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- Ömür Arslan, Dan P. Guralnik, Daniel E. Koditschek
- WAFR
- 2014

We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and actuated 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)

- Ömür Arslan, Dan P. Guralnik, Daniel E. Koditschek
- 2012 50th Annual Allerton Conference on…
- 2012

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* ϵ Conf (R<sup>d</sup>, J) and τ, a specified cluster hierarchy that the goal supports. We build a hybrid closed loop controller guaranteed to bring any other… (More)

- Jared Culbertson, Dan P. Guralnik, Peter F. Stiller
- ArXiv
- 2016

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 Carlsson and Mémoli to partition-based clustering, and the… (More)

- Ömür Arslan, Dan P. Guralnik, Daniel E. Koditschek
- Discrete Applied Mathematics
- 2017

In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity dnav 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”. At… (More)

- Dan P. Guralnik
- 2007

In this work we introduce a new combinatorial notion of boundary <C of an ω-dimensional cubing C. <C is defined to be the set of almost-equality classes of ultrafilters on the standard system of halfspaces of C, endowed with an order relation reflecting the interaction between the Tychonoff closures of the classes. When C arises as the dual of a cubulation… (More)

We present a centralized online (completely reactive) hybrid navigation algorithm for bringing a swarm of n perfectly sensed and actuated 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)

- Dan P. Guralnik, Daniel E. Koditschek
- 2012 50th Annual Allerton Conference on…
- 2012

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)

- Jared Culbertson, Dan P. Guralnik, Jakob Hansen, Peter F. Stiller
- ArXiv
- 2016

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 the… (More)

- Ömür Arslan, Dan P. Guralnik, Daniel E. Koditschek
- IEEE Transactions on Robotics
- 2016

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)

- Zhu Dekang, Dan P. Guralnik, Wang Xuezhi, Li Xiang, Bill Moran
- 2015 IEEE International Conference on Cyber…
- 2015

Clustering is a key component of most detectors of cyber-attacks, and increasingly, for both theoretical and practical reasons, methods that produce hierarchical clusterings (dendrograms) are being deployed in this context. In particular Single Linkage Hierarchical Clustering (SLHC) is attracting considerable interest. Existing clustering algorithms take no… (More)