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Research Article

A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology

  • Y. Dabaghian mail,

    dabaghia@bcm.edu

    Affiliations: Jan & Dan Duncan Neurological Research Institute, Baylor College of Medicine, Houston, Texas, United States of America, Department of Computational & Applied Mathematics, Rice University, Houston, Texas, United States of America

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  • F. Mémoli,

    Affiliations: Department of Mathematics, Stanford University, Palo Alto, California, United States of America, School of Computer Science, The University of Adelaide, Adelaide, Australia

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  • L. Frank,

    Affiliation: Department of Physiology, Keck Center for Integrative Neuroscience, University of California, San Francisco, California, United States of America

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  • G. Carlsson

    Affiliation: Department of Mathematics, Stanford University, Palo Alto, California, United States of America

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  • Published: August 09, 2012
  • DOI: 10.1371/journal.pcbi.1002581

Reader Comments (1)

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Model changes under phase precession?

Posted by greghale on 12 Aug 2012 at 20:15 GMT

Thanks for your paper. This is a very nice tool and an interesting way of thinking about what the hippocampus represents. Is it possible to do a back-of-the-envelope calculation to get a sense for how the parameters of your 'learning period' change, in the case that (1) we take phase precession into account, and (2) we use an integration time of about a gamma cycle, rather than a theta cycle? I understand the usefulness of the simplifying assumptions in the paper, and am curious about how the model reacts under the more realistic conditions - because it seems that phase precession may really change the temporal and spatial aspects of co-firing. Do you agree, or do you think the topological decoding isn't likely to be sensitive to that?
Thanks!
-Greg (from Matt Wilson's lab)

No competing interests declared.

RE: Model changes under phase precession?

greghale replied to greghale on 12 Aug 2012 at 20:16 GMT

Correction: 'learning region'

No competing interests declared.

RE: Model changes under phase precession?

dabaghian replied to greghale on 13 Aug 2012 at 00:38 GMT

Dear Greg, thanks for your interest and for your comments. Both the phase precession and the integration width do affect the shape of the learning region and the learning times. I don't have a simple back-of-the-envelope explanation of the effects that they produce, but our recent results (not included in this paper, we hope to publish them soon) indicate that the integration time of about a theta cycle is more meaningful and may actually give a more reliable estimate of the global learning time than the gamma cycle, so this aspect of the current results is reliable. The effect of theta precession is more subtle. These results are almost ready for publication, so I hope to provide a more detailed answer soon.

No competing interests declared.