Preprint server: Robert Ghrist
The author gratefully acknowledges the support of
DARPA and the
National Science
Foundation, specifically:
DARPA -
HR0011-07-1-0002 "SToMP: Sensor Topology & Minimal Planning"
NSF MPSA-MCS "Fundamental Geodesic Problems in Computational Topology"
DARPA - HR0011-05-1-0008 "Topological Tools for Sensors
and Systems"
NSF DMS - 0337713 "PECASE: Topological Methods
in Applied Mathematics"
NSF INT - 0089631 "East
Asia / Pacific: Topological methods in Nonlinear Dynamics"
NSF DMS - 9971629 "Topological
Techniques in Hydrodynamics"
NSF DMS - 9508846 "Knots and Links
in Three-Dimensional Flows"
Research papers: (sorted by
topics)
I.
Sensor networks
II. Geometric and topological
robotics
III. Contact
topology and hydrodynamics
IV. Knots,
links, and braids in dynamical systems
V. Expository papers
click on paper
titles to download a .pdf preprint version...
all papers appearing on this site are non-official, preprint versions, distinct
from the published version
SENSOR NETWORKS
Y. Baryshnikov and R. Ghrist,
Target enumeration via
Euler characteristic integrals I: sensor fields
, (posted 3/07), preprint. This is a revised form of the paper
Target enumeration in sensor networks via
integration with respect to Euler characteristic, (posted 1/07),
which is going to be expanded into two papers. Part 2 is in progress.
V. de Silva and R. Ghrist,
Coordinate-free coverage in sensor
networks with controlled
boundaries via homology,
(posted 8/05, revised, 1/06), Intl. J. Robotics Research. 25(12), 2006,
1205--1222.
V. de Silva and R. Ghrist,
Homological sensor networks,
(posted 11/05), Notices American Mathematical Society, 54(1), 2007,
10--17.
V. de Silva and R. Ghrist,
Coverage in sensor networks via
persistent homology,
(posted 11/05), to
appear, Alg. & Geom. Topology.
R. Ghrist,
Winding numbers for networks with weak angular data
,
(posted 11/06),
to appear in "Topology and Robotics", M. Berger, M. Farber, R. Ghrist, and D.
Koditschek eds., Contemporary Mathematics, AMS, 2007.
R. Ghrist, D. Lipsky, S. Poduri, and G. Sukhatme,
Surrounding nodes in coordinate-free networks, ,
(posted 6/06), Proc. Workshop in Algorithmic Foundations of Robotics,
2006.
V. de Silva, R. Ghrist and A. Muhammad,
Blind swarms for coverage in 2-d,
(posted 1/05), in Proc. Robotics Systems & Science, 2005.
R. Ghrist and A. Muhammad,
Coverage and hole detection in sensor networks via
homology, (posted 1/05), in
Proc. IPSN, 2005.
GEOMETRIC/TOPOLOGICAL
ROBOTICS
R. Ghrist and V. Peterson,
The geometry and topology of reconfiguration,
(posted 5/05), Advances
in Applied Mathematics 38, 2007, 302--323.
S. Alexander, R. Bishop, and R. Ghrist,
Pursuit and evasion in arbitrary dimensions,
(posted 1/06, revised 5/06), Proc. Robotics Systems &
Science.
E. Klavins, R.
Ghrist, and D. Lipsky,
A grammatical approach to self-organizing robotic systems,
(posted 7/05, revised 12/05), IEEE Trans. Aut. Controls,
2006.
R. Ghrist, J. O’Kane,and S.
LaValle,
Computing
Pareto optimal coordinations on roadmaps,
(posted 1/05), Intl. J. Robotics Research, 12(11), 997--1010, 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,
(posted 1/05), in Proc. Robotics Systems & Science, 2005.
R. Ghrist and S.
LaValle,
Nonpositive curvature and
Pareto-optimal coordination of robots,
(posted 9/04, revised 2/06), SIAM J. Control & Optimization,
45(5), 2006, 1697--1713.
