Related papers: Reparametrizations with given stop data
A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…
We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
We consider the problem of homotopy-type reconstruction of compact subsets $X\subset\R^N$ that have the Alexandrov curvature bounded above ($\leq$ $\kappa$) in the intrinsic length metric. The reconstructed spaces are in the form of…
In this article, we prove the stability with respect to the Hausdorff metric $d_H$ of the cut locus $\mathrm{Cut}(p, \mathfrak{g})$ of a point $p$ in a compact Riemannian manifold $(M, \mathfrak{g})$ under $C^2$ perturbation of the metric.…
This paper explores potential improvements to the Spatial-Temporal Matching algorithm for aligning the GPS trajectories to road networks. While this algorithm is effective, it presents some limitations in computational efficiency and the…
Graphs are fundamental tools for modeling pairwise interactions in complex systems. However, many real-world systems involve multi-way interactions that cannot be fully captured by standard graphs. Hypergraphs, which generalize graphs by…
A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…
We investigate the question of whether a non-constant absolutely continuous path can be reparametrized to be of unit speed with respect to the Kobayashi metric and be absolutely continuous. Even when the answer is "Yes," which isn't always…
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mapping in Hausdorff p-vector spaces, and the fixed point theorem for upper semicontinuous set-valued mappings in Hausdorff locally…
Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness…
A new similarity measure for two sets of S-parameters is proposed. It is constructed with the modified Hausdorff distance applied to S-parameter points in 3D space with real, imaginary and normalized frequency axes. New S-parameters…
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spaces. Two of the central tools in this area are the…
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
We develop persistent homology in the setting of filtrations of (Cech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted directed graphs, and filtrations of topological spaces. We use…
Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), arXiv:1504.02953] contains a mistake, which implies a weaker regularity…
The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after…
Finite sample size corrections to the reparametrization-invariant solution of the inverse problem of probability are computed, and shown to converge uniformly to the correct distribution.