Network discovery with DCM
Open accessAbstract
This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity. This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series. The implicit adjacency matrix specifies the form of the network (e.g., cyclic or acyclic) and its graph-theoretical attributes (e.g., degree distribution). The scheme is illustrated using functional magnetic resonance imaging (fMRI) time series to discover functional brain networks. Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies. Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs. Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations. The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks. The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions. We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies.
AI snapshot
Written from the paper’s full text.
TL;DR
This paper introduces a data-led DCM scheme for discovering directed, cyclic functional brain networks by Bayesian model selection over sparsity structures. It validates the approach in simulations and applies it to an attention-to-motion fMRI dataset, recovering a dense hierarchical network.
Key findings
- DCM can discover directed cyclic graphs by scoring reduced models from a single full-model inversion using the Savage-Dickey density ratio, with model spaces optionally constrained to bidirectional connections.
- In 200 Monte Carlo simulations, the model selection procedure attained 100% accuracy, i.e. 100% specificity and selectivity for identifying presence or absence of connections; in a 4-node simulation over 64 models, the true architecture had the greatest posterior probability under flat priors.
- In empirical attention-to-motion fMRI with 6 regions and 256 volumes, post hoc selection over 32,768 models found a clear optimum with over 80% model posterior; three of fifteen reciprocal connections were switched off, and the inferred hierarchy order was vis, sts, pfc, ppc, ag, fef.
- A phase-shuffled null analysis produced a much shallower log-evidence profile and retained four of fifteen connections, but with log-Bayes factors less than three relative to graphs with fewer connections.
Methods
- The generative model is DCM for fMRI with a neuronal model based on a random differential equation, \( \dot{x}=Ax+\omega \), motivated by centre manifold/slaving-principle and mean-field assumptions; the hemodynamic Balloon model is unchanged.
- Simulations generated synthetic fMRI from 3-node and 4-node networks over 256 bins of 3.22 s, comparing stochastic Generalised Filtering with a deterministic DCM using a discrete cosine basis; 200 Monte Carlo simulations tested sensitivity/specificity.
- Empirical analysis used an attention-to-motion fMRI dataset, six functionally defined regions, 256 volumes, full-model inversion followed by post hoc model selection, spectral embedding, and an asymmetry index for hierarchy.
Limitations
- Stated: simulations used the same model to generate and explain data, while empirical data offer no such guarantee; sensitivity/specificity as a function of observation noise still needs assessment; strong reciprocal connections with opposite signs were estimated inefficiently and unlikely to survive; priors were arbitrary and could be optimised; larger networks may make full-model inversion prohibitively long.
- Stated: the null phase-shuffled analysis retained four connections, described as slightly disappointing, though evidence for them was weak (log-Bayes factors <3).
- Evident: the empirical illustration uses one subject and an ad hoc region selection, with no group-level analysis; the neuronal model is a linear approximation that absorbs nonlinearities into fluctuations, and its hidden neuronal state is an unspecified phase variable, less physiologically grounded than DCMs for electromagnetic data.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
0 of 47 cited sources checked · 0 supported · 0 flagged
- Findingown data
The computational cost of using the Generalised Filtering scheme was less than the deterministic scheme (about 80 and 100 seconds per iteration during model inversion, respectively).
“Interestingly, the computational cost of using the Generalised Filtering scheme was less than the deterministic scheme (about 80 and 100 seconds per iteration during model inversion, respectively).”
Quote in the paperSubstantial claim - Findingown data
Generalised Filtering results are much more accurate and precise than the deterministic scheme (note the smaller confidence intervals).
“Figure 4 shows the equivalent results for Generalised Filtering, which are much more accurate and precise (note the smaller confidence intervals in the upper left panel).”
Quote in the paperSubstantial claim - Findingown data
Simulated fMRI data generated using Equation 5 and the hemodynamic equations of motion exhibit the characteristic amplitude and ultra slow fluctuations seen in resting state time-series.
“The results of these simulations are shown in Figure 2 and exhibit the characteristic amplitude and ultra slow fluctuations seen in resting state time-series.”
Quote in the paperNot a substantial claim - Findingown data
The use of positive and negative coupling parameters produces the anti-correlated responses seen between the first two nodes and the third.
“The use of positive and negative coupling parameters produces the anti-correlated responses seen between the first two nodes and the third (Figure 2, upper left panel).”
Quote in the paperNot a substantial claim - Findingown data
In contrast to deterministic schemes, stochastic DCM also infers the hidden physiological states that mediate neurovascular coupling (e.g., flow, volume and deoxyhemoglobin content).
“Crucially, in contrast to deterministic schemes, stochastic DCM also infers the hidden physiological states that mediate neurovascular coupling (e.g., flow, volume and deoxyhemoglobin content), which are shown in the upper right panel.”
Quote in the paperSubstantial claim
- Findingown data
The scheme had 100% specificity and selectivity for identifying the presence or absence of a connection.
“In other words, the correct adjacency structure (model) was selected in all cases and, implicitly, the scheme had a 100% specificity and selectivity for identifying the presence or absence of a connection.”
Quote in the paperSubstantial claim - Findingown data
Inferred neuronal activity in the visual region follows visual stimulation (high for attention and low for no attention).
“These results are presented to show that inferred neuronal activity in the visual region (highlighted in blue) follows visual stimulation (grey filled areas – high for attention and low for no attention).”
Quote in the paperSubstantial claim - Findingreasoning
The conditional estimates of individual connections shrank to the true value of zero under the optimal model.
“The key thing to note here is the shrinkage of the conditional estimates to the true value of zero, under the optimal model (see the central black dot in the upper right panel).”
Quote in the paperSubstantial claim - Findingown data
The model with the greatest evidence for phase-shuffled data retained four out of fifteen connections.
“The model with the greatest evidence retained four out of fifteen connections (see the conditional estimates under the reduced model on the lower right).”
Quote in the paperNot a substantial claim - Findingreasoning
Generally, models with more connections have greater evidence because they provide a more accurate explanation for the data.
“One can see that generally, models with more connections have greater evidence because they provide a more accurate explanation for the data.”
