Related papers: Reparametrizations of Continuous Paths
The aim of this article is to develop an explicit procedure that enables one to reconstruct any $C^1$ path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the…
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism…
We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge,…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
The input to the unrooted traveling repairman problem is an undirected metric graph and a subset of nodes, each of which has a time window of unit length. Given that a repairman can start at any location, the goal is to plan a route that…
We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential image consists of the locally homotopically constant objects. This gives a…
Every generic linear functional $f$ on a convex polytope $P$ induces an orientation on the graph of $P$. From the resulting directed graph one can define a notion of $f$-arborescence and $f$-monotone path on $P$, as well as a natural graph…
Let $M_i$ and $N_i$ be path-connected locally uniquely geodesic metric spaces that are not points and $f:\prod_{i=1}^m M_i\to \prod_{i=1}^n N_i$ be an isometry where $\prod_{i=1}^n N_i$ and $\prod_{i=1}^m M_i$ are given the sup metric. Then…
A bargraph is a self-avoiding lattice path with steps $U=(0,1)$, $H=(1,0)$ and $D=(0,-1)$ that starts at the origin and ends on the $x$-axis, and stays strictly above the $x$-axis everywhere except at the endpoints. Bargraphs have been…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
In this note one shows that the four persistence diagrams and measures defined in [5] are particular cases of the maps and the measures discussed in [2] and [1]
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
This article develops a new predictor-corrector algorithm for numerical path tracking in the context of polynomial homotopy continuation. In the corrector step it uses a newly developed Newton corrector algorithm which rejects an initial…
Lattice paths effectively model phenomena in chemistry, physics and probability theory. Asymptotic enumeration of lattice paths is linked with entropy in the physical systems being modeled. Lattice paths restricted to different regions of…
This paper proposes an automated method to detect, group and rectify arbitrarily-arranged coplanar repeated elements via energy minimization. The proposed energy functional combines several features that model how planes with coplanar…
Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees…