Self-Stabilizing Repeated Balls-into-Bins

We study the following synchronous process that we call "repeated balls-into-bins". The process is started by assigning $n$ balls to $n$ bins in an arbitrary way. In every subsequent round, from each non-empty bin one ball is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration "legitimate" if its maximum load is $\mathcal{O}(\log n)$. We prove that, starting from any configuration, the process will converge to a legitimate configuration in linear time and then it will only take on legitimate configurations over a period of length bounded by any polynomial in $n$, with high probability (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins in $\mathcal{O}(n \log^2 n)$ rounds, w.h.p

Characterizing the Conductivity and Enhancing the Piezoresistivity of Carbon Nanotube-Polymeric Thin Films.

The concept of lightweight design is widely employed for designing and constructing aerospace structures that can sustain extreme loads while also being fuel-efficient. Popular lightweight materials such as aluminum alloy and fiber-reinforced polymers (FRPs) possess outstanding mechanical properties, but their structural integrity requires constant assessment to ensure structural safety. Next-generation structural health monitoring systems for aerospace structures should be lightweight and integrated with the structure itself. In this study, a multi-walled carbon nanotube (MWCNT)-based polymer paint was developed to detect distributed damage in lightweight structures. The thin film's electromechanical properties were characterized via cyclic loading tests. Moreover, the thin film's bulk conductivity was characterized by finite element modeling

Optimal Dynamic Distributed MIS

Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in their degrees. The result trivially applies for the dynamic distributed model, in which edges or nodes may be inserted or deleted. In this paper, we take a different approach which exploits locality to the extreme, and show how to update an MIS in a dynamic distributed setting, either \emph{synchronous} or \emph{asynchronous}, with only \emph{a single adjustment} and in a single round, in expectation. These strong guarantees hold for the \emph{complete fully dynamic} setting: Insertions and deletions, of edges as well as nodes, gracefully and abruptly. This strongly separates the static and dynamic distributed models, as super-constant lower bounds exist for computing an MIS in the former. Our results are obtained by a novel analysis of the surprisingly simple solution of carefully simulating the greedy \emph{sequential} MIS algorithm with a random ordering of the nodes. As such, our algorithm has a direct application as a $3$-approximation algorithm for correlation clustering. This adds to the important toolbox of distributed graph decompositions, which are widely used as crucial building blocks in distributed computing. Finally, our algorithm enjoys a useful \emph{history-independence} property, meaning the output is independent of the history of topology changes that constructed that graph. This means the output cannot be chosen, or even biased, by the adversary in case its goal is to prevent us from optimizing some objective function.Comment: 19 pages including appendix and reference

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Self-stabilizing cluster routing in Manet using link-cluster architecture

We design a self-stabilizing cluster routing algorithm based on the link-cluster architecture of wireless ad hoc networks. The network is divided into clusters. Each cluster has a single special node, called a clusterhead that contains the routing information about inter and intra-cluster communication. A cluster is comprised of all nodes that choose the corresponding clusterhead as their leader. The algorithm consists of two main tasks. First, the set of special nodes (clusterheads) is elected such that it models the link-cluster architecture: any node belongs to a single cluster, it is within two hops of the clusterhead, it knows the direct neighbor on the shortest path towards the clusterhead, and there exist no two adjacent clusterheads. Second, the routing tables are maintained by the clusterheads to store information about nodes both within and outside the cluster. There are two advantages of maintaining routing tables only in the clusterheads. First, as no two neighboring nodes are clusterheads (as per the link-cluster architecture), there is no need to check the consistency of the routing tables. Second, since all other nodes have significantly less work (they only forward messages), they use much less power than the clusterheads. Therefore, if a clusterhead runs out of power, a neighboring node (that is not a clusterhead) can accept the role of a clusterhead. (Abstract shortened by UMI.)

A framework for proving the self-organization of dynamic systems

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems

Statistical characterization of spatio-temporal sediment dynamics in the Venice lagoon

Characterizing the dynamics of suspended sediment is crucial when investigating the long-term evolution of tidal landscapes. Here we apply a widely tested mathematical model which describes the dynamics of cohesive and noncohesive sediments, driven by the combined effect of tidal currents and wind waves, using 1 year long time series of observed water levels and wind data from the Venice lagoon. The spatiotemporal evolution of the computed suspended sediment concentration (SSC) is analyzed on the basis of the \u201cpeak over threshold\u201d theory. Our analysis suggests that events characterized by high SSC can be modeled as a marked Poisson process over most of the lagoon. The interarrival time between two consecutive over threshold events, the intensity of peak excesses, and the duration are found to be exponentially distributed random variables over most of tidal flats. Our study suggests that intensity and duration of over threshold events are temporally correlated, while almost no correlation exists between interarrival times and both durations and intensities. The benthic vegetation colonizing the central southern part of the Venice lagoon is found to exert a crucial role on sediment dynamics: vegetation locally decreases the frequency of significant resuspension events by affecting patiotemporal patterns of SSCs also in adjacent areas. Spatial patterns of the mean interarrival of over threshold SSC events are found to be less heterogeneous than the corresponding patterns of mean interarrivals of over threshold bottom shear stress events because of the role of advection/dispersion processes in mixing suspended sediments within the lagoon. Implications for long-term morphodynamic modeling of tidal environments are discussed