Quote in the paperNot a substantial claim - Findingown data
The results in Figure 7 demonstrate a reasonable correspondence between the proxy in Equation 9 and the log-evidence as approximated with the free-energy of each reduced model.
“The results in Figure 7 testify to the quality of the free-energy bound and demonstrate a reasonable correspondence between the proxy in Equation 9 and the log-evidence as approximated with the free-energy of each reduced model.”
Quote in the paperSubstantial claim - Findingown data
There are strong effective connections from the visual system to the prefrontal cortex.
“On the other hand, there are strong effective connections from the visual system to the prefrontal cortex.”
Quote in the paperNot a substantial claim - Findingown data
Of the reduced models with greater log-evidence than the full model, the model with the true architecture had the greatest posterior probability under flat priors over models.
“Of these, the model with the true architecture had, under flat priors over models, the greatest posterior probability.”
Quote in the paperSubstantial claim - Findingcitation
There was little evidence for the graph with four connections relative to graphs with fewer connections, with log-Bayes factors of less than three.
“However, there was little evidence for the graph with four connections relative to graphs with fewer connections (with log-Bayes factors of less than three; Kass & Raftery 1995).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Kass & Raftery 1995 source
Not checked in the free run.
- Findingown data
Three bidirectional connections have been switched off, as their parameter estimates are reduced to their prior value of zero.
“One can see that three (bidirectional) connections have been switched off, as their parameter estimates are reduced to their prior value of zero.”
Quote in the paperSubstantial claim - Findingown data
Changes in conditional estimate were positive when the error was negative and vice versa, on average.
“One would hope to see that these changes were positive when the error was negative (i.e., the estimate was too high) and vice versa. This is exactly what was found (on average).”
Quote in the paperSubstantial claim - Findingown data
The conditional densities of the coupling parameters following inversion of the full model were relatively accurate, with a slightly overconfident underestimate of the negative self-connections that had a prior precision of 128.
“As before, these are relatively accurate, with a slightly overconfident underestimate of the (negative) self-connections that had a prior precision of 128.”
Quote in the paperNot a substantial claim - Findingown data
We can be over 80% certain that a particular network architecture generated the observed fMRI data.
“In this case, we can be over 80% certain that a particular network architecture generated the observed fMRI data.”
Quote in the paperSubstantial claim - Findingnone given
The proxy scoring scheme based upon the Savage-Dickey density ratio works well for the time-series and levels of noise considered.
“More importantly, we introduced a proxy scoring scheme based upon the Savage-Dickey density ratio. This works well for the time-series and levels of noise considered.”
Quote in the paperSubstantial claim - Findingreasoning
The best model within each graph size shows the opposite behaviour; when the number of connections exceeds the true number, the log-evidence diminishes and always falls below that of the true model.
“However, the best model within each graph size shows the opposite behaviour; when the number of connections exceeds the true number, the log-evidence diminishes and always falls below that of the true model (here zero, by definition, and denoted by the red dot).”
Quote in the paperSubstantial claim - Findingown data
Seven of the 64 reduced models had a greater log-evidence than the full model.
“The resulting log-evidences over the 64 models are depicted on the upper right, showing that seven of the reduced models had a greater log-evidence than the full model.”
Quote in the paperSubstantial claim - Findingown data
Strong reciprocal connections with opposite signs were estimated inefficiently, with shrinkage to their prior mean of zero.
“This is because we found that strong reciprocal connections with opposite signs were estimated inefficiently, with shrinkage to their prior mean of zero.”
Quote in the paperSubstantial claim - Findingown data
In results of Figure 6, the difference in log-evidence between the best model and its nearest competitor was about six.
“For example, in results of Figure 6, the difference in log-evidence between the best model and its nearest competitor was about six.”
Quote in the paperSubstantial claim - Findingown data
Without biasing inference on models, the authors disclosed a hierarchical organisation of visual and prefrontal processing areas that has reasonable construct validity in terms of known functional anatomy.
“Furthermore, without biasing inference on models, we disclosed a hierarchical organisation of visual and prefrontal processing areas that has reasonable construct validity in terms of known functional anatomy.”
Quote in the paperSubstantial claim - Findingown data
Despite prior expectations not being part of the model, the inferred neural states conformed to what the authors hoped to elicit experimentally.
“Despite the fact that these expectations were not part of the model, the inferred neural states conformed to what we hoped to elicit experimentally.”
Quote in the paperNot a substantial claim - Interpretationnone given
Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs.
“Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs.”
Quote in the paperNot a substantial claim - Interpretationnone given
Network discovery with DCM uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series.
“This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series.”
Quote in the paperSubstantial claim - Interpretationnone given
DCM can recover the dynamic Bayesian dependency graph (connections in a network) using observed network activity.
“We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity.”
Quote in the paperSubstantial claim - Interpretationnone given
Reducing the dynamics to macroscopic variables necessarily induces fast fluctuations in these variables (system noise) even if the system is deterministic.
“(iii) reducing the dynamics to macroscopic variables necessarily induces fast fluctuations in these variables (cf., system noise) even if the system is deterministic”
Quote in the paperNot a substantial claim - Interpretationreasoning
The equivalent DBN is acyclic because future variables cannot affect past variables.
“Crucially, the equivalent DBN is acyclic because future variables cannot affect past variables.”
Quote in the paperSubstantial claim - Interpretationnone given
The DCM scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks.
“The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks.”
Quote in the paperNot a substantial claim - Interpretationreasoning
Equation 3 is a random differential equation, not a stochastic differential equation (in which the random terms are Markovian and have no smoothness).
“This is important because it means Equation 3 is a random differential equation, not a stochastic differential equation (in which the random terms are Markovian and have no smoothness).”
Quote in the paperSubstantial claim - Interpretationreasoning
For every DCM there is an equivalent Dynamic Bayesian Network whose nodes represent variables at successive time points.
“Formally speaking, for every DCM there is an equivalent Dynamic Bayesian Network (DBN), whose nodes represent variables at successive time points.”
Quote in the paperSubstantial claim - Interpretationown data
In this instance, there is little to be gained, either in terms of accuracy, completeness or computational efficiency, from the deterministic formulation.
