There is a growing interest in leveraging differential geometry in the machine learning community. Yet, the adoption of the associated geometric computations has been inhibited by the lack of a reference implementation. Such an implementation should typically allow its users: (i) to get intuition on concepts from differential geometry through a hands-on approach, often not provided by traditional textbooks; and (ii) to run geometric machine learning algorithms seamlessly, without delving into the mathematical details. To address this gap, we present the open-source Python package geomstats and introduce hands-on tutorials for differential geometry and geometric machine learning algorithms-Geometric Learning-that rely on it. Code and documentation: github.com/geomstats/geomstats and geomstats.ai.
Verifying behavioral or safety properties of hybrid systems, either at design stage such as state reachability and diagnosability, or on-line such as fault detection and isolation is a challenging task. We are concerned here with abstractions oriented towards hybrid systems diagnosability checking. The verification can be done on the abstraction by classical methods developed for discrete event systems extended with time constraints, which provide a counterexample in case of non-diagnosability. The absence of such a counterexample proves the diagnosability of the original hybrid system. In the presence of a counterexample, the first step is to check if it is not a spurious effect of the abstraction and actually exists for the hybrid system, witnessing thus non-diagnosability. Otherwise, we show how to refine the abstraction, guided by the elimination of the counterexample, and continue the process of looking for another counterexample until either a final result is obtained or we reach an inconclusive verdict. We make use of qualitative modeling and reasoning to compute discrete abstractions. Abstractions as timed automata are particularly studied as they allow one to handle time constraints that can be captured at a qualitative level from the hybrid system.
This article provides an overview of current European Commission effort in term of educational innovation to reduce the gap between research and industry which still is a barrier to the economic development. Entrepreneurial innovation & education driving Europe's digital transformation (EIT Digital for short) is an European-based initiative fostering I&E (innovation and entrepreneurship) by integrating education, research and business at different educational levels. For instance in EIT master programmes, students work together with industries and academics to have a faster go-to-market of research results. Summer schools are part of the master programs; three of them have been organised related to CPS (cyber-physical systems), critical infrastructure and, more recently, Industry 4.0. Past and present events are discussed and the experience from these events is reported. It is further analysed how the general setup of the summer school program is affecting the educational aspects and achievement of the intended learning outcomes.
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