Related papers: Slit-slide-sew bijections for oriented planar maps
In an upward planar 2-slope drawing of a digraph, edges are drawn as straight-line segments in the upward direction without crossings using only two different slopes. We investigate whether a given upward planar digraph admits such a…
For an oriented matroid M, and given a generic single element extension and a generic single element lifting of M, the main result of [1] provides a bijection between bases of M and certain reorientations of M induced by the…
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods…
We will define an operad $\mathcal{B}^0$ on planar rooted trees. $\mathcal{B}^0$ is analgous to the $NAP$-operad in the non-planar tree setting. We will define a family of "current-preserving" operads $\mathcal{B}^\lambda$ depending on a…
In this paper we prove bilinear Strichartz estimates for a solution to the Schr{\"o}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$. These…
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we present a bijective link between unicellular maps on a non-orientable surface and…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Associated with the $r$-Shi arrangement and $r$-Catalan arrangement in $\Bbb{R}^n$, we introduce a cubic matrix for each region to establish two bijections in a uniform way. Firstly, the positions of minimal positive entries in column…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
The Smith embedding of a finite planar map with two marked vertices, possibly with conductances on the edges, is a way of representing the map as a tiling of a finite cylinder by rectangles. In this embedding, each edge of the planar map…
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary…
Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While $st$-orderings do extend to directed graphs, especially…
We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…
Evidence suggests that oblique splits can significantly enhance the performance of decision trees. This paper explores the optimization of high-dimensional oblique splits for decision tree construction, establishing the Sufficient Impurity…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
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…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…