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Title: Markov blankets and Bayesian mechanics
Professor Karl J. Friston MB, BS, MA, MRCPsych, FMedSci, FRSB, FRS; Wellcome Principal Fellow; Scientific Director: Wellcome Trust Centre for Neuroimaging; Institute of Neurology, UCL; 12 Queen Square; London. WC1N 3BG UK
Abstract: This presentation offers a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (weakly mixing) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if a system can be differentiated from its external milieu, heat bath or environment, then the system’s internal and external states must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states. The existence of a Markov blanket means that internal states will appear to minimize a free energy functional of blanket states – via a variational principle of stationary action. Crucially, this free energy is the same quantity that is optimized in Bayesian inference. Therefore, the internal states (and their blanket) will appear to engage in active Bayesian inference. In other words, they will appear to model—and act on—their world to preserve their functional and structural integrity. This leads to a generalised homoeostasis and a simple form of autopoiesis – that can be neatly summarised as self-evidencing.
Bio-sketch
Karl Friston is a theoretical neuroscientist and authority on brain imaging. He invented statistical parametric mapping (SPM), voxel-based morphometry (VBM) and dynamic causal modelling (DCM). These contributions were motivated by schizophrenia research and theoretical studies of value-learning, formulated as the dysconnection hypothesis of schizophrenia. Mathematical contributions include variational Laplacian procedures and generalized filtering for hierarchical Bayesian model inversion. Friston currently works on models of functional integration in the human brain and the principles that underlie neuronal interactions. His main contribution to theoretical neurobiology is a free-energy principle for action and perception (active inference). Friston received the first Young Investigators Award in Human Brain Mapping (1996) and was elected a Fellow of the Academy of Medical Sciences (1999). In 2000 he was President of the international Organization of Human Brain Mapping. In 2003 he was awarded the Minerva Golden Brain Award and was elected a Fellow of the Royal Society in 2006. In 2008 he received a Medal, College de France and an Honorary Doctorate from the University of York in 2011. He became of Fellow of the Royal Society of Biology in 2012, received the Weldon Memorial prize and Medal in 2013 for contributions to mathematical biology and was elected as a member of EMBO (excellence in the life sciences) in 2014 and the Academia Europaea in (2015). He was the 2016 recipient of the Charles Branch Award for unparalleled breakthroughs in Brain Research and the Glass Brain Award, a lifetime achievement award in the field of human brain mapping. He holds Honorary Doctorates from the University of Zurich and Radboud University.
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Co-evolving individuals and the emergence of adaptive structures: group selection versus the individual.
Henrik Jeldtoft Jensen1,2, Katharina Brinck1
(1) Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, SW7 2AZ, UK; h.jensen@imperial.ac.uk
(2) Institute of Innovative Research, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan.
Ecosystems, whether biological or economical, say, are the emergent products of evolutionary and adaptive dynamics of a community of interacting agents. Through a combination of adaptive pressure arising from the external environmental and the co-adaptation within the community, agents evolve as a result of selection and networks of interdependence are produced. As community structures are formed, one may ask about the relative importance of selection of the individual compared to selection of the communities. This is the long-standing debate amongst evolutionary biologist concerning group selection versus individual selection. Without an appropriate quantitative modelling framework, the relative importance of bottom-up and top-down control is very difficult to phrase in a way sufficiently precise and transparent to allow one to determine if the selection of individuals according to their phenotype is more important than the selection acting at collective structures, i.e. group level. We present a way of quantifying the relative weight of natural selection and coadaptation grounded in information theory. We assess the relative role of bottom-up and top-down control in the evolution of ecological systems and analyse the information transfer in an individual based stochastic complex systems model, the Tangled Nature Model of evolutionary ecology. As coadaptation progresses, we show that ecological communities evolve from mainly bottom-up controlled early-successional systems to more strongly top-down controlled late-successional systems. Agents which have a high influence on selection transfer are also generally more abundant. Hence our findings imply that ecological communities are shaped by a dialogue of bottom-up and top-down control, where the role of the systemic selection and integrity becomes more pronounced the further the ecosystem is developed.
