Mathematics, Statistics and Applied Computational Methods

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 25022

Special Issue Editors

Department of Mathematics, ISCTE—Instituto Universitário de Lisboa, 1649-026 Libson, Portugal
Interests: applied mathematics; Bayesian statistics; Bayesian networks; graphical models; probabilities and stochastic processes; decision support systems
Special Issues, Collections and Topics in MDPI journals
1. Center of Naval Research and Science and Technology Department, Portuguese Naval Academy - Instituto Universitário Militar, 2810-001 Almada, Portugal
2. CEMAT, Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, Lisbon University, 1048-001 Lisboa, Portugal
Interests: applied mathematics; computational statistics; computational mathematics; biomedical statistics; decision support systems; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This special issue intends to address Computation and Mathematical Methods which are noticeably necessary for the understanding of many actual problems that arise in the applied sciences. Given the large scope of potential approached problems mentioned, the aim of this issue is to collect original and high-quality papers either focused essentially in the applied presented problems or more general theoretical views concerned with conceptual approaches of interest.

In this special issue we are interested in multidisciplinary research the convey different and innovative perspectives into the fields of computation, mathematical methods in applied sciences and data science.

Prof. Dr. Marina Alexandra Pedro Andrade
Prof. Maria Alves Teodoro
Guest Editors

Manuscript Submission Information

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Keywords

  • Computation
  • Computational Methods
  • Mathematics
  • Statistics
  • Graphical Models
  • Probabilities and Stochastic Processes
  • Applied Mathematics
  • Data Science

Published Papers (10 papers)

