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Complexity science uses computation to explore the physical and social sciences. In Think Complexity, you'll use graphs, cellular automata, and agent-based models to study topics in physics, biology, and economics. Whether you're an intermediate-level Python programmer or a student of computational modeling, you'll delve into examples of complex systems through a series of worked examples, exercises, case studies, and easy-to-understand explanations. In this updated second edition, you will: Work with NumPy arrays and SciPy methods, including basic signal processing and Fast Fourier Transform, Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines, Get Jupyter notebooks filled with starter code and solutions to help you re-implement and extend original experiments in complexity; and models of computation like Turmites, Turing machines, and cellular automata, Explore the philosophy of science, including the nature of scientific laws, theory choice, and realism and instrumentalism. Ideal as a text for a course on computational modeling in Python, Think Complexity also helps self-learners gain valuable experience with topics and ideas they might not encounter otherwise. --Back cover.

This paper assesses the role of socio-demographic triggers on Kolmogorov-based complexity in spoken English varieties. It thus contributes to the ongoing debate on contact and complexity in the sociolinguistic typological research community. Currently, evidence on whether socio-demographic triggers influence the morphosyntactic complexity of languages is controversial and inconclusive. Particularly controversial is the influence of the proportion of non-native speakers and the number of native speakers, which are both common proxies for language contact. In order to illuminate the issue from an English-varieties perspective, I use regression analysis to test several socio-demographic triggers in a corpus database of spoken English varieties. Language complexity here is operationalised in terms of Kolmogorov-based morphological and syntactic complexity. The results only partially support the idea that socio-demographic triggers influence morphosyntactic complexity in English varieties, i.e., speaker-related triggers turn out to be negative but non-significant. Yet, net migration rate shows a positive significant effect on morphological complexity which needs to be seen in the global context of English as a commodity and unequal access to English. I thus argue that socioeconomic triggers are better predictors for complexity than demographic speaker numbers. In sum, the paper opens up new horizons for research on language complexity.

Languages with many speakers tend to be structurally simple while small communities sometimes develop languages with great structural complexity. Paradoxically, the opposite pattern appears to be observed for non-structural properties of language such as vocabulary size. These apparently opposite patterns pose a challenge for theories of language change and evolution. We use computational simulations to show that this inverse pattern can depend on a single factor: ease of diffusion through the population. A population of interacting agents was arranged on a network, passing linguistic conventions to one another along network links. Agents can invent new conventions, or replicate conventions that they have previously generated themselves or learned from other agents. Linguistic conventions are either Easy or Hard to diffuse, depending on how many times an agent needs to encounter a convention to learn it. In large groups, only linguistic conventions that are easy to learn, such as words, tend to proliferate, whereas small groups where everyone talks to everyone else allow for more complex conventions, like grammatical regularities, to be maintained. Our simulations thus suggest that language, and possibly other aspects of culture, may become simpler at the structural level as our world becomes increasingly interconnected.

Background High language complexity impairs patients’ understanding and medical outcomes. While messengers accelerate communication, the language complexity of chats between patients and providers is poorly studied. This study analyses language complexity and communication characteristics of chat data from the PIA study, which significantly improved blood pressure control after 6 to 12 months. Methods The cluster-randomised controlled PIA study enrolled 848 hypertension patients (412 intervention, 436 control) from 64 German general practices. The PIA technology enabled a secured communication of blood pressure readings, medication plans and messages. The chats were analysed regarding frequency, length, response time and content. Language complexity was measured using the Flesch index with seven levels from ‘hard’ to ‘very simple’. The study is registered in the German Clinical Trials Register (DRKS00012680). Results In total, 4231 messages were sent between 24 general practitioners and 363 patients of the intervention arm between 09/20 and 09/21: 22% messages ( n  = 941) were automated (new medication plan or prescription available), while 78% were non-automated ( n  = 3290), with 41.1% of these messages originating from patients and 58.9% from practices. The average chat dialogue lasted 176.8 days (SD 9.8). Patients’ messages had a mean of 22.6 words (SD 22.6) compared to 16.8 (SD 19.4) by practices. Most messages (88.92%) from practices and 51.9% from patients addressed medication or treatments. Simple or very simple language was used in 90.5% of the messages both by patients and by physicians regardless of sociodemographic characteristics. BP improved with increased frequency of messages ( p  < 0.001). Conclusions This communication showed a remarkably low language complexity by physicians and patients and better control with more messages. The results support the use of digital communication for topics such as chronic hypertension care. Trial registration German Clinical Trials Register, DRKS00012680. Registered May 10th, 2019, https://www.drks.de/drks_web/setLocale_EN.do .

