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Mathematics, Volume 10, Issue 5 (March-1 2022) – 176 articles

Cover Story (view full-size image): In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are particular cases. We also consider some myths of fractional calculus and false fractional derivatives. The results are expected to contribute to limiting the appearance of derivatives that differ from existing ones just because they are defined on distinct domains and to prevent the ambiguous use of the concept of fractional derivatives. View this paper.
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Article
Compact Word-Serial Modular Multiplier Accelerator Structure for Cryptographic Processors in IoT Edge Nodes with Limited Resources
Mathematics 2022, 10(5), 848; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050848 - 07 Mar 2022
Viewed by 544
Abstract
IoT is extensively used in many infrastructure applications, including telehealth, smart homes, smart grids, and smart cities. However, IoT has the weakest link in system security since it often has low processing and power resources. It is important to implement the necessary cryptographic [...] Read more.
IoT is extensively used in many infrastructure applications, including telehealth, smart homes, smart grids, and smart cities. However, IoT has the weakest link in system security since it often has low processing and power resources. It is important to implement the necessary cryptographic primitives in these devices using extremely efficient finite field hardware structures. Modular multiplication is the core of cryptographic operators. Therefore, we present, in this work, a word-serial modular multiplier accelerator structure that provides the system designer with the ability to manage areas, delays, and energy consumption through selecting the appropriate embedded processor word size l. The modularity and regularity of the suggested multiplier structure makes it more suitable for implementation in ASIC technology. The ASIC implementation results indicates that the offered multiplier structure achieves area reduction compared to the competitive existing multiplier structures that vary from 76.2% to 98.5% for l=8, from 73.1% to 98.1% for l=16, and from 82.9% to 98.3% for l=32. Moreover, the energy reduction varies from 61.2% to 98.8% for l=8, from 67.7% to 98.3% for l=16, and from 76.1% to 98.8% for l=32. These results indicate that the proposed modular multiplier structure significantly outperforms the competitive ones, in terms of area and consumed energy, making it more suitable for utilization in resource-constrained IoT edge devices. Full article
(This article belongs to the Special Issue Mathematics Cryptography and Information Security 2021)
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Article
Comparative Multidimensional Analysis of the Current State of European Economies Based on the Complex of Macroeconomic Indicators
Mathematics 2022, 10(5), 847; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050847 - 07 Mar 2022
Viewed by 530
Abstract
The stability of the economy of any country is primarily determined by the totality of macroeconomic indicators that describe the current economic state. This article provides a multi-dimensional analysis of the macroeconomic situation in Europe according to the data of 2020. The purpose [...] Read more.
The stability of the economy of any country is primarily determined by the totality of macroeconomic indicators that describe the current economic state. This article provides a multi-dimensional analysis of the macroeconomic situation in Europe according to the data of 2020. The purpose of the article is to give a clear idea of the relative position of the economies of European countries, their proximity or the significance of their differences to determine each country’s place in the overall European economic system. Research objectives: (1) to identify the necessary macroeconomic indicators for the research; (2) to determine the direction of the impact of these indicators on the economic situation of European countries; (3) to carry out a cluster division of the studied countries with the identification of the main characteristics of each cluster; (4) to identify the main macroeconomic indicators that determine the level of welfare of European countries, (5) to reduce the dimension of the multi-dimensional economic space using integrated latent factors, (6) to build a fuzzy mathematical model to predict the level of welfare of the country when the specified values of latent factors are achieved. The methodological basis of the analysis is the methods of processing multi-dimensional information, such as multi-dimensional scaling, cluster analysis, factor analysis, multivariate regression analysis, analysis of variance, discriminant analysis, and fuzzy modelling methods. The multivariate data processing was performed using the SPSS and FuzzyTech computer programs. The results obtained in the article can be useful in carrying out macroeconomic reforms to improve the economic condition of the countries. Full article
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Article
The Grey Ten-Element Analysis Method: A Novel Strategic Analysis Tool
Mathematics 2022, 10(5), 846; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050846 - 07 Mar 2022
Cited by 1 | Viewed by 536
Abstract
In this paper, a new strategic analysis method is introduced, called the ten-element analysis (TEA) method to determine the firm’s strategic position in the market. The new method is grounded on the computation of the reflections of the external factors on the firm’s [...] Read more.
