Related papers: Tight embedding of modular lattices into partition…
Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…
The present work deals with the injection and packing of a flexible polymeric rod of length $L$ into a simply connected rectangular domain of area $XY$. As the injection proceeds, the rod bends over itself and it stores elastic energy in…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
We prove that the classification problem for graphs and several types of algebraic lattices (distributive, congruence and modular) up to isomorphism contains the classification problem for pairs of matrices up to simultaneous similarity.
We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular $(k,n)$ frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the…
We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question…
By a "Boolean inverse semigroup" we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are "tight" in a certain well…
Approximate lattices are aperiodic generalisations of lattices of locally compact groups that were first studied in seminal work of Yves Meyer. They are defined as those uniformly discrete approximate subgroups (symmetric subsets stable…
Autoregressive language models have demonstrated a remarkable ability to extract latent structure from text. The embeddings from large language models have been shown to capture aspects of the syntax and semantics of language. But what…
The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…
We show that real tight frames that generate lattices must be rational, and use this observation to describe a construction of lattices from vertex transitive graphs. In the case of irreducible group frames, we show that the corresponding…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.
In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…
Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two…