Mathematical and Computational Applications doi: 10.3390/mca26010021

Authors: Ahmad Taher Azar Fernando E. Serrano Nashwa Ahmad Kamal

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010020

Authors: Francisco-Ronay López-Estrada Guillermo Valencia-Palomo

Control-systems engineering is a multidisciplinary subject that applies automatic-control theory to design systems with desired behaviors in control environments [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca26010019

Authors: Peter Mitic

A model for financial stress testing and stability analysis is presented. Given operational risk loss data within a time window, short-term projections are made using Loess fits to sequences of lognormal parameters. The projections can be scaled by a sequence of risk factors, derived from economic data in response to international regulatory requirements. Historic and projected loss data are combined using a lengthy nonlinear algorithm to calculate a capital reserve for the upcoming year. The model is embedded in a general framework, in which arrays of risk factors can be swapped in and out to assess their effect on the projected losses. Risk factor scaling is varied to assess the resilience and stability of financial institutions to economic shock. Symbolic analysis of projected losses shows that they are well-conditioned with respect to risk factors. Specific reference is made to the effect of the 2020 COVID-19 pandemic. For a 1-year projection, the framework indicates a requirement for an increase in regulatory capital of approximately 3% for mild stress, 8% for moderate stress, and 32% for extreme stress. The proposed framework is significant because it is the first formal methodology to link financial risk with economic factors in an objective way without recourse to correlations.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010018

Authors: Riccardo Fazio

This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context, the numerical test is illustrated by two examples where we find meaningful numerical results.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010017

Authors: Thomas Daniel Fabien Casenave Nissrine Akkari David Ryckelynck

Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues: one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010016

Authors: Christopher Cullenbine Joseph Rohrer Erin Almand J. Steel Matthew Davis Christopher Carson Steven Hasstedt John Sitko Douglas Wickert

A closed-form equation, the Fizzle Equation, was derived from a mathematical model predicting Severe Acute Respiratory Virus-2 dynamics, optimized for a 4000-student university cohort. This equation sought to determine the frequency and percentage of random surveillance testing required to prevent an outbreak, enabling an institution to develop scientifically sound public health policies to bring the effective reproduction number of the virus below one, halting virus progression. Model permutations evaluated the potential spread of the virus based on the level of random surveillance testing, increased viral infectivity and implementing additional safety measures. The model outcomes included: required level of surveillance testing, the number of infected individuals, and the number of quarantined individuals. Using the derived equations, this study illustrates expected infection load and how testing policy can prevent outbreaks in an institution. Furthermore, this process is iterative, making it possible to develop responsive policies scaling the amount of surveillance testing based on prior testing results, further conserving resources.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010015

Authors: Marie-Sophie Hartig

It is common practice in science and engineering to approximate smooth surfaces and their geometric properties by using triangle meshes with vertices on the surface. Here, we study the approximation of the Gaussian curvature through the Gauss–Bonnet scheme. In this scheme, the Gaussian curvature at a vertex on the surface is approximated by the quotient of the angular defect and the area of the Voronoi region. The Voronoi region is the subset of the mesh that contains all points that are closer to the vertex than to any other vertex. Numerical error analyses suggest that the Gauss–Bonnet scheme always converges with quadratic convergence speed. However, the general validity of this conclusion remains uncertain. We perform an analytical error analysis on the Gauss–Bonnet scheme. Under certain conditions on the mesh, we derive the convergence speed of the Gauss–Bonnet scheme as a function of the maximal distance between the vertices. We show that the conditions are sufficient and necessary for a linear convergence speed. For the special case of locally spherical surfaces, we find a better convergence speed under weaker conditions. Furthermore, our analysis shows that the Gauss–Bonnet scheme, while generally efficient and effective, can give erroneous results in some specific cases.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010014

Authors: Maria Teresa Signes-Pont José Juan Cortés-Plana Higinio Mora-Mora

This paper presents a discrete compartmental Susceptible–Exposed–Infected–Recovered/Dead (SEIR/D) model to address the expansion of Covid-19. This model is based on a grid. As time passes, the status of the cells updates by means of binary rules following a neighborhood and a delay pattern. This model has already been analyzed in previous works and successfully compared with the corresponding continuous models solved by ordinary differential equations (ODE), with the intention of finding the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the disease. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both height and timing of the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010013

Authors: Luis Gerardo de la Fraga

In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating point (FP) numbers of 16 bits, and these last numbers are known as FP16. In this paper, it is considered that it is important to analyze differential evolution (DE) in these circumstances with the goal of reducing its consumption power, storage size of the variables, and improve its speed behavior. All these aspects become important if one needs to design a dedicated hardware, as an embedded DE within a circuit chip, that performs optimization. With these conditions DE is tested using three common multimodal benchmark functions: Rosenbrock, Rastrigin, and Ackley, in 10 dimensions. Results are obtained in software by simulating all numbers using C programming language.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010012

Authors: Andrea Giunta Gaetano Giunta Domenico Marino Francesco Oliveri

The aim of this work is to simulate a market behavior in order to study the evolution of wealth distribution. The numerical simulations are carried out on a simple economical model with a finite number of economic agents, which are able to exchange goods/services and money; the various agents interact each other by means of random exchanges. The model is micro founded, self-consistent, and predictive. Despite the simplicity of the model, the simulations show a complex and non-trivial behavior. First of all, we are able to recognize two solution classes, namely two phases, separated by a threshold region. The analysis of the wealth distribution of the model agents, in the threshold region, shows functional forms resembling empirical quantitative studies of the probability distributions of wealth and income in the United Kingdom and the United States. Furthermore, the decile distribution of the population wealth of the simulated model, in the threshold region, overlaps in a suggestive way with the real data of the Italian population wealth in the last few years. Finally, the results of the simulated model allow us to draw important considerations for designing effective policies for economic and human development.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010011

Authors: Fatima Oumellal Abdellah Lamnii

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they are applied to open and closed Hermite interpolation curves. Surface construction utilizing the studied trigonometric Hermite interpolation is explored and several examples obtained by the C1 trigonometric Hermite interpolation surface are given to show the usefulness of this method.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010010

Authors: MCA Editorial Office MCA Editorial Office

Peer review is the driving force of journal development, and reviewers are gatekeepers who ensure that MCA maintains its standards for the high quality of its published papers [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca26010009

Authors: Daniele Mortari Roberto Furfaro

This work presents a methodology to derive analytical functionals, with embedded linear constraints among the components of a vector (e.g., coordinates) that is a function a single variable (e.g., time). This work prepares the background necessary for the indirect solution of optimal control problems via the application of the Pontryagin Maximum Principle. The methodology presented is part of the univariate Theory of Functional Connections that has been developed to solve constrained optimization problems. To increase the clarity and practical aspects of the proposed method, the work is mostly presented via examples of applications rather than via rigorous mathematical definitions and proofs.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010008

Authors: Juan Frausto-Solis Leonor Hernández-Ramírez Guadalupe Castilla-Valdez Juan J. González-Barbosa Juan P. Sánchez-Hernández

The Job Shop Scheduling Problem (JSSP) has enormous industrial applicability. This problem refers to a set of jobs that should be processed in a specific order using a set of machines. For the single-objective optimization JSSP problem, Simulated Annealing is among the best algorithms. However, in Multi-Objective JSSP (MOJSSP), these algorithms have barely been analyzed, and the Threshold Accepting Algorithm has not been published for this problem. It is worth mentioning that the researchers in this area have not reported studies with more than three objectives, and the number of metrics they used to measure their performance is less than two or three. In this paper, we present two MOJSSP metaheuristics based on Simulated Annealing: Chaotic Multi-Objective Simulated Annealing (CMOSA) and Chaotic Multi-Objective Threshold Accepting (CMOTA). We developed these algorithms to minimize three objective functions and compared them using the HV metric with the recently published algorithms, MOMARLA, MOPSO, CMOEA, and SPEA. The best algorithm is CMOSA (HV of 0.76), followed by MOMARLA and CMOTA (with HV of 0.68), and MOPSO (with HV of 0.54). In addition, we show a complexity comparison of these algorithms, showing that CMOSA, CMOTA, and MOMARLA have a similar complexity class, followed by MOPSO.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010007

