4 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…
DG-Sensitive Pruning & a Complete Classification of DG Trees and Cycles
Hugh Geller, Desiree Martin, Henry Potts-Rubin
Given a squarefree monomial ideal of a polynomial ring , we show that if the minimal free resolution of admits the structure of a differential graded (dg)…
Canonical forms of neural ideals
Hugh Geller, R. G. Rebecca
Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial…
Minimal Free Resolutions of Fiber Products
Hugh Geller
We construct free resolutions for quotient rings , give conditions for the quotient to be realized as a fiber p…