Navigating Power Spectra: Metrics and Challenges

Outline
00:00 - Intro
00:47 - Mind the gap (metric)
03:16 - Moment problems and Nevanlinna interpolation
06:53 - “Everything relates to everything else”
11:27 - Distances between power spectra 
16:08 - Optimal mass transport and Schrödinger bridges
32:25 - Sinkhorn iteration and Wasserstein geometry
37:45 - Color of turbulence
41:38 - Thermodynamics and energy harvesting from heat baths
55:01 - Quantum mechanics
57:55 - Adjustable one-ports
1:07:20 - “Aha moments” and advice to future generations
1:12:20 - Outro

Links
Tryphon’s website: https://georgiou.eng.uci.edu/
Robustness analysis of nonlinear feedback systems: an input-output approach (paper): https://tinyurl.com/4785kxny
A topological approach to Nevanlinna–Pick interpolation (paper): https://tinyurl.com/4vudtz8c
A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint (paper): https://tinyurl.com/39enabuc
The meaning of distances in spectral analysis, IEEE CDC plenary 2007 (slides): https://tinyurl.com/mrytp7j8
Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part I (paper): https://tinyurl.com/2nbm3sa6
Y. Chen - https://tinyurl.com/37frfx67
M. Pavon - https://tinyurl.com/yjhbawhb
Mittag Lefler - https://tinyurl.com/29cjum7j
Stochastic control liasons (paper): https://tinyurl.com/4s8y775b
Sinkhorn iteration: https://tinyurl.com/ym5catr2
Color of turbulence (paper): https://tinyurl.com/5n77bepb
Harvesting energy from a periodic heat bath (paper): https://tinyurl.com/2vadpu93
Principles of lossless adjustable one-ports (paper): https://tinyurl.com/53v23yt4
Inerter: https://tinyurl.com/ya2bkkhw

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Acknowledgments and sponsors
This episode was supported by the National Centre of Competence in Research on «Dependable, ubiquitous automation» and the IFAC Activity fund. The podcast benefits from the help of an incredibly talented and passionate team. Special thanks to L. Seward, E. Cahard, F. Banis, F. Dörfler, J. Lygeros, ETH studio and mirrorlake . Music was composed by A New Element.