Peter. A. Robinson

The intricate network of axonal fibres that forms the mammalian cortical connectome has a complex topology, being organized in a way that is neither completely regular nor random, as well as a characteristic topography, in which specific anatomical locations are imbued with distinctive connectivity profiles. The mechanisms that give rise to such properties remain a mystery. Here, we formulate a simple analytic model derived from neural field theory that prioritizes physical constraints on connectome architecture by assuming that connectivity is preferentially concentrated between pairs of cortical locations that facilitate the excitation of resonant geometric modes of the cortex. We show that the model outperforms existing approaches in reproducing multiple topological and topographical properties of cortical connectomes mapped at spatial scales spanning orders of magnitude in humans, chimpanzees, macaques, marmosets, and mice, as mapped with either non-invasive diffusion magnetic resonance imaging or invasive viral tract-tracing. Our findings thus point to a fundamental role of geometry in shaping the multiscale architecture of cortical connectomes that has been conserved across 90 million years of evolution.

The brain expresses activity in complex spatiotemporal patterns, reflecting the influence of spatially distributed cytoarchitectural, biochemical, and genetic properties. The correspondence between these different “brain maps” is a topic of substantial interest. However, these maps possess intrinsic smoothness (spatial autocorrelation, SA) which can inflate spurious cross-correlations, leading to false positive associations. Identifying true associations requires knowledge about the distribution of correlations that arise by chance in the presence of SA. This null distribution can be generated from an ensemble of surrogate brain maps that preserve the intrinsic SA but break the correlations between maps. The present work introduces the “eigenstrapping” method, which performs a spectral decomposition of brain maps, such as fMRI activation patterns, expressed on cortical and subcortical surfaces, using geometric eigenmodes, and then randomly rotating these modes to produce SA-preserving surrogate brain maps. It is shown that these surrogates appropriately represent the null distribution of chance pairwise correlations, with expected false positive control superior to current state-of-the-art procedures. Eigenstrapping is fast, eschews the need for parametric assumptions about the nature of a map’s SA, and works with maps defined on smooth surfaces with a boundary, such as a single cortical hemisphere when the medial wall has been removed. Moreover, eigenstrapping generalizes to broader classes of null models than existing techniques, offering a unified approach for inference on cortical and subcortical maps, spatiotemporal processes, and complex patterns possessing higher-order correlations.

A model of time-dependent trade of goods between spatial locations is formulated via an electric circuit analogy, in which goods are analogous to charge and price to voltage, while producers and consumers are represented by sources and sinks of goods flow, which is represented by current, located at the nodes of a trade network. The core ansatz is that the flow of goods along each network link is driven by the voltage difference across that link, opposed by resistance that represents trade friction. Market prices are then determined indirectly by internal balances of flows, subject to external constraints on supply and demand. The model yields multiple outcomes that support its validity and applicability, including price setting via emergent balance of supply and demand, price fluctuations, traditional and generalized elasticities, network structure-flow relations, competition between producers, and substitution between suppliers, between consumers, and/or between trade links. All these results prove to be consistent with observed features of trade dynamics, thereby supporting the validity of the model. The new model is then used to derive the widely used gravity model of international trade from a mechanistic basis, yielding exponents consistent with published data and leading naturally to core-periphery structure, as observed in real trade networks. The analysis also implies that trade flows self-organize to minimize trade friction in the system as a whole, an emergent global outcome from the purely local dynamics of the populations of producers, consumers, and traders. Possible generalizations and further applications are outlined, including incorporation of asymmetry and capacity limits of trade links, constraints on supply and demand, behavioral responses, and coupling to models of investment strategies.

Objective. Disorders of consciousness (DoC) remain a significant challenge in neurology, with traditional brain stimulation therapies showing limited and inconsistent efficacy across patients. This study presents a novel computational approach grounded in neural field theory for constructing personalized stimulus signals designed to induce healthy-like neural activity patterns in individuals with DoC. Approach. We employ a simplified brain model fitted to the electroencephalogram (EEG) power spectrum of a DoC patient, simulating the individual’s neural dynamics. Using model equations and fitted parameters, we mathematically derive stimuli time series that cause the model to generate power spectra typical of healthy individuals. These stimuli are tailored for brain regions typically targeted by neuromodulation therapies, such as deep brain stimulation and repetitive transcranial magnetic stimulation. Main results. In silico simulations demonstrate that our method successfully induces healthy-like EEG power spectra in models fitted to DoC patients. Furthermore, when the model parameters were near a stability boundary, stimulation led to a bifurcation and lasting changes in the model’s activity beyond the stimulation period. Significance. By inducing healthy-like neural activity, this approach may effectively activate plasticity mechanisms during long-term treatment, potentially leading to sustained improvements in a patient’s condition. While further clinical adjustments and validation are needed, this method holds promise for improving therapeutic outcomes in DoC. Moreover, it offers potential extensions to other neurological conditions that could benefit from personalized brain stimulation therapies.

The mammalian brain is comprised of anatomically and functionally distinct regions. Substantial work over the past century has pursued construction of ever-more accurate maps of regional boundaries, using either expert judgement or data-driven clustering of functional, connectional, and/or architectonic properties. However, these approaches are often purely descriptive, have limited generalizability, and do not elucidate the underlying generative mechanisms that shape the regional organization of the brain. Here, we develop a novel approach that leverages a simple, hierarchical principle for generating a multiscale parcellation of any brain structure in any mammalian species using only its geometry. We show that this approach yields regions at any resolution scale that are more homogeneous than those defined in nearly all existing benchmark brain parcellations in use today across hundreds of anatomical, functional, cellular, and molecular brain properties measured in humans, macaques, marmosets, and mice. We additionally show how our method can be generalized to previously unstudied mammalian species for which no parcellations exist. Finally, we demonstrate how our approach captures the essence of a simple, hierarchical reaction-diffusion mechanism, in which the geometry of a brain structure shapes the spatial expression of putative patterning molecules linked to the formation of distinct regions through development. Our findings point to a highly conserved and universal influence of geometry on the regional organization of the mammalian brain.

