David Naccache, Ofer Yifrach-Stav
We provide the results of pattern recognition experiments on mathematical expressions. We give a few examples of conjectured results. None of which was thoroughly checked for novelty. We did not attempt to prove all the relations found and focused on their generation.
Marcel Hollenstein, David Naccache, Peter B. Rønne et al.
As humanity struggles to contain the global COVID-19 pandemic, privacy concerns are emerging regarding confinement, tracing and testing. The scientific debate concerning privacy of the COVID-19 tracing efforts has been intense, especially focusing on the choice between centralised and decentralised tracing apps. The privacy concerns regarding COVID-19 testing, however, have not received as much attention even though the privacy at stake is arguably even higher. COVID-19 tests require the collection of samples. Those samples possibly contain viral material but inevitably also human DNA. Patient DNA is not necessary for the test but it is technically impossible to avoid collecting it. The unlawful preservation, or misuse, of such samples at a massive scale may hence disclose patient DNA information with far-reaching privacy consequences. Inspired by the cryptographic concept of "Indistinguishability under Chosen Plaintext Attack", this paper poses the blueprint of novel types of tests allowing to detect viral presence without leaving persisting traces of the patient's DNA. Authors are listed in alphabetical order.
Marc Beunardeau, Éric Brier, Noémie Cartier et al.
As humanity struggles to contain the global Covid-19 infection, prophylactic actions are grandly slowed down by the shortage of testing kits. Governments have taken several measures to work around this shortage: the FDA has become more liberal on the approval of Covid-19 tests in the US. In the UK emergency measures allowed to increase the daily number of locally produced test kits to 100,000. China has recently launched a massive test manufacturing program. However, all those efforts are very insufficient and many poor countries are still under threat. A popular method for reducing the number of tests consists in pooling samples, i.e. mixing patient samples and testing the mixed samples once. If all the samples are negative, pooling succeeds at a unitary cost. However, if a single sample is positive, failure does not indicate which patient is infected. This paper describes how to optimally detect infected patients in pools, i.e. using a minimal number of tests to precisely identify them, given the a priori probabilities that each of the patients is healthy. Those probabilities can be estimated using questionnaires, supervised machine learning or clinical examinations. The resulting algorithms, which can be interpreted as informed divide-and-conquer strategies, are non-intuitive and quite surprising. They are patent-free. Co-authors are listed in alphabetical order.