On the Spread of Random Interleaver

For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this probability increases but very quickly converges to the value $1-e^{-2} \approx 0.8647$. Subsequently, we determine a lower bound on the probability of an interleaver having spread at least $s$. We show that this lower bound converges to the value $e^{-2(s-2)^{2}}$, as the blocklength increases.Comment: 5 pages, published in Proceedings of IEEE International Symposium on Information Theory 2005, Adelaide, Australi

Assessing the climate impacts of Chinese dietary choices using a telecoupled global food trade and local land use framework

Global emissions trajectories developed to meet the 2⁰C temperature target are likely to rely on the widespread deployment of negative emissions technologies and/or the implementation of substantial terrestrial carbon sinks. Such technologies include afforestation, carbon capture and storage (CCS) and bioenergy with carbon capture and storage (BECCS), but mitigation options for agriculture appear limited. For example, using the Global Calculator tool (http://www.globalcalculator.org/), under a 2⁰C pathway, the ‘forests and other land use’ sector is projected to become a major carbon sink, reaching -15 GtCO2e yr-1 by 2050, compared to fossil emissions of 21 GtCO2e yr-1. At the same time, rates of agricultural emissions remain static at about 6 GtCO2e yr-1, despite increasing demands for crop and livestock production to meet the forecast dietary demands of the growing and increasingly wealthy global population. Emissions in the Global Calculator are sensitive to the assumed global diet, and particularly to the level and type of meat consumption, which in turn drive global land use patterns and agricultural emissions. Here we assess the potential to use a modified down-scaled Global Calculator methodology embedded within the telecoupled global food trade framework, to estimate the agricultural emissions and terrestrial carbon stock impacts in China and Brazil, arising from a plausible range of dietary choices in China. These dietary choices are linked via telecoupling mechanisms to Brazilian crop production (e.g. Brazilian soy for Chinese animal feed provision) and drive land and global market dynamics. ‘Spill-over’ impacts will also be assessed using the EU and Malawi as case studies

Algebraic Shape Invariant Models

Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard $SO(2,1)$ potential algebra for Natanzon type potentials.Comment: 8 pages, 2 figure

The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via specific carrier spaces and group actions. In the SU(2) case connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.Comment: Latex, 17 page

China’s Emergence as a Global Recycling Hub – What Does it Mean for Circular Economy Approaches Elsewhere?

This Evidence Report investigates how China’s rise as a global recycling hub affects other countries’ prospects for moving towards a circular economy. This question has received little, if any, attention in the burgeoning literature on sustainability. There is substantial literature on global resource depletion, on the need to overcome the throwaway economy and on national and local attempts to move towards a circular economy. There is, however, little analysis of how the global trade in recycled materials, which is increasingly dominated by China, affects other countries’ attempts to build a circular economy.UK Department for International Developmen