Research interests of Uwe F. Mayer

While working in academia, mathematically I was interested in partial differential equations, evolution problems, free boundary problems, global analysis, differential geometry, and numerical simulations. My published mathematical work concentrates on geometric free boundary problems. For those problems, one has an initial curve or surface and a mathematical law which describes how the surface should evolve. The best known example is the one where the normal velocity is the mean curvature of the surface (possibly minus its average to force preservation of enclosed volume). However, there are many others, for example the Mullins-Sekerka flow, the surface diffusion flow, or the Willmore flow. Follow this link if you want to see a few numerical simulations. Besides on free boundary problems, I also previously worked on nonpositively curved metric spaces, in particular on questions concerning gradients.

For most of the past decade I switched my career and took on research positions in industry. I am focused on statistical learning, data mining and machine learning. I have several publications and patent applications in these areas as well, and also supervised one PhD student.

Research Publications

Clicking on a title will let you read an abstract and will give you download options.

Data Mining / Machine Learning

Generalized Statistical Methods for Mixed Exponential Families, Part II: Applications (with C. Levasseur and K. Kreutz-Delgado). Submitted for publication to IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) (September 2009).
Generalized Statistical Methods for Mixed Exponential Families, Part I: Theoretical Foundations (with C. Levasseur and K. Kreutz-Delgado). Submitted for publication to IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) (September 2009).
Classifying non-Gaussian and Mixed Data Sets in their Natural Parameter Space (with C. Levasseur and K. Kreutz-Delgado). Accepted for publication in the Proceedings of the Nineteenth IEEE Int'l Workshop on Machine Learning for Signal Processing, Grenoble, France (September 2009).
A Unifying Viewpoint of some Clustering Techniques Using Bregman Divergences and Extensions to Mixed Data Sets (with C. Levasseur, B. Burdge and K. Kreutz-Delgado). Proceedings of the 1st International Workshop on Data Mining and Artificial Intelligence (DMAI 2008) held in conjunction with the 11th IEEE International Conference on Computer and Information Technology, Khulna, Bangladesh (December 2008).
Generalized Statistical Methods for Unsupervised Minority Class Detection in Mixed Data Sets (with C. Levasseur, B. Burdge and K. Kreutz-Delgado). Proceedings of the 2008 IAPR Workshop on Cognitive Information Processing, Santorini, Greece, pp. 126-131 (2008).
Data-Pattern Discovery Methods for Detection in Nongaussian High-dimensional Data Sets (with C. Levasseur, K. Kreutz-Delgado, and G. Gancarz). Conference Record of the Thirty-Ninth Asilomar Conference on Signals, Systems and Computers, pp. 545-549 (2005).
Experimental Design for solicitation campaigns (with A. Sarkissian). Proceedings of KDD-2003, Washington, DC, pp. 717-722 (2003).

Mathematics
Self-intersections for the Willmore flow (with G. Simonett). Proceedings of the Seventh International Conference on Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics - EVEQ2000. Nonlinear Differential Equations Appl., 55, Birkhäuser, Basel, pp. 341--348 (2003).
A numerical scheme for axisymmetric solutions of curvature driven free boundary problems, with applications to the Willmore Flow (with G. Simonett). Interfaces and Free Boundaries, 4, no. 1, pp. 89-109 (2002).
Numerical solutions for the surface diffusion flow in three space dimensions. Comput. Appl. Math., 20, no. 3, pp. 361-379 (2001).
Loss of convexity for a modified Mullins-Sekerka model arising in diblock copolymer melts (with J. Escher). Archiv der Mathematik, 77, issue 5, pp. 434-448 (2001).
A singular example for the averaged mean curvature flow. Experimental Math., 10, no. 2, pp. 103-107 (2001).
A numerical scheme for free boundary problems that are gradient flows for the area functional. Europ. J. Appl. Math., 11, issue 2, pp. 61-80 (2000).
Self-intersections for the surface diffusion and the volume preserving mean curvature flow (with G. Simonett). Differential Integral Equations, 13, pp. 1189-1199 (2000).
On diffusion-induced grain-boundary motion (with G. Simonett), in Nonlinear Partial Differential Equations (Evanston, IL, 1998), Gui-Qiang Chen and Emmanuele DiBenedetto (editors). Contemporary Mathematics book series, Amer. Math. Soc., Providence, Rhode Island, pp. 231-240, 1999.
Classical solutions for diffusion-induced grain-boundary motion (with G. Simonett). J. Math. Anal. Appl., 234, pp. 660-674 (1999).
On the surface diffusion flow (with J. Escher and G. Simonett), in Navier-Stokes equations and related nonlinear problems (Palanga, 1997), VSP, Utrecht, pp. 69-79 (1998).
The surface diffusion flow for immersed hypersurfaces (with J. Escher and G. Simonett). SIAM J. Math. Anal., 29, no. 6, pp. 1419-1433 (1998).
Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom., 6, no. 2, pp. 199-253 (1998).
Two-sided Mullins-Sekerka flow does not preserve convexity, in Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi State, MS, 1997), J.Graef, R. Shivaji, B. Soni, J. Zhu (editors), Electronic J. Diff. Equ., Conference 01, 1997, pp. 171-179.
One-sided Mullins-Sekerka flow does not preserve convexity. Electronic J. Diff. Equ., 1993 no. 08, pp. 1-7 (1993).

Graduate Students

Cécile Levasseur, Ph.D. (Electical Engineering), University of California, San Diego (2009). Thesis: Generalized Statistical Methods for Mixed Exponential Families, jointly advised with Prof. Kenneth Kreutz-Delgado.
Carl-Heinz Kneisel, Diploma (Mathematics), Universität Hannover, Germany (2003). Thesis: On the global existence of non-convex solutions for the averaged mean curvature flow, advisor: Prof. Joachim Escher, numerical simulations provided by Uwe F. Mayer.

Patents

Comprehensive Identity Theft Protection System (with T. Crooks and M. Lazarus). United States Patent Application 20070124256 (filed 2006/06/02).
Fast Accurate Fuzzy Matching (with V. Narayanan and M. Blume). United States Patent Application 20080189279 (filed 2007/06/13).
Adaptive Analytics (with S. Zoldi, L. Peranich, J. Athwal and Sajama). United States Patent Application 20090222243 (2008/02/29).
Fraud Detection System For The Faster Payments System (with S. Zoldi). United States Patent Application 20090222369 (2008/05/13).

Other Publications

Clicking on a title will let you read an abstract and will give you download options.

The proof of Fermat's Last Theorem by R. Taylor and A. Wiles, written by Gerd Faltings, translated from German by Uwe F. Mayer. Notices of the AMS, 42 no. 7, pp. 743-746 (1995).
A proof that polynomials have roots. College Math Journal, 28 no. 1, p. 58 (1997).

Acknowledged in Publications by Others

Analysis 2, 1st Edition, Verlag Springer, 1995, by Wolfgang Walter.
Linux Benchmarking: Part 1 - Concepts, Linux Gazette, October 1997, Issue 22, by André D. Balsa.
Linux Benchmarking: Part 3 - Interpreting Benchmark Results, Linux Gazette, January 1998, Issue 24, by André D. Balsa.
C++ by Dissection: The Essentials of C++ Programming, 1st Edition, Addison Wesley Publishers, 2002, by Ira Pohl.

Back	mayer@math.utah.edu
	Last updated: Tue Sep 22 14:04:51 MDT 2009