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Volume 26, June

Math. Comput. Appl., Volume 26, Issue 3 (September 2021) – 17 articles

Cover Story (view full-size image): Ambulance response time (ART) is a key measurement of emergency medical services (EMS) because many victims require care within adequate time (e.g., cardiac arrest). Using retrospective data about emergencies (e.g., hour, location) and external data (i.e., traffic and weather data), this paper predicts the response time of ambulances while preserving the location privacy of the victim(s). The geo-indistinguishability privacy model was applied to sanitize each emergency scene, which is a state-of-the-art formal notion based on differential privacy. While predicting ART is a means to allow EMS to save more lives, this paper evaluates and discovers that it is also possible to do so while preserving victims’ location privacy. View this paper
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Article
Theory of Functional Connections Applied to Linear ODEs Subject to Integral Constraints and Linear Ordinary Integro-Differential Equations
Math. Comput. Appl. 2021, 26(3), 65; https://doi.org/10.3390/mca26030065 - 12 Sep 2021
Viewed by 270
Abstract
This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, [...] Read more.
This study shows how the Theory of Functional Connections (TFC) allows us to obtain fast and highly accurate solutions to linear ODEs involving integrals. Integrals can be constraints and/or terms of the differential equations (e.g., ordinary integro-differential equations). This study first summarizes TFC, a mathematical procedure to obtain constrained expressions. These are functionals representing all functions satisfying a set of linear constraints. These functionals contain a free function, g(x), representing the unknown function to optimize. Two numerical approaches are shown to numerically estimate g(x). The first models g(x) as a linear combination of a set of basis functions, such as Chebyshev or Legendre orthogonal polynomials, while the second models g(x) as a neural network. Meaningful problems are provided. In all numerical problems, the proposed method produces very fast and accurate solutions. Full article
(This article belongs to the Section Engineering)
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Article
A Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem
Math. Comput. Appl. 2021, 26(3), 64; https://doi.org/10.3390/mca26030064 - 10 Sep 2021
Viewed by 201
Abstract
The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed [...] Read more.
The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed to tackle the drawbacks of the EDAs, i.e., the lack of diversity of solutions and poor ability of exploitation. The hybridization approach, used in this investigation, uses a distance based ranking model and the moth-flame algorithm. The distance based ranking model is in charge of modelling the solution space distribution, through an exponential function, by measuring the distance between solutions; meanwhile, the heuristic moth-flame determines who would be the offspring, with a spiral function that identifies the new locations for the new solutions. Based on the results, the proposed scheme, called QCEDA, works to enhance the performance of those other EDAs that use complex probability models. The dispersion results of the QCEDA scheme are less than the other algorithms used in the comparison section. This means that the solutions found by the QCEDA are more concentrated around the best value than other algorithms, i.e., the average of the solutions of the QCEDA converges better than other approaches to the best found value. Finally, as a conclusion, the hybrid EDAs have a better performance, or equal in effectiveness, than the so called pure EDAs. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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Article
On the Elicitability and Risk Model Comparison of Emerging Markets Equities
Math. Comput. Appl. 2021, 26(3), 63; https://doi.org/10.3390/mca26030063 - 06 Sep 2021
Viewed by 264
Abstract
The need for comparative backtesting in the Basel III framework presents the challenge for ranking of internal value-at-risk (VaR) and expected shortfall (ES) models. We use a joint loss function to score the elicitable joint VaR and ES models to select competing tail [...] Read more.
