Space–time zero-inflated count models of Harbor seals

Environmental data are spatial, temporal, and often come with many zeros. In this paper, we included space–time random effects in zero-inflated Poisson (ZIP) and ‘hurdle’ models to investigate haulout patterns of harbor seals on glacial ice. The data consisted of counts, for 18 dates on a lattice grid of samples, of harbor seals hauled out on glacial ice in Disenchantment Bay, near Yakutat, Alaska. A hurdle model is similar to a ZIP model except it does not mix zeros from the binary and count processes. Both models can be used for zero-inflated data, and we compared space–time ZIP and hurdle models in a Bayesian hierarchical model. Space–time ZIP and hurdle models were constructed by using spatial conditional autoregressive (CAR) models and temporal first-order autoregressive (AR(1)) models as random effects in ZIP and hurdle regression models. We created maps of smoothed predictions for harbor seal counts based on ice density, other covariates, and spatio-temporal random effects. For both models predictions around the edges appeared to be positively biased. The linex loss function is an asymmetric loss function that penalizes overprediction more than underprediction, and we used it to correct for prediction bias to get the best map for space–time ZIP and hurdle models.

Deterministic Solutions for a Step-growth Polymerization

Chain topology, including branch node, chain link and cross-link dynamics that contribute to the number of elastically active strands and junctions, are calculated using purely deterministic derivations. Solutions are not coupled to population density distributions. An eigenzeit transformation assists in the conversion of expressions derived by chemical reaction principles from time to conversion space, yielding transport phenomena type expressions where the rate of change in the molar concentrations of branch nodes with respect to conversion is expressed as functions of the fraction of reactive sites on precursors and reactants. Analogies are hypothesized to exist in cross-linking space that effectively distribute branch nodes with i reacted moieties between cross-links having j bonds extending to the gel. To obtain solutions, reacted sites on nodes or links with finite chain extensions are examined in terms of stoichiometry associated with covalent bonding. Solutions replicate published results based on Miller and Macosko’s recursive procedure and results obtained from truncated weighted sums of population density distributions as suggested by Flory.