# 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

Brain Neurons Synapses Fixed Point Neuron Ring Topology Nonlinear Dynamics Graph In Graph Theory Neurosciences Calcium Information Theory Theorem Retinal Cone Photoreceptor Cells Signature Neuroscience Neural Networks Encoding Completion Homomorphism Sound Curve Threefolds Neural Network Linear Networks## Most Recent Publications

#### Core motifs predict dynamic attractors in combinatorial threshold-linear networks

Caitlyn Parmelee, Samantha Moore, Katherine Morrison, Carina Curto, 2022, PLoS One

#### 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

#### Periodic neural codes and sound localization in barn owls

Lindsey S. Brown, Carina Curto, 2022, Involve on p. 1-37

#### Sequential Attractors in Combinatorial Threshold-Linear Networks

Caitlyn Parmelee, Juliana Londono Alvarez, Carina Curto, Katherine Morrison, 2022, SIAM Journal on Applied Dynamical Systems on p. 1597-1630

#### 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

#### Relating network connectivity to dynamics

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

#### Predicting Neural Network Dynamics via Graphical Analysis

K Morrison, Carina Curto, 2019, ALGEBRAIC AND COMBINATORIAL COMPUTATIONAL BIOLOGY on p. 241-277

#### Analysis of Combinatorial Neural Codes: An Algebraic Approach

Carina Curto, Alan Veliz-Cuba, Nora Youngs, 2019, ALGEBRAIC AND COMBINATORIAL COMPUTATIONAL BIOLOGY on p. 213-240

## 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

#### 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

#### 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

#### Modeling and measurement of vesicle pools at the cone ribbon synapse

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

#### Threefold flops via matrix factorization

Carina Curto, David R. Morrison, 2013, Journal of Algebraic Geometry on p. 599-627

## 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