Drinfeld twists and algebraic bethe ansatz of the supersymmetric model associated with U-q(gl(m vertical bar n))

We construct the Drinfeld twists (or factorizing F-matrices) of the supersymmetric model associated with quantum superalgebra U-q(gl(m vertical bar n)), and obtain the completely symmetric representations of the creation operators of the model in the F-basis provided by the F-matrix. As an application of our general results, we present the explicit expressions of the Bethe vectors in the F-basis for the U-q(gl(2 vertical bar 1))-model (the quantum t-J model).

Species accumulation curves and their applications in parasite ecology

Species accumulation curves (SACs) chart the increase in recovery of new species as a function of some measure of sampling effort. Studies of parasite diversity can benefit from the application of SACs, both as empirical tools to guide sampling efforts and predict richness, and because their properties are informative about community patterns and the structure of parasite diversity. SACs can be used to infer interactivity in parasite infra-communities, to partition species richness into contributions from different spatial scales and different levels of the host hierarchy (individuals, populations and communities) or to identify modes of community assembly (niche versus dispersal). A historical tendency to treat individual hosts as statistically equivalent replicates (quadrats) seemingly satisfies the sample-based subgroup of SACs but care is required in this because of the inequality of hosts as sampling units. Knowledge of the true distribution of parasite richness over multiple host-derived and spatial scales is far from complete but SACs can improve the understanding of diversity patterns in parasite assemblages.

Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.