In this paper, a new strategic analysis method is introduced, called the ten-element analysis (TEA) method to determine the firm’s strategic position in the market. The new method is grounded on the computation of the reflections of the external factors on the firm’s internal factors through the changes of the values of the internal factors throughout the time when a lack of complete information regarding the environmental factors exists. The TEA method takes ten effective key elements of the firm into account and investigates their changes through a maximum of nine periods and a minimum of two periods. To conduct the model, the paper is mainly focused on four main rubrics, including the detection of the reflection of the firm’s environmental factors on the internal factors, deriving the strategic position of the firm from the reflections, the capability of the existing strategic models in determining the strategic position from the reflections in presence of uncertainty and incomplete information of the external factors. The method is applied to a dairy company in order to find its strategic position in the market. The results showed that the output of the TEA method and SWOT analysis is similar which makes the new method reliable to employ. The TEA method is developed under the grey environment to harness the uncertainty where a new grey comparison method is introduced to compare the grey numbers. Full article
(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)
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Article
Bio-Constrained Codes with Neural Network for Density-Based DNA Data Storage
Mathematics 2022, 10(5), 845; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050845 - 07 Mar 2022
Viewed by 624
Abstract
DNA has evolved as a cutting-edge medium for digital information storage due to its extremely high density and durable preservation to accommodate the data explosion. However, the strings of DNA are prone to errors during the hybridization process. In addition, DNA synthesis and [...] Read more.
DNA has evolved as a cutting-edge medium for digital information storage due to its extremely high density and durable preservation to accommodate the data explosion. However, the strings of DNA are prone to errors during the hybridization process. In addition, DNA synthesis and sequences come with a cost that depends on the number of nucleotides present. An efficient model to store a large amount of data in a small number of nucleotides is essential, and it must control the hybridization errors among the base pairs. In this paper, a novel computational model is presented to design large DNA libraries of oligonucleotides. It is established by integrating a neural network (NN) with combinatorial biological constraints, including constant GC-content and satisfying Hamming distance and reverse-complement constraints. We develop a simple and efficient implementation of NNs to produce the optimal DNA codes, which opens the door to applying neural networks for DNA-based data storage. Further, the combinatorial bio-constraints are introduced to improve the lower bounds and to avoid the occurrence of errors in the DNA codes. Our goal is to compute large DNA codes in shorter sequences, which should avoid non-specific hybridization errors by satisfying the bio-constrained coding. The proposed model yields a significant improvement in the DNA library by explicitly constructing larger codes than the prior published codes. Full article
(This article belongs to the Special Issue Biologically Inspired Computing)
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Article
Intermediate-Task Transfer Learning with BERT for Sarcasm Detection
Mathematics 2022, 10(5), 844; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050844 - 07 Mar 2022
Cited by 2 | Viewed by 726
Abstract
Sarcasm detection plays an important role in natural language processing as it can impact the performance of many applications, including sentiment analysis, opinion mining, and stance detection. Despite substantial progress on sarcasm detection, the research results are scattered across datasets and studies. In [...] Read more.
Sarcasm detection plays an important role in natural language processing as it can impact the performance of many applications, including sentiment analysis, opinion mining, and stance detection. Despite substantial progress on sarcasm detection, the research results are scattered across datasets and studies. In this paper, we survey the current state-of-the-art and present strong baselines for sarcasm detection based on BERT pre-trained language models. We further improve our BERT models by fine-tuning them on related intermediate tasks before fine-tuning them on our target task. Specifically, relying on the correlation between sarcasm and (implied negative) sentiment and emotions, we explore a transfer learning framework that uses sentiment classification and emotion detection as individual intermediate tasks to infuse knowledge into the target task of sarcasm detection. Experimental results on three datasets that have different characteristics show that the BERT-based models outperform many previous models. Full article
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Article
Performance Degradation Based on Importance Change and Application in Dissimilar Redundancy Actuation System
Mathematics 2022, 10(5), 843; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050843 - 07 Mar 2022
Viewed by 516
Abstract
The importance measure is a crucial method to identify and evaluate the system weak link. It is widely used in the optimization design and maintenance decision of aviation, aerospace, nuclear energy and other systems. The dissimilar redundancy actuation system (DRAS) is a key [...] Read more.
The importance measure is a crucial method to identify and evaluate the system weak link. It is widely used in the optimization design and maintenance decision of aviation, aerospace, nuclear energy and other systems. The dissimilar redundancy actuation system (DRAS) is a key aircraft control subsystem which performs aircraft attitude and flight trajectory control. Its performance and reliability directly affect the aircraft flight quality and flight safety. This paper considers the influence of the Birnbaum importance measure (BIM) and integrated importance measure (IIM) on the reliability changes of key components in DRAS. The differences of physical fault characteristics of different components due to performance degradation and power mismatch, are first considered. The reliability of each component in the system is then estimated by assuming that the stochastic degradation process of the DRAS components follows an inverse Gaussian (IG) process. Finally, the weak links of the system are identified using BIM and IIM, so that the resources can be reasonably allocated to the weak links during the maintenance period. The proposed method can provide a technical support for personnel maintenance, in order to improve the system reliability with a minimal lifecycle cost. Full article
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Article
A Bayesian EAP-Based Nonlinear Extension of Croon and Van Veldhoven’s Model for Analyzing Data from Micro–Macro Multilevel Designs
Mathematics 2022, 10(5), 842; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050842 - 07 Mar 2022
Viewed by 654
Abstract
Croon and van Veldhoven discussed a model for analyzing micro–macro multilevel designs in which a variable measured at the upper level is predicted by an explanatory variable that is measured at the lower level. Additionally, the authors proposed an approach for estimating this [...] Read more.
