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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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VI. Earth Life Emergence: Development of Body, Brain, Selves and Societies

2. Systems Neuroscience: Multiplex Networks and Critical Function

Di Ieva, Antonio, ed.. The Fractal Geometry of the Brain. New York: Springer, 2016. A Macquarie University, Sydney neuroscientist (search) collects the latest research in a dedicated volume on how much cerebral dynamics are graced and facilitated by nested self-similar topologies, aka “fractalomics.” Typical chapters are Does a Self-Similarity Logic Shape the Organization of the Nervous System? by Diego Guidolin, et al and The Fractal Geometry of the Human Brain: An Evolutionary Perspective by Michel Hofman (both Abstracts next). We also want to record parallel efforts by Luigi Agnati (search) and colleagues.

From the morphological point of view, the nervous system exhibits a fractal, self-similar geometry at various levels of observations, from single cells up to cell networks. From the functional point of view, it is characterized by a hierarchic organization in which self-similar structures (networks) of different miniaturizations are nested within each other. On this basis, the term “self-similarity logic” was introduced to describe a nested organization where at the various levels almost the same rules (logic) to perform operations are used. Thus, they can represent key concepts to describe its complexity and its concerted, holistic behavior. (Abstract excerpt, Guidolin, et al)

The evolution of the brain in mammals is characterized by changes in size, architecture, and internal organization. Also the geometry of the brain, and the size and shape of the cerebral cortex, has changed notably during evolution. Comparative studies of the cerebral cortex suggest that there are general architectural principles governing its growth and development. In this chapter some design principles and operational modes that underlie the fractal geometry and information processing capacity of the cerebral cortex in primates, including humans, will be explored. (Abstract, M. Hofman)

Di Ieva, Antonio, et al. Fractals in the Neurosciences. Part I: General Principles. The Neuroscientist. 20/4, 2014. Brain researchers with posts in Canada, Austria, Spain, Poland and Venezuela offer a good review to date of realizations that nature’s ubiquitous recurrence of the same forms everywhere indeed also braces and graces our cerebral faculty, as it facilitates our constant cognitive activities.

The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micro-networks and macro-networks are all factors that limit an Euclidean geometry and linear dynamics. The introduction of fractal geometry for the quantitative description of complex natural systems has been a major paradigm shift. Modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at molecular, anatomic, functional, and pathological levels. Fractal geometry is a mathematical model that offers a universal language for neurons and glial cells as well as the whole brain with its physiopathological spectrums. For a holistic view of fractal geometry of the brain, we review here the basic concepts and main applications. (Abstract excerpts)

Di Leva, Antonio, et al. Fractals in the Neurosciences. The Neuroscientist. 20/4, 2014. With Fabio Grizzi, Herbert Jelinek, Andras Pellionisz, and Gabriele Losa, theorists from Canada, Austria, Italy, Abu Dhabi, Australia, Switzerland and the USA who have previously proposed that such a topological “recursion” graces brain anatomy, physiology, and cognition since the 1990s here confirm its distinctive and effective presence.

The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives. Fractal geometry is a mathematical model that offers a universal language for the quantitative description of neurons and glial cells as well as the brain as a whole, with its complex three-dimensional structure, in all its physiopathological spectrums. For a holistic view of fractal geometry of the brain, we review here the basic concepts of fractal analysis and its main applications to the basic neurosciences. (Abstract)

Dixon, James, et al. Multifractal Dynamics in the Emergence of Cognitive Structure. Topics in Cognitive Science. Online October, 2011. With John Holden, Daniel Mirman, and Damian Stephen, now at Harvard, further quantifications of how “cognition is characterized by seamless interactions among multiple scales of organization (e.g., chemical, physiological, and environmental).”

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. (1)

Dogaru, Radu. Universality and Emergent Computation in Cellular Neural Networks. River Edge, NJ: World Scientific, 2003. A technical book on recurrent elemental cells that interact or “collaborate” in a nested fashion from which emerges an image or thought. In translation, what is again found is the universal creative system in its node and link, agent and relation (male and female) complementarity.

A similar hierarchical and cellular organization is revealed in language, which could be considered as “image of our brains.” Basic cells (phonemes or characters in the written language) collaborate in an emergent manner to form words, which then are again combined in phrases and so on providing a structured reflection of the outer world.
Recapitulating, universal characteristics of our world can be captured in the emergent dynamics of a cellular model where a population of similar cells exchanges information locally with the cells in their neighborhood. (1)

Donahoe, John and Vivian Packard Dorsel, eds. Neural-Networks Models of Cognition. Amsterdam: Elsevier Science, 1997. Self-organizing neural nets guide brain development, plasticity, perception, stimuli responses, reinforcement learning, and complex behavior.

