scholarly journals Parallel Metric Tree Embedding Based on an Algebraic View on Moore-Bellman-Ford

2018 ◽  
Vol 65 (6) ◽  
pp. 1-55
Author(s):  
Stephan Friedrichs ◽  
Christoph Lenzen
Keyword(s):  
Metric Tree

scholarly journals Quasi-metric tree inT0-quasi-metric spaces

2013 ◽  
Vol 160 (13) ◽  
pp. 1794-1801 ◽  
Author(s):  
Olivier Olela Otafudu
Keyword(s):  
Metric Spaces ◽  
Metric Tree

scholarly journals More on linear and metric tree maps

2021 ◽  
Vol 41 (1) ◽  
pp. 55-70
Author(s):  
Sergiy Kozerenko
Keyword(s):  
Metric Tree ◽  
Linear Maps ◽  
Markov Graphs ◽  
Functional Digraph ◽  
Vertex Sets

We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.

scholarly journals Space of signatures as inverse limits of Carnot groups

2021 ◽  
Author(s):  
Enrico Le Donne ◽  
Roger Zuest
Keyword(s):  
Metric Spaces ◽  
Carnot Group ◽  
Inverse System ◽  
Carnot Groups ◽  
Inverse Limits ◽  
Limit Space ◽  
Metric Tree ◽  
Geodesic Metric ◽  
Fixed Rank

We formalize the notion of limit of an inverse system of metric spaces with $1$-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank $n$ and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in $\mathbb R^n$, as introduced by Chen. Hambly-Lyons's result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in $\mathbb R^n$ can be approximated by projections of some geodesics in some Carnot group of rank $n$, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.

Dynamical inverse problem on a metric tree

2011 ◽  
Vol 27 (7) ◽  
pp. 075011 ◽  
Author(s):  
S A Avdonin ◽  
B P Belinskiy ◽  
J V Matthews
Keyword(s):  
Inverse Problem ◽  
Metric Tree

scholarly journals Leaf Peeling method for the wave equation on metric tree graphs

2020 ◽  
Vol 0 (0) ◽  
pp. 1-15 ◽  
Author(s):  
Sergei Avdonin ◽  
◽  
Yuanyuan Zhao ◽  
◽  
Keyword(s):  
Wave Equation ◽  
Tree Graphs ◽  
Metric Tree
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