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Fractal Fract
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Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and...
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Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: closed (15 January 2024) | Viewed by 12473

Special Issue Editors

Dr. Victor Leiva

E-Mail
Guest Editor
School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Interests: machine/statistical learning and modeling; clustering, PLS, and EM algorithm; artificial intelligence, big data, data mining, and data science; influence diagnostics
Special Issues, Collections and Topics in MDPI journals
Dr. Carlos Martin-Barreiro

E-Mail Website
Guest Editor
Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral (ESPOL), Guayaquil 090902, Ecuador
Interests: advanced applied multivariate analysis; statistical modeling

Special Issue Information

Dear Colleagues,

Quantum computing is considered a frontier of interdisciplinary research, involving fields ranging from computer science to physics and from chemistry to engineering. The stochastic nature of quantum physics results in the random essence of quantum computing. Therefore, statistics play an essential role in the development of quantum computing. In addition, quantum computing has great potential to revolutionize artificial intelligence, computational statistics, and data science. The objective of this Special Issue is to gather accounts of recent theoretical studies, simulation experiments, and empirical applications in the modeling of complex processes from various domains. For this Special Issue, we are seeking submissions on, but not limited to, fractal and fractional statistics for artificial intelligence, data science, and quantum computing. We strongly encourage interdisciplinary works and the solution of real-world problems.

Dr. Víctor Leiva
Dr. Carlos Martin-Barreiro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • artificial intelligence
  • big data
  • blockchain
  • data science
  • deep learning
  • fractal statistics
  • fractional statistical moments
  • fractional statistics
  • fractional stochastic differential equations
  • fractile/quantile regression
  • fuzzy logic
  • multivariate statistics
  • quantum annealing
  • quantum computing
  • quantum information
  • quantum machine learning
  • quantum statistics
  • software development
  • statistical learning
  • statistical modeling

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Published Papers (6 papers)

