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

Comm. Anal. Geom., 6, no. 2, pp. 199-253. 1998

Gradient flows on nonpositively curved metric spaces and harmonic maps

The notion of gradient flows is generalized to a metric space setting without any linear structure. The metric spaces considered are a generalization of Hilbert spaces. The properties of such metric spaces are used to set up a finite-difference scheme of variational form.

The proof of the Crandall-Liggett generation theorem is adapted to show convergence. The resulting flow generates a strongly continuous semigroup of Lipschitz-continuous mappings, is Lipschitz continuous in time for positive time, and decreases the energy functional along a path of steepest descent.

In case the underlying metric space is a Hilbert space, the solutions resulting from this new theory coincide with those obtained by classical methods. As an application, the harmonic map flow problem for maps from a manifold into a nonpositively curved metric space is considered, and the existence of a solution to the initial boundary value problem is established.

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SIAM J. Math. Anal., 29, no. 6, pp. 1419-1433. 1998

The surface diffusion flow for immersed hypersurfaces

Joachim Escher, Uwe Mayer, Gieri Simonett

We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.

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ICASSP, Seattle, vol. 5, pp. 2865-2868, May, 1998

Penalized maximum likelihood image reconstruction with min-max incorporation of noisy side information

Robinson Piramuthu, Alfred O Hero III

A method for incorporating anatomical MRI boundary side information into penalized maximum likelihood (PML) emission computed tomography (ECT) image reconstructions using a set of averaged Gibbs weights was proposed by Hero and Piramuthu (see Proc. of IEEE/EURASIP Workshop on Nonlinear Signal and Image Processing, 1997).

A quadratic penalty based on Gibbs weights was used to enforce smoothness constraints everywhere in the image except across the estimated boundary of the ROI.

In this methodology, a limiting form of the posterior distribution of the MRI boundary parameters was used to average the Gibbs weights obtained by Titus, Hero and Fessler (see IEEE Int. Conf. on Image Processing, vol.2, Laussane, 1996).

There is an improvement in performance over the method proposed by Titus et al., when the variance of boundary estimates from the MRI data becomes significant. Here, we present the empirical performance analysis of the proposed method of averaged Gibbs weights.

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Navier-Stokes equations and related nonlinear problems (Palanga, 1997), VSP, Utrecht, pp. 69-79. 1998

On the surface diffusion flow

Joachim Escher, Uwe Mayer, Gieri Simonett

In this paper we present recent existence, uniqueness, and stability results for the motion of immersed hypersurfaces driven by surface diffusion. We provide numerical simulations for curves and surfaces that exhibit the creation of singularities.

Moreover, our numerical simulations show that the flow causes a loss of embeddedness for some initially embedded configurations.

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ICIP, Chicago, October, 1998

Side information averaging method for PML emission tomography

Robinson Piramuthu, Alfred O Hero III

The authors previously presented a methodology for incorporating perfect extracted MRI anatomical boundary estimates to improve the performance of penalized likelihood (PL) emission computed tomography (ECT) image reconstruction and ECT tracer uptake estimation. This technique used a spatially variant quadratic Gibbs penalty which enforced smoothness everywhere in the ECT image except across the MRI-extracted boundary of the ROI.

When high quality estimates of the anatomical boundary are available and MRI and ECT images are perfectly registered, the performance of this Gibbs penalty method is very close to that attainable using perfect side information, i.e., an errorless anatomical boundary estimate. However when the variance of the MRI-extracted boundary estimate becomes significant this method performs poorly. Here we present a modified Gibbs penalty function which accounts for errors in side information based on an asymptotic min-max robustness approach.

The resulting penalty is implemented with a set of averaged Gibbs weights where the averaging is performed with respect to a limiting form of the min-max induced posterior distribution of the MRI boundary parameters. Examples are presented for tracer uptake estimation using the SAGE version of the EM algorithm and various parameterizations of the anatomical boundaries.

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Journal of the International Computer Chess Association (ICCA), March 1998

The significance of Kasparov versus Deep Blue and the future of computer chess

Dennis DeCoste

In this paper we argue that the recent Garry Kasparov vs. Deep Blue matches are significant for the field of artificial intelligence in several ways, including providing an example of valuable baseline benchmarks for more complex alternatives to contrast and justify themselves.

We will also briefly summarize some of the latest developments on computer chess research and highlight how our own work on a program called Chester tries to build on those developments to provide such justifications.

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AAAI Workshop on textual case-based reasoning. 1998

From Text to Cases: Machine Aided Text Categorization for Capturing Business Reengineering Cases

Catherine Baudin, Scott Waterman

Sharing business experience, such as client engagements, proposals or best practices, is an important part of the knowledge management task within large business organizations. While full text search is a first step at accessing textual material describing corporate experience, it does not highlight important concepts and similarities between business practices structured or operated differently.

Conceptual indexing languages, on the other hand, are high level indexing schemes based on taxonomies of domain concepts designed to provide a common language to describe, retrieve, and compare cases.

However, the effective use of these high level languages is limited by the fact that they require users to be able to *describe cases in terms an often large body of controlled vocabulary. The main challenge to using CBR and data mining technology for accessing and analyzing corporate knowledge is not in designing sophisticated inference mechanisms, but is in representing large bodies of qualitative information in textual form for reuse.

This knowledge representation task is the process of mapping textual information to predefined domain models designed by knowledgeable domain experts. We are experimenting with machine aided text categorization technology to support the creation of quality controlled repositories of corporate experience in the business domain.

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ACM CSCW 1998 Conference. 1998

Using Filtering Agents to Improve Prediction Quality in the GroupLens Research Collaborative Filtering System

Badrul Sarwar, Joseph Konstan, Al Borchers, Jon Herlocker, Brad Miller, John Riedl

No information

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AI Magazine 18(1): Spring 1997

Making an impact: Artificial Intelligence at the Jet Propulsion Laboratory

The National Aeronautics and Space Administration (NASA) is being challenged to perform more frequent and intensive space-exploration missions at greatly reduced cost. Nowhere is this challenge more acute than among robotic planetary exploration missions that the Jet Propulsion Laboratory (JPL) conducts for NASA.

This article describes recent and ongoing work on spacecraft autonomy and ground systems that builds on a legacy of existing success at JPL applying AI techniques to challenging computational problems in planning and scheduling, real-time monitoring and control, scientific data analysis, and design automation.

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Proceedings of the Third Conference on Knowledge Discovery and Data Mining (KDD-97), Newport Beach, CA, August 1997

Mining multivariate time-series sensor data to discover behavior envelopes

This paper addresses large-scale regression tasks using a novel combination of greedy input selection and asymmetric cost. Our primary goal is learning envelope functions suitable for automated detection of anomalies in future sensor data.

We argue that this new approach can be more effective than traditional techniques, such as static red-line limits, variance-based error bars, and general probability density estimation.

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