Publications

Publications
Publications
We strongly believe in open source and giving to our community. We work directly with researchers in academia and seek out new perspectives with our intern and fellowship programs. We generalize our solutions and release them to the world as open source projects. We host discussions and publish our results.

Publications

Experimental Math,10, no. 2, pp. 103-107. 2001

A singular example for the averaged mean curvature flow

An example of an embedded curve is presented which under numerical simulation of the averaged mean curvature flow develops first a loss of embeddedness, and then a singularity where the curvature becomes infinite, all in finite time.

This leads to the conjecture that not all smooth embedded curves persist for all times under the averaged mean curvature flow.

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The Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI01), August 3-5, 2001, University of Washington, Seattle, Washington, USA

Decision-Theoretic Planning with Concurrent Temporally Extended Actions

Khashayar Rohanimanesh, Sridhar Mahadevan

We investigate a model for planning under uncertainty with temporally extended actions, where multiple actions can be taken concurrently at each decision epoch. Our model is based on the options framework, and combines it with factored state space models, where the set of options can be partitioned into classes that affect disjoint state variables.

We show that the set of decision epochs for concurrent options defines a semi-Markov decision process, if the underlying temporally extended actions being parallelized are restricted to Markov options.

This property allows us to use SMDPalgorithms for computing the value function over concurrent options. The concurrent options model allows overlapping execution of options in order to achieve higher performance or in order to perform a complex task.

We describe a simple experiment using a navigation task which illustrates how concurrent options results in a faster plan when compared to the case when only one option is taken at a time.

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IEEE Conference on Robotics and Automation , (ICRA01), 2001, Seoul, South Korea

Learning Hierarchical Partially Observable Markov Decision Processes for Robot Navigation

Georgios Theocharous, Khashayar Rohanimanesh, Sridhar Mahadevan

We propose and investigate a general framework for hierarchical modeling of partially observable environments, such as oce buildings, using Hierarchical Hidden Markov Models (HHMMs). Our main goal is to explore hierarchical modeling as a basis for designing more ecient methods for model construction and useage.

As a case study we focus on indoor robot navigation and show how this framework can be used to learn a hierarchy of models of the environment at dierent levels of spatial abstraction. We introduce the idea of model reuse that can be used to combine already learned models into a larger model.

We describe an extension of the HHMM model to includes actions, which we call hierarchical POMDPs, and describe a modied hierarchical Baum-Welch algorithm to learn these models. We train dierent families of hierarchical models for a simulated and a real world corridor environment and compare them with the standard \at" representation of the same environment.

We show that the hierarchical POMDP approach, combined with model reuse, allows learning hierarchical models that t the data better and train faster than at models.

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Internet Commerce and Software Agents: Cases, Technologies and Opportunities. Rahman, S.M. and Bignall, R. eds. Idea Group. 2001

Distributed Recommender Systems: New Opportunities for Internet Commerce

Badrul Sarwar, Joseph Konstan, John Riedl, Badrul Sarwar, Joseph Konstan, John Riedl

No Information

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ICML Workshop on Machine Learning of Spatial Knowledge, July 2, 2000, Stanford University

Learning and Planning with Hierarchical Stochastic Models for Robot Navigation

Georgios Theocharous, Khashayar Rohanimanesh, Sridhar Mahadevan, Georgios Theocharous, Khashayar Rohanimanesh, Sridhar Mahadevan

We propose and investigate a method for hierarchical learning and planning in partially observable environments using the framework of Hierarchical Hidden Markov Models (HHMMs).

Our main goal is to use hierarchical modeling as a basis for exploring more efficient learning and planning algorithms. As a case study we focus on indoor robot navigation problem and will show how this framework can be used to learn a hierarchy of maps of the environment at different levels of spatial abstraction.

We train different families of HHMMs for a real corridor environment and compare them with the standard HMM representation of the same environment. We find significant bene ts to using HHMMs in terms of the fit of the model to the training data, localization of the robot, and the ability to infer the structure of the environment. We also introduce the idea of model reuse that can be used to combine already learned models into a larger model

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Differential Integral Equations, 13, pp. 1189-1199. 2000

Self-intersections for the surface diffusion and the volume preserving mean curvature flow

Uwe Mayer, Gieri Simonett

We prove that the surface diffusion flow and the volume preserving mean curvature flow can drive embedded hypersurfaces to self-intersections.

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Proceedings of the Seventh International Conference on Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics – EVEQ2000

Self-intersections for the Willmore Flow

Uwe Mayer, Gieri Simonett

We prove that the Willmore flow can drive embedded surfaces to self-intersections in finite time

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Nuclear Science Symposium and Medical Imaging Conference, Lyon, France, October 2000

Performance of parametric shape estimators for 2D and 3D imaging systems

Robinson Piramuthu, Alfred O Hero III

Presents Cramer-Rao (CR) bounds on error covariance for 2D and 3D parametric shape estimation. The motivation for this paper is ECT image reconstruction and uptake estimation with side information corresponding to organ boundaries extracted from high resolution MRI or CT.

It is important to understand the fundamental limitations on boundary estimation error covariance so as to gauge the utility of such side information. The authors present asymptotic forms of the Fisher information matrix for estimating 2D and 3D boundaries under a B-spline polar shape parameterization.

They show that circular (2D) and spherical (3D) shapes are the easiest to estimate in the sense of yielding maximum Fisher information. They also study the worst case shapes under near circularity and near sphericity constraints. Finally, a simulation is presented to illustrate the tightness of the CR bound for a simple 3D shape estimator utilizing edge filtering.

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