The edges of any hypergraph parametrize a monomial algebra called the edge subring of
the hypergraph. We study presentation ideals of these edge subrings, and describe their …

Relying on the combinatorial classification of toric ideals using their bouquet structure, we
focus on toric ideals of hypergraphs and study how they relate to general toric ideals. We …

We consider a large class of monomial maps respecting an action of the infinite symmetric
group, and prove that the toric ideals arising as their kernels are finitely generated up to …

To every toric ideal one can associate an oriented matroid structure, consisting of a graph
and another toric ideal, called bouquet ideal. The connected components of this graph are …

A neural code C 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 place cells, neurons …

To every simple toric ideal IT one can associate the strongly robust simplicial complex Δ T,
which determines the strongly robust property for all ideals that have IT as their bouquet …

We study the secant line variety of the Segre product of projective spaces using special
cumulant coordinates adapted for secant varieties. We show that the secant variety is …

We impose rank one constraints on marginalizations of a tensor, given by a simplicial
complex. Following work of Kirkup and Sullivant, such marginal independence models can …

To any toric ideal IA, encoded by an integer matrix A, we associate a matroid structure called
the bouquet graph of A and introduce another toric ideal called the bouquet ideal of A. We …

Social networks and other sparse data sets pose significant challenges for statistical
inference, since many standard statistical methods for testing model/data fit are not …