Croon and van Veldhoven discussed a model for analyzing micro–macro multilevel designs in which a variable measured at the upper level is predicted by an explanatory variable that is measured at the lower level. Additionally, the authors proposed an approach for estimating this model. In their approach, estimation is carried out by running a regression analysis on Bayesian Expected a Posterior (EAP) estimates. In this article, we present an extension of this approach to interaction and quadratic effects of explanatory variables. Specifically, we define the Bayesian EAPs, discuss a way for estimating them, and we show how their estimates can be used to obtain the interaction and the quadratic effects. We present the results of a “proof of concept” via Monte Carlo simulation, which we conducted to validate our approach and to compare two resampling procedures for obtaining standard errors. Finally, we discuss limitations of our proposed extended Bayesian EAP-based approach. Full article
(This article belongs to the Special Issue Bayesian Inference and Modeling with Applications)
Article
Reversible Data Hiding with a New Local Contrast Enhancement Approach
Mathematics 2022, 10(5), 841; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050841 - 07 Mar 2022
Viewed by 486
Abstract
Reversible data hiding schemes hide information into a digital image and simultaneously increase its contrast. The improvements of the different approaches aim to increase the capacity, contrast, and quality of the image. However, recent proposals contrast the image globally and lose local details [...] Read more.
Reversible data hiding schemes hide information into a digital image and simultaneously increase its contrast. The improvements of the different approaches aim to increase the capacity, contrast, and quality of the image. However, recent proposals contrast the image globally and lose local details since they use two common methodologies that may not contribute to obtaining better results. Firstly, to generate vacancies for hiding information, most schemes start with a preprocessing applied to the histogram that may introduce visual distortions and set the maximum hiding rate in advance. Secondly, just a few hiding ranges are selected in the histogram, which means that just limited contrast and capacity may be achieved. To solve these problems, in this paper, a novel approach without preprocessing performs an automatic selection of multiple hiding ranges into the histograms. The selection stage is based on an optimization process, and the iterative-based algorithm increases capacity at embedding execution. Results show that quality and capacity values overcome previous approaches. Additionally, visual results show how greyscale values are better differentiated in the image, revealing details globally and locally. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
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Article
Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models
Mathematics 2022, 10(5), 840; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050840 - 07 Mar 2022
Cited by 1 | Viewed by 438
Abstract
Optimal designs of constant-stress accelerated life test plans is one of the important topics in reliability studies. Many devices produced have very high reliability under normal operating conditions. The question then arises of how to make the optimal decisions on life test plans [...] Read more.
Optimal designs of constant-stress accelerated life test plans is one of the important topics in reliability studies. Many devices produced have very high reliability under normal operating conditions. The question then arises of how to make the optimal decisions on life test plans to collect sufficient information about the corresponding lifetime distributions. Accelerated life testing has become a popular approach to tackling this problem in reliability studies, which attempts to extrapolate from the information obtained from accelerated testing conditions to normal operating conditions. In this paper, we develop a general framework to obtain optimal constant-stress accelerated life test plans for one-shot devices with dependent components, subject to time and budget constraints. The optimal accelerated test plan considers an economical approach to determine the inspection time and the sample size of each accelerating testing condition so that the asymptotic variance of the maximum likelihood estimator for the mean lifetime under normal operating conditions is minimized. This study also investigates the impact of the dependence between components on the optimal designs and provides practical recommendations on constant-stress accelerated life test plans for one-shot devices with dependent components. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation II)
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Article
Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution
Mathematics 2022, 10(5), 839; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050839 - 07 Mar 2022
Cited by 1 | Viewed by 491
Abstract
Branching patterns are ubiquitous in nature; consequently, over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to have fractal properties; however, their non-homogeneity (i.e., [...] Read more.
Branching patterns are ubiquitous in nature; consequently, over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and resemblance to fractal trees, they are often thought to have fractal properties; however, their non-homogeneity (i.e., lack of strict self-similarity) is often ignored. In this paper we review and examine the use of the box-counting and sandbox methods to estimate the fractal dimensions of branching structures. We highlight the fact that these methods rely on an assumption of self-similarity that is not present in branching structures due to their non-homogeneous nature. Looking at the local slopes of the log–log plots used by these methods reveals the problems caused by the non-homogeneity. Finally, we examine the role of the canopies (endpoints or limit points) of branching structures in the estimation of their fractal dimensions. Full article
(This article belongs to the Special Issue Frontier in Fractals)
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Article
Parallel Stylometric Document Embeddings with Deep Learning Based Language Models in Literary Authorship Attribution
Mathematics 2022, 10(5), 838; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050838 - 07 Mar 2022
Viewed by 727
Abstract
This paper explores the effectiveness of parallel stylometric document embeddings in solving the authorship attribution task by testing a novel approach on literary texts in 7 different languages, totaling in 7051 unique 10,000-token chunks from 700 PoS and lemma annotated documents. We used [...] Read more.
