Kaitlyn Phillipson

activity

20102019

collaborators

4 papers

q-bio.NC2019

Classification of Open and Closed Convex Codes on Five Neurons

Sarah Ayman Goldrup, Kaitlyn Phillipson

Neural codes, represented as collections of binary strings, encode neural activity and show relationships among stimuli. Certain neurons, called place cells, have been shown experi…

math.AG2019

A Faster Solution to Smale's 17th Problem I: Real Binomial Systems

Grigoris Paouris, Kaitlyn Phillipson, J. Maurice Rojas

Suppose $F := (f_{1}, \dots, f_{n})$ is a system of random $n$ -variate polynomials with $f_{i}$ having degree $\leq d_{i}$ and the coefficient of $x_{1}^{a_{1}} \dots x_{n}^{a_{n}}$ in $f_{i}$ being a…

q-bio.NC2016

Gröbner Bases of Neural Ideals

Rebecca Garcia, Luis David García Puente, Ryan Kruse +5

The brain processes information about the environment via neural codes. The neural ideal was introduced recently as an algebraic object that can be used to better understand the co…

math.AG2010

Fewnomial Systems with Many Roots, and an Adelic Tau Conjecture

Kaitlyn Phillipson, J. Maurice Rojas

Consider a system F of n polynomials in n variables, with a total of n+k distinct exponent vectors, over any local field L. We discuss conjecturally tight bounds on the maximal num…