Mankind has long been fascinated by emergence in complex systems. With the rapidly
accumulating big data in almost every branch of science, engineering, and society, a golden …

In this paper, we investigate algorithmic randomness on more general spaces than the
Cantor space, namely computable metric spaces. To do this, we first develop a unified …

§ 1. Introduction. For most of its history, mathematics was algorithmic in nature. The
geometric claims in Euclid's Elements fall into two distinct categories:“problems,” which …

We extend the notion of randomness (in the version introduced by Schnorr) to computable
probability spaces and compare it to a dynamical notion of randomness: typicality. Roughly …

We propose the thesis that randomness is unpredictability with respect to an intended theory
and measurement. From this point of view we briefly discuss various forms of randomness …

We exhibit a close correspondence between $ L_1 $-computable functions and Schnorr
tests. Using this correspondence, we prove that a point $ x\in [0, 1]^ d $ is Schnorr random if …

We study the computability of conditional probability, a fundamental notion in probability
theory and Bayesian statistics. In the elementary discrete setting, a ratio of probabilities …

We consider the question of computing invariant measures from an abstract point of view.
We work in a general framework (computable metric spaces, computable measures and …

We investigate the class of computable probability distributions and explore the fundamental
limitations of using this class to describe and compute conditional distributions. In addition to …

We give a domain-theoretic semantics to a statistical programming language, using the plain
old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably …