We lower bound the rank of a tensor by a linear combination of the ranks of three of its
unfoldings, using Sylvester's rank inequality. In a similar way, we lower bound the symmetric …

In this thesis, we develop an algebraic and graph theoretical reinterpretation of tensor
networks and formats. We investigate properties of associated singular values and …

This survey provides an overview of common applications, both implicit and explicit, of"
tensors" and" tensor products" in the fields of data science and statistics. One goal is to …

The theory of Signatures [,] is a fast growing field which has demonstrated wide applicability
to a large range of fields, from finance to health monitoring [,,]. Computing signatures often …

We explore the connection between the rank of a polynomial and the singularities of its
vanishing locus. We first describe the singularity of generic polynomials of fixed rank. We …

This thesis explores optimization challenges within algebraic statistics, employing both
topological and geometrical methodologies to derive new insights. The main focus is the …

We explore the connection between the rank of a polynomial and the singularities of its
vanishing locus. We first describe the singularity of generic polynomials of fixed rank. We …

Using methods of Part I, we build a symmetric tensor whose rank differs from the symmetric
rank, for any infinite field F with char F= 2, 3. Part I of this series [47] gives a detailed …