# 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.

## Huck Affiliations

## Links

## Publication Tags

These publication tags are generated from the output of this researcher. Click any tag below to view other Huck researchers working on the same topic.

Fixed Point Neurons Nonlinear Dynamics Graph In Graph Theory Brain Synapses Topology Calcium Neuroscience Theorem Retinal Cone Photoreceptor Cells Signature Attractor Graphics Calculi Neuron Neural Networks Neurosciences Completion Neural Networks (Computer) Symmetric Matrix Synaptic Transmission Linear Networks Curve Calmodulin## Most Recent Publications

#### Stable fixed points of combinatorial threshold-linear networks

Carina Curto, Jesse Geneson, Katherine Morrison, 2024, Advances in Applied Mathematics

#### 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

#### 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

#### 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

#### 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

## 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

#### 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

#### 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

#### Pattern completion in symmetric threshold-linear networks

Carina Curto, Katherine Morrison, 2016, Neural Computation on p. 2825-2852

#### Predicting Neural Network Dynamics via Graphical Analysis

Katherine Morrison, Carina Curto, 2018, on p. 241-277

#### Relating network connectivity to dynamics: opportunities and challenges for theoretical neuroscience

Carina Curto, Katherine Morrison, 2019, Current Opinion in Neurobiology on p. 11-20

#### Algebraic signatures of convex and non-convex codes

Carina Curto, Elizabeth Gross, Jack Jeffries, Katherine Morrison, Zvi Rosen, Anne Shiu, Nora Youngs, 2019, Journal of Pure and Applied Algebra on p. 3919-3940

## 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