Related papers: Multilinear Hyperquiver Representations
To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed…
We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
Learning expressive representations for high-dimensional yet sparse features has been a longstanding problem in information retrieval. Though recent deep learning methods can partially solve the problem, they often fail to handle the…
We review the theory of quiver bundles over a K\"ahler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group G. We first study the case when G=O(V) or Sp(V), interpreting them as orthogonal…
A hypergraph is Sperner if no hyperedge contains another one. A Sperner hypergraph is equilizable (resp., threshold) if the characteristic vectors of its hyperedges are the (minimal) binary solutions to a linear equation (resp., inequality)…
We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.
Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization…
Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…
Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergraphs, we establish the multi-linear pseudo-PageRank (MLPPR)…
Pairwise Fisher graphs capture local covariance information, but they cannot distinguish an irreducible multi-observable radiation pattern from a collection of ordinary pairwise correlations. We show that this missing structure is naturally…
We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…
A line multigraph is obtained from a hypergraph as follows: the vertices of the multigraph correspond to the hyperedges of the hypergraph, and the number of edges between two vertices is given by the number of vertices shared by the…
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…
In this paper we construct strong exceptional collections of vector bundles on smooth projective varieties that have a prescribed endomorphism algebra. We prove the construction problem always have a solution. We consider some applications…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
We relate the notion of dimension expanders to quiver representations and their general subrepresentations, and use this relation to establish sharp existence results.
We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…