Omer Bobrowski

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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)
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)
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)
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)
" 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)