compared with brain dynamics. Further work and variations of the model were also examined. Full article
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Open AccessFeature PaperArticle
Managing Human Factors to Reduce Organisational Risk in Industry
Math. Comput. Appl. 2018, 23(4), 67; https://doi.org/10.3390/mca23040067 - 25 Oct 2018
Cited by 1
Abstract
Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making [...] Read more.
Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study related to a manufacturing process of a real-world winery is presented, and the proposed approach is applied to rank human factors resulting from a previous organisational risk evaluation from which suitable inference engines may be developed to better support risk management. Full article
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