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A Mathematical Model to Study the Human Brain Information Processing Dynamics

Received: 24 August 2015     Accepted: 15 September 2015     Published: 29 September 2015
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Abstract

This research work studies the human brain information processing dynamics by transforming the stage model formulated by Atkinson and Shiffrin into two deterministic mathematical models. This makes it more amenable to mathematical analysis. The two models are bottom-up processing mathematical model and top-down processing mathematical model. The bottom-up processing is data driven while the top-down processing is triggered by experience or prior knowledge. Both analytical and numerical methods are used in the analysis of the models. The existence and stability of equilibrium states of the models are investigated, and threshold values of certain parameters of the models arising from the investigation were obtained and interpreted in physical terms. Numerical experiments are also carried out using hypothetical data to further investigate the effect of certain parameters on the human brain information processing process. The results show that attention, repetition and rehearsal play significant roles in learning process. Furthermore, repetition and rehearsal is strongly recommended as an effective way of retaining information. In addition, the instructors should ensure that the students feel physically and psychologically safe in any environment in order to pay adequate attention.

Published in American Journal of Applied Mathematics (Volume 3, Issue 5)
DOI 10.11648/j.ajam.20150305.15
Page(s) 233-242
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Brain, Information Processing, Bottom-Up, Top-Down, Attention, Automaticity

References
[1] Abbot B. (2002). Human memory. Fort Wayne: Indiana University-Purdue University at Fort Wayne, Psychology Department. pp. 1-20. http://users.ipfw.edu/abbot/120/LongTermMemory.html.
[2] Atkinson, R. and Shiffrin, R. (1968). Human memory. A proposed system and its control processes. In K. Spence & J. Spence (Eds.), The psychology of learning and motivation. Princeton, NJ: Van Nostrand. pp. 1-5.
[3] Driscoll, M. (2001). Psychology of learning for assessment (2nd ed). Boston: Allyn and Bacon. p. 81.
[4] Gantmacher, F. R. (1964). Matrix Theory. Vol. II Chelsea Publishing Company, New York. p. 374.
[5] Gibson, J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin. 332pp.
[6] Grimshaw, R.. (1990). Nonlinear ordinary differential equations. Pi-Square Press, Nottingham. pp. 23-44.
[7] Huitt, W., (2000). The information processing approach. Educational Psychology Interactive. Valdosta, GA: Valdosta State University. pp. 4-12. http://chiron.valdosta.edu/whuitt/col/cogsys/infoproc.html.
[8] Jeffrey, D. S., Martin, P. and Geoffrey, F. W. (2007). Commented on top-down verses bottom up control of attention in the prefrontal and posterior parietal cortices. PubMed 44, www.sciencemag.org.
[9] Lin P. H, Luck S. J. (2009). The Influence of Similarity on Visual Working Memory Representations. Visual Cognition. 17(3):356–372.
[10] Miller, G., Galanter E. and Pribram, K. (1960). Plans and the structure of behavior. New York: Holt, Rinehart, & Winston. 226pp.
[11] Rosenholtz, R, Jie, H. and Krista, A. E (2012). Rethinking the role of top-down attention in vision effects attributable to a lossy representation in peripheral vision. PMC3272623. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3272623/.
[12] Sousa, D. (2001). How the Brain Learns. Thousand Oaks, California: Corwin Press. pp. 127 -175. http://www.pitt.edu/~suthers/infsci1042/attention.html.
[13] Stacey, T. L. and William, G., (2003). Information Processing and Memory: Theory and Applications. pp. 2-4. http://www.chiron.valdosta.edu.
[14] Suthers, D. (1996). Attention and automaticity. Pittsburgh: University of Pittsburg, Learning Research and Development Center. pp. 1-10. http://www.pitt.edu/~suthers/infsci1042/attention.html.
[15] Wei Z, Wang X. J, Wang H. D. (2012). From Distributed Resources to Limited Slots in Multiple-Item Working Memory: A Spiking Network Model with Normalization. The Journal of Neuroscience.32 (33):11228–11240.
[16] Zekveld, A. A., Heslenfeld, D. J, Festen, J. M. and Schoonhoven, R. (2006). The top-down and bottom-up processes in speech comprehension. Neuroimage. 32(4):1826-36. http://journals.ohiolink.edu/.
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  • APA Style

