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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 is 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


My Topological Signal Processing book
  1. 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.
  2. With Stephen Casey, Kasso Okoudjou and Brian Sadler, I helped to edit a volume Sampling Theory and Applications: A Centennial Celebration of Claude Shannon, published by Springer.

Preprints and Technical Reports


  1. (with Robert Green, Cliff Joslyn, Audun Myers, Michael Rawson). "The Topological Structures of the Orders of Hypergraphs." arXiv:2504.11760, April 2025.
  2. (with Sourya Dey and Tony Chiang). "Token embeddings violate the manifold hypothesis." arXiv:2504.01002, April 2025.
  3. (with Sourya Dey and Taisa Kushner). "Probing the topology of the space of tokens with structured prompts." arXiv:2503.15421, March 2025.
  4. (with Steve Huntsman, Ludmilla Huntsman), "A path to legal coherence through AI." (also at https://github.com/SteveHuntsman/LegalCoherence/blob/main/LegalCoherence20250204.pdf) February 2025.
  5. (with Michael Szulczewski, Alexis Allegra, Charlie Fornaca, Stephen Lynch, and Michael Postol), "Sheaf Theory for Data Assimilation in Earth System Models", AGU 2024. December 2024.
  6. (with Sourya Dey, Shauna Sweet), "The structure of the token space for large language models." arXiv:2410.08993, October 2024.
  7. (with Zander Memon, Maxwell Gualtieri), "Topological and geometric characterization of synthetic aperture sonar collections." arXiv:2409.15447, September 2024.
  8. (with Enzo Battistella, Sean English, Robert Green, Cliff Joslyn, Evgeniya Lagoda, Van Magnan, Audun Myers, Evan D. Nash), "Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs." arXiv:2405.04559, May 2024.
  9. (with Steve Huntsman and Ludmilla Huntsman), "Prospects for inconsistency detection using large language models and sheaves." arXiv:2401.16713, January 2024.
  10. (with Michael Wang), "Vulnerability detection through an adversarial fuzzing algorithm." arXiv:2307.11917, July 2023.
  11. (with Michael Rawson, Audun Myers, Robert Green, and Cliff Joslyn), "Formal concept lattice representations and algorithms for hypergraphs." arXiv:2307.11681, July 2023.
  12. (with Tate Altman), "CSV Dialect Detection using Dowker Complex.", American University Mathematics and Statistics Technical Report, July 2022.
  13. (with Zander Memon), "The Topology of Circular Synthetic Aperture Sonar Targets." arXiv:2205.11311
  14. (with Kenneth Ewing), "Metric comparisons of relations," arXiv:2105.01690
  15. (with Griffin Kearney and Kevin Palmowski), "Sheaf-theoretic framework for optimal network control." arXiv:2012.00120
  16. (with Kristopher Ambrose, Steve Huntsman, and Matvey Yutin) "Topological Differential Testing," arXiv:2003.00976
  17. (with Cliff A Joslyn, J Smart, Khushbu Agarwal, David Bridgeland, Adam Brown, Sutanay Choudhury, Brett Jefferson, Brenda Praggastis, Emilie Purvine, William P Smith, and Dimitri Zarzhitsky) "HyperThesis: Topological Hypothesis Management in a Hypergraph Knowledgebase." NIST Text Analytics Conference (TAC) 2018. https://tac.nist.gov/publications/2018/participant.papers/TAC2018.Hyperthesis.proceedings.pdf
  18. (with Chris Capraro, Cliff Joslyn, Emilie Purvine, Brenda Praggastis, Stephen Ranshous, Arun Sathanur) "Local homology of abstract simplicial complexes," arXiv:1805.11547
  19. (with Emilie Purvine and Cliff Joslyn), "A Category Theoretical Investigation of the Type Hierarchy for Heterogeneous Sensor Integration," arXiv:1609.02883
  20. "Modeling wireless network routing using sheaves," arXiv:1607.06023
  21. (with Jimmy Palladino) "Protocol-independent critical node detection," arXiv:1607.06022
  22. (with Tara Shreve and David D'Auria) "Angle-valued Spectral Filters for Image Analysis," AU-CAS-MathStats Technical Report No. 2016-1
  23. "Tracking before detection using partially ordered sets and optimization," AU-CAS-MathStats Technical Report No. 2015-5. arXiv:2401.12182
  24. "Topological Investigation of Target/Clutter Features in Sonar Data," AU-CAS-MathStats Technical Report No. 2015-3.
