10 citations · 25 across the 7 of their papers we have counts for
13 papers
Betti numbers of inductively pierced codes
Hugh Geller, Rebecca R. G., Alexandra Seceleanu +1
Neural ideals were introduced by Curto, Itskov, et al as an algebraic tool to study neural codes. In this paper, we use the notion of polarization introduced by Güntürkün, Jeffries…
Recognizing and Realizing Inductively Pierced Codes
Ryan Curry, R. Amzi Jeffs, Nora Youngs +1
We prove algebraic and combinatorial characterizations of the class of inductively pierced codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic i…
Order-forcing in Neural Codes
R. Amzi Jeffs, Caitlin Lienkaemper, Nora Youngs
Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding com…
The case for algebraic biology: from research to education
Matthew Macauley, Nora Youngs
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four div…
Algebraic signatures of convex and non-convex codes
Carina Curto, Elizabeth Gross, Jack Jeffries +4
A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as t…
Neural Ideal Preserving Homomorphisms
R. Amzi Jeffs, Mohamed Omar, Nora Youngs
The neural ideal of a binary code is an ideal in closely related to the vanishing ideal of . The n…
Neural Ideals in SageMath
Ethan Petersen, Nora Youngs, Ryan Kruse +3
A major area in neuroscience research is the study of how the brain processes spatial information. Neurons in the brain represent external stimuli via neural codes. These codes oft…
Neural ideals and stimulus space visualization
Elizabeth Gross, Nida Kazi Obatake, Nora Youngs
A neural code is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from…
Sparse Neural Codes and Convexity
R. Amzi Jeffs, Mohamed Omar, Natchanon Suaysom +2
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by…
Neural ring homomorphisms and maps between neural codes
Carina Curto, Nora Youngs
Neural codes are binary codes that are used for information processing and representation in the brain. In previous work, we have shown how an algebraic structure, called the {\it…
What makes a neural code convex?
Carina Curto, Elizabeth Gross, Jack Jeffries +5
Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information…
The neural ring: using algebraic geometry to analyze neural codes
Nora Youngs
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An impor…
The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
Carina Curto, Vladimir Itskov, Alan Veliz-Cuba +1
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive fie…