Towards Bayesian Data Compression

In order to handle large data sets omnipresent in modern science, efficient compression algorithms are necessary. Here, a Bayesian data compression (BDC) algorithm that adapts to the specific measurement situation is derived in the context of signal reconstruction. BDC compresses a data set under conservation of its posterior structure with minimal information loss given the prior knowledge on the signal, the quantity of interest. Its basic form is valid for Gaussian priors and likelihoods. For constant noise standard deviation, basic BDC becomes equivalent to a Bayesian analog of principal component analysis. Using Metric Gaussian Variational Inference, BDC generalizes to non-linear settings. In its current form, BDC requires the storage of effective instrument response functions for the compressed data and corresponding noise encoding the posterior covariance structure. Their memory demand counteract the compression gain. In order to improve this, sparsity of the compressed responses can be obtained by separating the data into patches and compressing them separately. The applicability of BDC is demonstrated by applying it to synthetic data and radio astronomical data. Still the algorithm needs further improvement as the computation time of the compression and subsequent inference exceeds the time of the inference with the original data.Comment: 39 pages, 15 figures, 1 table, for code, see https://gitlab.mpcdf.mpg.de/jharthki/bd

Photoionization in the time and frequency domain

Ultrafast processes in matter, such as the electron emission following light absorption, can now be studied using ultrashort light pulses of attosecond duration ($10^{-18}$s) in the extreme ultraviolet spectral range. The lack of spectral resolution due to the use of short light pulses may raise serious issues in the interpretation of the experimental results and the comparison with detailed theoretical calculations. Here, we determine photoionization time delays in neon atoms over a 40 eV energy range with an interferometric technique combining high temporal and spectral resolution. We spectrally disentangle direct ionization from ionization with shake up, where a second electron is left in an excited state, thus obtaining excellent agreement with theoretical calculations and thereby solving a puzzle raised by seven-year-old measurements. Our experimental approach does not have conceptual limits, allowing us to foresee, with the help of upcoming laser technology, ultra-high resolution time-frequency studies from the visible to the x-ray range.Comment: 5 pages, 4 figure

Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods

We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDFs) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgment. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties than traditional methods

Self-Similar Liquid Lens Coalescence

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on pre-wetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low-viscosity liquid. It is shown that these so-called "liquid lenses" merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structure of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics