Summary The human brain has undergone rapid expansion since humans diverged from other great apes, but the mechanism of this human-specific enlargement is still unknown. Here, we use cerebral organoids derived from human, gorilla, and chimpanzee cells to study developmental mechanisms driving evolutionary brain expansion. We find that neuroepithelial differentiation is a protracted process in apes, involving a previously unrecognized transition state characterized by a change in cell shape. Furthermore, we show that human organoids are larger due to a delay in this transition, associated with differences in interkinetic nuclear migration and cell cycle length. Comparative RNA sequencing (RNA-seq) reveals differences in expression dynamics of cell morphogenesis factors, including ZEB2, a known epithelial-mesenchymal transition regulator. We show that ZEB2 promotes neuroepithelial transition, and its manipulation and downstream signaling leads to acquisition of nonhuman ape architecture in the human context and vice versa, establishing an important role for neuroepithelial cell shape in human brain expansion.

AbstractThe human brain has undergone rapid expansion since humans diverged from other great apes, but the mechanism of this human-specific enlargement is still unknown. Here, we use cerebral organoids derived from human, gorilla and chimpanzee cells to study developmental mechanisms driving evolutionary brain expansion. We find that the differentiation of neuroepithelial cells to neurogenic radial glia is a protracted process in apes, involving a previously unrecognized transition state characterized by a change in cell shape. Furthermore, we show that human organoids are larger due to a delay in this transition. Temporally resolved RNA-seq from human and gorilla organoids reveals differences in gene expression patterns associated with cell morphogenesis, and in particular highlights ZEB2, a known regulator of epithelial-mesenchymal transition and cell shape. We show, through loss- and gain-of-function experiments, that ZEB2 promotes the progression of neuroepithelial differentiation, and its ectopic overexpression in human is sufficient to trigger a premature transition. Thus, by mimicking the nonhuman ape expression in human organoids, we are able to force the acquisition of nonhuman ape architecture, establishing for the first time, an instructive role of neuroepithelial cell shape in human brain expansion.

The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that is frequently encountered, for example in model parameter optimisation problems. Bilevel optimisation of parameters is a standard setting in areas such as variational regularisation problems and supervised machine learning. We present efficient and robust derivative-free methods called randomised Itoh-Abe methods. These are generalisations of the Itoh-Abe discrete gradient method, a wellknown scheme from geometric integration, which has previously only been considered in the smooth setting. We demonstrate that the method and its favourable energy dissipation properties are well-defined in the nonsmooth setting. Furthermore, we prove that whenever the objective function is locally Lipschitz continuous, the iterates almost surely converge to a connected set of Clarke stationary points. We present an implementation of the methods, and apply it to various test problems. The numerical results indicate that the randomised Itoh-Abe methods are superior to state-of-the-art derivative-free optimisation methods in solving nonsmooth problems while remaining competitive in terms of efficiency.

In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a generalised Bregman distance as the underlying metric. Its discrete-time counterparts, Bregman iterations and linearised Bregman iterations are popular regularisation schemes for inverse problems that incorporate a priori information without loss of contrast. Discrete gradient methods are tools from geometric numerical integration for preserving energy dissipation of dissipative differential systems. The resultant Bregman discrete gradient methods are unconditionally dissipative and achieve rapid convergence rates by exploiting structures of the problem such as sparsity. Building on previous work on discrete gradients for non-smooth, non-convex optimisation, we prove convergence guarantees for these methods in a Clarke subdifferential framework. Numerical results for convex and non-convex examples are presented. Keywords Non-convex optimisation • Non-smooth optimisation • Bregman iteration • Inverse scale space • Geometric numerical integration • Discrete gradient methods Mathematics Subject Classification 49M37 • 49Q15 • 65K10 • 90C26 This article is dedicated to Mila Nikolova whose keen interest and inspiring discussions have encouraged our research on geometric integration for optimisation. MB acknowledges support from the Leverhulme Trust Early Career Fellowship ECF-2016-611 'Learning from mistakes: a supervised feedback-loop for imaging applications'. ESR and CBS acknowledge support from CHiPS (Horizon 2020 RISE project grant) and from the Cantab Capital Institute for the Mathematics of Information. CBS acknowledges support from the Leverhulme Trust project on "Breaking the non-convexity barrier" EPSRC grant Nr EP/M00483X/1, and the EPSRC Centre Nr EP/N014588/1. Moreover, CBS acknowledges support from the RISE project NoMADS and the Alan Turing Institute.