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We propose a factorizability ansatz for angular bispectra which permits fast algorithms for forecasting, analysis, and simulation, yet is general enough to encompass many interesting CMB bispectra. We describe a suite of general algorithms…
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for…
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong…
This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…
We study the relation between certain non-degenerate lower Hessenberg infinite matrices $\mathcal{G}$ and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known…
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
We provide necessary and sufficient conditions for the Hessenberg recurrence matrix associated with a system of multiple orthogonal polynomials to admit a factorisation as a product of bidiagonal matrices. Using the Gauss-Borel…
Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or multiscaling functions used in signal processing. We introduce a fast…
Binary symmetry constraints are applied to the nonlinearization of spectral problems and adjoint spectral problems into so-called binary constrained flows, which provide candidates for finite-dimensional Liouville integrable Hamiltonian…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed…
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…
The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…