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Math. Comput. Appl., Volume 25, Issue 3 (September 2020) – 11 articles

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Open AccessArticle
Voigt Transform and Umbral Image
Math. Comput. Appl. 2020, 25(3), 49; https://doi.org/10.3390/mca25030049 - 31 Jul 2020
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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
Open AccessFeature PaperArticle
Robust qLPV Tracking Fault-Tolerant Control of a 3 DOF Mechanical Crane
Math. Comput. Appl. 2020, 25(3), 48; https://doi.org/10.3390/mca25030048 - 28 Jul 2020
Viewed by 246
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 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
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Open AccessArticle
Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem
Math. Comput. Appl. 2020, 25(3), 47; https://doi.org/10.3390/mca25030047 - 24 Jul 2020
Viewed by 311
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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Open AccessProject Report
How Europe Is Preparing Its Core Solution for Exascale Machines and a Global, Sovereign, Advanced Computing Platform
Math. Comput. Appl. 2020, 25(3), 46; https://doi.org/10.3390/mca25030046 - 20 Jul 2020
Viewed by 263
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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Open AccessFeature PaperArticle
Introducing BisQ, A Bicoherence-Based Nonlinear Index to Explore the Heart Rhythm
Math. Comput. Appl. 2020, 25(3), 45; https://doi.org/10.3390/mca25030045 - 18 Jul 2020
Viewed by 265
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 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 < 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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Open AccessArticle
A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model
Math. Comput. Appl. 2020, 25(3), 44; https://doi.org/10.3390/mca25030044 - 16 Jul 2020
Viewed by 195
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
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Open AccessFeature PaperArticle
A Transformational Modified Markov Process for Chord-Based Algorithmic Composition
Math. Comput. Appl. 2020, 25(3), 43; https://doi.org/10.3390/mca25030043 - 10 Jul 2020
Viewed by 250
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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Open AccessArticle
Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach
Math. Comput. Appl. 2020, 25(3), 42; https://doi.org/10.3390/mca25030042 - 10 Jul 2020
Viewed by 244
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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Open AccessFeature PaperArticle
ssMousetrack—Analysing Computerized Tracking Data via Bayesian State-Space Models in R
Math. Comput. Appl. 2020, 25(3), 41; https://doi.org/10.3390/mca25030041 - 09 Jul 2020
Viewed by 232
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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Open AccessFeature PaperArticle
Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems
Math. Comput. Appl. 2020, 25(3), 40; https://doi.org/10.3390/mca25030040 - 07 Jul 2020
Viewed by 251
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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Open AccessFeature PaperArticle
Windowing as a Sub-Sampling Method for Distributed Data Mining
Math. Comput. Appl. 2020, 25(3), 39; https://doi.org/10.3390/mca25030039 - 30 Jun 2020
Viewed by 290
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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