SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

It is well known that real-time human language processing is highly incremental and context-driven, and that the strength of a comprehender’s expectation for each word encountered is a key determinant of the difficulty of integrating that word into the preceding context. In reading, this differential difficulty is largely manifested in the amount of time taken to read each word. While numerous studies over the past thirty years have shown expectation-based effects on reading times driven by lexical, syntactic, semantic, pragmatic, and other information sources, there has been little progress in establishing the quantitative relationship between expectation (or prediction) and reading times. Here, by combining a state-of-the-art computational language model, two large behavioral data-sets, and non-parametric statistical techniques, we establish for the first time the quantitative form of this relationship, finding that it is logarithmic over six orders of magnitude in estimated predictability. This result is problematic for a number of established models of eye movement control in reading, but lends partial support to an optimal perceptual discrimination account of word recognition. We also present a novel model in which language processing is highly incremental well below the level of the individual word, and show that it predicts both the shape and time-course of this effect. At a more general level, this result provides challenges for both anticipatory processing and semantic integration accounts of lexical predictability effects. And finally, this result provides evidence that comprehenders are highly sensitive to relative differences in predictability – even for differences between highly unpredictable words – and thus helps bring theoretical unity to our understanding of the role of prediction at multiple levels of linguistic structure in real-time language comprehension.

ERP averaging is an extraordinarily successful method, but can only be applied to a limited range of experimental designs. We introduce the regression-based rERP framework, which extends ERP averaging to handle arbitrary combinations of categorical and continuous covariates, partial confounding, non-linear effects, and overlapping responses to distinct events, all within a single unified system. rERPs enable a richer variety of paradigms (including high-N naturalistic designs) while preserving the advantages of traditional ERPs. This article provides an accessible introduction to what rERPs are, why they are useful, how they are computed, and when we should expect them to be effective, particularly in cases of partial confounding. A companion article discusses how non-linear effects and overlap correction can be handled within this framework, as well as practical considerations around baselining, filtering, statistical testing, and artifact rejection. Free software implementing these techniques is available.

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