Journal Description
Mathematical and Computational Applications
Mathematical and Computational Applications
is an international, peer-reviewed, open access journal on applications of mathematical and/or computational techniques, published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within ESCI (Web of Science), MathSciNet, Inspec, and many other databases.
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 19.4 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2021).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our authors say about MCA.
Latest Articles
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 (registering DOI) - 29 Aug 2021
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.
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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.
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Open AccessArticle
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
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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
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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.
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Open AccessArticle
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
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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
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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.
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Open AccessArticle
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
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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: .
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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: . 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.
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Open AccessArticle
Definite Integral Involving Rational Functions of Powers and Exponentials Expressed in Terms of the Lerch Function
by
and
Math. Comput. Appl. 2021, 26(3), 58; https://doi.org/10.3390/mca26030058 - 18 Aug 2021
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
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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.
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Open AccessArticle
Using the Evolution Operator to Classify Evolution Algebras
Math. Comput. Appl. 2021, 26(3), 57; https://doi.org/10.3390/mca26030057 - 05 Aug 2021
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
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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.
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(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2021)
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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
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.
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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.
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(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation
by
and
Math. Comput. Appl. 2021, 26(3), 55; https://doi.org/10.3390/mca26030055 - 29 Jul 2021
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
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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.
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(This article belongs to the Section Natural Sciences)
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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
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.
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(This article belongs to the Section Engineering)
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Solving a Real-Life Distributor’s Pallet Loading Problem
by
and
Math. Comput. Appl. 2021, 26(3), 53; https://doi.org/10.3390/mca26030053 - 19 Jul 2021
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
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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 a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding times the area of the layer of level k (where ), 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.
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(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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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
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
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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.
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(This article belongs to the Section Engineering)
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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
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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
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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.
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Open AccessEditorial
Numerical Modelling and Simulation Applied to Head Trauma
Math. Comput. Appl. 2021, 26(3), 50; https://doi.org/10.3390/mca26030050 - 02 Jul 2021
Abstract
Traumatic brain injury (TBI) is one of the leading causes of death and disability [...]
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(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)
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Uncertainty, Spillovers, and Forecasts of the Realized Variance of Gold Returns
by
and
Math. Comput. Appl. 2021, 26(3), 49; https://doi.org/10.3390/mca26030049 - 02 Jul 2021
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)
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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.
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(This article belongs to the Special Issue Mathematical and Computational Applications in Finance and Economics)
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Analytical Equations Applied to the Study of Steel Profiles under Fire According to Different Nominal Temperature-Time Curves
Math. Comput. Appl. 2021, 26(2), 48; https://doi.org/10.3390/mca26020048 - 18 Jun 2021
Abstract
Some analytical methods are available for temperature evaluation in solid bodies. These methods can be used due to their simplicity and good results. The main goal of this work is to present the temperature calculation in different cross-sections of structural hot-rolled steel profiles
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Some analytical methods are available for temperature evaluation in solid bodies. These methods can be used due to their simplicity and good results. The main goal of this work is to present the temperature calculation in different cross-sections of structural hot-rolled steel profiles (IPE, HEM, L, and UAP) using the lumped capacitance method and the simplified equation from Eurocode 3. The basis of the lumped capacitance method is that the temperature of the solid body is uniform at any given time instant during a heat transient process. The profiles were studied, subjected to the fire action according to the nominal temperature–time curves (standard temperature-time curve ISO 834, external fire curve, and hydrocarbon fire curve). The obtained results allow verifying the agreement between the two methodologies and the influence in the temperature field due to the use of different nominal fire curves. This finding enables us to conclude that the lumped capacitance method is accurate and could be easily applied.
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(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2021)
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Open AccessFeature PaperReview
Review of Multi-Physics Modeling on the Active Magnetic Regenerative Refrigeration
Math. Comput. Appl. 2021, 26(2), 47; https://doi.org/10.3390/mca26020047 - 15 Jun 2021
Abstract
Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic
[...] Read more.
Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic regenerative refrigeration (AMRR) cycles. Initially, this effect was widely used for cryogenic applications to achieve very low temperatures. However, this technology must be improved to replace vapor-compression devices operating around room temperature. Therefore, over the last 30 years, a lot of studies have been done to obtain more efficient devices. Thus, the modeling is a crucial step to perform a preliminary study and optimization. In this paper, after a large introduction on MCE research, a state-of-the-art of multi-physics modeling on the AMRR cycle modeling is made. To end this paper, a suggestion of innovative and advanced modeling solutions to study magnetocaloric regenerator is described.
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(This article belongs to the Special Issue Characterization of Magnetocaloric Devices and Materials through Mathematical Models)
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Optimization of Power Generation Grids: A Case of Study in Eastern Mexico
Math. Comput. Appl. 2021, 26(2), 46; https://doi.org/10.3390/mca26020046 - 08 Jun 2021
Abstract
Optimization of energy resources is a priority issue for our society. An improper imbalance between demand and power generation can lead to inefficient use of installed capacity, waste of fuels, worse effects on the environment, and higher costs. This paper presents the preliminary
[...] Read more.
Optimization of energy resources is a priority issue for our society. An improper imbalance between demand and power generation can lead to inefficient use of installed capacity, waste of fuels, worse effects on the environment, and higher costs. This paper presents the preliminary results of a study of seventeen interconnected power generation plants situated in eastern Mexico. The aim of the research is to apply a linear programming model to find the system-optimal solution by minimizing operating costs for this grid of power plants. The calculations were made taking into account the actual parameters of each plant; the demand and production of energy were analyzed in four time periods of 6 h during a day. The results show the cost-optimal configuration of the current power infrastructure obtained from a simple implementation model in MATLAB® software. The contribution of this paper is to adapt a lineal progamming model for an electrical distribution network formed with different types of power generation technology. The study shows that fossil fuel plants, besides emitting greenhouse gases that affect human health and the environment, incur maintenance expenses even without operation. The results are a helpful instrument for decision-making regarding the rational use of available installed capacity.
