Hidden solitons in the Zabusky-Kruskal experiment: Analysis using the periodic, inverse scattering transform

Recent numerical work on the Zabusky--Kruskal experiment has revealed, amongst other things, the existence of hidden solitons in the wave profile. Here, using Osborne's nonlinear Fourier analysis, which is based on the periodic, inverse scattering transform, the hidden soliton hypothesis is corroborated, and the \emph{exact} number of solitons, their amplitudes and their reference level is computed. Other "less nonlinear" oscillation modes, which are not solitons, are also found to have nontrivial energy contributions over certain ranges of the dispersion parameter. In addition, the reference level is found to be a non-monotone function of the dispersion parameter. Finally, in the case of large dispersion, we show that the one-term nonlinear Fourier series yields a very accurate approximate solution in terms of Jacobian elliptic functions.Comment: 10 pages, 4 figures (9 images); v2: minor revision, version accepted for publication in Math. Comput. Simula

Natural language processing

Beginning with the basic issues of NLP, this chapter aims to chart the major research activities in this area since the last ARIST Chapter in 1996 (Haas, 1996), including: (i) natural language text processing systems - text summarization, information extraction, information retrieval, etc., including domain-specific applications; (ii) natural language interfaces; (iii) NLP in the context of www and digital libraries ; and (iv) evaluation of NLP systems

Machine translation evaluation resources and methods: a survey

We introduce the Machine Translation (MT) evaluation survey that contains both manual and automatic evaluation methods. The traditional human evaluation criteria mainly include the intelligibility, fidelity, fluency, adequacy, comprehension, and informativeness. The advanced human assessments include task-oriented measures, post-editing, segment ranking, and extended criteriea, etc. We classify the automatic evaluation methods into two categories, including lexical similarity scenario and linguistic features application. The lexical similarity methods contain edit distance, precision, recall, F-measure, and word order. The linguistic features can be divided into syntactic features and semantic features respectively. The syntactic features include part of speech tag, phrase types and sentence structures, and the semantic features include named entity, synonyms, textual entailment, paraphrase, semantic roles, and language models. The deep learning models for evaluation are very newly proposed. Subsequently, we also introduce the evaluation methods for MT evaluation including different correlation scores, and the recent quality estimation (QE) tasks for MT. This paper differs from the existing works\cite {GALEprogram2009, EuroMatrixProject2007} from several aspects, by introducing some recent development of MT evaluation measures, the different classifications from manual to automatic evaluation measures, the introduction of recent QE tasks of MT, and the concise construction of the content