2005年度大学院文学研究科修士論文・文学部卒業論文題目一覧

<p>(a) Comparison of the exact probability of survival, <i>ρ</i>(<i>L</i>), given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e032" target="_blank">Eq (17)</a>, with the approximations given by the scaling law <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e038" target="_blank">Eq (22)</a> and by the scaling law with the first correction to scaling, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e058" target="_blank">Eq (40)</a>, for different <i>m</i> and <i>L</i>. (b) The same taking the <i>y</i>–axis logarithmic. (c) The same data, taking the ratio between the approximation given by the scaling law [], <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e038" target="_blank">Eq (22)</a>, and the exact value of <i>ρ</i>(<i>L</i>). Larger values of <i>L</i> are included in this case. The program used to draw the figure is provided as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.s001" target="_blank">S1 File</a>.</p

Number of texts with <i>p</i>-value near zero (<i>p</i> < 0.01) in different ranges of <i>L</i> divided by the number of texts in the same ranges, for the fits of distributions <i>f</i>₁ and <i>f</i>₂.

<p>Values of <i>L</i> denote the geometric mean of ranges containing 1000 texts each. The higher value for the fit of <i>f</i>₁ (except for <i>L</i> below about 13000 tokens) denotes its worst performance.</p

Estimated probability density of <i>β</i> for fits with <i>p</i> ≥ 0.05, in different length ranges.

<p>We have divided both groups of accepted texts into 4 percentiles according to <i>L</i>. As in the previous figure, the normal kernel smoothing method is applied. (a) For distribution <i>f</i>₁. (b) For distribution <i>f</i>₂.</p

Histograms of <i>p</i>-values obtained when the Zipf-like distributions <i>f</i>₁, <i>f</i>₂, and <i>f</i>₃ are fitted to the texts of the English Project Gutenberg.

<p>The histograms just count the number of texts in each bin of width 0.01. Note the poor performance of distribution 3 and the best performance of 2. Power-law approximations to the histograms for <i>f</i>₁ and <i>f</i>₂, with respective exponents 0.74 and 0.78, are shown as a guide to the eye.</p

Mean value and standard deviation (represented by the shaded regions) of the distribution of the Zipf’s exponent <i>β</i> as a function of text length <i>L</i> for distributions <i>f</i>₁ and <i>f</i>₂.

<p>Note that the last bin of <i>f</i>₁ contains a single datapoint, and so its standard deviation is not defined.</p

Word frequencies from Project Gutenberg English texts

<p>A compressed folder containing 31075 numerical vectors. Each one represents word frequencies of an EBook from Project Gutenberg written in English. Vectors are named containing the ID number of their corresponding text in Project Gutenberg.</p

Estimated probability density functions of <i>p</i>-values conditioned to <i>p</i> ≥ 0.01 separating for different ranges of text length <i>L</i>. <i>p</i>-values correspond to the fitting of word frequencies to (a) distribution <i>f</i>₁ and (b) distribution <i>f</i>₂.

<p>We divide the distribution of text length into 15 intervals of 2 000 texts each. For distribution <i>f</i>₁ only the first seven groups (up to length 34 400) are displayed (beyond this value we do not have enough statistics to see the distribution of <i>p</i>-values greater than 0.01, as displayed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147073#pone.0147073.g006" target="_blank">Fig 6</a>; for distribution 2 this happens only in the last two groups). The intervals <i>L</i>_<i>i</i> range from <i>L</i>₁ = [115, 5291] to <i>L</i>₆ = [25739, 34378] and to <i>L</i>₁₃ = [89476, 103767].</p

Same as Fig 1a, but replacing the order parameter <i>ρ</i>(<i>L</i>) by <i>ρ</i>(<i>L</i>)/[1 − <i>ρ</i>(<i>L</i>)].

<p>The exact behavior is given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e060" target="_blank">Eq (41)</a>, and the scaling law with the first correction to scaling is given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.e064" target="_blank">Eq (45)</a>. It becomes clear how the performance of the finite-size scaling law is even better than for <i>ρ</i>(<i>L</i>), in particular for <i>m</i> > 1. The program used to draw the figure is provided as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0161586#pone.0161586.s001" target="_blank">S1 File</a>.</p

Complementary cumulative distributions (i.e., survival functions) of <i>p</i>-values obtained when our three distributions are fitted to the texts of the English Project Gutenberg.

<p>This corresponds, except for normalization, to the integral of the previous figure, but we have included a fourth curve for the fraction of texts whose <i>p</i>-values for fits 1 and 2 are both higher than the value marked in the abscissa. Note that the values of <i>p</i> can play the role of the significance level. The value for <i>p</i> = 0 is not shown, in order to have higher resolution.</p

Complementary cumulative distribution and probability mass function of text frequencies, for: (a) <i>A Chronicle of London, from 1089 to 1483</i> (anonymous); (b) <i>The Works of Charles and Mary Lamb</i>, Vol. V, edited by E. V. Lucas; (c) <i>A Popular History of France from the Earliest Times</i>, Vol. I, by F. Guizot.

<p>These texts are the ones with the largest length <i>L</i> (83 720, 239 018 and 2 081 respectively) of those that fulfill <i>p</i> > 1/2, for fits 1, 2 and 3 respectively. The exponent <i>β</i> takes values 1.96, 1.89, and 1.82, in each case.</p