Related papers: Reparametrizations with given stop data
The performance of deep neural networks is often attributed to their automated, task-related feature construction. It remains an open question, though, why this leads to solutions with good generalization, even in cases where the number of…
This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…
Computationally efficient solutions for pseudometrics quantifying deviation from topological conjugacy between dynamical systems are presented. Deviation from conjugacy is quantified in a Pareto optimal sense that accounts for spectral…
Graph-based methods have shown particular strengths in change-point detection (CPD) tasks for high-dimensional nonparametric settings. However, existing CPD research has rarely addressed data with repeated measurements or local group…
This document contains improved and updated proofs of convergence for the sampling method presented in our paper "Free-configuration Biased Sampling for Motion Planning".
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors),…
When one considers the collection $\mathcal{H}(\mathbb{R}^n)$ of all compact subsets of $\mathbb{R}^n$ and equip it with a topology, many questions can be asked about the topological space one ends up with. This is an example of a…
Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One…
In this paper, using altering distance functions we obtain a generalization of the results due to B.K. Das and S. Gupta as well as the results given by B. Samet and H. Yazid. Moreover, we study the so-called property P for the contraction…
Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for…
Medical images annotation is most of the time a repetitive hard task. Collecting old similar annotations and assigning them to new medical images may not only enhance the annotation process, but also reduce ambiguity caused by repetitive…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z^2 of the…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…
The Gromov--Hausdorff distance measures the difference in shape between compact metric spaces. While even approximating the distance up to any practical factor poses an NP-hard problem, its relaxations have proven useful for the problems in…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this problem in the frame of Riemannian geometry and geodesic paths between images. The associated…
We define a distance analogous to the Gromov-Hausdorff distance that enables the comparison of arbitrary quasi-isometric spaces. We also investigate properties preserved under limits with respect to this distance, as well as properties of…