Epidemics in networks of spatially correlated three-dimensional root-branching structures

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected- recovered (`SIR`) epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.

Dentin hypersensitivity clinical study comparing LILT and LEDT keeping the same irradiation parameters

Dentin hypersensitivity is a common condition associated with high dental pain. A new LED-based (light emitting diode) light source has been used as an experimental tool in some studies. Purpose: The main objective was to compare these two light sources emitting in the same spectral band (red from 625 to 660 nm) to promote pain relief. Material and methods: A total of 6 sessions were accomplished, being three irradiation sessions and three follow-up sessions. This single-blind study compared a control group (Placebo) and two other groups with different equipments: low laser intensity treatment (LILT) and a light emitting diode system treatment (LEDT). Results: The results showed that there is no statistical difference between LILT and LEDT groups, however, both were better than control group (p=0.01) in terms of treatment efficiency; there is no difference between the second and the third sessions for both treatment, it means that the third session was not necessary; finally, the improvement at the end of the entire research (follow up care of 30 days) was very expressive in comparison to pre-treatment situation for all teeth (p=0.01). Conclusion: LILT and LEDT were equally effective to treat dentine hypersensitivity, a 3rd treatment session was not necessary/two sessions are enough.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.