This paper explores the effectiveness of parallel stylometric document embeddings in solving the authorship attribution task by testing a novel approach on literary texts in 7 different languages, totaling in 7051 unique 10,000-token chunks from 700 PoS and lemma annotated documents. We used these documents to produce four document embedding models using Stylo R package (word-based, lemma-based, PoS-trigrams-based, and PoS-mask-based) and one document embedding model using mBERT for each of the seven languages. We created further derivations of these embeddings in the form of average, product, minimum, maximum, and l2 norm of these document embedding matrices and tested them both including and excluding the mBERT-based document embeddings for each language. Finally, we trained several perceptrons on the portions of the dataset in order to procure adequate weights for a weighted combination approach. We tested standalone (two baselines) and composite embeddings for classification accuracy, precision, recall, weighted-average, and macro-averaged F1-score, compared them with one another and have found that for each language most of our composition methods outperform the baselines (with a couple of methods outperforming all baselines for all languages), with or without mBERT inputs, which are found to have no significant positive impact on the results of our methods. Full article
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Article
Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues
Mathematics 2022, 10(5), 837; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050837 - 06 Mar 2022
Viewed by 693
Abstract
The electrical behaviour of a system, such as an electrode–tissue interface (ETI) or a biological tissue, can be used for its characterization. One way of accomplishing this goal consists of measuring the electrical impedance, that is, the opposition that a system exhibits to [...] Read more.
The electrical behaviour of a system, such as an electrode–tissue interface (ETI) or a biological tissue, can be used for its characterization. One way of accomplishing this goal consists of measuring the electrical impedance, that is, the opposition that a system exhibits to an alternating current flow as a function of frequency. Subsequently, experimental impedance data are fitted to an electrical equivalent circuit (EEC model) whose parameters can be correlated with the electrode processes occurring in the ETI or with the physiological state of a tissue. The EEC used in this paper is a reasonable approach for simple bio-electrodes or cell membranes, assuming ideal capacitances. We use the theory of optimal experimental design to identify the frequencies in which the impedance is measured, as well as the number of measurement repetitions, in such a way that the EEC parameters can be optimally estimated. Specifically, we calculate approximate and exact D-optimal designs by optimizing the determinant of the information matrix by adapting two of the most algorithms that are routinely used nowadays (REX random exchange algorithm and KL exchange algorithm). The D-efficiency of the optimal designs provided by the algorithms was compared with the design commonly used by experimenters and it is shown that the precision of the parameter estimates can be increased. Full article
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Article
An 8-Nodes 3D Hexahedral Finite Element and an 1D 2-Nodes Structural Element for Timoshenko Beams, Both Based on Hermitian Intepolation, in Linear Range
Mathematics 2022, 10(5), 836; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050836 - 06 Mar 2022
Viewed by 551
Abstract
The following article presents the elaboration and results obtained from a 3D finite element, of the 8-node hexahedron type with 6 degrees of freedom (DOF) per node (48 DOF per element) based on third degree Hermitian polynomials, and of a 2-node structural element, [...] Read more.
The following article presents the elaboration and results obtained from a 3D finite element, of the 8-node hexahedron type with 6 degrees of freedom (DOF) per node (48 DOF per element) based on third degree Hermitian polynomials, and of a 2-node structural element, with 6 DOF per node (12 DOF per element), based on third degree Hermitian polynomials and the theory of Timoshenko for beams. This article has two purposes; the first one is the formulation of a finite element capable of capturing bending effects, and the second one is to verify whether it is possible to obtain the deformation of the beam’s cross section of a structural member of the beam type, based on the deformations of its axis. The results obtained showed that the 8-node hexahedron FE was able to reproduce satisfactory results by simulating some cases of beams with different contour and load conditions, obtaining errors between 1% and 4% compared to the ANSYS software, educational version. Regarding the structural element of the beam type, it reproduced results that were not as precise as the FE Hexa 8, presenting errors of between 6% and 7% with regard to the axis but with error rounding between 10% and 20%. Full article
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Article
Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities
Mathematics 2022, 10(5), 835; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050835 - 06 Mar 2022
Cited by 1 | Viewed by 577
Abstract
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for [...] Read more.
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
A More Realistic Markov Process Model for Explaining the Disjunction Effect in One-Shot Prisoner’s Dilemma Game
Mathematics 2022, 10(5), 834; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050834 - 06 Mar 2022
Viewed by 525
Abstract
The quantum model has been considered to be advantageous over the Markov model in explaining irrational behaviors (e.g., the disjunction effect) during decision making. Here, we reviewed and re-examined the ability of the quantum belief–action entanglement (BAE) model and the Markov belief–action (BA) [...] Read more.
