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We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case…
Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The…
J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is…
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…
A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays, and transversal designs. Interest in constructing…
Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good…
Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of…
We investigate models of relations over a bounded continuous segment of real numbers, along with the natural linear order over the reals being provided as a "hard-coded" relation. This paper presents a generalization of a lemma from…
Binary relations derived from labeled rooted trees play an import role in mathematical biology as formal models of evolutionary relationships. The (symmetrized) Fitch relation formalizes xenology as the pairs of genes separated by at least…
This thesis is a study of large sets of unit vectors in $\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the maximal size of a set of lines with only…
Colouring problems arising from group-based constructions provide a natural link between combinatorics and algebra, particularly in the study of Cayley graphs and Latin squares. We introduce the notion of colouring bijections of finite…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short range…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
The non-Abelian exponentiation theorem has recently been generalised to correlators of multiple Wilson line operators. The perturbative expansions of these correlators exponentiate in terms of sets of diagrams called webs, which together…
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…
Several algorithmic meta-theorems on kernelization have appeared in the last years, starting with the result of Bodlaender et al. [FOCS 2009] on graphs of bounded genus, then generalized by Fomin et al. [SODA 2010] to graphs excluding a…
We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general…
We study a variety of different texture patterns in the basis in which the charged lepton mass matrix or neutrino mass matrix or neither are diagonal. The experimental results on the neutrinos provide sufficient restrictions to allow only a…
We investigate the representation theory of the valenced Temperley-Lieb algebras in mixed characteristic. These algebras, as described in characteristic zero by Flores and Peltola, arise naturally in statistical physics and conformal field…