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BACKGROUND: Diminished synaptic gain-the sensitivity of postsynaptic responses to neural inputs-may be a fundamental synaptic pathology in schizophrenia. Evidence for this is indirect, however. Furthermore, it is unclear whether pyramidal cells or interneurons (or both) are affected, or how these deficits relate to symptoms. \ud \ud METHODS: People with schizophrenia diagnoses (PScz) (n = 108), their relatives (n = 57), and control subjects (n = 107) underwent 3 electroencephalography (EEG) paradigms-resting, mismatch negativity, and 40-Hz auditory steady-state response-and resting functional magnetic resonance imaging. Dynamic causal modeling was used to quantify synaptic connectivity in cortical microcircuits. \ud \ud RESULTS: Classic group differences in EEG features between PScz and control subjects were replicated, including increased theta and other spectral changes (resting EEG), reduced mismatch negativity, and reduced 40-Hz power. Across all 4 paradigms, characteristic PScz data features were all best explained by models with greater self-inhibition (decreased synaptic gain) in pyramidal cells. Furthermore, disinhibition in auditory areas predicted abnormal auditory perception (and positive symptoms) in PScz in 3 paradigms. \ud \ud CONCLUSIONS: First, characteristic EEG changes in PScz in 3 classic paradigms are all attributable to the same underlying parameter change: greater self-inhibition in pyramidal cells. Second, psychotic symptoms in PScz relate to disinhibition in neural circuits. These findings are more commensurate with the hypothesis that in PScz, a primary loss of synaptic gain on pyramidal cells is then compensated by interneuron downregulation (rather than the converse). They further suggest that psychotic symptoms relate to this secondary downregulation.

Understanding information processing in the brain-and creating general-purpose artificial intelligence-are long-standing aspirations of scientists and engineers worldwide. The distinctive features of human intelligence are high-level cognition and control in various interactions with the world including the self, which are not defined in advance and are vary over time. The challenge of building human-like intelligent machines, as well as progress in brain science and behavioural analyses, robotics, and their associated theoretical formalisations, speaks to the importance of the world-model learning and inference. In this article, after briefly surveying the history and challenges of internal model learning and probabilistic learning, we introduce the free energy principle, which provides a useful framework within which to consider neuronal computation and probabilistic world models. Next, we showcase examples of human behaviour and cognition explained under that principle. We then describe symbol emergence in the context of probabilistic modelling, as a topic at the frontiers of cognitive robotics. Lastly, we review recent progress in creating human-like intelligence by using novel probabilistic programming languages. The striking consensus that emerges from these studies is that probabilistic descriptions of learning and inference are powerful and effective ways to create human-like artificial intelligent machines and to understand intelligence in the context of how humans interact with their world.

We present a hierarchical empirical Bayesian framework for testing hypotheses about neurotransmitters' concertation as empirical prior for synaptic physiology using ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography data (MEG). A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of individuals' neurophysiological observations. At the second level, individuals' 7T-MRS estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the group-wise evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction (BMR), parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare alternative model evidence of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the subset of synaptic connections that are influenced by individual differences in neurotransmitter levels, as measured by 7T-MRS. We demonstrate the method using resting-state MEG (i.e., task-free recording) and 7T-MRS data from healthy adults. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. Using within-subject split-sampling of the MEG dataset (i.e., validation by means of a held-out dataset), we show that model comparison for hypothesis testing can be highly reliable. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to reveal the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions.

Highlights • We leverage the idea of ‘Markov blanket’ as a statistical boundary to provide an analysis of partitions in neuronal systems. • We show this partition is applicable to multiple scales, from single neurons, brain regions, and brain-wide networks. • Based on the canonical micro-circuitry, our treatment has practical applications for effective connectivity. • Our proposed partition highlights the limitations of ‘modular’ proposals considering a single level of description., Recent characterisations of self-organising systems depend upon the presence of a ‘Markov blanket’: a statistical boundary that mediates the interactions between the inside and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. The notion of effective connectivity depends upon the dynamic coupling between functional units, whose form recapitulates that of a Markov blanket at each level of analysis. The nuance afforded by partitioning neural systems in this way highlights certain limitations of ‘modular’ perspectives of brain function that only consider a single level of description.

Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] - especially with the advent of light-controlled protein activation through optogenetics [5] - have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept - that can predict the emergence of form and the robust maintenance of complex anatomy - is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference - as understood in this framework - and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this 'first principle' approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble - as a first step in carcinogenesis as false 'beliefs' about what a cell should 'sense' and 'do'. We further show that simple modifications of the inference process can cause - and rescue - mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings.

