Special Issue "Mathematical Models and Methods in Various Sciences"

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

Deadline for manuscript submissions: 31 July 2023 | Viewed by 4747

Special Issue Editor

Dr. Dário Ferreira
E-Mail Website
Guest Editor
Department of Mathematics and Center of Mathematics and Applications, Universidade da Beira Interior, Covilhã, Portugal
Interests: applied statistics; data science; probability theory; statistical inference; statistical modeling

Special Issue Information

Dear Colleagues,

Symmetry describes the shape of a data distribution and is a central notion in statistics and data science. For example, when working with symmetric models, it is only necessary to model half of the model.

The aim of this Special Issue is to assemble innovative papers on theory, methodology, and applications of symmetric/asymmetric mathematical models and methods, applied to various areas of science.

We encourage submissions presenting original works with high scientific merit on statistical, computational, and mathematical approaches with an emphasis on behavioral science, biology, biomedical sciences, computer science, data analytics, economics and management, engineering, epidemiology, genomics and genetics, and medicine and social science.

Innovative applications and case studies in any scientific fields are welcome. Contributed papers covering, but not limited to, the following topics are expected:

  • Big data analysis
  • Biostatistics
  • Computational methods
  • Data examples
  • Economic statistics
  • Engineering statistics
  • Experimental design
  • Mathematical models
  • Mathematics and Statistics in Biology
  • Matrix Analysis
  • Multivariate Analysis
  • Simulation experiments
  • Survival analysis
  • Statistical Classification
  • Statistical Inference
  • Statistics in Medicine
  • Symmetrical/asymmetric Distributions
  • Symmetric/asymmetric models.

Dr. Dário Ferreira
Guest Editor

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 2000 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

  • applied mathematics
  • applied statistics
  • data science
  • mathematical statistics
  • model theory
  • probability theory
  • statistical inference
  • statistical modeling

Published Papers (7 papers)

