We present a class of shake-and-bake algorithms for generating (asymptotically) uniform points on the boundary of full-dimensional bounded polyhedra. We also report results of simulations for some elementary test problems.
Lexical co-occurrence models of semantic memory represent word meaning by vectors in a high-dimensional space. These vectors are derived from word usage, as found in a large corpus of written text. Typically, these models are fully automated, an advantage over models that represent semantics that are based on human judgments (e.g., feature-based models). A common criticism of co-occurrence models is that the representations are not grounded: Concepts exist only relative to each other in the space produced by the model. It has been claimed that feature-based models offer an advantage in this regard. In this article, we take a step toward grounding a cooccurrence model. A feed-forward neural network is trained using back propagation to provide a mapping from co-occurrence vectors to feature norms collected from subjects. We show that this network is able to retrieve the features of a concept from its co-occurrence vector with high accuracy and is able to generalize this ability to produce an appropriate list of features from the co-occurrence vector of a novel concept.
A sample of N units is taken from a population consisting of an unknown number of species. We are interested in estimating the number of species and the prediction function for future sampling. The prediction function is defined as the expected number of new species that will be found if an additional sample of size t N is taken for any positive real number t. In this paper we point out that an estimator suggested by Efron and Thisted lacks some essential properties of the true prediction function, for example, the property of alternating copositivity. As a result it cannot be used for large values of t. We propose an alternative estimator that possesses the essential properties and is easily obtained. We illustrate our estimator with two numerical examples and a simulation study.
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