  25. "Pseudosections of sheaves with consistency structures," AU-CAS-MathStats Technical Report No. 2015-2.
  26. (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
  27. (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.
  28. (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.
  29. "Sheaf invariants for information systems," AU-CAS-MathStats Technical Report 2014-2.
  30. (joint with Robert Ghrist and Hank Owen) "DTIME: Discrete Topological Imaging for Multipath Environments," University of Pennsylvania ESE Technical Report
  31. "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. "Constant rank factorisations of smooth maps, with applications to sonar," European Journal of Applied Mathematics, December 2022. (preprint arXiv:2112.05799)
  2. "Astronomy with Chaucer: Using an astrolabe to determine planetary orbits," American Journal of Physics, Volume 90, Number 10, October 2022. (preprint arXiv:2204.09677)
  3. "Aggregation sheaves for greedy modal decompositions," Journal of Physics Communications, April 2022. (preprint arXiv:2106.04445)
  4. (with Chris Capraro), "Super-resolving star clusters with sheaves," EURASIP Journal on Advances in Signal Processing, Volume 2022, Number 26, March 2022. (preprint arXiv:2106.08123)
  5. "Cosheaf Representations of Relations and Dowker Complexes" Journal of Applied and Computational Topology, 2021. (Preprint arXiv:2005.12348)
  6. (with Cliff Joslyn, Lauren Charles, Chris DePerno, Nicholas Gould, Kathleen Nowak, Brenda Praggastis, Emilie Purvine, Jennifer Strules, and Paul Whitney) "A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information," Sensors, Volume 20, 2020, 3418. (Also at arXiv:1912.05487)
  7. "Assignments to sheaves of pseudometric spaces," Compositionality, Volume 2, Number 2, 2020. (Also at arXiv:1805.08927)
  8. "Hunting for foxes with sheaves," Notices of the American Mathematical Society, Volume 66, Number 5, May 2019, pp. 661-676.
  9. (with Fernando Benadon and Andrew McGraw), "Quantitative Analysis of Temporal Structure in Cuban Guaguanco Drumming," Music and Science, Volume 1, July 4, 2018.
  10. (with Sean Fennell, Brian DiZio, and Jennifer Dumiak), "Geometry and topology of the space of sonar target echos," Journal of the Acoustical Society of America, volume 143, number 3, March 2018, pp. 1630-1645. (preprint version is AU-CAS-MathStats Technical Report No. 2016-2.)
  11. "Sheaves are the canonical datastructure for information integration," Information Fusion, 36 (2017), pp. 208-224. (preprint version is arxiv:1603.01446)
  12. "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)
  13. "Imaging geometric graphs using internal measurements," J. Differential Equations 260 (2016) 872-896.
  14. "Knowledge-based antenna pattern interpolation," IEEE Trans. Ant. Prop. Volume 62, Issue 1, January 2014, pp. 72-79. (preprint version is arXiv:1203.2528)
  15. "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
  16. "Asynchronous logic circuits and sheaf obstructions," Electronic Notes in Theoretical Computer Science (2012), pp. 159-177. Preprint version is arXiv:1008.2729.
  17. (with Robert Ghrist) "Topological localization via signals of opportunity," IEEE Trans. Sig. Proc, Vol. 60, No. 5, May 2012.
  18. (with Robert Ghrist) "Euler-Bessel and Euler-Fourier transforms," Inverse Problems, Vol. 27, No. 12, 2011. Preprint version is arxiv:1011.4494.
  19. "Classification of connecting solutions of semilinear parabolic equations," Electron. J. Diff. Eqns., Vol. 2011(2011), No. 61, pp. 1-10.
  20. "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.
  21. "Construction of eternal solutions for a semilinear parabolic equation," Electron. J. Diff. Eqns., Vol. 2008(2008), No. 139, pp. 1-8.
  22. "An asymptotic-numerical approach for examining global solutions to an ordinary differential equation," Ergodic Theory and Dynamical Systems, Vol. 29, (2009), pp. 223-253.
  23. "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.
  24. "A wavefront launching model for predicting channel impulse response," ACES Journal, vol. 22, no. 2, July 2007, pp 302-305.

