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Symmetry
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Probability and Statistics Theory in Symmetry and Application from Machine...
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Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 6691

Special Issue Editors

Dr. Youngsoo Seol

E-Mail Website
Guest Editor
Department of Information Sciences and Mathematics, Dong-A University, Busan 49315, Republic of Korea
Interests: limit theorems; random walks; Hawkes process; probability theory; stochastic process applications and data analytic and machine learning
Prof. Dr. Do-Young Kang

E-Mail Website
Guest Editor
Department of Nuclear Medicine, College of Medicine, Dong-A University, Busan 49201, Republic of Korea
Interests: brain; image classification; medical image processing; positron emission tomography; biomedical MRI; dementia; computerizedtomography; CNN; RNN; transformer; large language model; generative AI; multimodal data
Special Issues, Collections and Topics in MDPI journals
Dr. Sangjin Kim

E-Mail Website
Guest Editor
Department of Management and Information Systems, Dong-A University, Busan 49315, Republic of Korea
Interests: data mining; machine learning; deep learning; statistical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Probability and statistics in symmetry have become important topics of study in recent years, possessing wide applications in various fields including medicine, biology, economics, engineering, and physics. Specifically, stochastic processes have come to play fundamental roles in the mathematical model of phenomena in wide areas, such as symmetric random walks, random walks in a random environment, Hawkes processes, etc. The study of these phenomena and applications has led to the development of new stochastic processes. Some important probability laws are heavy-tailed distributions, which can be modeled with discretizations of random variables or measured by parameters of either new or old statistical models. The growing data resources have led to the introduction of a variety of distributions and their properties.

The adoption of machine learning and deep learning analytics in the bio-medical field with symmetry properties is progressing at a rapid pace, with some applications already finding use in pre-clinical and clinical settings. In addition, various types of bio-medical data continue to be used, and CNN, RNN, and transform technologies used for analysis continue to undergo further development. There are many types of bio-medical data, such as image data, pathological tissue data, waveform data, natural language data, genetic data, voice data, etc.

The purpose of this Special Issue is to provide a collection of articles that reflect the importance of statistics and probability in symmetry and its applications in several areas, and also to assemble the current research on the latest machine learning and deep learning techniques of various bio-medical data with symmetry properties. Additionally, we would welcome hypotheses for a fusion analysis technique of various bio-medical data.

Dr. Youngsoo Seol
Prof. Dr. Do-Young Kang
Dr. Sangjin Kim
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. Symmetry 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 2400 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

  • limit theorems
  • probability and statistics
  • stochastic processes and its applications

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Published Papers (5 papers)