Authors: Simone Balmelli Francesco Moresino

When designing a new product, conjoint analysis is a powerful tool to estimate the perceived value of the prospects. However, it has a drawback: when the product has too many attributes and levels, it may be difficult to administrate the survey to respondents because they will be overwhelmed by the too numerous questions. In this paper, we propose an alternative approach that permits us to bypass this problem. Contrary to conjoint analysis, which estimates respondents&rsquo; utility functions, our approach directly estimates market shares. This enables us to split the questionnaire among respondents and, therefore, to reduce the burden on each respondent as much as desired. However, this new method has two weaknesses that conjoint analysis does not have: first, inferences on a single respondent cannot be made; second, the competition&rsquo;s product profiles have to be known before administrating the survey. Therefore, our method has to be used when traditional methods are less easily implementable, i.e., when the number of attributes and levels is large.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010006

Authors: Iman Bahreini Toussi Abdolmajid Mohammadian Reza Kianoush

Liquid storage tanks subjected to base excitation can cause large impact forces on the tank roof, which can lead to structural damage as well as economic and environmental losses. The use of artificial intelligence in solving engineering problems is becoming popular in various research fields, and the Genetic Programming (GP) method is receiving more attention in recent years as a regression tool and also as an approach for finding empirical expressions between the data. In this study, an OpenFOAM numerical model that was validated by the authors in a previous study is used to simulate various tank sizes with different liquid heights. The tanks are excited in three different orientations with harmonic sinusoidal loadings. The excitation frequencies are chosen as equal to the tanks&rsquo; natural frequencies so that they would be subject to a resonance condition. The maximum pressure in each case is recorded and made dimensionless; then, using Multi-Gene Genetic Programming (MGGP) methods, a relationship between the dimensionless maximum pressure and dimensionless liquid height is acquired. Finally, some error measurements are calculated, and the sensitivity and uncertainty of the proposed equation are analyzed.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010005

Authors: Kalyanmoy Deb Proteek Chandan Roy Rayan Hussein

Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010004

Authors: Antonino Amoddeo

A mathematical model describing the interaction of cancer cells with the urokinase plasminogen activation system is represented by a system of partial differential equations, in which cancer cell dynamics accounts for diffusion, chemotaxis, and haptotaxis contributions. The mutual relations between nerve fibers and tumors have been recently investigated, in particular, the role of nerves in the development of tumors, as well neurogenesis induced by cancer cells. Such mechanisms are mediated by neurotransmitters released by neurons as a consequence of electrical stimuli flowing along the nerves, and therefore electric fields can be present inside biological tissues, in particular, inside tumors. Considering cancer cells as negatively charged particles immersed in the correct biological environment and subjected to an external electric field, the effect of the latter on cancer cell dynamics is still unknown. Here, we implement a mathematical model that accounts for the interaction of cancer cells with the urokinase plasminogen activation system subjected to a uniform applied electric field, simulating the first stage of cancer cell dynamics in a three-dimensional axial symmetric domain. The obtained numerical results predict that cancer cells can be moved along a preferred direction by an applied electric field, suggesting new and interesting strategies in cancer therapy.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010003

Authors: Benito Chen-Charpentier Clara Garza-Hume María Jorge

Marital relations depend on many factors which can increase the amount of satisfaction or unhappiness in the relation. A large percentage of marriages end up in divorce. While there are many studies about the causes of divorce and how to prevent it, there are very few mathematical models dealing with marital relations. In this paper, we present a continuous model based on the ideas presented by Gottman and coauthors. We show that the type of influence functions that describe the interaction between husband and wife is critical in determining the outcome of a marriage. We also introduce stochasticity into the model to account for the many factors that affect the marriage and that are not easily quantified, such as economic climate, work stress, and family relations. We show that these factors are able to change the equilibrium state of the couple.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010002

Authors: Zhuo-Jia Fu Lu-Feng Li De-Shun Yin Li-Li Yuan

In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.

]]>Mathematical and Computational Applications doi: 10.3390/mca26010001

Authors: Mehmet Ersoy Omar Lakkis Philip Townsend

We propose a one-dimensional Saint-Venant (open-channel) model for overland flows, including a water input&ndash;output source term modeling recharge via rainfall and infiltration (or exfiltration). We derive the model via asymptotic reduction from the two-dimensional Navier&ndash;Stokes equations under the shallow water assumption, with boundary conditions including recharge via ground infiltration and runoff. This new model recovers existing models as special cases, and adds more scope by adding water-mixing friction terms that depend on the rate of water recharge. We propose a novel entropy function and its flux, which are useful in validating the model&rsquo;s conservation or dissipation properties. Based on this entropy function, we propose a finite volume scheme extending a class of kinetic schemes and provide numerical comparisons with respect to the newly introduced mixing friction coefficient. We also provide a comparison with experimental data.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040080

Authors: Fernanda Beltrán Oliver Cuate Oliver Schütze

Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040079

Authors: Jismi Mathew Christophe Chesneau

The Lomax distribution is arguably one of the most useful lifetime distributions, explaining the developments of its extensions or generalizations through various schemes. The Marshall&ndash;Olkin length-biased Lomax distribution is one of these extensions. The associated model has been used in the frameworks of data fitting and reliability tests with success. However, the theory behind this distribution is non-existent and the results obtained on the fit of data were sufficiently encouraging to warrant further exploration, with broader comparisons with existing models. This study contributes in these directions. Our theoretical contributions on the the Marshall&ndash;Olkin length-biased Lomax distribution include an original compounding property, various stochastic ordering results, equivalences of the main functions at the boundaries, a new quantile analysis, the expressions of the incomplete moments under the form of a series expansion and the determination of the stress&ndash;strength parameter in a particular case. Subsequently, we contribute to the applicability of the Marshall&ndash;Olkin length-biased Lomax model. When combined with the maximum likelihood approach, the model is very effective. We confirm this claim through a complete simulation study. Then, four selected real life data sets were analyzed to illustrate the importance and flexibility of the model. Especially, based on well-established standard statistical criteria, we show that it outperforms six strong competitors, including some extended Lomax models, when applied to these data sets. To our knowledge, such comprehensive applied work has never been carried out for this model.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040078

Authors: Anouk F. G. Pelzer Alef E. Sterk

In this paper, we study a family of dynamical systems with circulant symmetry, which are obtained from the Lorenz-96 model by modifying its nonlinear terms. For each member of this family, the dimension n can be arbitrarily chosen and a forcing parameter F acts as a bifurcation parameter. The primary focus in this paper is on the occurrence of finite cascades of pitchfork bifurcations, where the length of such a cascade depends on the divisibility properties of the dimension n. A particularly intriguing aspect of this phenomenon is that the parameter values F of the pitchfork bifurcations seem to satisfy the Feigenbaum scaling law. Further bifurcations can lead to the coexistence of periodic or chaotic attractors. We also describe scenarios in which the number of coexisting attractors can be reduced through collisions with an equilibrium.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040077

Authors: Frédéric Dubas Kamel Boughrara

Electrical machines are used in many electrical engineering applications [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25040076

Authors: Perla Rubi Castañeda-Aviña Esteban Tlelo-Cuautle Luis Gerardo de la Fraga

The optimization of analog integrated circuits requires to take into account a number of considerations and trade-offs that are specific to each circuit, meaning that each case of design may be subject to different constraints to accomplish target specifications. This paper shows the single-objective optimization of a complementary metal-oxide-semiconductor (CMOS) four-stage voltage-controlled oscillator (VCO) to maximize the oscillation frequency. The stages are designed by using CMOS current-mode logic or differential pairs and are connected in a ring structure. The optimization is performed by applying differential evolution (DE) algorithm, in which the design variables are the control voltage and the transistors&rsquo; widths and lengths. The objective is maximizing the oscillation frequency under the constraints so that the CMOS VCO be robust to Monte Carlo simulations and to process-voltage-temperature (PVT) variations. The optimization results show that DE provides feasible solutions oscillating at 5 GHz with a wide control voltage range and robust to both Monte Carlo and PVT analyses.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040075

Authors: Nicholas Fantuzzi

Authors of the present Special Issue are gratefully acknowledged for writing papers of very high standard [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25040074

Authors: Fernando Alcántara-López Carlos Fuentes Fernando Brambila-Paz Jesús López-Estrada

