Dan P. Guralnik

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We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and ac-tuated point particles in Euclidean d space (for arbitrary n and d) to an arbitrary goal configuration with the guarantee of no collisions along the way. Our construction entails a discrete abstraction of configurations using(More)
This paper introduces and solves the problem of cluster-hierarchy-invariant particle navigation in Conf (R<sup>d</sup>, J). Namely, we are given a desired goal configuration, x* &#x03F5; Conf (R<sup>d</sup>, J) and &#x03C4;, a specified cluster hierarchy that the goal supports. We build a hybrid closed loop controller guaranteed to bring any other(More)
In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity d nav counts the steps along a " combing " of the Nearest Neighbor Interchange (NNI) graph of binary hierarchies, providing an efficient approximation to the (NP-hard) NNI distance in terms of " edit length(More)
We examine overlapping clustering schemes with functorial constraints , in the spirit of Carlsson–Mémoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in(More)
We propose a self-organizing database for perceptual experience capable of supporting autonomous goal-directed planning. The main contributions are: (i) a formal demonstration that the database is complex enough in principle to represent the homotopy type of the sensed environment; (ii) some initial steps toward a formal demonstration that the database(More)
This work draws its inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carls-son and Mémoli to partition-based clustering, and the(More)
Let X be a proper CAT(0) space. A halfspace system (or cubulation) of X is a set H of open halfspaces closed under h → X h and such that every x ∈ X has a neighbourhood intersecting only finitely many walls of H. Given a cubulation H, one uses the Sageev-Roller construction to form a cubing C(H). One setting in which cubulations were studied is that of a(More)
We introduce the use of hierarchical clustering for relaxed deterministic coordination and control of multiple robots. Traditionally, an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of(More)