Hierarchical rule generalization is a central aspect of Chiang’s hierarchical decoding model. “Hierarchical substitution” is the process by which generalized rules are used in decoding. We believe that hierarchical substitutions of semantically similar words are more likely to be grammatically well-formed than hierarchical substitutions of arbitrary words. In this paper, we extend the rule gene...

Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending product codes by adding global parities is studied and an upper bound on the minimum distance of such codes is obtained. Codes with one, two and three global par...

Aggregation functions on [0, 1] with annihilator 0 can be seen as a generalized product on [0, 1]. We study the generalized product on the bipolar scale [−1, 1], stressing the axiomatic point of view ( compare also [9]). Based on newly introduced bipolar properties, such as the bipolar increasingness, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product...

Abstract—In graph theory, different types of products of two graphs had been studied, e.g., Cartesian product, Tensor product, Strong product, etc. In this paper we generalize the concept of Cartesian product of graphs.We define 2 Cartesian product and more generally r Cartesian product of two graphs. We study these product mainly for path graphs. We also discuss connectedness of the new graph.

We give some variants of a new construction for caps. As an application of these constructions we obtain a 1216–cap in PG(9, 3) a 6464–cap in PG(11, 3) and several caps in ternary affine spaces of larger dimension, which lead to better asymptotics than the caps constructed by Calderbank and Fishburn [1]. These asymptotic improvements become visible in dimensions as low as 62, whereas the bound ...

Starting with a carefully formulated Dirichlet process (DP) mixture model, we derive a generalized product partition model (GPPM) in which the partition process is predictor-dependent. The GPPM generalizes DP clustering to relax the exchangeability assumption through the incorporation of predictors, resulting in a generalized Pólya urn scheme. In addition, the GPPM can be used for formulating f...

 In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

In this paper, we demonstrate that it is possible to apply collocation to compute vibrational energy levels of a five-atom molecule using an exact kinetic energy operator (with cross terms and coordinate-dependent coefficients). This is made possible by using (1) a pruned basis of products of univariate functions; (2) a Smolyak grid made from nested sequences of grids for each coordinate; (3) a...