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Under the Bayesian brain hypothesis, behavioral variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioral preferences when confronted with similar choices. For example, greedy preferences are a consequence of confident (or precise) beliefs over certain outcomes. Here, we offer an alternative account of behavioral variability using Rényi divergences and their associated variational bounds. Rényi bounds are analogous to the variational free energy (or evidence lower bound) and can be derived under the same assumptions. Importantly, these bounds provide a formal way to establish behavioral differences through an α parameter, given fixed priors. This rests on changes in α that alter the bound (on a continuous scale), inducing different posterior estimates and consequent variations in behavior. Thus, it looks as if individuals have different priors and have reached different conclusions. More specifically, α → 0 + optimization constrains the variational posterior to be positive whenever the true posterior is positive. This leads to mass-covering variational estimates and increased variability in choice behavior. Furthermore, α → + ∞ optimization constrains the variational posterior to be zero whenever the true posterior is zero. This leads to mass-seeking variational posteriors and greedy preferences. We exemplify this formulation through simulations of the multiarmed bandit task. We note that these α parameterizations may be especially relevant (i.e., shape preferences) when the true posterior is not in the same family of distributions as the assumed (simpler) approximate density, which may be the case in many real-world scenarios. The ensuing departure from vanilla variational inference provides a potentially useful explanation for differences in behavioral preferences of biological (or artificial) agents under the assumption that the brain performs variational Bayesian inference. [ABSTRACT FROM AUTHOR]

Active inference offers a first principle account of sentient behavior, from which special and important cases—for example, reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design—can be derived. Active inference finesses the exploitation-exploration dilemma in relation to prior preferences by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this letter, we consider a sophisticated kind of active inference using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about "what would happen if I did that" to "what I would believe about what would happen if I did that." The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states as opposed to states per se. We illustrate the competence of this scheme using numerical simulations of deep decision problems. [ABSTRACT FROM AUTHOR]

This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimized by both neural activity and plasticity. We show that such cost functions can be cast as a variational bound on model evidence under an implicit generative model. Using generative models based on partially observed Markov decision processes (POMDP), we show that neural activity and plasticity perform Bayesian inference and learning, respectively, by maximizing model evidence. Using mathematical and numerical analyses, we establish the formal equivalence between neural network cost functions and variational free energy under some prior beliefs about latent states that generate inputs. These prior beliefs are determined by particular constants (e.g., thresholds) that define the cost function. This means that the Bayes optimal encoding of latent or hidden states is achieved when the network's implicit priors match the process that generates its inputs. This equivalence is potentially important because it suggests that any hyperparameter of a neural network can itself be optimized—by minimization with respect to variational free energy. Furthermore, it enables one to characterize a neural network formally, in terms of its prior beliefs. [ABSTRACT FROM AUTHOR]

Timing emerges from a hierarchy of computations ranging from early encoding of physical duration (time sensation) to abstract time representations (time perception) suitable for storage and decisional processes. However, the neural basis of the perceptual experience of time remains elusive. To address this, we dissociate brain activity uniquely related to lower-level sensory and higher-order perceptual timing operations, using event-related fMRI. Participants compared subsecond (500 msec) sinusoidal gratings drifting with constant velocity (standard) against two probe stimuli: (1) control gratings drifting at constant velocity or (2) accelerating gratings, which induced illusory shortening of time. We tested two probe intervals: a 500-msec duration (Short) and a longer duration required for an accelerating probe to be perceived as long as the standard (Long—individually determined). On each trial, participants classified the probe as shorter or longer than the standard. This allowed for comparison of trials with an "Objective" (physical) or "Subjective" (perceived) difference in duration, based on participant classifications. Objective duration revealed responses in bilateral early extrastriate areas, extending to higher visual areas in the fusiform gyrus (at more lenient thresholds). By contrast, Subjective duration was reflected by distributed responses in a cortical/subcortical areas. This comprised the left superior frontal gyrus and the left cerebellum, and a wider set of common timing areas including the BG, parietal cortex, and posterior cingulate cortex. These results suggest two functionally independent timing stages: early extraction of duration information in sensory cortices and Subjective experience of duration in a higher-order cortical–subcortical timing areas. [ABSTRACT FROM AUTHOR]

