Research

18 pages, 331 KiB

Open AccessArticle

Mathematical Foundation of a Functional Implementation of the CNF Algorithm

by Francisco Miguel García-Olmedo, Jesús García-Miranda and Pedro González-Rodelas

Algorithms 2023, 16(10), 459; https://doi.org/10.3390/a16100459 - 27 Sep 2023

Viewed by 1292

The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the “distributivity” of [...] Read more.

The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the “distributivity” of logical disjunction versus conjunction. For those types of implementations, the loop iteration runs a comparison between formulas to decide when to stop. In this article, we explain how to pre-calculate the exact number of loop iterations, thus avoiding the work involved in the above-mentioned comparison. After that, it is possible to concatenate another loop focused now on the “associativity” of conjunction and disjunction. Also for that loop, we explain how to calculate the optimal number of rounds, so that the decisional comparison phase for stopping can be also avoided. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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22 pages, 726 KiB

Open AccessArticle

Implementation Aspects in Regularized Structural Equation Models

by Alexander Robitzsch

Algorithms 2023, 16(9), 446; https://doi.org/10.3390/a16090446 - 18 Sep 2023

Cited by 3 | Viewed by 1037

Abstract

This article reviews several implementation aspects in estimating regularized single-group and multiple-group structural equation models (SEM). It is demonstrated that approximate estimation approaches that rely on a differentiable approximation of non-differentiable penalty functions perform similarly to the coordinate descent optimization approach of regularized [...] Read more.

This article reviews several implementation aspects in estimating regularized single-group and multiple-group structural equation models (SEM). It is demonstrated that approximate estimation approaches that rely on a differentiable approximation of non-differentiable penalty functions perform similarly to the coordinate descent optimization approach of regularized SEMs. Furthermore, using a fixed regularization parameter can sometimes be superior to an optimal regularization parameter selected by the Bayesian information criterion when it comes to the estimation of structural parameters. Moreover, the widespread penalty functions of regularized SEM implemented in several R packages were compared with the estimation based on a recently proposed penalty function in the Mplus software. Finally, we also investigate the performance of a clever replacement of the optimization function in regularized SEM with a smoothed differentiable approximation of the Bayesian information criterion proposed by O’Neill and Burke in 2023. The findings were derived through two simulation studies and are intended to guide the practical implementation of regularized SEM in future software pieces. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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11 pages, 4847 KiB

Open AccessArticle

Optimal Confidence Regions for Weibull Parameters and Quantiles under Progressive Censoring

by Arturo J. Fernández

Algorithms 2023, 16(9), 427; https://doi.org/10.3390/a16090427 - 06 Sep 2023

Viewed by 780

Abstract

Confidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal conditional confidence [...] Read more.

Confidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal conditional confidence sets for two Weibull quantiles are also derived. Simulation-based algorithms are provided for computing the smallest-area regions with fixed confidence levels. Importantly, the proposed confidence sets satisfy the Sufficiency, Likelihood and Conditionality Principles in contrast to the unconditional regions based on maximum likelihood estimators and other insufficient statistics. The suggested perspective can be applied to parametric estimation and hypothesis testing, as well as to the determination of minimum-size confidence sets for other invariantly estimable functions of the Weibull parameters. A dataset concerning failure times of an insulating fluid is studied for illustrative and comparative purposes. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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18 pages, 4975 KiB

Open AccessArticle

A Mathematical Study on a Fractional-Order SEIR Mpox Model: Analysis and Vaccination Influence

by Iqbal M. Batiha, Ahmad A. Abubaker, Iqbal H. Jebril, Suha B. Al-Shaikh, Khaled Matarneh and Manal Almuzini

Algorithms 2023, 16(9), 418; https://doi.org/10.3390/a16090418 - 01 Sep 2023

Cited by 2 | Viewed by 972

Abstract

This paper establishes a novel fractional-order version of a recently expanded form of the Susceptible-Exposed-Infectious-Recovery (SEIR) Mpox model. This model is investigated by means of demonstrating some significant findings connected with the stability analysis and the vaccination impact, as well. In particular, we [...] Read more.

This paper establishes a novel fractional-order version of a recently expanded form of the Susceptible-Exposed-Infectious-Recovery (SEIR) Mpox model. This model is investigated by means of demonstrating some significant findings connected with the stability analysis and the vaccination impact, as well. In particular, we analyze the fractional-order Mpox model in terms of its invariant region, boundedness of solution, equilibria, basic reproductive number, and its elasticity. In accordance with an effective vaccine, we study the progression and dynamics of the Mpox disease in compliance with various scenarios of the vaccination ratio through the proposed fractional-order Mpox model. Accordingly, several numerical findings of the proposed model are depicted with the use of two numerical methods; the Fractional Euler Method (FEM) and Modified Fractional Euler Method (MFEM). Such findings demonstrate the influence of the fractional-order values coupled with the vaccination rate on the dynamics of the established disease model. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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15 pages, 5415 KiB

Open AccessArticle

Using Epidemiological Models to Predict the Spread of Information on Twitter

by Matteo Castiello, Dajana Conte and Samira Iscaro

Algorithms 2023, 16(8), 391; https://doi.org/10.3390/a16080391 - 17 Aug 2023

Cited by 1 | Viewed by 1167

Abstract

In this article, we analyze the spread of information on social media (Twitter) and purpose a strategy based on epidemiological models. It is well known that social media represent a strong tool to spread news and, in particular, fake news, due to the [...] Read more.