In a recent study, I demonstrated that large numbers of L2 (second language) speakers do not appear to influence the morphological or information-theoretic complexity of natural languages. This paper has three primary aims: First, I address recent criticisms of my analyses, showing that the points raised by my critics were already explicitly considered and analysed in my original work. Furthermore, I show that the proposed alternative analyses fail to withstand detailed examination. Second, I introduce new data on the information-theoretic complexity of natural languages, with the estimates derived from various language models—ranging from simple statistical models to advanced neural networks—based on a database of 40 multilingual text collections that represent a wide range of text types. Third, I re-analyse the information-theoretic and morphological complexity data using novel methods that better account for model uncertainty in parameter estimation, as well as the genealogical relatedness and geographic proximity of languages. In line with my earlier findings, the results show no evidence that large numbers of L2 speakers have an effect on natural language complexity.

The present study investigated the developmental trajectories of written language of two Chinese EFL learners in terms of complexity over one semester and explored the relationship between syntactic complexity and lexical complexity under the framework of Complex Dynamic Systems Theory (CDST). The data were processed using dynamic analyses (min-max graphs, moving correlations and Change-point analysis) to visualize the developmental process and variability of each subsystem of complexity with 4 measures (mean length of T-unit, mean length of clause, clauses per T-unit and VocD) and interactions between different subsystems. The results showed, first, that different subsystems of written language complexity developed dynamically and nonlinearly with different degrees of variability, and varied in the two participants. Second, interactions existed between syntactic complexity and lexical complexity, which shaped as competitors for Jenny but as connected growers for Helen. The results further deepened the understanding of the development in learners’ written complexity, providing significant implications for EFL writing teaching.

We propose a quantitative approach for quantifying morphological complexity of a language based on text. Several corpus-based methods have focused on measuring the different word forms that a language can produce. We take into account not only the productivity of morphological processes but also the predictability of those morphological processes. We use a language model that predicts the probability of sub-word sequences within a word; we calculate the entropy rate of this model and use it as a measure of predictability of the internal structure of words. Our results show that it is important to integrate these two dimensions when measuring morphological complexity, since languages can be complex under one measure but simpler under another one. We calculated the complexity measures in two different parallel corpora for a typologically diverse set of languages. Our approach is corpus-based and it does not require the use of linguistic annotated data.

One proposed mechanism of language change concerns the role played by second-language (L2) learners in situations of language contact. If sufficiently many L2 speakers are present in a speech community in relation to the number of first-language (L1) speakers, then those features which present a difficulty in L2 acquisition may be prone to disappearing from the language. This paper presents a mathematical account of such contact situations based on a stochastic model of learning and nonlinear population dynamics. The equilibria of a deterministic reduction of the model, describing a mixed population of L1 and L2 speakers, are fully characterized. Whether or not the language changes in response to the introduction of L2 learners turns out to depend on three factors: the overall proportion of L2 learners in the population, the strength of the difficulty speakers face in acquiring the language as an L2, and the language-internal utilities of the competing linguistic variants. These factors are related by a mathematical formula describing a phase transition from retention of the L2-difficult feature to its loss from both speaker populations. This supplies predictions that can be tested against empirical data. Here, the model is evaluated with the help of two case studies, morphological levelling in Afrikaans and the erosion of null subjects in Afro-Peruvian Spanish; the model is found to be broadly in agreement with the historical development in both cases.

Language use and social interactions have demonstrated a close relationship with cognitive measures. It is important to improve the understanding of language use and behavioral indicators from social context to study the early prediction of cognitive decline among healthy populations of older adults. This study aimed at predicting an important cognitive ability, working memory, of 98 healthy older adults participating in a 4-day-long naturalistic observation study. We used linguistic measures, part-of-speech (POS) tags, and social context information extracted from 7450 real-life audio recordings of their everyday conversations. The methods in this study comprise (1) the generation of linguistic measures, representing idea density, vocabulary richness, and grammatical complexity, as well as POS tags with natural language processing (NLP) from the transcripts of real-life conversations and (2) the training of machine learning models to predict working memory using linguistic measures, POS tags, and social context information. We measured working memory using (1) the Keep Track test, (2) the Consonant Updating test, and (3) a composite score based on the Keep Track and Consonant Updating tests. We trained machine learning models using random forest, extreme gradient boosting, and light gradient boosting machine algorithms, implementing repeated cross-validation with different numbers of folds and repeats and recursive feature elimination to avoid overfitting. For all three prediction routines, models comprising linguistic measures, POS tags, and social context information improved the baseline performance on the validation folds. The best model for the Keep Track prediction routine comprised linguistic measures, POS tags, and social context variables. The best models for prediction of the Consonant Updating score and the composite working memory score comprised POS tags only. The results suggest that machine learning and NLP may support the prediction of working memory using, in particular, linguistic measures and social context information extracted from the everyday conversations of healthy older adults. Our findings may support the design of an early warning system to be used in longitudinal studies that collects cognitive ability scores and records real-life conversations unobtrusively. This system may support the timely detection of early cognitive decline. In particular, the use of a privacy-sensitive passive monitoring technology would allow for the design of a program of interventions to enable strategies and treatments to decrease or avoid early cognitive decline.