robert ghrist

applied topology

click on the links to download preprints...

all versions are pre-publication drafts with eventual publication citations as listed

the author gratefully acknowledges the support of DARPA, the NSF, the AFOSR, and the ONR; of course, that doesn't mean they endorse what is written. neither does the university of pennsylvania. in fact, i don't think anyone except me and a few coauthors endorse the opinions expressed in these works. and even then, it's not a slam-dunk.

**CHRONOLOGICAL LISTING**

- [2020] R. Ghrist and H. Riess, “Cellular sheaves of lattices and the Tarski Laplacian", preprint.
- [2020] D. Lee and R. Ghrist, “Path signatures on Lie groups", preprint.
- [2020] J. Hansen and R. Ghrist, “Opinion dynamics on discourse sheaves", preprint.
- [2020] H.-R. Yoon and R. Ghrist, “Persistence by Parts: Multiscale Feature Detection by Distributed Persistent Homology", preprint.
- [2020] A. Speranzon, S. Shivkumar, and R. Ghrist, On Sensor Network Localization Exploiting Topological Constraints, to appear,
*Proc. Amer. Control Conf.*[ACC]. - [2019] J. Hansen and R. Ghrist, “Towards a spectral theory of cellular sheaves",
*J. Appl. Comput. Topology*, 3(4), 315-358. DOI:10.1007/s41468-019-00038-7. - [2019] A. Sizemore, J. Phillips-Cremins, R. Ghrist, and D. Bassett, "The importance of the whole: topological data analysis for the network neuroscientist",
*Network Neurosci.*, 3(3), 656-673. - [2018] Y. Baryshnikov and R. Ghrist, “Minimal unimodal decompositions on trees", preprint,
*J. Appl. Comput. Topology,*4(), 199-209. DOI:10.1007/s41468-019-00046-7. - [2018] R. Ghrist, R. Levanger, and H. Mai “Persistent homology and Euler integral transforms",
*J. Appl. Comput. Topology*, 2(1-2), 55-60. - [2017] Y. Baryshnikov and R. Ghrist, “Stokes' Theorem, data, and the polar ice caps",
*Amer. Math. Monthly*125:9, 830-834, 2018. - [2017] R. Ghrist, “Homological Algebra and Data", in
*The Mathematics of Data*, IAS/Park City Mathematics Volume 25, 273-325. - [2016] G. Henselman and R. Ghrist, “Matroid filtrations and computational persistent homology", preprint.
- [2016] C. Giusti, R. Ghrist and D. Bassett, “Two's company, three (or more) is a simplex: algebraic-topological tools for understanding higher-order structure in neural data",
*J. Comput. Neurosci.*41(1), 1-14. - [2015] R. Ghrist and S. Krishnan, “Positive Alexander duality for pursuit and evasion", to appear,
*SIAM J. Appl. Alg. and Geom.* - [2015] S. Bhattachayra and R. Ghrist, “Path homotopy invariants and their application to optimal trajectory planning", to appear,
*Proc. IMA Conf. on Mathematics & Robotics*. - [2014] J. Curry, R. Ghrist, and V. Nanda, “Discrete Morse theory for computing cellular sheaf cohomology"
*Found. of Comput. Math.*, DOI 10.1007/s10208-015-9266-8, June 2015. - [2014] C. Jun, S. Bhattachayra, and R. Ghrist (2014), “Pursuit-evasion games on normal distributions", in
*Proc. IROS*, 2014. - [2014] S. Bhattachayra, R. Ghrist, and V. Kumar, “Persistent homology in Z
_{2}coefficients for robot path planning in uncertain environments",*IEEE Trans. on Robotics*, 31(3), 578 - 590, 2015. - [2013] R. Ghrist, "MOOCs and the Future of Mathematics ", opinion,
*Notices AMS*, Nov. 2013, 1277. - [2013] R. Ghrist and S. Krishnan, "A Topological Max-Flow-Min-Cut Theorem", in
*Proc. Global Sig. Inf. Proc.* - [2012] R. Ghrist, D. Lipsky, J. Derenick, and A. Speranzon, “Topological landmark-based navigation and mapping”, eternal preprint.
