Dear all, the DFG Research Unit ADYN invites you to their next online seminar session on Zoom: *Monday, February 3rd, 17:00 CET*. Link: https://rwth.zoom-x.de/j/68837156442?pwd=H4OW7bUYYAMXSPiqvxXuEMuTTmk7VY.1 Meeting-ID: 688 3715 6442 Kenncode: 593098 The following talks will be given: (1) "A New Look on an Old Counter Example of Doeblin Measures" by Noam Berger Steiger (Technical University of Munich) (2) "Noisy Linear Group Testing: Exact Thresholds and Efficient Algorithms" by Olga Scheftelowitsch (TU Dortmund University) Abstracts: (1) We consider an example from 2017 of a Doeblin function that admits two extremal Doeblin measures, and see that's variants thereof provide counter examples to a number of conjectures, in particular we get a non-mixing Doeblin measure, and Doeblin functions that admit Doeblin measures of different entropies. I will start by giving a thorough introduction to the topic of Doeblin functions and measures. Based on an old work with Hoffman and Sidoravicius, and a new work with Conache, Johansson and Öberg. (2) In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability α, independent of all other items. In the (over-)idealized noiseless setting, tests are positive exactly if any of the tested items are defective. We study a more realistic model in which observed test results are subject to noise, i.e., tests can display false positive or false negative results with constant positive probabilities. We determine precise constants c such that cnlogn tests are required to recover the infection status of every individual for both adaptive and non-adaptive group testing: in the former, the selection of groups to test can depend on previously observed test results, whereas it cannot in the latter. Additionally, for both settings, we provide efficient algorithms that identify all defective items with the optimal amount of tests with high probability. Thus, we completely solve the problem of binary noisy group testing in the studied setting. For more information on ADYN and the seminar series, visit our website using the link https://adyn.informatik.rwth-aachen.de/ . Best, Tim