To exhibit social intelligence, animals have to recognize whom they are communicating with. One way to make this inference is to select among internal generative models of each conspecific who may be encountered. However, these models also have to be learned via some form of Bayesian belief updating. This induces an interesting problem: When receiving sensory input generated by a particular conspecific, how does an animal know which internal model to update? We consider a theoretical and neurobiologically plausible solution that enables inference and learning of the processes that generate sensory inputs (e.g., listening and understanding) and reproduction of those inputs (e.g., talking or singing), under multiple generative models. This is based on recent advances in theoretical neurobiology—namely, active inference and post hoc (online) Bayesian model selection. In brief, this scheme fits sensory inputs under each generative model. Model parameters are then updated in proportion to the probability that each model could have generated the input (i.e., model evidence). The proposed scheme is demonstrated using a series of (real zebra finch) birdsongs, where each song is generated by several different birds. The scheme is implemented using physiologically plausible models of birdsong production. We show that generalized Bayesian filtering, combined with model selection, leads to successful learning across generative models, each possessing different parameters. These results highlight the utility of having multiple internal models when making inferences in social environments with multiple sources of sensory information. [ABSTRACT FROM AUTHOR]

This paper characterizes impulsive behavior using a patch-leaving paradigm and active inference—a framework for describing Bayes optimal behavior. This paradigm comprises different environments (patches) with limited resources that decline over time at different rates. The challenge is to decide when to leave the current patch for another to maximize reward. We chose this task because it offers an operational characterization of impulsive behavior, namely, maximizing proximal reward at the expense of future gain. We use a Markov decision process formulation of active inference to simulate behavioral and electrophysiological responses under different models and prior beliefs. Our main finding is that there are at least three distinct causes of impulsive behavior, which we demonstrate by manipulating three different components of the Markov decision process model. These components comprise (i) the depth of planning, (ii) the capacity to maintain and process information, and (iii) the perceived value of immediate (relative to delayed) rewards. We show how these manipulations change beliefs and subsequent choices through variational message passing. Furthermore, we appeal to the process theories associated with this message passing to simulate neuronal correlates. In future work, we will use this scheme to identify the prior beliefs that underlie different sorts of impulsive behavior—and ask whether different causes of impulsivity can be inferred from the electrophysiological correlates of choice behavior. [ABSTRACT FROM AUTHOR]

To act upon the world, creatures must change continuous variables such as muscle length or chemical concentration. In contrast, decision making is an inherently discrete process, involving the selection among alternative courses of action. In this article, we consider the interface between the discrete and continuous processes that translate our decisions into movement in a Newtonian world—and how movement informs our decisions. We do so by appealing to active inference, with a special focus on the oculomotor system. Within this exemplar system, we argue that the superior colliculus is well placed to act as a discrete-continuous interface. Interestingly, when the neuronal computations within the superior colliculus are formulated in terms of active inference, we find that many aspects of its neuroanatomy emerge from the computations it must perform in this role. [ABSTRACT FROM AUTHOR]

This article offers a formal account of curiosity and insight in terms of active (Bayesian) inference. It deals with the dual problem of inferring states of the world and learning its statistical structure. In contrast to current trends in machine learning (e.g., deep learning), we focus on how people attain insight and understanding using just a handful of observations, which are solicited through curious behavior. We use simulations of abstract rule learning and approximate Bayesian inference to show that minimizing (expected) variational free energy leads to active sampling of novel contingencies. This epistemic behavior closes explanatory gaps in generative models of the world, thereby reducing uncertainty and satisfying curiosity. We then move from epistemic learning to model selection or structure learning to show how abductive processes emerge when agents test plausible hypotheses about symmetries (i.e., invariances or rules) in their generative models. The ensuing Bayesian model reduction evinces mechanisms associated with sleep and has all the hallmarks of "aha" moments. This formulation moves toward a computational account of consciousness in the pre-Cartesian sense of sharable knowledge (i.e., con: "together"; scire: "to know"). [ABSTRACT FROM AUTHOR]