Wright and Bourke's compelling article rightly points out that existing models of embryogenesis fail to explain the mechanisms and functional significance of the dynamic connections among neurons. We pursue their account of Dynamic Logic by appealing to the Markov blanket formalism that underwrites the Free Energy Principle. We submit that this allows one to model embryogenesis as self-organisation in a dynamical system that minimises free-energy. The ensuing formalism may be extended to also explain the autonomous emergence of cognition, specifically in the brain, as a dynamic self-assembling process.

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.

While attention is widely recognised as central to perception, the term is often used to mean very different things. Prominent theories of attention - notably the premotor theory - relate it to planned or executed eye movements. This contrasts with the notion of attention as a gain control process that weights the information carried by different sensory channels. We draw upon recent advances in theoretical neurobiology to argue for a distinction between attentional gain mechanisms and salience attribution. The former depends upon estimating the precision of sensory data, while the latter is a consequence of the need to actively engage with the sensorium. Having established this distinction, we consider the intimate relationship between attention and salience.

Mohan et al offer an exhaustive and compelling survey of different paradigms for understanding an embodied exchange with the world. They describe a new way of looking at motor control that has emerged over the past years, – a view that resolves many issues with previous (optimal motor control) formulations. Pleasingly, this new way of looking at things picks up on historical themes that date back to the 19th century. For example, notions of synergy formation and the equilibrium point hypothesis, re-emerge with a new simplicity and explanatory power, when one takes a holistic and enactive view of embodied behaviour. Indeed, one might trace the ideas explored in Mohan et al back to foundational notions enshrined in ideomotor theory and Helmholtz's notion of unconscious inference. This new way of looking at things is centred on the notion of a forward or generative model that plays the functional role of a “plastic configurable internal representation of the body (body schema) as a critical link enabling the seamless continuum between motor control and imagery.” Mohan et al.

Survival requires the implementation of adaptive changes that demand energy resources. The efficient regulation of energetic resources thus plays a critical role in enabling systems to adapt to the demands of their internal and external environments. The framework of active inference explains how living organisms can build probabilistic models that enable them to predict, track, and regulate energy expenditure in the short and long run. The aim of the paper is to characterize the physiological changes that accompany stress, and the relationship between these changes and the loss of confidence in a system's predictions about its internal and external milieu—ultimately manifesting as depressive symptomatology. We identify the systems that underwrite goal-directed behavior, and the neuroendocrine and immunological systems, as the hierarchical controller that regulates energy resources. In doing so, we establish an etiological pathway from allostatic overload to depression via active inference.

The active inference framework, and in particular its recent formulation as a partially observable Markov decision process (POMDP), has gained increasing popularity in recent years as a useful approach for modelling neurocognitive processes. This framework is highly general and flexible in its ability to be customized to model any cognitive process, as well as simulate predicted neuronal responses based on its accompanying neural process theory. It also affords both simulation experiments for proof of principle and behavioral modelling for empirical studies. However, there are limited resources that explain how to build and run these models in practice, which limits their widespread use. Most introductions assume a technical background in programming, mathematics, and machine learning. In this paper we offer a step-by-step tutorial on how to build POMDPs, run simulations using standard MATLAB routines, and fit these models to empirical data. We assume a minimal background in programming and mathematics, thoroughly explain all equations, and provide exemplar scripts that can be customized for both theoretical and empirical studies. Our goal is to provide the reader with the requisite background knowledge and practical tools to apply active inference to their own research. We also provide optional technical sections and several appendices, which offer the interested reader additional technical details. This tutorial should provide the reader with all the tools necessary to use these models and to follow emerging advances in active inference research.

Mismatch negativity (MMN) is a differential electrophysiological response measuring cortical adaptability to unpredictable stimuli. MMN is consistently attenuated in patients with psychosis. However, the genetics of MMN are uncharted, limiting the validation of MMN as a psychosis endophenotype. We therefore performed a transcriptome-wide association study of 728 individuals, which revealed two genes (FAM89A and ENGASE) whose expression in cortical tissues is associated with MMN. Enrichment analyses of neurodevelopmental expression signatures showed that genes associated with MMN tend to be overexpressed in frontal cortex during prenatal development but significantly downregulated in adulthood. In our Endophenotype Ranking Value calculation comparing MMN and three other candidate psychosis endophenotypes (lateral ventricular volume and two auditory-verbal learning measures), MMN was considerably superior. These results yield promising insights into sensory processing in the cortex and endorse the notion of MMN as a psychosis endophenotype.