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Research

15 pages, 1210 KiB  
Article
Fractional Transformation-Based Decentralized Robust Control of a Coupled-Tank System for Industrial Applications
by Muhammad Z. U. Rahman, Victor Leiva, Asim Ghaffar, Carlos Martin-Barreiro, Aashir Waleed, Xavier Cabezas and Cecilia Castro
Fractal Fract. 2023, 7(8), 590; https://doi.org/10.3390/fractalfract7080590 - 30 Jul 2023
Cited by 2 | Viewed by 1688
Abstract
Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and [...] Read more.
Petrochemical and dairy industries, waste management, and paper manufacturing fall under the category of process industries where flow and liquid control are essential. Even when liquids are mixed or chemically treated in interconnected tanks, the fluid and flow should constantly be observed and controlled, especially when dealing with nonlinearity and imperfect plant models. In this study, we propose a nonlinear dynamic multiple-input multiple-output (MIMO) plant model. This model is then transformed through linearization, a technique frequently utilized in the analysis and modeling of fractional processes, and decoupling for decentralized fixed-structure H-infinity robust control design. Simulation tests based on MATLAB and SIMULINK are subsequently executed. Numerous assessments are conducted to evaluate tracking performance, external disturbance rejection, and plant parameter fluctuations to gauge the effectiveness of the proposed model. The objective of this work is to provide a framework that anticipates potential outcomes, paving the way for implementing a reliable controller synthesis for MIMO-connected tanks in real-world scenarios. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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25 pages, 1283 KiB  
Article
New Classifier Ensemble and Fuzzy Community Detection Methods Using POP Choquet-like Integrals
by Xiaohong Zhang, Haojie Jiang and Jingqian Wang
Fractal Fract. 2023, 7(8), 588; https://doi.org/10.3390/fractalfract7080588 - 30 Jul 2023
Cited by 1 | Viewed by 1462
Abstract
Among various data analysis methods, classifier ensemble (data classification) and community network detection (data clustering) have aroused the interest of many scholars. The maximum operator, as the fusion function, was always used to fuse the results of the base algorithms in the classifier [...] Read more.
Among various data analysis methods, classifier ensemble (data classification) and community network detection (data clustering) have aroused the interest of many scholars. The maximum operator, as the fusion function, was always used to fuse the results of the base algorithms in the classifier ensemble and the membership degree of nodes to classes in the fuzzy community. It is vital to use generalized fusion functions in ensemble and community applications. Since the Pseudo overlap function and the Choquet-like integrals are two new fusion functions, they can be combined as a more generalized fusion function. Along this line, this paper presents new classifier ensemble and fuzzy community detection methods using a pseudo overlap pair (POP) Choquet-like integral (expressed as a fraction). First, the pseudo overlap function pair is proposed to replace the product operator of the Choquet integral. Then, the POP Choquet-like integrals are defined to perform the combinatorial step of ensembles of classifiers and to generalize the GN modularity for the fuzzy community network. Finally, two new algorithms are designed for experiments, and some computational experiments with other algorithms show the importance of POP Choquet-like integrals. All of the experimental results show that our algorithms are practical. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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21 pages, 1153 KiB  
Article
On Fuzzy and Crisp Solutions of a Novel Fractional Pandemic Model
by Kalpana Umapathy, Balaganesan Palanivelu, Víctor Leiva, Prasantha Bharathi Dhandapani and Cecilia Castro
Fractal Fract. 2023, 7(7), 528; https://doi.org/10.3390/fractalfract7070528 - 4 Jul 2023
Cited by 6 | Viewed by 1401
Abstract
Understanding disease dynamics is crucial for accurately predicting and effectively managing epidemic outbreaks. Mathematical modeling serves as an essential tool in such understanding. This study introduces an advanced susceptible, infected, recovered, and dead (SIRD) model that uniquely considers the evolution of the death [...] Read more.
Understanding disease dynamics is crucial for accurately predicting and effectively managing epidemic outbreaks. Mathematical modeling serves as an essential tool in such understanding. This study introduces an advanced susceptible, infected, recovered, and dead (SIRD) model that uniquely considers the evolution of the death parameter, alongside the susceptibility and infection states. This model accommodates the varying environmental factors influencing disease susceptibility. Moreover, our SIRD model introduces fractional changes in death cases, which adds a novel dimension to the traditional counts of susceptible and infected individuals. Given the model’s complexity, we employ the Laplace-Adomian decomposition method. The method allows us to explore various scenarios, including non-fuzzy non-fractional, non-fuzzy fractional, and fuzzy fractional cases. Our methodology enables us to determine the model’s equilibrium positions, compute the basic reproduction number, confirm stability, and provide computational simulations. Our study offers insightful understanding into the dynamics of pandemic diseases and underscores the critical role that mathematical modeling plays in devising effective public health strategies. The ultimate goal is to improve disease management through precise predictions of disease behavior and spread. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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25 pages, 1447 KiB  
Article
On a Novel Dynamics of a SIVR Model Using a Laplace Adomian Decomposition Based on a Vaccination Strategy
by Prasantha Bharathi Dhandapani, Víctor Leiva, Carlos Martin-Barreiro and Maheswari Rangasamy
Fractal Fract. 2023, 7(5), 407; https://doi.org/10.3390/fractalfract7050407 - 18 May 2023
Cited by 5 | Viewed by 2028
Abstract
In this paper, we introduce a SIVR model using the Laplace Adomian decomposition. This model focuses on a new trend in mathematical epidemiology dedicated to studying the characteristics of vaccination of infected communities. We analyze the epidemiological parameters using equilibrium stability and numerical [...] Read more.
In this paper, we introduce a SIVR model using the Laplace Adomian decomposition. This model focuses on a new trend in mathematical epidemiology dedicated to studying the characteristics of vaccination of infected communities. We analyze the epidemiological parameters using equilibrium stability and numerical analysis techniques. New mathematical strategies are also applied to establish our epidemic model, which is a pandemic model as well. In addition, we mathematically establish the chance for the next wave of any pandemic disease and show that a consistent vaccination strategy could control it. Our proposal is the first model introducing a vaccination strategy to actively infected cases. We are sure this work will serve as the basis for future research on COVID-19 and pandemic diseases since our study also considers the vaccinated population. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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22 pages, 583 KiB  
Article
The Continuous Bernoulli Distribution: Mathematical Characterization, Fractile Regression, Computational Simulations, and Applications
by Mustafa Ç. Korkmaz, Víctor Leiva and Carlos Martin-Barreiro
Fractal Fract. 2023, 7(5), 386; https://doi.org/10.3390/fractalfract7050386 - 6 May 2023
Cited by 8 | Viewed by 2686
Abstract
The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties [...] Read more.
The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties of the continuous Bernoulli distribution and formulates a fractile or quantile regression model for a unit response using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and the fractile regression model. Real-world datasets from science and education are analyzed to illustrate the modeling abilities of the continuous Bernoulli distribution and the exponentiated continuous Bernoulli quantile regression model. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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28 pages, 1589 KiB  
Article
A Novel Regression Model for Fractiles: Formulation, Computational Aspects, and Applications to Medical Data
by Víctor Leiva, Josmar Mazucheli and Bruna Alves
Fractal Fract. 2023, 7(2), 169; https://doi.org/10.3390/fractalfract7020169 - 7 Feb 2023
Cited by 8 | Viewed by 1718
Abstract
Covariate-related response variables that are measured on the unit interval frequently arise in diverse studies when index and proportion data are of interest. A regression on the mean is commonly used to model this relationship. Instead of relying on the mean, which is [...] Read more.
Covariate-related response variables that are measured on the unit interval frequently arise in diverse studies when index and proportion data are of interest. A regression on the mean is commonly used to model this relationship. Instead of relying on the mean, which is sensitive to atypical data and less general, we can estimate such a relation using fractile regression. A fractile is a point on a probability density curve such that the area under the curve between that point and the origin is equal to a specified fraction. Fractile or quantile regression modeling has been considered for some statistical distributions. Our objective in the present article is to formulate a novel quantile regression model which is based on a parametric distribution. Our fractile regression is developed reparameterizing the initial distribution. Then, we introduce a functional form based on regression through a link function. The main features of the new distribution, as well as the density, distribution, and quantile functions, are obtained. We consider a brand-new distribution to model the fractiles of a continuous dependent variable (response) bounded to the interval (0, 1). We discuss an R package with random number generators and functions for probability density, cumulative distribution, and quantile, in addition to estimation and model checking. Instead of the original distribution-free quantile regression, parametric fractile regression has lately been employed in several investigations. We use the R package to fit the model and apply it to two case studies using COVID-19 and medical data from Brazil and the United States for illustration. Full article
(This article belongs to the Special Issue Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing)
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