The seminar "Information Flow and Its Applications" that took place in Schloss Dagstuhl in August 2012, has been the latest in a series of meetings concerning information flow that began with the 2008 Clifford Lectures by Samson Abramsky at Tulane University, and continued with two further meetings on informatic phenomena at Tulane, as well as a previous Dagstuhl seminar on "The Semantics of Information" https://www.dagstuhl.de/10232. The seminar "Information Flow and Its Applications" brought together mathematicians, computer scientists, physicists and researchers from related disciplines such as computational biology who are working on problems concerning information and information flow.

The seminar gathered 21 participants in addition to the 3 organizers, in the studious but cosy atmosphere of Schloss Dagstuhl. Armed with slides and chalks, each speaker described in terms as simple as can be, the questions and problems they were trying to solve, which, as the title of the seminar suggests, had all in common the issue of the representation and analysis of information flows.

The hypothesis underlying the organization of the seminar was the following: information flows leave on substrates which transport and transform data along time and space. From the modeling, analysis or simulation of these substrates will emerge unifying techniques or concepts. It is understood that such substrate can be artificial, for instance in the case of an electrical circuit, or natural, as in the complex signaling pathways that govern cellular fate. Moreover, information may be treated by systems in a designed manner, for instance a computer that processes its inputs according to a determined program, or be the result of evolution, like the internet which is a perfect example of a system that carries and processes information in spite of the absence of a pre-existing specification.

Although traditionally information processing is studied by distinct communities, scattered along the Artificial-Natural and Designed-Evolved axes, it is noteworthy that this separation is, to some extent, a historical artifact in the sense that artificial systems may be the fruit of evolution (as the internet) while natural ones may be used in a purely specified manner (as in synthetic biology). It is therefore natural to expect that tools and techniques developed in one field may be also relevant to others.

Another unifying scheme of the seminar was the emphasis on the use of formal languages in the representation of information flows. Indeed once "a real world" computing system, such as the cell or a quantum circuit, is abstracted as a formal programming language, one may then start to apply techniques imported from theoretical computer science. In the study of evolved systems, these techniques may be used to extract a specification of what is being observed, while in the context of systems where a specification is a priori at disposal, one may use these techniques to verify that the way information is processed conforms to the expectation.

Over the 4 days of talks, which gave rise to feedback that went beyond the expectation of the organizers, the participants of the seminar "Information Flow and its Applications" have had the opportunity to listen to talks ranging from Systems Biology to Theoretical Physics, from Quantum Computing to the study of Ecological systems. As organizers, we believe that the original guess that Information Flow should be a topic of its own was largely a good one.