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We present a didactic introduction to spectral Dynamic Causal Modelling (DCM), a Bayesian state-space modelling approach used to infer effective connectivity from non-invasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modelling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all variables--at all time lags--including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

Acknowledgements: Special thanks to Thomas Parr for our virtual conversations about Active Inference., Humans display astonishing skill in learning about the environment in which they operate. They assimilate a rich set of affordances and interrelations among different elements in particular contexts, and form flexible abstractions (i.e., concepts) that can be generalised and leveraged with ease. To capture these abilities, we present a deep hierarchical Active Inference model of goal-directed behaviour, and the accompanying belief update schemes implied by maximising model evidence. Using simulations, we elucidate the potential mechanisms that underlie and influence concept learning in a spatial foraging task. We show that the representations formed-as a result of foraging-reflect environmental structure in a way that is enhanced and nuanced by Bayesian model reduction, a special case of structure learning that typifies learning in the absence of new evidence. Synthetic agents learn associations and form concepts about environmental context and configuration as a result of inferential, parametric learning, and structure learning processes-three processes that can produce a diversity of beliefs and belief structures. Furthermore, the ensuing representations reflect symmetries for environments with identical configurations.

A growing body of evidence highlights the intricate linkage of exteroceptive perception to the rhythmic activity of the visceral body. In parallel, interoceptive inference theories of affective perception and self-consciousness are on the rise in cognitive science. However, thus far no formal theory has emerged to integrate these twin domains; instead, most extant work is conceptual in nature. Here, we introduce a formal model of cardiac active inference, which explains how ascending cardiac signals entrain exteroceptive sensory perception and uncertainty. Through simulated psychophysics, we reproduce the defensive startle reflex and commonly reported effects linking the cardiac cycle to affective behaviour. We further show that simulated 'interoceptive lesions' blunt affective expectations, induce psychosomatic hallucinations, and exacerbate biases in perceptual uncertainty. Through synthetic heart-rate variability analyses, we illustrate how the balance of arousal-priors and visceral prediction errors produces idiosyncratic patterns of physiological reactivity. Our model thus offers a roadmap for computationally phenotyping disordered brain-body interaction.

Brain research has in recent years indisputably entered a new epoch, driven bysubstantialmethodologicaladvances and digitallyenabled data integration and modeling at multiple scales –from molecules to the whole system. Major advances are emerging at theintersection of neurosciencewith technology and computing. This new science of the brain integrates high-quality basic research,systematic data integration across multiple scales, a new culture of large-scale collaboration andtranslation into applications. A systematic approach, as pioneered in Europe’s Human Brain Project(HBP), will be essential in meeting the pressing medical andtechnological challenges of the comingdecade. The aims of this paper are To develop a concept for the coming decade of digital brain research To discuss it with the research community at large, with the aim of identifying points of convergence and common goals To provide a scientific framework for current and future development of EBRAINS To inform and engage stakeholders, funding organizations and research institutions regarding future digital brain research To identify and address key ethical and societal issues While we do not claim that there is a ‘one size fits all’ approach to addressing these aspects, we areconvinced that discussions around the theme of digital brain research will help drive progress in thebroader field of neuroscience. You can submit your comments here and be considered for co-authorship Or become a supporter by clicking here More information below Comments on this manuscript are welcome This manuscriptis a living document that is being further developed in a participatory process. The work has been initiated by the Science and Infrastructure Board of the Human Brain Project (HBP). Now, the entire research community is invited to contribute to shaping the vision by submitting comments.Comments can be submitted via an online commentary form here. All submitted comments will be considered and discussed. The final decision on whether edits or additions will be made to the next version of the manuscript based on an individual comment will be made by the Science and Infrastructure Board (SIB) of the Human Brain Project (HBP) at regular intervals. The final version of the manuscript will be prepared and published in the next months. Comments may be submitted until the end of May, 2023. Every researcher is welcome to provide comment or indicate support for the contents of this paper and jointly shape the future of brain research. Supporters of the paper: Pietro Avanzini, Marc Beyer, Maria Del Vecchio, Jitka Annen, Maurizio Mattia, Steven Laureys, Rosanne Edelenbosch, Rafael Yuste, Jean-Pierre Changeux, Linda Richards, Hye Weon Jessica Kim, Chrysoula Samara, Luis Miguel González de la Garza, Nikoleta Petalidou, Vasudha Kulkarni, Cesar David Rincon, Isabella O'Shea, Munira Tamim Electricwala, Nicola Palomero-Gallagher, Bernd Carsten Stahl, Bahar Hazal Yalcinkaya, Meysam Hashemi, Carola Sales Carbonell, Marcel Carrère, Anthony Randal McIntosh, Hiba Sheheitli, Abolfazl Ziaeemehr, Martin Breyton, Giovanna Ramos Queda, Anirudh NIhalani Vattikonda, Gyorgy Buzsaki George Ogoh, William Knight Torbjørn V Ness, MIchiel van der Vlag, Mu-ming Poo.