50 citations · 101 across the 11 of their papers we have counts for
17 papers
On the Number of Equilibria Balancing Newtonian Point Masses with a Central Force
Nickolas Arustamyan, Christopher Cox, Erik Lundberg +2
We consider the critical points (equilibria) of a planar potential generated by Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect…
Sparse moments of univariate step functions and allele frequency spectra
Zvi Rosen, Georgy Scholten, Cynthia Vinzant
We study the univariate moment problem of piecewise-constant density functions on the interval and its consequences for an inference problem in population genetics. We show…
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…
Algebraic matroids in action
Zvi Rosen, Jessica Sidman, Louis Theran
In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics…
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…
Hyperplane Neural Codes and the Polar Complex
Vladimir Itskov, Alex Kunin, Zvi Rosen
Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane…
Geometry of the sample frequency spectrum and the perils of demographic inference
Zvi Rosen, Anand Bhaskar, Sebastien Roch +1
The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The…
Convex Neural Codes in Dimension 1
Zvi Rosen, Yan X. Zhang
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimen…
Algebraic Tools for the Analysis of State Space Models
Nicolette Meshkat, Zvi Rosen, Seth Sullivant
We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveyin…
The geometry of rank-one tensor completion
Thomas Kahle, Kaie Kubjas, Mario Kummer +1
The geometry of the set of restrictions of rank-one tensors to some of their coordinates is studied. This gives insight into the problem of rank-one completion of partial tensors.…
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…
Algebraic Systems Biology: A Case Study for the Wnt Pathway
Elizabeth Gross, Heather A. Harrington, Zvi Rosen +1
Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We dem…
Parameter-free methods distinguish Wnt pathway models and guide design of experiments
Adam L. MacLean, Zvi Rosen, Helen M. Byrne +1
The canonical Wnt signaling pathway, mediated by -catenin, is crucially involved in development, adult stem cell tissue maintenance and a host of diseases including cancer. We u…
Matrix Completion for the Independence Model
Kaie Kubjas, Zvi Rosen
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of el…
Computing Algebraic Matroids
Zvi Rosen
An affine variety induces the structure of an algebraic matroid on the set of coordinates of the ambient space. The matroid has two natural decorations: a circuit polynomial attach…
Algebraic matroids with graph symmetry
Franz J. Király, Zvi Rosen, Louis Theran
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example r…
Line arrangements modeling curves of high degree: equations, syzygies and secants
Gregory Burnham, Zvi Rosen, Jessica Sidman +1
We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be…