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Neural Ideals in SageMath

  • Ethan Petersen
  • Nora Youngs
  • Ryan Kruse
  • Dane Miyata
  • Rebecca Garcia
  • Luis David García PuenteEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

A major area in neuroscience research is the study of how the brain processes spatial information. Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem consists in determining what stimulus space features can be extracted directly from a neural code. The neural ideal is an algebraic object that encodes the full combinatorial data of a neural code. This ideal can be expressed in a canonical form that directly translates to a minimal description of the receptive field structure intrinsic to the code. Here, we describe a SageMath package that contains several algorithms related to the canonical form of a neural ideal.

Keywords

Canonical form Neural codes Neural ideal Neural ring 

References

  1. 1.
    Curto, C., Itskov, V., Veliz-Cuba, A., Youngs, N.: The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bull. Math. Biol. 75(9), 1571–1611 (2013).  https://doi.org/10.1007/s11538-013-9860-3MathSciNetCrossRefzbMATHGoogle Scholar
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    O’Keefe, J., Dostrovsky, J.: The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain Res. 34(1), 171–175 (1971). http://www.sciencedirect.com/science/article/pii/0006899371903581CrossRefGoogle Scholar
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    Stein, W., et al.: Sage Mathematics Software (Version 7.2.0). The Sage Developers (2016). http://www.sagemath.org
  4. 4.
    Youngs, N.: Neural ideal: a Matlab package for computing canonical forms (2015). http://github.com/nebneuron/neural-ideal

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ethan Petersen
    • 1
  • Nora Youngs
    • 2
  • Ryan Kruse
    • 3
  • Dane Miyata
    • 4
  • Rebecca Garcia
    • 5
  • Luis David García Puente
    • 5
    Email author
  1. 1.Department of MathematicsRose-Hulman Institute of TechnologyTerre HauteUSA
  2. 2.Department of Mathematics and StatisticsColby CollegeWatervilleUSA
  3. 3.Mathematics DepartmentCentral CollegePellaUSA
  4. 4.Department of MathematicsUniversity of OregonEugeneUSA
  5. 5.Department of Mathematics and StatisticsSam Houston State UniversityHuntsvilleUSA

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