Related papers: The search for small association schemes with nonc…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
We extend a classification of irreducible, almost-commutative geometries whose spectral action is dynamically non-degenerate, to internal algebras that have six simple summands. We find essentially four particle models: An extension of the…
We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov's…
The perfect matching association scheme is a set of relations on the perfect matchings of the complete graph on $2n$ vertices. The relations between perfect matchings are defined by the cycle structure of the union of any two perfect…
An imprimitive symmetric indecomposable association scheme of rank $5$ is said to be Higmanian. In the present paper, we prove a necessary and sufficient condition for a Higmanian association scheme with two nontrivial parabolics to be…
In this paper, we obtain classification results for higher-dimensional analogues of classical association schemes called association schemes on triples (ASTs). We present an algorithm that enumerates all ASTs on a fixed number of vertices…
Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to…
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…
A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…
The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
In this paper, we study association schemes on the anisotropic points of classical polar spaces. Our main result concerns non-degenerate elliptic and hyperbolic quadrics in PG$(n,q)$ with $q$ odd. We define relations on the anisotropic…
A key step in mechanistic modelling of dynamical systems is to conduct a structural identifiability analysis. This entails deducing which parameter combinations can be estimated from a given set of observed outputs. The standard…
To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
An association scheme is called amorphic if every possible fusion of relations gives rise to another association scheme. In earlier work, we showed that if an association scheme has at most one relation that is neither strongly regular of…
We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,\alpha}$-regularity for arbitrary…
The minimum rank problem is to determine for a graph $G$ the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacency matrix of $G$. Here $G$ is taken to be a circulant graph,…
We revisit the Bose-Mesner algebra of the perfect matching association scheme. Our main results are: 1. An inductive algorithm, based on solving linear equations, to compute the eigenvalues of the orbital basis elements given the central…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…