Omer Bobrowski
I am an
Assistant Research Professor in the
Mathematics Department at Duke University.
Contact Information
Office: 222
Physics Building
Phone: (919) 660-2878
Email: olmlelrl@lmlaltlhl.ldlulklel.leldlu
Durham,
NC 27708
Research Interests
Stochastic topology. More specifically - algebraic topology of random fields and complexes.
Statistical theory for topological data analysis (TDA).
Statistical models and applications for TDA.
Probability and stochastic processes.
A Neat (?) Simulation
Move your mouse to change angles, and you can click the following:
z/x - zoom in/out
left/right - change size
up/down - speed
f/g - fluctuations (more/less)
r - start over
p - pause (on/off)
s - show a slice (on/off)
0-9 - take a screenshot
Publications
Topology of Random
Geometric Complexes: A Survey
O. Bobrowski, M. Kahle
Submitted, arXiv:1409.4734, 2014.
PDF
Topological Consistency via Kernel Estimation
O. Bobrowski, S. Mukherjee and J. Taylor
Submitted, arXiv:1407.5272, 2014.
PDF
The Topology of Probability Distributions on Manifolds
O. Bobrowski, and S. Mukherjee
Probability Theory and Related Fields, 2014, DOI:10.1007/s00440-014-0556-x.
PDF
Crackle: The Homology of Noise
R.J. Adler, O. Bobrowski, and S. Weinberger
To appear in Discrete and Computational Geometry (previous version - arXiv:1301:1466), 2014.
PDF
Distance
Functions, Critical Points, and the Topology of Random Cech Complexes
O. Bobrowski, R.J. Adler
To appear in Homology, Homotopy and Applications (previous version - arXiv:1107:4775), 2014.
PDF
Euler
Integration of Gaussian Random Fields and Persistent Homology
O. Bobrowski, M.S. Borman
Journal of Topology and Analysis, 4(1), 2012.
PDF
Persistent
Homology for Random Fields and Complexes
R.J. Adler, O. Bobrowski, M.S.
Borman, E. Subag
and S. Weinberger
Borrowing Strength: Theory Powering Applications, A festschrift for
Lawrence D. Brown. IMS Collections Vol. 6, 2010.
PDF
Bayesian
Filtering in Spiking Neural Networks: Noise, Adaptation and
Multisensory Integration
O. Bobrowski, R. Meir and Y. C. Eldar
Neural Computation 21(5), 2009.
PDF,
online
appendix.
A
Neural Network Implementing Optimal State Estimation Based on Dynamic
Spike Train Decoding
O. Bobrowski, R. Meir, S.
Shoham and
Y. C. Eldar
Neural
Information Processing Systems (NIPS 2007).
PDF
Theses
PhD Thesis: Algebraic Topology of Random
Fields and Complexes
Advisor: Prof. Robert J. Adler
PDF
MSc Thesis: Real Time Spike Train Decoding
by Neural Networks
Advisors: Prof. Ron Meir and Prof. Yonina C. Eldar
Teaching
MATH212
- Multivariate Calculus