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Preprints and Technical Reports

1. (joint with Robert Ghrist) "Topological localization via signals of opportunity," which introduces a new paradigm for localization, mapping, and tracking using opportunistic signals. It also presents experimental data collected to validate the theory. Submitted to IEEE Trans. Sig. Proc.
2. (with Robert Ghrist and Justin Curry) "Euler calculus and its applications to signals and sensing," submitted.
3. "Inverse problems in geometric graphs using internal measurements," arXiv:1008.2933, which discusses algorithms and underlying theory for solving imaging problems in multipath-dominant, opportunistically illuminated environments.
4. (joint with Robert Ghrist and Hank Owen) "DTIME: Discrete Topological Imaging for Multipath Environments," University of Pennsylvania ESE Technical Report
5. "Asynchronous logic circuits and sheaf obstructions," arXiv:1008.2729, which describes a new constructible sheaf framework for analyzing the temporal behavior of logic circuity.
6. "Instability of a parabolic equation with a quadratic nonlinearity," arXiv:0704.3989, which gives an explicit construction showing that a certain critical point whose linearization is stable is in fact unstable. This is not a new result, but the proof is a good example of the blow-up method of H. Fujita.

Journal and Conference Papers

1. (with Robert Ghrist) "Euler-Bessel and Euler-Fourier transforms," Inverse Problems, Vol. 27, No. 12, 2011. Preprint version is arxiv:1011.4494.
2. "Classification of connecting solutions of semilinear parabolic equations," Electron. J. Diff. Eqns., Vol. 2011(2011), No. 61, pp. 1-10.
3. "A cell complex structure for the space of heteroclines for a semilinear parabolic equation," Electron. J. Diff. Eqns., Vol. 2009(2009), No. 16, pp. 1-17.
4. "Construction of eternal solutions for a semilinear parabolic equation," Electron. J. Diff. Eqns., Vol. 2008(2008), No. 139, pp. 1-8.
5. "An asymptotic-numerical approach for examining global solutions to an ordinary differential equation," Ergodic Theory and Dynamical Systems, Vol. 29, (2009), pp. 223-253.
6. "IMEX method convergence for a semilinear parabolic equation," J. Differential Equations, vol. 241, no. 2, October 2007, pp 225-236; doi:10.1016/j.jde.2007.07.001.
7. "A wavefront launching model for predicting channel impulse response," ACES Journal, vol. 22, no. 2, July 2007, pp 302-305.
8. "Polarizing frequency of a fluid plasma antenna element," IEEE Antennas and Propagation Society Symposium, 2004.

Patents

1. (with Andy Davis, Harvey Schuman, Don McPherson, John Wiley, David Hagenmayer) "Bench-Top Measurement Method, Apparatus and System for Phased Array Radar Apparatus Calibration," accepted for filing by the USPTO on February 11, 2011 under Application No. 13/025652.

Selected Talks

• "Euler integral transforms and applications." Workshop on Computational Topology. Fields Institute. November 8, 2011.
• "Sounding your surroundings." IMA Summer School on Topological Analysis. University of Pennsylvania. Week of July 25, 2011.
• "Measuring Topology and Geometry by Distributed Sensing." NRO Technical Seminar, July 11, 2011. Also at Drexel University (April 14, 2011), Lehigh University (October 13, 2010), Tulane University (October 28, 2010). Demonstrated acoustic sounding equipment to supply opportunistic localization data.
• (poster) "Sheaf theoretic invariants for computational networks." NMMC 2011, May 16, 2011.
• "Logic circuits as sheaves." NSA Mathematics Colloquium. March 4, 2011. Also at Tulane University, March 25, 2011.
• (poster) "Euler characteristic integrals in signal processing." FFT 2011. February 17, 2011.
• "Forays into signal processing using the Euler characteristic integral." Princeton University, February 12, 2010.
• "Constructible sheaves and their cohomology for asynchronous logic and computation." GETCO 2010, Aalborg, Denmark. January 14, 2010. Also at DARPA SToMP meeeting, February 18, 2010.
• "Localization of Mobile Receivers using Opportunistic Signals." PASSHEMA Conference, Mansfield University. March 21, 2009.
• "Frequency assignment in land mobile radio systems." Applied Mathematics and Computational Science Seminar, University of Pennsylvania. October 10, 2008.
• "Some finite dimensionality results for the space of heteroclinic orbits of a semilinear parabolic equation." Dynamics Seminar, Cornell University. February 1, 2008.
• "Dynamics of a semilinear parabolic equation." Joint Mathematics Meetings, San Diego, California. January 6, 2008.
• "Instability of an equilibrium of a nonlinear parabolic equation with a negative definite linearization." Applied Mathematics Seminar, Université de Provence. March 13, 2007.
• "Towards a characterization of the dynamics of a semilinear parabolic differential equation." Mathematical Sciences Seminar, Cornell University. November 8, 2006.
• "Tug-of-war: how nonlinearity and the Laplacian interact." Olivetti Club, Cornell University. April 25, 2006.
• "Do electrons really spin?" Mathematical Sciences Seminar, Cornell University. February 8, 2006.
• "Studying the bifurcation behavior of a nonlinear PDE." Mathematical Sciences Seminar, Cornell University. October 5, 2005.
• "Polarizing frequency of a fluid plasma antenna element." Mathematical Sciences Seminar, Cornell University. November 8, 2004.