E. Klavins, R.
Ghrist, and D. Lipsky,
Graph
grammars for self-assembling robotic systems,
(posted 11/02), in
Proc. Intl. Conf. Robotics
and Automation 2004.
R. Ghrist, J. O’Kane, and S. LaValle,
Pareto-optimal coordination on roadmaps,
(posted 2/04), in Proc. Workshop in Algorithmic Foundations of Robotics 2004.
A. Abrams and R. Ghrist,
State
complexes for metamorphic robot systems,
(posted 4/03, revised 8/03), preprint. Intl. J. of Robotics Research,
23(7,8), 809--824, 2004.
R. Ghrist,
Shape complexes for
metamorphic robot systems,
(posted 7/02, revised 11/02), in
Proc. Workshop in Algorithmic Foundations of Robotics 2002.
R. Ghrist and D. Koditschek,
Safe, cooperative robot
dynamics on graphs
, (posted 2/00), SIAM J. Control & Optimization. 40(5), 1556-1575, 2002.
A. Abrams and R. Ghrist,
Finding topology in a factory:
configuration spaces,
(posted 9/00), American Mathematics Monthly, 109, 140-150, February 2002.
R. Ghrist,
Configuration spaces and
braid groups on graphs in robotics,
(posted, 10/98). In Braids,
Links, and Mapping Class Groups: the Proceedings of Joan Birman's
70th Birthday, AMS/IP Studies in Mathematics volume 24, 29-40, 2001.
R. Ghrist and D. Koditschek,
Safe cooperative robotic motions via dynamics on graphs,
Eighth Intl. Symp. on
Robotic Research, Y. Nakayama, ed., Springer-Verlag,
81-92, 1998.
CONTACT
TOPOLOGY AND HYDRODYNAMICS
R. Ghrist,
On the contact topology and geometry of ideal fluids,
(posted
12/05), To appear in Handbook of Mathematical Fluid Dynamics IV.
R.
Ghrist and R. Komendarczyk,
Overtwisted energy-minimizing curl eigenfields,
(posted 12/04), preprint version.
Nonlinearity, 19(1), 41--52, 2006.
J. Etnyre and R.
Ghrist, Generic hydrodynamic instability for curl
eigenfields,
(posted 6/03), SIAM J. Appl. Dynamical Systems,
22(3), 819--833.
J. Etnyre and R. Ghrist,
An index for closed orbits of Beltrami fields,
(posted 1/01), Physica D 159, 180-189 (2001).
R. Ghrist,
Steady nonintegrable high-dimensional fluids,
(posted
9/00), Lett. Math.
Phys. 55: 193-204, 2001.
R. Ghrist and R. Komendarczyk,
Topological features of inviscid
flows, (updated
7/01), in Geometry
and Topology of Fluids, NATO ASI Series II vol. 47, Kluwer
Press, 183-202, 2002.
J. Etnyre and R. Ghrist,
Contact topology and hydrodynamics III: knotted
flowlines,
(posted 6/99), Transactions of the
Amer. Math. Soc., 352 (2000), 5781-5794.
J. Etnyre and R. Ghrist,
Contact topology and hydrodynamics II: solid
tori,
(posted 7/99, revised 1/01), Ergodic Theory & Dynamical Systems
,22 (2002), no. 3,
819--833.
J. Etnyre and R. Ghrist,
Contact topology and hydrodynamics I: Beltrami fields and
the Seifert Conjecture,
(revised, 2/99), Nonlinearity 13, 441-458, 2000.
J. Etnyre and R. Ghrist,
Contact topology and Anosov flows,
(revised 9/99), in Topology & its Applications 124
(2002), no. 2, 211--219.
J. Etnyre and R. Ghrist,
Tight contact structures via
dyanmics,
(revised 7/98). Proc. Amer. Math. Soc., 127, 3697-3706, 1999.