Background There is growing interest in ultra-high field magnetic resonance imaging (MRI) in cognitive and clinical neuroscience studies. However, the benefits offered by higher field strength have not been evaluated in terms of effective connectivity and dynamic causal modelling (DCM). New method In this study, we address the validity of DCM for 7T functional MRI data at two levels. First, we evaluate the predictive validity of DCM estimates based upon 3T and 7T in terms of reproducibility. Second, we assess improvements in the efficiency of DCM estimates at 7T, in terms of the entropy of the posterior distribution over model parameters (i.e., information gain). Results Using empirical data recorded during fist-closing movements with 3T and 7T fMRI, we found a high reproducibility of average connectivity and condition-specific changes in connectivity – as quantified by the intra-class correlation coefficient (ICC = 0.862 and 0.936, respectively). Furthermore, we found that the posterior entropy of 7T parameter estimates was substantially less than that of 3T parameter estimates; suggesting the 7T data are more informative – and furnish more efficient estimates. Compared with existing methods In the framework of DCM, we treated field-dependent parameters for the BOLD signal model as free parameters, to accommodate fMRI data at 3T and 7T. In addition, we made the resting blood volume fraction a free parameter, because different brain regions can differ in their vascularization. Conclusions In this paper, we showed DCM enables one to infer changes in effective connectivity from 7T data reliably and efficiently.

The central and autonomic nervous systems can be defined by their anatomical, functional and neurochemical characteristics, but neither functions in isolation. For example, fundamental components of autonomically mediated homeostatic processes are afferent interoceptive signals reporting the internal state of the body and efferent signals acting on interoceptive feedback assimilated by the brain. Recent predictive coding (interoceptive inference) models formulate interoception in terms of embodied predictive processes that support emotion and selfhood. We propose interoception may serve as a way to investigate holistic nervous system function and dysfunction in disorders of brain, body and behaviour. We appeal to predictive coding and (active) interoceptive inference, to describe the homeostatic functions of the central and autonomic nervous systems. We do so by (i) reviewing the active inference formulation of interoceptive and autonomic function, (ii) survey clinical applications of this formulation and (iii) describe how it offers an integrative approach to human physiology; particularly, interactions between the central and peripheral nervous systems in health and disease.

Although the relationship between resting-state functional connectivity and task-related activity has been addressed, the relationship between task and resting-state directed or effective connectivity – and its behavioral concomitants – remains elusive. We evaluated effective connectivity under an N-back working memory task in 24 participants using stochastic dynamic causal modelling (DCM) of 7 T fMRI data. We repeated the analysis using resting-state data, from the same subjects, to model connectivity among the same brain regions engaged by the N-back task. This allowed us to: (i) examine the relationship between intrinsic (task-independent) effective connectivity during resting (Arest) and task states (Atask), (ii) cluster phenotypes of task-related changes in effective connectivity (Btask) across participants, (iii) identify edges (Btask) showing high inter-individual effective connectivity differences and (iv) associate reaction times with the similarity between Btask and Arest in these edges. We found a strong correlation between Arest and Atask over subjects but a marked difference between Btask and Arest. We further observed a strong clustering of individuals in terms of Btask, which was not apparent in Arest. The task-related effective connectivity Btask varied highly in the edges from the parietal to the frontal lobes across individuals, so the three groups were clustered mainly by the effective connectivity within these networks. The similarity between Btask and Arest at the edges from the parietal to the frontal lobes was positively correlated with 2-back reaction times. This result implies that a greater change in context-sensitive coupling – from resting-state connectivity – is associated with faster reaction times. In summary, task-dependent connectivity endows resting-state connectivity with a context sensitivity, which predicts the speed of information processing during the N-back task.

