## SSS Abstracts |

Because of the time limit, I will not show the proof of the main theorem, but will demonstrate how this theorem leads to the Freudenthal suspension theorem, an important corollary for understanding higher-dimensional loop structures of spheres.

This is joint work with Eric Finster, Eric Finster, Dan Licata and Peter LeFanu Lumsdaine, and was presented under the same title in LICS 2016.

In partial fulfillment of the Speaking Requirement.

In our work, we focus on the simple task of grasping. In particular, we investigate the effect of object size, weight, and position as well as the presence of a balance requirement on whether bimanual grasping is used in a bowl-moving task. Grasp poses are also collected and analyzed. We find that position and balance have a strong effect on bimanual usage, and weight has a weaker effect. Size, weight, and balance (but not position) affect the pose used to grasp the bowls. We conclude that the choice of strategy is most likely determined by stability requirements and the desire to minimize both body rotation and the need to reach across the body.

Finally, I discuss applications of this work to computer graphics and robotics.

In partial fulfillment of the Speaking Requirement.

In Partial Fulfillment of the Speaking Requirement

Joint work with Prof. S. K. Dwivedy and Prof. Prithwijit Guha at the Indian Institute of Technology Guwahati, accepted at the International Conference of Pattern Recognition, 2016.

This talk will present an active perception and exploration framework that enables planetary robots to efficiently explore rich, significantly 3D environments including pits, caves, RSL, and geysers. The approach seeks to achieve real-time operation on computationally constrained systems while ensuring energy efficient information acquisition. The trajectory generation formulation is based on state-lattice motion primitives and evaluation of the Cauchy-Schwarz Quadratic Mutual Information at each lattice state. Trajectories are selected by maximizing a measure of information gain per expected execution cost (e.g., time or energy). An extension to the exploration framework that considers multi-modal sensing and mapping will also be presented.

Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.

Joint work with Anupam Datta, Arunesh Sinha, Yair Zick

Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.

We then present a semi-dynamic data structure that maintains the Voronoi diagram of a set S of n sites in convex position. This data structure supports the insertion of a new site p (and hence the addition of its Voronoi cell) and finds the asymptotically minimal number K of edge insertions and removals needed to obtain the diagram of S including p from the diagram of the original S, in time O(K polylog n) worst case, which is O(sqrt{n} ;polylog n) amortized by the aforementioned combinatorial result.

The most distinctive feature of this data structure is that the graph of the Voronoi diagram is maintained explicitly at all times and can be retrieved and traversed in the natural way; this contrasts with other structures supporting nearest neighbor queries in that they do not maintain the Voronoi diagram after each insertion. This structure supports general search operations on the current Voronoi diagram, which can, for example, be used to perform point location queries in the cells of the current Voronoi diagram in O(log n) time, or to determine whether two given sites are neighbors in the Delaunay triangulation

Joint work with Luis Barba, John Iacono, and Stefan Langerman

Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.

In this paper we show that Adams' algorithms are both work efficient and highly parallel (polylog span) across four different balancing schemes--AVL trees, red-black trees, weight balanced trees and treaps. To do this we use careful, but simple, algorithms for JOIN that maintain certain invariants, and our proof is (mostly) generic across the schemes. To understand how the algorithms perform in practice we have also implemented them (all code except JOIN is generic across the balancing schemes). Interestingly the implementations on all four balancing schemes and three set functions perform similarly in time and speedup (more than 45x on 64 cores). We also compare the performance of our implementation to other existing libraries and algorithms.

Presented in Partial Fulfillment of the CSD Speaking Skills Requirement.