Eduardo G. Altmann

Recurrence time analysis, long-term correlations, and extreme events.

The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincaré recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent gamma, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different gamma, which shows a lack of invariance under the change of observables.

Beyond Word Frequency: Bursts, Lulls, and Scaling in the Temporal Distributions of Words

Background Zipfs discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well. Methodology/Principal Findings By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type – a measure of the logicality of each word – and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage. Conclusions/Significance Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipfs law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics.

Stochastic Model for the Vocabulary Growth in Natural Languages

Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany(Received 4 December 2012; revised manuscript received 20 March 2013; published 14 May 2013)Weproposeastochasticmodelforthenumberofdifferentwordsinagivendatabasewhichincorporatesthe dependenceonthedatabasesizeandhistoricalchanges.Themain featureofourmodelistheexistenceof two different classes of words: (i) a finite number of core words, which have higher frequency and donot affect the probability of a new word to be used, and (ii) the remaining virtually infinite number ofnoncore words, which have lower frequency and, once used, reduce the probability of a new word to beused in the future. Our model relies on a careful analysis of the Google Ngram database of bookspublished in the last centuries, and its main consequence is the generalization of Zipf’s and Heaps’ law totwo-scaling regimes. We confirm that these generalizations yield the best simple description of the dataamong generic descriptive models and that the two free parameters depend only on the language but noton the database. From the point of view of our model, the main change on historical time scales is thecomposition of the specific words included in the finite list of core words, which we observe to decayexponentially in time with a rate of approximately 30 words per year for English.

Leaking chaotic systems

There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. A unified treatment of leaking systems is provided and applications to different physical problems, in both the classical and quantum pictures, are reviewed. The treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption and/or transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the limacon family of billiards illustrate the main text. Regarding billiard dynamics, it is emphasized that a correct discrete-time representation can be given only in terms of the so-called true-time maps, while traditional Poincare maps lead to erroneous results. Perron-Frobenius-type operators are generalized so that they describe true-time maps with partial leaks.

On the origin of long-range correlations in texts

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical properties of our linguistic output has to be highly correlated in time. An example are the robust observations, still largely not understood, of correlations on arbitrary long scales in literary texts. In this paper we explain how long-range correlations flow from highly structured linguistic levels down to the building blocks of a text (words, letters, etc..). By combining calculations and data analysis we show that correlations take form of a bursty sequence of events once we approach the semantically relevant topics of the text. The mechanisms we identify are fairly general and can be equally applied to other hierarchical settings.

Optimal Noise Maximizes Collective Motion in Heterogeneous Media

We study the effect of spatial heterogeneity on the collective motion of self-propelled particles (SPPs). The heterogeneity is modeled as a random distribution of either static or diffusive obstacles, which the SPPs avoid while trying to align their movements. We find that such obstacles have a dramatic effect on the collective dynamics of usual SPP models. In particular, we report about the existence of an optimal (angular) noise amplitude that maximizes collective motion. We also show that while at low obstacle densities the system exhibits long-range order, in strongly heterogeneous media collective motion is quasi-long-range and exists only for noise values in between two critical values, with the system being disordered at both large and low noise amplitudes. Since most real systems have spatial heterogeneities, the finding of an optimal noise intensity has immediate practical and fundamental implications for the design and evolution of collective motion strategies.

Niche as a determinant of word fate in online groups

Patterns of word use both reflect and influence a myriad of human activities and interactions. Like other entities that are reproduced and evolve, words rise or decline depending upon a complex interplay between their intrinsic properties and the environments in which they function. Using Internet discussion communities as model systems, we define the concept of a word niche as the relationship between the word and the characteristic features of the environments in which it is used. We develop a method to quantify two important aspects of the size of the word niche: the range of individuals using the word and the range of topics it is used to discuss. Controlling for word frequency, we show that these aspects of the word niche are strong determinants of changes in word frequency. Previous studies have already indicated that word frequency itself is a correlate of word success at historical time scales. Our analysis of changes in word frequencies over time reveals that the relative sizes of word niches are far more important than word frequencies in the dynamics of the entire vocabulary at shorter time scales, as the language adapts to new concepts and social groupings. We also distinguish endogenous versus exogenous factors as additional contributors to the fates of words, and demonstrate the force of this distinction in the rise of novel words. Our results indicate that short-term nonstationarity in word statistics is strongly driven by individual proclivities, including inclinations to provide novel information and to project a distinctive social identity.

Comparing intermittency and network measurements of words and their dependence on authorship

Many features of texts and languages can now be inferred from statistical analyses using concepts from complex networks and dynamical systems. In this paper, we quantify how topological properties of word co-occurrence networks and intermittency (or burstiness) in word distribution depend on the style of authors. Our database contains 40 books by eight authors who lived in the nineteenth and twentieth centuries, for which the following network measurements were obtained: the clustering coefficient, average shortest path lengths and betweenness. We found that the two factors with stronger dependence on authors were skewness in the distribution of word intermittency and the average shortest paths. Other factors such as betweenness and Zipfs law exponent show only weak dependence on authorship. Also assessed was the contribution from each measurement to authorship recognition using three machine learning methods. The best performance was about 65% accuracy upon combining complex networks and intermittency features with the nearest-neighbor algorithm of automatic authorship. From a detailed analysis of the interdependence of the various metrics, it is concluded that the methods used here are complementary for providing short- and long-scale perspectives on texts, which are useful for applications such as the identification of topical words and information retrieval.

Recurrence time statistics for finite size intervals

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected by a kind of memory effect. We interpret this effect as being related to the unstable periodic orbits inside the interval. Although it is restricted to a few short times it changes the whole distribution of recurrences. We show that for systems with strong mixing properties the exponential decay converges to the Poissonian statistics when the width of the interval goes to zero. However, we alert that special attention to the size of the interval is required in order to guarantee that the short time memory effect is negligible when one is interested in numerically or experimentally calculated Poincare recurrence time statistics.

Probing the Statistical Properties of Unknown Texts: Application to the Voynich Manuscript

While the use of statistical physics methods to analyze large corpora has been useful to unveil many patterns in texts, no comprehensive investigation has been performed on the interdependence between syntactic and semantic factors. In this study we propose a framework for determining whether a text (e.g., written in an unknown alphabet) is compatible with a natural language and to which language it could belong. The approach is based on three types of statistical measurements, i.e. obtained from first-order statistics of word properties in a text, from the topology of complex networks representing texts, and from intermittency concepts where text is treated as a time series. Comparative experiments were performed with the New Testament in 15 different languages and with distinct books in English and Portuguese in order to quantify the dependency of the different measurements on the language and on the story being told in the book. The metrics found to be informative in distinguishing real texts from their shuffled versions include assortativity, degree and selectivity of words. As an illustration, we analyze an undeciphered medieval manuscript known as the Voynich Manuscript. We show that it is mostly compatible with natural languages and incompatible with random texts. We also obtain candidates for keywords of the Voynich Manuscript which could be helpful in the effort of deciphering it. Because we were able to identify statistical measurements that are more dependent on the syntax than on the semantics, the framework may also serve for text analysis in language-dependent applications.