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An Accurate and Stable Filtered Explicit Scheme for Biopolymerization Processes in the Presence of Perturbations
Lisa Davis,
Faranak Pahlevani,
Timmy Susai Rajan
Issue:
Volume 10, Issue 6, December 2021
Pages:
121-137
Received:
31 August 2021
Accepted:
13 October 2021
Published:
5 November 2021
Abstract: The focus of this paper is the development, numerical simulation and parameter analysis of a model of the transcription of ribosomal RNA in highly transcribed genes. Inspired by the well-known classic Lighthill-Whitham-Richards (LWR) traffic flow model, a linear advection continuum model is used to describe the DNA transcription process. In this model, elongation velocity is assumed to be essentially constant as RNA polymerases move along the strand through different phases of gene transcription. One advantage of using the linear model is that it allows one to quantify how small perturbations in elongation velocity and inflow parameters affect important biology measures such as Average Transcription Time (ATT) for the gene. The ATT per polymerase is the amount of time an individual RNAP spends traveling through the DNA strand. The numerical treatment for model simulations includes introducing a low complexity and time accurate method by adding a simple linear time filter to the classic upwind scheme. This improved method is modular and requires a minimal modification of adding only one line of code resulting in increased accuracy without increased computational expense. In addition, it removes the overdamping of upwind. A stability condition for the new algorithm is derived, and numerical computations illustrate stability and convergence of the filtered scheme as well as improved ATT estimation.
Abstract: The focus of this paper is the development, numerical simulation and parameter analysis of a model of the transcription of ribosomal RNA in highly transcribed genes. Inspired by the well-known classic Lighthill-Whitham-Richards (LWR) traffic flow model, a linear advection continuum model is used to describe the DNA transcription process. In this mo...
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Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables
Frédéric Béré,
Kpèbbèwèrè Cédric Somé,
Remi Guillaume Bagré,
Pierre Clovis Nitiéma
Issue:
Volume 10, Issue 6, December 2021
Pages:
138-145
Received:
14 September 2021
Accepted:
11 October 2021
Published:
11 November 2021
Abstract: This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We succeeded in determining a subsequence which allows us to establish a convergence in law of the extremes of this type of random variable while passing by the determination of a speed of convergence. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type. These results will allow us to analyze, in a document, not only the convergence in moment of order of the other extremes of the random variables of geometric type but also the general asymptotic behavior of the extremes of a serie of random variables with integer value. This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We first made the case of the fact that the random variables of geometric type could be constructed from the random variables of exponential distribution and that they were not only integer variables but also that in general there were no sequences standards that allowed their extremes to converge. To do this, we first built a convergent ϕ(k) subsequence which we then used to define a geometric type Tϕ(k) subsequence of random variables. We have also proved the convergence in distribution of the extremes of the random variables Tϕ(k). We have also exhibited the resulting limit law. Finally, in this document, we have dealt with the multivariate case of random variables of geometric type. We considered two independent samples of random variables of geometric types. Using a copula of extreme values, in particular the logistic copula, we proposed a joint limit distribution of two independent samples of subsequences of geometric type random variables. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type.
Abstract: This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We succeeded in determining a subsequence which allows us to establish a co...
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A Weighted Analytic Center for Second-Order Cone Constraints
Bamanga Dawuda,
Shafiu Jibrin,
Ibrahim Abdullahi
Issue:
Volume 10, Issue 6, December 2021
Pages:
146-155
Received:
18 October 2021
Accepted:
15 November 2021
Published:
27 November 2021
Abstract: This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton’s-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton’s method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton’s exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton’s exact line search.
Abstract: This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton’s-like methods, CG methods use only the gradient and not the Hessian to minimize a functio...
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Predicting PM2.5 Concentrations Using Stacking-based Ensemble Model
Haoyuan Zhang,
Yilun Jin,
Jiaxuan Shi,
Shuai Zhang
Issue:
Volume 10, Issue 6, December 2021
Pages:
156-162
Received:
31 July 2021
Accepted:
22 November 2021
Published:
2 December 2021
Abstract: With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health. With a decade of development, artificial intelligence technology has given birth to various prediction models with high-performance, in particular, brought new impetus to the prediction of PM2.5 concentrations. In this study, a stacking-based ensemble model with self-adaptive hyper-parameter optimization is proposed to solve the PM2.5 concentrations prediction problem. First, the raw data are preprocessed with the normalization method to reduce the influence of the different orders of magnitude of input variables on model performance. Second, the Bayesian optimization method is used to optimize the hyper-parameters of the base predictors to improve their performance. Finally, a stacking ensemble method is applied to integrate the optimized base predictors into an ensemble model for final prediction. In the experiments, two datasets from the air quality stations in different areas are tested with four metrics to evaluate the performance of the proposed model in PM2.5 concentration prediction. The experimental results show that the proposed model outperforms other baseline models in solving the PM2.5 concentrations prediction problem.
Abstract: With the increasingly serious air pollution problem, PM2.5 concentration, as an effective indicator to evaluate air quality, has attracted extensive attention from all sectors of society. Accurate prediction of PM2.5 concentrations is of great significance in providing the public with early air pollution warning information to protect public health...
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Stochastic Stability and Optimal Control Analysis for a Tobacco Smoking Model
Anwarud Din,
Peijiang Liu,
Ting Cui
Issue:
Volume 10, Issue 6, December 2021
Pages:
163-185
Received:
26 November 2021
Accepted:
20 December 2021
Published:
29 December 2021
Abstract: In this paper, a smoking model, which takes snuffing class and Brownian motion into consideration and is thus an extension of previously studied deterministic smoking models. We analytically show that this extended model system has one and only one positively bounded solution for any nonnegative initial values for the state variables. Interestingly, we find that the model system can exhibit sharp threshold characteristics whatever values of the basic reproductive number. By analyzing persistence, extinction and stationary distribution, we also find that the stochastic system is ergodic only when the coefficients of the noise terms are small. To eliminate gradually the infection out of the community, we introduce a stochastic system of two control variables and perform analysis, with results that can provide guidelines for tobacco control department. Results obtained by theoretical analysis are verified by numerical simulations.
Abstract: In this paper, a smoking model, which takes snuffing class and Brownian motion into consideration and is thus an extension of previously studied deterministic smoking models. We analytically show that this extended model system has one and only one positively bounded solution for any nonnegative initial values for the state variables. Interestingly...
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