Paulo Gonçalves

Inria senior researcher in the project DANTE
A joint team of Inria Rhone-Alpes and ENS Lyon (LIP)

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Signal Processing applied to Networks Description: In this domain, we aim at defining relevant concepts and at formalizing adapted mathematical tools to measure, to analyze and to model the dynamic properties of networks described as dynamic graphs. To this end, I leverage my background on non-stationary signal processing combine with some expertise in network metrology to address the following series of important questions:
  • Measure: What is the pertinent information on networks dynamics? How to disclose and how to chacterize non-stationarity in time-varying networks? What are the effects of time resolution and of space granularity?
  • Analyze: Is there causality bewteen the time changes of a network (e.g. structural organisation, interaction/contacts statistics...) and the properties (stationarity, scale invariance, diffusion) of the process running on top of it? How to generalize spectral graph theory to a sound concept of time-frequency graph representations?
  • Model: What is the appropriate level for modeling the dynamical mechanisms (agent behavior? interactions randomness?) How can we reduce the system complexity? Are the proposed models accurately identifiable? Do perfect simulation algorithms exist?
Time-Frequency Analysis
Time-Scale Analysis
Wavelets and Fractals
Wavelets History
by I. Daubechies
Wavelets and Statistics
Other applications

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