A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

An accurate algorithm for solving initial value problems (IVPs) which are highly oscillatory is proposed. The proposed method is based on a novel technique of extending the standard spectral homotopy analysis method (SHAM) and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise spectral homotopy analysis method (PSHAM). The applicability of the proposed method is examined on the differential equation system modeling HIV infection of CD4+ T cells and the Genesio-Tesi system which is known to be chaotic and highly oscillatory. Also, for the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. The method is compared to MATLAB’s ode45 inbuilt solver as a measure of accuracy and efficiency

A family of similarity measures for q‐rung orthopair fuzzy sets and their applications to multiple criteria decision making

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.One worthwhile way of expressing imprecise information is the q‐rung orthopair fuzzy sets (q‐ROFSs), which extend intuitionistic fuzzy sets and Pythagorean fuzzy sets. The main goal of this contribution is to further extend the concept of similarity measure for q‐ROFSs, which not only endows the similarity framework with more ability to create new ones but also inherits all essential properties of a logical similarity measure. This contribution proposes a class of novel similarity measures for q‐ROFSs by drawing a general framework of existing q‐ROFS similarity and q‐ROFS distance measures. These q‐ROFS similarity measures enable us to overcome the theoretical drawbacks of the existing measures in the case where they are used individually. In the application part of the contribution, a pattern recognition problem on classification of building materials with a number of known building materials is reconsidered. The study of this particular case shows that the proposed family of similarity measures consistently classify the unknown building material pattern with the same known building material pattern. Then, an experimental case study regarding a problem of classroom teaching quality is re‐examined for the comparison of the performance of proposed similarity measures against the existing ones. The salient features of the proposed similarity measures in comparison to the existing qROFS similarity measures, are as follows: (i) a number of existing q‐ROFS similarity measures are inherently correlation coefficients, and they satisfy only a limited number of essential properties of a comprehensive similarity measure; (ii) several existing q‐ROFS similarity measures lead sometimes to nonlogical results, more specifically, to the same maximum similarity value for different q‐ROFSs; (iii) a variety of existing q‐ROFS similarity measures depend on subjective parameters, which either hinder their application in practice or increase their computational cost. In brief, following this direction of research, we will prove the superiority of the developed similarity measures over the existing ones from both theoretical and experimental viewpoints

Numerical solution for IVP in volterra type linear integrodifferential equations system

A method is proposed to determine the numerical solution of system of linear Volterra integrodifferential equations (IDEs) by using Bezier curves. The Bezier curves are chosen as piecewise polynomials of degree n, and Bezier curves are determined on [t0, tf] by n+1 control points. The efficiency and applicability of the presented method are illustrated by some numerical examples

Multiobjective Optimal Control of HIV Dynamics

Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved

Maximizing of Asymptomatic Stage of Fast Progressive HIV Infected Patient Using Embedding Method

Attachée au Département de russe de l’université de Bristol, directrice du Centre for Russian and East European Cultural Studies, Birgit Beumers est spécialiste de la culture russe contemporaine au sens large. Après une thèse consacrée à Jurij Ljubimov au théâtre de la Taganka, Beumers s’est ensuite tournée vers le cinéma et fédère actuellement autour d’elle un courant de recherche anglo-saxon qui se place dans l’optique des « cultural studies » et de la sémiologie, et participe très largemen..

An Adaptive Memetic Algorithm With Dynamic Population Management for Designing HIV Multidrug Therapies

In this paper, a mathematical model of human immunodeficiency virus (HIV) is utilized and an optimization problem is proposed, with the final goal of implementing an optimal 900-day structured treatment interruption (STI) protocol. Two type of commonly used drugs in highly active antiretroviral therapy (HAART), reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are considered. In order to solving the proposed optimization problem an adaptive memetic algorithm with population management (AMAPM) is proposed. The AMAPM uses a distance measure to control the diversity of population in genotype space and thus preventing the stagnation and premature convergence. Moreover, the AMAPM uses diversity parameter in phenotype space to dynamically set the population size and the number of crossovers during the search process. Three crossover operators diversify the population, simultaneously. The progresses of crossover operators are utilized to set the number of each crossover per generation. In order to escaping the local optima and introducing the new search directions toward the global optima, two local searchers assist the evolutionary process. In contrast to traditional memetic algorithms, the activation of these local searchers is not random and depends on both the diversity parameters in genotype space and phenotype space. The capability of AMAPM in finding optimal solutions compared with three popular metaheurestics is introduced

Generalized Variant Support Vector Machine

With the advancement in information technology, datasets with an enormous amount of data are available. The classification task on these datasets is more time- and memory-consuming as the number of data increases. The support vector machine (SVM), which is arguably the most popular classification technique, has disappointing performance in dealing with large datasets due to its constrained optimization problem. To deal with this challenge, the variant SVM (VSVM) has been utilized which has the fraction ({1}/{2})b{2} in its primal objective function, where b is the bias of the desired hyperplane. The VSVM has been solved with different optimization techniques in more time- and memory-efficient fashion. However, there is no guarantee that its optimal solution is the same as the standard SVM. In this paper, we introduce the generalized VSVM (GVSVM) which has the fraction ({1}/{2t})b{2} in its primal objective function, for a fixed positive scalar t. Further, we present the thorough theoretical insights that indicate the optimal solution of the GVSVM tends to the optimal solution of the standard SVM as t rightarrow infty . One vital corollary is to derive a closed-form formula to obtain the bias term in the standard SVM. Such a formula obviates the need of approximating it, which is the modus operandi to date. An efficient neural network is then proposed to solve the GVSVM dual problem, which is asymptotically stable in the sense of Lyapunov and converges globally exponentially to the exact solution of the GVSVM. The proposed neural network has less complexity in architecture and needs fewer computations in each iteration in comparison to the existing neural solutions. Experiments confirm the efficacy of the proposed recurrent neural network and the proximity of the GVSVM and the standard SVM solutions with more significant values of t. Information and Communication Technolog