A hybrid swarming computing approach to solve the biological nonlinear Leptospirosis system

A next-generation dynamic programming language Julia: Its features and applications in biological science

BACKGROUND

The advent of Julia as a sophisticated and dynamic programming language in 2012 represented a significant milestone in computational programming, mathematical analysis, and statistical modeling. Having reached its stable release in version 1.9.0 on May 7, 2023, Julia has developed into a powerful and versatile instrument. Despite its potential and widespread adoption across various scientific and technical domains, there exists a noticeable knowledge gap in comprehending its utilization within biological sciences.

THE AIM OF REVIEW

This comprehensive review aims to address this particular knowledge gap and offer a thorough examination of Julia's fundamental characteristics and its applications in biology.

KEY SCIENTIFIC CONCEPTS OF THE REVIEW

The review focuses on a research gap in the biological science. The review aims to equip researchers with knowledge and tools to utilize Julia's capabilities in biological science effectively and to demonstrate the gap. It paves the way for innovative solutions and discoveries in this rapidly evolving field. It encompasses an analysis of Julia's characteristics, packages, and performance compared to the other programming languages in this field. The initial part of this review discusses the key features of Julia, such as its dynamic and interactive nature, fast processing speed, ease of expression manipulation, user-friendly syntax, code readability, strong support for multiple dispatch, and advanced type system. It also explores Julia's capabilities in data analysis, visualization, machine learning, and algorithms, making it suitable for scientific applications. The next section emphasizes the importance of using Julia in biological research, highlighting its seamless integration with biological studies for data analysis, and computational biology. It also compares Julia with other programming languages commonly used in biological research through benchmarking and performance analysis. Additionally, it provides insights into future directions and potential challenges in Julia's applications in biology.

A neural network computational structure for the fractional order breast cancer model

The current study provides the numerical performances of the fractional kind of breast cancer (FKBC) model, which are based on five different classes including cancer stem cells, healthy cells, tumor cells, excess estrogen, and immune cells. The motive to introduce the fractional order derivatives is to present more precise solutions as compared to integer order. A stochastic computing reliable scheme based on the Levenberg Marquardt backpropagation neural networks (LMBNNS) is proposed to solve three different cases of the fractional order values of the FKBC model. A designed dataset is constructed by using the Adam solver in order to reduce the mean square error by taking the data performances as 9% for both testing and validation, while 82% is used for training. The correctness of the solver is approved through the negligible absolute error and matching of the solutions for each model's case. To validates the accuracy, and consistency of the solver, the performances based on the error histogram, transition state, and regression for solving the FKBC model.

Hybridization of the swarming and interior point algorithms to solve the Rabinovich-Fabrikant system

In this study, a trustworthy swarming computing procedure is demonstrated for solving the nonlinear dynamics of the Rabinovich-Fabrikant system. The nonlinear system's dynamic depends upon the three differential equations. The computational stochastic structure based on the artificial neural networks (ANNs) along with the optimization of global search swarming particle swarm optimization (PSO) and local interior point (IP) algorithms, i.e., ANNs-PSOIP is presented to solve the Rabinovich-Fabrikant system. An objective function based on the differential form of the model is optimized through the local and global search methods. The correctness of the ANNs-PSOIP scheme is observed through the performances of achieved and source solutions, while the negligible absolute error that is around 10^-05-10^-07 also represent the worth of the ANNs-PSOIP algorithm. Furthermore, the consistency of the ANNs-PSOIP scheme is examined by applying different statistical procedures to solve the Rabinovich-Fabrikant system.

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model’s endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective.

A stochastic numerical approach for a class of singular singularly perturbed system

In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness and accuracy.

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.

Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations

In this paper, a special class of boundary value problems, −▵u=λuq+ur,inΩ,u>0, inΩ,n·∇u+g(u)u=0,on∂Ω, where 0<q<1<r<N+2N−2 and g:[0,∞)→(0,∞) is a nondecreasing C1 function. Here, Ω⊂RN(N≥3) is a bounded domain with smooth boundary ∂Ω and λ>0 is a parameter. The existence of the solution is verified via sub- and super-solutions method. In addition, the influences of parameters on the minimum solution are also discussed. The second positive solution is obtained by using the variational method.