This article describes a process theory based on active inference and belief propagation. Starting from the premise that all neuronal processing (and action selection) can be explained by maximizing Bayesian model evidence--or minimizing variational free energy--we ask whether neuronal responses can be described as a gradient descent on variational free energy.Using a standard (Markov decision process) generativemodel,we derive the neuronal dynamics implicit in this description and reproduce a remarkable range of well-characterized neuronal phenomena. These include repetition suppression, mismatch negativity, violation responses, place-cell activity, phase precession, theta sequences, theta-gamma coupling, evidence accumulation, race-to-bound dynamics, and transfer of dopamine responses. Furthermore, the (approximately Bayes' optimal) behavior prescribed by these dynamics has a degree of face validity, providing a formal explanation for reward seeking, context learning, and epistemic foraging. Technically, the fact that a gradient descent appears to be a valid description of neuronal activity means that variational free energy is a Lyapunov function for neuronal dynamics, which therefore conform to Hamilton's principle of least action. [ABSTRACT FROM AUTHOR]

This letter offers a computational account of Pavlovian conditioning in the cerebellum based on active inference and predictive coding. Using eyeblink conditioning as a canonical paradigm, we formulate a minimal generative model that can account for spontaneous blinking, startle responses, and (delay or trace) conditioning. We then establish the face validity of the model using simulated responses to unconditioned and conditioned stimuli to reproduce the sorts of behavior that are observed empirically. The scheme's anatomical validity is then addressed by associating variables in the predictive coding scheme with nuclei and neuronal populations to match the (extrinsic and intrinsic) connectivity of the cerebellar (eyeblink conditioning) system. Finally, we try to establish predictive validity by reproducing selective failures of delay conditioning, trace conditioning, and extinction using (simulated and reversible) focal lesions. Although rather metaphorical, the ensuing scheme can account for a remarkable range of anatomical and neurophysiological aspects of cerebellar circuitry--and the specificity of lesion-deficit mappings that have been established experimentally. From a computational perspective, this work shows how conditioning or learning can be formulated in terms of minimizing variational free energy (or maximizing Bayesian model evidence) using exactly the same principles that underlie predictive coding in perception. [ABSTRACT FROM AUTHOR]

The rubber hand illusion (RHI) paradigm--in which illusory bodily ownership is induced by synchronous tactile stimulation of a participant's (hidden) hand and a (visible) surrogate-- allows one to investigate how the brain resolves conflicting multisensory evidence during perceptual inference. To identify the functional anatomy of the RHI, we used multichannel EEG, acquired under three conditions of tactile stimulation. Evoked potentials were averaged from EEG signals registered to the timing of brushstrokes to the participant's hand. The participant's hand was stroked either in the absence of an artificial hand (REAL) or synchronously with an artificial hand, which either lay in an anatomically plausible (CONGRUENT) or impossible (INCONGRUENT) position. The illusion was reliably elicited in the CONGRUENT condition. For right-hand stimulation, significant differences between conditions emerged at the sensor level around 55 msec after the brushstroke at left frontal and right parietal electrodes. Response amplitudes were smaller for illusory (CONGRUENT) compared with non-illusory (INCONGRUENT and REAL) conditions in the contra-lateral perirolandic region (pre- and postcentral gyri), superior and inferior parietal lobule, whereas veridical perception of the artificial hand (INCONGRUENT) amplified responses at a scalp region overlying the contralateral postcentral gyrus and inferior parietal lobule compared with the remaining two conditions. Left-hand stimulation produced similar contralateral patterns. These results are consistent with predictive coding models of multisensory integration and may reflect the attenuation of somatosensory precision that is required to resolve perceptual hypotheses about conflicting multisensory input. [ABSTRACT FROM AUTHOR]

Deciding how much evidence to accumulate before making a decision is a problem we and other animals often face, but one that is not completely understood. This issue is particularly important because a tendency to sample less information (often known as reflection impulsivity) is a feature in several psychopathologies, such as psychosis. A formal understanding of information sampling may therefore clarify the computational anatomy of psychopathology. In this theoretical letter, we consider evidence accumulation in terms of active (Bayesian) inference using a generic model of Markov decision processes. Here, agents are equipped with beliefs about their own behavior--in this case, that they will make informed decisions. Normative decision making is then modeled using variational Bayes to minimize surprise about choice outcomes. Under this scheme, different facets of belief updating map naturally onto the functional anatomy of the brain (at least at a heuristic level). Of particular interest is the key role played by the expected precision of beliefs about control, which we have previously suggested may be encoded by dopaminergic neurons in the midbrain. We show that manipulating expected precision strongly affects how much information an agent characteristically samples, and thus provides a possible link between impulsivity and dopaminergic dysfunction. Our study therefore represents a step toward understanding evidence accumulation in terms of neurobiologically plausible Bayesian inference and may cast light on why this process is disordered in psychopathology. [ABSTRACT FROM AUTHOR]

