Cartier Crystals have finite global dimension

We show that the category of quasi-coherent Cartier crystals is equivalent to the category of unit Cartier modules on an F-finite noetherian ring R, and that these equivalent categories have finite global dimension, by showing that every quasi-coherent Cartier crystal has a finite injective resolution. The length of the resolution is uniformly bounded by a bound only depending on R. Our result should be viewed as a generalization of a result of Ma showing that the category of unit R[F]-modules over a F-finite regular ring R has finite global dimension dim R + 1.Comment: 11 page

Explaining differences between unaligned table snapshots

We study the problem of explaining differences between two snapshots of the same database table including record insertions, deletions and in particular record updates. Unlike existing alternatives, our solution induces transformation functions and does not require knowledge of the correct alignment between the record sets. This allows profiling snapshots of tables with unspecified or modified primary keys. In such a problem setting, there are always multiple explanations for the differences. Our goal is to find the simplest explanation. We propose to measure the complexity of explanations on the basis of minimum description length in order to formulate the task as an optimization problem. We show that the problem is NP-hard and propose a heuristic search algorithm to solve practical problem instances. We implement a prototype called Affidavit to assess the explanatory qualities of our approach in experiments based on different real-world data sets. We show that it can scale to both a large number of records and attributes and is able to reliably provide correct explanations under practical levels of modifications

uDecide: A protégé plugin for multiattribute decision making

This paper introduces the Protege plugin uDecide. With the help of uDecide it is possible to solve multi-attribute decision making problems encoded in a straight forward extension of standard Description Logics. The formalism allows to specify background knowledge in terms of an ontology, while each attribute is represented as a weighted class expression. On top of such an approach one can compute the best choice (or the best k-choices) taking background knowledge into account in the appropriate way. We show how to implement the approach on top of existing semantic web technologies and demonstrate its benefits with the help of an interesting use case that illustrates how to convert an existing web resource into an expert system with the help of uDecide