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Article information
2015 , Volume 20, ¹ 1, p.53-62
Suleymanov Y.A., Gafarov F.M., Khushutdinov N.R., Yemelyanova N.A.
Optimization of calculation of matter concentration in the diffusion equation with a time-dependent source
Purpose. This paper addresses an acceleration of numerical experiments in the study of the evolution of neural networks based on structural plasticity. Structural plasticity is related to the anatomical structure of neurons and connections between them. Modeling of the growth for neuron axons is a complex and lengthy process, requiring the use of cumbersome calculations. Axon growth is controlled by diffusion substance AGM, which is released by neurons and the axon tip is perceived it as a guidance signal. Since the numerical solution of the diffusion equation with timedependent source is a complex process and resource-intensive process, it is necessary to optimize the program. Methodology. In this paper we have developed a method which reduces the time of numerical experiments for the modeling of the evolution of neural networks. This method allows us to reduce the number of iterations in the calculation of the concentration of the AGM substance. The developed model is implemented using the method of parallel computing. The method is applied for the numerical solution of the diffusion equation with a time-dependent source. Findings. During the numerical analysis we simulated a neural network, which consists of a set of neurons arranged in the three-dimensional space. The model also contains the mechanism of axon branching. Axon branching occurs through the formation of a new branch in the axis of the axon. The growth and branching of axons and dendrites leads to anatomical changes of the neural networks (structural plasticity). Originality ⁄ value. Application of the proposed method for reduction of the number of iterations in the process for calculation of the concentration of AGM significantly reduces the time of numerical experiments without increasing computational resources. This method can be used in applications which use the diffuusion equation (conduction) with a time-dependent source.
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Keywords: diffusion equation, numerical optimization, neural networks
Author(s):
Suleymanov Yanis Adisovich
Position: Student
Office: Kazan Federal University, Institute of Computer Mathematics and Information Technologies
Address: 420008, Russia, Kazan, 18 Kremlyovskaya St.
E-mail: yaniscom@mail.ru
Gafarov Fail Mubarakovich
PhD. , Associate Professor
Office: Kazan Federal University, Institute of Computer Mathematics and Information Technologies
Address: 420008, Russia, Kazan, 18 Kremlyovskaya St.
E-mail: fgafarov@yandex.ru
Khushutdinov Nail Rustamovich
Dr. , Associate Professor
Office: Kazan Federal University, Institute of Computer Mathematics and Information Technologies
Address: 420008, Russia, Kazan, 18 Kremlyovskaya St.
E-mail: nail.khusnutdinov@gmail.com
Yemelyanova Natalya Aleksandrovna
PhD. , Associate Professor
Office: Kazan branch of Moscow State University of Railway Engineering
Address: 420078, Russia, Kazan, 18 Kremlyovskaya St.
E-mail: prl70@mail.ru
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Bibliography link:
Suleymanov Y.A., Gafarov F.M., Khushutdinov N.R., Yemelyanova N.A. Optimization of calculation of matter concentration in the diffusion equation with a time-dependent source // Computational technologies. 2015. V. 20. ¹ 1. P. 53-62
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