A note on growing binary trees

The class ? of binary search trees is studied. A leaf is a vertex of degree 0; ?_n is the subset of ? consisting of trees with n leaves. We grow trees in ?_n from ?_n ? 1 thereby inducing a probability measure on ?_n. We will show that the expected value of the average leaf distance of t ∈ ?_n is asymptotic to log₂n as n → ∞.     

Quasi-localized representation of electronic band structures in cubic crystals

Tabulated results and formulae are given for the parametrization of electronic band structures in simple cubic, body-centered cubic and face-centred cubic systems. This technique is based on the decoupling transformation and does not involve least squares fitting.A band labelling scheme is introduced which allows the decoupling transformation to be used to define the energy matrix of Wannier states in copper. This approach is used to re-examine the significance of the tight binding approximation for the d-states and to relate Fermi surface parameters directly to calculated band energies.     

On the calculation of charge densities in crystals

A general method is given for determining the spatial charge distribution of a filled electronic band using Bloch state charge distributions determined at very few k points. Formulae are given for several important cases.     

Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.     

Population dynamics with global regulation: the conserved Fisher equation

We introduce and study a conserved version of the Fisher equation. Within a population biology context, this model describes spatially extended populations in which the total number of individuals is fixed due to either biotic or environmental factors. We find a rich spectrum of dynamical phases including a pseudotraveling wave and, in the presence of the Allee effect, a phase transition from a locally constrained high density state to a low density fragmented state.     

Using links between speech perception and speech production to evaluate different acoustic metrics: a preliminary report

This paper examines whether correlations between speech perception and speech production exist, and, if so, whether they might provide a way of evaluating different acoustic metrics. The cues listeners use for many phonemic distinctions are not known, often because many different acoustic cues are highly correlated with one another, making it difficult to distinguish among them. Perception-production correlations may provide a new means of doing so. In the present paper, correlations were examined between acoustic measures taken on listeners' perceptual prototypes for a given speech category and on their average production of members of that category. Significant correlations were found for VOT among stop consonants, and for spectral peaks (but not centroids or skewness) for voiceless fricatives. These results suggest that correlations between speech perception and production may provide a methodology for evaluating different proposed acoustic metrics.