The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia&ndash;Cardano equations.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040073

Authors: Xiatong Cai Abdolmajid Mohammadian Hamidreza Shirkhani

Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040072

Authors: José-Yaír Guzmán-Gaspar Efrén Mezura-Montes Saúl Domínguez-Isidro

This study presents an empirical comparison of the standard differential evolution (DE) against three random sampling methods to solve robust optimization over time problems with a survival time approach to analyze its viability and performance capacity of solving problems in dynamic environments. A set of instances with four different dynamics, generated by two different configurations of two well-known benchmarks, are solved. This work also introduces a comparison criterion that allows the algorithm to discriminate among solutions with similar survival times to benefit the selection process. The results show that the standard DE holds a good performance to find ROOT solutions, improving the results reported by state-of-the-art approaches in the studied environments. Finally, it was found that the chaotic dynamic, disregarding the type of peak movement in the search space, is a source of difficulty for the proposed DE algorithm.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040071

Authors: Md. Taksir Hasan Majumder Md. Mahabur Rahman Anindya Iqbal M. Sohel Rahman

Homoglyphs are pairs of visual representations of Unicode characters that look similar to the human eye. Identifying homoglyphs is extremely useful for building a strong defence mechanism against many phishing and spoofing attacks, ID imitation, profanity abusing, etc. Although there is a list of discovered homoglyphs published by Unicode consortium, regular expansion of Unicode character scripts necessitates a robust and reliable algorithm that is capable of identifying all possible new homoglyphs. In this article, we first show that shallow Convolutional Neural Networks are capable of identifying homoglyphs. We propose two variations, both of which obtain very high accuracy (99.44%) on our benchmark dataset. We also report that adoption of transfer learning allows for another model to achieve 100% recall on our dataset. We ensemble these three methods to obtain 99.72% accuracy on our independent test dataset. These results illustrate the superiority of our ensembled model in detecting homoglyphs and suggest that our model can be used to detect new homoglyphs when increasing Unicode characters are added. As a by-product, we also prepare a benchmark dataset based on the currently available list of homoglyphs.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040070

Authors: Julien Petitgirard Tony Piguet Philippe Baucour Didier Chamagne Eric Fouillien Jean-Christophe Delmare

The study concerns the winding head thermal design of electrical machines in difficult thermal environments. The new approach is adapted for all basic shapes and solves the thermal behaviour of a random wire layout. The model uses the nodal method but does not use the common homogenization method for the winding slot. The layout impact can be precisely studied to find different hotspots. To achieve this a Delaunay triangulation provides the thermal links between adjoining wires in the slot. Vorono&iuml; tessellation gives a cutting to estimate thermal conductance between adjoining wires. This thermal behaviour is simulated in cell cutting and it is simplified with the thermal bridge notion to obtain a simple solving of these thermal conductances. The boundaries are imposed on the slot borders with Dirichlet condition. Then solving with many Dirichlet conditions is described. Some results show different possible applications with rectangular and round shapes, one ore many boundaries, different limit condition values and different layouts. The model can be integrated into a larger model that represents the stator to have best results.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040069

Authors: Christophe Guyeux

Asynchronous iterations have long been used in distributed computing algorithms to produce calculation methods that are potentially faster than a serial or parallel approach, but whose convergence is more difficult to demonstrate. Conversely, over the past decade, the study of the complex dynamics of asynchronous iterations has been initiated and deepened, as well as their use in computer security and bioinformatics. The first work of these studies focused on chaotic discrete dynamical systems, and links were established between these dynamics on the one hand, and between random or complex behaviours in the sense of the theory of the same name. Computer security applications have focused on pseudo-random number generation, hash functions, hidden information, and various security aspects of wireless sensor networks. At the bioinformatics level, this study of complex systems has allowed an original approach to understanding the evolution of genomes and protein folding. These various contributions are detailed in this review article, which is an extension of the paper “An update on the topological properties of asynchronous iterations” presented during the Sixth International Conference on Parallel, Distributed, GPU and Cloud Computing (Pareng 2019).

]]>Mathematical and Computational Applications doi: 10.3390/mca25040068

Authors: Desmond Adair Martin Jaeger

Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040067

Authors: Anna Kirkpatrick Kalen Patton Prasad Tetali Cassie Mitchell

Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic Model (NNTM) is commonly used to identify such properties (number of hairpins, maximum ladder distance, etc.), it is difficult to know whether the resultant values fall within expected dispersion thresholds for a given energy function. The goal of this study was to construct a Markov chain capable of examining the dispersion of RNA secondary structures and branching properties obtained from NNTM energy function minimization independent of a specific nucleotide sequence. Plane trees are studied as a model for RNA secondary structure, with energy assigned to each tree based on the NNTM, and a corresponding Gibbs distribution is defined on the trees. Through a bijection between plane trees and 2-Motzkin paths, a Markov chain converging to the Gibbs distribution is constructed, and fast mixing time is established by estimating the spectral gap of the chain. The spectral gap estimate is obtained through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. The resulting algorithm can be used as a tool for exploring the branching structure of RNA, especially for long sequences, and to examine branching structure dependence on energy model parameters. Full exposition is provided for the mathematical techniques used with the expectation that these techniques will prove useful in bioinformatics, computational biology, and additional extended applications.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040066

Authors: Seifu Endris Yimer Poom Kumam Anteneh Getachew Gebrie

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040065

Authors: Jismi Mathew Christophe Chesneau

It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall&ndash;Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall&ndash;Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040064

Authors: Lorenzo G. Resca Nicholas A. Mecholsky

Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area V1, is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical magnification factors. Once unfolded, V1 has a convex three-dimensional shape, which can be mathematically modeled as a surface of revolution embedded in three-dimensional Euclidean space. Thus, we solve the problem of differential geometry and geodesy for the mapping of the visual field to V1, involving both isotropic and non-isotropic cortical magnification factors of a most general form. We provide illustrations of our technique and results that apply to V1 surfaces with curve profiles relevant to vision research in general and to visual phenomena such as &lsquo;crowding&rsquo; effects and eye movement guidance in particular. From a mathematical perspective, we also find intriguing and unexpected differential geometry properties of V1 surfaces, discovering that geodesic orbits have alternative prograde and retrograde characteristics, depending on the interplay between local curvature and global topology.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040063

Authors: Anthony Overmars Sitalakshmi Venkatraman

The security of RSA relies on the computationally challenging factorization of RSA modulus N=p1&nbsp;p2 with N&nbsp;being a large semi-prime consisting of two primes p1and&nbsp;p2, for the generation of RSA keys in commonly adopted cryptosystems. The property of p1&nbsp;and&nbsp;p2, both congruent to 1 mod 4, is used in Euler&rsquo;s factorization method to theoretically factorize them. While this caters to only a quarter of the possible combinations of primes, the rest of the combinations congruent to 3 mod 4 can be found by extending the method using Gaussian primes. However, based on Pythagorean primes that are applied in RSA, the semi-prime has only two sums of two squares in the range of possible squares N&minus;1,&nbsp;N/2&nbsp;. As N becomes large, the probability of finding the two sums of two squares becomes computationally intractable in the practical world. In this paper, we apply Pythagorean primes to explore how the number of sums of two squares in the search field can be increased thereby increasing the likelihood that a sum of two squares can be found. Once two such sums of squares are found, even though many may exist, we show that it is sufficient to only find two solutions to factorize the original semi-prime. We present the algorithm showing the simplicity of steps that use rudimentary arithmetic operations requiring minimal memory, with search cycle time being a factor for very large semi-primes, which can be contained. We demonstrate the correctness of our approach with practical illustrations for breaking RSA keys. Our enhanced factorization method is an improvement on our previous work with results compared to other factorization algorithms and continues to be an ongoing area of our research.

