Graph signal processing (GSP) tries to device appropriate tools to process signals supported on graphs by generalizing classical methods from signal processing of time-series and images -- such as smoothing, filtering and interpolation of signals supported on the nodes of a graph. Typically, this involves leveraging the structure of the graph as encoded in the spectral properties of the graph Laplacian. In certain scenarios, such as traffic network analysis, the signals of interest are however naturally defined on the edges of a graph, rather than on the nodes. After a brief recap of the central ideas of GSP, we examine why standard tools from GSP may not be suitable for the analysis of such edge signals.  More specifically, we discuss how the underlying notion of 'signal vs noise' inherited from typically considered variants of the graph Laplacian are not suitable when dealing with edge signals that encode flows.  To overcome this limitation, we devise signal processing tools based on the Hodge-Laplacian and the associated discrete Hodge Theory for simplicial (and cellular) complexes. We discuss applications of these ideas for signal smoothing, semi-supervised and active learning for edge-flows on discrete or discretized spaces. Part of the programme of the research training group UnRAVeL is a series of introductory lectures on the topics of "randomness" and "uncertainty" in UnRAVeL’s research thrusts: Algorithms and complexity, verification, logic and languages, and their application scenarios. The main aim is to

Dear all, this is a reminder for Michael Schaub's talk on Signal processing on graphs and complexes <https://www.unravel.rwth-aachen.de/go/id/tbarp?lidx=1> taking place *today at 16:30* in room 5053.2 and on Zoom. Please find the details below. provide doctoral researchers as well as master students a broad overview of the subjects of UnRAVeL. Science undergoes continuous change and lives from the constant quest for novel and better results, which are presented at conferences and in journals. This year, 10 UnRAVeL professors will present some of their most recent research successes. Everyone interested, in particular doctoral researchers and master students, are invited to attend the UnRAVeL lecture series 2022 and engage in discussions with the researchers. The talks take place on Tuesdays, 16:30–18:00 in room 5053.2 in the ground floor of building E2. All events are hybrid. To join remotely, please use https://rwth.zoom.us/j/96003885007?pwd=aUczMVdVU0ZXVGtQUFpwQnJHQUFhUT09 / Meeting ID: 960 0388 5007 / Passcode: 273710 Please find a list of all scheduled talks on the UnRAVeL website <https://www.unravel.rwth-aachen.de/cms/UnRAVeL/Studium/~pzix/Ringvorlesung-Veranstaltung/?lidx=1> and below: * 19/04/2022 Michael Schaub: Signal processing on graphs and complexes * 26/04/2022 Nils Nießen: Acceptance of Driverless Trains * 03/05/2022 Jürgen Giesl: Improving Automatic Complexity Analysis of Probabilistic and Non-Probabilistic Integer Programs * 10/05/2022 Martin Grohe: Graph Representations Based on Homomorphisms * 17/05/2022 Christina Büsing: A Branch & Bound Algorithm for Robust Binary Optimization with Budget Uncertainty * 24/05/2022 Erika Ábrahám: The Challenge of Compositionality for Stochastic Hybrid Systems * 21/06/2022 Sebastian Trimpe: Uncertainty Bounds for Gaussian Process Regression with Applications to Safe Control and Learning * 28/06/2022 Britta Peis: Stackelberg Network Pricing Games * 05/07/2022 Gerhard Lakemeyer: Tractable Reasoning in First-Order Knowledge Bases We are looking forward to seeing many of you in the UnRAVeL survey lecture "What's New in UnRAVeL?". Best regards, Andreas Klinger, Birgit Willms, and Tim Seppelt Logo