Related papers: Geometry-Aware Merge Tree Comparisons for Time-Var…
The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…
A merge tree is a topological descriptor of a real-valued function. Merge trees are used in visualization and topological data analysis, either directly or as a means to another end: computing a 0-dimensional persistence diagram,…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance.…
This paper introduces a novel stability measure for edit distances between merge trees of piecewise linear scalar fields. We apply the new measure to various metrics introduced recently in the field of scalar field comparison in scientific…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis, and have been used…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains…
Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…
Comparative analysis of scalar fields in scientific visualization often involves distance functions on topological abstractions. This paper focuses on the merge tree abstraction (representing the nesting of sub- or superlevel sets) and…
We introduce an approach for updating older tree inventories with geographic coordinates using street-level panorama images and a global optimization framework for tree instance matching. Geolocations of trees in inventories until the early…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
CONTEXT. Attack treesare a recommended threat modeling tool, but there is no established method to compare them. OBJECTIVE. We aim to establish a method to compare "real" attack trees, based on both the structure of the tree itself and the…
In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
In this paper we introduce the horizon visibility graph, a simple extension to the popular horizontal visibility graph representation of a time series, and show that it possesses a rigorous mathematical foundation in computational algebraic…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…