High-density percolation on the modified Bethe lattice.

High-density percolation is the formation of a system spanning cluster of vertices with at least m occupied neighbors. We discuss high-density percolation on the modified Bethe lattice in terms of the theory of large random graphs with arbitrary degree distributions. Using the formalism of generating functions, we derive expressions for the cluster size distribution, the percolation threshold, the percolation probability, and the mean size of finite clusters. We show that the critical exponents ß=γ=1. Additionally, numerical solutions and simulation results for the percolation probability and mean size of finite clusters are compared for illustration.

Speech and prosody characteristics of adults with mental retardation.

Audio-recorded continuous speech samples from forty 20-50-year-old noninstitutionalized persons with mental retardation were selected from a database of 192 samples. Descriptive data on segmental and suprasegmental characteristics were obtained using close phonetic transcription as input to linguistic analyses software. For this sample of adults with mental retardation, speech and prosody status were not statistically associated with gender or gross level of mental retardation, but were associated with estimated probability of independent living. Speech and prosody analyses and content analyses of transcribers' comments yielded diacritic-level profiles of these speakers' linguistic and paralinguistic behaviors in continuous speech. Additional analyses of the error data tested alternative sources of processing involvement within a four-stage speech production model. A cognitive capacity constraint, which limits the speaker's ability to allocate resources to phonological encoding, is proposed as a sufficient explanation for the obtained pattern of token-to-token inconsistency of articulation. An additional sociolinguistic constraint is hypothesized to account for reduced prosodic and paralinguistic competence in continuous discourse. Both constraints are amenable to intervention programming. Findings fail to support the view that the potential for long-term speech prosody competence in individuals with mental retardation is limited by speech-motor constraints. Discussion includes intervention considerations in the context of current trends in special education.