Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

Quantum computation as geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

Reference values for whole body and cerebral multi-frequency bio-impedance data in neonates less than 12 h postpartum

Multiple frequency bio-electrical impedance analysis (MFBIA) may be useful for monitoring fluid balance in newborn infants or to provide early prediction of the outcome following perinatal asphyxia. A reference range of data is needed for identification of babies with abnormal impedance values. This was a cross-sectional observational study in 84 term and near-term healthy neonates less than 12 h postpartum. Whole body and cerebral MFBIA measurements were performed at the bedside in the post-natal ward. Gestational age, post-natal age, gender, birthweight, head circumference and foot length measures were recorded. Reference values for impedance at the characteristic frequency (Z(C)) and resistance at zero frequency (R-0) are reported for whole body and cerebral impedance. Significant correlations (p < 0.05) were observed between whole body impedance and birthweight, footlength and head circumference. Females had a significantly higher whole body R0 than males. Cerebral impedance did not correlate significantly with any of the demographic measures and therewere no gender differences observed for cerebral impedance. The reference range for whole body multi-frequency bio-impedance values in term and near-term infants within the first 12 h postpartum can be calculated from the footlength (FL) using the following equations: Z(C) = (942.9 - 4.818* FL) +/- 124.6 Omega; R-0 = (1042 - 4.520(*)FL) +/- 135.5 Omega. For cerebral impedance the reference range is 29.5-48.7 Omega for Z(C) and 33.7-58.0 Omega for R-0.

Tree species diversity and ecosystem function: Can tropical multi-species plantations generate greater productivity?

Results from the humid tropics of Australia demonstrate that diverse plantations can achieve greater productivity than monocultures. We found that increases in both the observed species number and the effective species richness were significantly related to increased levels of productivity as measured by stand basal area or mean individual tree basal area. Four of five plantation species were more productive in mixtures with other species than in monocultures, offering on average, a 55% increase in mean tree basal area. A general linear model suggests that species richness had a significant effect on mean individual tree basal area when environmental variables were included in the model. As monoculture plantations are currently the preferred reforestation method throughout the tropics these results suggest that significant productivity and ecological gains could be made if multi-species plantations are more broadly pursued. (c) 2006 Elsevier B.V. All rights reserved.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.

Assessment of epidermal cell viability by near infrared multi-photon microscopy following ballistic delivery of gold micro-particles

The use of gene guns in ballistically delivering DNA vaccine coated gold micro-particles to skin can potentially damage targeted cells, therefore influencing transfection efficiencies. In this paper, we assess cell death in the viable epidermis by non-invasive near infrared two-photon microscopy following micro-particle bombardment of murine skin. We show that the ballistic delivery of micro-particles to the viable epidermis can result in localised cell death. Furthermore, experimental results show the degree of cell death is dependant on the number of micro-particles delivered per unit of tissue surface area. Micro-particles densities of 0.16 +/- 0.27 (mean +/- S.D.), 1.35 +/- 0.285 and 2.72 +/- 0.47 per 1000 mu m(2) resulted in percent deaths of 3.96 +/- 5.22, 45.91 +/- 10.89, 90.52 +/- 12.28, respectively. These results suggest that optimization of transfection by genes administered with gene guns is - among other effects - a compromise of micro-particle payload and cell death. (c) 2005 Elsevier Ltd. All rights reserved.

Teleportation via Multi-Qubit Channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of 2L qubits. In this procedure a protocol is employed whereby L Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the 2(2L)-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects 2L qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.