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The surge of research in image segmentation has yielded remarkable performance gains but also exposed a reproducibility crisis. A major contributor is performance evaluation, where both selection and implementation of metrics play critical…
It has been claimed in Aldous, Miermont and Pitman [PTRF, 2004] that all L\'evy trees are mixings of inhomogeneous continuum random trees. We give a rigorous proof of this claim in the case of a stable branching mechanism, relying on a new…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI)…
In this study, we address the challenge of disturbance estimation in legged robots by introducing a novel continuous-time online feedback-based disturbance observer that leverages measurable variables. The distinct feature of our observer…
In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a…
This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset.…
We contribute to the discussion on parsing performance in NLP by introducing a measurement that evaluates the differences between the distributions of edge displacement (the directed distance of edges) seen in training and test data. We…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as clouds of unordered points. In the 0-dimensional case the…
With a view on graph clustering, we present a definition of vertex-to-vertex distance which is based on shared connectivity. We argue that vertices sharing more connections are closer to each other than vertices sharing fewer connections.…
Many real systems can be represented as networks whose analysis can be very informative regarding the original system's organisation. In the past decade community detection received a lot of attention and is now an active field of research.…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a…
The subject of this paper is to study conformance checking for timed models, that is, process models that consider both the sequence of events in a process as well as the timestamps at which each event is recorded. Time-aware process mining…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
For a graph $G$, and two distinct vertices $u$ and $v$ of $G$, let $n_G(u,v)$ be the number of vertices of $G$ that are closer in $G$ to $u$ than to $v$. Miklavi\v{c} and \v{S}parl (arXiv:2011.01635v1) define the distance-unbalancedness of…
We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of…
The normalized edit distance is one of the distances derived from the edit distance. It is useful in some applications because it takes into account the lengths of the two strings compared. The normalized edit distance is not defined in…