High n-gram occurrence probability in baroque, classical and romantic melodies

International Journal of Modern Physics C ◽

10.1142/s0129183121500236 ◽

2020 ◽

pp. 2150023

Author(s):

Alejandro Hernández-Fuentes ◽

M. del Castillo-Mussot ◽

Candelario Hernández-Gómez

Keyword(s):

Occurrence Probability ◽

Simple Method ◽

Random Sequences ◽

Musical Genre ◽

N Gram ◽

Stretched Exponentials

An [Formula: see text]-gram in music is defined as an ordered sequence of [Formula: see text] notes of a melodic sequence [Formula: see text]. [Formula: see text] is calculated as the average of the occurrence probability without self-matches of all [Formula: see text]-grams in [Formula: see text]. Then, [Formula: see text] is compared to the averages Shuff[Formula: see text] and Equip[Formula: see text], calculated from random sequences constructed with the same length and set of symbols in [Formula: see text] either by shuffling a given sequence or by distributing the set of symbols equiprobably. For all [Formula: see text], both [Formula: see text], [Formula: see text], and this differences increases with [Formula: see text] and the number of notes, which proves that notes in musical melodic sequences are chosen and arranged in very repetitive ways, in contrast to random music. For instance, for [Formula: see text] and for all analyzed genres we found that [Formula: see text], while [Formula: see text] and [Formula: see text]. [Formula: see text] of baroque and classical genres are larger than the romantic genre one. [Formula: see text] vs [Formula: see text] is very well fitted to stretched exponentials for all songs. This simple method can be applied to any musical genre and generalized to polyphonic sequences.

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Occurrence Probability of Structured Motifs in Random Sequences

Journal of Computational Biology ◽

10.1089/10665270260518254 ◽

2002 ◽

Vol 9 (6) ◽

pp. 761-773 ◽

Cited By ~ 28

Author(s):

S. Robin ◽

J.-J. Daudin ◽

H. Richard ◽

M.-F. Sagot ◽

S. Schbath

Keyword(s):

Occurrence Probability ◽

Random Sequences ◽

Structured Motifs

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Pitches that Wire Together Fire Together: Scale Degree Associations Across Time Predict Melodic Expectations

10.31234/osf.io/4qjac ◽

2021 ◽

Author(s):

Niels Verosky ◽

Emily Morgan

Keyword(s):

Statistical Learning ◽

Transition Probabilities ◽

Multinomial Logistic Regression ◽

Statistical Information ◽

Learning Processes ◽

Variable Order ◽

Coefficient Estimates ◽

Simple Method ◽

Listener Responses ◽

N Gram

The ongoing generation of expectations is fundamental to listeners’ experience of music, but research into types of statistical information that listeners extract from musical melodies has tended to emphasize transition probabilities and n-grams, with limited consideration given to other types of statistical learning that may be relevant. Temporal associations between scale degrees represent a different type of information present in musical melodies that can be learned from musical corpora using expectation networks, a computationally simple method based on activation and decay. Expectation networks infer the expectation of encountering one scale degree followed in the near (but not necessarily immediate) future by another given scale degree, with previous work suggesting that scale degree associations learned by expectation networks better predict listener ratings of pitch similarity than transition probabilities. The current work outlines how these learned scale degree associations can be combined to predict melodic continuations and tests the resulting predictions on a dataset of listener responses to a musical cloze task previously used to compare two other models of melodic expectation, a variable-order Markov model (IDyOM) and Temperley’s music-theoretically motivated model. Under multinomial logistic regression, all three models explain significant unique variance in human melodic expectations, with coefficient estimates highest for expectation networks. These results suggest that generalized scale degree associations informed by both adjacent and non-adjacent relationships between melodic notes influence listeners’ melodic predictions above and beyond n-gram context, highlighting the need to consider a broader range of statistical learning processes that may underlie listeners’ expectations for upcoming musical events.

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Advanced Statistical Testing of Quantum Random Number Generators

Entropy ◽

10.3390/e20110886 ◽

2018 ◽

Vol 20 (11) ◽

pp. 886 ◽

Cited By ~ 3

Author(s):

Aldo Martínez ◽

Aldo Solis ◽

Rafael Díaz Hernández Rojas ◽

Alfred U'Ren ◽

Jorge Hirsch ◽

...

Keyword(s):

Monte Carlo ◽

Monte Carlo Methods ◽

Random Number ◽

Quantum States ◽

Statistical Testing ◽

Random Numbers ◽

Simple Method ◽

Random Number Generators ◽

Random Sequences ◽

Natural Laws

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered in experimental implementations and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.

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A simple way for producing holographic filters suitable for image improvement

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108271 ◽

1978 ◽

Vol 36 (1) ◽

pp. 226-227

Author(s):

K.-H. Herrmann ◽

E. Reuber ◽

P. Schiske

Keyword(s):

Transfer Functions ◽

Diffraction Order ◽

Lateral Position ◽

Simple Method ◽

Spatial Frequencies ◽

Resolution Electron ◽

Wiener Filters ◽

Image Improvement ◽

Optical Reconstruction ◽

Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

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Rotary Beveling for In Situ Thin-Section Microscopy of Cell Cultures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100099192 ◽

1981 ◽

Vol 39 ◽

pp. 550-551

Author(s):

Dean A. Handley ◽

Jack T. Alexander ◽

Shu Chien

Keyword(s):

Cell Growth ◽

Cell Cultures ◽

Molecular Interactions ◽

Convenient Method ◽

Petri Dish ◽

Simple Method ◽

Thin Section Microscopy ◽

Thin Sectioning ◽

Organic Fluids

In situ preparation of cell cultures for ultrastructural investigations is a convenient method by which fixation, dehydration and embedment are carried out in the culture petri dish. The in situ method offers the advantage of preserving the native orientation of cell-cell interactions, junctional regions and overlapping configurations. In order to section after embedment, the petri dish is usually separated from the polymerized resin by either differential cryo-contraction or solvation in organic fluids. The remaining resin block must be re-embedded before sectioning. Although removal of the petri dish may not disrupt the native cellular geometry, it does sacrifice what is now recognized as an important characteristic of cell growth: cell-substratum molecular interactions. To preserve the topographic cell-substratum relationship, we developed a simple method of tapered rotary beveling to reduce the petri dish thickness to a dimension suitable for direct thin sectioning.

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