We quantify the scientific potential for exoplanet imaging with the mid-infrared E-ELT Imager and Spectrograph (METIS) foreseen as one of the instruments of the European Extremely Large Telescope (E-ELT). We focus on two main science cases: (1) the direct detection of known gas giant planets found by radial velocity (RV) searches; and (2) the direct detection of small (1-4 R ⊕ ) planets around the nearest stars. Under the assumptions made in our modelling, in particular on the achievable inner working angle and sensitivity, our analyses reveal that within a reasonable amount of observing time METIS is able to image > 20 already known, RV-detected planets in at least one filter. Many more suitable planets with dynamically determined masses are expected to be found in the coming years with the continuation of RV-surveys and the results from the GAIA astrometry mission. In addition, by extrapolating the statistics for close-in planets found by Kepler, we expect METIS might detect &10 small planets with equilibrium temperatures between 200 and 500 K around the nearest stars. This means that (1) METIS will help constrain atmospheric models for gas giant planets by determining for a sizable sample their luminosity, temperature and orbital inclination; and (2) METIS might be the first instrument to image a nearby (super-) Earth-sized planet with an equilibrium temperature near that expected to enable liquid water on a planet surface.

Scientific investigations in medicine and beyond increasingly require observations to be described by more features than can be simultaneously visualized. Simply reducing the dimensionality by projections destroys essential relationships in the data. Similarly, traditional clustering algorithms introduce data bias that prevents detection of natural structures expected from generic nonlinear processes. We examine how these problems can best be addressed, where in particular we focus on two recent clustering approaches, Phenograph and Hebbian learning clustering, applied to synthetic and natural data examples. Our results reveal that already for very basic questions, minimizing clustering bias is essential, but that results can benefit further from biased post-processing.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

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