34 citations · 45 across the 5 of their papers we have counts for
6 papers
Using oriented matroids to find low rank structure in presence of nonlinearity
Caitlin Lienkaemper
Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves…
Combinatorial geometry of neural codes, neural data analysis, and neural networks
Caitlin Lienkaemper
This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells an…
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…
Oriented Matroids and Combinatorial Neural Codes
Alexander Kunin, Caitlin Lienkaemper, Zvi Rosen
A combinatorial neural code is convex if it arises as the intersection pattern of convex open subsets of . We relate the emerging theory…
Geometry, combinatorics, and algebra of inductively pierced codes
Caitlin Lienkaemper
Convex neural codes are combinatorial structures describing the intersection pattern of a collection of convex sets. Inductively pierced codes are a particularly nice subclass of n…
Obstructions to convexity in neural codes
Caitlin Lienkaemper, Anne Shiu, Zev Woodstock
How does the brain encode spatial structure? One way is through hippocampal neurons called place cells, which become associated to convex regions of space known as their receptive…