Message passing and Monte Carlo algorithms: connecting fixed points with metastable states

Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in the Edwards-Anderson model in 2-dimensions these approximations predict a spin glass transition at finite $T$. Here we show that the spin glass solutions of the Cluster Variational Method (CVM) at plaquette level do describe well actual metastable states of the system. Moreover, we prove that these states can be used to predict non trivial statistical quantities, like the distribution of the overlap between two replicas. Our results support the idea that message passing algorithms can be helpful to accelerate Monte Carlo simulations in finite dimensional systems.Comment: 6 pages, 6 figure

On the flexibility of complex systems

Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the system must satisfy a set of random dense linear constraints. By statistical mechanics techniques, we describe the transition between a non-flexible system in which the constraints are not fully satisfied, to a flexible system, in which the constraints can be satisfied in many ways. This phase transition is described in terms of the appearance of zeros modes in the statistical mechanics problem

New Zealand farm structure change and intensification

This report presents information about the numbers of farms in New Zealand. The different sources providing such data report very different figures and trends over time, but they all seem to indicate an overall trend of decrease in total farm numbers over the last decades, which appears to be due mainly to a decrease in the numbers of grazing and fattening farms and in the number of arable farms. The distribution of farms by size range over time shows an increase in the proportion of both the smallest and the largest ones, at the expense of the midsized categories. However, different trends can be observed depending on the farm type. The report then explores the change in livestock numbers over time. Thus, during the last 20 years, the main trends consist in an overall decrease in sheep and beef numbers, while dairy and deer numbers increased. To conclude, the report deals with the question of intensification in New Zealand farming systems. It underlines the increase in numbers of cows per hectare and production per cow in the dairy sector, and the increase in lambing rates and carcase weights in the sheep and beef sector. These changes can be linked to the increasing expenditure in agricultural research and development as well as the increasing use of services such as herd testing. Also reported is the growing use of fertilisers in New Zealand agriculture