Professor Omer Bobrowski

Profile

Omer Bobrowski is a Professor in Mathematical Data Science. His research primarily centres on stochastic topology and its applications in data analysis. His theoretical work studies phase transitions in stochastic topology and the distribution of noise in applied topological tools. On the applied side, he develops statistical methods for topological data analysis (TDA) and explores the use of TDA in fields such as signal processing and natural language processing.

Research

Publications

PREPRINTS:

[31] Weak Universality in Random Persistent Homology and Scale-Invariant Functionals
O. Bobrowski and P. Skraba, arXiv:2406.05553 [ arXiv ]

[30] Functional Limit Theorems for Local Functionals of Dynamic Point Processes
E. Onaran, O. Bobrowski, and R. Adler, arXiv:2310:17775 [ arXiv ]

PUBLISHED PAPERS:

[29] Morse Theory for the k-NN Distance Function
Y. Reani and O. Bobrowski, arXiv:2403:12792 [ Journal ]   [ arXiv ]

[28] Cluster-Persistence for Weighted Graphs
O. Bobrowski and P. Skraba, Entropy 25(12), 1587, 2023 [ Journal ]   [ arXiv ]

[27] A Coupled Alpha Complex
Y. Reani and O. Bobrowski, Journal of Computational Geometry 14(1), 221-256, 2023 [ Journal ]   [ arXiv ]

[26] A Universal Null-Distribution for Topological Data Analysis
O. Bobrowski and P. Skraba, Scientific Reports 13(1), 12274, 2023 [ Journal ]   [ arXiv ]

[25] Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime
E. Onaran, O. Bobrowski, and R. Adler,The Annals of Applied Probability, 33(5), 3958-3986, 2023 [ Journal ]   [ arXiv ]

[24] Cycle Registration in Persistent Homology with Applications in Topological Bootstrap
Y. Reani and O. Bobrowski. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(5), 5579-5593, 2023 [ Journal ]   [ arXiv ]

[23] Poisson Process Approximation Under Stabilization and Palm Coupling
O. Bobrowski, M. Schulte, D. Yogeshwaran, Annales Henri Lebesgue (5), 1489-1534, 2022 [ Journal ]   [ arXiv ]

[22] Homological Connectivity in Random Čech Complexes
O. Bobrowski, Probability Theory and Related Fields 183(3-4), 715-788, 2022 [ Journal ]   [ arXiv ]

[21] Unsupervised Geometric and Topological Approaches for Cross-Lingual Sentence Representation and Comparison
S.H. Meirom and O. Bobrowski, Proceedings of the 7th Workshop on Representation Learning for NLP, 173-183, 2022 [ Journal ]

[20] Alarm Sound Detection Using Topological Signal Processing
T. Fireaizen, S. Ron, and O. Bobrowski, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2022 [ Journal ]

[19] On the Spectrum of Dense Random Geometric Graphs
K. Adhikari, R. Adler, O. Bobrowski, and R. Rosenthal, The Annals of Applied Probability 32(3), 1734-1773, 2022 [ Journal ]   [ arXiv ]

[18] Random Simplicial Complexes: Models and Phenomena (Book Chapter)
O. Bobrowski and D. Krioukov. High-Order Systems, 59-96, 2022 [ Journal ]   [ arXiv ]

[17] Homological Percolation: The Formation of Giant k-Cycles
O. Bobrowski and P. Skraba, International Mathematics Research Notices 2022(8), 6186-6213, 2022 [ Journal ]   [ arXiv ]

[16] Joint Geometric and Topological Analysis of Hierarchical Datasets
L. Aloni, O. Bobrowski, and R. Talmon. Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD), 478-493, 2021 [ Journal ]   [ arXiv ]

[15] Probabilistic Convergence and Stability of Random Mapper Graphs
A. Brown, O. Bobrowski, E. Munch, and B. Wang, Journal of Applied and Computational Topology 5, 99-140, 2021. [ Journal ]   [ arXiv ]

[14] Convergence of Persistence Diagrams for Topological Crackle
T. Owada and O. Bobrowski, Bernoulli 26(3), 2275-2310, 2020 [ Journal ]   [ arXiv ]

[13] Homological Percolation and the Euler Characteristic
O. Bobrowski and P. Skraba, Physical Review E. 101, 032404:1-16, 2020 [ Journal ]   [ arXiv ]

[12] Random Čech Complexes on Riemannian Manifolds
O. Bobrowski and G. Oliveira, Random Structures & Algorithms 54(3), 373-412, 2019  [ Journal ]   [ arXiv ]

[11] Topology of Random Geometric Complexes: A Survey
O. Bobrowski and M. Kahle, Journal of Applied and Computational Topology 1(3-4): 331-364, 2018 [ Journal ]   [ arXiv ]

[10] Maximally Persistent Cycles in Random Geometric Complexes
O. Bobrowski, M. Kahle and P. Skraba, The Annals of Applied Probability 27(4): 2032-2060, 2017 [ Journal ]   [ arXiv ]

[9] On the Vanishing of Homology in Random Čech Complexes
O. Bobrowski and S. Weinberger, Random Structures & Algorithms 51(1): 14-51, 2017 [ Journal ]   [ arXiv ]

[8] Topological Consistency via Kernel Estimation
O. Bobrowski, S.Mukherjee, and J. Taylor, Bernoulli 23 (1): 288-328, 2017 [ Journal ]   [ arXiv ]

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

[6] Crackle: The Homology of Noise
R.J. Adler, O. Bobrowski, and S. Weinberger, Discrete & Computational Geometry 52 (4): 680-704, 2014 [ Journal ]   [ arXiv ]

[5] Distance Functions, Critical Points and the Topology of Random Čech Complexes
O. Bobrowski and R.J. Adler, Homology, Homotopy and Applications 16 (2): 311-344, 2014 [ Journal ]   [ arXiv ]

[4] Euler Integration of Gaussian Random Fields and Persistent Homology
O. Bobrowski and M.S. Borman, Journal of Topology and Analysis 4 (01): 49-70, 2012 [ Journal ]   [ arXiv ]

[3] Persistent Homology for Random Fields and Complexes
R.J. Adler, O. Bobrowski, M.S. Borman, E. Subag, and S. Weinberger, IMS Collections Vol. 6: 124-143, 2010 [ Journal ]   [ arXiv ]

[2] Bayesian Filtering in Spiking Neural Networks: Noise, Adaptation and Multisensory Integration
O. Bobrowski, R. Meir, and Y.C. Eldar, Neural Computation 21 (5): 1277-1320, 2009 [ Journal ]

[1] A Neural Network Implementing Optimal State Estimation Based on Dynamic Spike Train Decoding
O. Bobrowski, R. Meir, S. Shoham, and Y.C. Eldar, Advances in Neural Information Processing Systems (NIPS) 20: 145-152, 2007 [ Journal ]

Grants

Topological Phase Transitions in Stochastic Geometry
Omer Bobrowski
£396,018 EPSRC Engineering and Physical Sciences Research Council (01-04-2024 - 31-03-2027)

Universality in Topological Data Analysis
Omer Bobrowski and Primoz Skraba
£330,778 Leverhulme Trust (01-02-2024 - 31-01-2027)