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Research

Article
A Gamma Process with Three Sources of Variability
Symmetry 2023, 15(1), 162; https://doi.org/10.3390/sym15010162 - 05 Jan 2023
Viewed by 225
Abstract
Degradation modeling requires to consider the complexity of both the internal structure of highly reliable products and the environmental conditions, to define appropriate models to obtain estimations about the reliability and quality. These conditions reflect different sources of variability that need to be [...] Read more.
Degradation modeling requires to consider the complexity of both the internal structure of highly reliable products and the environmental conditions, to define appropriate models to obtain estimations about the reliability and quality. These conditions reflect different sources of variability that need to be considered in the aims of obtaining accurate estimations. Although several models have been proposed in the literature, few of them consider several simultaneous sources of variability. In this paper, we propose a model based on the gamma process that considers three sources of variability, specifically in the threshold, the initial level of degradation, and in the scale parameter of the gamma process. The model considers a convolution operation of the threshold and the initial level to then be characterized via numerical integration with the gamma process with random scale. The obtained results showed that the model can be used to model the degradation of products with these sources of variability, which means that it can used for case studies where both the initial level and threshold are inherently random and the randomness in the scale parameter can be proved. The performance is illustrated with a comprehensive simulation study and with the application in a case study. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
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Article
Queue-Size Distribution in a Discrete-Time Finite-Capacity Model with a Single Vacation Mechanism
Symmetry 2022, 14(11), 2350; https://doi.org/10.3390/sym14112350 - 08 Nov 2022
Viewed by 393
Abstract
In the paper a finite-capacity discrete-time queueing system with geometric interarrival times and generally distributed processing times is studied. Every time when the service station becomes idle it goes for a vacation of random duration that can be treated as a power-saving mechanism. [...] Read more.
In the paper a finite-capacity discrete-time queueing system with geometric interarrival times and generally distributed processing times is studied. Every time when the service station becomes idle it goes for a vacation of random duration that can be treated as a power-saving mechanism. Application of a single vacation policy is one way for the system to achieve symmetry in terms of system operating costs. A system of differential equations for the transient conditional queue-size distribution is established. The solution of the corresponding system written for double probability generating functions is found using the analytical method based on a linear algebraic approach. Moreover, the representation for the probability-generating function of the stationary queue-size distribution is obtained. Numerical study illustrating theoretical results is attached as well. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
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Article
Synergies vs. Clustering Only of Depressive Symptoms in Diabetes and Co-Occurring Conditions: Symmetric Indicators with Asymmetric, Bidirectional Influences in MIMIC Models
Symmetry 2022, 14(11), 2275; https://doi.org/10.3390/sym14112275 - 30 Oct 2022
Viewed by 708
Abstract
I extend multiple indicators multiple causes (MIMIC) models to unveil unbiased, asymmetric, bidirectional influences using indicators of the same items within variable-defined subgroups. The strategy discerns (1) item-variation in interaction (and derivative) terms that capture synergies and cluster together (formative or causal indicators) [...] Read more.
I extend multiple indicators multiple causes (MIMIC) models to unveil unbiased, asymmetric, bidirectional influences using indicators of the same items within variable-defined subgroups. The strategy discerns (1) item-variation in interaction (and derivative) terms that capture synergies and cluster together (formative or causal indicators) from (2) item-variation in duplicate terms when items lack synergy and cluster together only (reflective or effect indicators). An item may reveal either or both influences. These symmetric indicators yield estimates of (1) the unique variation and synergy of each formative indicator within the structural model portion of the MIMIC model (based on moderated regression) and (2) the remaining shared variation in the reflective indicator within the measurement model portion (based on confirmatory factor analysis). I reveal two patterns of comorbidity in disease subgroups of a specific co-occurring condition across a community sample of older adults and in age and gender subsamples. First, as structural model indicators, depressive symptoms may display different synergies as they cluster within a disease subgroup of diabetes and a specific co-occurring condition. As measurement model indicators, depressive symptoms capture non-synergistic clustering within the disease subgroup. Second, diabetes may mediate the co-occurring condition when depressive symptoms lack synergies but cluster within the disease subgroup. Researchers should distinguish both comorbidity patterns, which have different implications. I offer insights for adaptive modeling, conceptualizing and screening symptom clusters, metabolomics, and economic or social monitoring. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
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Article
Bivariate Proportional Hazard Models: Structure and Inference
Symmetry 2022, 14(10), 2073; https://doi.org/10.3390/sym14102073 - 06 Oct 2022
Viewed by 420
Abstract
We focus on a variety of bivariate models with proportional hazard components. Models with proportional hazard marginals are described together with a selection of models with propor- tional hazard conditional distributions. The bivariate distributions with marginal proportional hazards distributions are shown to be [...] Read more.
We focus on a variety of bivariate models with proportional hazard components. Models with proportional hazard marginals are described together with a selection of models with propor- tional hazard conditional distributions. The bivariate distributions with marginal proportional hazards distributions are shown to be closely related to certain known bivariate exponential models. Two distinct kinds of conditional specification are investigated. Discussion is provided of cases with hazard function components that are (1) completely unknown, (2) known to belong to given parametric families and (3) completely known. Since the models are designed for use with survival data, it is inevitable that the marginal and conditional distributions will be asymmetric. However, logarithmic transformations in some cases will result in symmetric component distributions. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
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Article
Suitability of the Single Transferable Vote as a Replacement for Largest Remainder Proportional Representation
Symmetry 2022, 14(8), 1648; https://doi.org/10.3390/sym14081648 - 10 Aug 2022
Viewed by 511
Abstract
There are two main approaches to achieving proportional representation in elections: the single transferable vote and methods based on party lists. This paper discusses ways to use the single transferable vote while using some of the main features used with the largest remainder [...] Read more.
There are two main approaches to achieving proportional representation in elections: the single transferable vote and methods based on party lists. This paper discusses ways to use the single transferable vote while using some of the main features used with the largest remainder method, such as the electoral threshold. The investigation has shown that the Weighted Inclusive Gregory method is a suitable replacement for the largest remainder method when it is desirable to avoid wasted votes and to handle independent candidates in a straightforward way, but it is also desirable to keep the results as close to the ones achieved under the largest remainder method as possible. The investigation also led to the development of an algorithm for using the single transferable vote when preference lists are based on party lists, exploiting commonalities and symmetries between the patterns of preferences given in the votes. It has been shown that such an algorithm makes the calculations faster than the use of ordinary implementations of the single transferable vote when the numbers of seats and candidates are high, as commonly happens when methods based on party lists are used. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
Article
A Boundedly Rational Decision-Making Model Based on Weakly Consistent Preference Relations
Symmetry 2022, 14(5), 918; https://doi.org/10.3390/sym14050918 - 30 Apr 2022
Viewed by 672
Abstract
Completeness is one of the basic assumptions about the rational preference relation in classical decision theory. Strongly and weakly consistent preferences are presented by abandoning the completeness of the rational preference relation. Some expansion and contraction conditions are proposed and the relationships between [...] Read more.
Completeness is one of the basic assumptions about the rational preference relation in classical decision theory. Strongly and weakly consistent preferences are presented by abandoning the completeness of the rational preference relation. Some expansion and contraction conditions are proposed and the relationships between these conditions of rationality are discussed. The relationships between the conditions of rationality and boundedly rational choice behavior based on strongly and weakly consistent preferences are analyzed and discussed. Furthermore, an example about the choices of chocolates with interval ordinal numbers is given to explain some of the main conclusions in this paper. The results can be used as references for the study of boundedly rational decisions. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
Article
Reliability Analysis with Wiener-Transmuted Truncated Normal Degradation Model for Linear and Non-Negative Degradation Data
Symmetry 2022, 14(2), 353; https://doi.org/10.3390/sym14020353 - 10 Feb 2022
Viewed by 681
Abstract
The degradation rates of many engineering systems are always positive in practical applications. In some cases, the degradation process is approximately linear, such as train wheel wear degradation and an increase in the operating current of laser devices. In this paper we introduce [...] Read more.
The degradation rates of many engineering systems are always positive in practical applications. In some cases, the degradation process is approximately linear, such as train wheel wear degradation and an increase in the operating current of laser devices. In this paper we introduce a degradation modeling and reliability estimation method based on the Wiener process with a transmuted-truncated normal distribution (TTND). The TTND is employed to characterize unit-to-unit variability due to its flexibility in capturing symmetry and the asymmetrical behavior of the drift variable of the Wiener process. A Wiener process with TTND is applied to model the degradation processes of the deteriorating systems in two cases. In the first case, we assume that the degradation process is unaffected by measurement uncertainties, whereas in the second case, the measurement uncertainties are considered. The exact and explicit expressions of PDFs and the reliability functions are derived based on the concept of first hitting time. The Gibbs sampling technique and the Metropolis–Hastings algorithm are employed to obtain the Bayesian estimates of the model’s parameters. The efficiency and the feasibility of the presented approach are demonstrated through numerical examples, with Monte Carlo simulation and a practical application with laser degradation data. Furthermore, deviance information criteria (DIC) are used to compare the proposed model and some existing models. The result indicated that the proposed approach provided better reliability estimation results. Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)
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