]]>Mathematical and Computational Applications doi: 10.3390/mca25040062

Authors: Paweł Olejnik

Nonlinear dynamics takes its origins from physics and applied mathematics [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25030061

Authors: Christophe Bastien Clive Neal-Sturgess Huw Davies Xiang Cheng

In the real world, the severity of traumatic injuries is measured using the Abbreviated Injury Scale (AIS). However, the AIS scale cannot currently be computed by using the output from finite element human computer models, which currently rely on maximum principal strains (MPS) to capture serious and fatal injuries. In order to overcome these limitations, a unique Organ Trauma Model (OTM) able to calculate the threat to the life of a brain model at all AIS levels is introduced. The OTM uses a power method, named Peak Virtual Power (PVP), and defines brain white and grey matter trauma responses as a function of impact location and impact speed. This research has considered ageing in the injury severity computation by including soft tissue material degradation, as well as brain volume changes due to ageing. Further, to account for the limitations of the Lagrangian formulation of the brain model in representing hemorrhage, an approach to include the effects of subdural hematoma is proposed and included as part of the predictions. The OTM model was tested against two real-life falls and has proven to correctly predict the post-mortem outcomes. This paper is a proof of concept, and pending more testing, could support forensic studies.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030060

Authors: Yi Hong

This article exploits arbitrage valuation bounds on currency basket options. Instead of using a sophisticated model to price these options, we consider a set of pricing models that are consistent with the prices of available hedging assets. In the absence of arbitrage, we identify valuation bounds on currency basket options without model specifications. Our results extend the work in the literature by seeking tight arbitrage valuation bounds on these options. Specifically, the valuation bounds are enforced by static portfolios that consist of both cross-currency options and individual options denominated in the numeraire currency.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030059

Authors: Conghua Wen Junwei Wei

This article aims to study the schemes of forecasting the volatilities of Chinese futures markets and sector stocks. An improved method based on the cyclical two-component model (CTCM) introduced by Harris et al. in 2011 is provided. The performance of CTCM is compared with the benchmark model: Heterogeneous Autoregressive model of Realized Volatility type (HAR-RV type). The impact of open interest for futures market is included in HAR-RV type model. We employ 3 different evaluation rules to determine the most efficient models when the results of different evaluation rules are inconsistent. The empirical results show that CTCM is more accurate than HAR-RV type in both estimation and forecasting. The results also show that the realized range-based tripower volatility (RTV) is the most efficient estimator for both Chinese futures markets and sector stocks.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030058

Authors: Minh Nguyen Mehmet Aktas Esra Akbas

The growth of social media in recent years has contributed to an ever-increasing network of user data in every aspect of life. This volume of generated data is becoming a vital asset for the growth of companies and organizations as a powerful tool to gain insights and make crucial decisions. However, data is not always reliable, since primarily, it can be manipulated and disseminated from unreliable sources. In the field of social network analysis, this problem can be tackled by implementing machine learning models that can learn to classify between humans and bots, which are mostly harmful computer programs exploited to shape public opinions and circulate false information on social media. In this paper, we propose a novel topological feature extraction method for bot detection on social networks. We first create weighted ego networks of each user. We then encode the higher-order topological features of ego networks using persistent homology. Finally, we use these extracted features to train a machine learning model and use that model to classify users as bot vs. human. Our experimental results suggest that using the higher-order topological features coming from persistent homology is promising in bot detection and more effective than using classical graph-theoretic structural features.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030057

Authors: Oscar-David Ramírez-Cárdenas Felipe Trujillo-Romero

In this work, the sensorless speed control of a brushless direct current motor utilizing a neural network is presented. This control is done using a two-layer neural network that uses the backpropagation algorithm for training. The values provided by a Proportional, Integral, and Derivative (PID) control to this type of motor are used to train the network. From this PID control, the velocity values and their corresponding signal control (u) are recovered for different values of load pairs. Five different values of load pairs were used to consider the entire working range of the motor to be controlled. After carrying out the training, it was observed that the proposed network could hold constant load pairs, as well as variables. Several tests were carried out at the simulation level, which showed that control based on neural networks is robust. Finally, it is worth mentioning that this control strategy can be realized without the need for a speed sensor.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030056

Authors: Ildeberto Santos-Ruiz Francisco-Ronay López-Estrada Vicenç Puig Guillermo Valencia-Palomo

This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook&ndash;White equation for an operating interval of the pipeline from the flow and pressure measurements at the pipe ends. The proposed method has been implemented in MATLAB and validated in a serpentine-shaped experimental pipeline by contrasting the theoretical friction for the estimated coefficients obtained from the Darcy&ndash;Weisbach equation for a set of steady-state measurements.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030055

Authors: Mario Heras-Cervantes Adriana del Carmen Téllez-Anguiano Juan Anzurez-Marín Elisa Espinosa-Juárez

In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the process. In order to facilitate the implementation control strategies to maintain the heating power regulated in the distillation process, it is necessary to represent adequately the heating power actuator behavior; therefore, three different models (switching, nonlinear and fuzzy Takagi&ndash;Sugeno) of a DC-DC Buck-Boost power converter, selected to regulate the electric power regarding the heating power, are presented and compared. Considering that the online measurements of the two main variables of the converter, the inductor current and the capacitor voltage, are not always available, two different fuzzy observers (with and without sliding modes) are developed to allow monitoring the physical variables in the converter. The observers response is compared to determine which has a better performance. The role of the observer in estimating the state variables with the purpose of using them in the sensors fault diagnosis, using the analytical redundancy concept, likewise, from the estimation of these variables other non-measurable can be determined; for example, the caloric power. The stability analysis and observers gains are obtained by linear matrix inequalities (LMIs). The observers are validated by MATLAB&reg; simulations to verify the observers convergence and analyze their response under system disturbances.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030054

Authors: Safeer Hussain Khan Timilehin Opeyemi Alakoya Oluwatosin Temitope Mewomo

In each iteration, the projection methods require computing at least one projection onto the closed convex set. However, projections onto a general closed convex set are not easily executed, a fact that might affect the efficiency and applicability of the projection methods. To overcome this drawback, we propose two iterative methods with self-adaptive step size that combines the Halpern method with a relaxed projection method for approximating a common solution of variational inequality and fixed point problems for an infinite family of multivalued relatively nonexpansive mappings in the setting of Banach spaces. The core of our algorithms is to replace every projection onto the closed convex set with a projection onto some half-space and this guarantees the easy implementation of our proposed methods. Moreover, the step size of each algorithm is self-adaptive. We prove strong convergence theorems without the knowledge of the Lipschitz constant of the monotone operator and we apply our results to finding a common solution of constrained convex minimization and fixed point problems in Banach spaces. Finally, we present some numerical examples in order to demonstrate the efficiency of our algorithms in comparison with some recent iterative methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030053

Authors: Penglei Gao Rui Zhang Xi Yang

Stock index price prediction is prevalent in both academic and economic fields. The index price is hard to forecast due to its uncertain noise. With the development of computer science, neural networks are applied in kinds of industrial fields. In this paper, we introduce four different methods in machine learning including three typical machine learning models: Multilayer Perceptron (MLP), Long Short Term Memory (LSTM) and Convolutional Neural Network (CNN) and one attention-based neural network. The main task is to predict the next day&rsquo;s index price according to the historical data. The dataset consists of the SP500 index, CSI300 index and Nikkei225 index from three different financial markets representing the most developed market, the less developed market and the developing market respectively. Seven variables are chosen as the inputs containing the daily trading data, technical indicators and macroeconomic variables. The results show that the attention-based model has the best performance among the alternative models. Furthermore, all the introduced models have better accuracy in the developed financial market than developing ones.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030052

Authors: Naveed Iqbal Humaira Yasmin Bawfeh K. Kometa Adel A. Attiya

This article deals with Sisko fluid flow exhibiting peristaltic mechanism in an asymmetric channel with sinusoidal wave propagating down its walls. The channel walls in heat transfer process satisfy the convective conditions. The flow and heat transfer equations are modeled and non-dimensionalized. Analysis has been carried out subject to low Reynolds number and long wavelength considerations. Analytical solution is obtained by using the regular perturbation method by taking Sisko fluid parameter as a perturbed parameter. The shear-thickening and shear-thinning properties of Sisko fluid in the present nonlinear analysis are examined. Comparison is provided between Sisko fluid outcomes and viscous fluids. Velocity and temperature distributions, pressure gradient and streamline pattern are addressed with respect to different parameters of interest. Trapping and pumping processes have also been studied. As a result, the thermal analysis indicates that the implementation of a rise in a non-Newtonian parameter, the Biot numbers and Brinkman number increases the thermal stability of the liquid.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030051