“In short, (in this instance) there is little to be gained, either in terms of accuracy, completeness or computational efficiency, from the deterministic formulation.”
Quote in the paperSubstantial claim - Interpretationreasoning
The distribution of eigenvalues (rates of dissipation) induces a separation of temporal scales, so that Equation 1 can be approximated by Equation 3.
“The crucial thing here is that the distribution of eigenvalues (rates of dissipation) induces a separation of temporal scales, so that we can approximate Equation 1 with: 3”
Quote in the paperSubstantial claim - Interpretationcitation
The form of the model emerges naturally from the slaving principle, which applies to coupled dynamical systems that self-organise.
“Here, we have shown how this form emerges naturally from a basic but fundamental principle (the slaving principle), which applies to coupled dynamical systems that self-organise (Ginzburg and Landau 1950; Haken 1983).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Ginzburg and Landau 1950
Not checked in the free run.
- cites Haken 1983
Not checked in the free run.
- Premisecitation
In recent years, the number of models over which people search in DCM has grown enormously, to the extent that DCM is now used to discover the best model over very large model-spaces.
“However, in recent years, the number of models over which people search (the model-space) has grown enormously; to the extent that DCM is now used to discover the best model over very large model-spaces (e.g., Stephan et al., 2010; Penny et al., 2010).”
Quote in the paperSubstantial claim0 of 2 sources checked - Interpretationreasoning
DCM discovery discloses the underlying network in a way that equivalent analyses of functional connectivity cannot aspire to.
“Furthermore, DCM discovery discloses the underlying network in a way that equivalent analyses of functional connectivity cannot aspire to.”
Quote in the paperNot a substantial claim - Interpretationreasoning
A DCM can be structurally cyclic, but its underlying Bayesian dependency graph is acyclic.
“This means that a DCM can be structurally cyclic (e.g., nodes can be reciprocally connected); however, the underlying Bayesian dependency graph is acyclic.”
Quote in the paperSubstantial claim - Interpretationreasoning
The time-constants (implicit in the model parameters) of macroscopic network dynamics are much longer than the microscopic time constants (e.g., effective membrane time constants).
“One important insight from this motivation is that the time-constants (implicit in the model parameters) of macroscopic network dynamics are much longer than the microscopic time constants (e.g., effective membrane time constants).”
Quote in the paperSubstantial claim - Interpretationreasoning
Under zero mean priors, a zero entry in the adjacency matrix prohibits an effective connection, establishing an anti-edge between the respective regions.
“Under zero mean priors (as for all coupling parameters in DCM for fMRI), a zero entry in the adjacency matrix thus prohibits an effective connection, establishing an anti-edge between the respective regions.”
Quote in the paperSubstantial claim - Study design and conductnone given
There was nothing in the data selection or modelling that could bias the conditional estimates of directed coupling to produce the hierarchical order.
“Note that there was nothing in the data selection or modelling that could bias the conditional estimates of directed coupling to produce this result.”
Quote in the paperNot a substantial claim - Premisecitation
In comparison to bottom-up influences, the net effects of top-down connections on their targets are inhibitory.
“There are several strands of empirical and theoretical evidence to suggest that, in comparison to bottom-up influences, the net effects of top-down connections on their targets are inhibitory”
Quote in the paperSubstantial claim0 of 2 sources checked - Interpretationown data
Model evidence automatically penalises redundant parameters or complexity.
“This reflects the fact that model evidence automatically penalises redundant parameters or complexity.”
Quote in the paperSubstantial claim - Interpretationown data
The current results show that it is possible to achieve 100% sensitivity and specificity with cyclic graphs, provided one uses an appropriate generative model to make inferences about effective connectivity.
“The current results show that it is possible to achieve 100% sensitivity and specificity, with cyclic graphs, provided one uses an appropriate generative model to make inferences about effective connectivity.”
Quote in the paperSubstantial claim - Interpretationreasoning
Equation 9 provides an internal test of the quality of the free-energy bound on log-evidence.
“Furthermore, Equation 9 provides an internal test of the quality of the free-energy bound on log-evidence.”
Quote in the paperSubstantial claim - Interpretationreasoning
The hierarchical order can be taken as an incidental face validation of the discovery scheme.
“As such, it can be taken as an incidental face validation of the discovery scheme.”
Quote in the paperNot a substantial claim - Interpretationnone given
Each model can be formed from a fully connected model by switching off various coupling parameters.
“We can do this by exploiting the fact that each model can be formed from a fully connected model by switching off various coupling parameters.”
Quote in the paperSubstantial claim - Premisecitation
Comprehensive analyses of large connectivity databases demonstrate a very strong tendency of cortico-cortical connections to be reciprocal.
“More recently, this notion was confirmed in comprehensive analyses of large connectivity databases demonstrating a very strong tendency of cortico-cortical connections to be reciprocal (Kötter & Stephan 2003).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Kötter & Stephan 2003
Not checked in the free run.
- Premisereasoning
Phase-shuffled data only contain evidence for a graph with no edges.
“Phase-shuffled data only contain evidence for a graph with no edges.”
Quote in the paperSubstantial claim - Interpretationreasoning
By approximating the log-evidence of any reduced model nested within the full model from the conditional density over the full model's parameters, one only needs to invert a single model to score an arbitrary number of reduced models efficiently.
“If we can find a way to approximate the log-evidence of any reduced model (graph), nested within the full model, from the conditional density over the parameters of the full model, then we only need to invert a single model (i.e., the full model) to score an arbitrary number of reduced models extremely efficiently.”
Quote in the paperSubstantial claim - Interpretationcitation
This form of model selection implements automatic relevance determination by optimising the model evidence with respect to model hyperparameters.
“This reflects the fact that this form of model selection implements automatic relevance determination (MacKay 1995), by virtue of optimising the model evidence with respect to model hyperparameters; in this instance, the shrinkage priors prescribed by an adjacency matrix.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites MacKay 1995 source
Not checked in the free run.
- Premisecitation
The bidirectional coupling assumption rests on longstanding anatomical observations that it is rare for two cortical areas to be connected in the absence of a reciprocal connection.
