Persistent Memories in Transient Networks

  • Andrey Babichev
  • Yuri DabaghianEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 191)


Spatial awareness in mammals is based on an internalized representation of the environment, encoded by large networks of spiking neurons. While such representations can last for a long time, the underlying neuronal network is transient : neuronal cells die every day, synaptic connections appear and disappear, the networks constantly change their architecture due to various forms of synaptic and structural plasticity. How can a network with a dynamic architecture encode a stable map of space? We address this question using a physiological model of a “flickering” neuronal network and demonstrate that it can maintain a robust topological representation of space.


Simplicial Complex Cell Assembly Spike Train Betti Number Place Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work was supported by the NSF 1422438 grant and by Houston Bioinformatics Endowment Fund.


  1. 1.
    O’Keefe, J., Nadel, L.: The Hippocampus as a Cognitive Map, vol. xiv, p. 570. Clarendon Press; Oxford University Press, New York (1978)Google Scholar
  2. 2.
    Tolman, E.C.: Cognitive maps in rats and men. Psychol. Rev. 55, 189–208 (1948)CrossRefGoogle Scholar
  3. 3.
    Tolman, P.J., White, A.M., Minai, A.: Spatial processing in the brain: the activity of hippocampal place cells. Ann. Rev. Neurosci. 24, 459–486 (2001)CrossRefGoogle Scholar
  4. 4.
    Harris, K.D., Csicsvari, J., Hirase, H., Dragoi, G., Buzsaki, G.: Organization of cell assemblies in the hippocampus. Nature 424, 552–556 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Buzsaki, G.: Neural syntax: cell assemblies, synapsembles, and readers. Neuron 68, 362–385 (2010)CrossRefGoogle Scholar
  6. 6.
    Gothard, K.M., Skaggs, W.E., McNaughton, B.L.: Dynamics of mismatch correction in the hippocampal ensemble code for space: interaction between path integration and environmental cues. J. Neurosci. 16, 8027–8040 (1996)Google Scholar
  7. 7.
    Leutgeb, J.K., Leutgeb, S., Treves, A., Meyer, R., Barnes, C.A., et al.: Progressive transformation of hippocampal neuronal representations in “morphed” environments. Neuron 48, 345–358 (2005)CrossRefGoogle Scholar
  8. 8.
    Alvernhe, A., Sargolini, F., Poucet, B.: Rats build and update topological representations through exploration. Anim. Cogn. 15, 359–368 (2012)CrossRefGoogle Scholar
  9. 9.
    Poucet, B., Herrmann, T.: Exploratory patterns of rats on a complex maze provide evidence for topological coding. Behav. Process. 53, 155–162 (2001)CrossRefGoogle Scholar
  10. 10.
    Dabaghian, Y., Brandt, V.L., Frank, L.M.: Reconceiving the hippocampal map as a topological template. eLife 10.7554/eLife.03476 (2014)Google Scholar
  11. 11.
    Dabaghian, Y., Mmoli, F., Frank, L., Carlsson, G.: A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS. Comput. Biol. 8, e1002581 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Arai, M., Brandt, V., Dabaghian, Y.: The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map. PLoS Comput. Biol. 10, e1003651 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Wang, Y., Markram, H., Goodman, P.H., Berger, T.K., Ma, J., et al.: Heterogeneity in the pyramidal network of the medial prefrontal cortex. Nat. Neurosci. 9, 534–542 (2006)CrossRefGoogle Scholar
  14. 14.
    Bi, G-q., Poo, M-m.: Synaptic modification by correlated activity: Hebb’s postulate revisited. Ann. Rev. Neurosci. 24, 139–166 (2001)Google Scholar
  15. 15.
    Magee, J.C., Johnston, D.: A synaptically controlled, associative signal for hebbian plasticity in Hippocampal neurons. Science 275, 209–213 (1997)Google Scholar
  16. 16.
    Meck, W.H., Church, R.M., Olton, D.S.: Hippocampus, time, and memory. Behav. Neurosci. 127, 655–668 (2013)CrossRefGoogle Scholar
  17. 17.
    Clayton, N.S., Bussey, T.J., Dickinson, A.: Can animals recall the past and plan for the future? Nat. Rev. Neurosci. 4, 685–691 (2003)CrossRefGoogle Scholar
  18. 18.
    Brown, M.F., Farley, R.F., Lorek, E.J.: Remembrance of places you passed: social spatial working memory in rats. J. Exper. Psychol. 33, 213–224 (2007)Google Scholar
  19. 19.
    Alexandroff, P.: Untersuchungen Uber Gestalt und Lage Abgeschlossener Mengen Beliebiger Dimension. Ann. Math. 30, 101–187 (1928)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Čech, E.: Theorie generale de lhomologie dans une space quelconque. Fundamenta mathematicae 19, 149–183 (1932)zbMATHGoogle Scholar
  21. 21.
    Curto, C., Itskov, V.: Cell groups reveal structure of stimulus space. PLoS Comput. Biol. 4, e1000205 (2008)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  23. 23.
    Aleksandrov, P.: Elementary Concepts of Topology, p. 63. F. Ungar Pub, Co, New York (1965)Google Scholar
  24. 24.
    Babichev, A., Cheng, S., Dabaghian, Y.: Topological Schemas of Cognitive Maps and Spatial Learning in the Hippocampus. In submition (2015). arXiv:1509.00171
  25. 25.
    Babichev, A., Memoli, F., Ji, D., Dabaghian, Y.: Combinatorics of Place Cell Coactivity and Hippocampal Maps. In submition (2015). arXiv:1509.01677
  26. 26.
    Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45, 61–75 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Zomorodian, A.J.: Topology for Computing, vol. xiii, p. 243. Cambridge University Press, UK (2005)Google Scholar
  28. 28.
    Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction, vol. xii, p. 241. American Mathematical Society, Providence, R.I. (2010)Google Scholar
  29. 29.
    Ambjørn, J., Carfora, M., Marzuoli, A.: The Geometry of Dynamical Triangulations, vol. viii, p. 197. Springer, Berlin (1997)Google Scholar
  30. 30.
    Hamber, H.W.: Quantum gravitation: the Feynman path integral approach, vol. xvii, p. 342. Springer, Berlin (2009). (Nuclear Physics B - Proceedings Supplements 94, 689–692)Google Scholar
  31. 31.
    Barbieri, R., Frank, L.M., Nguyen, D.P., Quirk, M.C., Solo, V., et al.: Dynamic analyses of information encoding in neural ensembles. Neural Comput. 16, 277–307 (2004)CrossRefzbMATHGoogle Scholar
  32. 32.
    Buzsaki, G.: Theta oscillations in the hippocampus. Neuron 33, 325–340 (2002)CrossRefGoogle Scholar
  33. 33.
    Buzsaki, G.: Theta rhythm of navigation: link between path integration and landmark navigation, episodic and semantic memory. Hippocampus 15, 827–840 (2005)CrossRefGoogle Scholar
  34. 34. JPlex freeware was developed by ComTop group, Stanford University

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Jan and Dan Duncan Neurological Research Institute, Baylor College of MedicineHoustonUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

Personalised recommendations