The term 'stress' - coined in 1936 - has many definitions, but until now has lacked a theoretical foundation. Here we present an information-theoretic approach - based on the 'free energy principle' - defining the essence of stress; namely, uncertainty. We address three questions: What is uncertainty? What does it do to us? What are our resources to master it? Mathematically speaking, uncertainty is entropy or 'expected surprise'. The 'free energy principle' rests upon the fact that self-organizing biological agents resist a tendency to disorder and must therefore minimize the entropy of their sensory states. Applied to our everyday life, this means that we feel uncertain, when we anticipate that outcomes will turn out to be something other than expected - and that we are unable to avoid surprise. As all cognitive systems strive to reduce their uncertainty about future outcomes, they face a critical constraint: Reducing uncertainty requires cerebral energy. The characteristic of the vertebrate brain to prioritize its own high energy is captured by the notion of the 'selfish brain'. Accordingly, in times of uncertainty, the selfish brain demands extra energy from the body. If, despite all this, the brain cannot reduce uncertainty, a persistent cerebral energy crisis may develop, burdening the individual by 'allostatic load' that contributes to systemic and brain malfunction (impaired memory, atherogenesis, diabetes and subsequent cardio- and cerebrovascular events). Based on the basic tenet that stress originates from uncertainty, we discuss the strategies our brain uses to avoid surprise and thereby resolve uncertainty.

The development of large-scale network models that infer the effective (directed) connectivity among neuronal populations from neuroimaging data represents a key challenge for computational neuroscience. Dynamic causal models (DCMs) of neuroimaging and electrophysiological data are frequently used for inferring effective connectivity but are presently restricted to small graphs (typically up to 10 regions) in order to keep model inversion computationally feasible. Here, we present a novel variant of DCM for functional magnetic resonance imaging (fMRI) data that is suited to assess effective connectivity in large (whole-brain) networks. The approach rests on translating a linear DCM into the frequency domain and reformulating it as a special case of Bayesian linear regression. This paper derives regression DCM (rDCM) in detail and presents a variational Bayesian inversion method that enables extremely fast inference and accelerates model inversion by several orders of magnitude compared to classical DCM. Using both simulated and empirical data, we demonstrate the face validity of rDCM under different settings of signal-to-noise ratio (SNR) and repetition time (TR) of fMRI data. In particular, we assess the potential utility of rDCM as a tool for whole-brain connectomics by challenging it to infer effective connection strengths in a simulated whole-brain network comprising 66 regions and 300 free parameters. Our results indicate that rDCM represents a computationally highly efficient approach with promising potential for inferring whole-brain connectivity from individual fMRI data., NeuroImage, 155, ISSN:1053-8119, ISSN:1095-9572

Effective connectivity is commonly assessed using blood oxygenation level-dependent (BOLD) signals. In (Havlicek et al., 2015), we presented a novel, physiologically informed dynamic causal model (P-DCM) that extends current generative models. We demonstrated the improvements afforded by P-DCM in terms of the ability to model commonly observed neuronal and vascular transients in single regions. Here, we assess the ability of the novel and previous DCM variants to estimate effective connectivity among a network of five ROIs driven by a visuo-motor task. We demonstrate that connectivity estimates depend sensitively on the DCM used, due to differences in the modeling of hemodynamic response transients; such as the post-stimulus undershoot or adaptation during stimulation. In addition, using a novel DCM for arterial spin labeling (ASL) fMRI that measures BOLD and CBF signals simultaneously, we confirmed our findings (by using the BOLD data alone and in conjunction with CBF). We show that P-DCM provides better estimates of effective connectivity, regardless of whether it is applied to BOLD data alone or to ASL time-series, and that all new aspects of P-DCM (i.e. neuronal, neurovascular, hemodynamic components) constitute an improvement compared to those in the previous DCM variants. In summary, (i) accurate modeling of fMRI response transients is crucial to obtain valid effective connectivity estimates and (ii) any additional hemodynamic data, such as provided by ASL, increases the ability to disambiguate neuronal and vascular effects present in the BOLD signal.

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior.

Neural models describe brain activity at different scales, ranging from single cells to whole brain networks. Here, we attempt to reconcile models operating at the microscopic (compartmental) and mesoscopic (neural mass) scales to analyse data from microelectrode recordings of intralaminar neural activity. Although these two classes of models operate at different scales, it is relatively straightforward to create neural mass models of ensemble activity that are equipped with priors obtained after fitting data generated by detailed microscopic models. This provides generative (forward) models of measured neuronal responses that retain construct validity in relation to compartmental models. We illustrate our approach using cross spectral responses obtained from V1 during a visual perception paradigm that involved optogenetic manipulation of the basal forebrain. We find that the resulting neural mass model can distinguish between activity in distinct cortical layers – both with and without optogenetic activation – and that cholinergic input appears to enhance (disinhibit) superficial layer activity relative to deep layers. This is particularly interesting from the perspective of predictive coding, where neuromodulators are thought to boost prediction errors that ascend the cortical hierarchy., Highlights • Biophysical mean field model fitted to data from different cortical layers. • Neural mass model combined with a laminar-specific forward model. • Fitted V1 data with and without optogenetic activation of the basal forebrain. • Test of Predictive Coding based on the role of neuromodulation. • Increase in prediction error activity due to cholinergic effects.

In this opinion paper, we describe a combined view of functional and effective brain connectivity along with the free-energy principle for investigating persistent disruptions in brain networks of patients with focal epilepsy. These changes are likely reflected in effective connectivity along the cortical hierarchy and construct the basis of increased local functional connectivity in focal epilepsy. We propose a testable framework based on dynamic causal modelling and functional connectivity analysis with the capacity of explaining commonly observed connectivity changes during interictal periods. We then hypothesise their possible relation with disrupted free-energy minimisation in the Bayesian brain. This may offer a new approach for neuroimaging to specifically develop and address hypotheses regarding the network pathomechanisms underlying epileptic phenotypes., Highlights • A combined view of functional brain connectivity and dynamic causal modeling of persistent networks changes in focal epilepsy. • Increased functional connectivity in focal epilepsy is likely reflected in effective connectivity of cortical hierarchy. • A testable framework based on dynamic causal modeling and functional connectivity analysis during interictal periods.

Highlights • Optimal behaviour is quintessentially belief based. • Behaviour can be described as optimising expected free energy. • Expected free energy entails pragmatic and epistemic value. • Habits are learned by observing one’s own goal directed behaviour. • Habits are then selected online during active inference., This paper offers an active inference account of choice behaviour and learning. It focuses on the distinction between goal-directed and habitual behaviour and how they contextualise each other. We show that habits emerge naturally (and autodidactically) from sequential policy optimisation when agents are equipped with state-action policies. In active inference, behaviour has explorative (epistemic) and exploitative (pragmatic) aspects that are sensitive to ambiguity and risk respectively, where epistemic (ambiguity-resolving) behaviour enables pragmatic (reward-seeking) behaviour and the subsequent emergence of habits. Although goal-directed and habitual policies are usually associated with model-based and model-free schemes, we find the more important distinction is between belief-free and belief-based schemes. The underlying (variational) belief updating provides a comprehensive (if metaphorical) process theory for several phenomena, including the transfer of dopamine responses, reversal learning, habit formation and devaluation. Finally, we show that active inference reduces to a classical (Bellman) scheme, in the absence of ambiguity.

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin–Huxley neuronal networks with Newman–Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus – and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity – and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.

This Opinion article considers the implications for functional anatomy of how we represent temporal structure in our exchanges with the world. It offers a theoretical treatment that tries to make sense of the architectural principles seen in mammalian brains. Specifically, it considers a factorisation between representations of temporal succession and representations of content or, heuristically, a segregation into when and what. This segregation may explain the central role of the hippocampus in neuronal hierarchies while providing a tentative explanation for recent observations of how ordinal sequences are encoded. The implications for neuroanatomy and physiology may have something important to say about how self-organised cell assembly sequences enable the brain to exhibit purposeful behaviour that transcends the here and now.

Seizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5–10 min compared to approximately 1–2 h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated., Highlights • We describe a DCM procedure that provides efficient inversion of seizure activity. • Similar accuracy but substantially more efficient compared to standard DCM methods. • Physiological fluctuations over different timescales can be specified. • This scheme should contribute to understanding seizure activity using DCM.

Contemporary psychiatry faces major challenges. Its syndrome-based disease classifi cation is not based on mechanisms and does not guide treatment, which largely depends on trial and error. The development of therapies is hindered by ignorance of potential beneficiary patient subgroups. Neuroscientific and genetics research have yet to affect disease definitions or contribute to clinical decision making. In this challenging setting, what should psychiatric research focus on? In two companion papers, we present a list of problems nominated by clinicians and researchers from different disciplines as candidates for future scientific investigation of mental disorders. These problems are loosely grouped into challenges concerning nosology and diagnosis (this Personal View) and problems related to pathogenesis and aetiology (in the companion Personal View). Motivated by successful examples in other disciplines, particularly the list of Hilbert's problems in mathematics, this subjective and eclectic list of priority problems is intended for psychiatric researchers, helping to re-focus existing research and providing perspectives for future psychiatric science.

This is the second of two companion papers proposing priority problems for research on mental disorders. Whereas the first paper focuses on questions of nosology and diagnosis, this Personal View concerns pathogenesis and aetiology of psychiatric diseases. We hope that this (non-exhaustive and subjective) list of problems, nominated by scientists and clinicians from different fields and institutions, provides guidance and perspectives for choosing future directions in psychiatric science.