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Research

18 pages, 659 KiB  
Article
Mathematical and Statistical Modelling for Assessing COVID-19 Superspreader Contagion: Analysis of Geographical Heterogeneous Impacts from Public Events
by Conceição Leal, Leonel Morgado and Teresa A. Oliveira
Mathematics 2023, 11(5), 1156; https://doi.org/10.3390/math11051156 - 26 Feb 2023
Cited by 1 | Viewed by 1053
Abstract
During a pandemic, public discussion and decision-making may be required in face of limited evidence. Data-grounded analysis can support decision-makers in such contexts, contributing to inform public policies. We present an empirical analysis method based on regression modelling and hypotheses testing to assess [...] Read more.
During a pandemic, public discussion and decision-making may be required in face of limited evidence. Data-grounded analysis can support decision-makers in such contexts, contributing to inform public policies. We present an empirical analysis method based on regression modelling and hypotheses testing to assess events for the possibility of occurrence of superspreading contagion with geographically heterogeneous impacts. We demonstrate the method by evaluating the case of the May 1st, 2020 Demonstration in Lisbon, Portugal, on regional growth patterns of COVID-19 cases. The methodology enabled concluding that the counties associated with the change in the growth pattern were those where likely means of travel to the demonstration were chartered buses or private cars, rather than subway or trains. Consequently, superspreading was likely due to travelling to/from the event, not from participating in it. The method is straightforward, prescribing systematic steps. Its application to events subject to media controversy enables extracting well founded conclusions, contributing to informed public discussion and decision-making, within a short time frame of the event occurring. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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26 pages, 1317 KiB  
Article
The Extended Exponential-Weibull Accelerated Failure Time Model with Application to Sudan COVID-19 Data
by Adam Braima S. Mastor, Abdulaziz S. Alghamdi, Oscar Ngesa, Joseph Mung’atu, Christophe Chesneau and Ahmed Z. Afify
Mathematics 2023, 11(2), 460; https://doi.org/10.3390/math11020460 - 15 Jan 2023
Cited by 2 | Viewed by 2037
Abstract
A fully parametric accelerated failure time (AFT) model with a flexible, novel modified exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is proposed. The model is presented using the multi-parameter survival regression model, where more than one [...] Read more.
A fully parametric accelerated failure time (AFT) model with a flexible, novel modified exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is proposed. The model is presented using the multi-parameter survival regression model, where more than one distributional parameter is linked to the covariates. The model formulation, probabilistic functions, and some of its sub-models were derived. The parameters of the introduced model are estimated using the maximum likelihood approach. An extensive simulation study is used to assess the estimates’ performance using different scenarios based on the baseline hazard shape. The proposed model is applied to a real-life right-censored COVID-19 data set from Sudan to illustrate the practical applicability of the proposed AFT model. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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23 pages, 2198 KiB  
Article
Communication Times Reconstruction in a Telecontrolled Client–Server Scheme: An Approach by Kalman Filter Applied to a Proprietary Real-Time Operating System and TCP/IP Protocol
by Jorge Salvador Valdez-Martínez, Pedro Guevara-López, Gustavo Delgado-Reyes, Diana Lizet González-Baldovinos, Jose Luis Cano-Rosas, Manuela Calixto-Rodriguez, Jonathan Villanueva-Tavira and Hector Miguel Buenabad-Arias
Mathematics 2022, 10(20), 3885; https://doi.org/10.3390/math10203885 - 19 Oct 2022
Cited by 1 | Viewed by 1121
Abstract
Nowadays, various systems were developed in the telecommunications field which make use of technologies for the transmission and reception of information. One of these technologies is the Internet, which was developed in tandem with scientific growth. Therefore, its application in the control of [...] Read more.
Nowadays, various systems were developed in the telecommunications field which make use of technologies for the transmission and reception of information. One of these technologies is the Internet, which was developed in tandem with scientific growth. Therefore, its application in the control of various industrial processes has a notable influence. In this context, there are industrial processes that, due to the potential danger they represent to human beings, must be controlled by means of a remote control system. Such systems can be implemented through client–server communication schemes, which form a network of computers to exchange information. In the exchange of information, delay times are generated. These inactivity times have a close relationship with the latency in the communication network and have a negative impact on the performance of closed-loop control systems. In this sense, for physical implementation, it is essential to measure and mathematically characterize their magnitudes in order to know their variability and thus be able to design control strategies that compensate for their effects. Hence, this research paper presents the reconstruction of the communication times measured from a telecontrol system, where it is assumed that only one subsystem acts as the controller and the other one acts as the controlled. In other words, this paper addresses a control scheme type of single-input-single-output system (SISO). This reconstruction is based on the Kalman filter, which estimates the communication times that are measured on an experimental test bench with a client–server communication scheme. Communication times are characterized as stochastic processes. So, in order to validate the reconstruction presented, the level of dependence between the random processes is evaluated by analyzing their moments of probability as well as their covariance moments. Finally, an analysis based on the mean square error is presented, through which it can be concluded that the reconstruction technique used allows one to know the dynamics of the communication times generated by the remote control process presented in this research. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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13 pages, 974 KiB  
