Carina's papers

PhD theses supervised:
Juliana Londono Alvarez (2024)
Attractor-based models for sequences and pattern generation in neural circuits
Caitlin Lienkaemper (2022)
Combinatorial geometry of neural codes, neural data analysis, and neural networks
Caitlyn Parmelee (2016)
Applications of Discrete Mathematics for Understanding Dynamics of Synapses and Networks in Neuroscience
Nora Youngs (2014)
The Neural Ring: Using Algebraic Geometry to Analyze Neural Codes

publications

NEW! (#33)
TLN/CTLN Review Paper (with Katie Morrison):

Graph rules for recurrent neural network dynamics
Notices of the AMS, Vol. 70(4), April 2023.
Notices link, pdf

Graph rules for recurrent neural network dynamics: extended version
arXiv link and pdf

Categories:

A. Neural network theory (TLNs/CTLNs/etc.): 10, 14, 18, 23, 24, 26, 30, 31, 32, 33, 34, 35, 37, 38

B. Topology in neuroscience: 5, 13, 16, 19, 20, 25, 28, 30

C. Algebra and combinatorics of neural codes: 12, 13, 20, 21, 22, 25, 27, 29, 36

D. Data-driven modeling and data analysis in neuroscience: 4, 6, 7, 8, 9, 15, 16, 17

E. Physics and mathematical physics: 0, 1, 2, 3, 11

Preprints/Submitted:

38. C. Curto, C. Langdon, K. Morrison. Combinatorial geometry of threshold-linear networks. arXiv.org preprint.

37. C. Curto, C. Langdon, K. Morrison. Robust motifs of threshold-linear networks. arXiv.org preprint.

36. C. Curto, R. Vera. The Leray dimension of a convex code. arXiv.org preprint.

Published/Accepted:

35. K. Morrison, A. Degeratu, V. Itskov, C. Curto. Diversity of emergent dynamics in competitive threshold-linear networks. SIAM J. of Applied Dynamical Systems, Vol 23(1), 2024. arXiv.org preprint, and Matlab code.

34. C. Curto, J. Geneson, K. Morrison. Stable fixed points of combinatorial threshold-linear networks. Advances in Applied Mathematics, Vol 154, 2024. arXiv.org preprint.

33. C. Curto, K. Morrison. Graph rules for recurrent neural network dynamics. Notices of the AMS, Vol. 70(4), April 2023. Notices link, pdf, and extended version on arXiv.

32. C. Parmelee, S. Moore, K. Morrison*, C. Curto*. Core motifs predict dynamic attractors in combinatorial threshold-linear networks. (*equal last authors) PLoS ONE 17(3): e0264456, 2022. arXiv.org preprint.

31. C. Parmelee, J. Londono Alvarez, C. Curto*, K. Morrison*. Sequential attractors in combinatorial threshold-linear networks. (*equal last authors) SIAM J. Applied Dynamical Systems, Vol. 21, No. 2, pp. 1597-1630, 2022. pdf and supp

30. D. Egas Santander, S. Ebli, A. Patania, N. Sanderson, F. Burtscher, K. Morrison*, C. Curto*. Nerve theorems for fixed points of neural networks. E. Gasparovic et al. (eds.): Research in Computational Topology 2, Association for Women in Mathematics Series 30, 2022. pdf

29. L. Brown, C. Curto. Periodic codes and sound localization in barn owls. Involve, a Journal of Mathematics, vol 15, no. 1, pp. 1-37, 2022. pdf

28. C. Curto, J. Paik, I. Rivin. Betti curves of rank one symmetric matrices. F. Nielsen and F. Barbaresco (Eds.): Geometric Science of Information, 5th International Conference, GSI 2021, Paris, France, July 21-23, 2021, Proceedings, LNCS 12829, pp. 645-655, 2021. pdf

27. C. Curto, N. Youngs. Neural ring homomorphisms and maps between neural codes. Baas N., Carlsson G., Quick G., Szymik M., Thaule M. (eds) Topological Data Analysis, Abel Symposia, vol 15. Springer, Cham., 2020. pdf

26. C. Curto, K. Morrison. Relating network connectivity to dynamics: opportunities and challenges for theoretical neuroscience. Current Opinion in Neurobiology, Vol 58, pp. 11-20, 2019. pdf

25. C. Curto, E. Gross, J. Jeffries, K. Morrison, Z. Rosen, A. Shiu, N. Youngs. Algebraic signatures of convex and non-convex codes. Journal of Pure and Applied Algebra, 2019. pdf and arXiv.org preprint.

24. C. Curto, J. Geneson, K. Morrison. Fixed points of competitive threshold-linear networks. Neural Computation, vol. 31, pp. 94-155, 2019. pdf and arXiv.org preprint.

23. K. Morrison, C. Curto. Predicting neural network dynamics via graphical analysis. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. pdf, arXiv.org preprint, and Matlab code.

