Multiple regression techniques for modelling dates of first performances of Shakespeare-era plays

Moscato, Pablo; Craig, Hugh; Egan, Gabriel; Haque, Mohammad Nazmul; Huang, Kevin; Sloan, Julia; Oliveira, Jon Corrales de

doi:10.1016/j.eswa.2022.116903

“…It is based on representing the unknown target function as an analytic continued fraction. The resulting method, called Continued Fraction Regression (cfr), has been demonstrated to have competitive performance on a variety of regression problems 9 , 10 , including in materials science 11 and physics 12 , 13 . In Ref.…”

Section: Analytic Continued Fractions and Symbolic Regression Methodsmentioning

confidence: 99%

“…We refer to Ref. 9 to see how complex functions, like the Gamma Function, can be well approximated using these choices and how they perform on 94 real-world datasets of the Penn Machine Learning Database.…”

Section: Analytic Continued Fractions and Symbolic Regression Methodsmentioning

confidence: 99%

New alternatives to the Lennard-Jones potential

Moscato,

Haque

2024

Sci Rep

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We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to $$r^{-6}$$ r - 6 and to a very simple $$depth=1$$ d e p t h = 1 truncated continued fraction with integer coefficients and depending on $$n^{-r}$$ n - r only, where n is a natural number (with $$n=13$$ n = 13 for Xe, $$n=16$$ n = 16 for Kr, $$n=17$$ n = 17 for Ar, and $$n=27$$ n = 27 for Neon). For Helium (He), the data is well approximated with a function having only one variable $$n^{-r}$$ n - r with $$n=31$$ n = 31 and a truncated continued fraction with $$depth=2$$ d e p t h = 2 (i.e., the third convergent of the expansion). Also, for He, we have found an interesting $$depth=0$$ d e p t h = 0 result, a Dirichlet polynomial of the form $$k_1 \, 6^{-r} + k_2 \, 48^{-r} + k_3 \, 72^{-r}$$ k 1 6 - r + k 2 48 - r + k 3 72 - r (with $$k_1, k_2, k_3$$ k 1 , k 2 , k 3 all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.

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“…We used a method based on multivariate regression using an analytic continued fraction representation of our target function of interest [20][21][22][23][24] . We looked at approximating E(n) as follows:…”

Section: A First Approximation Using Continued Fraction Regressionmentioning

confidence: 99%

Continued fractions and the Thomson Problem

Moscato

¹

,

Haque

²

,

Moscato

³

2022

Preprint

2

0

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We introduce new analytical approximations of the minimum electrostatic energy configuration of n electrons, E(n), when they are constrained to be on the surface of a unit sphere. Using 454 putative optimal configurations we searched for approximations of the form E(n) = (n2/2) e g(n) where g(n) was obtained via a memetic algorithm that searched for truncated analytic continued fractions finally obtaining one with Mean Squared Error equal to 4.5744×10^(-8). Using the Online Encyclopedia of Integer Sequences, we searched over 350,000 sequences and, for small values of n, we identified a strong correlation of the highest residual of our best approximations with the sequence of integers n defined by the condition that n2 +12 is a prime. We also observed an interesting correlation with the behaviour of the smallest angle α(n), measured in radians, subtended by the vectors associated with the nearest pair of electrons in the optimal configuration. When using both √n and α(n) as variables a very simple approximation formula for E(n) was obtained with MSE = 7.9963×10^(-8). When expanded as a power series in infinity, we observe that an unknown constant of an expansion as a function of n-1/2 of E(n) first proposed by Glasser and Every in 1992 as -1.1039, and later refined by Morris, Deaven and Ho as -1.104616 in 1996, may actually be very close to -1-π/30.

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“…Stylometric analysis was also used to identify gender diferences is Shakespeare's characters [Savoy, 2022]. Some previous work was focused on the changes in Shakespeare's style in the temporal domain, using quantitative analysis aiming at the pro ling of stylistic change over time [Brainerd, 1980;Taylor, 1987;Moscato et al, 2022], and identifying dates of compositions by analysis of the style [Forsyth, 1999;Stamou, 2007]. For instance, regression analysis of Shakespeare's style was used to estimate the dates of creation of the plays [Moscato et al, 2022].…”

Section: Introductionmentioning

confidence: 99%

“…Some previous work was focused on the changes in Shakespeare's style in the temporal domain, using quantitative analysis aiming at the pro ling of stylistic change over time [Brainerd, 1980;Taylor, 1987;Moscato et al, 2022], and identifying dates of compositions by analysis of the style [Forsyth, 1999;Stamou, 2007]. For instance, regression analysis of Shakespeare's style was used to estimate the dates of creation of the plays [Moscato et al, 2022]. Multivariate analysis of Shakespeare plays showed quantitatively that the writing style is sensitive to the date of composition, and some exceptions can be explained by multiple authorship [Brainerd, 1980].…”

Section: Introductionmentioning

confidence: 99%

A data science and machine learning approach to continuous analysis of Shakespeare's plays

Swisher

¹

,

Shamir

²

2023

Journal of Data Mining &Amp; Digital Humanities

1

0

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The availability of quantitative text analysis methods has provided new ways of analyzing literature in a manner that was not available in the pre-information era. Here we apply comprehensive machine learning analysis to the work of William Shakespeare. The analysis shows clear changes in the style of writing over time, with the most significant changes in the sentence length, frequency of adjectives and adverbs, and the sentiments expressed in the text. Applying machine learning to make a stylometric prediction of the year of the play shows a Pearson correlation of 0.71 between the actual and predicted year, indicating that Shakespeare's writing style as reflected by the quantitative measurements changed over time. Additionally, it shows that the stylometrics of some of the plays is more similar to plays written either before or after the year they were written. For instance, Romeo and Juliet is dated 1596, but is more similar in stylometrics to plays written by Shakespeare after 1600. The source code for the analysis is available for free download.

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Multiple regression techniques for modelling dates of first performances of Shakespeare-era plays

Cited by 10 publications

References 30 publications

New alternatives to the Lennard-Jones potential

New alternatives to the Lennard-Jones potential

Continued fractions and the Thomson Problem

A data science and machine learning approach to continuous analysis of Shakespeare's plays

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