Related papers: Computing Hypermatrix Spectra with the Poisson Pro…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
We give some graph theoretical formulas for the trace $Tr_k(\mathbb {T})$ of a tensor $\mathbb {T}$ which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the study of the spectra of…
Through the theory of Lie bi-algebroids and generalized complex structures, one could define a cohomology theory naturally associated to a holomorphic Poisson structure. It is known that it is the hypercohomology of a bi-complex such that…
We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra…
To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods…
A pleasant family of graphs defined by Godsil and McKay is shown to have easily computed eigenvalues in many cases.
The problem of extracting photoproduction amplitudes uniquely from so called complete experiments is discussed. This problem can be considered either for the extraction of full production amplitudes, or for the determination of multipoles.…
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…
A popular trick for computing a pairwise co-occurrence matrix is the product of an incidence matrix and its transpose. We present an analog for higher order tuple co-occurrences using the face-splitting product, or alternately known as the…
We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable…
We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view.
We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and…
Computing multivariate derivatives of matrix-like expressions in the compact, coordinate free fashion is very important for both theory and applied computations (e.g. optimization and machine learning). The critical components of such…
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the $UOSp(2\vert 1)$ supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already…
The exact solution for the two particle spectrum of the Heisenberg-Peierls one dimensional spin chain is given by working in the fermionic representation. The resulting equations for the eigenvalues are, in some sense, similar to those of…
We completely determine the spectrum of an $I$-graph, that is, the eigenvalues of its adjacency matrix. We apply our result to prove known characterizations of connectedness and bipartiteness in $I$-graphs by using an spectral approach.…
In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of…
The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formulate a nonperturbative theory of the power spectrum for…