Computer-aided detection aims to improve breast cancer screening programs by helping radiologists to evaluate digital mammography (DM) exams. DM exams are generated by devices from different vendors, with diverse characteristics between and even within vendors. Physical properties of these devices and postprocessing of the images can greatly influence the resulting mammogram. This results in the fact that a deep learning model trained on data from one vendor cannot readily be applied to data from another vendor. This paper investigates the use of tailored transfer learning methods based on adversarial learning to tackle this problem. We consider a database of DM exams (mostly bilateral and two views) generated by Hologic and Siemens vendors. We analyze two transfer learning settings: 1) unsupervised transfer, where Hologic data with soft lesion annotation at pixel level and Siemens unlabelled data are used to annotate images in the latter data; 2) weak supervised transfer, where exam level labels for images from the Siemens mammograph are available. We propose tailored variants of recent state-of-the-art methods for transfer learning which take into account the class imbalance and incorporate knowledge provided by the annotations at exam level. Results of experiments indicate the beneficial effect of transfer learning in both transfer settings. Notably, at 0.02 false positives per image, we achieve a sensitivity of 0.37, compared to 0.30 of a baseline with no transfer. Results indicate that using exam level annotations gives an additional increase in sensitivity.

We introduce computable actions of computable groups and prove the following versions of effective Birkhoff’s ergodic theorem. Let Γ be a computable amenable group, then there always exists a canonically computable tempered two-sided Følner sequence (F_n)_{n≥ 1} in Γ. For a computable, measure-preserving, ergodic action of Γ on a Cantor space { 0 , 1 } ^ℕ endowed with a computable probability measure μ, it is shown that for every bounded lower semicomputable function f on { 0 , 1 } ^ℕ and for every Martin-Löf random ω∈ { 0 , 1 } ^ℕ the equalitylimn→∞1|Fn|∑g∈Fnf(g⋅ω)=∫fdμholds, where the averages are taken with respect to a canonically computable tempered two-sided Følner sequence (F_n)_{n≥ 1}. We also prove the same identity for all lower semicomputable f’s in the special case when Γ is a computable group of polynomial growth and F_n := B(n) is the Følner sequence of balls around the neutral Γ.

We re-examine the theory of systems with quasi-discrete spectrum initiated in the 1960's by Abramov, Hahn, and Parry. In the first part, we give a simpler proof of the Hahn-Parry theorem stating that each minimal topological system with quasidiscrete spectrum is isomorphic to a certain affine automorphism system on some compact Abelian group. Next, we show that a suitable application of Gelfand's theorem renders Abramov's theorem-the analogue of the Hahn-Parry theorem for measure-preserving systems-a straightforward corollary of the Hahn-Parry result. In the second part, independent of the first, we present a shortened proof of the fact that each factor of a totally ergodic system with quasi-discrete spectrum (a "QDS-system") again has quasi-discrete spectrum and that such systems have zero entropy. Moreover, we obtain a complete algebraic classification of the factors of a QDS-system. In the third part, we apply the results of the second to the (still open) question whether a Markov quasi-factor of a QDS-system is already a factor of it. We show that this is true when the system satisfies some algebraic constraint on the group of quasi-eigenvalues, which is satisfied, e.g., in the case of the skew shift.