Related papers: Over then Under Tangles
We introduce the notion of AIR tilting subcategories of extended hearts of $t$-structures on a triangulated category associated with silting subcategories. This notion generalizes $\tau_{[d]}$-tilting pairs of extended finitely generated…
Let $\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $\Lambda=\operatorname{End}_{\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal…
When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to…
Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in…
We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish…
We formalize the problem of online learning-unlearning, where a model is updated sequentially in an online setting while accommodating unlearning requests between updates. After a data point is unlearned, all subsequent outputs must be…
A laycle is the categorical analogue of a lazy cocycle. Twines (as introduced by Bruguieres) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If $c$ is a braiding, the double braiding $c^2$ is…
Trellises are crucial graphical representations of codes. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. Iterative decoding concretely motivates such theory. In…
Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…
A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this…
We consider the problem of untangling a given (non-planar) straight-line circular drawing $\delta_G$ of an outerplanar graph $G=(V, E)$ into a planar straight-line circular drawing by shifting a minimum number of vertices to a new position…
The Standard Model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary, is still…
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…
We develop a theory of Lie algebroids over differentiable stacks that extends the standard theory of Lie algebroids over manifolds. In particular we show that Lie algebroids satisfy descent for submersions, define the category of Lie…
Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater…
The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and planar straight-line graphs. For the latter, several variants have been studied (e.g., edge slides and edge…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…
Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling drawing each edge of a bundle separately as in metro-maps and call our method ordered bundles. To…