J. Etnyre and R. Ghrist,
Stratified integrals and unknots in inviscid
flows,
(revised, 4/99), Contemporary Mathematics, 246,
99-112, 1999.
KNOT
THEORY IN DYNAMICAL SYSTEMS
R. Ghrist and R.C. Vandervorst,
Braids and scalar parabolic PDEs,
(posted 4/04). Preprint.
R. Ghrist and E. Kin,
Flowlines transverse to knot and
link fibrations,
(posted 1/03, revised 11/03). Pacific J. Math., 217(1),
61--86.
R. Ghrist, J.B.Vandenberg,
and R.C. Vandervorst,
Morse
theory on spaces of braids with applications to Lagrangian
dynamics,
(posted 5/01, updated 10/02). Invent. Math. 152(no.2), pp. 369--432,
2003.
R. Ghrist and R. Vandervorst,
Braids and parabolic dynamics, (posted
6/02), in Proceedings of New
Directions in Dynamics Systems: Kyoto 2002.
R. Ghrist, J.B.Vandenberg, and R.C.
Vandervorst,
Closed
characteristics of fourth-order twist systems via braids
, (posted 4/00), Comptes Rendues
de l'Academie des Sciences I, 331, 861-865, 2000.
R. Ghrist,
Resonant
gluing bifurcations,
(posted 9/99), Intl. J. Bifurcation and Chaos,
10 (9), 2141-2160, 2000.
J. Etnyre and R. Ghrist,
Gradient flows on plane fields,
(revised 4/99), Commentarii Mathematici
Helvetici, 74, 507-529, 1999.
R. Ghrist and T. Young,
From Morse-Smale to all knots and links, Nonlinearity
(11), 1111-1125, 1998.
R. Ghrist,
Accumulations of
infinite links, Topology and its Applications,
(81), 171-184, 1997.
R. Ghrist, P. Holmes, and M. Sullivan,
Knots
and Links in Three-Dimensional Flows. Springer Lecture Notes in
Mathematics, Volume 1654, Springer-Verlag, Berlin,
1997.
R. Ghrist,
Branched 2-manifolds
supporting all links, Topology,
36(2), 423-438, 1997.
R. Ghrist and P. Holmes,
An ODE
whose solutions contain all knots, Int. J. of Bifurcation and Chaos,
6(5), 779-800, 1996.
R. Ghrist,
Flows on $S^3$ supporting
all links as orbits, Electronic Research Announcements of the AMS,
1(2), 91-97, 1995.
R. Ghrist and P. Holmes,
Knotting
within the gluing bifurcation,
in IUTAM Symposium on Nonlinearilty and Chaos in the Enginnering
Dynamics, J. Thompson and S. Bishop, eds., John Wiley Press, 299-315, 1994.
EXPOSITORY
PAPERS
R. Ghrist,
Barcodes: the persistent topology of data,
(posted 11/06), Amer. Math. Soc. Current Events Bulletin, Jan.
2007.
V. de Silva and R. Ghrist,
Homological sensor networks,
(posted 11/05), Notices Amer. Math. Soc, 54(1), 2007, 10--17.
R. Ghrist,
On the contact topology and geometry of ideal fluids,
(posted
12/05), To appear in Handbook of Mathematical Fluid Dynamics IV.
R. Ghrist,
Braids and differential
equations,
(posted 12/00), Proceedings International Congress
of Mathematicians, 2006.
R. Ghrist and R. Komendarczyk,
Topological features of inviscid
flows, (updated 7/01), Geometry and
Topology of Fluids, NATO ASI Series II vol. 47, Kluwer
Press, 183-202, 2002.
A. Abrams and R. Ghrist,
Finding topology in a factory: configuration
spaces, (posted 9/00), preprint version. The American
Mathematics Monthly, 109, 140-150, February 2002.
R. Ghrist,
Chaotic knots and wild
dynamics, Chaos, Solitons, and Fractals
(9:4/5), 583-598, 1998.
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