- [2012] S. Bhattachayra, R. Ghrist, and V. Kumar, “Multi-robot Coverage and Exploration on Riemannian Manifolds with Boundary”,
*Intl. J. Robotics. Res.*33(1):113-137, 2013. - [2012] Y. Cai and R. Ghrist, “Cyclic network automata and cohomological waves”, in
*Proc. Info. Proc. in Sensor Networks (IPSN) 2014*. - [2012] S. Bhattachayra, D. Lipsky, R. Ghrist, and V. Kumar, “Homology Classes of Cycles in Punctured Euclidean Spaces”, preprint.
- [2012] Y. Baryshnikov, R. Ghrist, and M. Wright, “Hadwiger's Theorem for data,”
*Adv. in Math.*, 245, 573-586, 2013. - [2011] J. Curry, R. Ghrist, and M. Robinson, “Euler calculus and its applications to signals and sensing,”
*Proc. Sympos. Appl. Math.*, AMS, 2012. - [2011] M. Robinson and R. Ghrist, “Topological localization via signals of opportunity,”
*IEEE Trans. Signal Processing*, 60(5), 2362-2373, 2012. - [2011] Y. Baryshnikov and R. Ghrist, “Unimodal Category and Topological Statistics,”
*Proc. NOLTA*, 2011. - [2011] R. Ghrist and M. Robinson, “Euler-Bessel and Euler-Fourier Transforms,”
*Inverse Problems,*27(12), 124006, 2011. - [2011] R. Ghrist and Y. Hiraoka, “Applications of sheaf cohomology and exact sequences to network coding,” in
*Proc. NOLTA*, 2011. - [2011] Y. Baryshnikov, R. Ghrist, and D. Lipsky, “Inversion of Euler integral transforms with applications to sensor data,”
*Inverse Problems*27(12), 124001, 2011. - [2011] P. Dlotko, M. Juda, M. Mrozek, and R. Ghrist, “Distributed computation of coverage in sensor networks by homological methods”,
*Applicable Algebra in Engineering, Communication and Computing,*23 (1-2), 29-58, 2012. - [2011] M. Katsev, A. Yershova, B. Tovar, R. Ghrist, and S. LaValle, “Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot,”
*IEEE Transactions on Robotics*, 27(1). 113-128, 2011. - [2010] R. Ghrist, “Applied Algebraic Topology & Sensor Networks,” a manu-script text. (caveat! file>50megs!)
- [2010] Y. Baryshnikov and R. Ghrist, “Euler integration for definable functions,”
*Proc. National Acad. Sci.*, 107(21), May 25, 9525-9530, 2010. Published version available at journal. - [2010] R. Ghrist, J.B. Van den Berg, R. Vandervorst, and W. Wojcik, “Braid Floer homology,”
*J. Diff. Eqns*, 259(5), 1663-1721, 2015. - [2010] S. Alexander, R. Bishop, and R. Ghrist, "Total curvature and simple pursuit on domains of curvature bounded above,"
*Geom. Dedicata*, 149(1), 275-290, 2010. - [2010] E. Chambers, V. de Silva, J. Erickson, and R. Ghrist, “Rips complexes for planar point sets,"
*Disc. Comput. Geom.*, 44(1), 75-90. - [2010] R. Ghrist, “Configuration spaces, braids, and robotics,”
*Lecture Note Series, Inst. Math. Sci., NUS*, vol. 19, World Scientific, 263-304. - [2009] S. Alexander, R. Bishop, and R. Ghrist, "Capture pursuit games on unbounded domains,"
*Ensiegn. Math.*, 55, 103-125. - [2009] Y. Baryshnikov and R. Ghrist, "Target enumeration via Euler characteristic integrals,"
*SIAM J. Appl. Math.*, 70(3), 825-844. - [2009] R. Ghrist and R. Vandervorst, “Braids and parabolic scalar PDEs,''
*Transactions Amer. Math. Soc.*, 361, 2755-2788. - [2008] R. Ghrist, “Barcodes: The persistent topology of data,''
*Bull. Amer. Math. Soc.*, 45(1) 61-75. Published article available from the AMS. - [2008] R. Ghrist, “Three examples of applied and computational homology,"
*Nieuw Archief voor Wiskunde*5/9(2). - [2008] Y. Baryshnikov and R. Ghrist, “Target enumeration via integration over planar sensor networks,” in
*Proc. Robotics: Science & Systems.*

