This work describes a classification of the N-soliton solutions of the Kadomtsev-Petviashvili II equation in terms of chord diagrams of N chords joining pairs of 2N points. The different classes of N-solitons are enumerated by the distribution of crossings of the chords. The generating function of the chord diagrams is expressed as a continued fraction, special cases of which are moment generat...

This study examined the representational nature of configural response learning using a task that required simultaneous keypresses with 2 or 3 fingers, similar to the production of chords on the piano. If the benefits of learning are related to the retrieval of individual stimulus-response mappings, performance should depend on the frequencies of the individual responses forming each chord. Alt...

Previous psychological studies have shown that musical chords primed by Western musical scale in a tonal and modal schema are perceived in a hierarchy of stability. We investigated such priming effects on auditory magnetic responses to tonic-major and submediant-minor chords preceded by major scales and tonic-minor and submediant-major chords preceded by minor scales. Musically trained subjects...

Musical expertise is associated with structural and functional changes in the brain that underlie facilitated auditory perception. We investigated whether the phase locking (PL) and amplitude modulations (AM) of neuronal oscillations in response to musical chords are correlated with musical expertise and whether they reflect the prototypicality of chords in Western tonal music. To this aim, we ...

In this paper we analyze the problem of partitioning a continuous curve into n parts with equal successive chords, the curve EquiPartition problem (EP). The goal is to locate n− 1 consecutive curve points, so that the curve can be divided into n segments with equal chords under a distance function. We adopt a level set approach to prove that for any continuous injective curve in a metric space ...

The sphere and circumscribing cylinder engraved on Archimedes’ tombstone commemorate his landmark discovery that their volumes and surface areas are related by the same constant ratio 2/3. He discovered the volume relation and many other geometrical results by mechanical balancing. In particular, he found the volume of a cylindrical wedge by introducing the special balancing shown in Figures 1a...

We investigate the association between musical chords and lyrics by analysing a large dataset of user-contributed guitar tablatures. Motivated by the idea that the emotional content of chords is reflected in the words used in corresponding lyrics, we analyse associations between lyrics and chord categories. We also examine the usage patterns of chords and lyrics in different musical genres, his...

It is currently believed that timbre plays a primary role in the identification of songs from very brief excerpts music. However, its specific contribution, and those other characteristics music, remain unclear. The aim present study was to investigate contributions chord type, voicing, duration participants’ ability identify their opening chords, played on piano alone or one instrument. Ninety...