Authors: Jesus R. Pulido-Luna Jorge A. López-Rentería Nohe R. Cazarez-Castro

In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030050

Authors: Ana Arnal Fernando Casas Cristina Chiralt

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet&ndash;Magnus expansion for periodic systems, the quantum averaging technique, and the Lie&ndash;Deprit perturbative algorithms. Even the standard perturbation theory fits in this framework. The approach is based on carrying out an appropriate change of coordinates (or picture) in each case, and it can be formulated for any time-dependent linear system of ordinary differential equations. All of the procedures (except the standard perturbation theory) lead to approximate solutions preserving by construction unitarity when applied to the time-dependent Schr&ouml;dinger equation.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030049

Authors: Silvia Licciardi Rosa Maria Pidatella Marcello Artioli Giuseppe Dattoli

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030048

Authors: Francisco-Ronay López-Estrada Oscar Santos-Estudillo Guillermo Valencia-Palomo Samuel Gómez-Peñate Carlos Hernández-Gutiérrez

The main aim of this paper is to propose a robust fault-tolerant control for a three degree of freedom (DOF) mechanical crane by using a convex quasi-Linear Parameter Varying (qLPV) approach for modeling the crane and a passive fault-tolerant scheme. The control objective is to minimize the load oscillations while the desired path is tracked. The convex qLPV model is obtained by considering the nonlinear sector approach, which can represent exactly the nonlinear system under the bounded nonlinear terms. To improve the system safety, tolerance to partial actuator faults is considered. Performance requirements of the tracking control system are specified in an H&infin; criteria that guarantees robustness against measurement noise, and partial faults. As a result, a set of Linear Matrix Inequalities is derived to compute the controller gains. Numerical experiments on a realistic 3 DOF crane model confirm the applicability of the control scheme.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030047

Authors: Guash Haile Taddele Poom Kumam Anteneh Getachew Gebrie Kanokwan Sitthithakerngkiet

In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030046

Authors: Mario Kovač Philippe Notton Daniel Hofman Josip Knezović

In this paper, we present an overview of the European Processor Initiative (EPI), one of the cornerstones of the EuroHPC Joint Undertaking, a new European Union strategic entity focused on pooling the Union&rsquo;s and national resources on HPC to acquire, build and deploy the most powerful supercomputers in the world within Europe. EPI started its activities in December 2018. The first three years drew processor and platform designers, embedded software, middleware, applications and usage experts from 10 EU countries together to co-design Europe&rsquo;s first HPC Systems on Chip and accelerators with its unique Common Platform (CP) technology. One of EPI&rsquo;s core activities also takes place in the automotive sector, providing architectural solutions for a novel embedded high-performance computing (eHPC) platform and ensuring the overall economic viability of the initiative.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030045

Authors: José Luis Hernández-Caceres René Iván González-Fernández Marlis Ontivero-Ortega Guido Nolte

Nonlinear frequency coupling is assessed with bispectral measures, such as bicoherence. In this study, BisQ, a new bicoherence-derived index, is proposed for assessing nonlinear processes in cardiac regulation. To find BisQ, 110 ten-minute ECG traces obtained from 55 participants were initially studied. Via bispectral analysis, a bicoherence matrix (BC) was obtained from each trace (0.06 to 1.8 Hz with a resolution of 0.01 Hz). Each frequency pair in BC was tested for correlation with the HRV recurrent quantification analysis (RQA) index Lmean, obtained from tachograms from the same ECG trace. BisQ is the result of adding BC values corresponding to the three frequency pairs exhibiting the highest correlation with Lmean. BisQ values were estimated for different groups of subjects: healthy persons, persons with arrhythmia, persons with epilepsy, and preterm neonates. ECG traces from persons with arrhythmia showed no significant differences in BisQ values respect to healthy persons, while persons with epilepsy and neonates showed higher BisQ values (p &lt; 0.05; Mann-Whitney U-test). BisQ reflects nonlinear interactions at the level of sinus-and atrial-ventricular nodes, and most likely cardiorespiratory coupling as well. We expect that BisQ will allow for further exploration of cardiac nonlinear dynamics, complementing available HRV indices.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030044

Authors: Abraham Efraim Rodriguez-Mata Yaneth Bustos-Terrones Victor Gonzalez-Huitrón Pablo Antonio Lopéz-Peréz Omar Hernández-González Leonel Ernesto Amabilis-Sosa

The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter&ndash;Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables that are very difficult to measure in rivers with online sensors, such as Biochemical Oxygen Demand (BOD). We propose the design of a novel Fractional Order High Gain Observer (FOHO) and consider the use of Lyapunov convergence functions to demonstrate stability, as it is compared to classical extended Luenberger Observer published in the literature, to study the convergence in BOD estimation in rivers. The proposed methodology was used to estimated Dissolved oxygen (DO) and BOD monitoring of River Culiacan, Sinaloa, Mexico. The use of fractional order in high-gain observers has a very effective effect on BOD estimation performance, as shown by our numerical studies. The theoretical results have shown that robust observer design can help solve problems in estimating complex variables.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030043

Authors: Meirav Amram Etan Fisher Shai Gul Uzi Vishne

The goal of this research is to maximize chord-based composition possibilities given a relatively small amount of information. A transformational approach, based in group theory, was chosen, focusing on chord intervals as the components of a modified Markov process. The Markov process was modified to balance between average harmony, representing familiarity, and entropy, representing novelty. Uniform triadic transformations are suggested as a further extension of the transformational approach, improving the quality of tonality. The composition algorithms are demonstrated given a short chord progression and also given a larger database of albums by the Beatles. Results demonstrate capabilities and limitations of the algorithms.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030042

Authors: Yasushi Ota Naoki Mizutani

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers&rsquo;s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030041

Authors: Antonio Calcagnì Massimiliano Pastore Gianmarco Altoé

Recent technological advances have provided new settings to enhance individual-based data collection and computerized-tracking data have became common in many behavioral and social research. By adopting instantaneous tracking devices such as computer-mouse, wii, and joysticks, such data provide new insights for analysing the dynamic unfolding of response process. ssMousetrack is a R package for modeling and analysing computerized-tracking data by means of a Bayesian state-space approach. The package provides a set of functions to prepare data, fit the model, and assess results via simple diagnostic checks. This paper describes the package and illustrates how it can be used to model and analyse computerized-tracking data. A case study is also included to show the use of the package in empirical case studies.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030040

Authors: Daniel Jodlbauer Ulrich Langer Thomas Wick

Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature.

]]>Mathematical and Computational Applications doi: 10.3390/mca25030039

Authors: David Martínez-Galicia Alejandro Guerra-Hernández Nicandro Cruz-Ramírez Xavier Limón Francisco Grimaldo

Windowing is a sub-sampling method, originally proposed to cope with large datasets when inducing decision trees with the ID3 and C4.5 algorithms. The method exhibits a strong negative correlation between the accuracy of the learned models and the number of examples used to induce them, i.e., the higher the accuracy of the obtained model, the fewer examples used to induce it. This paper contributes to a better understanding of this behavior in order to promote windowing as a sub-sampling method for Distributed Data Mining. For this, the generalization of the behavior of windowing beyond decision trees is established, by corroborating the observed negative correlation when adopting inductive algorithms of different nature. Then, focusing on decision trees, the windows (samples) and the obtained models are analyzed in terms of Minimum Description Length (MDL), Area Under the ROC Curve (AUC), Kulllback&ndash;Leibler divergence, and the similitude metric Sim1; and compared to those obtained when using traditional methods: random, balanced, and stratified samplings. It is shown that the aggressive sampling performed by windowing, up to 3% of the original dataset, induces models that are significantly more accurate than those obtained from the traditional sampling methods, among which only the balanced sampling is comparable in terms of AUC. Although the considered informational properties did not correlate with the obtained accuracy, they provide clues about the behavior of windowing and suggest further experiments to enhance such understanding and the performance of the method, i.e., studying the evolution of the windows over time.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020038

Authors: Konrad Lang Sarah Stryeck David Bodruzic Manfred Stepponat Slave Trajanoski Ursula Winkler Stefanie Lindstaedt

