Omer Bobrowski

I am no longer at Duke. I moved to Technion Israel Institute of Technology.
This is my new website:
http://omer.net.technion.ac.il

 

I am a Visiting Assistant Professor in the Mathematics Department at Duke University.

Contact Information

Office: 222 Physics Building

Phone: (919) 660-2878

Email: olmlelrl@lmlaltlhl.ldlulklel.leldlu

Department of Mathematics

Duke University

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.

Publications

       Maximally Persistent Cycles in Random Geometric Complexes
O. Bobrowski, M. Kahle, and P. Skraba
Submitted, arXiv:1509.04347, 2015.
PDF

       On the Vanishing of Homology in Random Čech Complexes
O. Bobrowski, and S. Weinberger
Submitted, arXiv:1507.06945, 2015.
PDF

       The Topology of Probability Distributions on Manifolds
O. Bobrowski, and S. Mukherjee
Probability Theory and Related Fields 161 (3-4): 651-686, 2015
PDF

       Topology of Random Geometric Complexes: A Survey
O. Bobrowski, M. Kahle
To appear in: Topology in Statistical Inference, the Proceedings of Symposia in Applied Mathematics, arXiv:1409.4734, 2014.
PDF

       Topological Consistency via Kernel Estimation
O. Bobrowski, S. Mukherjee and J. Taylor
To Appear in Bernoulli, arXiv:1407.5272, 2014.
PDF

       Crackle: The Homology of Noise
R.J. Adler, O. Bobrowski, and S. Weinberger
Discrete and Computational Geometry 52 (4): 680-704, 2014
PDF

       Distance Functions, Critical Points, and the Topology of Random Cech Complexes
O. Bobrowski, R.J. Adler
Homology, Homotopy and Applications 16 (2): 311-344, 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

Fall 2015:
MATH/STAT 690 - Topics in Probability
STAT 130 - Probability and Statistics in Engineering


Fall 2014/2013/2013:
MATH 212 - Mutlivariate Calculus

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