The need for comparative backtesting in the Basel III framework presents the challenge for ranking of internal value-at-risk (VaR) and expected shortfall (ES) models. We use a joint loss function to score the elicitable joint VaR and ES models to select competing tail risk models for the top 9 emerging markets equities and the emerging markets composite index. We achieve this with the model confidence set (MCS) procedure. Our analysis span two sub-sample periods representing turbulent (Eurozone and Global Financial crises periods) and tranquil (post-Global Financial crisis period) market conditions. We find that many of the markets risk models are time-invariant and independent of market conditions. But for China and South Africa this is not true because their risk models are time-varying, market conditions-dependent, percentile-dependent and heterogeneous. Tail risk modelling may be difficult compared to other markets. The resemblance between China and South Africa can stem from the closeness between their equities composition. However, generally, there is evidence of more homogeneity than heterogeneity in risk models. This is indicated by a minimum of three models (out of six) per equity in most of the countries. This may ease the burden for risk managers to find the optimal set of models. Our study is important for internal risk modelling, regulatory oversight, reduce regulatory arbitrage and may bolster confidence in international investors with respect to emerging markets equities. Full article
(This article belongs to the Special Issue Mathematical and Computational Applications in Finance and Economics)
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Article
On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions
Math. Comput. Appl. 2021, 26(3), 62; https://doi.org/10.3390/mca26030062 - 29 Aug 2021
Viewed by 198
Abstract
In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. [...] Read more.
In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best. Full article
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Article
New Stable, Explicit, Shifted-Hopscotch Algorithms for the Heat Equation
Math. Comput. Appl. 2021, 26(3), 61; https://doi.org/10.3390/mca26030061 - 26 Aug 2021
Viewed by 245
Abstract
Our goal was to find more effective numerical algorithms to solve the heat or diffusion equation. We created new five-stage algorithms by shifting the time of the odd cells in the well-known odd-even hopscotch algorithm by a half time step and applied different [...] Read more.
Our goal was to find more effective numerical algorithms to solve the heat or diffusion equation. We created new five-stage algorithms by shifting the time of the odd cells in the well-known odd-even hopscotch algorithm by a half time step and applied different formulas in different stages. First, we tested 105 = 100,000 different algorithm combinations in case of small systems with random parameters, and then examined the competitiveness of the best algorithms by testing them in case of large systems against popular solvers. These tests helped us find the top five combinations, and showed that these new methods are, indeed, effective since quite accurate and reliable results were obtained in a very short time. After this, we verified these five methods by reproducing a recently found non-conventional analytical solution of the heat equation, then we demonstrated that the methods worked for nonlinear problems by solving Fisher’s equation. We analytically proved that the methods had second-order accuracy, and also showed that one of the five methods was positivity preserving and the others also had good stability properties. Full article
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Article
Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
Math. Comput. Appl. 2021, 26(3), 60; https://doi.org/10.3390/mca26030060 - 25 Aug 2021
Viewed by 261
Abstract
This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of [...] Read more.
This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of view, the extension consists of the addition to each phase equation of a term depending on the gradient of the pressure of the other phase, leading to a coupled system of differential equations. The obtained system is much more involved than the classical Darcy system since it involves the Forchheimer equation in addition to the Darcy one. This model is more appropriate when there is a substantial difference between the phases’ velocities, for instance in the case of gas/water phases, and applications in oil recovery using gas flooding. Based on the Buckley–Leverett theory, including capillary pressure, we derive an explicit expression of the phases’ velocities and fractional water flows in terms of the gradient of the capillary pressure, and the total constant velocity. Various scenarios are considered, and the respective numerical simulations are presented. In particular, comparisons with the classical models (without phase coupling) are provided in terms of breakthrough time among others. Eventually, we provide a post-processing method for the derivation of the solution of the new coupled system using the classical non-coupled system. This method is of interest for industry since it allows for including the phase coupling approach in existing numerical codes and software (designed for solving classical models) without major technical changes. Full article
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Article
A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems
Math. Comput. Appl. 2021, 26(3), 59; https://doi.org/10.3390/mca26030059 - 24 Aug 2021
Viewed by 208
Abstract
An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y=w2y. [...] Read more.
An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y=w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics. Full article
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Article
Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function
Math. Comput. Appl. 2021, 26(3), 58; https://doi.org/10.3390/mca26030058 - 18 Aug 2021
Viewed by 234
Abstract
This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving [...] Read more.