Acknowledgements
Simulations have been run on the High Performance Cluster by the Imperial College Computing Service whom we thank sincerely for providing these facilities. KB thanks Imperial Colleges Department of Mathematics for funding her PhD work.
References
[1] K. Brinck and H.J. Jensen, The evolution of ecosystem ascendency in a complex systems based model. J. Theo. Biol.. 428, 18-25 (2017)
[2] K. Brinck and H.J. Jensen, Bottom-up versus top-down control and the transfer of information complex model ecosystems. (Brinck’s PhD thesis and manuscript in preparation).
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Thermodynamics of Self-Organization in Fluid-Solid Interacting Systems
Ashwin Vaidya
Department of Mathematical Sciences, Montclair State University, Montclair, NJ.
Email: vaidyaa@montclair.edu
The interaction of fluids with solids is an age old problem and has given rise to several interesting mathematical and physical problems on pattern formation, stability and bifurcations. Pattern formation is seen to be a consequence of thermodynamic disequilibrium in the system and lends itself to mechanical and thermodynamic arguments, among which is the well known principle of Maximum Entropy Production (MEP). This theory has proven to be effective in certain contexts although its overarching effectiveness as a universal principle and connections to several other variational principles in physics remain to be established. The terminal orientation of a rigid body in a fluid is a relatively simple example of a dissipative system out of thermodynamic equilibrium and serves as a perfect testing ground for the validity of the MEP principle.
A body interacting with fluid generates flow around it resulting in dissipative losses. Typically, dynamical equations have been employed in deriving the equilibrium states of such immersed bodies in fluids, but they are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally heavy and time consuming.
Our previous work [1,2] has revealed that the MEP principle is a reliable tool to help predict the equilibrium orientation of highly symmetric bodies such as cylinders and spheroids, near thermodynamic equilibrium. In recent work [3], we expand our analysis to examine bodies with lesser symmetry (for instance, a half-cylinder in a flow) and Reynolds numbers (inertial parameter) substantially greater than zero, which render the problem far from thermodynamic equilibrium. Experiments and numerical studies indicate that symmetry-breaking and inertia have a nuanced effect on the MEP principle, giving rise to interesting variations from MEP. This talk will focus on some of the results described above. Extensions of this study to other types of pattern selection and fluid structure interaction problems will also be discussed.
References
1. B.J.Chung and A. Vaidya, An optimal principle in fluid-structure interaction, Physica D, 237( 22), 2945-2951, 2008.
2. B.J. Chung, McDermid, K. and A. Vaidya, On the affordances of the MaxEP principle, European Physical Journal B: Condensed Matter and Complex Systems, 87, 2014.
3. B. Chung, B. Ortega, A. Vaidya, Entropy Production in a Fluid-Solid System Far From Thermodynamic Equilibrium, European Physical Journal E: Soft Matter and Biological Physics, 40: 105, 2017.
Information flow and energy landscape of mind states
Marco Alberto Javarone1,2 and Srivas Chennu1
1 School of Computing, University of Kent, UK
2 nChain LDT, London, UK
Abstract. States of mind, as the consciousness, result from the collective dynamics occurring in the Brain. Broadly speaking, the latter works as a transducer, where particle interactions at synaptic level generate an electrical current flowing through dendrites and axons, and vice versa.
From the point of view of statistical physics, a state of mind can be viewed as an equilibrium state, corresponding from different possible brain configurations. Therefore, as for a much simpler spin model, the set of the different brain configurations can be pictured in an energy landscape. For instance, considering two living states like consciousness and unconsciousness, the former is expected to have an energy higher than the latter, as well as a higher information flow (e.g. among the different components, as brain areas).
Although the provided description may sound speculative, we deem that EEG signals (i.e. those resulting from the electrical activity of the brain) might be exploited for providing some insightful clue that supports our picture of mind and brain dynamics.
