Shared Information -- New Insights and Problems in Decomposing Information in Complex Systems

How can the information that a set ${X_{1},...,X_{n}}$ of random variables contains about another random variable $S$ be decomposed? To what extent do different subgroups provide the same, i.e. shared or redundant, information, carry unique information or interact for the emergence of synergistic information? Recently Williams and Beer proposed such a decomposition based on natural properties for shared information. While these properties fix the structure of the decomposition, they do not uniquely specify the values of the different terms. Therefore, we investigate additional properties such as strong symmetry and left monotonicity. We find that strong symmetry is incompatible with the properties proposed by Williams and Beer. Although left monotonicity is a very natural property for an information measure it is not fulfilled by any of the proposed measures. We also study a geometric framework for information decompositions and ask whether it is possible to represent shared information by a family of posterior distributions. Finally, we draw connections to the notions of shared knowledge and common knowledge in game theory. While many people believe that independent variables cannot share information, we show that in game theory independent agents can have shared knowledge, but not common knowledge. We conclude that intuition and heuristic arguments do not suffice when arguing about information.Comment: 20 page

Unique Information via Dependency Constraints

The partial information decomposition (PID) is perhaps the leading proposal for resolving information shared between a set of sources and a target into redundant, synergistic, and unique constituents. Unfortunately, the PID framework has been hindered by a lack of a generally agreed-upon, multivariate method of quantifying the constituents. Here, we take a step toward rectifying this by developing a decomposition based on a new method that quantifies unique information. We first develop a broadly applicable method---the dependency decomposition---that delineates how statistical dependencies influence the structure of a joint distribution. The dependency decomposition then allows us to define a measure of the information about a target that can be uniquely attributed to a particular source as the least amount which the source-target statistical dependency can influence the information shared between the sources and the target. The result is the first measure that satisfies the core axioms of the PID framework while not satisfying the Blackwell relation, which depends on a particular interpretation of how the variables are related. This makes a key step forward to a practical PID.Comment: 15 pages, 7 figures, 2 tables, 3 appendices; http://csc.ucdavis.edu/~cmg/compmech/pubs/idep.ht

Secret Sharing and Shared Information

Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret sharing schemes are systems of variables in which it is very clearly specified which subsets have information about the secret. As such, they provide perfect model systems for information decompositions. However, following this intuition too far leads to an information decomposition with negative partial information terms, which are difficult to interpret. One possible explanation is that the partial information lattice proposed by Williams and Beer is incomplete and has to be extended to incorporate terms corresponding to higher order redundancy. These results put bounds on information decompositions that follow the partial information framework, and they hint at where the partial information lattice needs to be improved.Comment: 9 pages, 1 figure. The material was presented at a Workshop on information decompositions at FIAS, Frankfurt, in 12/2016. The revision includes changes in the definition of combinations of secret sharing schemes. Section 3 and Appendix now discusses in how far existing measures satisfy the proposed properties. The concluding section is considerably revise

Analysis and control of complex collaborative design systems

This paper presents a novel method for modelling the complexity of collaborative design systems based on its analysis and proposes a solution to reducing complexity and improving performance of such systems. The interaction and interfacing properties among many components of a complex design system are analysed from different viewpoints and then a complexity model for collaborative design is established accordingly. In order to simplify complexity and improve performance of collaborative design, a general solution of decomposing a whole system into sub-systems and using unified interface mechanism between them has been proposed. This proposed solution has been tested with a case study. It has been shown that the proposed solution is meaningful and practical

Authority in the Context of Distributed Knowledge

The notion of distributed knowledge is increasingly often invoked in discussions of economic organization. In particular, the claim that authority is inefficient as a means of coordination in the context of distributed knowledge has become widespread. However, very little analysis has been dedicated to the relation between economic organization and distributed knowledge. In this paper, we concentrate on the role of authority as a coordination mechanism under conditions of distributed knowledge, and also briefly discuss other issues of economic organization. We clarify the meanings of authority and distributed knowledge, and criticize the above claim by arguing that authority may be a superior mechanism of coordination under distributed knowledge. We also discuss how distributed knowledge influences the boundaries of firms. Our arguments rely on insights in problem-solving and on ideas from organizational economics.Distributed knowledge, existence of authority, problem-solving, the boundaries of the firm

Modularity in action.GNU/Linux and free/Open source sotfware development model unleashed.

Organizational and managerial theories of modularity applied to the design and production of complex artifacts are used to interpret the rise and success of Free/Open Source Software methodologies and practices in software engineeringmodularity; software project management; free/open source software; division of labor; coordination; information hiding