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors – derived from dynamic causal modelling (DCM) of EEG data – for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters – as measured by the Kullback-Leibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proof-of-principle that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation.

Dynamic causal modeling (DCM) is a Bayesian framework for inferring effective connectivity among brain regions from neuroimaging data. While the validity of DCM has been investigated in various previous studies, the reliability of DCM parameter estimates across sessions has been examined less systematically. Here, we report results of a software comparison with regard to test-retest reliability of DCM for fMRI, using a challenging scenario where complex models with many parameters were applied to relatively few data points. Specifically, we examined the reliability of different DCM implementations (in terms of the intra-class correlation coefficient, ICC) based on fMRI data from 35 human subjects performing a simple motor task in two separate sessions, one month apart. We constructed DCMs of motor regions with fair to excellent reliability of conventional activation measures. Using classical DCM (cDCM) in SPM5, we found that the test-retest reliability of DCM results was high, both concerning the model evidence (ICC=0.94) and the model parameter estimates (median ICC=0.47). However, when using a more recent DCM version (DCM10 in SPM8), test-retest reliability was reduced notably. Analyses indicated that, in our particular case, the prior distributions played a crucial role in this change in reliability across software versions. Specifically, when using cDCM priors for model inversion in DCM10, this not only restored reliability but yielded even better results than in cDCM. Analyzing each component of the objective function in DCM, we found a selective change in the reliability of posterior mean estimates. This suggests that tighter regularization afforded by cDCM priors reduces the possibility of local extrema in the objective function. We conclude this paper with an outlook to ongoing developments for overcoming the software-dependency of reliability observed in this study, including global optimization and empirical Bayesian procedures.

Psychostimulants, such as methylphenidate, are thought to improve information processing in motivation-reward and attention-activation networks by enhancing the effects of more relevant signals and suppressing those of less relevant ones; however the nature of such reciprocal influences remains poorly understood. To explore this question, we tested the effect of methylphenidate on performance and associated brain activity in the Anticipation, Conflict, Reward (ACR) task. Sixteen healthy adult volunteers, ages 21-45, were scanned twice using functional magnetic resonance imaging (fMRI) as they performed the ACR task under placebo and methylphenidate conditions. A three-way repeated measures analysis of variance, with cue (reward vs. non-reward), target (congruent vs. incongruent) and medication condition (methylphenidate vs. placebo) as the factors, was used to analyze behaviors on the task. Blood oxygen level dependent (BOLD) signals, reflecting task-related neural activity, were evaluated using linear contrasts. Participants exhibited significantly greater accuracy in the methylphenidate condition than the placebo condition. Compared with placebo, the methylphenidate condition also was associated with lesser task-related activity in components of attention-activation systems irrespective of the reward cue, and less task-related activity in components of the reward-motivation system, particularly the insula, during reward trials irrespective of target difficulty. These results suggest that methylphenidate enhances task performance by improving efficiency of information processing in both reward-motivation and in attention-activation systems.

Executive control of attention regulates our thoughts, emotion and behavior. Individual differences in executive control are associated with task-related differences in brain activity. But it is unknown whether attentional differences depend on endogenous (resting state) brain activity and to what extent regional fluctuations and functional connectivity contribute to individual variations in executive control processing. Here, we explored the potential contribution of intrinsic brain activity to executive control by using resting-state functional magnetic resonance imaging (fMRI). Using the amplitude of low-frequency fluctuations (ALFF) as an index of spontaneous brain activity, we found that ALFF in the right precuneus (PCUN) and the medial part of left superior frontal gyrus (msFC) was significantly correlated with the efficiency of executive control processing. Crucially, the strengths of functional connectivity between the right PCUN/left msFC and distributed brain regions, including the left fusiform gyrus, right inferior frontal gyrus, left superior frontal gyrus and right precentral gyrus, were correlated with individual differences in executive performance. Together, the ALFF and functional connectivity accounted for 67% of the variability in behavioral performance. Moreover, the strength of functional connectivity between specific regions could predict more individual variability in executive control performance than regionally specific fluctuations. In conclusion, our findings suggest that spontaneous brain activity may reflect or underpin executive control of attention. It will provide new insights into the origins of inter-individual variability in human executive control processing.