“This (bidirectional coupling) assumption rests on longstanding anatomical observations (Zeki & Shipp 1988) that it is rare for two cortical areas to be connected in the absence of a reciprocal connection (there are rare but important exceptions in sub-cortical circuits).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Zeki & Shipp 1988 source
Not checked in the free run.
- Interpretationcitation
The relative log-evidence of a reduced model, given data, is equal to the log-posterior minus the log-prior that its reduced parameters are zero, under a full model.
“Equation 8 says that the relative log-evidence of a reduced model, given some data, is equal to the log-posterior minus the log-prior that its reduced parameters are zero, under a full model.”
Quote in the paperSubstantial claim - Premisenone given
Network analyses using functional connectivity or diffusion weighted MRI data cannot ask whether a connection is larger in one direction relative to another, because they are restricted to the analysis of undirected (simple) graphs.
“Network analyses using functional connectivity or diffusion weighted MRI data cannot ask whether a connection is larger in one direction relative to another, because they are restricted to the analysis of undirected (simple) graphs.”
Quote in the paperSubstantial claim - Interpretationown data
Spectral embedding suggests that the frontal eye fields play a central and supraordinate role in this network, being remote from the visual region but predominating in strength of efferent connections.
“Spectral embedding suggests that the frontal eye fields (fef) play a central and supraordinate role in this network, in the sense that they are remote from the visual region but predominate in terms of the strength of their efferent connections.”
Quote in the paperSubstantial claim - Interpretationreasoning
Exhaustive search over models is seldom possible in practice because the combinatorics of deploying k edges among n nodes becomes unmanageable when the graph is large.
“Although, in principle, it should be easy to optimise the model (adjacency matrix) with an exhaustive search, this is seldom possible in practice. This is because the combinatorics of deploying k edges among n nodes becomes unmanageable when the size of the graph is large.”
Quote in the paperSubstantial claim - Interpretationcitation
The greater strength of backward connections is sensible given the greater abundance of backward connections anatomically, both within the cortical hierarchy and from cortex to subcortical structures.
“This is entirely sensible, given the greater abundance of backward connections anatomically, both within the cortical hierarchy and from cortex to subcortical structures (e.g., Sillito & Jones 2002).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Sillito & Jones 2002
Not checked in the free run.
- Interpretationown data
DCM can be applied in a purely data-led way to fMRI studies.
“In summary, we have seen how DCM can be applied in a purely data-led way to fMRI studies.”
Quote in the paperSubstantial claim - Interpretationown data
The results in this paper can be regarded as proof of principle that it is possible to recover the true network, provided that one has ideal (but not untypical) data.
“The results in this paper can be regarded as proof of principle that it is possible to recover the true network, provided that one has ideal (but not untypical) data.”
Quote in the paperSubstantial claim - Interpretationown data
Even with real data, the post hoc model selection proposed for network discovery appears to identify anti-edges, provided one pays attention to the relative evidence for alternative models.
“In short, even with real data, the post hoc model selection proposed for network discovery appears to identify anti-edges, provided one pays attention to the relative evidence for alternative models.”
Quote in the paperSubstantial claim - Interpretationreasoning
Strong reciprocal connections with opposite signs are unlikely to survive post hoc optimization.
“This means that they are unlikely to survive post hoc optimization.”
Quote in the paperNot a substantial claim - Interpretationnone given
The paper described a solution to searches on large model-spaces which finesse problems due to combinatorics on connections and computational overhead.
“We have also described a solution to searches on large model-spaces which finesse problems due to combinatorics on connections and computational overhead.”
Quote in the paperSubstantial claim - Premisereasoning
One motivation for inventing DCM was to address the shortcomings of autoregressive and underlying Markovian models.
“In fact, one motivation for inventing DCM was to address the shortcomings of autoregressive and underlying Markovian models.”
Quote in the paperSubstantial claim - Premisereasoning
The restriction to DAGs means that IMaGES only returns acyclic (feed-forward) graphs of effective connectivity.
“The restriction to DAGs means, however, that IMaGES only returns acyclic (feed-forward) graphs of effective connectivity.”
Quote in the paperNot a substantial claim
- May combine two claims. 39
- Classified as probably not a substantial claim. 35
- The quote only partly states this claim. 1
May combine two claims.
Findingown dataThe deterministic scheme, modelling fluctuations with fixed temporal basis functions, underestimates the coupling strengths and consequently overestimates the amplitude of the neuronal fluctuations (represented by exogenous inputs) causing them (i.e., it overestimates the parameters C θ).
“It can been seen that the deterministic scheme, modelling fluctuations with fixed temporal basis functions, underestimates the coupling strengths and consequently overestimates the amplitude of the neuronal fluctuations (represented by exogenous inputs) causing them (i.e., it overestimates the parameters C θ).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe deterministic scheme's estimates are not invalid, in that the true values lie within the conditional confidence intervals; however, this model provides inefficient estimates in relation to Generalised Filtering.
“This is not an invalid result, in that the true values lie within the conditional confidence intervals; however, this model provides inefficient estimates in relation to Generalised Filtering:”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe prefrontal cortex and visual region are the furthest apart in anatomical space but the closest pair of nodes in functional space.
“Interestingly, the prefrontal cortex (pfc) and visual region (vis) are the furthest apart in anatomical space but the closest pair of nodes in functional space.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThere is an interesting structure to the anti-edges that speaks to the well known segregation of dorsal and ventral pathways in the visual system: the missing connections are between the superior temporal sulcus and the early visual system, and between the ventral superior temporal sulcus/angular gyrus and dorsal posterior parietal cortex.
“There is an interesting structure to the anti-edges that speaks to the well known segregation of dorsal and ventral pathways in the visual system (Ungerleider & Haxby 1994): The missing connections are between (i) the superior temporal sulcus and the early visual system, and (ii) the (ventral) superior temporal sulcus/angular gyrus and (dorsal) posterior parietal cortex.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Ungerleider & Haxby 1994 source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Findingown dataThe inversion of the full model took about 16 minutes, while the post hoc search took about 16 seconds.
“The inversion of the full model took about 16 minutes (about 16 iterations of about one minute each), while the post hoc search took about 16 seconds.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe data and noise in these simulations had a standard deviation of about 0.35 and exp(−4/2) ≈ 0.14, respectively, giving a signal to noise ratio of about 2.6.