The quantum model has been considered to be advantageous over the Markov model in explaining irrational behaviors (e.g., the disjunction effect) during decision making. Here, we reviewed and re-examined the ability of the quantum belief–action entanglement (BAE) model and the Markov belief–action (BA) model in explaining the disjunction effect considering a more realistic setting. The results indicate that neither of the two models can truly represent the underlying cognitive mechanism. Thus, we proposed a more realistic Markov model to explain the disjunction effect in the prisoner’s dilemma game. In this model, the probability transition pattern of a decision maker (DM) is dependent on the information about the opponent’s action, Also, the relationship between the cognitive components in the evolution dynamics is moderated by the DM’s degree of subjective uncertainty (DSN). The results show that the disjunction effect can be well predicted by a more realistic Markov model. Model comparison suggests the superiority of the proposed Markov model over the quantum BAE model in terms of absolute model performance, relative model performance, and model flexibility. Therefore, we suggest that the key to successfully explaining the disjunction effect is to consider the underlying cognitive mechanism properly. Full article
(This article belongs to the Special Issue Quantitative Methods for Social Sciences)
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Article
A Simple, Accurate and Semi-Analytical Meshless Method for Solving Laplace and Helmholtz Equations in Complex Two-Dimensional Geometries
Mathematics 2022, 10(5), 833; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050833 - 05 Mar 2022
Cited by 1 | Viewed by 493
Abstract
A localized virtual boundary element–meshless collocation method (LVBE-MCM) is proposed to solve Laplace and Helmholtz equations in complex two-dimensional (2D) geometries. “Localized” refers to employing the moving least square method to locally approximate the physical quantities of the computational domain after introducing the [...] Read more.
A localized virtual boundary element–meshless collocation method (LVBE-MCM) is proposed to solve Laplace and Helmholtz equations in complex two-dimensional (2D) geometries. “Localized” refers to employing the moving least square method to locally approximate the physical quantities of the computational domain after introducing the traditional virtual boundary element method. The LVBE-MCM is a semi-analytical and domain-type meshless collocation method that is based on the fundamental solution of the governing equation, which is different from the traditional virtual boundary element method. When it comes to 2D problems, the LVBE-MCM only needs to calculate the numerical integration on the circular virtual boundary. It avoids the evaluation of singular/strong singular/hypersingular integrals seen in the boundary element method. Compared to the difficulty of selecting the virtual boundary and evaluating singular integrals, the LVBE-MCM is simple and straightforward. Numerical experiments, including irregular and doubly connected domains, demonstrate that the LVBE-MCM is accurate, stable, and convergent for solving both Laplace and Helmholtz equations. Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis)
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Article
Multiphysics Mathematical Modeling and Flow Field Analysis of an Inflatable Membrane Aeroshell in Suborbital Reentry
Mathematics 2022, 10(5), 832; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050832 - 05 Mar 2022
Viewed by 494
Abstract
In the present study, a multiphysics mathematical model for reproducing the flow field characteristics of an inflatable aeroshell was developed to study the aerodynamic properties of the flow around a membrane reentry vehicle. Firstly, the configuration and flight sequence of a membrane reentry [...] Read more.
In the present study, a multiphysics mathematical model for reproducing the flow field characteristics of an inflatable aeroshell was developed to study the aerodynamic properties of the flow around a membrane reentry vehicle. Firstly, the configuration and flight sequence of a membrane reentry vehicle used in the experiment were introduced. Secondly, mathematical equations of multiphysics fields, such as the Navier–Stokes equations, the heat conduction equation, and the membrane deformation equation, were introduced and numerically solved. The variation characteristics of the flow properties during the aerodynamic heating of a membrane vehicle were studied and discussed in detail under the conditions of different flight altitudes. The results showed that for the membrane vehicle, the high-temperature flow field at the front of its capsule was in a state of thermal non-equilibrium with the decrease of flight altitude and its membrane deformation degree was proportional to the pressure. The translational temperature and electron number density of the plasma flow around the aeroshell remained at a relatively low level for the membrane vehicle so that the blackout phenomenon scarcely occurred during its atmospheric reentry. Full article
(This article belongs to the Section Mathematical Physics)
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Article
Towards a Highly Available Model for Processing Service Requests Based on Distributed Hash Tables
Mathematics 2022, 10(5), 831; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050831 - 05 Mar 2022
Viewed by 462
Abstract
This work aims to identify techniques leading to a highly available request processing service by using the natural decentralization and the dispersion power of the hash function involved in a Distributed Hash Table (DHT). High availability is present mainly in systems that: scale [...] Read more.