In this paper, we revisit the problem of Bayesian model selection (BMS) at the group level. We originally addressed this issue in Stephan et al. (2009) , where models are treated as random effects that could differ between subjects, with an unknown population distribution. Here, we extend this work, by (i) introducing the Bayesian omnibus risk (BOR) as a measure of the statistical risk incurred when performing group BMS, (ii) highlighting the difference between random effects BMS and classical random effects analyses of parameter estimates, and (iii) addressing the problem of between group or condition model comparisons. We address the first issue by quantifying the chance likelihood of apparent differences in model frequencies. This leads to the notion of protected exceedance probabilities. The second issue arises when people want to ask “whether a model parameter is zero or not” at the group level. Here, we provide guidance as to whether to use a classical second-level analysis of parameter estimates, or random effects BMS. The third issue rests on the evidence for a difference in model labels or frequencies across groups or conditions. Overall, we hope that the material presented in this paper finesses the problems of group-level BMS in the analysis of neuroimaging and behavioural data.

Reward outcome signalling in the sensory cortex is held as important for linking stimuli to their consequences and for modulating perceptual learning in response to incentives. Evidence for reward outcome signalling has been found in sensory regions including the visual, auditory and somatosensory cortices across a range of different paradigms, but it is unknown whether the population of neurons signalling rewarding outcomes are the same as those processing predictive stimuli. We addressed this question using a multivariate analysis of high-resolution functional magnetic resonance imaging (fMRI), in a task where subjects were engaged in instrumental learning with visual predictive cues and auditory signalled reward feedback. We found evidence that outcome signals in sensory regions localise to the same areas involved in stimulus processing. These outcome signals are non-specific and we show that the neuronal populations involved in stimulus representation are not their exclusive target, in keeping with theoretical models of value learning. Thus, our results reveal one likely mechanism through which rewarding outcomes are linked to predictive sensory stimuli, a link that may be key for both reward and perceptual learning., Highlights • Rewarding outcomes reactivate sensory regions involved in stimulus representation. • Within these regions reward is not directed specifically to stimulus-coding neurons. • This resembles a teaching signal predicted by reinforcement learning models.

Lohmann et al. (this issue) make three unremarkable observations about model selection and use them to critique dynamic causal modelling—a Bayesian model selection procedure based on causal models of dynamical systems (Marreiros et al., 2010). In this response, we unpack their misconceptions and try to answer their questions.

Mesial temporal lobe epilepsy (mTLE) is the most prevalent form of focal epilepsy, and hippocampal sclerosis (HS) is considered the most frequent associated pathological finding. Recent connectivity studies have shown that abnormalities, either structural or functional, are not confined to the affected hippocampus, but can be found in other connected structures within the same hemisphere, or even in the contralesional hemisphere. Despite the role of hippocampus in memory functions, most of these studies have explored network properties at resting state, and in some cases compared connectivity values with neuropsychological memory scores. Here, we measured magnetoencephalographic responses during verbal working memory (WM) encoding in left mTLE patients and controls, and compared their effective connectivity within a frontotemporal network using dynamic causal modelling. Bayesian model comparison indicated that the best model included bilateral, forward and backward connections, linking inferior temporal cortex (ITC), inferior frontal cortex (IFC), and the medial temporal lobe (MTL). Test for differences in effective connectivity revealed that patients exhibited decreased ipsilesional MTL-ITC backward connectivity, and increased bidirectional IFC-MTL connectivity in the contralesional hemisphere. Critically, a negative correlation was observed between these changes in patients, with decreases in ipsilesional coupling among temporal sources associated with increases contralesional frontotemporal interactions. Furthermore, contralesional frontotemporal interactions were inversely related to task performance and level of education. The results demonstrate that unilateral sclerosis induced local and remote changes in the dynamic organization of a distributed network supporting verbal WM. Crucially, pre-(peri) morbid factors (educational level) were reflected in both cognitive performance and (putative) compensatory changes in physiological coupling., Highlights ► Effects of hippocampal sclerosis (HS) on effective connectivity were evaluated. ► HS induced a network adjustment in the ipsilesional and the contralesional hemisphere. ► Strength in ipsilesional and contralesional couplings was negatively related. ► Contralesional couplings were inversely related to performance and level of education. ► These findings support the notion that network alterations underlie cognitive decline.

