1. Why were you initially drawn to the study of computation and randomness? 2 1.1. Physical randomness (classical) 2 1.2. Physical randomness (quantum) 2 1.3. Algorithmic randomness 3 1.4. Computer science randomness 3 1.5. Biology 4 2. What have we learned? 4 2.1. Physical randomness (classical) 5 2.2. Physical randomness (quantum) 5 2.3. Algorithmic randomness 5 2.4. Randomness in computer sc...

It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still weaker than Martin-Löf randomness.

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle (which we call the “classical approach”). The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the informat...

Social networks tend to contain some amount of randomness and some amount of non-randomness. The amount of randomness versus non-randomness affects the properties of a social network. In this paper, we theoretically analyze graph randomness and present a framework which provides a series of non-randomness measures at levels of edge, node, and the overall graph. We show that graph nonrandomness ...