29. C. Curto, C. Langdon, K. Morrison. Robust motifs of threshold-linear networks. preprint.

28. K. Morrison, A. Degeratu, V. Itskov, C. Curto. Diversity of emergent dynamics in competitive threshold-linear networks: a preliminary report. preprint, and Matlab code.

27. C. Curto, R. Vera. The Leray dimension of a convex code. preprint.

26. C. Curto, N. Youngs. Neural ring homomorphisms and maps between neural codes. Submitted. preprint.


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, in press, 2019. preprint.

24. C. Curto, J. Geneson, K. Morrison. Fixed points of competitive threshold-linear networks. Neural Computation, in press, 2019. 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. 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.

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 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, 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, 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, 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, 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, preprint.

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

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

PhD thesis:

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

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