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- Robert J. Adler, Omer Bobrowski, Mathew S. Borman, Eliran Subag, Shmuel Weinberger
- 2010

We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the… (More)

- Omer Bobrowski, Ron Meir, Yonina C. Eldar
- Neural Computation
- 2009

A key requirement facing organisms acting in uncertain dynamic environments is the real-time estimation and prediction of environmental states, based on which effective actions can be selected. While it is becoming evident that organisms employ exact or approximate Bayesian statistical calculations for these purposes, it is far less clear how these putative… (More)

- Omer Bobrowski, Ron Meir, Shy Shoham, Yonina C. Eldar
- NIPS
- 2007

It is becoming increasingly evident that organisms acting in uncertain dynamical environments often employ exact or approximate Bayesian statistical calculations in order to continuously estimate the environmental state, integrate information from multiple sensory modalities, form predictions and choose actions. What is less clear is how these putative… (More)

We study the homology of simplicial complexes built via deter-ministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates the vertices, the homology of these complexes can either become trivial as the number n of vertices grows, or can contain more and more complex structures. The different… (More)

- E. Abramov, I. Slutsky, +497 authors D. Inbar
- 2007

As mentioned in the paper, the full derivation of the filtering equation (2.4) is presented in [1]. The derivation in [1] is more general than the context of the paper, and uses very sophisticated mathematical tools. In this appendix we present a simplified outline of this derivation. We are aware that in our particular case of interest, the same results… (More)

A key requirement facing organisms, or agents in general, acting in uncertain dynamic environments is the real-time estimation and prediction of environmental states, based upon which effective actions can be selected. In this work we show how an agent may use a simple real time neural network, receiving noisy multisensory input signals, to solve these… (More)

- Robert J. Adler, Omer Bobrowski, Shmuel Weinberger
- Discrete & Computational Geometry
- 2014

- Robert J. Adler, Omer Bobrowski, +4 authors Richard Peng
- 2015

[4] Lior Aronshtam and Nathan Linial. The threshold for d-collapsibility in random complexes*.ishing of top homology in random simplicial complexes. [11] Omer Bobrowski and Matthew Kahle. Topology of random geometric complexes: a survey. [12] Omer Bobrowski and Sayan Mukherjee. The topology of probability distributions on manifolds.

" What is the Dimension of the Internet? " The large-scale structure of the Internet (or, rather of the graph of the Autonomous System Nodes) has been attracting a lot of attention by the researchers for decades. One family of attractive models for this graph stipulates that it "looks like" is if sampled from a hyperbolic plane. We discuss possible tests… (More)