Highlights ► A brief introduction to the analysis of directed connectivity in brain networks. ► An overview of advances in Granger causality and dynamic causal modelling. ► A comparative evaluation of both approaches in terms of their pros and cons., This review considers state-of-the-art analyses of functional integration in neuronal macrocircuits. We focus on detecting and estimating directed connectivity in neuronal networks using Granger causality (GC) and dynamic causal modelling (DCM). These approaches are considered in the context of functional segregation and integration and — within functional integration — the distinction between functional and effective connectivity. We review recent developments that have enjoyed a rapid uptake in the discovery and quantification of functional brain architectures. GC and DCM have distinct and complementary ambitions that are usefully considered in relation to the detection of functional connectivity and the identification of models of effective connectivity. We highlight the basic ideas upon which they are grounded, provide a comparative evaluation and point to some outstanding issues.

Conventionally, set-level inference on statistical parametric maps (SPMs) is based on the topological features of an excursion set above some threshold—for example, the number of clusters or Euler characteristic. The expected Euler characteristic—under the null hypothesis—can be predicted from an intrinsic measure or volume of the SPM, such as the resel counts or the Lipschitz–Killing curvatures (LKC). We propose a new approach that performs a null hypothesis omnibus test on an SPM, by testing whether its intrinsic volume (described by LKC coefficients) is different from the volume of the underlying residual fields: intuitively, whether the number of peaks in the statistical field (testing for signal) and the residual fields (noise) are consistent or not. Crucially, this new test requires no arbitrary feature-defining threshold but is nevertheless sensitive to distributed or spatially extended patterns. We show the similarities between our approach and conventional topological inference—in terms of false positive rate control and sensitivity to treatment effects—in two and three dimensional simulations. The test consistently improves on classical approaches for moderate (> 20) degrees of freedom. We also demonstrate the application to real data and illustrate the comparison of the expected and observed Euler characteristics over the complete threshold range., Highlights ► We calculate SPM intrinsic volume through the Euler Characteristic over thresholds. ► We compare these volume estimates to those obtained using classical methods. ► A multivariate test on these volume estimates gives a threshold free test of the null.

Parkinson's disease is a common and debilitating condition, caused by aberrant activity in a complex basal ganglia–thalamocortical circuit. Therapeutic advances rely on characterising interactions in this circuit. However, recording electrophysiological responses over the entire circuit is impractical. Dynamic causal modelling offers large-scale models of predictive value based on a limited or partial sampling of complex networks. Using dynamic causal modelling, we determined the network changes underlying the pathological excess of beta oscillations that characterise the Parkinsonian state. We modelled data from five patients undergoing surgery for deep brain stimulation of more than one target. We found that connections to and from the subthalamic nucleus were strengthened and promoted beta synchrony, in the untreated compared to the treated Parkinsonian state. Dynamic causal modelling was able to replicate the effects of lesioning this nucleus and may provide a new means of directing the search for therapeutic targets., Highlights ► Novel model of basal ganglia-cortical system based on data from Parkinson’s patients. ► Model exposes criticality of connections to and from subthalamic nucleus in PD. ► Model able to replicate the effects of known surgical interventions in PD. ► Allows in silico tests of candidate therapeutic interventions in circuit disorders.

In Kilner et al. [Kilner, J.M., Kiebel, S.J., Friston, K.J., 2005. Applications of random field theory to electrophysiology. Neurosci. Lett. 374, 174–178.] we described a fairly general analysis of induced responses—in electromagnetic brain signals—using the summary statistic approach and statistical parametric mapping. This involves localising induced responses—in peristimulus time and frequency—by testing for effects in time–frequency images that summarise the response of each subject to each trial type. Conventionally, these time–frequency summaries are estimated using post‐hoc averaging of epoched data. However, post‐hoc averaging of this sort fails when the induced responses overlap or when there are multiple response components that have variable timing within each trial (for example stimulus and response components associated with different reaction times). In these situations, it is advantageous to estimate response components using a convolution model of the sort that is standard in the analysis of fMRI time series. In this paper, we describe one such approach, based upon ordinary least squares deconvolution of induced responses to input functions encoding the onset of different components within each trial. There are a number of fundamental advantages to this approach: for example; (i) one can disambiguate induced responses to stimulus onsets and variably timed responses; (ii) one can test for the modulation of induced responses—over peristimulus time and frequency—by parametric experimental factors and (iii) one can gracefully handle confounds—such as slow drifts in power—by including them in the model. In what follows, we consider optimal forms for convolution models of induced responses, in terms of impulse response basis function sets and illustrate the utility of deconvolution estimators using simulated and real MEG data., Highlights ► We propose a new approach to analysis of induced responses in M/EEG. ► The General Linear Model is used to model continuous power as in fMRI 1st-level. ► The results can be presented as conventional time–frequency images. ► Our method is better for experiments with variable timing and overlapping events.