Michael Robinson



(The content on these pages may be freely used for educational, noncommercial purposes provided appropriate references are provided. Commericial users are kindly asked to contact me first.)

Tutorials


It's more of a multi-media online short course than a publication, but my DARPA Tutorial on Sheaves in Data Analytics is a pretty comprehensive introduction to applied sheaf theory. It includes a number of videos as well as example software and datasets. Be sure to check it out!

Books



I have published a book called Topological Signal Processing, which explains how topology in general, and sheaf theory in particular, can be used to develop new and powerful algorithms for signal processing. Here is the errata page for the book.

Preprints and Technical Reports


  1. (with Jen Dumiak, Sean Fennell, and Brian DiZio) "Topological investigation of target/clutter features in sonar data," AU-CAS-MathStats Technical Report No. 2016-2.
  2. (with Emilie Purvine and Cliff Joslyn), "A Category Theoretical Investigation of the Type Hierarchy for Heterogeneous Sensor Integration," arXiv:1609.02883
  3. "Modeling wireless network routing using sheaves," arXiv:1607.06023
  4. (with Jimmy Palladino) "Protocol-independent critical node detection," arXiv:1607.06022
  5. (with Tara Shreve and David D'Auria) "Angle-valued Spectral Filters for Image Analysis," AU-CAS-MathStats Technical Report No. 2016-1
  6. "Tracking before detection using partially ordered sets and optimization," AU-CAS-MathStats Technical Report No. 2015-5.
  7. "Topological Investigation of Target/Clutter Features in Sonar Data," AU-CAS-MathStats Technical Report No. 2015-3.
  8. "Pseudosections of sheaves with consistency structures," AU-CAS-MathStats Technical Report No. 2015-2.
  9. (with Cliff Joslyn, Emilie Hogan, and Chris Capraro) "Conglomeration of heterogeneous content using local topology," which outlines an approach to heterogeneous data fusion using sheaves. AU-CAS-MathStats Technical Report 2015-1
  10. (with Matthew Hubler and Mark Verdi) "Experimental validation of the azimuthal high frequency cutoff of high resolution satellite radar images of the ocean," which shows that (1) a theoretical model of the azimuthal high frequency cutoff in maritime radar images is correct, but (2) that this is not the dominant factor in determining azimuthal blurring -- the resolution can be considerably better.
  11. (with Morgan DeHart, Matt Hubler, Mark Verdi, and Zhu Zhu) "Measuring Ocean Winds from Space Using a Radar Satellite," AU-CAS-MathStats Technical Report 2014-1.
  12. "Sheaf invariants for information systems," AU-CAS-MathStats Technical Report 2014-2.
  13. (joint with Robert Ghrist and Hank Owen) "DTIME: Discrete Topological Imaging for Multipath Environments," University of Pennsylvania ESE Technical Report
  14. "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.

Refereed Journal Articles


  1. "Sheaves are the canonical datastructure for information integration," Information Fusion, 36 (2017), pp. 208-224. (preprint version is arxiv:1603.01446)
  2. "A Topological Lowpass Filter for Quasiperiodic Signals," IEEE Signal Processing Letters, vol. 23, no. 12, December 2016, pp. 1771-1775. (preprint version is arXiv:1607.06032)
  3. "Imaging geometric graphs using internal measurements," J. Differential Equations 260 (2016) 872-896.
  4. "Knowledge-based antenna pattern interpolation," IEEE Trans. Ant. Prop. Volume 62, Issue 1, January 2014, pp. 72-79. (preprint version is arXiv:1203.2528)
  5. "Multipath-dominant, pulsed doppler analysis of rotating blades," IET Radar Sonar and Navigation, Volume 7, Issue 3, March 2013, pp. 217-224. Preprint version is arXiv:1204.4366
  6. "Asynchronous logic circuits and sheaf obstructions," Electronic Notes in Theoretical Computer Science (2012), pp. 159-177. Preprint version is arXiv:1008.2729.
  7. (with Robert Ghrist) "Topological localization via signals of opportunity," IEEE Trans. Sig. Proc, Vol. 60, No. 5, May 2012.
  8. (with Robert Ghrist) "Euler-Bessel and Euler-Fourier transforms," Inverse Problems, Vol. 27, No. 12, 2011. Preprint version is arxiv:1011.4494.
  9. "Classification of connecting solutions of semilinear parabolic equations," Electron. J. Diff. Eqns., Vol. 2011(2011), No. 61, pp. 1-10.
  10. "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.
  11. "Construction of eternal solutions for a semilinear parabolic equation," Electron. J. Diff. Eqns., Vol. 2008(2008), No. 139, pp. 1-8.
  12. "An asymptotic-numerical approach for examining global solutions to an ordinary differential equation," Ergodic Theory and Dynamical Systems, Vol. 29, (2009), pp. 223-253.
  13. "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.
  14. "A wavefront launching model for predicting channel impulse response," ACES Journal, vol. 22, no. 2, July 2007, pp 302-305.

