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Cognitive Neurodynamics

, Volume 5, Issue 2, pp 145–160 | Cite as

Visualization for understanding of neurodynamical systems

  • Włodzisław DuchEmail author
  • Krzysztof Dobosz
Research Article

Abstract

Complex neurodynamical systems are quite difficult to analyze and understand. New type of plots are introduced to help in visualization of high-dimensional trajectories and show global picture of the phase space, including relations between basins of attractors. Color recurrence plots (RPs) display distances from each point on the trajectory to all other points in a two-dimensional matrix. Fuzzy Symbolic Dynamics (FSD) plots enhance this information mapping the whole trajectory to two or three dimensions. Each coordinate is defined by the value of a fuzzy localized membership function, optimized to visualize interesting features of the dynamics, showing to which degree a point on the trajectory belongs to some neighborhood. The variance of the trajectory within the attraction basin plotted against the variance of the synaptic noise provides information about sizes and shapes of these basins. Plots that use color to show the distance between each trajectory point and a larger number of selected reference points (for example centers of attractor basins) are also introduced. Activity of 140 neurons in the semantic layer of dyslexia model implemented in the Emergent neural simulator is analyzed in details showing different aspects of neurodynamics that may be understood in this way. Influence of connectivity and various neural properties on network dynamics is illustrated using visualization techniques. A number of interesting conclusions about cognitive neurodynamics of lexical concept activations are drawn. Changing neural accommodation parameters has very strong influence on the dwell time of the trajectories. This may be linked to attention deficits disorders observed in autism in case of strong enslavement, and to ADHD-like behavior in case of weak enslavement.

Keywords

Neurodynamics Symbolic dynamics Visualization of multidimensional time series Attractor networks Attractor dynamics Recurrence plots 

Notes

Acknowledgments

We are grateful for the support of the Polish Ministry of Education and Science through Grant No N519 578138.

References

  1. Aisa B, Mingus B, O’Reilly RC (2008) The emergent neural modeling system. Neural Netw 21(8):1146–1152PubMedCrossRefGoogle Scholar
  2. Bilder RM, Sabb FW, Cannon TD, London ED, Jentsch JD, Parker DS, Poldrack RA, Evans C, Freimer NB (2009) Phenomics: the systematic study of phenotypes on a genome-wide scale. Neuroscience 164(1):30–42PubMedCrossRefGoogle Scholar
  3. Consortium for Neuropsychiatric Phenomics (2011) http://www.phenomics.ucla.edu/
  4. Cox TF, Cox MAA (2001) Multidimensional scaling (2nd edn). Chapman & Hall, LondonGoogle Scholar
  5. Dawkins R (1989) The selfish gene (2nd edn., new ed.), Chap. 11. Memes: the new replicators. Oxford University Press, OxfordGoogle Scholar
  6. Distin K (2005) The selfish meme: a critical reassessment. Cambridge University Press, CambridgeGoogle Scholar
  7. Duch W (2005) Uncertainty of data, fuzzy membership functions, and multi-layer perceptrons. IEEE Trans Neural Netw 16(1):10–23PubMedCrossRefGoogle Scholar
  8. Duch W (2009) Consciousness and attention in autism spectrum disorders. In: Coma and consciousness. Clinical, societal and ethical implications. In: Satellite symposium of the 13th annual meeting of the association for the scientific studies of consciousness, Berlin, p 46Google Scholar
  9. Dobosz K, Duch W (2010) Understanding neurodynamical systems via fuzzy symbolic dynamics. Neural Netw 23:487–496PubMedCrossRefGoogle Scholar
  10. Eckmann JP, Kamphorst SO, Ruelle D (1987) Recurrence plots of dynamical systems. Europhys Lett 5:973–977CrossRefGoogle Scholar
  11. Freeman W (2000) Neurodynamics: an exploration in mesoscopic brain dynamics. Springer, BerlinGoogle Scholar
  12. Gepner B, Feron F (2009) Autism: a world changing too fast for a mis-wired brain. Neurosci Biobehav Rev 33(8):1227–1242PubMedCrossRefGoogle Scholar
  13. Hao, B, Zheng, W (eds) (1998) Applied symbolic dynamics and chaos. World Scientific, SingaporeGoogle Scholar
  14. Harth E, Tzanakou E (1974) ALOPEX: a stochastic method for determining visual receptive fields. Vis Res 14:1475–1482PubMedCrossRefGoogle Scholar
  15. Kawakubo Y, Maekawa H, Itoh K, Hashimoto O, Iwanami A (2007) Electrophysiological abnormalities of spatial attention in adults with autism during the gap overlap task. Clin Neurophysiol 118(7):1464–1471PubMedCrossRefGoogle Scholar
  16. Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall, Englewood CliffsGoogle Scholar
  17. Landry R, Bryson SE (2004) Impaired disengagement of attention in young children with autism. J Child Psychol Psychiatry 45(6):1115–1122PubMedCrossRefGoogle Scholar
  18. Martín-Loeches M, Hinojosa JA, Fernández-Frías C, Rubia FJ (2001) Functional differences in the semantic processing of concrete and abstract words. Neuropsychologia 39(10):1086–1096PubMedCrossRefGoogle Scholar
  19. Marwan N, Romano MC, Thiel M, Kurths J (2007) Recurrence plots for the analysis of complex systems. Phys Reports 438:237–329CrossRefGoogle Scholar
  20. Marwan N, Wessel N, Meyerfeldt U, Schirdewan A, Kurths J (2002) Recurrence plot based measures of complexity and its application to heart rate variability data. Phys Rev E 66:026702CrossRefGoogle Scholar
  21. Muresan RC, Savin C (2007) Resonance or integration? Self-sustained dynamics and excitability of neural microcircuits. J Neurophysiol 97(3):1911–1930PubMedCrossRefGoogle Scholar
  22. O’Reilly RC, Munakata Y (2000) Computational explorations in cognitive neuroscience. MIT Press, CambridgeGoogle Scholar
  23. Pinto D et al (2010) Functional impact of global rare copy number ariation in autism spectrum disorders. Nature 466:368–372PubMedCrossRefGoogle Scholar
  24. Sanei S, Chambers JA (2008) EEG signal processing. Wiley, New YorkGoogle Scholar
  25. Seth AK (2008) Causal networks in simulated neural systems. Cogn Neurodyn 2:49–64PubMedCrossRefGoogle Scholar
  26. Spivey M (2007) The continuity of mind. Oxford University Press, New YorkGoogle Scholar
  27. Wang J, Conder JA, Blitzer DN, Shinkareva SV (2010) Neural representation of abstract and concrete concepts: a meta-analysis of neuroimaging studies. Hum Brain Mapp 31(10):1459–1468PubMedCrossRefGoogle Scholar
  28. Webber CL Jr., Zbilut JP (1994) Dynamical assessment of physiological systems and states using recurrence plot strategies. J Appl Physiol 76:965–973PubMedGoogle Scholar
  29. Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427CrossRefGoogle Scholar
  30. Zbilut JP, Webber CL Jr. (1992) Embeddings and delays as derived from quantification of recurrence plots. Phys Lett A 171:199–203CrossRefGoogle Scholar
  31. Zimmerman, AW (eds) (2008) Autism: current theories and evidence. Humana Press, CliftonGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of InformaticsNicolaus Copernicus UniversityToruńPoland
  2. 2.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland
  3. 3.School of Computer ScienceNanyang Technological UniversitySingaporeSingapore

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