Book Chapters


  1. (with Steve Hunstman and Jimmy Palladino), "Topology for Cyber Applications", in Mathematics in Cyber Research, Paul Goethals, (ed.), Taylor and Francis, 2022. (preprint arXiv:2008.03299)
  2. "Sheaf and duality methods for analyzing multi-model systems," in Novel Methods in Harmonic Analysis Volume II, Pesenson, I., Le Gia, Q.T., Mayeli, A., Mhaskar, H., Zhou, D.-X. (eds.), Springer, 2017. (preprint version is arXiv:1604.04647.)
  3. "A sheaf-theoretic perspective on sampling", in Sampling Theory, a Renaissance, Goetz Pfander (ed.), 2015. (preprint version is arxiv:1405.0324.)
  4. (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. (preprint arXiv:1202.0275

Refereed Archival Conference Proceedings


  1. (with Sourya Dey, Shauna Sweet, Andrew Lauziere, Jonathan Daugherty, and Caitlin Burgess), "Analyzing Large Language Model Behavior via Embedding Analysis." in AHFE 2024: Accelerating Open Access Science in Human Factors Engineering and Human-Centered Computing, December 2024.
  2. (with Tate Altman, Denley Lam, Letitia W. Li), "Unsupervised clustering of file dialects according to monotonic decompositions of mixtures, LangSec 2023, a subconference of IEEE Security and Privacy, May 2023. (preprint arXiv:2304.09082)
  3. (with Letitia W. Li, Cory Anderson, and Steve Huntsman), "Statistical detection of format dialects using the weighted Dowker complex," LangSec 2022, a subconference of IEEE Security and Privacy, May 2022. (organizer version) (preprint arXiv:2201:08267)
  4. (with Michael Rawson), "Instability of Manifold Reach and a Stable Combinatorial Reach." Online International Conference on Computational Harmonic Analysis, 2021. https://ps-mathematik.univie.ac.at/e/talks/Rawson_2021-06_Online_ICCHA_2021_Rawson%20(1).pdf.
  5. "Looking for non-compliant documents using error messages from multiple parsers." LangSec 2021, a subconference of IEEE Security & Privacy, May 28, 2021. (organizer version) (preprint arXiv:2012.10211)
  6. (with Robert Green, Robert Cardona, Jacob Cleveland, Joseph Ozbolt, Alan Hylton, and Robert Short), "Dude where's my stars: a novel topologically justified approach to star tracking", 2021 IEEE Aerospace Conference, NASA Technical Report 20205008929, March 2021.
  7. (with Steve Huntsman) "The geometry of syntax and semantics for directed file transformations," LangSec 2020, a subconference of IEEE Security & Privacy, May 21, 2020. arXiv:2001.04952 (slides and video)
  8. Michael Robinson, Janelle Henrich, Chris Capraro, Peter Zulch, "Dynamic Sensor Fusion Using Local Topology," 2018 IEEE Aerospace Conference, Big Sky, Montana, March 7, 2018.
  9. Emilie Purvine, Sinan Aksoy, Cliff Joslyn, Kathleen Nowak, Brenda Praggastis, Michael Robinson, "A Topological Approach to Representational Data Models", in Yamamoto S., Mori H. (eds) Human Interface and the Management of Information. Interaction, Visualization, and Analytics. HIMI 2018.
  10. 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.
  11. (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.
  12. "Simplicial Complex Sampling in Inference using Exact Sequences." Data Algorithms and Problems on Graphs (DAPG), Columbia University. September 28, 2015.
  13. "Universal factorizations of quasiperiodic functions," Sampling Theory and Applications, Washington, DC, 2015. (preprint version is arXiv:1501.06190)
  14. "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.)
  15. (with Cliff Joslyn and Emilie Hogan), "Towards a topological framework for integrating semantic information sources," Semantic Technologies for Intelligence, Defense, and Security (STIDS), 2014.
  16. "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)
  17. "The Nyquist theorem for cellular sheaves," Sampling Theory and Applications 2013, Bremen, Germany.
  18. "Polarizing frequency of a fluid plasma antenna element," IEEE Antennas and Propagation Society Symposium, 2004. (preprint)

Software


PySheaf logo
  1. The Python sheaf library pysheaf.
  2. A simple Python library for local simplicial homology and relative simplicial homology: simplicialHomology.

Patents


  1. "System and method for antenna pattern estimation," U.S. Patent No. 10,031,171 granted 24 July 2018. (A continuation of U.S. Patent No. 9,255,953.)
  2. (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.
  3. "System and method for antenna pattern estimation," U.S. Patent No. 9,255,953 granted 9 February 2016.
  4. (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


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