Life sciences (LS) are advanced in research data management, since LS have established disciplinary tools for data archiving as well as metadata standards for data reuse. However, there is a lack of tools supporting the active research process in terms of data management and data analytics. This leads to tedious and demanding work to ensure that research data before and after publication are FAIR (findable, accessible, interoperable and reusable) and that analyses are reproducible. The initiative CyVerse US from the University of Arizona, US, supports all processes from data generation, management, sharing and collaboration to analytics. Within the presented project, we deployed an independent instance of CyVerse in Graz, Austria (CAT) in frame of the BioTechMed association. CAT helped to enhance and simplify collaborations between the three main universities in Graz. Presuming steps were (i) creating a distributed computational and data management architecture (iRODS-based), (ii) identifying and incorporating relevant data from researchers in LS and (iii) identifying and hosting relevant tools, including analytics software to ensure reproducible analytics using Docker technology for the researchers taking part in the initiative. This initiative supports research-related processes, including data management and analytics for LS researchers. It also holds the potential to serve other disciplines and provides potential for Austrian universities to integrate their infrastructure in the European Open Science Cloud.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020037

Authors: Vicente-Josué Aguilera-Rueda Nicandro Cruz-Ramírez Efrén Mezura-Montes

We present a novel bi-objective approach to address the data-driven learning problem of Bayesian networks. Both the log-likelihood and the complexity of each candidate Bayesian network are considered as objectives to be optimized by our proposed algorithm named Nondominated Sorting Genetic Algorithm for learning Bayesian networks (NS2BN) which is based on the well-known NSGA-II algorithm. The core idea is to reduce the implicit selection bias-variance decomposition while identifying a set of competitive models using both objectives. Numerical results suggest that, in stark contrast to the single-objective approach, our bi-objective approach is useful to find competitive Bayesian networks especially in the complexity. Furthermore, our approach presents the end user with a set of solutions by showing different Bayesian network and their respective MDL and classification accuracy results.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020036

Authors: Tilmann Glimm Jianying Zhang

We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020035

Authors: Tijani A. Apalara Aminu M. Nass Hamdan Al Sulaimani

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result is established without any additional internal or boundary damping term and without imposing any restrictive growth assumption on the nonlinear term, provided the wave speeds of the first equations of the system are equal.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020034

Authors: Zeinab Mansour Maryam Al-Towailb

In this paper, we introduce the complementary q-Lidstone interpolating polynomial of degree 2 n , which involves interpolating data at the odd-order q-derivatives. For this polynomial, we will provide a q-Peano representation of the error function. Next, we use these results to prove the existence of solutions of the complementary q-Lidstone boundary value problems. Some examples are included.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020033

Authors: Juan Carlos Cortés López Marc Jornet Sanz

Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate may be slow with the number of realizations and the discontinuity and peaked points of the target density may not be correctly captured. In this work, we analyze the applicability of a parametric method based on Monte Carlo simulation for the density estimation of certain random variable transformations. This approach has important applications in the setting of differential equations with input random parameters.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020032

Authors: Gustavo-Adolfo Vargas-Hákim Efrén Mezura-Montes Edgar Galván

This work presents the assessment of the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and one of its variants to optimize a proposed electric power production system. Such variant implements a chaotic model to generate the initial population, aiming to get a better distributed Pareto front. The considered power system is composed of solar, wind and natural gas power sources, being the first two renewable energies. Three conflicting objectives are considered in the problem: (1) power production, (2) production costs and (3) CO2 emissions. The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is also adopted in the comparison so as to enrich the empirical evidence by contrasting the NSGA-II versions against a non-Pareto-based approach. Spacing and Hypervolume are the chosen metrics to compare the performance of the algorithms under study. The obtained results suggest that there is no significant improvement by using the variant of the NSGA-II over the original version. Nonetheless, meaningful performance differences have been found between MOEA/D and the other two algorithms.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020031

Authors: Antonio Hervás Pedro Pablo Soriano Joan Guàrdia i Olmos Maribel Peró Roberto Capilla José Miguel Montañana

Currently, one of the challenges of universities is attracting talent in students, researchers, and teachers. The transition from high school to college requires a student to take a succession of decisions that will shape their future. For this reason, knowledge of the motivations of the students, their family, and their personal environment, to choose a particular degree and/or university to pursue their higher studies, would allow universities to efficiently adjust their recruitment strategies. In this article, a study was developed based on a structural equation model of the access to the Spanish Public University System (SUPE), which can help with supply and demand problems, recruitment actions and policies, and other strategic decisions. This was done through an extensive survey of first-year students of Spanish universities. The results allowed us to obtain the parameters of the model, which showed that the fit between the model and the data obtained were excellent at a global level and acceptable as well in all knowledge areas. The objective of the structural model was to provide a general view of the behavior of the students when deciding the degree and university in which they are going to study, and can help in the decision making of university leaders and to understand some behaviors of the Spanish Public University System.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020030

Authors: Aline Hosry Roger Nakad Sachin Bhalekar

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing the efficiency and validity of the method that we introduce.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020029

Authors: Desmond Adair Aigul Nagimova Martin Jaeger

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton&rsquo;s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020028

Authors: Maria Amélia R. Loja Joaquim I. Barbosa

This book constitutes the printed edition of the Special Issue Numerical and Symbolic Computation: Developments and Applications&mdash;2019, published by Mathematical and Computational Applications (MCA) and comprises a collection of articles related to works presented at the 4th International Conference in Numerical and Symbolic Computation&mdash;SYMCOMP 2019&mdash;that took place in Porto, Portugal, from April 11th to April 12th 2019 [...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25020027

Authors: Aliyu Muhammed Awwal Lin Wang Poom Kumam Hassan Mohammad Wiboonsak Watthayu

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve ℓ 1 -norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020026

Authors: Muhammad Akram Shumaiza José Alcantud

The Analytical Hierarchy Process (AHP) is arguably the most popular and factual approach for computing the weights of attributes in the multi-attribute decision-making environment. The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking family of multi-criteria decision-making techniques for evaluating a finite set of alternatives, that relies on multiple and inconsistent criteria. One of its main advantages is the variety of admissible preference functions that can measure the differences between alternatives, in response to the type and nature of the criteria. This research article studies a version of the PROMETHEE technique that encompasses multipolar assessments of the performance of each alternative (relative to the relevant criteria). As is standard practice, first we resort to the AHP technique in order to quantify the normalized weights of the attributes by the pairwise comparison of criteria. Afterwards the m-polar fuzzy PROMETHEE approach is used to rank the alternatives on the basis of conflicting criteria. Six types of generalized criteria preference functions are used to measure the differences or deviations of every pair of alternatives. A partial ranking of alternatives arises by computing the positive and negative outranking flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ranking of alternatives is achieved by the inspection of the net flow of alternatives, and this is known as PROMETHEE II. Two comparative analysis are performed. A first study checks the impact of different types of preference functions. It considers the usual criterion preference function for all criteria. In addition, we compare the technique that we develop with existing multi-attribute decision-making methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020025

Authors: Ana F. Mota Maria Amélia R. Loja Joaquim I. Barbosa José A. Rodrigues

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and the corresponding estimations of their material properties&mdash;in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure&rsquo;s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020023

Authors: Diana Gamboa Carlos E. Vázquez Paul J. Campos

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic &beta; -cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey&ndash;predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic &beta; -cell population growth and leukocyte population growth via the immune response. In this scenario, &beta; -cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and &beta; -cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell&ndash;cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the &beta; -cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness&mdash;that is, a condition wherein the pancreatic &beta; -cell population holds and there are no antigen cells labeled by the activated macrophages.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020024

Authors: Yue Wang Jinchuan Zhou Jingyong Tang

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020022

Authors: Milan Toma Rosalyn Chan-Akeley Christopher Lipari Sheng-Han Kuo

Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method of smoothed particle hydrodynamics is used to simulate the fluid flow, induced by the impact, simultaneously with finite element analysis to solve the large deformations in the brain model. Main Outcomes and Results: Mechanism of injury resulting in concussion is demonstrated. The locations with the highest stress values on the brain parenchyma are shown. Conclusions: Our simulations found that the damage to the brain resulting from the contrecoup injury is more severe than that resulting from the coup injury. Additionally, we show that the contrecoup injury does not always appear on the side opposite from where impact occurs.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020021