In this work, we show that electrophysiological responses during pitch perception are best explained by distributed activity in a hierarchy of cortical sources and, crucially, that the effective connectivity between these sources is modulated with pitch strength. Local field potentials were recorded in two subjects from primary auditory cortex and adjacent auditory cortical areas along the axis of Heschl's gyrus (HG) while they listened to stimuli of varying pitch strength. Dynamic causal modeling was used to compare system architectures that might explain the recorded activity. The data show that representation of pitch requires an interaction between nonprimary and primary auditory cortex along HG that is consistent with the principle of predictive coding. [ABSTRACT FROM AUTHOR]

Most experiments on the ''neural correlates of consciousness'' employ stimulus reportability as an operational definition of what is consciously perceived. The interpretation of such experiments therefore depends critically on understanding the neural basis of stimulus reportability. Using a high volume of fMRI data, we investigated the neural correlates of stimulus reportability using a partial report object detection paradigm. Subjects were presented with a random array of circularly arranged disc-stimuli and were cued, after variable delays (following stimulus offset), to report the presence or absence of a disc at the cued location, using variable motor actions. By uncoupling stimulus processing, decision, and motor response, we were able to use signal detection theory to deconstruct the neural basis of stimulus reportability. We show that retinotopically specific responses in the early visual cortex correlate with stimulus processing but not decision or report; a network of parietal/temporal regions correlates with decisions but not stimulus presence, whereas classical motor regions correlate with report. These findings provide a basic framework for understanding the neural basis of stimulus reportability without the theoretical burden of presupposing a relationship between reportability and consciousness. [ABSTRACT FROM AUTHOR]

Previous studies of patients with phonological and surface alexia have demonstrated a double dissociation between the reading of pseudo words and words with atypical spelling-to-sound relationships. A corresponding double dissociation in the neuronal activation patterns for pseudo words and exception words has not, however, been consistently demonstrated in normal subjects. Motivated by the literature on acquired alexia, the present study contrasted pseudo words to exception words and explored how neuronal interactions within the reading system are inf luenced by word type. Functional magnetic resonance imaging was used to measure neuronal responses during reading in 22 healthy volunteers. The direct comparison of reading pseudo words and exception words revealed a double dissociation within the left frontal cortex. Pseudo words preferentially increased left dorsal premotor activation, whereas exception words preferentially increased left pars triangularis activation. Critically, these areas correspond to those previously associated with phonological and semantic processing, respectively. Word-type dependent interactions between brain areas were then investigated using dynamic causal modeling. This revealed that increased activation in the dorsal premotor cortex for pseudo words was associated with a selective increase in effective connectivity from the posterior fusiform gyrus. In contrast, increased activation in the pars triangularis for exception words was associated with a selective increase in effective connectivity from the anterior fusiform gyrus. The present investigation is the first to identify distinct neuronal mechanisms for semantic and phonological contributions to reading. [ABSTRACT FROM AUTHOR]

In this study, we combined functional magnetic resonance imaging (fMRI) and dynamic causal modeling (DCM) to investigate whether object category effects in the occipital and temporal cortex are mediated by inputs from early visual cortex or parietal regions. Resolving this issue may provide anatomical constraints on theories of category specificity— which make different assumptions about the underlying neurophysiology. The data were acquired by Ishai, Ungerleider, Martin, Schouten, and Haxby (1999, 2000) and provided by the National fMRI Data Center (http://www.fmridc.org). The original authors used a conventional analysis to estimate differential effects in the occipital and temporal cortex in response to pictures of chairs, faces, and houses. We extended this approach by estimating neuronal interactions that mediate category effects using DCM. DCM uses a Bayesian framework to estimate and make inferences about the influence that one region exerts over another and how this is affected by experimental changes. DCM differs from previous approaches to brain connectivity, such as multivariate autoregressive models and structural equation modeling, as it assumes that the observed hemodynamic responses are driven by experimental changes rather than endogenous noise. DCM therefore brings the analysis of brain connectivity much closer to the analysis of regionally specific effects usually applied to functional imaging data. We used DCM to estimate the influence that V3 and the superior/inferior parietal cortex exerted over category-responsive regions and how this was affected by the presentation of houses, faces, and chairs. We found that category effects in occipital and temporal cortex were mediated by inputs from early visual cortex. In contrast, the connectivity from the superior/inferior parietal area to the category-responsive areas was unaffected by the presentation of chairs, faces, or houses. These findings indicate that category effects in the occipital and temporal cortex can be mediated by bottom–up mechanisms—a finding that needs to be embraced by models of category specificity. [ABSTRACT FROM AUTHOR]

