Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyze and predict the progress of disease spreading in spatially-structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is in uenced only by that of its neighbours. In a recent paper the percolation paradigm has been generalised to incorporate synergistic interactions in host infectivity and susceptibility and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by rst formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently tting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model tting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease control strategies that de ect epidemics from invasive to non-invasive regimes are discussed

Hidden structure in amorphous solids

Recent theoretical studies of amorphous silicon [Y. Pan et al. Phys. Rev. Lett. 100 206403 (2008)] have revealed subtle but significant structural correlations in network topology: the tendency for short (long) bonds to be spatially correlated with other short (long) bonds). These structures were linked to the electronic band tails in the optical gap. In this paper, we further examine these issues for amorphous silicon, and demonstrate that analogous correlations exist in amorphous SiO2, and in the organic molecule, b-carotene. We conclude with a discussion of the origin of the effects and its possible generality

Making Real-World Connections In High School Mathematics: The Effectiveness Of A Professional Development Program In Changing Teachers’ Knowledge, Beliefs, And Practices

The study aimed to assess the impact of a professional development workshop at changing secondary mathematics teachers’ knowledge, beliefs, and practices related to real-world applications of algebra. It also addressed gaps in the research literature related to teacher knowledge of how algebra is used by professionals in non-academic settings and their beliefs about the relevance of algebra to their students’ lives. The observational study employed mixed methods. Principal components analysis was conducted on responses to an online questionnaire. Pre-test vs. post-test comparisons were made for workshop participants. Treatment vs. control comparisons were also made using a nationally representative random sample of secondary mathematics teachers as the control group. Results from the statistical analysis of the quantitative data showed the professional development program had a positive impact on teachers’ knowledge and practice related to real-world connections of algebra. Results from qualitative content analysis of semi-structured interview transcripts with treatment and control teachers revealed that teachers have limited knowledge of how algebra is used in the world outside of school. Further research is needed to better understand teacher knowledge about applications of the mathematics they teach, teacher beliefs about the relevance of their curricula, the impact these have on their instruction