Related papers: Multilinear Hyperquiver Representations
We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…
Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are…
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver. Significant success has been obtained in applying the…
Tree tensor networks such as the tensor train format are a common tool for high dimensional problems. The associated multivariate rank and accordant tuples of singular values are based on different matricizations of the same tensor. While…
Shmuel Friedland and Giorgio Ottaviani's beautiful constant term expression for the number of singular vector tuples of generic tensors is used to derive a rational generating function for these numbers, that in turn, is used to obtain an…
Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
In this article we introduce a definition of k-uniform thresholds hypergraphs through a binary sequence, a natural extension of the classical definition for thresholds graphs. We characterize some of its eigenvalues and multiplicities by…
We compute the joint distributions of arbitrary numbers of eigenvectors of real and complex symmetric random tensors by the quantum field theoretical methods which were previously used to compute the mean distributions. We obtain the random…
We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
A generalized eigenvector of a hypermatrix, called the universal (U-) eigenvector, is proposed, which extended the notion of diagonal (D-) eigenvectors in the literature. Using the semi-tensor product, the homogeneous U-eigenequation can be…
This article is based on my lecture notes from summer schools at the Universities of Utah (June 2007) and Warwick (September 2007). We provide an introduction to explicit methods in the study of moduli spaces of quiver representations and…
In this paper we obtain bounds for the extreme entries of the principal eigenvector of hypergraphs; these bounds are computed using the spectral radius and some classical parameters such as maximum and minimum degrees. We also study…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
Graphs (i.e., networks) have become an integral tool for the representation and analysis of relational data. Advances in data gathering have lead to multi-relational data sets which exhibit greater depth and scope. In certain cases, this…