Related papers: A Structural Average of Labeled Merge Trees for Un…
A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…
This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
This paper outlines a method to determine whether two label-regular directed trees, are isomorphic and when they are almost isomorphic. The approach involves reinterpreting label-regular directed trees as universal covers of rooted graphs.…
In recent years there has been a paradigm shift from the study of local task-related activation to the organization and functioning of large-scale functional and structural brain networks. However, a long-standing challenge in this…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
This paper introduces \textit{measurement trees}, a novel class of metrics designed to combine various constructs into an interpretable multi-level representation of a measurand. Unlike conventional metrics that yield single values,…
We introduce the concept of Most, and Least, Compact Spanning Trees - denoted respectively by $T^*(G)$ and $T^\#(G)$ - of a simple, connected, undirected and unweighted graph $G(V, E, W)$. For a spanning tree $T(G) \in \mathcal{T}(G)$ to be…
In scientific visualization, scalar fields are often compared through edit distances between their merge trees. Typical tasks include ensemble analysis, feature tracking and symmetry or periodicity detection. Tree edit distances represent…
Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…
Uncertainty estimation methods are expected to improve the understanding and quality of computer-assisted methods used in medical applications (e.g., neurosurgical interventions, radiotherapy planning), where automated medical image…
We propose to compose dynamic tree structures that place the objects in an image into a visual context, helping visual reasoning tasks such as scene graph generation and visual Q&A. Our visual context tree model, dubbed VCTree, has two key…
Let $G$ be a connected graph with vertex set $V(G)$, and denote by $d_G(u,v)$ the distance from $u$ to $v$ in $G$, for any $u,v \in V(G)$. The average distance of an $n$-vertex connected graph $G$, denoted by $\mu(G)$, is defined to be the…
A structural graph summary is a small graph representation that preserves structural information necessary for a given task. The summary is used instead of the original graph to complete the task faster. We introduce multi-view structural…
Semi-supervised learning relaxes the need of large pixel-wise labeled datasets for image segmentation by leveraging unlabeled data. A prominent way to exploit unlabeled data is to regularize model predictions. Since the predictions of…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized coloring numbers. Our parameters are based on new…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
Let $F$ be a function on pairs of vertices. An {\em $F$- labeling scheme} is composed of a {\em marker} algorithm for labeling the vertices of a graph with short labels, coupled with a {\em decoder} algorithm allowing one to compute…