    Shikaa Samuel, Taparki Richard, Ajai John Tyavbee, Aboiyar Terhemen. (2015). A Mathematical Model to Study the Human Brain Information Processing Dynamics. American Journal of Applied Mathematics, 3(5), 233-242. https://doi.org/10.11648/j.ajam.20150305.15

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    ACS Style

    Shikaa Samuel; Taparki Richard; Ajai John Tyavbee; Aboiyar Terhemen. A Mathematical Model to Study the Human Brain Information Processing Dynamics. Am. J. Appl. Math. 2015, 3(5), 233-242. doi: 10.11648/j.ajam.20150305.15

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    AMA Style

    Shikaa Samuel, Taparki Richard, Ajai John Tyavbee, Aboiyar Terhemen. A Mathematical Model to Study the Human Brain Information Processing Dynamics. Am J Appl Math. 2015;3(5):233-242. doi: 10.11648/j.ajam.20150305.15

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  • @article{10.11648/j.ajam.20150305.15,
      author = {Shikaa Samuel and Taparki Richard and Ajai John Tyavbee and Aboiyar Terhemen},
      title = {A Mathematical Model to Study the Human Brain Information Processing Dynamics},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {5},
      pages = {233-242},
      doi = {10.11648/j.ajam.20150305.15},
      url = {https://doi.org/10.11648/j.ajam.20150305.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150305.15},
      abstract = {This research work studies the human brain information processing dynamics by transforming the stage model formulated by Atkinson and Shiffrin into two deterministic mathematical models. This makes it more amenable to mathematical analysis. The two models are bottom-up processing mathematical model and top-down processing mathematical model. The bottom-up processing is data driven while the top-down processing is triggered by experience or prior knowledge. Both analytical and numerical methods are used in the analysis of the models. The existence and stability of equilibrium states of the models are investigated, and threshold values of certain parameters of the models arising from the investigation were obtained and interpreted in physical terms. Numerical experiments are also carried out using hypothetical data to further investigate the effect of certain parameters on the human brain information processing process. The results show that attention, repetition and rehearsal play significant roles in learning process. Furthermore, repetition and rehearsal is strongly recommended as an effective way of retaining information. In addition, the instructors should ensure that the students feel physically and psychologically safe in any environment in order to pay adequate attention.},
     year = {2015}
    }
    

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    T1  - A Mathematical Model to Study the Human Brain Information Processing Dynamics
    AU  - Shikaa Samuel
    AU  - Taparki Richard
    AU  - Ajai John Tyavbee
    AU  - Aboiyar Terhemen
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    N1  - https://doi.org/10.11648/j.ajam.20150305.15
    DO  - 10.11648/j.ajam.20150305.15
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    EP  - 242
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20150305.15
    AB  - This research work studies the human brain information processing dynamics by transforming the stage model formulated by Atkinson and Shiffrin into two deterministic mathematical models. This makes it more amenable to mathematical analysis. The two models are bottom-up processing mathematical model and top-down processing mathematical model. The bottom-up processing is data driven while the top-down processing is triggered by experience or prior knowledge. Both analytical and numerical methods are used in the analysis of the models. The existence and stability of equilibrium states of the models are investigated, and threshold values of certain parameters of the models arising from the investigation were obtained and interpreted in physical terms. Numerical experiments are also carried out using hypothetical data to further investigate the effect of certain parameters on the human brain information processing process. The results show that attention, repetition and rehearsal play significant roles in learning process. Furthermore, repetition and rehearsal is strongly recommended as an effective way of retaining information. In addition, the instructors should ensure that the students feel physically and psychologically safe in any environment in order to pay adequate attention.
    VL  - 3
    IS  - 5
    ER  - 

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Author Information
  • Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria

  • Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria

  • Department of Science Education, Taraba State University, Jalingo, Nigeria

  • Department of Mathematics, Statistics and Computer Science, University of Agriculture, Makurdi, Nigeria

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