- [2008] J. Jung and R. Ghrist, “Pareto optimal multi-robot coordination with acceleration constraints,” in
*Proc. Intl. Conf. Robotics & Automation.* - [2007] R. Ghrist, “Winding numbers for networks with weak angular data,” in
*Topology and Robotics*, Contemporary Mathematics, AMS. - [2007] V. de Silva and R. Ghrist, “Homological sensor networks,”
*Notices Amer. Math. Soc.*, 54(1), 10-17. Published article available from the AMS. - [2007] V. de Silva and R. Ghrist, “Coverage in sensor networks via persistent homology,”
*Alg. & Geom. Topology*, 7, 339-–358. - [2007] R. Ghrist, “On the contact geometry and topology of ideal fluids,”
*Handbook of Mathematical Fluid Dynamics*, Vol. IV., 1-38. - [2007] R. Ghrist and V. Peterson, “The geometry and topology of reconfiguration,”
*Adv. Appl. Math.*, 38, 302–323. - [2006] V. de Silva and R. Ghrist, “Coordinate-free coverage in sensor networks with controlled boundaries,”
*Intl. J. Robotics Research*, 25(12), 1205-1222. - [2006] R. Ghrist and S. LaValle, “Nonpositive curvature and Pareto optimal motion planning,”
*SIAM J. Control & Opt.*, 45(5), 1697-1713. - [2006] E. Klavins, R. Ghrist, and D. Lipsky, “The graph grammatical approach to self-organizing robotic systems,”
*IEEE Trans. Automatic Controls*, 51(6), 949-962. - [2006] R. Ghrist and R. Komendarczyk, “Overtwisted energy-minimizing curl eigenfields,”
*Nonlinearity*, 19(1), 41-52. - [2005] R. Ghrist, J. O'Kane, and S. LaValle, “Computing Pareto-optimal coordinations on roadmaps,”
*Intl. J. Robotics Research*, 12(11), 997-1010. - [2005] J. Etnyre and R. Ghrist, “Generic hydrodynamic instability for curl eigenfields,”
*SIAM J. Appl. Dynamical Systems*, 4(2), 377-390. - [2006] R. Ghrist “Braids and differential equations,'' in Proc. International Congress of Mathematicians, vol. III, 1-26.
- [2006] R. Ghrist, D. Lipsky, S. Poduri, and G. Sukhatme, “Node isolation in coordinate-free networks,'' in Proc. Workshop on Algorithmic Foundations of Robotics.

- [2006] S. Alexander, R. Bishop, and R. Ghrist, “Pursuit and evasion on nonconvex domains of arbitrary dimensions,'' in Proc. Robotics: Science & Systems.
- [2005] A. Yershova, B. Tovar, R. Ghrist, and S. LaValle, “Bitbots: Simple robots solving complex tasks,'' in Proc. AAAI.

- [2005] V. de Silva, R. Ghrist, and A. Muhammad, “Blind swarms for coverage in 2-d,'' in Proc. Robotics, Systems and Science.
- [2005] R. Ghrist and A. Muhammad, “Coverage and hole detection in sensor networks via homology,'' in Proc. Information Processing in Sensor Networks.
- [2004] A. Abrams and R. Ghrist, “State complexes for metamorphic robots,”
*Intl. J. Robotics Research*, 23(7,8), 809-824. - [2004] R. Ghrist and E. Kin, “Flowlines transervse to knot and link fibrations,”
*Pacific J. Math.*, 217(1), 61-86. - [2004] R. Ghrist, J. O'Kane, and S. LaValle, “Pareto optimal coordination on roadmaps,'' in
*Proc. Workshop on Algorithmic Foundations of Robotics*, 2004.

- [2004] R. Ghrist, and D. Lipsky, “Grammatical self-assembly for planar tiles,'' in
*Proc. Intl. Conf. on MEMS, Nano, and Smart Systems*.

