INTRODUCTION The subject of this note is another inductive principle, which can be regarded as a direct generalization of the minimum description length (MDL) and minimum message length (MML) principles. We will describe the work started at the Computer Learning Research Centre (Royal Holloway, University of London) related to this new principle, which we call the complexity approximation principle (CAP). Both MDL and MML principles can be interpreted as Kolmogorov complexity approximation principles (as explained in Rissanen [1, 2] and Wallace and Freeman [3]; see also [4]). It is shown in [5] and [6] that it is possible to generalize Kolmogorov complexity to describe the optimal performance in different `games of prediction'. Using this general notion, called predictive complexity,itis straightforward to extend the MDL and MML principles to our more general CAP. In Section 2 we define predictive complexity, in Section 3 several examples are given and in Section 4

By following the guidelines set in one of our previous papers, in this paper we face the problem of Kolmogorov complexity estimate for binary strings by making use of a Genetic Programming approach. This consists in evolving a population of Lisp programs looking for the "optimal" program that generates a given string. By taking into account several target binary strings belonging to different formal languages, we show the effectiveness of our approach in obtaining an approximation from the above of the Kolmogorov complexity function. Moreover, the adequate choice of "similar" target strings allows our system to show very interesting computational strategies. Experimental results indicate that our tool achieves promising compression rates for binary strings belonging to formal languages. Furthermore, even for more complicated strings our method can work, provided that some degree of loss is accepted. These results constitute a first step in using Kolmogorov complexit...

Activity of the U.S. Government. This material is based upon work funded in whole or in part by the U.S. Government and any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the U.S. Government. Quantitative Models from Qualitative Data: Case Studies in Agent-Based Socio-political Modeling Many socio-economic policy, planning and assessment questions arise because not enough is known about their subjects. While inaccessibility and lack of hard data are the very challenges that may make a computer model invaluable, they are also reasons why many modeling and simulation applications are never undertaken. The authors have found that qualitative agent-based models that are appropriately focused can prove surprisingly rich in quantitative data. Such models, accompanied by a thorough delineation of the applicable scope and context, have provided important insights into otherwise inscrutable systems. Building on early lessons learned in qualitative modeling (Dixon & Reynolds 2003), broader issues of qualitative modeling are explored. Case studies include negotiations, historical research, and leadership succession. 1

Distance function design is a fundamental problem underlying much of data mining. Numerous methods designed to solve a variety of problems ranging from clustering to nearest-neighbor retrieval require some concept of distance with which to compare objects. Approaches can be classified as user-driven methods, in which complex distance functions are induced from user input or other sources of labels and feedback