The effect of stimulus rate and its interaction with stimulus type on brain activity during reading was investigated using functional magnetic resonance imaging (fMRI). This (i) enabled the segregation of brain regions showing differential responses, (ii) identified the optimum experimental design parameters for maximizing sensitivity, and (iii) allowed us to evaluate further the sources of discrepancy between positron emission tomography (PET) and fMRI signals. The effect of visual word rate has already been investigated in a previous PET study. However, rate effects can be very different in PET and fMRI, as seen in previous studies of auditory word processing. In this work, we attempt to replicate rate-sensitive activations observed with PET using fMRI. Our objective was to characterize the discrepancies in regionally specific ratesensitive effects between the two imaging modalities. Subjects were presented with words and pseudowords at varying rates while performing a silent reading task. The analysis specifically identified regions showing (i) an effect of stimulus rate on brain activity during reading; (ii) modulation of this effect by word type; and (iii) increased activity during reading relative to rest, but with no dependence on stimulus rate. The results identified similar effects of rate for words and pseudowords (no interactions between rate and word type reached significance). Irrespective of word type, strong positive linear effects of rate (i.e., activity increasing with rate) were detected in visual areas, right superior temporal gyrus, and bilateral precentral gyrus. These findings replicate the results of the previous PET study, confirming that activation in regions associated with visual processing and response generation increases with the number of stimuli. Likewise, we detected rate-independent effects reported in the previous PET study in bilateral anterior middle temporal, inferior frontal, and superior parietal regions. These results differentiate the functionally specific responses in rate-dependent and rate-independent areas. However, for negative effects of rate, fMRI did not replicate the effects seen in PET, suggesting some form of hemodynamic "rectification." The discussion focuses on differences between evoked rCBF and BOLD signals. [ABSTRACT FROM AUTHOR]

We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive 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 modeling 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 measurements-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., Competing Interests: Competing Interests: The authors have declared that no competing interests exist., (© 2024 Massachusetts Institute of Technology.)

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature., Competing Interests: Competing Interests: The authors have declared that no competing interests exist., (© 2023 Massachusetts Institute of Technology.)

At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions-and analyses-of distributed brain responses: namely, functional segregation and integration . There are currently two main approaches to characterizing functional integration. The first is a mechanistic modeling of connectomics in terms of directed effective connectivity that mediates neuronal message passing and dynamics on neuronal circuits. The second phenomenological approach usually characterizes undirected functional connectivity (i.e., measurable correlations), in terms of intrinsic brain networks, self-organized criticality, dynamical instability, and so on. This paper describes a treatment of effective connectivity that speaks to the emergence of intrinsic brain networks and critical dynamics. It is predicated on the notion of Markov blankets that play a fundamental role in the self-organization of far from equilibrium systems. Using the apparatus of the renormalization group , we show that much of the phenomenology found in network neuroscience is an emergent property of a particular partition of neuronal states, over progressively coarser scales. As such, it offers a way of linking dynamics on directed graphs to the phenomenology of intrinsic brain networks., Competing Interests: Competing Interests: The authors have declared that no competing interests exist., (© 2020 Massachusetts Institute of Technology.)

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions., Competing Interests: Competing Interests: The authors have declared that no competing interests exist., (© 2020 Massachusetts Institute of Technology.)

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity . This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM-with functional connectivity priors-is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper., Competing Interests: Competing Interests: The authors have declared that no competing interests exist.