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Research

24 pages, 1608 KiB  
Article
Symmetry in Genetic Distance Metrics: Quantifying Variability in Neurological Disorders for Personalized Treatment of Alzheimer’s and Dementia
by Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Marco Antonio Márquez-Vera, Ricardo A. Barrera-Cámara, Alejandro Fuentes-Penna, Eric Simancas-Acevedo, Miguel A. Ruiz-Jaimes, Juan M. Xicoténcatl-Pérez and Julio Cesar Ramos-Fernández
Symmetry 2025, 17(2), 172; https://doi.org/10.3390/sym17020172 - 23 Jan 2025
Viewed by 781
Abstract
This paper aims to adapt and apply genetic distance metrics in biomedical signal processing to improve the classification and monitoring of neurological disorders, specifically Alzheimer’s disease and frontotemporal dementia. The primary objectives are: (1) to quantify the variability in EEG signal patterns among [...] Read more.
This paper aims to adapt and apply genetic distance metrics in biomedical signal processing to improve the classification and monitoring of neurological disorders, specifically Alzheimer’s disease and frontotemporal dementia. The primary objectives are: (1) to quantify the variability in EEG signal patterns among the distinct subtypes of neurodegenerative disorders and healthy individuals, and (2) to explore the potential of a novel genetic similarity metric in establishing correlations between brain signal dynamics and clinical progression. Using a dataset of resting-state EEG recordings (eyes closed) from 88 subjects (36 with Alzheimer’s disease, 23 with frontotemporal dementia, and 29 healthy individuals), a comparative analysis of brain activity patterns was conducted. Symmetry plays a critical role in the proposed genetic similarity metric, as it captures the balanced relationships between intra- and inter-group EEG signal patterns. Our findings demonstrate that this approach significantly improves disease subtype identification and highlights the potential of the genetic similarity metric to optimize the predictive models. Furthermore, this methodology supports the development of personalized therapeutic interventions tailored to individual patient profiles, making a novel contribution to the field of neurological signal analysis and advancing the application of EEG in personalized medicine. Full article
(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)
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16 pages, 4201 KiB  
Article
Bivariate Log-Symmetric Regression Models Applied to Newborn Data
by Helton Saulo, Roberto Vila and Rubens Souza
Symmetry 2024, 16(10), 1315; https://doi.org/10.3390/sym16101315 - 5 Oct 2024
Cited by 1 | Viewed by 1149
Abstract
This paper introduces bivariate log-symmetric models for analyzing the relationship between two variables, assuming a family of log-symmetric distributions. These models offer greater flexibility than the bivariate lognormal distribution, allowing for better representation of diverse distribution shapes and behaviors in the data. The [...] Read more.
This paper introduces bivariate log-symmetric models for analyzing the relationship between two variables, assuming a family of log-symmetric distributions. These models offer greater flexibility than the bivariate lognormal distribution, allowing for better representation of diverse distribution shapes and behaviors in the data. The log-symmetric distribution family is widely used in various scientific fields and includes distributions such as log-normal, log-Student-t, and log-Laplace, among others, providing several options for modeling different data types. However, there are few approaches to jointly model continuous positive and explanatory variables in regression analysis. Therefore, we propose a class of generalized linear model (GLM) regression models based on bivariate log-symmetric distributions, aiming to fill this gap. Furthermore, in the proposed model, covariates are used to describe its dispersion and correlation parameters. This study uses a dataset of anthropometric measurements of newborns to correlate them with various biological factors, proposing bivariate regression models to account for the relationships observed in the data. Such models are crucial for preventing and controlling public health issues. Full article
(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)
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16 pages, 297 KiB  
Article
Empirical Likelihood for Composite Quantile Regression Models with Missing Response Data
by Shuanghua Luo, Yu Zheng and Cheng-yi Zhang
Symmetry 2024, 16(10), 1314; https://doi.org/10.3390/sym16101314 - 5 Oct 2024
Viewed by 1289
Abstract
Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically χ2. Secondly, without an estimation of the asymptotic covariance, [...] Read more.
Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically χ2. Secondly, without an estimation of the asymptotic covariance, confidence intervals are constructed for the regression coefficients. Thirdly, three estimators are presented for the regression parameters to obtain its asymptotic distribution. The finite sample performance is assessed through simulation studies, and the symmetry confidence intervals of the parametric are constructed. Finally, the effectiveness of the proposed methods is illustrated by analyzing a real-world data set. Full article
(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)
12 pages, 392 KiB  
Article
A New Extension of the Exponentiated Weibull–Poisson Family Using the Gamma-Exponentiated Weibull Distribution: Development and Applications
by Kuntalee Chaisee, Manad Khamkong and Pawat Paksaranuwat
Symmetry 2024, 16(7), 780; https://doi.org/10.3390/sym16070780 - 21 Jun 2024
Viewed by 968
Abstract
This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous [...] Read more.
This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality. Full article
(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)
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23 pages, 338 KiB  
Article
Conditional Strong Law of Large Numbers under G-Expectations
by Jiaqi Zhang, Yanyan Tang and Jie Xiong
Symmetry 2024, 16(3), 272; https://doi.org/10.3390/sym16030272 - 25 Feb 2024
Viewed by 1486
Abstract
In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points [...] Read more.
In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one. Full article
(This article belongs to the Special Issue Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data)
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