- [2004] E. Klavins, R. Ghrist, and D. Lipsky, “Graph grammars for self-assembling robot systems,'' in
*Proc. Intl. Conf. on Robotics & Automation*. - [2003] R. Ghrist, J.B.Van den Berg, and R.C. Vandervorst, “Morse theory on braids with applications to Lagrangian systems,”
*Invent. Math.*, 152(2), 369-432. - [2002] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics II: Solid tori,”
*Ergod. Thy. & Dyn. Sys.*, 22(3), 819-833. - [2002] J. Etnyre and R. Ghrist, “Contact topology and Anosov flows,”
*Top. & its Appl.*, 124 (2), 211-219. - [2002] R. Ghrist and D. Koditschek, “Safe cooperative robot dynamics on graphs,”
*SIAM J. Cont. & Opt.*, 40(5), 1556-1575. - [2002] A. Abrams and R. Ghrist, “Finding topology in a factory: configuration space,”
*Amer. Math. Monthly*, 109, 140-150. - [2002] R. Ghrist, “Shape complexes for metamorphic robots,'' in
*Algorithmic Foundations of Robotics*V, J. Boissonnat et al. eds., STAR 7, Springer, 185-201. - [2002] R. Ghrist and R. Komendarczyk, “Topological features of inviscid flows,” in
*Introduction to the Geometry and Topology of Fluid Flows*, NATO-ASI Series II, vol. 47, Kluwer Press, 183-202. - [2001] J. Etnyre and R. Ghrist, “An index for closed orbits in Beltrami fields,”
*Physica D*, 159(3-4), 180-189. - [2001] R. Ghrist, “Steady nonintegrable high-dimensional fluids,”
*Lett. Math. Phys.*, 55(3), 193-204. - [2001] R. Ghrist, “Configuration spaces of graphs and robotics,” in
*Braids, Links, and Mapping Class Groups: the Proceedings of Joan Birman's 70th Birthday*, AMS/IP Studies in Mathematics, vol. 24, 29-40. - [2000] R. Ghrist, J.B.Vandenberg, and R.C. Vandervorst, “Closed characteristics of fourth-order twist systems via braids,”
*C. R. Acad. Sci. Paris Ser. I*, 331, 861- 865. - [2000] J. Etnyre and R. Ghrist,) “Contact topology and hydrodynamics III: knotted orbits,”
*Trans. Amer. Math. Soc.*, 352, 5781-5794. - [2000] R. Ghrist, “Resonant gluing bifurcations,”
*Intl. J. Bifurcation and Chaos*, 10(9), 2141-2160. - [2000] J. Etnyre and R. Ghrist, “Contact topology and hydrodynamics I: Beltrami fields and the Seifert Conjecture,”
*Nonlinearity*13, 441-458. - [2000] R. Ghrist, E. Klavins, and D. Koditschek, “Cyclic regulation of patterns,''
*Proc. Workshop on Algorithmic Foundations of Robotics*, B. Donald, K. Lynch, and D. Rus, eds., 205-220. - [1999] J. Etnyre and R. Ghrist, “Plane field flows,”
*Comment. Math. Helv.*, 74, 507-529. - [1999] J. Etnyre and R. Ghrist, “Construction of tight 3-manifolds via dynamics,”
*Proc. Amer. Math. Soc.*, 127, 3697-3706. - [1999] J. Etnyre and R. Ghrist, “Stratified integrals and unknots in inviscid flows,”
*Cont. Math*., 246,99-112. - [1999] R. Ghrist and D. Koditschek, “Safe Cooperative Robot Dynamics on Graphs,'' in
*Hybrid Systems and AI: Modeling, Analysis and Control of Discrete and Continuous Systems, AAAI*, SS-99-05, 65-70.

- [1998] R. Ghrist and T. Young, “From Morse-Smale to all links,”
*Nonlinearity*, 11, 1111-1125. - [1998] R. Ghrist, “Chaotic knots and wild dynamics”,
*Chaos, Solitons, and Fractals*, 9(4/5), 583-598. - [1997] R. Ghrist, P. Holmes, and M. Sullivan,
*Knots and Links in Three-Dimensional Flows*, Lecture Notes in Mathematics, Volume 1654, Springer-Verlag. - [1997] R. Ghrist, “Accumulations of infinite links,”
*Topology and its Applications*, 81, 171-184. - [1997] R. Ghrist, “Branched 2-manifolds supporting all links,”
*Topology*, 36(2), 423-438. - [1996] R. Ghrist and P. Holmes, “An ODE whose solutions contain all knots,”
*Intl. J. Bifurcation and Chaos*, 6(5), 779-800. - [1995] R. Ghrist, “Flows on S
^{3}supporting all links as orbits,”*Electronic Research Announcements of the AMS*, 1(2), 91-97. - [1994] R. Ghrist and P. Holmes, “Knotting within the gluing bifurcation,'' in
*IUTAM Symposium on Nonlinearity and Chaos in Engineering Dynamics*, J. M. T. Thompson and S. R. Bishop, Ed., John Wiley Press, 299-315. - [1993] R. Ghrist and P. Holmes, “Knots and orbit genealogies in three dimensional flows,'' in
*Bifurcations and Periodic Orbits of Vector Fields*, NATO ASI Series C, Volume 408, Kluwer Academic Publishers, 185-239.