“The data and noise in these simulations had a standard deviation of about 0.35 and exp(−4/2) ≈ 0.14, respectively, giving a signal to noise ratio of about 2.6.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataChanges in blood flow are in the order of 10%, which is in the physiologically plausible range.
“It can be seen that changes in blood flow are in the order of 10%, which is in the physiologically plausible range.”
Quote in the paperNot a substantial claimThe quote only partly states this claim.
Findingown dataThe hierarchical ordering of nodes that maximises the average strength of forward connections relative to their backward homologue was vis, sts, pfc, ppc, ag, and fef.
“The resulting order was vis, sts, pfc, ppc, ag, and fef, which is not dissimilar to the vertical deployment of the nodes in functional embedding space (Figure 12; lower panel).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataPost hoc model selection following inversion of phase-shuffled data resulted in a nearly edgeless graph, with a log-evidence profile much shallower than for unshuffled data by an order of magnitude.
“This selection should result in an edgeless graph, which is nearly the case but not quite: It can be seen that the log-evidence profile is much shallower in comparison to the analysis of unshuffled data (by an order of magnitude).”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe model selection procedure attained 100% accuracy; the correct adjacency structure was selected in all cases.
“However, this assessment was unnecessary because the model selection procedure attained 100% accuracy. In other words, the correct adjacency structure (model) was selected in all cases and, implicitly, the scheme had a 100% specificity and selectivity for identifying the presence or absence of a connection.”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone givenFor a typical fMRI study, model inversion takes about five to ten minutes on a modern computer and post hoc model selection takes a few seconds.
“For a typical fMRI study, model inversion takes about five to ten minutes on a modern computer and post hoc model selection takes a few seconds.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThis is a surprisingly dense network, in which all but three of the fifteen reciprocal connections appear to be necessary to explain observed responses.
“This is a surprisingly dense network, in which all but three of the fifteen reciprocal connections appear to be necessary to explain observed responses.”
Quote in the paperSubstantial claimMay combine two claims.
Findingnone givenBoth inversion of the full model and its post hoc optimization are sensitive to the shrinkage priors over the parameters.
“Finally, both inversion of the full model and its post hoc optimization are sensitive to the shrinkage priors over the parameters.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe strength of backward connections can be greater than the strength of forward connections; all top-down connections from the frontal eye fields were stronger in absolute terms than the equivalent bottom-up connections.
“A striking result from this data-led application was that the strength of backward connections can be greater than the strength of forward connections: note all top-down connection from the frontal eye fields were stronger in absolute terms than the equivalent bottom-up connections (Figure 12).”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Findingnone givenIncreasing levels of observation noise reduces the posterior confidence in non-zero connections and predisposes them to removal during post hoc optimisation.
“Increasing levels of noise reduces the posterior confidence in non-zero connections and predisposes them to removal during post hoc optimisation.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningThis difference translates into a log-odds ratio of about exp(6) ≈ 400:1 or a Z-score of about 2.8.
“This translates into a log-odds ratio of about exp(6) ≈ 400 :1 or a Z-score of about 2.8.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone givenThe DCM network discovery scheme can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies.
“Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable), S4 (based).
Interpretationnone givenStochastic or random fluctuations are inevitable when modelling self-organised dynamics at a macroscopic scale.
“This distinction is important because stochastic or random fluctuations are inevitable, when modelling self-organised dynamics at a macroscopic scale.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationThe DCM used in this paper is exactly the same as conventional DCM for fMRI but includes endogenous fluctuations represented by random differential equations.
“This is exactly the same as the conventional DCM for fMRI but includes endogenous fluctuations, which are represented by random differential equations (Li et al. 2010).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Li et al. 2010
Not checked in the free run.
May combine two claims.
InterpretationreasoningThe analytic nature of these fluctuations renders the model non-Markovian and calls for inversion schemes that eschew Markovian assumptions.
“The last point is crucial because it renders the model non-Markovian and calls for (inversion) schemes that eschew Markovian assumptions (e.g., Generalised Filtering: Friston et al 2010; Li et al., 2011).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Friston et al 2010 source
Not checked in the free run.
- cites Li et al., 2011
Not checked in the free run.
May combine two claims.
PremisecitationThe implicit difference in log-evidence for two models with and without a connection is the log-Bayes factor and is the most efficient statistic for testing their relative likelihood.
“The implicit difference in log-evidence for these two models is the log-Bayes factor and (by the Neyman-Pearson Lemma) is the most efficient statistic for testing the relative likelihood of both models.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Neyman-Pearson Lemma
Not checked in the free run.
May combine two claims.
InterpretationreasoningBy scoring all possible models, one can in principle identify conditional dependencies and discover the underlying dependency graph.
“This means, in principle, we have a straightforward way to identify conditional dependencies and, by scoring all possible models, discover the underlying dependency graph.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenThe arguments in the paper apply to any complex distributed system with coupled nonlinear dynamics.
“Although we will focus on neuronal systems, the following arguments apply to any complex distributed system with coupled nonlinear dynamics.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationGeneralised Filtering represents hidden states in generalised coordinates of motion and absorbs unknown (time-invariant) parameters into the filter.
“Recently, we introduced a Generalised Filtering scheme (Friston et al., 2010) that represents hidden states in generalised coordinates of motion and absorbs unknown (time-invariant) parameters into the filter.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Friston et al., 2010 source
Not checked in the free run.
May combine two claims.
InterpretationreasoningOnly the slow dynamics are communicated among nodes, which means distributed activity can be modelled with a small number of macroscopic variables (e.g. one per node) with fast fluctuations specific to each node.
“We will see that only the slow dynamics are communicated among nodes, which means we can model distributed activity with a small number of macroscopic variables (e.g. one per node) with fast fluctuations that are specific to each node.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationDCM for fMRI rests on a generative model that has two components: a neuronal model describing interactions in a distributed network of neuronal populations, and a component mapping neuronal activity to observed hemodynamic responses.
“DCM for fMRI rests on a generative model that has two components.”
Quote in the paperSubstantial claim0 of 3 sources checkedClassified as probably not a substantial claim.
