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

The lower cut-off for the frequency distribution of lemmas (<i>a</i>_<i>l</i>) versus the lower cut-off for the frequency distribution of word forms (<i>a</i>_<i>w</i>).

<p>The line <i>a</i>_<i>l</i> = <i>a</i>_<i>w</i> is also shown (solid line).</p

The fit of a linear model for the relationship between exponents (<i>γ</i>_<i>w</i> and <i>γ</i>_<i>l</i>) and the relationship between cut-offs (<i>a</i>_<i>w</i> and <i>a</i>_<i>l</i>).

<p><i>c</i>₁ and <i>c</i>₃ stand for slopes and <i>c</i>₂ and <i>c</i>₄ stand for intercepts. The error bars correspond to one standard deviation. A Student’s <i>t</i>-test is applied to investigate if the slopes are significantly different from one and if the intercepts are significantly different from zero. The resulting <i>p</i>-values indicate that in all cases the slopes are compatible with being equal to one. The intercepts are compatible with zero for the exponents, but seem to be incompatible for the cut-offs.</p

Characteristics of the books analyzed.

<p>¹Clarissa: Or the History of a Young Lady.</p><p>²Moby-Dick; or, The Whale.</p><p>³El ingenioso hidalgo don Quijote de la Mancha (1605)—The Ingenious Gentleman Don Quixote of La Mancha (title in English); including second part: El ingenioso caballero don Quijote de la Mancha (1615).</p><p>⁴Artamène ou le Grand Cyrus—Artamène, or Cyrus the Great.</p><p>⁵Le Vicomte de Bragelonne ou Dix ans plus tard—The Vicomte of Bragelonne: Ten Years Later.</p><p>⁶Seven Brothers.</p><p>⁷Spring and the Untimely Return of Winter.</p><p>⁸The Story of my Parents.</p><p>⁹Madeleine and Georges de Scudéry.</p><p>The length of each book <i>L</i> is measured in millions of tokens.</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

Analysis of the association between random variables using Pearson and Spearman correlations as statistics.

<p><i>ρ</i> is the value of the correlation statistic and <i>p</i> is the <i>p</i>-value of a two-sided test with null hypothesis <i>ρ</i> = 0, calculated through permutations of one of the variables (the results can be different if <i>p</i> is calculated from a <i>t</i>–test). The sample size is</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

Zipf’s Law for Word Frequencies: Word Forms versus Lemmas in Long Texts - Fig 3

<p>(a) Probability mass functions <i>f</i>(<i>n</i>) of the absolute frequencies <i>n</i> of words and lemmas in <i>La Regenta</i>, together with their fits, under rescaling of both axis. The collapse of the tails indicates the compatibility of both power-law exponents. (b) The same for, from top to bottom, <i>Artamène, Bragelonne</i> (both in French), <i>Seitsemän v., Kevät ja t</i>., and <i>Vanhempieni r</i>. (all three in Finnish). The rescaled distributions are multiplied in addition by factors 1, 10⁻², etc., for a clearer visualization.</p

Power-law fitting results for words and lemmas, denoted respectively by subindices <i>w</i> and <i>l</i>.

<p><i>V</i> is the number of types (vocabulary size), <i>n</i>_<i>m</i> is the maximum frequency of the distribution, <i>N</i>_<i>a</i> is the number of types in the power-law tail, i.e., with <i>n</i> ≥ <i>a</i>, <i>a</i> is the minimum value for which the power-law fit holds, and <i>γ</i> and <i>σ</i> are the power-law exponent and its standard deviation, respectively. 2<i>σ</i>_<i>d</i>, the double of the standard deviation <i>σ</i>_<i>d</i> is also given. <i>σ</i>_<i>d</i> is the standard deviation of <i>γ</i>_<i>l</i>−<i>γ</i>_<i>w</i> assuming independence, which is </p><p></p><p></p><p></p><p><mi>σ</mi><mi>d</mi></p><mo>=</mo><p></p><p></p><p><mi>σ</mi><mi>w</mi><mn>2</mn></p><mo>+</mo><p><mi>σ</mi><mi>l</mi><mn>2</mn></p><p></p><p></p><p></p><p></p><p></p>. The last column provides ℓ₁, the number of lemmas associated to only one word form. Notice that the lemma exponent is very close to the one found in Ref. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129031#pone.0129031.ref029" target="_blank">29</a>] for the tail of a double power-law fitting, except for <i>Moby-Dick</i> and <i>Ulysses</i>.<p></p