In this article, we analyze the spread of information on social media (Twitter) and purpose a strategy based on epidemiological models. It is well known that social media represent a strong tool to spread news and, in particular, fake news, due to the fact that they are free and easy to use. First, we propose an algorithm to create a proper dataset in order to employ the ignorants–spreaders–recovered epidemiological model. Then, we show that to use this model to study the diffusion of real news, parameter estimation is required. We show that it is also possible to accurately predict the evolution of news spread and its peak in terms of the maximum number of people who share it and the time when the peak occurs trough a process of data reduction, i.e., by using only a part of the built dataset to optimize parameters. Numerical results based on the analysis of real news are also provided to confirm the applicability of our proposed model and strategy. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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11 pages, 278 KiB

Open AccessCommunication

Equivalence between LC-CRF and HMM, and Discriminative Computing of HMM-Based MPM and MAP

by Elie Azeraf, Emmanuel Monfrini and Wojciech Pieczynski

Algorithms 2023, 16(3), 173; https://doi.org/10.3390/a16030173 - 21 Mar 2023

Cited by 1 | Viewed by 1325

Abstract

Practitioners have used hidden Markov models (HMMs) in different problems for about sixty years. Moreover, conditional random fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We propose two contributions: First, we show that [...] Read more.

Practitioners have used hidden Markov models (HMMs) in different problems for about sixty years. Moreover, conditional random fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We propose two contributions: First, we show that the basic linear-chain CRFs (LC-CRFs), considered as different from HMMs, are in fact equivalent to HMMs in the sense that for each LC-CRF there exists an HMM—that we specify—whose posterior distribution is identical to the given LC-CRF. Second, we show that it is possible to reformulate the generative Bayesian classifiers maximum posterior mode (MPM) and maximum a posteriori (MAP), used in HMMs, as discriminative ones. The last point is of importance in many fields, especially in natural language processing (NLP), as it shows that in some situations dropping HMMs in favor of CRFs is not necessary. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

20 pages, 584 KiB

Open AccessArticle

About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm

by Warren Hare and Gabriel Jarry-Bolduc

Algorithms 2023, 16(2), 84; https://doi.org/10.3390/a16020084 - 03 Feb 2023

Cited by 1 | Viewed by 1296

Abstract

This paper examines a calculus-based approach to building model functions in a derivative-free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivative-free trust-region method are implemented. The first [...] Read more.

This paper examines a calculus-based approach to building model functions in a derivative-free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivative-free trust-region method are implemented. The first version builds model functions by using a calculus-based approach, and the second version builds model functions by directly considering the objective function. The numerical experiments demonstrate that the calculus-based approach provides better results in most situations and significantly better results in specific situations. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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15 pages, 1459 KiB

Open AccessArticle

An Effective Staff Scheduling for Shift Workers in Social Welfare Facilities for the Disabled

by Hee Jun Ryu, Ye Na Jo, Won Jun Lee, Ji Won Cheong, Boo Yong Moon and Young Dae Ko

Algorithms 2023, 16(1), 41; https://doi.org/10.3390/a16010041 - 09 Jan 2023

Viewed by 2237

Abstract

The efficient management of social worker personnel is important since it involves a huge portion in its operations. However, the burnout and turnover rates of social workers are very high, which is due to dissatisfaction with the irregular and unequal schedules, despite the [...] Read more.

The efficient management of social worker personnel is important since it involves a huge portion in its operations. However, the burnout and turnover rates of social workers are very high, which is due to dissatisfaction with the irregular and unequal schedules, despite the continuous improvement in the treatment of social workers and the enactment of work-related legislation in Korea. This means that changes in policy do not significantly contribute to improving worker satisfaction, which shows the necessity of the strategies to prevent the turnover of workers. Therefore, this study aims to propose a strategy for the staff scheduling of workers that considers the fairness in the shift distribution among workers and the individual preference for shift work by using the linear programming. A survey about the preferences for shift work is conducted that targeted the employees of a welfare facility in Korea to enhance the practicality of the model. The effectiveness and applicability of the developed mathematical model are verified by deriving a deterministic schedule for a worker via the system parameters that were obtained based on the survey and the rules of the welfare facility in the numerical experiment. Compared to the conventional schedule, the derived schedule shows an improvement in the deviations in the number of shifts workers and a reflection of the personal preferences. This can raise the social worker’s satisfaction, which will decrease intention on burnouts and turnover. It will consequently facilitate on managing human resources in welfare facilities. Full article

(This article belongs to the Special Issue Mathematical Models and Their Applications IV)

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