This paper gives new integrals related to a class of special functions. This paper also showcases the derivation of definite integrals involving the quotient of functions with powers and the exponential function expressed in terms of the Lerch function and special cases involving fundamental constants. The goal of this paper is to expand upon current tables of definite integrals with the aim of assisting researchers in need of new integral formulae. Full article
Article
Using the Evolution Operator to Classify Evolution Algebras
Math. Comput. Appl. 2021, 26(3), 57; https://doi.org/10.3390/mca26030057 - 05 Aug 2021
Viewed by 295
Abstract
Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A [...] Read more.
Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is given and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions is also analyzed and constructed. Full article
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Article
Preserving Geo-Indistinguishability of the Emergency Scene to Predict Ambulance Response Time
Math. Comput. Appl. 2021, 26(3), 56; https://doi.org/10.3390/mca26030056 - 04 Aug 2021
Viewed by 493
Abstract
Emergency medical services (EMS) provide crucial emergency assistance and ambulatory services. One key measurement of EMS’s quality of service is their ambulances’ response time (ART), which generally refers to the period between EMS notification and the moment an ambulance arrives on the scene. [...] Read more.
Emergency medical services (EMS) provide crucial emergency assistance and ambulatory services. One key measurement of EMS’s quality of service is their ambulances’ response time (ART), which generally refers to the period between EMS notification and the moment an ambulance arrives on the scene. Due to many victims requiring care within adequate time (e.g., cardiac arrest), improving ARTs is vital. This paper proposes to predict ARTs using machine-learning (ML) techniques, which could be used as a decision-support system by EMS to allow a dynamic selection of ambulance dispatch centers. However, one well-known predictor of ART is the location of the emergency (e.g., if it is urban or rural areas), which is sensitive data because it can reveal who received care and for which reason. Thus, we considered the ‘input perturbation’ setting in the privacy-preserving ML literature, which allows EMS to sanitize each location data independently and, hence, ML models are trained only with sanitized data. In this paper, geo-indistinguishability was applied to sanitize each emergency location data, which is a state-of-the-art formal notion based on differential privacy. To validate our proposals, we used retrospective data of an EMS in France, namely Departmental Fire and Rescue Service of Doubs, and publicly available data (e.g., weather and traffic data). As shown in the results, the sanitization of location data and the perturbation of its associated features (e.g., city, distance) had no considerable impact on predicting ARTs. With these findings, EMSs may prefer using and/or sharing sanitized datasets to avoid possible data leakages, membership inference attacks, or data reconstructions, for example. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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Article
Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation
Math. Comput. Appl. 2021, 26(3), 55; https://doi.org/10.3390/mca26030055 - 29 Jul 2021
Viewed by 284
Abstract
The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It [...] Read more.
The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-difference scheme is conditionally stable and converges to the first order. Using the fractional Riccati equation as an example, the computational accuracy of the numerical method is analyzed. It is shown that with an increase in the nodes of the computational grid, the order of computational accuracy tends to unity, i.e., to the theoretical value of the order of accuracy. Full article
(This article belongs to the Section Natural Sciences)
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Article
Alternative Initial Probability Tables for Elicitation of Bayesian Belief Networks
Math. Comput. Appl. 2021, 26(3), 54; https://doi.org/10.3390/mca26030054 - 28 Jul 2021
Viewed by 357
Abstract
Bayesian Belief Networks are used in many fields of application. Defining the conditional dependencies via conditional probability tables requires the elicitation of expert belief to fill these tables, which grow very large quickly. In this work, we propose two methods to prepare these [...] Read more.
Bayesian Belief Networks are used in many fields of application. Defining the conditional dependencies via conditional probability tables requires the elicitation of expert belief to fill these tables, which grow very large quickly. In this work, we propose two methods to prepare these tables based on a low number of input parameters using specific structures and one method to generate the table using probability tables of each relation of a child node with a certain parent. These tables can be used further as a starting point for elicitation. Full article
(This article belongs to the Section Engineering)
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Article
Solving a Real-Life Distributor’s Pallet Loading Problem
Math. Comput. Appl. 2021, 26(3), 53; https://doi.org/10.3390/mca26030053 - 19 Jul 2021
Cited by 1 | Viewed by 442
Abstract
We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a [...] Read more.
