Remark7 We have much flexibility in the choice ofp, such as p = 1/2 or p = 1/n. If j {st+q,st+q+1,,st+2q 1} mod n, then new edges cannot be added because they have been connected. B.3 ProofofTheorem4 We first provide the following three lemmas. As a result, only the nodes in{2mvt+`: r vt+1 ` vt} are idle, i.e., 2vt r nodes are idle. Then, since nand v are coprime, for any0 m1 < m2 < n, mod(m1 vt, n) 6= mod(m2 vt, n).

Data-driven Clinical Decision Support Systems (CDSS) have the potential to improve and standardise care with personalised probabilistic guidance. However, the size of data required necessitates collaborative learning from analogous CDSS's, which are often unsharable or imperfectly interoperable (IIO), meaning their feature sets are not perfectly overlapping. We propose Modular Clinical Decision Support Networks (MoDN) which allow flexible, privacy-preserving learning across IIO datasets, while providing interpretable, continuous predictive feedback to the clinician. MoDN is a novel decision tree composed of feature-specific neural network modules. It creates dynamic personalised representations of patients, and can make multiple predictions of diagnoses, updatable at each step of a consultation. The modular design allows it to compartmentalise training updates to specific features and collaboratively learn between IIO datasets without sharing any data.

This paper studies parallelization schemes for stochastic Vector Quantization algorithms in order to obtain time speed-ups using distributed resources. We show that the most intuitive parallelization scheme does not lead to better performances than the sequential algorithm. Another distributed scheme is therefore introduced which obtains the expected speed-ups. Then, it is improved to fit implementation on distributed architectures where communications are slow and inter-machines synchronization too costly. The schemes are tested with simulated distributed architectures and, for the last one, with Microsoft Windows Azure platform obtaining speed-ups up to 32 Virtual Machines.