Related papers: Merge trees in discrete Morse theory
We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the…
We study Morse theory of the (power) distance function to a set of points in $\mathbb{R}^n$. We describe the topology of the union of the corresponding set of growing balls by a Morse poset. The Morse poset is related to the power…
When following the growth of structure in the Universe, we propose replacing merger trees with merger graphs, in which haloes can both merge and split into separate pieces. We show that this leads to smoother mass growth and eliminates…
We study a broad class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the resulting Morse functions, via planar contact trees constructed from Newton-Puiseux roots of the polar…
Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the…
We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are…
We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose…
We present a way to normalize a combinatorial Morse function into an integer-valued canonical representative of the set of discrete Morse functions inducing a given gradient field.
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers, and torus orbits on certain homogeneous varieties. In…
Model performance is frequently reported only for the overall population under consideration. However, due to heterogeneity, overall performance measures often do not accurately represent model performance within specific subgroups. We…
This paper describes experiments, on two domains, to investigate the effect of averaging over predictions of multiple decision trees, instead of using a single tree. Other authors have pointed out theoretical and commonsense reasons for…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
We introduce a notion of Morse shellings (and tilings) on finite simplicial complexes which extends the classical one and its relation to discrete Morse theory.Skeletons and barycentric subdivisions of Morse shellable (or tileable)…
The use of cumulative incidence functions for characterizing the risk of one type of event in the presence of others has become increasingly popular over the past decade. The problems of modeling, estimation and inference have been treated…
We systematically develop the multivariable counterpart of the theory of weighted shifts on rooted directed trees. Capitalizing on the theory of product of directed graphs, we introduce and study the notion of multishifts on directed…
We develop the theory of meta-iteration trees, that is, iteration trees whose base "model" is itself an ordinary iteration tree. We prove a comparison theorem for meta-iteration strategies parallel to the one for ordinary iteration…
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operators in question.
We construct measures invariant with respect to equivalence relations which are graphed by horospheric products of trees. The construction is based on using conformal systems of boundary measures on treed equivalence relations. The…
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…