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Yuri Dabaghian1

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We propose a novel mechanism for border cells, which are neurons that fire at the edges of environments. This approach uses discrete complex analysis to explain border-bound firing in grid cell models.

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Mathematical Physics

Background:

  • Grid cells are key components of the brain's navigation system, exhibiting spatially periodic firing patterns.
  • Existing models primarily explain grid cell function within environments, but less is known about border cell mechanisms.
  • Border cells are hypothesized to signal the boundaries of navigated spaces.

Purpose of the Study:

  • To propose a unified mechanism for the emergence of border cells.
  • To link discrete complex analysis with oscillatory models of grid cells.
  • To explain how neurons can increase activity at environmental frontiers.

Main Methods:

  • Utilizing discrete complex analysis on a triangular lattice.
  • Constructing discrete epitomes of complex-analytic functions.
  • Extending oscillatory models of grid cells to incorporate border-bound firing.
  • Developing a network model of border-firing neurons.

Main Results:

  • Demonstrated that discrete complex analysis can naturally produce border-cell-like activity.
  • Showed that oscillatory grid cell models can be extended to generate cells firing at environmental boundaries.
  • Successfully constructed a network model consistent with these findings.

Conclusions:

  • Discrete complex analysis provides a powerful framework for understanding neural computation in navigation.
  • The proposed mechanism offers a parsimonious explanation for border cell function.
  • This work bridges mathematical frameworks with neurobiological observations in spatial cognition.