As the field of migration studies evolves in the digital age, big data analytics emerge as a potential game-changer, promising unprecedented granularity, timeliness, and dynamism in understanding migration patterns. However, the epistemic value added by this data explosion remains an open question. This paper critically appraises the claim, investigating the extent to which big data augments, rather than merely replicates, traditional data insights in migration studies. Through a rigorous literature review of empirical research, complemented by a conceptual analysis, we aim to map out the methodological shifts and intellectual advancements brought forth by big data. The potential scientific impact of this study extends into the heart of the discipline, providing critical illumination on the actual knowledge contribution of big data to migration studies. This, in turn, delivers a clarified roadmap for navigating the intersections of data science, migration research, and policymaking.

This is the first of a two-part paper. We formulate a data-driven method for constructing finite-volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker–Planck equation. A method is employed that allows for flexibility in partitioning state space, generalizes to function spaces, applies to arbitrarily long sequences of time-series data, is robust to noise and quantifies uncertainty with respect to finite sample effects. After applying the method, one is left with Markov states (cell centres) and a random matrix approximation to the generator. When used in tandem, they emulate the statistics of the underlying system. We illustrate the method on the Lorenz equations (a three-dimensional ordinary differential equation) saving a fluid dynamical application for Part 2 (Souza, J. Fluid Mech., vol. 997, 2024, A2).

This is the second part of a two-part paper. We apply the methodology of the first paper (Souza, J. Fluid Mech., vol. 997, 2024, A1) to construct a data-driven finite-volume discretization of the Liouville/Fokker–Planck equation of a high-dimensional dynamical system, i.e. the compressible Euler equations with gravity and rotation evolved on a thin spherical shell. We show that the method recovers a subset of the statistical properties of the underlying system, steady-state distributions of observables and autocorrelations of particular observables, as well as revealing the global Koopman modes of the system. We employ two different strategies for the partitioning of a high-dimensional state space, and explore their consequences.

This paper aims at exploring the dynamic interplay between advanced technological developments in AI and Big Data and the sustained relevance of theoretical frameworks in scientific inquiry. It questions whether the abundance of data in the AI era reduces the necessity for theory or, conversely, enhances its importance. Arguing for a synergistic approach, the paper emphasizes the need for integrating computational capabilities with theoretical insight to uncover deeper truths within extensive datasets. The discussion extends into computational social science, where elements from sociology, psychology, and economics converge. The application of these interdisciplinary theories in the context of AI is critically examined, highlighting the need for methodological diversity and addressing the ethical implications of AI-driven research. The paper concludes by identifying future trends and challenges in AI and computational social science, offering a call to action for the scientific community, policymakers, and society. Being positioned at the intersection of AI, data science, and social theory, this paper illuminates the complexities of our digital era and inspires a re-evaluation of the methodologies and ethics guiding our pursuit of knowledge.

Second language (L2) learners need to acquire large vocabularies to approach native-like proficiency. Many controlled experiments have investigated the factors facilitating and hindering word learning; however, few studies have validated these findings in real-world learning scenarios. We use data from the language learning app Lingvist to explore how L2 word learning is affected by valence (positivity/negativity) and concreteness of target words and their linguistic contexts. We found that valence, but not concreteness, affects learning. Users learned positive and negative words better than neutral ones. Moreover, positive words are learned best in positive contexts and negative words in more negative contexts. Word and context valence effects are strongest on the learner’s second encounter with the target word and diminish across subsequent encounters. These findings provide support for theories of embodied cognition and the lexical quality hypothesis and point to the linguistic factors that make learning words, and by extension languages, faster.

High-dimensional dynamical systems projected onto a lower-dimensional manifold cease to be deterministic and are best described by probability distributions in the projected state space. Their equations of motion map onto an evolution operator with a deterministic component, describing the projected dynamics, and a stochastic one representing the neglected dimensions. This is illustrated with data-driven models for a moderate-Reynolds-number turbulent channel. It is shown that, for projections in which the deterministic component is dominant, relatively ‘physics-free’ stochastic Markovian models can be constructed that mimic many of the statistics of the real flow, even for fairly crude operator approximations, and this is related to general properties of Markov chains. Deterministic models converge to steady states, but the simplified stochastic models can be used to suggest what is essential to the flow and what is not.

The socioeconomic role of guanxi networks among individuals has been widely recorded, yet macro-level analysis has been sparse in empirical research. This research fills that gap by presenting the first nationally representative evidence illustrating the connection between regional guanxi culture and population mobility among cities in China, with a particular focus on instrumental guanxi culture. To quantify guanxi culture, we employ online search indices related to gift giving, a measure which is challenging to capture through traditional survey data. Applying matched prefecture-level data spanning from 2011 to 2019, the panel model reveals a strong negative correlation between a city's instrumental guanxi culture and inbound migration, while sentimental guanxi culture exhibits a positive correlation with inbound mobility. This research not only adds to the existing theories by exploring the macro-level effects of both instrumental and sentimental guanxi practices but also introduces an innovative method for quantifying guanxi culture through big data analysis.

The synchronisation between rotating turbulent flows in periodic boxes is investigated numerically. The flows are coupled via a master–slave coupling, taking the Fourier modes with wavenumber below a given value $k_m$ as the master modes. It is found that synchronisation happens when $k_m$ exceeds a threshold value $k_c$, and $k_c$ depends strongly on the forcing scheme. In rotating Kolmogorov flows, $k_c\eta$ does not change with rotation in the range of rotation rates considered, $\eta$ being the Kolmogorov length scale. Even though the energy spectrum has a steeper slope, the value of $k_c\eta$ is the same as that found in isotropic turbulence. In flows driven by a forcing term maintaining constant energy injection rate, synchronisation becomes easier when rotation is stronger. Here, $k_c\eta$ decreases with rotation, and it is reduced significantly for strong rotations when the slope of the energy spectrum approaches $-3$. It is shown that the conditional Lyapunov exponent for a given $k_m$ is reduced by rotation in the flows driven by the second type of forcing, but it increases mildly with rotation for the Kolmogorov flows. The local conditional Lyapunov exponents fluctuate more strongly as rotation is increased, although synchronisation occurs as long as the average conditional Lyapunov exponents are negative. We also look for the relationship between $k_c$ and the energy spectra of the Lyapunov vectors. We find that the spectra always seem to peak at approximately $k_c$, and synchronisation fails when the energy spectra of the conditional Lyapunov vectors have a local maximum in the slaved modes.