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We present a new algorithm for computing zigzag persistent homology, an algebraic structure which encodes changes to homology groups of a simplicial complex over a sequence of simplex additions and deletions. Provided that there is an algorithm that multiplies two n×n matrices in M(n) time, our algorithm runs in O(M(n) + n<sup>2</sup> log<sup>2</sup>… (More)

We present a clustering scheme that combines a mode-seeking phase with a cluster merging phase in the corresponding density map. While mode detection is done by a standard graph-based hill-climbing scheme, the novelty of our approach resides in its use of <i>topological persistence</i> to guide the merging of clusters. Our algorithm provides additional… (More)

—We study the distributed desynchronization problem for graphs with arbitrary topology. Motivated by the severe computational limitations of sensor networks, we present a randomized algorithm for network desynchronization that uses an extremely lightweight model of computation, while being robust to link volatility and node failure. These techniques also… (More)

We present a robust approach to data collection, aggregation, and dissemination problems in sensor networks. Our method is based on the idea of a <i>sweep</i> over the network: a wavefront that traverses the network, passes over each node exactly once, and performs the desired operation(s). We do not require global information about the sensor field such as… (More)

Given a real-valued function f defined over some metric space X, is it possible to recover some structural information about f from the sole information of its values at a finite set L ⊆ X of sample points, whose pairwise distances in X are given? We provide a positive answer to this question. More precisely, taking advantage of recent advances on the front… (More)

The resource limited nature of WSNs require that protocols implemented on these networks be energy-efficient, scalable and distributed. This paper presents an analysis of a novel combined routing and MAC protocol. The protocol achieves energy-efficiency by minimizing signaling overhead through state-less routing decisions that are made at the receiver… (More)

In today's world, we follow news which is distributed globally. Significant events are reported by different sources and in different languages. In this work, we address the problem of tracking of events in a large multilingual stream. Within a recently developed system Event Registry we examine two aspects of this problem: how to compare articles in… (More)

In this paper, we combine two ideas: persistence-based clustering and the Heat Kernel Signature (HKS) function to obtain a multi-scale isometry invariant mesh segmentation algorithm. The key advantages of this approach is that it is tunable through a few intuitive parameters and is stable under near-isometric deformations. Indeed the method comes with… (More)

Figure 1: Robustness assignment for critical point trajectories for a 2D time-varying vector field from a combustion simulation. The trajectories are mapped to colors based on their (dynamic) robustness values. The zoomed-in versions show robustness pairings among the trajectories: same color segments are paired to each other. (a) and (c) involve fold and… (More)