Applied and Computational Mathematics for Digital Environments

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

Deadline for manuscript submissions: closed (6 January 2023) | Viewed by 22162

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Special Issue Editor

Institute of Informational Technologies, Federal State Budget Educational Institution of Higher Education, MIREA—Russian Technological University, 78, Vernadsky Avenue, 119454 Moscow, Russia
Interests: population-based optimization algorithms; applied mathematics; machine learning; deep learning; data mining; fuzzy set theory; classification; pattern recognition; algorithms
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Special Issue Information

Dear Colleagues,

It is necessary to consider the possibility of applying the principles of computational mathematics and informatics to optimize the study and modeling of various real-world phenomena with the use of intelligent software and hardware platforms based on math apparatus and appropriate modules. Practical implementations of mathematical, bio-inspired algorithms and models for developed software applications in the digital environments of corporate information systems of industrial enterprise paradigm-based "Industry 4.0" will be proposed in this Special Issue of Mathematics entitled "Applied and Computational Mathematics for Digital Environments".

The Special Issue will consider scientific research, applied engineering tasks, and problems in the following areas:

  • Building mathematical, structural, and information models of intelligent computer systems for monitoring and managing the parameters of the digital environments;
  • Software and mathematical technologies in the implementation of intelligent monitoring and computer control of digital environments’ parameters;
  • Application of mathematical models, internet of things technologies, machine learning, and artificial intelligence for big data analysis of digital environments;
  • Mathematical models and algorithms for identifying stable patterns between the parameters of digital environments and their complex and separate influence;
  • Mathematical modeling, machine learning, and their implementation within the concept of "smart" digital environments.

Prof. Dr. Liliya Demidova
Guest Editor

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Keywords

  • artificial intelligence
  • big data
  • machine learning
  • digital environments

Published Papers (13 papers)

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Editorial

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5 pages, 391 KiB  
Editorial
Applied and Computational Mathematics for Digital Environments
by Liliya A. Demidova
Mathematics 2023, 11(7), 1629; https://doi.org/10.3390/math11071629 - 28 Mar 2023
Viewed by 948
Abstract
Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [...] Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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Research

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39 pages, 2288 KiB  
Article
A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature
by Liliya A. Demidova
Mathematics 2023, 11(4), 792; https://doi.org/10.3390/math11040792 - 04 Feb 2023
Cited by 4 | Viewed by 1053 | Correction
Abstract
This paper deals with the problem of diagnosing oncological diseases based on blood protein markers. The goal of the study is to develop a novel approach in decision-making on diagnosing oncological diseases based on blood protein markers by generating datasets that include various [...] Read more.
This paper deals with the problem of diagnosing oncological diseases based on blood protein markers. The goal of the study is to develop a novel approach in decision-making on diagnosing oncological diseases based on blood protein markers by generating datasets that include various combinations of features: both known features corresponding to blood protein markers and new features generated with the help of mathematical tools, particularly with the involvement of the non-linear dimensionality reduction algorithm UMAP, formulas for various entropies and fractal dimensions. These datasets were used to develop a group of multiclass kNN and SVM classifiers using oversampling algorithms to solve the problem of class imbalance in the dataset, which is typical for medical diagnostics problems. The results of the experimental studies confirmed the feasibility of using the UMAP algorithm and approximation entropy, as well as Katz and Higuchi fractal dimensions to generate new features based on blood protein markers. Various combinations of these features can be used to expand the set of features from the original dataset in order to improve the quality of the received classification solutions for diagnosing oncological diseases. The best kNN and SVM classifiers were developed based on the original dataset augmented respectively with a feature based on the approximation entropy and features based on the UMAP algorithm and the approximation entropy. At the same time, the average values of the metric MacroF1-score used to assess the quality of classifiers during cross-validation increased by 16.138% and 4.219%, respectively, compared to the average values of this metric in the case when the original dataset was used in the development of classifiers of the same name. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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28 pages, 40305 KiB  
Article
On Improving Adaptive Problem Decomposition Using Differential Evolution for Large-Scale Optimization Problems
by Aleksei Vakhnin, Evgenii Sopov and Eugene Semenkin
Mathematics 2022, 10(22), 4297; https://doi.org/10.3390/math10224297 - 16 Nov 2022
Cited by 5 | Viewed by 1845
Abstract
Modern computational mathematics and informatics for Digital Environments deal with the high dimensionality when designing and optimizing models for various real-world phenomena. Large-scale global black-box optimization (LSGO) is still a hard problem for search metaheuristics, including bio-inspired algorithms. Such optimization problems are usually [...] Read more.
Modern computational mathematics and informatics for Digital Environments deal with the high dimensionality when designing and optimizing models for various real-world phenomena. Large-scale global black-box optimization (LSGO) is still a hard problem for search metaheuristics, including bio-inspired algorithms. Such optimization problems are usually extremely multi-modal, and require significant computing resources for discovering and converging to the global optimum. The majority of state-of-the-art LSGO algorithms are based on problem decomposition with the cooperative co-evolution (CC) approach, which divides the search space into a set of lower dimensional subspaces (or subcomponents), which are expected to be easier to explore independently by an optimization algorithm. The question of the choice of the decomposition method remains open, and an adaptive decomposition looks more promising. As we can see from the most recent LSGO competitions, winner-approaches are focused on modifying advanced DE algorithms through integrating them with local search techniques. In this study, an approach that combines multiple ideas from state-of-the-art algorithms and implements Coordination of Self-adaptive Cooperative Co-evolution algorithms with Local Search (COSACC-LS1) is proposed. The self-adaptation method tunes both the structure of the complete approach and the parameters of each algorithm in the cooperation. The performance of COSACC-LS1 has been investigated using the CEC LSGO 2013 benchmark and the experimental results has been compared with leading LSGO approaches. The main contribution of the study is a new self-adaptive approach that is preferable for solving hard real-world problems because it is not overfitted with the LSGO benchmark due to self-adaptation during the search process instead of a manual benchmark-specific fine-tuning. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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32 pages, 3465 KiB  
Article
Machine Learning Feedback Control Approach Based on Symbolic Regression for Robotic Systems
by Askhat Diveev and Elizaveta Shmalko
Mathematics 2022, 10(21), 4100; https://doi.org/10.3390/math10214100 - 03 Nov 2022
Cited by 3 | Viewed by 1253
Abstract
A control system of an autonomous robot produces a control signal based on feedback. This type of control implies the control of an object according to its state that is mathematically the control synthesis problem. Today there are no universal analytical methods for [...] Read more.
A control system of an autonomous robot produces a control signal based on feedback. This type of control implies the control of an object according to its state that is mathematically the control synthesis problem. Today there are no universal analytical methods for solving the general synthesis problem, and it is solved by certain particular approaches depending on the type of control object. In this paper, we propose a universal numerical approach to solving the problem of optimal control with feedback using machine learning methods based on symbolic regression. The approach is universal and can be applied to various objects. However, the use of machine learning methods imposes two aspects. First, when using them, it is necessary to reduce the requirements for optimality. In machine learning, optimization algorithms are used, but strictly optimal solutions are not sought. Secondly, in machine learning, analytical proofs of the received properties of solutions are not required. In machine methods, a set of tests is carried out and it is shown that this is sufficient to achieve the required properties. Thus, in this article, we initially introduce the fundamentals of machine learning control, introduce the basic concepts, properties and machine criteria for application of this technique. Then, with regard to the introduced notations, the feedback optimal control problem is considered and reformulated in order to add to the problem statement that such a property adjusts both the requirements of stability and optimality. Next, a description of the proposed approach is presented, theoretical formulations are given, and its efficiency is demonstrated on the computational examples in mobile robot control tasks. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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33 pages, 530 KiB  