Interpretationnone givenA detailed examination of DCM for fMRI discloses the central importance and nature of fluctuations in neurophysiologic states, which have been ignored in classical deterministic variants of dynamic causal modelling.
“This more detailed examination of DCM for fMRI discloses the central importance (and nature) of fluctuations in neurophysiologic states, which have been ignored in classical (deterministic) variants of dynamic causal modelling.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Interpretationnone givenA dynamic causal model is formally a Bayesian dependency graph, in which the form of the dependencies among hidden states are described with deterministic or random differential equations.
“It is important to realise that a dynamic causal model is (formally) a Bayesian dependency graph, in which the form of the dependencies among hidden states are described with deterministic or random differential equations.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThese fluctuations are analytic (continuously differentiable).
“(iv) these fluctuations are analytic (continuously differentiable).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable).
InterpretationreasoningPriors on the parameters should allow for slow dynamics.
“This is important because it suggests that priors on the parameters should allow for slow dynamics.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenDCM eschews Markovian assumptions about the serial independence of random fluctuations.
“Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe equations for endogenous fluctuations can be regarded as a bilinear approximation to any nonlinear model of neuronal dynamics.
“These equations can be regarded as a [bi]linear approximation to any nonlinear model of neuronal dynamics.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe dynamics of coupled systems can be summarised with a small number of macroscopic variables that describe their behaviour.
“It is presented to make four key points: (i) The dynamics of coupled systems can be summarised with a small number of macroscopic variables that describe their behaviour;”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
PremisecitationfMRI signals scale with the predominant frequency of neuronal activity.
“This is because it is generally assumed that fMRI signals scale with the predominant frequency of neuronal activity (Kilner et al., 2005; Laufs & Duncan 2007; Rosa et al., 2010).”
Quote in the paperSubstantial claim0 of 3 sources checkedMay combine two claims.
PremisecitationThe slow modes flow on the centre manifold and enslave the fast modes, which the centre manifold attracts (the slaving principle).
“The slow modes (which flow on the centre manifold) are then said to enslave the fast modes (which the centre manifold attracts): this is the “slaving principle” (Ginzburg and Landau 1950; Carr 1981; Haken 1983).”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Ginzburg and Landau 1950
Not checked in the free run.
- cites Carr 1981
Not checked in the free run.
- cites Haken 1983
Not checked in the free run.
May combine two claims.
InterpretationreasoningThere is no real difference between hidden states and parameters in DCM; therefore, it should be possible to cast unknown fluctuations in neuronal states as unknown parameters.
“The nature of these generalised schemes speaks to the fact that there is no real difference between hidden states and parameters in DCM; therefore, it should be possible to cast unknown fluctuations in neuronal states as unknown parameters.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningAn exhaustive model search can finesse the missing region problem, provided the source of common input is part of the full model and one can invert it.
“This is because an exhaustive model search will preclude a false inference of conditional dependency between two unconnected nodes, provided the source of common input is part of the full model (and that one can invert it).”
Quote in the paperSubstantial claim- Rests on an assumption: The source of common input is part of the full model and one can invert it.
Classified as probably not a substantial claim.
InterpretationreasoningExogenous inputs are prior expectations (usually based on known experimental design) about hidden neuronal fluctuations.
“Equation 6 has been introduced to show the formal connection between stochastic and deterministic DCM and promote a particular perspective on exogenous inputs: namely, that they are prior expectations (usually based on known experimental design) about hidden neuronal fluctuations.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe time constants of macroscopic dynamics are necessarily greater than those of the underlying microscopic dynamics.
“(ii) the time constants of these macroscopic dynamics are necessarily greater than those of the underlying macroscopic dynamics;”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationDCM has historically been portrayed as a hypothesis-led approach to understanding distributed neuronal architectures underlying observed brain responses.
“Historically, Dynamic Causal Modelling (DCM) has been portrayed as a hypothesis-led approach to understanding distributed neuronal architectures underlying observed brain responses (Friston et al., 2003).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Friston et al., 2003 source
Not checked in the free run.
Classified as probably not a substantial claim. May combine two claims.
InterpretationreasoningThis perspective provides a graceful link (conceptually and practically) between activation and resting-state studies; i.e., activation studies can be treated as task-free and vice-versa.
“This perspective is exploited in the last section and provides a graceful link (conceptually and practically) between activation and resting-sate studies; i.e., activation studies can be treated as task-free and vice-versa.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationIn DCM, models are usually inverted by optimising a free-energy bound on the model log-evidence, assuming the posterior is approximately Gaussian (the Laplace assumption).
“In DCM, models are usually inverted by optimising a free-energy bound F (y, q) ≤ ln p(y | m) on the model log-evidence (or log marginal likelihood of the data y conditioned upon a model m), assuming the posterior is approximately Gaussian (the Laplace assumption).”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites Friston et al., 2003 source
Not checked in the free run.
- cites [2007]
Not checked in the free run.
- cites [2010]
Not checked in the free run.
- The authors state this as an assumption: The posterior is approximately Gaussian (the Laplace assumption).
Probably not a substantial claim: may not pass S3 (load-bearing).
Premisenone givenThe random differential equation (Equation 5) is the one used in stochastic DCM for fMRI (ignoring bilinear terms and exogenous inputs).
“Crucially, this is the random differential equation used in stochastic DCM for fMRI (ignoring bilinear terms and exogenous inputs).”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningThese connections do not mean direct monosynaptic connections; they show conditional dependencies mediated in a neuronally plausible polysynaptic fashion, which cannot be explained by regional activities in the other nodes considered.
“This does not mean that there are direct (monosynaptic) connections between these regions; it means they show conditional dependencies that are mediated in a neuronally plausible (polysynaptic) fashion, which cannot be explained by regional activities in the other nodes we considered.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe resulting order places the visual cortex at the bottom of the hierarchy and the frontal eye fields at the top, which is expected from the functional anatomy of these regions.
“This is a pleasing result because it places the visual cortex at the bottom of the hierarchy and the frontal eye fields at the top, which we would expect from the functional anatomy of these regions.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
Interpretationnone givenThe assumption of reciprocal coupling is not necessary for network discovery; it is used here to demonstrate how prior beliefs can constrain model spaces.
