Entropy on Spin Factors

Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher. In this paper we will study the properties of Bregman divergences for convex bodies of rank 2. The two most important convex bodies of rank 2 can be identified with the bit and the qubit. We demonstrate that if a convex body of rank 2 has a Bregman divergence that satisfies sufficiency then the convex body is spectral and if the Bregman divergence is monotone then the convex body has the shape of a ball. A ball can be represented as the state space of a spin factor, which is the most simple type of Jordan algebra. We also study the existence of recovery maps for Bregman divergences on spin factors. In general the convex bodies of rank 2 appear as faces of state spaces of higher rank. Therefore our results give strong restrictions on which convex bodies could be the state space of a physical system with a well-behaved entropy function.Comment: 30 pages, 6 figure

Unintended effects and their detection in genetically modified crops

Generic relationships are abstraction patterns used for structuring information across application domains. They play a central role in information modeling. However, the state of the art of handling generic relationships leaves open a number of problems, like differences in the definition of some generic relationships in various data models and differences in the importance given to some generic relationships, considered as first-class constructs in some models and as special cases of other relationships in other models. To address those problems, we define a list of dimensions to characterize the semantics of generic relationships in a clear and systematic way. The list aims to offer a uniform and comprehensive analysis grid for generic relationships, drawn from a careful analysis of commonalities and differences among the generic relationships discussed in the literature. The usefulness of those dimensions is illustrated by reviewing significant generic relationships, namely, materialization, role, aggregation, grouping, and ownership. Based on those dimensions, a new metamodel for relationships is proposed

An Aggregation Model and its C++ Implementation

Object-oriented conceptual models strive to capture more semantics in order to better represent requirements of real-world applications. Aggregation is a powerful construct for semantic modeling. Intuitively, it relates a composite object to its component objects. This paper presents a new version of aggregation, with a generalized version of cardinality constraints and a new subcategorization of part relationships, with an associated transitivity rule. An implementation in C++ is also presented