Article
Relaxation Subgradient Algorithms with Machine Learning Procedures
by Vladimir Krutikov, Svetlana Gutova, Elena Tovbis, Lev Kazakovtsev and Eugene Semenkin
Mathematics 2022, 10(21), 3959; https://doi.org/10.3390/math10213959 - 25 Oct 2022
Cited by 4 | Viewed by 1219
Abstract
In the modern digital economy, optimal decision support systems, as well as machine learning systems, are becoming an integral part of production processes. Artificial neural network training as well as other engineering problems generate such problems of high dimension that are difficult to [...] Read more.
In the modern digital economy, optimal decision support systems, as well as machine learning systems, are becoming an integral part of production processes. Artificial neural network training as well as other engineering problems generate such problems of high dimension that are difficult to solve with traditional gradient or conjugate gradient methods. Relaxation subgradient minimization methods (RSMMs) construct a descent direction that forms an obtuse angle with all subgradients of the current minimum neighborhood, which reduces to the problem of solving systems of inequalities. Having formalized the model and taking into account the specific features of subgradient sets, we reduced the problem of solving a system of inequalities to an approximation problem and obtained an efficient rapidly converging iterative learning algorithm for finding the direction of descent, conceptually similar to the iterative least squares method. The new algorithm is theoretically substantiated, and an estimate of its convergence rate is obtained depending on the parameters of the subgradient set. On this basis, we have developed and substantiated a new RSMM, which has the properties of the conjugate gradient method on quadratic functions. We have developed a practically realizable version of the minimization algorithm that uses a rough one-dimensional search. A computational experiment on complex functions in a space of high dimension confirms the effectiveness of the proposed algorithm. In the problems of training neural network models, where it is required to remove insignificant variables or neurons using methods such as the Tibshirani LASSO, our new algorithm outperforms known methods. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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18 pages, 4544 KiB  
Article
Complex Color Space Segmentation to Classify Objects in Urban Environments
by Juan-Jose Cardenas-Cornejo, Mario-Alberto Ibarra-Manzano, Daniel-Alberto Razo-Medina and Dora-Luz Almanza-Ojeda
Mathematics 2022, 10(20), 3752; https://doi.org/10.3390/math10203752 - 12 Oct 2022
Cited by 1 | Viewed by 1470
Abstract
Color image segmentation divides the image into areas that represent different objects and focus points. One of the biggest problems in color image segmentation is the lack of homogeneity in the color of real urban images, which generates areas of over-segmentation when traditional [...] Read more.
Color image segmentation divides the image into areas that represent different objects and focus points. One of the biggest problems in color image segmentation is the lack of homogeneity in the color of real urban images, which generates areas of over-segmentation when traditional color segmentation techniques are used. This article describes an approach to detecting and classifying objects in urban environments based on a new chromatic segmentation to locate focus points. Based on components a and b on the CIELab space, we define a chromatic map on the complex space to determine the highest threshold values by comparing neighboring blocks and thus divide various areas of the image automatically. Even though thresholds can result in broad segmentation areas, they suffice to locate centroids of patches on the color image that are then classified using a convolutional neural network (CNN). Thus, this broadly segmented image helps to crop only outlying areas instead of classifying the entire image. The CNN is trained to use six classes based on the patches drawn from the database of reference images from urban environments. Experimental results show a high score for classification accuracy that confirms the contribution of this segmentation approach. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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24 pages, 4710 KiB  
Article
Description of the Distribution Law and Non-Linear Dynamics of Growth of Comments Number in News and Blogs Based on the Fokker-Planck Equation
by Dmitry Zhukov, Julia Perova and Vladimir Kalinin
Mathematics 2022, 10(6), 989; https://doi.org/10.3390/math10060989 - 19 Mar 2022
Cited by 2 | Viewed by 1774
Abstract
The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynamic distribution [...] Read more.
The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynamic distribution (the change in number of comments over time) in some cases has an S-shaped character, and in some cases a more complex two-stage character. This depends on the time interval between the appearance of a comment at the first level and a comment attached to that comment. The power law for the stationary probability density of news distribution by the number of comments can be obtained from the solution of the stationary Fokker-Planck equation, if a number of assumptions are made in its derivation. In particular, we assume that the drift coefficient μ(x) responsible in the Fokker-Planck equation for a purposeful change in the state of system x (x is the current number of comments on that piece of news) linearly depends on the state x, and the diffusion coefficient D(x) responsible for a random change depends quadratically on x. The solution of the unsteady Fokker-Planck differential equation with these assumptions made it possible to obtain an analytical equation for the probability density of transitions between the states of the system per unit of time, which is in good agreement with the observed data, considering the effect of the delay time between the appearance of the first-level comment and the comment on that comment. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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26 pages, 421 KiB  
Article
Knowledge Dynamics and Behavioural Equivalences in Multi-Agent Systems
by Bogdan Aman and Gabriel Ciobanu
Mathematics 2021, 9(22), 2869; https://doi.org/10.3390/math9222869 - 11 Nov 2021
Cited by 3 | Viewed by 944
Abstract
We define a process calculus to describe multi-agent systems with timeouts for communication and mobility able to handle knowledge. The knowledge of an agent is represented as sets of trees whose nodes carry information; it is used to decide the interactions with other [...] Read more.
We define a process calculus to describe multi-agent systems with timeouts for communication and mobility able to handle knowledge. The knowledge of an agent is represented as sets of trees whose nodes carry information; it is used to decide the interactions with other agents. The evolution of the system with exchanges of knowledge between agents is presented by the operational semantics, capturing the concurrent executions by a multiset of actions in a labelled transition system. Several results concerning the relationship between the agents and their knowledge are presented. We introduce and study some specific behavioural equivalences in multi-agent systems, including a knowledge equivalence able to distinguish two systems based on the interaction of the agents with their local knowledge. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