“Despite this strong motivation for introducing symmetry constraints on the adjacency matrix, it should be noted that the assumption of reciprocal coupling is not necessary for network discovery; it is used here to demonstrate how prior beliefs can constrain model spaces.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationcitationThis reflects the strength of coupling between these nodes and the tight functional integration between visual and prefrontal areas during visual attention tasks.
“This reflects the strength of the coupling between these nodes and more generally the tight functional integration between visual and prefrontal areas during visual attention tasks (e.g., Desimone & Duncan 1995; Gazzaley et al. 2007).”
Quote in the paperNot a substantial claim0 of 2 sources checkedMay combine two claims.
InterpretationreasoningA finite value in the adjacency matrix means that the connection has finite variance and its posterior estimate can take non-zero values.
“Conversely, a finite value in the adjacency matrix means that the connection has finite variance and that its posterior estimate can take non-zero values.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThese simulation results show only that it is possible to recover the connectivity structure from realistic responses; this rests on having the right generative model.
“It should be remembered that these simulation results show only that it is possible to recover the connectivity structure from realistic responses; however, this clearly rests on having the right generative model.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone givenThe reciprocal coupling constraint does not mean that effective connection strengths are identical for both directions; posterior estimates of coupling can be very different.
“Furthermore, this constraint does not mean that the effective connection strengths are identical for both directions of a reciprocal connection: the posterior estimates of coupling can be very different.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
PremisecitationPredictive coding holds that top-down predictions suppress prediction errors in lower levels of a hierarchy.
“Theoretically, this is consistent with predictive coding, where top-down predictions suppress prediction errors in lower levels of a hierarchy”
Quote in the paperSubstantial claim0 of 3 sources checkedProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
InterpretationreasoningIn principle, the scheme can handle much larger networks; however, the time taken to invert the full model may become prohibitively long because the number of free parameters increases quadratically with the number of nodes.
“In principle, the scheme can handle much larger networks; however, the time taken to invert the (full) model may become prohibitively long (because the number of free parameters increases quadratically with the number of nodes).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningThe coupling parameters are themselves state and implicitly time-dependent.
“From the point of view of generative models, this suggests that the coupling parameters are themselves state and implicitly time-dependent.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationThe importance of backward connections or top-down influences fits comfortably with predictive coding accounts of brain function, which emphasise the importance of predictions generated in a top-down fashion.
“Furthermore, the importance of backward connections or top-down influences fits comfortably with predictive coding accounts of brain function, which emphasise the importance of predictions that are generated in a top-down fashion (Rao & Ballard 1999; Friston 2005).”
Quote in the paperNot a substantial claim0 of 2 sources checkedProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
InterpretationcitationHaving access to the adjacency matrices summarising functional brain architectures (in terms of effective connectivity) opens the door to graph theoretic analyses that leverage important advances in network theory.
“Finally, having access to the adjacency matrices summarising functional brain architectures (in terms of effective connectivity) opens the door to graph theoretic analyses that leverage important advances in network theory (e.g., Bullmore & Sporns 2009).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Bullmore & Sporns 2009 source
Not checked in the free run.
May combine two claims.
PremisecitationGranger causality and DBN rest on the theory of Martingales (Markovian assumptions), which may be inappropriate for real dynamical systems whose fast fluctuations are analytic and may show critical slowing.
“Granger causality and DBN rest on the theory of Martingales (i.e. Markovian assumptions), which may be inappropriate for real dynamical systems, whose fast fluctuations are analytic and may themselves show critical slowing (i.e., non-Markovian or long-memory behaviour); see Roebroeck et al. (2009) and Friston (2009) for discussion.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Roebroeck et al. (2009)
Not checked in the free run.
- cites Friston (2009)
Not checked in the free run.
Classified as probably not a substantial claim. May combine two claims.
Study design and conductown dataThe level of noise used in the simulations is not unrealistic but guaranteed a strong connection could be estimated with a high degree of precision.
“The level of noise used in the simulations is not unrealistic but guaranteed a strong connection could be estimated with a high degree of precision.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationModel averaging and selection procedures currently applied to free-energy approximations following inversion of reduced models can be applied to the post hoc log-evidence used for model discovery.
“In a similar vein, model averaging and selection procedures currently applied to the free-energy approximations following inversion of reduced models can be applied to the post hoc log-evidence used for model discovery (see Stephan et al. 2010 for an overview of these procedures).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Stephan et al. 2010 source
Not checked in the free run.
May combine two claims.
Interpretationown dataThis reflects the efficiency of the model selection and explains why the authors were able to identify the correct model in all the simulations.
“This reflects the efficiency of the model selection and explains why we were able to identify the correct model in all the simulations.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningBecause DCM is a linear approximation, nonlinearities that cause chaotic itinerancy in real biological time-series are absorbed into the fluctuating terms inferred during model inversion.
“Because our DCM is a linear approximation, these nonlinearities are absorbed into the fluctuating terms that are inferred during model inversion.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationThe shrinkage priors can themselves be optimised using the same formalism behind post hoc model optimization.
“however, these priors can themselves be optimised using the same formalism behind post hoc model optimization (see Friston and Penny 2011).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Friston and Penny 2011
Not checked in the free run.
Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing), S4 (based).
InterpretationreasoningNetwork discovery can also be applied to bilinear and nonlinear DCMs to discover functional architectures with nonlinear (state-dependent) effects.
“In short, network discovery can also be applied to bilinear and nonlinear DCMs to discover functional architectures with nonlinear (state-dependent) effects.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing).
InterpretationcitationOne can model state-dependency and ensuing itinerancy by adding nonlinear (quadratic) terms to the coupling matrix.
“One can model this state-dependency, and ensuing itinerancy, by simply adding nonlinear (quadratic) terms to the coupling matrix as described in Stephan et al., (2008).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Stephan et al., (2008) source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
InterpretationreasoningThe computational expediency of functional connectivity and Granger causal schemes means they can handle vast numbers of nodes and may play a helpful role in identifying candidate networks for analyses of directed effective connectivity.
