We study the compressibility of enumerations, and its role in the relative Kolmogorov complexity of computably enumerable sets, with respect to density. With respect to a strong and a weak form of compression, we examine the gain: the amount of auxiliary information embedded in the compressed enumeration. Strong compression and weak gainless compression is shown for any computably enumerable set, and a positional game is studied toward understanding strong gainless compression.

We study the problem of identifying a probability distribution for some given randomly sampled data in the limit, in the context of algorithmic learning theory as proposed recently by Vinanyi and Chater. We show that there exists a computable partial learner for the computable probability measures, while by Bienvenu, Monin and Shen it is known that there is no computable learner for the computable probability measures. Our main result is the characterization of the oracles that compute explanatory learners for the computable (continuous) probability measures as the high oracles. This provides an analogue of a well-known result of Adleman and Blum in the context of learning computable probability distributions. We also discuss related learning notions such as behaviorally correct learning and orther variations of explanatory learning, in the context of learning probability distributions from data.

Looks like Apple's Face ID technology isn't really that secure after all. After being previously tricked by a $150 mask, the Cupertino giant's new biometric system that was introduced with iPhone X is once again fooled by a 3D-printed mask even when the "Require Attention" feature is turned on. On Monday, Vietnamese security company Bkav once again proved that Apple's Face ID can easily be tricked when one has the right resources. The company apparently shared a video clip showing an iPhone X getting unlocked by a $200 3D printed mask made of stone powder. Bkav's new video comes 2 weeks after the company made headlines in mid-November for showing that a mask could easily bypass Face ID.