This work aims to identify techniques leading to a highly available request processing service by using the natural decentralization and the dispersion power of the hash function involved in a Distributed Hash Table (DHT). High availability is present mainly in systems that: scale well, are balanced and are fault tolerant. These are essential features of the Distributed Hash Tables (DHTs), which have been used mainly for storage purposes. The novelty of this paper’s approach is essentially based on hash functions and decentralized Distributed Hash Tables (DHTs), which lead to highly available data solutions, which a main building block to obtain an improved platform that offers high availability for processing clients’ requests. It is achieved by using a database constructed also on a DHT, which gives high availability to its data. Further, the model requires no changes in the interface, that the request processing service already has towards its clients. Subsequently, the DHT layer is added, for the service to run on top of it, and also a load balancing front end, in order to make it highly available, towards its clients. The paper shows, via experimental validation, the good qualities of the new request processing service, by arguing its improved scalability, load balancing and fault tolerance model. Full article
(This article belongs to the Special Issue Automatic Control and Soft Computing in Engineering)
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Article
A Heuristic-Based Simulation for an Education Process to Learn about Optimization Applications in Logistics and Transportation
Mathematics 2022, 10(5), 830; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050830 - 05 Mar 2022
Viewed by 570
Abstract
In the context of the DigiLab4U international project, this paper describes a simulation-based serious game that can be used as a virtual teaching lab in higher education courses, especially in Industrial and Systems Engineering, Data Science, Management Science and Operations Research, as well [...] Read more.
In the context of the DigiLab4U international project, this paper describes a simulation-based serious game that can be used as a virtual teaching lab in higher education courses, especially in Industrial and Systems Engineering, Data Science, Management Science and Operations Research, as well as Computer Science. The learning activity focuses on understanding distribution logistics problems related to transportation optimization using different techniques. These optimization challenges include the vehicle routing problem, the arc routing problem, and the team orienteering problem. As a result of the learning process in the virtual lab, it is expected that students acquire competencies and skills related to logistics and transportation challenges as well as problem-solving. These competencies and skills can be precious for students’ future careers, since they increase students’ analytical skills, capacity to understand heuristic-based algorithms, teamwork and interdisciplinary communication skills, programming skills, and statistical abilities. A preliminary version of this training activity has already been used in MSc and PhD courses held at universities in Spain, Italy, Ireland, and Portugal. Full article
(This article belongs to the Special Issue Business Games and Numeric Simulations in Economics and Management)
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Article
Cost-Sensitive Broad Learning System for Imbalanced Classification and Its Medical Application
Mathematics 2022, 10(5), 829; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050829 - 05 Mar 2022
Cited by 1 | Viewed by 543
Abstract
As an effective and efficient discriminative learning method, the broad learning system (BLS) has received increasing attention due to its outstanding performance without large computational resources. The standard BLS is derived under the minimum mean square error (MMSE) criterion, while MMSE is with [...] Read more.
As an effective and efficient discriminative learning method, the broad learning system (BLS) has received increasing attention due to its outstanding performance without large computational resources. The standard BLS is derived under the minimum mean square error (MMSE) criterion, while MMSE is with poor performance when dealing with imbalanced data. However, imbalanced data are widely encountered in real-world applications. To address this issue, a novel cost-sensitive BLS algorithm (CS-BLS) is proposed. In the CS-BLS, many variations can be adopted, and CS-BLS with weighted cross-entropy is analyzed in this paper. Weighted penalty factors are used in CS-BLS to constrain the contribution of each sample in different classes. The samples in minor classes are allocated higher weights to increase their contributions. Four different weight calculation methods are adopted to the CS-BLS, and thus, four CS-BLS methods are proposed: Log-CS-BLS, Lin-CS-BLS, Sqr-CS-BLS, and EN-CS-BLS. Experiments based on artificially imbalanced datasets of MNIST and small NORB are firstly conducted and compared with the standard BLS. The results show that the proposed CS-BLS methods have better generalization and robustness than the standard BLS. Then, experiments on a real ultrasound breast image dataset are conducted, and the results demonstrate that the proposed CS-BLS methods are effective in actual medical diagnosis. Full article
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Article
Bayes in Wonderland! Predictive Supervised Classification Inference Hits Unpredictability
Mathematics 2022, 10(5), 828; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050828 - 05 Mar 2022
Viewed by 463
Abstract
The marginal Bayesian predictive classifiers (mBpc), as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and, hence, tacitly assume the independence of the observations. Due to saturation in learning of generative model parameters, the adverse effect of this false [...] Read more.
The marginal Bayesian predictive classifiers (mBpc), as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and, hence, tacitly assume the independence of the observations. Due to saturation in learning of generative model parameters, the adverse effect of this false assumption on the accuracy of mBpc tends to wear out in the face of an increasing amount of training data, guaranteeing the convergence of these two classifiers under the de Finetti type of exchangeability. This result, however, is far from trivial for the sequences generated under Partition Exchangeability (PE), where even umpteen amount of training data does not rule out the possibility of an unobserved outcome (Wonderland!). We provide a computational scheme that allows the generation of the sequences under PE. Based on that, with controlled increase of the training data, we show the convergence of the sBpc and mBpc. This underlies the use of simpler yet computationally more efficient marginal classifiers instead of simultaneous. We also provide a parameter estimation of the generative model giving rise to the partition exchangeable sequence as well as a testing paradigm for the equality of this parameter across different samples. The package for Bayesian predictive supervised classifications, parameter estimation and hypothesis testing of the Ewens sampling formula generative model is deposited on CRAN as PEkit package. Full article
(This article belongs to the Topic Machine and Deep Learning)
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Article
A Neural Network Type Approach for Constructing Runge–Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions
Mathematics 2022, 10(5), 827; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050827 - 04 Mar 2022
Viewed by 423
Abstract
We analyze a set of explicit Runge–Kutta pairs of orders six and five that share no extra properties, e.g., long intervals of periodicity or vanishing phase-lag etc. This family of pairs provides five parameters from which one can freely pick. Here, we use [...] Read more.
We analyze a set of explicit Runge–Kutta pairs of orders six and five that share no extra properties, e.g., long intervals of periodicity or vanishing phase-lag etc. This family of pairs provides five parameters from which one can freely pick. Here, we use a Neural Network-like approach where these coefficients are trained on a couple of model periodic problems. The aim of this training is to produce a pair that furnishes best results after using certain intervals and tolerance. Then we see that this pair performs very well on a wide range of problems with periodic solutions. Full article
(This article belongs to the Section Computational and Applied Mathematics)
Article
Some (p, q)-Integral Inequalities of Hermite–Hadamard Inequalities for (p, q)-Differentiable Convex Functions
Mathematics 2022, 10(5), 826; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050826 - 04 Mar 2022
Cited by 1 | Viewed by 500
Abstract
In this paper, we establish a new (p,q)b-integral identity involving the first-order (p,q)b-derivative. Then, we use this result to prove some new (p,q)b-integral inequalities related [...] Read more.
In this paper, we establish a new (p,q)b-integral identity involving the first-order (p,q)b-derivative. Then, we use this result to prove some new (p,q)b-integral inequalities related to Hermite–Hadamard inequalities for (p,q)b-differentiable convex functions. Furthermore, our main results are used to study some special cases of various integral inequalities. The newly presented results are proven to be generalizations of some integral inequalities of already published results. Finally, some examples are given to illustrate the investigated results. Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)
Article
Fractional Growth Model with Delay for Recurrent Outbreaks Applied to COVID-19 Data
Mathematics 2022, 10(5), 825; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050825 - 04 Mar 2022
Viewed by 670
Abstract
There are a great many epidemiological models that have been implemented to describe COVID-19 data; however, few attempted to reproduce the entire phenomenon due to the complexity of modeling recurrent outbreaks. In this work a fractional growth model with delay is developed that [...] Read more.
There are a great many epidemiological models that have been implemented to describe COVID-19 data; however, few attempted to reproduce the entire phenomenon due to the complexity of modeling recurrent outbreaks. In this work a fractional growth model with delay is developed that implements the Caputo fractional derivative with 0<β1. Furthermore, in order to preserve the nature of the phenomenon and ensure continuity in the derivatives of the function, a method is proposed to construct an initial condition function to implement in the model with delay. This model is analyzed and generalized to model recurrent outbreaks. The model is applied to fit data of cumulative confirmed cases from Mexico, the United States, and Russia, obtaining excellent fitting corroborated by the coefficient of determination, where R2>0.9995 in all cases. Lastly, as a result of the implementation of the delay effect, the global phenomenon was decomposed into its local parts, allowing for directly comparing each outbreak and its different characteristics. Full article
(This article belongs to the Special Issue Mathematical Methods and Models in Epidemiology)
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Article
A Novel βSA Ensemble Model for Forecasting the Number of Confirmed COVID-19 Cases in the US
Mathematics 2022, 10(5), 824; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050824 - 04 Mar 2022
Viewed by 519
Abstract
In December 2019, Severe Special Infectious Pneumonia (SARS-CoV-2)–the novel coronavirus (COVID-19)– appeared for the first time, breaking out in Wuhan, China, and the epidemic spread quickly to the world in a very short period time. According to WHO data, ten million people have [...] Read more.
In December 2019, Severe Special Infectious Pneumonia (SARS-CoV-2)–the novel coronavirus (COVID-19)– appeared for the first time, breaking out in Wuhan, China, and the epidemic spread quickly to the world in a very short period time. According to WHO data, ten million people have been infected, and more than one million people have died; moreover, the economy has also been severely hit. In an outbreak of an epidemic, people are concerned about the final number of infections. Therefore, effectively predicting the number of confirmed cases in the future can provide a reference for decision-makers to make decisions and avoid the spread of deadly epidemics. In recent years, the α-Sutte indicator method is an excellent predictor in short-term forecasting; however, the α-Sutte indicator uses fixed static weights. In this study, by adding an error-based dynamic weighting method, a novel β-Sutte indicator is proposed. Combined with ARIMA as an ensemble model (βSA), the forecasting of the future COVID-19 daily cumulative number of cases and the number of new cases in the US are evaluated from the experiment. The experimental results show that the forecasting accuracy of βSA proposed in this study is better than other methods in forecasting with metrics MAPE and RMSE. It proves the feasibility of adding error-based dynamic weights in the β-Sutte indicator in the area of forecasting. Full article
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Article
An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics
Mathematics 2022, 10(5), 823; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050823 - 04 Mar 2022
Viewed by 623
Abstract
Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically [...] Read more.
Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically detailed mechanistic models that require the identification of high-dimensional parameter vectors. An important aspect to identify in electromechanics (EM) models are active mechanics parameters that govern cardiac contraction and relaxation. In this study, we present a novel, fully automated, and efficient approach for personalising biophysically detailed active mechanics models using a two-step multi-fidelity solution. In the first step, active mechanical behaviour in a given 3D EM model is represented by a purely phenomenological, low-fidelity model, which is personalised at the organ scale by calibration to clinical cavity pressure data. Then, in the second step, median traces of nodal cellular active stress, intracellular calcium concentration, and fibre stretch are generated and utilised to personalise the desired high-fidelity model at the cellular scale using a 0D model of cardiac EM. Our novel approach was tested on a cohort of seven human left ventricular (LV) EM models, created from patients treated for aortic coarctation (CoA). Goodness of fit, computational cost, and robustness of the algorithm against uncertainty in the clinical data and variations of initial guesses were evaluated. We demonstrate that our multi-fidelity approach facilitates the personalisation of a biophysically detailed active stress model within only a few (2 to 4) expensive 3D organ-scale simulations—a computational effort compatible with clinical model applications. Full article
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Article
Traveling Waves for the Generalized Sinh-Gordon Equation with Variable Coefficients
Mathematics 2022, 10(5), 822; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050822 - 04 Mar 2022
Viewed by 418
Abstract
The sinh-Gordon equation is simply the classical wave equation with a nonlinear sinh source term. It arises in diverse scientific applications including differential geometry theory, integrable quantum field theory, fluid dynamics, kink dynamics, and statistical mechanics. It can be used to describe generic [...] Read more.
The sinh-Gordon equation is simply the classical wave equation with a nonlinear sinh source term. It arises in diverse scientific applications including differential geometry theory, integrable quantum field theory, fluid dynamics, kink dynamics, and statistical mechanics. It can be used to describe generic properties of string dynamics for strings and multi-strings in constant curvature space. In the present paper, we study a generalized sinh-Gordon equation with variable coefficients with the goal of obtaining analytical traveling wave solutions. Our results show that the traveling waves of the variable coefficient sinh-Gordon equation can be derived from the known solutions of the standard sinh-Gordon equation under a specific selection of a choice of the variable coefficients. These solutions include some real single and multi-solitons, periodic waves, breaking kink waves, singular waves, periodic singular waves, and compactons. These solutions might be valuable when scientists model some real-life phenomena using the sinh-Gordon equation where the balance between dispersion and nonlinearity is perturbed. Full article
(This article belongs to the Special Issue Advanced Methods in Computational Mathematical Physics)
Article
Reconstructing Dynamic 3D Models with Small Data by Integrating Position-Based Dynamics and PDE-Based Modelling
Mathematics 2022, 10(5), 821; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050821 - 04 Mar 2022
Viewed by 496
Abstract
Simulation with position-based dynamics is very popular due to its high efficiency. However, it has the weaknesses of lacking details when too few vertices are involved in simulation and inefficiency when too many vertices are used for simulation. To tackle this problem, in [...] Read more.
Simulation with position-based dynamics is very popular due to its high efficiency. However, it has the weaknesses of lacking details when too few vertices are involved in simulation and inefficiency when too many vertices are used for simulation. To tackle this problem, in this paper, we propose a new method of reconstructing dynamic 3D models with small data. The core elements of the proposed approach are a curve-represented geometric model and a physics-based mathematical model defined by dynamic partial differential equations. We first use the simulation method of position-based dynamics to generate a group of keyframe poses, which are used to create the deformation animation of a 3D model. Then, wireframe curves are extracted from skin deformation shapes of the 3D model at different keyframe poses. A physics-based mathematical model defined by dynamic partial differential equations is proposed. Its closed-form solution is obtained to represent the extracted curves, which are used to reconstruct the deformation models at different keyframe poses. Experimental examples and comparisons made in this paper indicate that the proposed method of reconstructing dynamic 3D models can greatly reduce data size while keeping good details. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
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Article
Networks with Complex Weights: Green Function and Power Series
Mathematics 2022, 10(5), 820; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050820 - 04 Mar 2022
Viewed by 456
Abstract
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated with corresponding reversible Markov chains, i.e., where the [...] Read more.
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated with corresponding reversible Markov chains, i.e., where the edge weights are positive. Under suitable conditions, these lead to comparison of series of matrix powers which express those kernels. We show that the notions of transience and recurrence extend by analytic continuation to the complex-weighted case even when the network is infinite. Thus, a variety of methods known for Markov chains extend to that setting. Full article
(This article belongs to the Special Issue Latest Advances in Random Walks Dating Back to One Hundred Years)
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Article
Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring
Mathematics 2022, 10(5), 819; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050819 - 04 Mar 2022
Cited by 1 | Viewed by 450
Abstract
This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood [...] Read more.
This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data. Full article
(This article belongs to the Special Issue Probability and Statistics in Quality and Reliability Engineering)
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