22. C. Curto, A. Veliz-Cuba, N. Youngs. Analysis of combinatorial neural codes: an algebraic approach. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. pdf

21. C. Curto, V. Itskov. Combinatorial neural codes. Handbook of Discrete and Combinatorial Mathematics, Second Edition, edited by Kenneth H. Rosen, CRC Press, 2018. pdf

20. C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What makes a neural code convex? SIAM J. Appl. Algebra Geometry, vol. 1, pp. 222-238, 2017. pdf, SIAGA link, and arXiv.org preprint

19. C. Curto. What can topology tells us about the neural code? Bulletin of the AMS, vol. 54, no. 1, pp. 63-78, 2017. pdf, Bulletin link.
Note: This is a write-up of my talk for the Current Events Bulletin held at the 2016 Joint Math Meetings in Seattle. CEB Booklet

18. C. Curto, K. Morrison. Pattern completion in symmetric threshold-linear networks. Neural Computation, Vol 28, pp. 2825-2852, 2016. pdf, arXiv.org preprint.

17. W.B. Thoreson, M.J. Van Hook, C. Parmelee, C. Curto. Modeling and measurement of vesicle pools at the cone ribbon synapse: changes in release probability are solely responsible for voltage-dependent changes in release. Synapse, 70:1-14, 2016. pdf

16. C. Giusti, E. Pastalkova, C. Curto*, V. Itskov* (*equal last authors). Clique topology reveals intrinsic geometric structure in neural correlations. PNAS, vol. 112, no. 44, pp. 13455-13460, 2015. pdf+supp, PNAS link.

15. M.J. Van Hook, C. Parmelee, M. Chen, K.M. Cork, C. Curto, W.B. Thoreson. Calmodulin enhances ribbon replenishment and shapes filtering of synaptic transmission by cone photoreceptors. Journal of General Physiology, 144:357-378, 2014. pdf

14. C. Curto, A. Degeratu, V. Itskov. Encoding binary neural codes in networks of threshold-linear neurons. Neural Computation, Vol 25, pp. 2858-2903, 2013. pdf, arXiv.org preprint.

13. C. Curto, V. Itskov, A. Veliz-Cuba, N. Youngs. The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bulletin of Mathematical Biology, Volume 75, Issue 9, pp. 1571-1611, 2013. pdf, arXiv.org preprint.

12. C. Curto, V. Itskov, K. Morrison, Z. Roth, J.L. Walker. Combinatorial neural codes from a mathematical coding theory perspective. Neural Computation, Vol 25(7):1891-1925, 2013. pdf, arXiv.org preprint.

11. C. Curto, D.R. Morrison. Threefold flops via matrix factorization. Journal of Algebraic Geometry, Vol 22(4), 2013, pp. 599-627. pdf, arXiv.org preprint.

10. C. Curto, A. Degeratu, V. Itskov. Flexible memory networks. Bulletin of Mathematical Biology, Vol 74(3):590-614, 2012. pdf, arXiv.org preprint.

9. V. Itskov*, C. Curto*, E. Pastalkova, G. Buzsaki. Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus. Journal of Neuroscience, Vol. 31(8):2828-2834, 2011. pdf, supplementary materials, and supplementary movie. (*equal contribution)

8. K.D. Harris, P. Bartho, P. Chadderton, C. Curto, J. de la Rocha, L. Hollender, V. Itskov, A. Luczak, S. Marguet, A. Renart, S. Sakata. How do neurons work together? Lessons from auditory cortex. Hearing Research, Vol. 271(1-2), 2011, pp. 37-53. pdf

7. P. Bartho, C. Curto, A. Luczak, S. Marguet, K.D. Harris. Population coding of tone stimuli in auditory cortex: dynamic rate vector analysis. European Journal of Neuroscience, Vol. 30(9), 2009, pp. 1767-1778. pdf

6. C. Curto, S. Sakata, S. Marguet, V. Itskov, K.D. Harris. A simple model of cortical dynamics explains variability and state-dependence of sensory responses in urethane-anesthetized auditory cortex. Journal of Neuroscience, Vol. 29(34):10600-10612, 2009. pdf and supplementary figures.

5. C. Curto*, V. Itskov*. Cell groups reveal structure of stimulus space. PLoS Computational Biology, Vol. 4(10): e1000205, 2008. pdf, supplementary text, supplementary figures, and open-access link. (*equal contribution)

4. V. Itskov, C. Curto, K.D. Harris. Valuations for spike train prediction. Neural Computation, Vol. 20(3), 2008, pp. 644-667. pdf

3. C. Curto. Matrix model superpotentials and ADE singularities. Advances in Theoretical and Mathematical Physics, Vol. 12 (2), 2008, pp. 353-404. pdf, arxiv.org preprint.

2. C.A. Kletzing, J.D. Scudder, E.E. Dors, C. Curto. Auroral source region: Plasma properties of the high-latitude plasma sheet. Journal of Geophysical Research, 108 (A10), 1360, 2003. pdf

1. C. Curto, S.J. Gates, V.G.J. Rodgers. Superspace geometrical realization of the N-extended super Virasoro algebra and its dual. Physics Letters B 480, 2000, pp. 337-347. pdf, arxiv.org preprint.

PhD thesis:

0. C. Curto. Matrix model superpotentials and Calabi-Yau spaces: an ADE classification. Ph.D. thesis, 2005. pdf, arxiv.org preprint.
This work resulted in two publications: #3 and #11 above.

Return to my main page.