Related papers: Dynamic Light Spanners in Doubling Metrics
A `symbolic dynamical system' is a continuous transformation F:X-->X of a closed perfect subset X of A^V, where A is a finite set and V is countable. (Examples include subshifts, odometers, cellular automata, and automaton networks.) The…
Monitoring urban tree dynamics is vital for supporting greening policies and reducing risks to electrical infrastructure. Airborne laser scanning has advanced large-scale tree management, but challenges remain due to complex urban…
It was recently found that there are very close connections between the existence of additive spanners (subgraphs where all distances are preserved up to an additive stretch), distance preservers (subgraphs in which demand pairs have their…
A finite subset $X$ of the Euclidean space is called an $m$-distance set if the number of distances between two distinct points in $X$ is equal to $m$. An $m$-distance set $X$ is said to be maximal if any vector cannot be added to $X$ while…
In this article, we present a construction of a spanner on a set of $n$ points in $\mathbf{R}^d$ that we call a heavy path WSPD spanner. The construction is parameterized by a constant $s > 2$ called the separation ratio. The size of the…
We present a novel dynamic light scattering setup to probe, with time and space resolution, the microscopic dynamics of soft matter systems confined within millimeter-sized spherical drops. By using an ad-hoc optical layout, we tackle the…
Let $A$ and $B$ be disjoint, non-adjacent vertex-sets in an undirected, connected graph $G$, whose vertices are associated with positive weights. We address the problem of identifying a minimum-weight subset of vertices $S\subseteq V(G)$…
If $X$ is a geodesic metric space and $x_1,x_2,x_3\in X$, a geodesic triangle $T=\{x_1,x_2,x_3\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\delta$-hyperbolic (in the Gromov sense)…
A simply structured distributed observer is described for estimating the state of a continuous-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
For a weighted graph $G = (V, E, w)$ and a designated source vertex $s \in V$, a spanning tree that simultaneously approximates a shortest-path tree w.r.t. source $s$ and a minimum spanning tree is called a shallow-light tree (SLT).…
In this paper, the dynamic case of a system made up of two blocks connected by a string over a smooth pulley is revisited. One mass lies on a horizontal surface without friction, and the other mass has a vertical displacement. The motion…
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that the doubling constant of the measure can be chosen to be…
Let $X=\{x_i:i\in\mathbb{Z}\}$, $\dots<x_{i-1}<x_i<x_{i+1}<\dots$, be a sampling set which is separated by a constant $\gamma>0$. Under certain conditions on $\phi$, it is proved that if there exists a positive integer $\nu$ such that…
A tree $t$-spanner of a graph $G$ is a spanning tree $T$ in which the distance between any two adjacent vertices of $G$ is at most $t$. The smallest $t$ for which $G$ has a tree $t$-spanner is called tree stretch index. The…
Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs.…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
We show that the optical transparency of suspended graphene is defined by the fine structure constant, alpha, the parameter that describes coupling between light and relativistic electrons and is traditionally associated with quantum…
Given a set $S$ of $n$ points in the plane, we consider the problem of answering range selection queries on $S$: that is, given an arbitrary $x$-range $Q$ and an integer $k > 0$, return the $k$-th smallest $y$-coordinate from the set of…
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…
Optical tweezers has emerged as a powerful tool in manipulating microscopic particles and in measuring weak forces of the order of a pico-Newton. As a result, it has found wide applications ranging from material science to biology.…