Sparse Fault-Tolerant BFS Trees

This paper addresses the problem of designing a sparse {\em fault-tolerant} BFS tree, or {\em FT-BFS tree} for short, namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the surviving part $T'$ of $T$ still contains a BFS spanning tree for (the surviving part of) $G$. Our main results are as follows. We present an algorithm that for every $n$-vertex graph $G$ and source node $s$ constructs a (single edge failure) FT-BFS tree rooted at $s$ with O(n \cdot \min\{\Depth(s), \sqrt{n}\}) edges, where \Depth(s) is the depth of the BFS tree rooted at $s$. This result is complemented by a matching lower bound, showing that there exist $n$-vertex graphs with a source node $s$ for which any edge (or vertex) FT-BFS tree rooted at $s$ has $\Omega(n^{3/2})$ edges. We then consider {\em fault-tolerant multi-source BFS trees}, or {\em FT-MBFS trees} for short, aiming to provide (following a failure) a BFS tree rooted at each source $s\in S$ for some subset of sources $S\subseteq V$. Again, tight bounds are provided, showing that there exists a poly-time algorithm that for every $n$-vertex graph and source set $S \subseteq V$ of size $\sigma$ constructs a (single failure) FT-MBFS tree $T^*(S)$ from each source $s_i \in S$, with $O(\sqrt{\sigma} \cdot n^{3/2})$ edges, and on the other hand there exist $n$-vertex graphs with source sets $S \subseteq V$ of cardinality $\sigma$, on which any FT-MBFS tree from $S$ has $\Omega(\sqrt{\sigma}\cdot n^{3/2})$ edges. Finally, we propose an $O(\log n)$ approximation algorithm for constructing FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result stating that there exists no $\Omega(\log n)$ approximation algorithm for these problems under standard complexity assumptions

Simulations of the angular dependence of the dipole-dipole interaction among Rydberg atoms

The dipole-dipole interaction between two Rydberg atoms depends on the relative orientation of the atoms and on the change in the magnetic quantum number. We simulate the effect of this anisotropy on the energy transport in an amorphous many atom system subject to a homogeneous applied electric field. We consider two experimentally feasible geometries and find that the effects should be measurable in current generation imaging experiments. In both geometries atoms of $p$ character are localized to a small region of space which is immersed in a larger region that is filled with atoms of $s$ character. Energy transfer due to the dipole-dipole interaction can lead to a spread of $p$ character into the region initially occupied by $s$ atoms. Over long timescales the energy transport is confined to the volume near the border of the $p$ region which is suggestive of Anderson localization. We calculate a correlation length of 6.3~$\mu$m for one particular geometry.Comment: 6 pages, 5 figures, revised draf

Randomized Local Network Computing

International audienceIn this paper, we carry on investigating the line of research questioning the power of randomization for the design of distributed algorithms. In their seminal paper, Naor and Stockmeyer [STOC 1993] established that, in the context of network computing, in which all nodes execute the same algorithm in parallel, any construction task that can be solved locally by a randomized Monte-Carlo algorithm can also be solved locally by a deterministic algorithm. This result however holds in a specific context. In particular, it holds only for distributed tasks whose solutions that can be locally checked by a deterministic algorithm. In this paper, we extend the result of Naor and Stockmeyer to a wider class of tasks. Specifically, we prove that the same derandomization result holds for every task whose solutions can be locally checked using a 2-sided error randomized Monte-Carlo algorithm. This extension finds applications to, e.g., the design of lower bounds for construction tasks which tolerate that some nodes compute incorrect values. In a nutshell, we show that randomization does not help for solving such resilient tasks

Training Package for Emergency Medical Teams Deployed to Disaster Stricken Areas: Has 'TEAMS' Achieved its Goals?

In spite of their good intentions, Emergency Medical Teams (EMTs) were relatively disorganized for many years. To enhance the efficient provision of EMT's field team work, the Training for Emergency Medical Teams and European Medical Corps (TEAMS) project was established. The purpose of this study was to assess the effectiveness and quality of the TEAMS training package in 2 pilot training programs in Germany and Turkey. A total of 19 German and 29 Turkish participants completed the TEAMS training package. Participants were asked to complete a set of questionnaires designed to assess self-efficacy, team work, and quality of training. The results suggest an improvement for both teams' self-efficacy and team work. The self-efficacy scale improved from 3.912 (± 0.655 SD) prior to training to 4.580 (± 0.369 SD) after training (out of 5). Team work improved from 3.085 (± 0.591 SD) to 3.556 (± 0.339 SD) (out of 4). The overall mean score of the quality of the training scale was 4.443 (± 0.671 SD) (out of 5). In conclusion, The TEAMS Training Package for Emergency Medical Teams has been demonstrated to be effective in promoting EMT team work capacities, and it is considered by its users to be a useful and appropriate tool for addressing their perceived needs

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Far-from-equilibrium Ostwald ripening in electrostatically driven granular powders

We report the first experimental study of cluster size distributions in electrostatically driven granular submonolayers. The cluster size distribution in this far-from-equilibrium process exhibits dynamic scaling behavior characteristic of the (nearly equilibrium) Ostwald ripening, controlled by the attachment and detachment of the "gas" particles. The scaled size distribution, however, is different from the classical Wagner distribution obtained in the limit of a vanishingly small area fraction of the clusters. A much better agreement is found with the theory of Conti et al. [Phys. Rev. E 65, 046117 (2002)] which accounts for the cluster merger.Comment: 5 pages, to appear in PR

A gas emitted by Neurospora crassa

We investigated whether gases other than carbon dioxide are produced by N. crassa. A peak corresponding to ethylene has been detected using gas chromatography. Mass spectroscopy, however, indicated that the gas produced might be carbon monoxide which, surprisingly, migrated with the same chromatographic retention time as ethylene. Our results emphasize the need for caution when interpreting results based solely on gas chromatographic data

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results