Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribution subject to the Stirling approximation; (ii) an explanation for the need to maximize entropy (or minimize cross-entropy) to find the most probable realization; and (iii) new, generalized definitions of entropy and cross-entropy - supersets of the Boltzmann principle - applicable to non-multinomial systems. The combinatorial basis is therefore of much broader scope, with far greater power of application, than the information-theoretic and axiomatic bases. The generalized definitions underpin a new discipline of ``{\it combinatorial information theory}'', for the analysis of probabilistic systems of any type. Jaynes' generic formulation of statistical mechanics for multinomial systems is re-examined in light of the combinatorial approach. (abbreviated abstract)Comment: 45 pp; 1 figure; REVTex; updated version 5 (incremental changes

Addressing the Bard: Learning Ideas

The Scottish Poetry Library has published a new, provocative and exciting anthology of Burns poems, launched in the Year of Homecoming and of Burns’s 250th anniversary. What makes this anthology different is that twelve contemporary poets have been asked to select one of Burns’s poems and to respond to it. The result is an eclectic collection with some unexpected choices and responses that enlighten, challenge and amuse us. All of the response poems provide insight into Burns’s original work and some may have a more direct resonance with modern readers. In addition to the book itself, these supporting resources are being provided on the Learning and Teaching Scotland website. The material has been developed by Liz Niven, poet, writer, and Scots-language educator, and Maureen Farrell, an English teacher and now teacher educator from the University of Glasgow

Distance isn’t dead : An empirical evaluation of food miles-based preference changes

Food miles measure the distance food travels to reach consumers plates. Although substituting local food for imported produce will not necessarily reduce greenhouse gas (GHG) emissions, the food miles movement is an intuitively appealing idea to consumers and supported by import-competing producers. We investigate the economic implications of food miles-induced preference changes in Europe using a global, economy-wide model. We observe large welfare losses for New Zealand and several Sub-Saharan African nations. This suggests that food miles campaigns will increase global inequality without necessarily improving environmental outcomes. We then consider the implications of our results for New Zealand businesses and government agencies. We conclude that there is an ongoing requirement for careful monitoring of offshore consumer trends and that New Zealand firms need to demonstrate their sustainability credentials to avoid suffering negative demand shocks.food miles, non-tariff barriers, trade protection