To this end, we analyze EEG signals by using a novel method, which establishes a direct link between energy and information flow that we have in the brain.
In particular, the proposed method is defined as follows:
1) Measure the functional connectivity (by using the wPLI index), between electrodes, at different frequencies.
2) For each channel (e.g. delta, theta, etc) a connectivity matrix is defined, i.e. a network where nodes correspond to electrodes, whose correlations are mapped to edges.
3) Edges are transformed into ‘electrical resistances’, so that each network becomes an 'electrical circuit'.
4) Considering the relative power of each channel, and the ‘effective resistance’ between pairs of electrodes, we compute the ‘current’ circulating through each network.
Eventually, we apply this method on EEG signals recorded on individuals undergoing a deep sedation.
Figure 1. Averaged current (I) in each network. The black line indicates the summation of all currents. Measures are performed on the following states: C: conscious, S: sedation, U: unconscious, R: recovering. Results have been averaged over different nine healthy individuals.
Figure 1 shows results of our early analyses. Remarkably, on average, the value of the current decreases as an individual reaches a deep unconscious state. In particular, in full agreement with our previous description, we speculate that the current we are measuring might represent a kind of information flow in the brain, so that unconscious states lead to a reduced flow. In addition, studying topological variations in EEG networks, we identified some symmetries that could be related to conservation principles in the brain.
It is worth to highlight that while further investigations, as those we are currently performing on real data, are mandatory for corroborating the provided overview, preliminary results seem to be promising for obtaining a holistic description of the brain. Notably, a description where 'information' and 'energy' transform each other giving rise to what we call mind.
Structure from noise: Mental errors yield abstract representations of events
Christopher W. Lynn1, Ari E. Kahn2,3, & Danielle S. Bassett1,3,4,5
1Department of Physics & Astronomy, College of Arts and Sciences, University of Pennsylvania, Philadelphia, PA 19104 USA
2Department of Neuroscience, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 USA
3Department of Bioengineering, School of Engineering and Applied Sciences, University of Pennsylvania, Philadelphia, PA 19104 USA
4Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 USA
5Department of Electrical & Systems Engineering, School of Engineering and Applied Sciences, University of Pennsylvania, Philadelphia, PA 19104 USA
Humans are adept at uncovering complex associations in the world around them, yet the underlying mechanisms remain poorly understood. Intuitively, learning the higher-order network structure of statistical relationships should involve sophisticated mental processes, expending valuable computational resources. Here we propose a competing perspective: that higher-order associations actually arise from natural errors in learning. In particular, we hypothesize that, when building models of the world, the brain is finely-tuned to maximize accuracy while simultaneously minimizing the use of computational resources. From this simple assumption, we show that the free energy principle necessarily leads to a maximum entropy description of people's internal expectations about the transition structures underlying sequences of ordered events. As we vary the amount of statistical noise in our model, we find that higher-order features of transition networks organically come into focus while the fine-scale structure fades away, thus providing a concise mechanism explaining an array of previously observed network effects on human expectations. Additionally, our model asserts that human expectations should depend critically on the different topological scales in a transition network, a prediction that we subsequently test and validate in a novel experiment. Generally, the surprising role of statistical noise in shaping human expectations highlights the value of simple thermodynamic models for understanding cognition, with relevance for learning and planning as well as diagnosing and treating psychiatric disorders.
References:
[1] C.W. Lynn, A.E. Kahn, and D.S. Bassett, Structure from noise: Mental errors yield abstract representations of events. (Submitted, https://arxiv.org/abs/1805.12491)
[2] A.E. Kahn, E.A. Karuza, J.M. Vettel, and D.S. Bassett, Network constraints on learnability of probabilistic motor sequences. (In Revision at Nat. Hum. Behav., https://arxiv.org/abs/1709.03000)
[3] E.A. Karuza, A.E. Kahn, S.L. Thompson-Schill, and D.S. Bassett, Process reveals structure: How a network is traversed mediates expectations about its architecture. Scientific Reports 7, 12733, 2017.
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