1. Brain modes and network discovery Karl Friston The past decade has seen tremendous advances in characterising functional integration in the brain. Much of this progress is set against the backdrop of a key dialectic between functional and effective connectivity. My talk will focus on the application of dynamic causal modelling to resting state timeseries or endogenous neuronal activity. A special focus will be on advances in network discovery and Bayesian model reduction. I will survey recent (and rapid) developments in modelling distributed neuronal fluctuations (e.g., stochastic, spectral and symmetric DCM for fMRI) – and how this modelling rests upon functional connectivity. I hope to highlight the intimate relationship between functional and effective connectivity and how one informs the other. Emergent dynamics from large scale brain networks in health and disease

3. The forward (dynamic causal) model Endogenous fluctuations Effective connectivity Functional connectivity Observed timeseries

4. A connectivity reconstruction problem: A degenerate (many-to-one) mapping between effective and functional connectivity

5. The forward (dynamic causal) model Endogenous fluctuations Effective connectivity Functional connectivity Observed timeseries

6. Bayesian model inversion Endogenous fluctuations Effective connectivity Functional connectivity Observed timeseries Posterior density Log model evidence (Free energy) Richard Feynman

7. The past decade has seen tremendous advances in characterising functional integration in the brain. Much of this progress is set against the backdrop of a key dialectic between functional and effective connectivity. My talk will focus on the application of dynamic causal modelling to resting state timeseries or endogenous neuronal activity. A special focus will be on advances in network discovery and Bayesian model reduction. I will survey recent (and rapid) developments in modelling distributed neuronal fluctuations (e.g., stochastic, spectral and symmetric DCM for fMRI) – and how this modelling rests upon functional connectivity. I hope to highlight the intimate relationship between functional and effective connectivity and how one informs the other. Brain modes and network discovery Karl Friston Emergent dynamics from large scale brain networks in health and disease

8. Bayesian model comparison Bayesian model inversion Endogenous fluctuations Posterior density Log model evidence Bayesian model averaging

9. Bayesian model inversion Posterior density Log model evidence Model evidence and Ockham’s principle AccuracyComplexity fMRI models EEG models fMRI data EEG data Evidence is afforded by data …

10. And the concept of reduced models This means that we only have to invert the full model to score all reduced models; c.f., the Savage-Dickey density ratio Armani, Calvin Klein and Versace design houses did not refuse this year to offer very brave and reduced models of the “Thong” and “Tango”. The designers consider that a man with the body of Apollo should not obscure the wonderful parts of his body. Bayesian model reduction

11. Simulating the response of a four-node network And recovering (discovering) the true architecture Complexity

12. An empirical example (with six nodes) 020040060080010001200 -4 -2 0 2 vis: responses 020040060080010001200 -5 0 5 ag: responses 020040060080010001200 -2 0 2 4 sts: responses 020040060080010001200 -4 -2 0 2 ppc: responses 020040060080010001200 -5 0 5 fef: responses 020040060080010001200 -5 0 5 pfc: responses time {seconds} 0.00 0.00 -0.57 -0.28 -0.17 -0.31 0.00 0.00 -0.34 0.00 -0.37 -0.42 0.57 0.34 0.00 -0.45 -0.43 -0.51 0.28 0.00 0.45 0.00 0.00 -0.25 0.17 0.37 0.43 0.00 0.00 -0.28 0.31 0.42 0.51 0.25 0.28 0.00 'vis' 'sts' 'pfc' 'ppc' 'ag' 'fef' Differences in reciprocal connectivity

13. The past decade has seen tremendous advances in characterising functional integration in the brain. Much of this progress is set against the backdrop of a key dialectic between functional and effective connectivity. My talk will focus on the application of dynamic causal modelling to resting state timeseries or endogenous neuronal activity. A special focus will be on advances in network discovery and Bayesian model reduction. I will survey recent (and rapid) developments in modelling distributed neuronal fluctuations (e.g., stochastic, spectral and symmetric DCM for fMRI) – and how this modelling rests upon functional connectivity. I hope to highlight the intimate relationship between functional and effective connectivity and how one informs the other. Brain modes and network discovery Karl Friston Emergent dynamics from large scale brain networks in health and disease

14. The forward (dynamic causal) model Endogenous fluctuations Observed timeseries Endogenous fluctuations Deterministic DCM

15. The forward (dynamic causal) model Endogenous fluctuations Observed timeseries Stochastic DCM

16. 123456789 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 True and MAP connections Extrinsic coupling parameter Stochastic DCM Deterministic DCM vs. Simulated responses of a three node network

17. The forward (dynamic causal) model Endogenous fluctuations Observed timeseries Spectral DCM

18. The forward (dynamic causal) model Endogenous fluctuations Spectral DCM

19. The forward (dynamic causal) model Endogenous fluctuations Spectral DCM Complex cross-spectra

20. Network or graph generating data -0.3 -0.20.4 0.2 050100150200250300 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Endogenous fluctuations time (seconds) amplitude 050100150200250300 -0.1 -0.05 0 0.05 0.1 Hidden states time (seconds) amplitude Hemodynamic response and noise 050100150200250300 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 time (seconds) amplitude Region 1 Region 2 Region 3 123456789 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 True and MAP connections Simulated responses of a three node network

21. The effect of scan length:

22. The past decade has seen tremendous advances in characterising functional integration in the brain. Much of this progress is set against the backdrop of a key dialectic between functional and effective connectivity. My talk will focus on the application of dynamic causal modelling to resting state timeseries or endogenous neuronal activity. A special focus will be on advances in network discovery and Bayesian model reduction. I will survey recent (and rapid) developments in modelling distributed neuronal fluctuations (e.g., stochastic, spectral and symmetric DCM for fMRI) – and how this modelling rests upon functional connectivity. I hope to highlight the intimate relationship between functional and effective connectivity and how one informs the other. Brain modes and network discovery Karl Friston Emergent dynamics from large scale brain networks in health and disease

23. The forward (dynamic causal) model Endogenous fluctuations What if the connectivity was symmetrical? Symmetrical DCM

24. The forward (dynamic causal) model Endogenous fluctuations Symmetrical DCM

25. The forward (dynamic causal) model Endogenous fluctuations Symmetrical DCM In the absence of measurement noise, effective connectivity becomes the negative inverse functional connectivity

26. The forward (dynamic causal) model Endogenous fluctuations Large DCMs Breaking the symmetry:

27. The forward (dynamic causal) model Log evidence Accuracy Complexity Number of modes ( m ) Principal modes in the language system

28. Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry. chapter 1, “The Law of Gravitation,” p. 34 Richard Feynman

29. Thank you And thanks to Bharat Biswal Christian Büchel CC Chen Jean Daunizeau Olivier David Marta Garrido Sarah Gregory Lee Harrison Joshua Kahan Stefan Kiebel Baojuan Li Andre Marreiros Rosalyn Moran Hae-Jeong Park Will Penny Adeel Razi Mohamed Seghier Klaas Stephan And many others