The effects of nonuniformities in axonal connectivity on natural modes of brain activity are explored to determine their contributions to modal eigenvalues, structure, and communication and to clarify the limits of validity of widely used uniform-connectivity approximations. Preferred channels of communication are demonstrated that are supported by natural modes of mean connectivity and resulting activity. The effects of axonal tracts on these modes are calculated using perturbation methods, and it is found that modes and their spectra are only moderately perturbed by even the largest white matter tracts. However, perturbations of activity are greatly magnified when modes are near-critical and realistic connectivity and gain perturbations can then enable rapid responses to stimuli on the observed timescales of evoked responses. It is thus argued that dynamic mode-mode communication channels complement ones based on white matter tracts and that both rely on near-criticality to have their observed effects.

A compact description of the frequency structure and topography of human alpha-band rhythms is obtained by use of the first four brain activity eigenmodes previously derived from corticothalamic neural field theory. Just two eigenmodes that overlap in frequency are found to reproduce the observed topography of the classical alpha rhythm for subjects with a single, occipitally concentrated alpha peak in their electroencephalograms. Alpha frequency splitting and relative amplitudes of double alpha peaks are explored analytically and numerically within this four-mode framework using eigenfunction expansion and perturbation methods. These effects are found to result primarily from the different eigenvalues and corticothalamic gains corresponding to the eigenmodes. Three modes with two non-overlapping frequencies suffice to reproduce the observed topography for subjects with a double alpha peak, where the appearance of a distinct second alpha peak requires an increase of the corticothalamic gain of higher eigenmodes relative to the first. Conversely, alpha blocking is inferred to be linked to a relatively small attention-dependent reduction of the gain of the relevant eigenmodes, whose effect is enhanced by the near-critical state of the brain and whose sign is consistent with inferences from neural field theory. The topographies and blocking of the mu and tau rhythms within the alpha-band are explained analogously via eigenmodes. Moreover, the observation of three rhythms in the alpha band is due to there being exactly three members of the first family of spatially nonuniform modes. These results thus provide a simple, unified description of alpha band rhythms and enable experimental observations of spectral structure and topography to be linked directly to theory and underlying physiology.

In Pang, Aquino et al. (2023)¹, we presented multiple lines of evidence to indicate that brain geometry plays a previously under-appreciated role in shaping dynamics. Mansour et al. raise concerns about one specific analysis, in which we showed that eigenmodes derived from the geometry of the human cortex can reconstruct diverse activity maps generated with functional magnetic resonance imaging (fMRI) better than eigenmodes derived from connectomes estimated with diffusion MRI (dMRI). Here, we address their concerns and show how our findings and conclusions remain valid.

Bias and discrimination in appointment processes such as hiring decisions (and analogous selection procedures for performance evaluations, promotions, scholarships, and awards), are quantified statistically via the binomial distribution. These statistical measures are described and an easily used webapp for calculating them is provided. The measures considered include the likelihood that a given number of appointments arose from a fair process and the likelihood that an existing process would give rise to a fair outcome if it were repeated. These methods are illustrated by applying them to sex (including gender) discrimination and racial discrimination in senior appointments in the Australian university sector; both conscious and unconscious biases are included. Significant sex discrimination is found to have existed in the appointments of university chief executives (Vice Chancellors) who were in office in 2018, but with a moderate chance that current processes will yield fair outcomes in the future. However, there is no evidence of strong sex discrimination in the country’s eight main research universities for senior appointments (i.e., Faculty Deans and members of their governing Boards or Senates) for those in office as of 2021. However, at the same dates, extreme racial discrimination was implicit in the selection procedures for both Vice Chancellors and senior appointments in all these universities. The University of Sydney’s senior appointments were found to have had the most racially biased outcomes among the country’s eight main research universities. Significantly, there is negligible statistical likelihood of achieving racially unbiased outcomes in the future in any of the contexts considered, unless the selection procedures are significantly modified.

The brain expresses activity in complex spatiotemporal patterns, reflected in the influence of spatially distributed cytoarchitectural, biochemical, and genetic properties. The correspondence between these multimodal "brain maps" may reflect underlying causal pathways and is hence a topic of substantial interest. However, these maps possess intrinsic smoothness (spatial autocorrelation, SA) which can inflate spurious cross-correlations, leading to false positive associations. Identifying true associations requires knowledge about the distribution of correlations that arise by chance in the presence of SA. This null distribution can be generated from an ensemble of surrogate brain maps that preserve internal SA but break correlations between maps. The present work introduces "eigenstrapping", using a spectral decomposition of cortical and subcortical surfaces in terms of geometric eigenmodes, and then randomly rotating these modes to produce SA-preserving surrogate brain maps. It is shown that these surrogates appropriately represent the null distribution of chance pairwise correlations, with similar or superior false positive control to current state-of-the-art procedures. Eigenstrapping is fast, eschews the need for parametric assumptions about the nature of the SA, and works with maps defined on smooth surfaces with or without a boundary. It generalizes to broader classes of null models than existing techniques, offering a unified approach for inference on cortical and subcortical maps, spatiotemporal processes, and complex patterns possessing higher-order correlations.