Dumas, Guillaume, et al. Anatomical Connectivity Influences both Intra- and Inter-Brain Synchronizations. PLoS One. 7/5, 2013. As cited by Kelso, et al, 2013 herein, CNRS and Universite Pierre et Marie Curie Paris neuroscientists are able to quantify an extension of the internal coordination dynamics of a human brain to a dyad of interacting individuals. How much then, we ought to wonder, might our proximate and distant communications be taking upon the essence of a true social and global neurosphere.

Recent development in diffusion spectrum brain imaging combined to functional simulation has the potential to further our understanding of how structure and dynamics are intertwined in the human brain. At the intra-individual scale, neurocomputational models have already started to uncover how the human connectome constrains the coordination of brain activity across distributed brain regions. In parallel, at the inter-individual scale, nascent social neuroscience provides a new dynamical vista of the coupling between two embodied cognitive agents. Using EEG hyperscanning to record simultaneously the brain activities of subjects during their ongoing interaction, we have previously demonstrated that behavioral synchrony correlates with the emergence of inter-brain synchronization. Here, we use a biophysical model to quantify to what extent inter-brain synchronizations are related to the anatomical and functional similarity of the two brains in interaction. Results show a potential dynamical property of the human connectome to facilitate inter-individual synchronizations and thus may partly account for our propensity to generate dynamical couplings with others. (Abstract)

To conclude, the nascent social neuroscience could be taken as a new theoretical and experimental workspace in the study of complex systems coupling. Previous studies have already demonstrated the theoretical possibility for dynamical modeling of complex social behavior and sensorimotor coupling in agents. In parallel, neurobiological models have also been proposed to adopt a dynamical and developmental account of sociocognitive functions at the neural level. The hyperscanning technique starts to provide evidence of the relationships between neural dynamics and social coordination dynamics. Our findings encourage the development of a computational social neuroscience through the extension of existent models at an interindividual level. It could provide new insights about the neurobiological mechanisms underlying social cognition and related pathologies. (10)

Expert, Paul, et al. Self-Similar Correlation Function in Brain Resting-State Functional Magnetic Resonance Imaging. Journal of the Royal Society Interface. Online September 22, 2010. In contrast to 2011 Greg Paperin, et al (2011) in this journal who describe a generic complex system, this contribution explains its iconic presence in human cerebral function. A research team from Imperial College London and Northwestern University that includes Henrik Jensen, Kim Christensen, and Dante Chialvo, as a meld of statistical physics with nonlinear science via self-organized criticalities, report their findings of a spatial and temporal scale invariance across many neural realms. By so doing, as cited next, nature’s essential complementarity is once again revealed. Our brains are equally poised in a mutual balance of local concerns within a global context, the same yang and yin, me and we, entity and environment, as everywhere else.

An important problem in neuroscience is to understand the mechanism by which the human brain’s 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e. they are functionally integrated. We show that this two-point correlation function extracted from resting-state functional magnetic resonance imaging data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behaviour of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. (1)

From a dynamical systems perspective, the uncovered self-similarity implies that the brain dynamics is permanently at an intermediate state between two extremes, one that is strongly correlated across large distances, producing transient highly integrated cortex states, and the other in which only nearby clusters are acting in sync. This scenario, of long-range correlations in space and time, is only conceivable in dynamical systems at criticality and could be the manner in which the cortex can manage to produce an arbitrarily large repertoire of interaction patterns among arbitrarily distant cortical sites. (6)

Fernando, Chrisantha, et al. Selectionist and Evolutionary Approaches to Brain Function. Frontiers in Computational Neuroscience. 6/Art. 24, 2012. With Eors Szathmary and Phil Husbands, another contribution that articulates the deep affinity of neural activities with life’s long iterative development. As Richard Watson, Hava Siegelmann, John Mayfield, Steven Frank, and increasing number contend, this achieves a 21st century appreciation of how “natural selection” actually applies. While a winnowing optimization toward “good enough to survive” goes on, the discovery of dynamic, learning-like, algorithms can now provide a prior genetic-like guidance.

