Mathematical and Computational Applications

18 pages, 8519 KiB

Open AccessArticle

Computing Brain White and Grey Matter Injury Severity in a Traumatic Fall

by Christophe Bastien, Clive Neal-Sturgess, Huw Davies and Xiang Cheng

Math. Comput. Appl. 2020, 25(3), 61; https://doi.org/10.3390/mca25030061 - 22 Sep 2020

Cited by 4 | Viewed by 4476

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) [...] Read more.

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. Full article

(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)

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30 pages, 656 KiB

Open AccessArticle

Arbitrage Bounds on Currency Basket Options

by Yi Hong

Math. Comput. Appl. 2020, 25(3), 60; https://doi.org/10.3390/mca25030060 - 17 Sep 2020

Viewed by 2558

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Intelligent Computation and Its Applications in Financial Technology)

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20 pages, 1510 KiB

Open AccessArticle

Volatility Forecasting Based on Cyclical Two-Component Model: Evidence from Chinese Futures Markets and Sector Stocks

by Conghua Wen and Junwei Wei

Math. Comput. Appl. 2020, 25(3), 59; https://doi.org/10.3390/mca25030059 - 10 Sep 2020

Viewed by 2209

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Intelligent Computation and Its Applications in Financial Technology)

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16 pages, 611 KiB

Open AccessFeature PaperArticle

Bot Detection on Social Networks Using Persistent Homology

by Minh Nguyen, Mehmet Aktas and Esra Akbas

Math. Comput. Appl. 2020, 25(3), 58; https://doi.org/10.3390/mca25030058 - 4 Sep 2020

Cited by 5 | Viewed by 4127

Abstract

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 [...] Read more.

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. Full article

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20 pages, 4911 KiB

Open AccessArticle

Sensorless Speed Tracking of a Brushless DC Motor Using a Neural Network

by Oscar-David Ramírez-Cárdenas and Felipe Trujillo-Romero

Math. Comput. Appl. 2020, 25(3), 57; https://doi.org/10.3390/mca25030057 - 4 Sep 2020

Cited by 12 | Viewed by 4147

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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12 pages, 1697 KiB

Open AccessFeature PaperArticle

Simultaneous Optimal Estimation of Roughness and Minor Loss Coefficients in a Pipeline

by Ildeberto Santos-Ruiz, Francisco-Ronay López-Estrada, Vicenç Puig and Guillermo Valencia-Palomo

Math. Comput. Appl. 2020, 25(3), 56; https://doi.org/10.3390/mca25030056 - 1 Sep 2020

Cited by 10 | Viewed by 5360

Abstract

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–White equation for an operating [...] Read more.

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–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–Weisbach equation for a set of steady-state measurements. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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24 pages, 2893 KiB

Open AccessArticle

Analysis and Comparison of Fuzzy Models and Observers for DC-DC Converters Applied to a Distillation Column Heating Actuator

by Mario Heras-Cervantes, Adriana del Carmen Téllez-Anguiano, Juan Anzurez-Marín and Elisa Espinosa-Juárez

Math. Comput. Appl. 2020, 25(3), 55; https://doi.org/10.3390/mca25030055 - 28 Aug 2020

Cited by 2 | Viewed by 2279

Abstract

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 [...] Read more.

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–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

^{®}

simulations to verify the observers convergence and analyze their response under system disturbances. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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25 pages, 638 KiB

Open AccessArticle

Relaxed Projection Methods with Self-Adaptive Step Size for Solving Variational Inequality and Fixed Point Problems for an Infinite Family of Multivalued Relatively Nonexpansive Mappings in Banach Spaces

by Safeer Hussain Khan, Timilehin Opeyemi Alakoya and Oluwatosin Temitope Mewomo

Math. Comput. Appl. 2020, 25(3), 54; https://doi.org/10.3390/mca25030054 - 24 Aug 2020

Cited by 33 | Viewed by 2778

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Section Natural Sciences)

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16 pages, 760 KiB

Open AccessArticle

The Application of Stock Index Price Prediction with Neural Network

by Penglei Gao, Rui Zhang and Xi Yang

Math. Comput. Appl. 2020, 25(3), 53; https://doi.org/10.3390/mca25030053 - 18 Aug 2020

Cited by 41 | Viewed by 11207

Abstract

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 [...] Read more.

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’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. Full article

(This article belongs to the Special Issue Intelligent Computation and Its Applications in Financial Technology)

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19 pages, 599 KiB

Open AccessArticle

Effects of Convection on Sisko Fluid with Peristalsis in an Asymmetric Channel

by Naveed Iqbal, Humaira Yasmin, Bawfeh K. Kometa and Adel A. Attiya

Math. Comput. Appl. 2020, 25(3), 52; https://doi.org/10.3390/mca25030052 - 17 Aug 2020

Cited by 14 | Viewed by 2572

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics and Heat & Mass Transfer)

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13 pages, 47242 KiB

Open AccessArticle

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

by Jesus R. Pulido-Luna, Jorge A. López-Rentería and Nohe R. Cazarez-Castro

Math. Comput. Appl. 2020, 25(3), 51; https://doi.org/10.3390/mca25030051 - 14 Aug 2020

Cited by 5 | Viewed by 2554

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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20 pages, 1645 KiB

Open AccessFeature PaperArticle

Exponential Perturbative Expansions and Coordinate Transformations

by Ana Arnal, Fernando Casas and Cristina Chiralt

Math. Comput. Appl. 2020, 25(3), 50; https://doi.org/10.3390/mca25030050 - 13 Aug 2020

Cited by 1 | Viewed by 2469

Abstract

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–Magnus expansion for periodic systems, the quantum averaging technique, and the Lie–Deprit perturbative algorithms. Even the standard perturbation theory [...] Read more.

