Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems

It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states are not generally well-preserved under the type of decoherence typical of experiments involving large clouds of atoms or ions. In particular, symmetric states are rapidly degraded under models of decoherence that act identically but locally on the different members of the ensemble. Using an approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric Hilbert space, we explore potential pitfalls in the design and interpretation of experiments on spin-squeezing and collective atomic phenomena when the properties of the symmetric states are extended to systems where they do not apply.Comment: 13 pages, 7 figure

Efficient feedback controllers for continuous-time quantum error correction

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model

Food-web structure in relation to environmental gradients and predator-prey ratios in tank-bromeliad ecosystems

Little is known of how linkage patterns between species change along environmental gradients. The small, spatially discrete food webs inhabiting tank-bromeliads provide an excellent opportunity to analyse patterns of community diversity and food-web topology (connectance, linkage density, nestedness) in relation to key environmental variables (habitat size, detrital resource, incident radiation) and predators: prey ratios. We sampled 365 bromeliads in a wide range of understorey environments in French Guiana and used gut contents of invertebrates to draw the corresponding 365 connectance webs. At the bromeliad scale, habitat size (water volume) determined the number of species that constitute food-web nodes, the proportion of predators, and food-web topology. The number of species as well as the proportion of predators within bromeliads declined from open to forested habitats, where the volume of water collected by bromeliads was generally lower because of rainfall interception by the canopy. A core group of microorganisms and generalist detritivores remained relatively constant across environments. This suggests that (i) a highly-connected core ensures food-web stability and key ecosystem functions across environments, and (ii) larger deviations in food-web structures can be expected following disturbance if detritivores share traits that determine responses to environmental changes. While linkage density and nestedness were lower in bromeliads in the forest than in open areas, experiments are needed to confirm a trend for lower food-web stability in the understorey of primary forests

Inferring Ecological Processes from Taxonomic, Phylogenetic and Functional Trait β-Diversity

Understanding the influences of dispersal limitation and environmental filtering on the structure of ecological communities is a major challenge in ecology. Insight may be gained by combining phylogenetic, functional and taxonomic data to characterize spatial turnover in community structure (β-diversity). We develop a framework that allows rigorous inference of the strengths of dispersal limitation and environmental filtering by combining these three types of β-diversity. Our framework provides model-generated expectations for patterns of taxonomic, phylogenetic and functional β-diversity across biologically relevant combinations of dispersal limitation and environmental filtering. After developing the framework we compared the model-generated expectations to the commonly used “intuitive” expectation that the variance explained by the environment or by space will, respectively, increase monotonically with the strength of environmental filtering or dispersal limitation. The model-generated expectations strongly departed from these intuitive expectations: the variance explained by the environment or by space was often a unimodal function of the strength of environmental filtering or dispersal limitation, respectively. Therefore, although it is commonly done in the literature, one cannot assume that the strength of an underlying process is a monotonic function of explained variance. To infer the strength of underlying processes, one must instead compare explained variances to model-generated expectations. Our framework provides these expectations. We show that by combining the three types of β-diversity with model-generated expectations our framework is able to provide rigorous inferences of the relative and absolute strengths of dispersal limitation and environmental filtering. Phylogenetic, functional and taxonomic β-diversity can therefore be used simultaneously to infer processes by comparing their empirical patterns to the expectations generated by frameworks similar to the one developed here

Brain mass estimation by head circumference and body mass methods in neonatal glycaemic modelling and control

Introduction: Hyperglycaemia is a common complication of stress and prematurity in extremely low-birth-weight infants. Model-based insulin therapy protocols have the ability to safely improve glycaemic control for this group. Estimating non-insulin-mediated brain glucose uptake by the central nervous system in these models is typically done using population-based body weight models, which may not be ideal. Method: A head circumference-based model that separately treats small-for-gestational-age (SGA) and appropriate-for-gestational-age (AGA) infants is compared to a body weight model in a retrospective analysis of 48 patients with a median birth weight of 750g and median gestational age of 25 weeks. Estimated brain mass, model-based insulin sensitivity (SI) profiles, and projected glycaemic control outcomes are investigated. SGA infants (5) are also analyzed as a separate cohort. Results: Across the entire cohort, estimated brain mass deviated by a median 10% between models, with a per-patient median difference in SI of 3.5%. For the SGA group, brain mass deviation was 42%, and per-patient SI deviation 13.7%. In virtual trials, 87-93% of recommended insulin rates were equal or slightly reduced (δ<0.16mU/h) under the head circumference method, while glycaemic control outcomes showed little change. Conclusion: The results suggest that body weight methods are not as accurate as head circumference methods. Head circumference-based estimates may offer improved modelling accuracy and a small reduction in insulin administration, particularly for SGA infants. © 2014 Elsevier Ireland Ltd