Long-Range Correlations in Sentence Series from A Story of the Stone

Fractality and Variability in Canonical and Non-Canonical English Fiction and in Non-Fictional Texts

This study investigates global properties of three categories of English text: canonical fiction, non-canonical fiction, and non-fictional texts. The central hypothesis of the study is that there are systematic differences with respect to structural design features between canonical and non-canonical fiction, and between fictional and non-fictional texts. To investigate these differences, we compiled a corpus containing texts of the three categories of interest, the Jena Corpus of Expository and Fictional Prose (JEFP Corpus). Two aspects of global structure are investigated, variability and self-similar (fractal) patterns, which reflect long-range correlations along texts. We use four types of basic observations, (i) the frequency of POS-tags per sentence, (ii) sentence length, (iii) lexical diversity, and (iv) the distribution of topic probabilities in segments of texts. These basic observations are grouped into two more general categories, (a) the lower-level properties (i) and (ii), which are observed at the level of the sentence (reflecting linguistic decoding), and (b) the higher-level properties (iii) and (iv), which are observed at the textual level (reflecting comprehension/integration). The observations for each property are transformed into series, which are analyzed in terms of variance and subjected to Multi-Fractal Detrended Fluctuation Analysis (MFDFA), giving rise to three statistics: (i) the degree of fractality ( H ), (ii) the degree of multifractality ( D ), i.e., the width of the fractal spectrum, and (iii) the degree of asymmetry ( A ) of the fractal spectrum. The statistics thus obtained are compared individually across text categories and jointly fed into a classification model (Support Vector Machine). Our results show that there are in fact differences between the three text categories of interest. In general, lower-level text properties are better discriminators than higher-level text properties. Canonical fictional texts differ from non-canonical ones primarily in terms of variability in lower-level text properties. Fractality seems to be a universal feature of text, slightly more pronounced in non-fictional than in fictional texts. On the basis of our results obtained on the basis of corpus data we point out some avenues for future research leading toward a more comprehensive analysis of textual aesthetics, e.g., using experimental methodologies.

Estimating Predictive Rate-Distortion Curves via Neural Variational Inference

The Predictive Rate–Distortion curve quantifies the trade-off between compressing information about the past of a stochastic process and predicting its future accurately. Existing estimation methods for this curve work by clustering finite sequences of observations or by utilizing analytically known causal states. Neither type of approach scales to processes such as natural languages, which have large alphabets and long dependencies, and where the causal states are not known analytically. We describe Neural Predictive Rate–Distortion (NPRD), an estimation method that scales to such processes, leveraging the universal approximation capabilities of neural networks. Taking only time series data as input, the method computes a variational bound on the Predictive Rate–Distortion curve. We validate the method on processes where Predictive Rate–Distortion is analytically known. As an application, we provide bounds on the Predictive Rate–Distortion of natural language, improving on bounds provided by clustering sequences. Based on the results, we argue that the Predictive Rate–Distortion curve is more useful than the usual notion of statistical complexity for characterizing highly complex processes such as natural language.

Sampling frequency dependent visibility graphlet approach to time series

Recent years have witnessed special attention on complex network based time series analysis. To extract evolutionary behaviors of a complex system, an interesting strategy is to separate the time series into successive segments, map them further to graphlets as representatives of states, and extract from the state (graphlet) chain transition properties, called graphlet based time series analysis. Generally speaking, properties of time series depend on the time scale. In reality, a time series consists of records that are sampled usually with a specific frequency. A natural question is how the evolutionary behaviors obtained with the graphlet approach depend on the sampling frequency? In the present paper, a new concept called the sampling frequency dependent visibility graphlet is proposed to answer this problem. The key idea is to extract a new set of series in which the successive elements have a specified delay and obtain the state transition network with the graphlet based approach. The dependence of the state transition network on the sampling period (delay) can show us the characteristics of the time series at different time scales. Detailed calculations are conducted with time series produced by the fractional Brownian motion, logistic map and Rössler system, and the empirical sentence length series for the famous Chinese novel entitled A Story of the Stone. It is found that the transition networks for fractional Brownian motions with different Hurst exponents all share a backbone pattern. The linkage strengths in the backbones for the motions with different Hurst exponents have small but distinguishable differences in quantity. The pattern also occurs in the sentence length series; however, the linkage strengths in the pattern have significant differences with that for the fractional Brownian motions. For the period-eight trajectory generated with the logistic map, there appear three different patterns corresponding to the conditions of the sampling period being odd/even-fold of eight or not both. For the chaotic trajectory of the logistic map, the backbone pattern of the transition network for sampling 1 saturates rapidly to a new structure when the sampling period is larger than 2. For the chaotic trajectory of the Rössler system, the backbone structure of the transition network is initially formed with two self-loops, the linkage strengths of which decrease monotonically with the increase of the sampling period. When the sampling period reaches 9, a new large loop appears. The pattern saturates to a complex structure when the sampling period is larger than 11. Hence, the new concept can tell us new information on the trajectories. It can be extended to analyze other series produced by brains, stock markets, and so on.

Evolution of scaling behaviors embedded in sentence series from A Story of the Stone

The novel entitled A Story of the Stone provides us precise details of life and social structure of the 18th century China. Its writing lasted a long duration of about 10 years, in which the author’s habit may change significantly. It had been published anonymously up to the beginning of the 20th century, which left a mystery of the author’s attribution. In the present work we focus our attention on scaling behavior embedded in the sentence series from this novel, hope to find how the ideas are organized from single sentences to the whole text. Especially we are interested in the evolution of scale invariance to monitor the changes of the author’s language habit and to find some clues on the author’s attribution. The sentence series are separated into a total of 69 non-overlapping segments with a length of 500 sentences each. The correlation dependent balanced estimation of diffusion entropy (cBEDE) is employed to evaluate the scaling behaviors embedded in the short segments. It is found that the total, the part attributed currently to Xueqin Cao (X-part), and the other part attributed to E Gao (E-part), display scale invariance in a large scale up to 10³ sentences, while their scaling exponents are almost identical. All the segments behave scale invariant in considerable wide scales, most of which reach one third of the length. In the curve of scaling exponent versus segment number, the X-part has rich patterns with averagely larger values, while the E-part has a U-shape with a significant low bottom. This finding is a new clue to support the attribution of the E-part to E Gao.