IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v461y2016icp409-418.html
   My bibliography  Save this article

Emergence of the small-world architecture in neural networks by activity dependent growth

Author

Listed:
  • Gafarov, F.M.

Abstract

In this paper, we propose a model describing the growth and development of neural networks based on the latest achievements of experimental neuroscience. The model is based on two evolutionary equations. The first equation is for the evolution of the neurons state and the second is for the growth of axon tips. By using the model, we demonstrated the neuronal growth process from disconnected neurons to fully connected three-dimensional networks. For the analysis of the network’s connections structure, we used the random graphs theory methods. It is shown that the growth in neural networks results in the formation of a well-known “small-world” network model. The analysis of the connectivity distribution shows the presence of a strictly non-Gaussian but no scale-free degree distribution for the in-degree node distribution. In terms of the graphs theory, this study developed a new model of dynamic graph.

Suggested Citation

  • Gafarov, F.M., 2016. "Emergence of the small-world architecture in neural networks by activity dependent growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 409-418.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:409-418
    DOI: 10.1016/j.physa.2016.06.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116302849
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.06.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Perotti, Juan I. & Tamarit, Francisco A. & Cannas, Sergio A., 2006. "A scale-free neural network for modelling neurogenesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 71-75.
    2. Weaver, Iain S., 2015. "Preferential attachment in randomly grown networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 85-92.
    3. Martín-Hernández, J. & Wang, H. & Van Mieghem, P. & D’Agostino, G., 2014. "Algebraic connectivity of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 92-105.
    4. Colman, E.R. & Rodgers, G.J., 2013. "Complex scale-free networks with tunable power-law exponent and clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5501-5510.
    5. Zhang, Zhongzhi & Zhou, Shuigeng & Shen, Zhen & Guan, Jihong, 2007. "From regular to growing small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 765-772.
    6. Park, Chang-hyun & Kim, Soo Yong & Kim, Yun-Hee & Kim, Kyungsik, 2008. "Comparison of the small-world topology between anatomical and functional connectivity in the human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5958-5962.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pi, Xiaochen & Tang, Longkun & Chen, Xiangzhong, 2021. "A directed weighted scale-free network model with an adaptive evolution mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Daewon Chung & Insoo Sohn, 2023. "Neural Network Optimization Based on Complex Network Theory: A Survey," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    3. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    4. Li, Xin & Wu, Haotian & Scoglio, Caterina & Gruenbacher, Don, 2015. "Robust allocation of weighted dependency links in cyber–physical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 316-327.
    5. Mite Mijalkov & Joana B Pereira & Giovanni Volpe, 2020. "Delayed correlations improve the reconstruction of the brain connectome," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-22, February.
    6. Rueda, Diego F. & Calle, Eusebi, 2017. "Using interdependency matrices to mitigate targeted attacks on interdependent networks: A case study involving a power grid and backbone telecommunications networks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 16(C), pages 3-12.
    7. Chen Yang & Tingting Liu & Xiaohong Chen & Yiyang Bian & Yuewen Liu, 2020. "HNRWalker: recommending academic collaborators with dynamic transition probabilities in heterogeneous networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 123(1), pages 429-449, April.
    8. Wang, Jianrong & Wang, Jianping & Li, Lei & Yang, Bo, 2018. "A novel relay selection strategy based on deterministic small world model on CCN," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 559-568.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:409-418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.