19 pages, 724 KiB  
Article
Not Another Computer Algebra System: Highlighting wxMaxima in Calculus
by Natanael Karjanto and Husty Serviana Husain
Mathematics 2021, 9(12), 1317; https://doi.org/10.3390/math9121317 - 08 Jun 2021
Cited by 7 | Viewed by 2962
Abstract
This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into classrooms to enhance students’ understanding of Calculus [...] Read more.
This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into classrooms to enhance students’ understanding of Calculus concepts. For many mathematics educators who have been using CAS, this material is of great interest, particularly for secondary teachers and university instructors who plan to introduce an alternative CAS into their classrooms. By highlighting both the strengths and limitations of the software, we hope that it will stimulate further debate not only among mathematics educators and software users but also also among symbolic computation and software developers. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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18 pages, 3575 KiB  
Article
The Influence of Transport Link Density on Conductivity If Junctions and/or Links Are Blocked
by Anton Aleshkin
Mathematics 2021, 9(11), 1278; https://doi.org/10.3390/math9111278 - 02 Jun 2021
Cited by 1 | Viewed by 1542
Abstract
This paper examines some approaches to modeling and managing traffic flows in modern megapolises and proposes using the methods and approaches of the percolation theory. The author sets the task of determining the properties of the transport network (percolation threshold) when designing such [...] Read more.
This paper examines some approaches to modeling and managing traffic flows in modern megapolises and proposes using the methods and approaches of the percolation theory. The author sets the task of determining the properties of the transport network (percolation threshold) when designing such networks, based on the calculation of network parameters (average number of connections per crossroads, road network density). Particular attention is paid to the planarity and nonplanarity of the road transport network. Algorithms for building a planar random network (for modeling purposes) and calculating the percolation thresholds in the resulting network model are proposed. The article analyzes the resulting percolation thresholds for road networks with different relationship densities per crossroad and analyzes the effect of network density on the percolation threshold for these structures. This dependence is specified mathematically, which allows predicting the qualitative characteristics of road network structures (percolation thresholds) in their design. The conclusion shows how the change in the planar characteristics of the road network (with adding interchanges to it) can improve its quality characteristics, i.e., its overall capacity. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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14 pages, 2891 KiB  
Article
A Mathematical Method for Determining the Parameters of Functional Dependencies Using Multiscale Probability Distribution Functions
by Ilya E. Tarasov
Mathematics 2021, 9(10), 1085; https://doi.org/10.3390/math9101085 - 12 May 2021
Cited by 3 | Viewed by 1932
Abstract
This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter [...] Read more.
This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter “scale of the error probability distribution function” and allows one to synthesize the deviation functions, forming spaces with a nonlinear metric, based on the existing assumptions about the sources of errors and noise. The existing method of regression analysis can be obtained from the considered method as a special case. The article examines examples of analysis of experimental data and shows the high resistance of the method to the appearance of single outliers in the sample under study. Since the introduction of an independent parameter increases the number of computations, for the practical application of the method in measuring and information systems, the architecture of a specialized computing device of the “system on a chip” class and practical approaches to its implementation based on programmable logic integrated circuits are considered. Full article
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12 pages, 1333 KiB  
Article
Technology Stack Selection Model for Software Design of Digital Platforms
by Evgeny Nikulchev, Dmitry Ilin and Alexander Gusev
Mathematics 2021, 9(4), 308; https://doi.org/10.3390/math9040308 - 04 Feb 2021
Cited by 7 | Viewed by 2928
Abstract
The article is dedicated to the development of a mathematical model and methodology for evaluating the effectiveness of integrating information technology solutions into digital platforms using virtual simulation infrastructures. The task of selecting a stack of technologies is formulated as the task of [...] Read more.
The article is dedicated to the development of a mathematical model and methodology for evaluating the effectiveness of integrating information technology solutions into digital platforms using virtual simulation infrastructures. The task of selecting a stack of technologies is formulated as the task of selecting elements from sets of possible solutions. This allows us to develop a mathematically unified approach to evaluating the effectiveness of different solutions, such as choosing programming languages, choosing Database Management System (DBMS), choosing operating systems and data technologies, and choosing the frameworks used. Introduced technology compatibility operation and decomposition of the evaluation of the efficiency of the technology stack at the stages of the life cycle of the digital platform development allowed us to reduce the computational complexity of the formation of the technology stack. A methodology based on performance assessments for experimental research in a virtual software-configurable simulation environment has been proposed. The developed solution allows the evaluation of the performance of the digital platform before its final implementation, while reducing the cost of conducting an experiment to assess the characteristics of the digital platform. It is proposed to compare the characteristics of digital platform efficiency based on the use of fuzzy logic, providing the software developer with an intuitive tool to support decision-making on the inclusion of the solution in the technology stack. Full article
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Other

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4 pages, 1290 KiB  
Correction
Correction: Demidova, L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. Mathematics 2023, 11, 792
by Liliya A. Demidova
Mathematics 2023, 11(9), 2150; https://doi.org/10.3390/math11092150 - 04 May 2023
Viewed by 524
Abstract
The author wishes to make the following corrections to this paper [...] Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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