Authors: Mohammad Hosseini-Farid MaryamSadat Amiri-Tehrani-Zadeh Mohammadreza Ramzanpour Mariusz Ziejewski Ghodrat Karami

Knowing the precise material properties of intracranial head organs is crucial for studying the biomechanics of head injury. It has been shown that these biological tissues are significantly rate-dependent; hence, their material properties should be determined with respect to the range of deformation rate they experience. In this paper, a validated finite element human head model is used to investigate the biomechanics of the head in impact and blast, leading to traumatic brain injuries (TBI). We simulate the head under various directions and velocities of impacts, as well as helmeted and unhelmeted head under blast shock waves. It is demonstrated that the strain rates for the brain are in the range of 36 to 241 s&minus;1, approximately 1.9 and 0.86 times the resulting head acceleration under impacts and blast scenarios, respectively. The skull was found to experience a rate in the range of 14 to 182 s&minus;1, approximately 0.7 and 0.43 times the head acceleration corresponding to impact and blast cases. The results of these incident simulations indicate that the strain rates for brainstem and dura mater are respectively in the range of 15 to 338 and 8 to 149 s&minus;1. These findings provide a good insight into characterizing the brain tissue, cranial bone, brainstem and dura mater, and also selecting material properties in advance for computational dynamical studies of the human head.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020020

Authors: Francisco Solis Silvia Jerez Roberto Ku-Carrillo Sandra Delgadillo

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We discover an unexpected oscillatory parametrical behavior of the perturbed family.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020019

Authors: José A. Rodrigues

The microenvironment of the tumor is a key factor regulating tumor cell invasion and metastasis. The effects of physical factors in tumorigenesis is unclear. Shear stress, induced by liquid flow, plays a key role in proliferation, apoptosis, invasion, and metastasis of tumor cells. The mathematical models have the potential to elucidate the metastatic behavior of the cells&rsquo; membrane exposed to these microenvironment forces. Due to the shape configuration of the cancer cells, Non-uniform Rational B-splines (NURBS) lines are very adequate to define its geometric model. The Isogeometric Analysis allows a simplified transition of exact CAD models into the analysis avoiding the geometrical discontinuities of the traditional Galerkin traditional techniques. In this work, we use an isogeometric analysis to model the fluid-generated forces that tumor cells are exposed to in the vascular and tumor microenvironments, in the metastatic process. Using information provided by experimental tests in vitro, we present a suite of numerical experiments which indicate, for standard configurations, the metastatic behavior of cells exposed to such forces. The focus of this paper is strictly on geometrical sensitivities to the shear stress&rsquo; exhibition for the cell membrane, this being its innovation.

]]>Mathematical and Computational Applications doi: 10.3390/mca25020018

Authors: Weiming Zhang Dapan Li Xuyang Lou Dezhi Xu

In this paper, a prescribed performance adaptive backstepping control (PPABC) strategy is proposed to control the speed of a winding segmented permanent magnet linear synchronous motor (WS-PMLSM) with variable parameters and an unknown load disturbance. Firstly, a mathematical model of WS-PMLSM is provided. Then, the prescribed performance technique is introduced in the adaptive backstepping control to improve the transient performance and ensures the tracking error converges within a predetermined range. In addition, a constrained command filter is introduced to address the problem of differential expansion which exists in the traditional backstepping method, and a filter compensation signal is designed against the filter error. Moreover, the adaptive law is designed based on Lyapunov stability theory to estimate the uncertainties caused by parameter changes and load disturbances. The stability of the proposed control strategy is given and the simulation of the control system is carried out under the proposed PPABC in contrast with another backstepping control and traditional PI control. Finally, the experiment is conducted to further show the effectiveness of the proposed controller.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010017

Authors: Majid Ebrahimi Moghadam Hamid Falaghi Mahdi Farhadi

One of the effective ways of reducing power system losses is local compensation of part of the reactive power consumption by deploying shunt capacitor banks. Since the capacitor&rsquo;s impedance is frequency-dependent and it is possible to generate resonances at harmonic frequencies, it is important to provide an efficient method for the placement of capacitor banks in the presence of nonlinear loads which are the main cause of harmonic generation. This paper proposes a solution for a multi-objective optimization problem to address the optimal placement of capacitor banks in the presence of nonlinear loads, and it establishes a reasonable reconciliation between costs, along with improvement of harmonic distortion and a voltage index. In this paper, while using the harmonic power flow method to calculate the electrical quantities of the grid in terms of harmonic effects, the non-dominated sorting genetic (NSGA)-II multi-objective genetic optimization algorithm was used to obtain a set of solutions named the Pareto front for the problem. To evaluate the effectiveness of the proposed method, the problem was tested for an IEEE 18-bus system. The results were compared with the methods used in eight other studies. The simulation results show the considerable efficiency and superiority of the proposed flexible method over other methods.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010016

Authors: Corina Plata Pablo J. Prieto Ramon Ramirez-Villalobos Luis N. Coria

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010015

Authors: Daniele Polucci Michele Marchetti Simone Fiori

The present paper deals with nonlinear, non-monotonic data regression. This paper introduces an efficient algorithm to perform data transformation from non-monotonic to monotonic to be paired with a statistical bivariate regression method. The proposed algorithm is applied to a number of synthetic and real-world non-monotonic data sets to test its effectiveness. The proposed novel non-isotonic regression algorithm is also applied to a collection of data about strontium isotope stratigraphy and compared to a LOWESS regression tool.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010014

Authors: Youcef Benmessaoud Daoud Ouamara Frédéric Dubas Mickael Hilairet

This paper investigates the permanent-magnet (PM) eddy-current losses in multi-phase PM synchronous machines (PMSM) with concentric winding and surface-mounted PMs. A hybrid multi-layer model, combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell&ndash;Fourier method (i.e., the formal resolution of Maxwell&rsquo;s equations by using the separation of variables method and the Fourier&rsquo;s series), performs the eddy-current loss calculations. First, the magnetic flux density was obtained from the 2-D generic MEC and then subjected to the Fast Fourier Transform (FFT). The semi-analytical model includes the automatic mesh of static/moving zones, the saturation effect and zones connection in accordance with rotor motion based on a new approach called &ldquo;Air-gap sliding line technic&rdquo;. The results of the hybrid multi-layer model were compared with those obtained by three-dimensional (3-D) nonlinear finite-element analysis (FEA). The PM eddy-current losses were estimated on different paths for different segmentations as follow: (i) one segment (no segmentation), (ii) five axial segments, and (iii) two circumferential segments, where the non-uniformity loss distribution is shown. The top of PMs presents a higher quantity of losses compared to the bottom.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010013

Authors: Vania Lara-Ortiz Ivan Salgado David Cruz-Ortiz Alejandro Guarneros Misael Magos-Sanchez Isaac Chairez

This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state restrictions in the device articulations; this means the maximum and minimum angular ranges, to avoid any possible damage to the structure. The controller uses an active compensation method to estimate the unknown dynamics of the WBRD by means of an extended state observer. The sequence of movements for the gait cycle of a WBRD is represented as a class of hybrid system by alternative reference frameworks placed at the first and the last link. The stability analysis employs a class of Hybrid Barrier Lyapunov Function to ensure the fulfillment of the angular restrictions in the robotic device. The proposed controller is evaluated using a numerical simulation system based on the virtual version of the WBRD. Moreover, experimental results confirmed that the H-ADRC may endorse the realization of the proposed gait cycle despite the presence of perturbations and modeling uncertainties. The H-ADRC is compared against a proportional derivative (PD) controller and a proportional-integral-derivative (PID) controller. The H-ADRC shows a superior performance as a consequence of the estimation provided by the homogeneous extended state observer.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010012

Authors: Fábio A. O. Fernandes Ricardo J. Alves de Sousa Mariusz Ptak Johannes Wilhelm

Every year, thousands of people die in the European Union as a direct result of road accidents. Helmets are one of the most important types of personal safety gear. The ECE R22.05 standard, adopted in 2000, is responsible for the certification of motorcycle helmets in the European Union and in many other countries. Two decades later, it is still being used with the same requirements, without any update. The aim of this work is to evaluate the efficacy of a motorcycle helmet certified by such standard, using computational models as an assessment tool. First, a finite element model of a motorcycle helmet available on the market was developed and validated by simulating the same impacts required by the standard. Then, a finite element model of the human head is used as an injury prediction tool to assess its safety performance. Results indicate a significant risk of brain injury, which is in accordance with previous studies available in the literature. Therefore, this work underlines and emphasizes the need of improving the requirements of ECE R22.05.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010011