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–Magnus expansion for periodic systems, the quantum averaging technique, and the Lie–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 Schrödinger equation. Full article

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12 pages, 257 KiB

Open AccessArticle

Voigt Transform and Umbral Image

by Silvia Licciardi, Rosa Maria Pidatella, Marcello Artioli and Giuseppe Dattoli

Math. Comput. Appl. 2020, 25(3), 49; https://doi.org/10.3390/mca25030049 - 31 Jul 2020

Cited by 2 | Viewed by 1951

Abstract

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 [...] Read more.

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. Full article

12 pages, 467 KiB

Open AccessFeature PaperArticle

Robust qLPV Tracking Fault-Tolerant Control of a 3 DOF Mechanical Crane

by Francisco-Ronay López-Estrada, Oscar Santos-Estudillo, Guillermo Valencia-Palomo, Samuel Gómez-Peñate and Carlos Hernández-Gutiérrez

Math. Comput. Appl. 2020, 25(3), 48; https://doi.org/10.3390/mca25030048 - 28 Jul 2020

Cited by 12 | Viewed by 3211

Abstract

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 [...] Read more.

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_{\infty}

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. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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24 pages, 2170 KiB

Open AccessArticle

Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem

by Guash Haile Taddele, Poom Kumam, Anteneh Getachew Gebrie and Kanokwan Sitthithakerngkiet

Math. Comput. Appl. 2020, 25(3), 47; https://doi.org/10.3390/mca25030047 - 24 Jul 2020

Cited by 7 | Viewed by 2492

Abstract

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 [...] Read more.

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. Full article

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8 pages, 2929 KiB

Open AccessProject Report

How Europe Is Preparing Its Core Solution for Exascale Machines and a Global, Sovereign, Advanced Computing Platform

by Mario Kovač, Philippe Notton, Daniel Hofman and Josip Knezović

Math. Comput. Appl. 2020, 25(3), 46; https://doi.org/10.3390/mca25030046 - 20 Jul 2020

Cited by 6 | Viewed by 4913

Abstract

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’s and national resources on HPC to acquire, build and deploy [...] Read more.

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’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’s first HPC Systems on Chip and accelerators with its unique Common Platform (CP) technology. One of EPI’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. Full article

(This article belongs to the Special Issue High-Performance Computing 2020)

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15 pages, 3733 KiB

Open AccessFeature PaperArticle

Introducing BisQ, A Bicoherence-Based Nonlinear Index to Explore the Heart Rhythm

by José Luis Hernández-Caceres, René Iván González-Fernández, Marlis Ontivero-Ortega and Guido Nolte

Math. Comput. Appl. 2020, 25(3), 45; https://doi.org/10.3390/mca25030045 - 18 Jul 2020

Cited by 1 | Viewed by 2905

Abstract

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 [...] Read more.

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 L_mean, 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 L_mean. 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 < 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. Full article

(This article belongs to the Special Issue Heart Rate Variability: Algorithms and Software Tools)

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16 pages, 614 KiB

Open AccessArticle

A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model

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

Math. Comput. Appl. 2020, 25(3), 44; https://doi.org/10.3390/mca25030044 - 16 Jul 2020

Cited by 6 | Viewed by 2567

Abstract

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–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables [...] Read more.

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–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. Full article

(This article belongs to the Special Issue Advanced Mathematics and Computational Applications in Control Systems Engineering)

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14 pages, 608 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Transformational Modified Markov Process for Chord-Based Algorithmic Composition

by Meirav Amram, Etan Fisher, Shai Gul and Uzi Vishne

Math. Comput. Appl. 2020, 25(3), 43; https://doi.org/10.3390/mca25030043 - 10 Jul 2020

Cited by 2 | Viewed by 2842

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Section Natural Sciences)

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15 pages, 456 KiB

Open AccessArticle

Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

by Yasushi Ota and Naoki Mizutani

Math. Comput. Appl. 2020, 25(3), 42; https://doi.org/10.3390/mca25030042 - 10 Jul 2020

Cited by 1 | Viewed by 2274

Abstract

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the [...] Read more.

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’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. Full article

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18 pages, 797 KiB

Open AccessFeature PaperArticle

ssMousetrack—Analysing Computerized Tracking Data via Bayesian State-Space Models in R

by Antonio Calcagnì, Massimiliano Pastore and Gianmarco Altoé

Math. Comput. Appl. 2020, 25(3), 41; https://doi.org/10.3390/mca25030041 - 9 Jul 2020

Viewed by 2426

Abstract

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 [...] Read more.

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. Full article

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21 pages, 989 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems

by Daniel Jodlbauer, Ulrich Langer and Thomas Wick

Math. Comput. Appl. 2020, 25(3), 40; https://doi.org/10.3390/mca25030040 - 7 Jul 2020

Cited by 16 | Viewed by 3483

Abstract

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, [...] Read more.

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. Full article

(This article belongs to the Special Issue High-Performance Computing 2020)

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20 pages, 426 KiB

Open AccessFeature PaperArticle

Windowing as a Sub-Sampling Method for Distributed Data Mining

by David Martínez-Galicia, Alejandro Guerra-Hernández, Nicandro Cruz-Ramírez, Xavier Limón and Francisco Grimaldo

Math. Comput. Appl. 2020, 25(3), 39; https://doi.org/10.3390/mca25030039 - 30 Jun 2020

Cited by 1 | Viewed by 3260

Abstract

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 [...] Read more.

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–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. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications)

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Math. Comput. Appl., Volume 25, Issue 3 (September 2020) – 23 articles

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