The Kučera-Gács theorem [Kuč85, Gác86] is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-Löf random real. If the computation of the first n bits of a sequence requires n + h(n) bits of the random oracle, then h is the redundancy of the computation. Kučera implicitly achieved redundancy n log n while Gács used a more elaborate coding procedure w...

We analyze, by means of Granger causality (GC), the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. While we show that fully conditioned GC (CGC) is not affected by synergy, the pairwise analysis fails to prove synergetic effects. In cases when the number of samples is low, thus making the fully condition...

A redundancy allocation problem (RAP) is a well-known NP-hard problem that involves the selection of elements and redundancy levels to maximize the system reliability under various system-level constraints. In many practical design situations, reliability apportionment is complicated because of the presence of several conflicting objectives that cannot be combined into a single-objective functi...