Authors: Abdelhak Mekahlia Eric Semail Franck Scuiller Hussein Zahr

For three-phase induction machines supplied by sinusoidal current, it is usual to model the n-bar squirrel-cage by an equivalent two-phase circuit. For a multiphase induction machine which can be supplied with different harmonics of current, the reduced-order model of the rotor must be more carefully chosen in order to predict the pulsations of torque. The proposed analysis allows to avoid a wrong design with non-sinusoidal magnetomotive forces. An analytical approach is proposed and confirmed by Finite-Element modelling at first for a three-phase induction machine and secondly for a five-phase induction machine.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010010

Authors: Behnaz Sheikh Hoseini Muhammad Akram Mehrnaz Sheikh Hosseini Hossein Rashmanlou Rajab Ali Borzooei

Graph models are found everywhere in natural and human made structures, including process dynamics in physical, biological and social systems. The product of graphs are appropriately used in several combinatorial applications and in the formation of different structural models. In this paper, we present a new product of graphs, namely, maximal product of two vague graphs. Then we describe certain concepts, including strongly, completely, regularity and connectedness on a maximal product of vague graphs. Further, we consider some results of edge regular and totally edge regular in a maximal product of vague graphs. Finally, we present an application for optimization of the biomass based on a maximal product of vague graphs.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010009

Authors: Nikolay Banichuk Svetlana Ivanova Evgeny Makeev Juha Jeronen Tero Tuovinen

The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement. Then, the panel displacement, accounting also for the fluid&ndash;structure interaction, is analyzed with the help of the weak form of the governing partial differential equation, using a Galerkin method. In the first part of this paper, we represent the traveling panel by a single partial differential equation in weak form, using an added-mass approximation of the exact fluid reaction. In the second part, we apply a Galerkin method for dynamic stability analysis of the panel, and present an analytical investigation of static stability loss (divergence, buckling) based on the added-mass model.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010008

Authors: Muhammad Akram Danish Saleem Talal Al-Hawary

In a network model, the evaluation information given by decision makers are occasionally of types: yes, abstain, no, and refusal. To deal with such problems, we use mathematical models based on picture fuzzy sets. The spherical fuzzy model is more versatile than the picture fuzzy model as it broadens the space of uncertain and vague information, due to its outstanding feature of vast space of participation of acceptable triplets. Graphs are a mathematical representation of networks. Thus to deal with many real-world phenomena represented by networks, spherical fuzzy graphs can be used to model different practical scenarios in a more flexible manner than picture fuzzy graphs. In this research article, we discuss two operations on spherical fuzzy graphs (SFGs), namely, symmetric difference and rejection; and develop some results regarding their degrees and total degrees. We describe certain concepts of irregular SFGs with several important properties. Further, we present an application of SFGs in decision making.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010007

Authors: Abdel-Rahman Hedar Wael Deabes Majid Almaraashi Hesham H. Amin

Enhancing Evolutionary Algorithms (EAs) using mathematical elements significantly contribute to their development and control the randomness they are experiencing. Moreover, the automation of the primary process steps of EAs is still one of the hardest problems. Specifically, EAs still have no robust automatic termination criteria. Moreover, the highly random behavior of some evolutionary operations should be controlled, and the methods should invoke advanced learning process and elements. As follows, this research focuses on the problem of automating and controlling the search process of EAs by using sensing and mathematical mechanisms. These mechanisms can provide the search process with the needed memories and conditions to adapt to the diversification and intensification opportunities. Moreover, a new quadratic coding and quadratic search operator are invoked to increase the local search improving possibilities. The suggested quadratic search operator uses both regression and Radial Basis Function (RBF) neural network models. Two evolutionary-based methods are proposed to evaluate the performance of the suggested enhancing elements using genetic algorithms and evolution strategies. Results show that for both the regression, RBFs and quadratic techniques could help in the approximation of high-dimensional functions with the use of a few adjustable parameters for each type of function. Moreover, the automatic termination criteria could allow the search process to stop appropriately.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010006

Authors: MCA Editorial Office

The editorial team greatly appreciates the reviewers who have dedicated their considerable time and expertise to the journal’s rigorous editorial process over the past 12 months, regardless of whether the papers are finally published or not[...]

]]>Mathematical and Computational Applications doi: 10.3390/mca25010005

Authors: Alberto Fraile Roberto Martínez Daniel Fernández

Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we present a simple representation of prime numbers in two dimensions that allows us to formulate a number of conjectures that may lead to important avenues in the field of research on prime numbers. In particular, although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps between them present a remarkable and intriguing property: a clear exponential decay in the frequency of gaps vs. gap size. The smaller the gaps, the more frequently they appear. Additionally, the sequence of zeroes, despite being non-consecutive numbers, contains a number of primes approximately equal to n / log n , n being the number of terms in the sequence.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010004

Authors: Mehdi Karami Khorramabadi Majid Yarahmadi Mojtaba Ghiyasi

It is considerably important to calculate the cost efficiency in data envelopment analysis for the efficiency evaluation of decision-making units. The present paper develops the classical cost efficiency model in which all the input prices are constant and certain for each decision-making unit, considering undesirable outputs under the semi-disposability assumption. The proposed models are interval and uncertain under the constant returns to scale and also variable returns to scale assumptions, for the easy solution of which, their lower and upper bounds are obtained on the basis of the theorem presented in the text. In order to simulate the proposed models and show their scientific capabilities, additionally, 56 electricity producing thermal power plants in Iran were studied in 2015. Results of the present study show that under both assumptions of constant returns to scale and variable returns to scale, the highest cost efficiency bounds belonged to the combined and steam cycle power plants. Moreover, the average of lower and upper cost efficiency bounds of the power plants under study were 34% and 35%, respectively, in 2015, under the constant returns to scale assumption, and 52% and 54%, respectively, under the variable returns to scale assumption.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010003

Authors: Carlos Ignacio Hernández Castellanos Oliver Schütze Jian-Qiao Sun Sina Ober-Blöbaum

In this paper, we present a novel evolutionary algorithm for the computation of approximate solutions for multi-objective optimization problems. These solutions are of particular interest to the decision-maker as backup solutions since they can provide solutions with similar quality but in different regions of the decision space. The novel algorithm uses a subpopulation approach to put pressure towards the Pareto front while exploring promissory areas for approximate solutions. Furthermore, the algorithm uses an external archiver to maintain a suitable representation in both decision and objective space. The novel algorithm is capable of computing an approximation of the set of interest with good quality in terms of the averaged Hausdorff distance. We underline the statements on some academic problems from literature and an application in non-uniform beams.

]]>Mathematical and Computational Applications doi: 10.3390/mca25010002

Authors: Abigail Bowers Jared Bunn Myles Kim

Computational models for multicellular biological systems, in both in vitro and in vivo environments, require solving systems of differential equations to incorporate molecular transport and their reactions such as release, uptake, or decay. Examples can be found from drugs, growth nutrients, and signaling factors. The systems of differential equations frequently fall into the category of the diffusion-reaction system due to the nature of the spatial and temporal change. Due to the complexity of equations and complexity of the modeled systems, an analytical solution for the systems of the differential equations is not possible. Therefore, numerical calculation schemes are required and have been used for multicellular biological systems such as bacterial population dynamics or cancer cell dynamics. Finite volume methods in conjunction with agent-based models have been popular choices to simulate such reaction-diffusion systems. In such implementations, the reaction occurs within each finite volume and finite volumes interact with one another following the law of diffusion. The characteristic of the reaction can be determined by the agents in the finite volume. In the case of cancer cell growth dynamics, it is observed that cell behavior can be different by a matter of a few cell size distances because of the chemical gradient. Therefore, in the modeling of such systems, the spatial resolution must be comparable to the cell size. Such spatial resolution poses an extra challenge in the development and execution of the computational model due to the agents sitting over multiple finite volumes. In this article, a few computational methods for cell surface-based reaction for the finite volume method will be introduced and tested for their performance in terms of accuracy and computation speed.

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