We consider approaches to brain dynamics and function that have been claimed to be Darwinian. These include Edelman’s theory of neuronal group selection, Changeux’s theory of synaptic selection and selective stabilization of pre-representations, Seung’s Darwinian synapse, Loewenstein’s synaptic melioration, Adam’s selfish synapse, and Calvin’s replicating activity patterns. Except for the last two, the proposed mechanisms are selectionist but not truly Darwinian, because no replicators with information transfer to copies and hereditary variation can be identified in them. Bayesian models and reinforcement learning are formally in agreement with selection dynamics. A classification of search algorithms is shown to include Darwinian replicators (evolutionary units with multiplication, heredity, and variability) as the most powerful mechanism for search in a sparsely occupied search space. Finally, we review our recent attempts to construct and analyze simple models of true Darwinian evolutionary units in the brain in terms of connectivity and activity copying of neuronal groups. (Abstract)

The production of functional molecules is critical for life and also for an increasing proportion of industry. It is also important that genes represent what in cognitive science has been called a “physical symbol system.” Today, the genetic code is an arguably symbolic mapping between nucleotide triplets and amino acids. Moreover, enzymes “know” how to transform a substrate into a product, much like a linguistic rule “knows” how to act on some linguistic constructions to produce others. How can such functionality arise? Combinatorial chemistry is one of the possible approaches. The aim is to generate-and-test a complete library of molecules up to a certain length. (9)

In summary we have distinguished between selectionist and truly Darwinian theories, and have proposed a truly Darwinian theory of Darwinian Neurodynamics. The suggestion that true Darwinian evolution can happen in the brain during, say, complex thinking, or the development of language in children, is ultimately an empirical issue. Three possible outcomes are possible: (i) nothing beyond the synapse level undergoes Darwinian evolution in the brain; (ii) units of evolution will be identified that are very different from our “toy model” suggestions in this paper (and elsewhere); and (iii) some of the units correspond, with more complex details, to our suggested neuronal replicators. (17)

Fornito, Alex, et al. Bridging the Gap between Connectome and Transcriptome. Trends in Cognitive Sciences. 23/1, 2019. Into the year 2019, advances such as imaging techniques and computational graphics allow Monash University, Australia clinical neuroscientists to discern spatial and temporal relations from DNA nucleotides to protein interactions via innate network paths. The wide use of –omic suffixes implies how important the genetic factors are in neural activity. The article glossary contains a Hierarchical Modularity term as another example of how nature’s universal complexity is so manifest in our own cerebral raiment.

The recent construction of brain-wide gene expression atlases, which measure the transcriptional activity of thousands of genes in multiple anatomical locations, has made it possible to connect spatial variations in gene expression to distributed properties of connectome structure and function. These analyses have revealed that spatial patterning of gene expression and neuronal connectivity are closely linked, following broad spatial gradients that track regional variations in microcircuitry, inter-regional connectivity, and functional specialisation. Superimposed on these gradients are more specific associations between gene expression and connectome topology that appear conserved across diverse species and different resolution scales. (Abstract)

The transcriptome is the set of all RNA molecules in one cell or a population of cells. It broadly “transcribes” genome DNA to proteome proteins. A connectome is a comprehensive map of neural networks in the brain. In another view, it includes mappings of all neural connections within an organism’s nervous system. (Wikipedia)

Fornito, Alex, et al. Competitive and Cooperative Dynamics of Large-Scale Brain Functional Networks Supporting Recollection. Proceedings of the National Academy of Sciences. 109/12788, 2012. University of Melbourne and Cambridge University behavioral neuroscientists further verify the presence of nature’s balanced complementarity of a relative agent-like neuronal or network semi-autonomy and a more relational modularity across cerebral anatomy and activities. Consider with Olaf Sporns 2012 herein who uses the phrase “segregation and integration” to similarly describe.

Analyses of functional interactions between large-scale brain networks have identified two broad systems that operate in apparent competition or antagonism with each other. One system, termed the default mode network (DMN), is thought to support internally oriented processing. The other system acts as a generic external attention system (EAS) and mediates attention to exogenous stimuli. Using methods to isolate task-related, context-dependent changes in functional connectivity between these systems, we show that increased cooperation between the DMN and a specific right-lateralized frontoparietal component of the EAS is associated with more rapid memory recollection. We also show that these cooperative dynamics are facilitated by a dynamic reconfiguration of the functional architecture of the DMN into core and transitional modules, with the latter serving to enhance integration with frontoparietal regions. In particular, the right posterior cingulate cortex may act as a critical information-processing hub that provokes these context-dependent reconfigurations from an intrinsic or default state of antagonism. Our findings highlight the dynamic, context-dependent nature of large-scale brain dynamics and shed light on their contribution to individual differences in behavior. (Abstract)

Freeman, Walter. A Neurobiological Theory of Meaning in Perception. International Journal of Bifurcation and Chaos. 13/9, 2003. The first of a five part series, this article is subtitled: “Information and Meaning in Nonconvergent and Nonlocal Brain Dynamics.” Highly technical neuroscience which argues that the current emphasis on information processing misses the main activity going on: an organism’s attempt to make sense of its environment. In this regard, information and meaning might appear as left and right hemisphere complements.

The aim of this tutorial is to document a novel approach to brain function, in which the key to understanding is the capacity of brains for self-organization. (2493)

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