Entropy of Some Models of Sparse Random Graphs With Vertex-Names

Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some model-dependent rate constant c. The mathematical content of this paper is the (often easy) calculation of c for a variety of models, in particular for various standard random graph models adapted to this setting. Our broader purpose is to publicize this particular setting as a natural setting for future theoretical study of data compression for graphs, and (more speculatively) for discussion of unorganized versus organized complexity.Comment: 31 page

Making GATT Dolphin-Safe: Trade and the Environment

The Swedish municipalities have traditionally, as suppliers of gas, electricity and district heating to end-use consumers, been one of the key actors of national energy politics. Yet, although Swedish district heating systems typically are owned by the public, neither electricity nor heat production is always under public control. This has historically imposed limitations on municipal plans for own CHP (Combined Heat and Power) plants and district heating systems. Previous research in the field have established that an organisational division between companies active in either heat or electricity supply was one of the most serious challenges for municipal engagement in energy affairs after WW2. Yet, in many cases municipal energy departments have engaged in joint cooperation projects with process industries and power companies, in order to utilize technical expertise and industrial waste heat for the build-up of the local energy system. Processes of initiating, developing and maintaining such cooperation projects - and the erection of municipal CHP plats - are focused upon here. The purpose of this research project is to describe and analyse the roles played by two municipalities (Helsingborg and Gävle) in the years 1945-1983. The specific research questions were as follows: How were different socio-technical systems for electricity and heat supply introduced and how were different alternatives received within the frames of the municipal organisations? What was the impact of competition between different alternatives on the development of the local energy systems? It shows that strategies for municipal-industrial cooperation are vital for the possibilities of municipal energy companies to come to terms with the organisational gulf between power and heat companies. It is argued that the forming of strategical alliances can illustrate how municipal organisations not always act in autonomous positions. It can rather be the other way round - it is strategies for cooperation and competition that make the municipality a key actor in the local energy system

Financing Georgia's Schools: A Primer

Georgia's nearly 1.5 million students make it the ninth largest state K-12 school system in the United States. Furthermore, Georgia has one of the fastest growing school enrollments in the nation, registering an increase of 12.2 percent between 1996 and 2002. Educating these students requires substantial financial resources. The purpose of this Primer is to explain how education in Georgia is financed and to point out some of the major school financing issues confronting the state. Report No.8

A sensitivity analysis of cross-country growth regressions

A vast amount of literature uses cross-country regressions to find empirical links between policy indicators and long-run average growth rates. The authors study whether the conclusions from existing studies are robust or fragile when small changes in the list of independent variables occur. They find that although"policy"appears to be importantly related to growth, there is no strong independent relationship between growth and almost every existing policy indicator. They also find that very few macroeconomic variables are robustly correlated with cross-country growth rates. They clarify the conditions under which one finds convergence of per capita output levels and confirm the positive correlation between the share of investment in GDP and long-run growth. They conclude that all findings using the share of exports in GDP could be obtained almost identically using the total trade or import share and also that few commonly used fiscal indicators are robustly correlated with growth. Finally, the authors highlight the importance of considering alternative specifications in cross-country growth regressions.Economic Theory&Research,Achieving Shared Growth,Governance Indicators,Inequality,Environmental Economics&Policies