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(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
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Variational Bayesian Learning of SMoGs: Modelling and Their Application to Synthetic Aperture Radar
Math. Comput. Appl. 2021, 26(2), 45; https://doi.org/10.3390/mca26020045 - 07 Jun 2021
Abstract
We show how modern Bayesian Machine Learning tools can be effectively used in order to develop efficient methods for filtering Earth Observation signals. Bayesian statistical methods can be thought of as a generalization of the classical least-squares adjustment methods where both the unknown
[...] Read more.
We show how modern Bayesian Machine Learning tools can be effectively used in order to develop efficient methods for filtering Earth Observation signals. Bayesian statistical methods can be thought of as a generalization of the classical least-squares adjustment methods where both the unknown signals and the parameters are endowed with probability distributions, the priors. Statistical inference under this scheme is the derivation of posterior distributions, that is, distributions of the unknowns after the model has seen the data. Least squares can then be thought of as a special case that uses Gaussian likelihoods, or error statistics. In principle, for most non-trivial models, this framework requires performing integration in high-dimensional spaces. Variational methods are effective tools for approximate inference in Statistical Machine Learning and Computational Statistics. In this paper, after introducing the general variational Bayesian learning method, we apply it to the modelling and implementation of sparse mixtures of Gaussians (SMoG) models, intended to be used as adaptive priors for the efficient representation of sparse signals in applications such as wavelet-type analysis. Wavelet decomposition methods have been very successful in denoising real-world, non-stationary signals that may also contain discontinuities. For this purpose we construct a constrained hierarchical Bayesian model capturing the salient characteristics of such sets of decomposition coefficients. We express our model as a Dirichlet mixture model. We then show how variational ideas can be used to derive efficient methods for bypassing the need for integration: the task of integration becomes one of optimization. We apply our SMoG implementation to the problem of denoising of Synthetic Aperture Radar images, inherently affected by speckle noise, and show that it achieves improved performance compared to established methods, both in terms of speckle reduction and image feature preservation.
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(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2019)
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Learning Adaptive Coarse Spaces of BDDC Algorithms for Stochastic Elliptic Problems with Oscillatory and High Contrast Coefficients
Math. Comput. Appl. 2021, 26(2), 44; https://doi.org/10.3390/mca26020044 - 06 Jun 2021
Abstract
In this paper, we consider the balancing domain decomposition by constraints (BDDC) algorithm with adaptive coarse spaces for a class of stochastic elliptic problems. The key ingredient in the construction of the coarse space is the solutions of local spectral problems, which depend
[...] Read more.
In this paper, we consider the balancing domain decomposition by constraints (BDDC) algorithm with adaptive coarse spaces for a class of stochastic elliptic problems. The key ingredient in the construction of the coarse space is the solutions of local spectral problems, which depend on the coefficient of the PDE. This poses a significant challenge for stochastic coefficients as it is computationally expensive to solve the local spectral problems for every realization of the coefficient. To tackle this computational burden, we propose a machine learning approach. Our method is based on the use of a deep neural network (DNN) to approximate the relation between the stochastic coefficients and the coarse spaces. For the input of the DNN, we apply the Karhunen–Loève expansion and use the first few dominant terms in the expansion. The output of the DNN is the resulting coarse space, which is then applied with the standard adaptive BDDC algorithm. We will present some numerical results with oscillatory and high contrast coefficients to show the efficiency and robustness of the proposed scheme.
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(This article belongs to the Special Issue Domain Decomposition Methods)
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Simple Algebraic Expressions for the Prediction and Control of High-Temperature Annealed Structures by Linear Perturbation Analysis
Math. Comput. Appl. 2021, 26(2), 43; https://doi.org/10.3390/mca26020043 - 01 Jun 2021
Abstract
The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures
[...] Read more.
The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures from initial void cylindrical trenches, driven by surface diffusion, is introduced. This algebraic model provides a simple and fast way to calculate expressions to predict the final geometrical characteristics, based on linear perturbation analysis. The obtained results are similar to most compared literature data, especially, to those in which a final transformation is reached. Additionally, the model can be applied in any materials affected by the surface diffusion. With such a model, the calculation of void structure design points is greatly simplified not only in the semiconductors field but in other engineering fields where surface diffusion phenomenon is studied.
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(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)
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Applied Computer Vision and Pattern Recognition
Editors-in-Chief: Antonio Fernández-Caballero, Byung-Gyu Kim, Hugo Pedro ProençaDeadline: 31 March 2022
Conferences
8–10 September 2021
9th International Workshop on Numerical and Evolutionary Optimization (NEO 2021)

Special Issues
Special Issue in
MCA
Domain Decomposition Methods
Guest Editor: Victorita DoleanDeadline: 15 September 2021
Special Issue in
MCA
Advances in Computational Fluid Dynamics and Heat & Mass Transfer
Guest Editors: Mohammad Mehdi Rashidi, Somchai Wongwises, Abdul-Majid Wazwaz, Mostafa Safdari ShadlooDeadline: 15 October 2021
Special Issue in
MCA
Characterization of Magnetocaloric Devices and Materials through Mathematical Models
Guest Editors: Antony Plait, Frédéric DubasDeadline: 31 December 2021
Special Issue in
MCA
Set Oriented Numerics 2021
Guest Editors: Oliver Junge, Kathrin Padberg-Gehle, Sebastian Peitz, Oliver SchützeDeadline: 28 February 2022


