Simple Deterministic Algorithms for Generating “Good” Musical Rhythms

2016 ◽  
pp. 1-18
Author(s):  
Godfried T. Toussaint
Keyword(s):  
Deterministic Algorithms ◽  
Musical Rhythms

scholarly journals Maximum Likelihood Analysis of Rare Binary Traits Under Different Modes of Inheritance

Genetics ◽  
1996 ◽  
Vol 143 (4) ◽  
pp. 1819-1829 ◽  
Author(s):  
G Thaller ◽  
L Dempfle ◽  
I Hoeschele
Keyword(s):  
Maximum Likelihood ◽  
Mixed Model ◽  
Major Gene ◽  
Likelihood Ratio Statistic ◽  
Information Criterion ◽  
Genetic Models ◽  
Parameter Estimates ◽  
Gene Effects ◽  
Binary Traits ◽  
Deterministic Algorithms

Abstract Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals Gaussian variant of Freivalds’ algorithm for efficient and reliable matrix product verification

2020 ◽  
Vol 26 (4) ◽  
pp. 273-284
Author(s):  
Hao Ji ◽  
Michael Mascagni ◽  
Yaohang Li
Keyword(s):  
False Positive ◽  
Measure Zero ◽  
Matrix Multiplication ◽  
Numerical Linear Algebra ◽  
Floating Point ◽  
Matrix Product ◽  
Computing Environment ◽  
Deterministic Algorithms ◽  
Product Verification ◽  
Point Arithmetic

AbstractIn this article, we consider the general problem of checking the correctness of matrix multiplication. Given three n\times n matrices 𝐴, 𝐵 and 𝐶, the goal is to verify that A\times B=C without carrying out the computationally costly operations of matrix multiplication and comparing the product A\times B with 𝐶, term by term. This is especially important when some or all of these matrices are very large, and when the computing environment is prone to soft errors. Here we extend Freivalds’ algorithm to a Gaussian Variant of Freivalds’ Algorithm (GVFA) by projecting the product A\times B as well as 𝐶 onto a Gaussian random vector and then comparing the resulting vectors. The computational complexity of GVFA is consistent with that of Freivalds’ algorithm, which is O(n^{2}). However, unlike Freivalds’ algorithm, whose probability of a false positive is 2^{-k}, where 𝑘 is the number of iterations, our theoretical analysis shows that, when A\times B\neq C, GVFA produces a false positive on set of inputs of measure zero with exact arithmetic. When we introduce round-off error and floating-point arithmetic into our analysis, we can show that the larger this error, the higher the probability that GVFA avoids false positives. Moreover, by iterating GVFA 𝑘 times, the probability of a false positive decreases as p^{k}, where 𝑝 is a very small value depending on the nature of the fault on the result matrix and the arithmetic system’s floating-point precision. Unlike deterministic algorithms, there do not exist any fault patterns that are completely undetectable with GVFA. Thus GVFA can be used to provide efficient fault tolerance in numerical linear algebra, and it can be efficiently implemented on modern computing architectures. In particular, GVFA can be very efficiently implemented on architectures with hardware support for fused multiply-add operations.

Combining genetic and deterministic algorithms for locating actuators on space structures

1996 ◽  
Vol 33 (3) ◽  
pp. 422-427 ◽  
Author(s):  
Hiroshi Furuya ◽  
Raphael T. Haftka
Keyword(s):  
Space Structures ◽  
Deterministic Algorithms

scholarly journals Rhythm Politics in a Changing Brazil: A Study of the Musical Mobilization of Voters by Bolsonaro and Haddad in the 2018 Election

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Kjetil Klette Bøhler
Keyword(s):  
Political Movements ◽  
Right Wing ◽  
Election Campaigns ◽  
Left Wing ◽  
Political Awareness ◽  
Public Events ◽  
Right Wing Populism ◽  
The Right ◽  
Musical Rhythms

This article investigates the role of music in presidential election campaigns and political movements inspired by theoretical arguments in Henri Lefebvre’s Rhythmanalysis, John Dewey ́s pragmatist rethinking of aesthetics and existing scholarship on the politics of music. Specifically, it explores how musical rhythms and melodies enable new forms of political awareness, participation, and critique in an increasingly polarized Brazil through an ethnomusicological exploration of how left-wing and right-wing movements used music to disseminate politics during the 2018 election that culminated in the presidency of Jair Messias Bolsonaro. Three lessons can be learned. First, in Brazil, music breathes life, energy, and affective engagement into politics—sung arguments and joyful rhythms enrich public events and street demonstrations in complex and dynamic ways. Second, music is used by right-wing and left-wing movements in unique ways. For Bolsonaro supporters and right-wing movements, jingles, produced as part of larger election campaigns, were disseminated through massive sound cars in the heart of São Paulo while demonstrators sang the national anthem and waved Brazilian flags. In contrast, leftist musical politics appears to be more spontaneous and bohemian. Third, music has the ability to both humanize and popularize bolsonarismo movements that threaten human rights and the rights of ethnic minorities, among others, in contemporary Brazil. To contest bolsonarismo, Trumpism, and other forms of extreme right-wing populism, we cannot close our ears and listen only to grooves of resistance and songs of freedom performed by leftists. We must also listen to the music of the right.

scholarly journals Prefrontal High Gamma in ECoG tags periodicity of musical rhythms in perception and imagination

2019 ◽  
Author(s):  
S. A. Herff ◽  
C. Herff ◽  
A. J. Milne ◽  
G. D. Johnson ◽  
J. J. Shih ◽  
...  
Keyword(s):  
Auditory Processing ◽  
Right Hemisphere ◽  
Brain Activity ◽  
Activity Patterns ◽  
Superior Temporal Gyrus ◽  
Gamma Activity ◽  
Rhythm Perception ◽  
High Gamma ◽  
The Right ◽  
Musical Rhythms

AbstractRhythmic auditory stimuli are known to elicit matching activity patterns in neural populations. Furthermore, recent research has established the particular importance of high-gamma brain activity in auditory processing by showing its involvement in auditory phrase segmentation and envelope-tracking. Here, we use electrocorticographic (ECoG) recordings from eight human listeners, to see whether periodicities in high-gamma activity track the periodicities in the envelope of musical rhythms during rhythm perception and imagination. Rhythm imagination was elicited by instructing participants to imagine the rhythm to continue during pauses of several repetitions. To identify electrodes whose periodicities in high-gamma activity track the periodicities in the musical rhythms, we compute the correlation between the autocorrelations (ACC) of both the musical rhythms and the neural signals. A condition in which participants listened to white noise was used to establish a baseline. High-gamma autocorrelations in auditory areas in the superior temporal gyrus and in frontal areas on both hemispheres significantly matched the autocorrelation of the musical rhythms. Overall, numerous significant electrodes are observed on the right hemisphere. Of particular interest is a large cluster of electrodes in the right prefrontal cortex that is active during both rhythm perception and imagination. This indicates conscious processing of the rhythms’ structure as opposed to mere auditory phenomena. The ACC approach clearly highlights that high-gamma activity measured from cortical electrodes tracks both attended and imagined rhythms.

Interactions between auditory and dorsal premotor cortex during synchronization to musical rhythms

NeuroImage ◽  
2006 ◽  
Vol 32 (4) ◽  
pp. 1771-1781 ◽  
Author(s):  
Joyce L. Chen ◽  
Robert J. Zatorre ◽  
Virginia B. Penhune
Keyword(s):  
Premotor Cortex ◽  
Dorsal Premotor Cortex ◽  
Musical Rhythms
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