We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected. The stability requirement imposes the following: (a) to load at level k+1 a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding α times the area of the layer of level k (where α1), and (b) to limit with a given threshold the difference between the highest and the lowest box of a layer. The compression constraint defines the maximum weight that each layer k can sustain; hence, the total weight of the layers loaded over k must not exceed that value. Some stability and compression constraints are considered in other works, but to our knowledge, none are defined as faced in a real-life problem. We present a matheuristic approach which works in two phases. In the first, a number of layers are defined using classical 2D bin packing algorithms, applied to a smart selection of boxes. In the second phase, the layers are packed on the minimum number of pallets by means of a specialized MILP model solved with Gurobi. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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Article
Applying the Swept Rule for Solving Two-Dimensional Partial Differential Equations on Heterogeneous Architectures
Math. Comput. Appl. 2021, 26(3), 52; https://doi.org/10.3390/mca26030052 - 17 Jul 2021
Viewed by 366
Abstract
The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating [...] Read more.
The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems and three key parameters: problem size, GPU block size, and work distribution. Our solver showed a speedup range of 0.22–2.69 for the heat diffusion equation and 0.52–1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs. Full article
(This article belongs to the Section Engineering)
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Article
A Novel Reconstruction Method to Increase Spatial Resolution in Electron Probe Microanalysis
Math. Comput. Appl. 2021, 26(3), 51; https://doi.org/10.3390/mca26030051 - 14 Jul 2021
Viewed by 377
Abstract
The spatial resolution of electron probe microanalysis (EPMA), a non-destructive method to determine the chemical composition of materials, is currently restricted to a pixel size larger than the volume of interaction between beam electrons and the material, as a result of limitations on [...] Read more.
The spatial resolution of electron probe microanalysis (EPMA), a non-destructive method to determine the chemical composition of materials, is currently restricted to a pixel size larger than the volume of interaction between beam electrons and the material, as a result of limitations on the underlying k-ratio model. Using more sophisticated models to predict k-ratios while solving the inverse problem of reconstruction offers a possibility to increase the spatial resolution. Here, a k-ratio model based on the deterministic M1-model in Boltzmann Continuous Slowing-Down approximation (BCSD) will be utilized to present a reconstruction method for EPMA which is implemented as a PDE-constrained optimization problem. Iterative gradient-based optimization techniques are used in combination with the adjoint state method to calculate the gradient in order to solve the optimization problem efficiently. The accuracy of the spatial resolution still depends on the number and quality of the measured data, but in contrast to conventional reconstruction methods, an overlapping of the interaction volumes of different measurements is permissible without ambiguous solutions. The combination of k-ratios measured with various electron beam configurations is necessary for a high resolution. Attempts to reconstruct materials with synthetic data show challenges that occur with small reconstruction pixels, but also indicate the potential to improve the spatial resolution in EPMA using the presented method. Full article
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Editorial
Numerical Modelling and Simulation Applied to Head Trauma
Math. Comput. Appl. 2021, 26(3), 50; https://doi.org/10.3390/mca26030050 - 02 Jul 2021
Viewed by 392
Abstract
Traumatic brain injury (TBI) is one of the leading causes of death and disability [...] Full article
(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)
Article
Uncertainty, Spillovers, and Forecasts of the Realized Variance of Gold Returns
Math. Comput. Appl. 2021, 26(3), 49; https://doi.org/10.3390/mca26030049 - 02 Jul 2021
Viewed by 413
Abstract
Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) [...] Read more.
Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) counterparts. We go beyond earlier research in that we do not focus exclusively on U.S.-based measures of uncertainty, and in that we account for international spillovers of uncertainty. Our results, based on the Lasso estimator, show that, across the various model configurations that we study, uncertainty has a more systematic effect on out-of-sample forecast accuracy than spillovers. Our results have important implications for investors in terms of, for example, pricing of related derivative securities and the development of portfolio-allocation strategies. Full article
(This article belongs to the Special Issue Mathematical and Computational Applications in Finance and Economics)
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