The structure of humpback whale (Megaptera novaeangliae) songs was examined using information theory techniques. The song is an ordered sequence of individual sound elements separated by gaps of silence. Song samples were converted into sequences of discrete symbols by both human and automated classifiers. This paper analyzes the song structure in these symbol sequences using information entropy estimators and autocorrelation estimators. Both parametric and nonparametric entropy estimators are applied to the symbol sequences representing the songs. The results provide quantitative evidence consistent with the hierarchical structure proposed for these songs by Payne and McVay [Science 173, 587-597 (1971)]. Specifically, this analysis demonstrates that: (1) There is a strong structural constraint, or syntax, in the generation of the songs, and (2) the structural constraints exhibit periodicities with periods of 6-8 and 180-400 units. This implies that no empirical Markov model is capable of representing the songs' structure. The results are robust to the choice of either human or automated song-to-symbol classifiers. In addition, the entropy estimates indicate that the maximum amount of information that could be communicated by the sequence of sounds made is less than 1 bit per second.
Bottlenose dolphins (tursiops truncatus) produce individually distinctive narrow-band "signature whistles." These whistles may be differentiated by the structure of their frequency contours. An algorithm is presented for extracting frequency contours from whistles and comparing two such contours. This algorithm performs nonuniform time dilation to align the contours and provides a quantitative distance measure between the contours. Two recognition experiments using the algorithm on three dolphin whistles from each of five individuals classified 15 out of 15 single-loop whistles correctly, and 14 out of 15 central loops for multiple-loop whistles correctly.
This paper describes the development of continuous-time and discrete-time signals and systems concept inventory exams for undergraduate electrical engineering curricula. Both exams have twenty-five multiple choice questions to assess students' understanding of core concepts in these courses. The questions require little or no computation, and contain incorrect answers that capture common student misconceptions. The design of both exams is discussed, as are ongoing studies evaluating the exams at four campuses. Preliminary results from administering the continuous-time exam as a pre-test and post-test indicate a normalized gain of 0.24 ± 0.08 for traditional lecture courses, consistent with reported results for the Force Concept Inventory exam in lecture courses for freshman physics. 1
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