The progress is right there in the plots — the data speaks for itself.
Proud to have contributed to this journey of making the invisible visible.

For me, this is the most exciting part: watching how improvements in calibration and the growing array translate directly into cleaner, more reliable data.

For the data observed by the EHT in 2021, I had the privilege of leading the data calibration using rPICARD the CASA calibration software developed by Michael Janßen, who co-lead the project together with Paul Tiede.

If you want to find out more take a look at our paper here: www.aanda.org/articles/aa/...

But since the strength with which the effect happens is dependent on the viewing angle, we can use the temporal symmerty to constrain it - in the case of sgr a* we find that it must be quite edge-on. But of course the concept can be used on any other source as well!

We can thus use it for something to search for process that break temporal asymmetry: for instance gravitational lensing when it is combined with doppler boosting: close to a black hole both have to happen, but they happen with different speeds, and thus leave a characteristic break in the timing.

in the astronomy context (there seems to be some useage of this in turbulence theory, which is however a bit different than our context). But other than that this - third order - structure function is also super useful because it ONLY senses the temporal asymmetry.

Skewness tells you how asymmetric your distribution is - thus, if we take the cube instead of the square of the time series pairs we get a quantity that measures thr temporal (a)symmetry. Yeay, but so what ? First, from a purely academic standpoint we were the first to realise this property

But,.... How does this connect to temporal symmerty? Again take a peak at the illustration above: what the structure function measures is the variance of the light curve pairs, and if you remember you statistics 1 - 1, recall the skewness of a distribution.

The illustration above shows the idea. Now the structure function is a just as usefull as the fourier fransform, for instance if you want to look for periods you'd search for dips in the structure function at given time scale: The period corresponds to the time lag where the variances is minimal.

This sounds more difficult than it is, time lags are really just data point pairs in the original time series. To compute the structure function one takes square of the data point pairs and squares them. thus structure function is just SF(dt) = c x sum ( flux_pairs ) squared; where c is a norming.

This is why astronomers very often revert to something called the structure function, which is technically the same as the Fourier transform, but uses "time lags" instead of "frequencies" as conjugate space of the time series.

or one can find "critical timescales" on which the behavior of the source changes (identify by changes in the slope of the Fourier transform). Now technically, taking the fourrier transform of time series requires infinite equally sampled data points, but astronomical data is very finite and gapy.

show periodic behaviour linked to their feeding habits and their common orbit.
One basic tool that is used in the study of time series is the so-called power spectral density, that is the #fourriertransform of the light curve. It is useful because peaks in the fourier transform give away periods,