Carina Curto
Professor of Mathematics

- 331 McAllister
- ccurto@psu.edu
- (814) 863-9119
Research Summary
Mathematics applied to and arising from theoretical and computational neuroscience. Neural network theory and neural coding. Applied algebra, topology, and geometry.
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Publication Tags
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Neurons Brain Fixed Point Synapses Nonlinear Dynamics Neuron Ring Topology Graph In Graph Theory Calcium Information Theory Retinal Cone Photoreceptor Cells Theorem Neural Networks Neuroscience Encoding Calculi Completion Symmetric Matrix Linear Models Linear Networks Homomorphism Curve Computer Neural Networks Neural NetworkMost Recent Publications
Graph Rules for Recurrent Neural Network Dynamics
Carina Curto, Katherine Morrison, 2023, Notices of the American Mathematical Society on p. 536-551
Graph rules for recurrent neural network dynamics: extended version
Carina Curto, K Morrison, 2023, arXiv preprint arXiv:2301.12638
Sequential Attractors in Combinatorial Threshold-Linear Networks
Caitlyn Parmelee, Juliana Alvarez, Carina Curto, K Morrison, 2022, SIAM Journal on Applied Dynamical Systems on p. 1597--1630
Nerve theorems for fixed points of neural networks
Daniela Santander, Stefania Ebli, Alice Patania, Nicole Sanderson, Felicia Burtscher, K Morrison, Carina Curto, 2022, on p. 129--165
Periodic neural codes and sound localization in barn owls
Lindsey S. Brown, Carina Curto, 2022, Involve on p. 1-37
Core motifs predict dynamic attractors in combinatorial threshold-linear networks
Caitlyn Parmelee, Samantha Moore, K Morrison, Carina Curto, 2022, PLoS One on p. e0264456
Sequence generation in inhibition-dominated neural networks
Caitlyn Parmelee, Juliana Alvarez, Carina Curto, K Morrison, 2022, arXiv preprint arXiv:2212.08211
Nerve Theorems for Fixed Points of Neural Networks
Daniela Egas Santander, Stefania Ebli, Alice Patania, Nicole Sanderson, Felicia Burtscher, Katherine Morrison, Carina Curto, 2022, on p. 129-165
Betti Curves of Rank One Symmetric Matrices
Carina Curto, Joshua Paik, Igor Rivin, 2021, on p. 645-655
Neural Ring Homomorphisms and Maps Between Neural Codes
Carina Pamela Curto, Nora Youngs, 2020, on p. 163-180
Most-Cited Papers
Clique topology reveals intrinsic geometric structure in neural correlations
Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov, 2015, Proceedings of the National Academy of Sciences of the United States of America on p. 13455-13460
The Neural Ring: An Algebraic Tool for Analyzing the Intrinsic Structure of Neural Codes
Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs, 2013, The Bulletin of Mathematical Biophysics on p. 1571-1611
What can topology tell us about the neural code?
Carina Curto, 2017, Bulletin of the American Mathematical Society on p. 63-78
What makes a neural code convex?
Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Mohamed Omar, Zvi Rosen, Anne Shiu, Nora Youngs, 2017, SIAM Journal on Applied Algebra and Geometry on p. 222-238
Calmodulin enhances ribbon replenishment and shapes filtering of synaptic transmission by cone photoreceptors
Matthew J. van Hook, Caitlyn M. Parmelee, Minghui Chen, Karlene M. Cork, Carina Curto, Wallace B. Thoreson, 2014, Journal of General Physiology on p. 357-378
Combinatorial neural codes from a mathematical coding theory perspective
Carina Curto, Vladimir Itskov, Katherine Morrison, Zachary Roth, Judy L. Walker, 2013, Neural Computation on p. 1891-1925
Fixed points of competitive threshold-linear networks
Carina Curto, Jesse Geneson, Katherine Morrison, 2019, Neural Computation on p. 94-155
Modeling and measurement of vesicle pools at the cone ribbon synapse: Changes in release probability are solely responsible for voltage-dependent changes in release
Wallace B. Thoreson, Matthew J. Van hook, Caitlyn Parmelee, Carina Curto, 2016, Synapse on p. 1-14
Encoding binary neural codes in networks of threshold-linear neurons
Carina Curto, Anda Degeratu, Vladimir Itskov, 2013, Neural Computation on p. 2858-2903
Pattern completion in symmetric threshold-linear networks
Carina Curto, Katherine Morrison, 2016, Neural Computation on p. 2825-2852
News Articles Featuring Carina Curto
Jun 29, 2020
Penn State faculty members express concerns regarding university’s fall reopening plan
While Penn State faculty and staff feel a return to in-person instruction will benefit students academically, it may not be worth the health risks posed by the coronavirus.
Full Article
Apr 21, 2020
The Theorem That Applies to Everything from Search Algorithms to Epidemiology
On a recent episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I talked with Carina Curto, a mathematician at Penn State University who specializes on mathematics applied to biology and neuroscience. You can listen to the episode here or at kpknudson.com, where there is also a transcript.
Full Article