“Having said this, the computational expediency of functional connectivity and Granger causal schemes mean that they can handle (in principle) vast numbers of nodes and may therefore play a helpful role in identifying candidate networks for the analyses of (directed) effective connectivity described in this paper.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationDCM is used routinely to invert models with thousands of free parameters.
“Having said this, DCM is used routinely to invert models with thousands of free parameters (e.g. DCM for induced electromagnetic sources; Chen et al. 2008).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Chen et al. 2008 source
Not checked in the free run.
Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).
InterpretationcitationThere is no reason why exactly the same approach could not be applied to the activity of distributed modes, such as those from principal or independent component analysis.
“Although we have illustrated the approach using region specific summaries of fMRI data from an activation study, there is no reason why exactly the same approach could not be applied to the activity of distributed modes, such as those from principal or independent component analysis (cf, Havlicek et al., 2010).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Havlicek et al., 2010 source
Not checked in the free run.
May combine two claims.
PremisecitationGranger causality may not be appropriate for fMRI time-series and performs poorly in comparison to structural (non-dynamic) approaches based upon partial correlations.
“However, there is a growing appreciation that Granger causality may not be appropriate for fMRI time-series (e.g., Nalatore et al 2007) and performs poorly in comparison to structural (non-dynamic) approaches based upon partial correlations (Smith et al., 2010).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Nalatore et al 2007 source
Not checked in the free run.
- cites Smith et al., 2010
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenPost hoc log-evidences can be used for random effects model selection for group studies.
“Similarly, post hoc log-evidences can be used for random effects model selection for group studies).”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningThis provides a DCM based on nonlinear random differential equations that can, in principle, be inverted using Generalised Filtering.
“This provides a DCM based on nonlinear random differential equations that can, in principle, be inverted using Generalised Filtering.”
Quote in the paperNot a substantial claim
The authors state this as an assumption.
The dynamics of neuronal states in one node evolve according to some unknown and immensely complicated equations of motion.
“We will first assume that the dynamics of neuronal states in one node ξ = [ξ1,ξ2,…]T evolve according to some unknown and immensely complicated equations of motion: 1ξ.=f(ξ)`ζ.1=f1(ζ1,…,ζN)ζ.2=f2(ζ1,…,ζN)ζ.3=…”
The authors state this as an assumption.
The mapping U− :ξ → ζ is chosen so that it conforms locally to the generalised eigenvectors U(ξ) of the Jacobian.
“We assume that this mapping U− :ξ → ζ is chosen so that it conforms locally to the generalised eigenvectors U(ξ) of the Jacobian = ∂f/∂ξ, with eigenvalues U−U = λ.”
The authors state this as an assumption.
The eigenvalues associated with each mode are distributed sparsely; one or a small number are near zero, whereas the rest are large and negative.
“Namely, we make the assumption that the eigenvalues λk=Uk−ℑUk associated with each mode ζk=Uk−ξ are distributed sparsely; λ1>λ2>λ3…∈ℜ. That is, one or a small number of them are near zero, whereas the rest are large and negative.”
The authors state this as an assumption.
The dynamics of one node are determined by the mean or average activity in another (mean-field assumption).
“To simplify the model of responses distributed over n nodes, we adopt a mean-field assumption (see Deco et al., 2008).”
The authors state this as an assumption.
Each neuron in one node sees a sufficiently large number of neurons in another to render the effective influence the same as the average over all neurons in the source node.
“Intuitively, this is like assuming that each neuron in one node ‘sees’ a sufficiently large number of neurons in another to render the effective influence the same as the average over all neurons in the source node.”
The authors state this as an assumption.
The posterior is approximately Gaussian (the Laplace assumption).
“assuming the posterior is approximately Gaussian (the Laplace assumption).”
The authors state this as an assumption.
Neuronal fluctuations are the predominant source of hemodynamics and hemodynamic fluctuations are largely neuronal in origin.
“This essentially treats neuronal fluctuations as the predominant source of hemodynamics and assumes hemodynamic fluctuations are largely neuronal in origin.”
The authors state this as an assumption.
All connections in the brain are directed and reciprocal.
“To finesse this problem we can assume all connections in the brain are directed and reciprocal.”
The paper relies on this without support.
The source of common input is part of the full model and one can invert it.
“provided the source of common input is part of the full model (and that one can invert it).”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
DCM, originally developed for task data, has recently been extended to allow modelling of resting-state data and to search across a wide range of possible network matrix models.
“while DCM, originally developed for task data, has recently been extended [54] to allow modelling of resting-state data, and to search across a wide range of possible network matrix models”
From Functional connectomics from resting-state fMRI (2013) · cites this paper as [54]
The citation lists haven’t been fetched yet
References 109 · Cited by 283
- Authors
- Friston, K. J., Li, B., Daunizeau, J., & Stephan, K. E.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Friston, Karl J.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2011-06
- Volume
- 56
- Issue
- 3
- Pages
- 1202-1221
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC3094760
- OpenAlex
- W2021655476
- Semantic Scholar
- ede2127bc798ea16e3a93627f7dce29a6e709ac7
- Cited by
- 283
- References
- 109
- Citations by year
- 2026: 8 · 2025: 10 · 2024: 8 · 2023: 12 · 2022: 12 · 2021: 13 · 2020: 10 · 2019: 19 · 2018: 16 · 2017: 21 · 2016: 29 · 2015: 27 · 2014: 27 · 2013: 25 · 2012: 23
- FWCI
- 13.54
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- NeuroImage (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, other-oa)
- UCL Discovery (University College London) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Wellcome Trust
- China Scholarship Council (CSC)
- SystemsX.ch
- University of Zurich
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- network discovery, dynamic causal modeling, Bayesian model selection, functional connectivity, directed graphs, cyclic graphs, effective connectivity, fMRI time series, resting-state fMRI, brain networks, sparsity structure
- MeSH terms
- Algorithms, Bayes Theorem, Brain Mapping, Computer Simulation, Hemodynamics, Humans, Image Processing, Computer-Assisted, Magnetic Resonance Imaging, Models, Neurological, Motion Perception, Nerve Net, Stochastic Processes, Visual Perception, Models, Statistical, Causality, Normal Distribution
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