Book Chapters


  1. "Sheaf and duality methods for analyzing multi-model systems," in Novel Methods in Harmonic Analysis, Pesenson, I., Le Gia, Q.T., Mayeli, A., Mhaskar, H., Zhou, D.-X. (eds.), Springer, in press. (preprint version is arXiv:1604.04647.)
  2. "A sheaf-theoretic perspective on sampling", in Sampling Theory, a Renaissance, Goetz Pfander (ed.), 2015. (preprint version is arxiv:1405.0324.)
  3. (with Robert Ghrist and Justin Curry) "Euler calculus and its applications to signals and sensing," in Proceedings of Symposia in Applied Mathematics: Advances in Applied and Computational Topology, Afra Zomorodian (ed.), 2012.

Refereed Archival Conference Proceedings


  1. Cliff Joslyn, Brenda Praggastis, Emilie Purvine, Arun Sathanur, Michael Robinson, Stephen Ranshous, "Local Homology Dimension as a Network Science Measure", in SIAM Workshop on Network Science 2016, July 15-16, 2016, Boston, pages 86-87.
  2. (with Harish Chintakunta and Hamid Krim), "Introduction to the special session on Topological Data Analysis," IEEE Conf. on Acoustics, Speech, and Signal Processing (ICASSP) 2016, Shanghai, China.
  3. "Simplicial Complex Sampling in Inference using Exact Sequences." Data Algorithms and Problems on Graphs (DAPG), Columbia University. September 28, 2015.
  4. "Universal factorizations of quasiperiodic functions," Sampling Theory and Applications, Washington, DC, 2015. (preprint version is arXiv:1501.06190)
  5. "Analyzing wireless communication network vulnerability with homological invariants," IEEE Global Conference on Signal and Information Processing (GlobalSIP) 2014, Atlanta, Georgia. (preprint version is arXiv:1311.1532.)
  6. (with Cliff Joslyn and Emilie Hogan), "Towards a topological framework for integrating semantic information sources," Semantic Technologies for Intelligence, Defense, and Security (STIDS), 2014.
  7. "Understanding networks and their behaviors using sheaf theory," IEEE Global Conference on Signal and Information Processing (GlobalSIP) 2013, Austin, Texas. (preprint version is arXiv:1308.4621)
  8. "The Nyquist theorem for cellular sheaves," Sampling Theory and Applications 2013, Bremen, Germany.
  9. "Polarizing frequency of a fluid plasma antenna element," IEEE Antennas and Propagation Society Symposium, 2004. (preprint)

Software



  1. The Python sheaf library pysheaf.

Patents


  1. (with James Gonnella) "Methods and Systems for Local Principal Axis Rotation Angle Transform," U.S. Patent No. 9,651,661 B2 granted 16 May 2017.
  2. "System and method for antenna pattern extrapolation," U.S. Patent No. 9,255,953 granted 9 February 2016.
  3. (with Andy Davis, Harvey Schuman, Don McPherson, John Wiley, David Hagenmayer) "Bench-Top Measurement Method, Apparatus and System for Phased Array Radar Apparatus Calibration," U.S. Patent No. 8,686,896 granted 16 August 2012.

Selected Talks


Student Publications