Complexity for extended dynamical systems

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same role as the metric entropy for classical dynamical systems. We introduce this notion as an almost sure limit on orbits of the system. Moreover we prove a kind of variational principle for this complexity.Comment: 29 page

Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.springerlink.com/content/1432-0916/

Topological chaos: what may this mean ?

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact that some dynamical properties may be considered more chaotic than others

GA4GH: International policies and standards for data sharing across genomic research and healthcare.

The Global Alliance for Genomics and Health (GA4GH) aims to accelerate biomedical advances by enabling the responsible sharing of clinical and genomic data through both harmonized data aggregation and federated approaches. The decreasing cost of genomic sequencing (along with other genome-wide molecular assays) and increasing evidence of its clinical utility will soon drive the generation of sequence data from tens of millions of humans, with increasing levels of diversity. In this perspective, we present the GA4GH strategies for addressing the major challenges of this data revolution. We describe the GA4GH organization, which is fueled by the development efforts of eight Work Streams and informed by the needs of 24 Driver Projects and other key stakeholders. We present the GA4GH suite of secure, interoperable technical standards and policy frameworks and review the current status of standards, their relevance to key domains of research and clinical care, and future plans of GA4GH. Broad international participation in building, adopting, and deploying GA4GH standards and frameworks will catalyze an unprecedented effort in data sharing that will be critical to advancing genomic medicine and ensuring that all populations can access its benefits