Article
Problem-Based Learning and Applied Mathematics
by Sofia Rézio, Marina Pedro Andrade and Maria Filomena Teodoro
Mathematics 2022, 10(16), 2862; https://doi.org/10.3390/math10162862 - 11 Aug 2022
Cited by 4 | Viewed by 7001
Abstract
Problem-based learning (PBL) is a teaching method that appeared in the early 1960s and is widely applied in distinct areas nowadays. In the presented manuscript, we describe a PBL methodology use restricted to applied mathematics for problem solving among a group of engineering [...] Read more.
Problem-based learning (PBL) is a teaching method that appeared in the early 1960s and is widely applied in distinct areas nowadays. In the presented manuscript, we describe a PBL methodology use restricted to applied mathematics for problem solving among a group of engineering students in a Portuguese university. In the pandemic context, it was a huge challenge both for the students and for the teacher. Supported by the available literature, the experiment was defined. As it is well known, teachers are not only knowledge transmitters but also designers of teaching initiatives. Thus, teachers and students both have a large role in PBL methodologies, where collaboration, reflection and concepts discussion are essential. In the presented pedagogical challenge, students were devoted to integrating the previous knowledge acquired and the one acquired during the project. This process improved their new competences—both personal and team work. Despite being a recent pedagogical method, PBL is revealed to be an important teaching tool. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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14 pages, 297 KiB  
Article
Achieving Security in Proof-of-Proof Protocol with Non-Zero Synchronization Time
by Lyudmila Kovalchuk, Volodymyr Kostanda, Oleksandr Marukhnenko and Oleksii Pozhylenkov
Mathematics 2022, 10(14), 2422; https://doi.org/10.3390/math10142422 - 11 Jul 2022
Cited by 1 | Viewed by 898
Abstract
Among the most significant problems that almost any blockchain faces are the problems of increasing its throughput (i.e., the number of transactions per unit of time) and the problem of a long waiting time before block confirmation. Thus, for example, in the most [...] Read more.
Among the most significant problems that almost any blockchain faces are the problems of increasing its throughput (i.e., the number of transactions per unit of time) and the problem of a long waiting time before block confirmation. Thus, for example, in the most common BTC blockchain, according to various estimates, throughput is from 3 to 7 tps (transactions per second), and the average block confirmation time (block is considered confirmed if it has at least 6 blocks over it) is 1 h. At the same time, it is impossible to solve these problems directly by increasing the block size or increasing block generation intensity because this leads to essentially a decrease in the security of the blockchain in the first turn against double spend and splitting attacks. Such problems lead to the inconvenience of the practical use of cryptocurrencies to pay for goods and services. Proposed a few years ago, the PoP consensus protocol potentially helps to solve the problem of increasing blockchain throughput, although it was originally intended to ensure the stability of “young” blockchains, with “small” PoW, through the use of a secure blockchain, such as BTC. A blockchain that has provable security is called the security-provided blockchain (SPB), and one that uses SPB to achieve its security is called the security-inherited blockchain. In this paper, we give explicit formulas which describe how the number of confirmation blocks in the security-inherited blockchain, which is sufficient to achieve a given security level of this blockchain to a double spend attack, depends on the parameters of both blockchains. It is essential that we use a realistic model to obtain the results, taking into account the synchronization times of both blockchains. Such a model is much closer to the real situation, but at the same time, it leads to significant analytical difficulties in obtaining results. The obtained formulas are convenient for numerical calculations, the numerous examples of which are also given in this work. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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42 pages, 1092 KiB  
Article
The Representation Theory of Neural Networks
by Marco Armenta and Pierre-Marc Jodoin
Mathematics 2021, 9(24), 3216; https://doi.org/10.3390/math9243216 - 13 Dec 2021
Cited by 10 | Viewed by 4449
Abstract
In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we represent using a network quiver [...] Read more.
In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical object that we represent using a network quiver. Furthermore, we show that network quivers gently adapt to common neural network concepts such as fully connected layers, convolution operations, residual connections, batch normalization, pooling operations and even randomly wired neural networks. We show that this mathematical representation is by no means an approximation of what neural networks are as it exactly matches reality. This interpretation is algebraic and can be studied with algebraic methods. We also provide a quiver representation model to understand how a neural network creates representations from the data. We show that a neural network saves the data as quiver representations, and maps it to a geometrical space called the moduli space, which is given in terms of the underlying oriented graph of the network, i.e., its quiver. This results as a consequence of our defined objects and of understanding how the neural network computes a prediction in a combinatorial and algebraic way. Overall, representing neural networks through the quiver representation theory leads to 9 consequences and 4 inquiries for future research that we believe are of great interest to better understand what neural networks are and how they work. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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16 pages, 2602 KiB  
Article
A New Method for Time Normalization Based on the Continuous Phase: Application to Neck Kinematics
by Carlos Llopis-Albert, William Ricardo Venegas Toro, Nidal Farhat, Pau Zamora-Ortiz and Álvaro Felipe Page Del Pozo
Mathematics 2021, 9(23), 3138; https://doi.org/10.3390/math9233138 - 05 Dec 2021
Cited by 2 | Viewed by 2416
Abstract
There is growing interest in analyzing human movement data for clinical, sport, and ergonomic applications. Functional Data Analysis (FDA) has emerged as an advanced statistical method for overcoming the shortcomings of traditional analytic methods, because the information about continuous signals can be assessed [...] Read more.
There is growing interest in analyzing human movement data for clinical, sport, and ergonomic applications. Functional Data Analysis (FDA) has emerged as an advanced statistical method for overcoming the shortcomings of traditional analytic methods, because the information about continuous signals can be assessed over time. This paper takes the current literature a step further by presenting a new time scale normalization method, based on the Hilbert transform, for the analysis of functional data and the assessment of the effect on the variability of human movement waveforms. Furthermore, a quantitative comparison of well-known methods for normalizing datasets of temporal biomechanical waveforms using functional data is carried out, including the linear normalization method and nonlinear registration methods of functional data. This is done using an exhaustive database of human neck flexion-extension movements, which encompasses 423 complete cycles of 31 healthy subjects measured in two trials of the experiment on different days. The results show the advantages of the novel method compared to existing techniques in terms of computational cost and the effectiveness of time-scale normalization on the phase differences of curves and on the amplitude of means, which are assessed by Root Mean Square (RMS) values of functional means of angles, angular velocities, and angular accelerations. Additionally, the confidence intervals are obtained through a bootstrapping process. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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23 pages, 634 KiB  
Article
Projections of Tropical Fermat-Weber Points
by Weiyi Ding and Xiaoxian Tang
Mathematics 2021, 9(23), 3102; https://doi.org/10.3390/math9233102 - 01 Dec 2021
Viewed by 1146
Abstract
This paper is motivated by the difference between the classical principal component analysis (PCA) in a Euclidean space and the tropical PCA in a tropical projective torus as follows. In Euclidean space, the projection of the mean point of a given data set [...] Read more.
This paper is motivated by the difference between the classical principal component analysis (PCA) in a Euclidean space and the tropical PCA in a tropical projective torus as follows. In Euclidean space, the projection of the mean point of a given data set on the principle component is the mean point of the projection of the data set. However, in tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set on a tropical polytope is a Fermat-Weber point of the projection of the data set. This is caused by the difference between the Euclidean metric and the tropical metric. In this paper, we focus on the projection on the tropical triangle (the three-point tropical convex hull), and we develop one algorithm and its improved version, such that for a given data set in the tropical projective torus, these algorithms output a tropical triangle, on which the projection of a Fermat-Weber point of the data set is a Fermat-Weber point of the projection of the data set. We implement these algorithms in R language and test how they work with random data sets. We also use R language for numerical computation. The experimental results show that these algorithms are stable and efficient, with a high success rate. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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18 pages, 654 KiB  
Article
An Efficient Algorithm for Convex Biclustering
by Jie Chen and Joe Suzuki
Mathematics 2021, 9(23), 3021; https://doi.org/10.3390/math9233021 - 25 Nov 2021
Viewed by 1516
Abstract
We consider biclustering that clusters both samples and features and propose efficient convex biclustering procedures. The convex biclustering algorithm (COBRA) procedure solves twice the standard convex clustering problem that contains a non-differentiable function optimization. We instead convert the original optimization problem to a [...] Read more.
We consider biclustering that clusters both samples and features and propose efficient convex biclustering procedures. The convex biclustering algorithm (COBRA) procedure solves twice the standard convex clustering problem that contains a non-differentiable function optimization. We instead convert the original optimization problem to a differentiable one and improve another approach based on the augmented Lagrangian method (ALM). Our proposed method combines the basic procedures in the ALM with the accelerated gradient descent method (Nesterov’s accelerated gradient method), which can attain O(1/k2) convergence rate. It only uses first-order gradient information, and the efficiency is not influenced by the tuning parameter λ so much. This advantage allows users to quickly iterate among the various tuning parameters λ and explore the resulting changes in the biclustering solutions. The numerical experiments demonstrate that our proposed method has high accuracy and is much faster than the currently known algorithms, even for large-scale problems. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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24 pages, 1336 KiB  
Article
Jewel: A Novel Method for Joint Estimation of Gaussian Graphical Models
by Claudia Angelini, Daniela De Canditiis and Anna Plaksienko
Mathematics 2021, 9(17), 2105; https://doi.org/10.3390/math9172105 - 31 Aug 2021
Cited by 1 | Viewed by 1887
Abstract
In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a [...] Read more.
In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks. Full article
(This article belongs to the Special Issue Mathematics, Statistics and Applied Computational Methods)
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