Metric on a Statistical Space-Time

We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on such a space-time. This matrix is the metric on that manifold. We apply these ideas to a simple model and show that the Lorentzian metric can be obtained if we assumed that the probability distributions describing space-time fluctuations have complex values. Such complex probability distributions appear in non-Hermitian quantum mechanics.Comment: 7 page

Differential Entropy on Statistical Spaces

We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can only be localized within a certain volume and exhibit thus a feature of fuzziness. This implies that Riemann integrability of relevant integrals is no longer secured. Some discussion on the specialization of this formalism to quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd International Conference on Cybernetics and Information Technologies, Systems and Applications (CITSA 2005) and the 11th International Conference on Information Systems Analysis and Synthesis (ISAS 2005), to be held in Orlando, USA, on July 14-17, 200

Design principles for secure integration of information

The purpose of this paper is to twofold. Firstly, we will show how various conflicts which may arise in a mediated system can be handled by means of annotated constraint logic. Secondly, we will briefly discuss some security related issues in a mediator architecture and possible solutions which can be implemented within our system

Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field must be a quantized dynamical degree of freedom. On the other hand, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus undiscernable. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.Comment: 8 pages, 4 figures. To appear in Proc. Natl. Acad. Sc

Dynamics of the Fisher Information Metric

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric. We postulate that this functional of the dynamical variable $g^{\mu\nu}(\theta^i)$ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.Comment: 11 page

MECHANIZED CULTURAL REASONING AS A TOOL TO ASSESS TRUST IN VIRTUAL ENTERPRISES

International audienceThe globalized knowledge society generates virtual enterprises that are usually set up and managed on the web, and the new trend is to make the relevant technologies avail- able on intelligent portable devices. The existence of trust is a mandatory condition to make such enterprises successful. Trust has many facets ranging from very theoretical ones to fully heuristic features. One point is that trust can arise when one understands better the behavior of partners. In this paper we outline a new technology leading to the possibility to include inter-cultural issues among the factors having a strong impact on trust. This technology is called Abstraction-Based Information Technology. Its goal is to enable to design tools in articial intelligence to perform so-called cultural reasoning that ensures better trust among inter-cultural communities.We outline how Abstraction- Based Information Technology becomes feasible when working with virtual knowledge communities. An argument in favor of our approach is that it relies on a bottom-up ap- proach, particularly suitable for the web technology and for intelligent wearable devices. The solution of intercultural troubles then amounts to solve knowledge con icts among virtual knowledge communities