Modelling and quantifying the effect of heterogeneity in soil physical conditions on fungal growth

Despite the importance of fungi in soil ecosystem services, a theoretical framework that links soil management strategies with fungal ecology is still lacking. One of the key challenges is to understand how the complex geometrical shape of pores in soil affects fungal spread and species interaction. Progress in this area has long been hampered by a lack of experimental techniques for quantification. In this paper we use X-ray computed tomography to quantify and characterize the pore geometry at microscopic scales (30 μm) that are relevant for fungal spread in soil. We analysed the pore geometry for replicated samples with bulk-densities ranging from 1.2–1.6 g/cm3. The bulk-density of soils significantly affected the total volume, mean pore diameter and connectivity of the pore volume. A previously described fungal growth model comprising a minimal set of physiological processes required to produce a range of phenotypic responses was used to analyse the effect of these geometric descriptors on fungal invasion, and we showed that the degree and rate of fungal invasion was affected mainly by pore volume and pore connectivity. The presented experimental and theoretical framework is a significant first step towards understanding how environmental change and soil management impact on fungal diversity in soils

Generalised dimensions of measures on almost self-affine sets

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees

A multifractal zeta function for cookie cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures

The horizon problem for prevalent surfaces

We investigate the box dimensions of the horizon of a fractal surface defined by a function $f \in C[0,1]^2$. In particular we show that a prevalent surface satisfies the `horizon property', namely that the box dimension of the horizon is one less than that of the surface. Since a prevalent surface has box dimension 3, this does not give us any information about the horizon of surfaces of dimension strictly less than 3. To examine this situation we introduce spaces of functions with surfaces of upper box dimension at most \alpha, for \alpha $\in$ [2,3). In this setting the behaviour of the horizon is more subtle. We construct a prevalent subset of these spaces where the lower box dimension of the horizon lies between the dimension of the surface minus one and 2. We show that in the sense of prevalence these bounds are as tight as possible if the spaces are defined purely in terms of dimension. However, if we work in Lipschitz spaces, the horizon property does indeed hold for prevalent functions. Along the way, we obtain a range of properties of box dimensions of sums of functions

The geometry of fractal percolation

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions: {itemize} the statements work for all directions, not almost all, the statements are true for more general projections, for example radial projections onto a circle, in the case $\dim_H >1$, each projection has not only positive Lebesgue measure but also has nonempty interior. {itemize}Comment: Survey submitted for AFRT2012 conferenc

A DECISION SUPPORT AID FOR BEEF CATTLE INVESTMENT USING EXPERT SYSTEMS

The beef cattle investment decision provides an excellent opportunity to increase the economic efficiency of beef cattle production. The investment questions that face beef cattle producers are of interest to beef cattle producers, educators, and financial institutions involved in lending to beef cattle producing firms. This study develops a decision support aid utilizing expert system technology to assist beef cattle producers in making well-founded investment decisions with respect to the firm's beef cattle herd.Beef cattle investment, Decision support, Export systems, Livestock Production/Industries,