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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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VII. WumanKinder: An Emergent Earthomo Transition in Individuality

2. Systems Neuroscience: Multiplex Networks and Critical Function

Sporns, Olaf. Graph Theory Methods: Applications in Brain Networks. Dialogues in Clinical Neuroscience. 20/2, 2018. The Indiana University neuropsychologist (search) is a leading theorist in this enchanted field as it weaves through the 2010s toward epic achievements. This paper is notably cited as a basis for Max Bertolero and Danielle Bassett’s Scientific American (July 2019) popular review (above). As many other realms, mathematic findings of equally real interconnections between previously found discrete objects and entities are fostering a relational revolution from particles and galaxies to persons and societies. See also The Diverse Club by Max Bertolero, et al in Nature Communications (8/1277, 2017).

Network neuroscience is a thriving and rapidly expanding field. Empirical data on brain networks, from molecular to behavioral scales, are increasing in size and complexity. These developments require appropriate tools and methods that model and analyze brain network data, such as those provided by graph theory. This brief review surveys commonly used and neurobiologically apt graph measures and techniques. Among these, the detection of network communities or modules, and of central network elements that facilitate communication and signal transfer are particularly salient. We note a growing use of generative models, temporal and multilayer networks, as well as algebraic topology. (Abstract excerpt)

Sporns, Olaf. Network Attributes for Segregation and Integration in the Human Brain. Current Opinion in Neurobiology. 23/2, 2018. We record this entry by the Indiana University neurotheorist in mid 2018 to show how far collaborative studies of neural topologies and dynamic communications have advanced in just five years. In 2013 the endeavor was beginning to quantify independent, universally manifest, multiple node and link topologies. As the Abstract notes, they did infer a reciprocal dynamic of semi-autonomous modules and associations within cerebral realms and activities.

Network studies of large-scale brain connectivity have begun to reveal attributes that promote the segregation and integration of neural information: communities and hubs. Network communities are sets of regions that are strongly interconnected among each other while connections between members of different communities are less dense. The clustered connectivity of network communities supports functional segregation and specialization. Network hubs link communities to one another and ensure efficient communication and information integration. This review surveys a number of recent reports on network communities and hubs, and their role in integrative processes. An emerging focus is the shifting balance between segregation and integration over time, which manifest in continuously changing patterns of functional interactions between regions, circuits and systems. (Abstract)

Sporns, Olaf. Network Attributes for Segregation and Integration in the Human Brain. Current Opinion in Neurobiology. 23/1, 2012. As intimated for ages, people are being quantified by way of our very cerebral endowments as true microcosmic exemplars and portals. Akin to a growing number of citations here, and throughout, the Indiana University neuroscientist evinces how a human brain is graced by nature’s universal geometries of networks, modules, communities and their dynamical interrelations. Along with Alex Fortino, et al, above, and others, this is achieved by a reciprocity of autonomy and assembly. See in the same journal (22/1, 2012) “Human Connectomics” by Sporns and Timothy Behrens, and Sporns’ new book Discovering the Human Connectome (MIT Press, 2012). And one might recall the British neuroscientist Charles Sherrington famous metaphor from his 1942 Man on His Nature of a thoughtful brain as an “enchanted loom.”

Network studies of large-scale brain connectivity have begun to reveal attributes that promote the segregation and integration of neural information: communities and hubs. Network communities are sets of regions that are strongly interconnected among each other while connections between members of different communities are less dense. The clustered connectivity of network communities supports functional segregation and specialization. Network hubs link communities to one another and ensure efficient communication and information integration. This review surveys a number of recent reports on network communities and hubs, and their role in integrative processes. An emerging focus is the shifting balance between segregation and integration over time, which manifest in continuously changing patterns of functional interactions between regions, circuits and systems. (Abstract)

The great topmost sheet of the mass, that where hardly a light had twinkled or moved, becomes now a sparkling field of rhythmic flashing points with trains of traveling sparks hurrying hither and thither. The brain is waking and with it the mind is returning. It is as if the Milky Way entered upon some cosmic dance. Swiftly the head mass becomes an enchanted loom where millions of flashing shuttles weave a dissolving pattern, always a meaningful pattern though never an abiding one; a shifting harmony of subpatterns. (Sherrington)

Sporns, Olaf. Networks of the Brain. Cambridge: MIT Press, 2010. As a good indication of a field reaching mature acceptance, the Indiana University computational neuroscientist here presents a book-length review of this conceptual revolution. Fourteen chapters cover all aspects of generic networks, neuroanatomy, dynamic cognition, neural small worlds, and so on. Once more nature repeats in our very cranium its universal, self-organized criticality of “hierarchical modularity” and “nested levels of clustered communities.”

This book has been a single long argument for a similar shift (as in genetics) toward networks and complex systems approaches in neurosciences. The study of brain networks defines a new and promising direction for uncovering the mechanisms by which the collective action of large numbers of nerve cells give rise to the complexity of the human mind. (325) I have argued throughout the book for the considerable power of applying network science and network thinking to neural systems. From the dynamics of social groups to the behavior of single cognitive agents, from the structural and functional connectivity of their neural systems to the morphology and metabolism of individual neurons, and the interactions of their component biomolecules – to modify a popular phrase, its networks all the way down. (325)

Sporns, Olaf. Small-World Connectivity, Motif Composition, and Complexity of Fractal Neuronal Connections. BioSystems. 85/1, 2006. We reprint the abstract to fully convey this cerebral microcosm.

Connection patterns of the cerebral cortex consist of pathways linking neuronal populations across multiple levels of scale, from whole brain regions to local minicolumns. This nested interconnectivity suggests the hypothesis that cortical connections are arranged in fractal or self-similar patterns. We describe a simple procedure to generate fractal connection patterns that aim at capturing the potential self-similarity and hierarchical ordering of neuronal connections. We examine these connection patterns by calculating a broad range of structural measures, including small-world attributes and motif composition, as well as some global measures of functional connectivity, including complexity. As we vary fractal patterns by changing a critical control parameter, we find strongly correlated changes in several structural and functional measures, suggesting that they emerge together and are mutually linked. Measures obtained from some modeled fractal patterns closely resemble those of real neuroanatomical data sets, supporting the original hypothesis.

Sporns, Olaf. The Non-Random Brain: Efficiency, Economy, and Complex Dynamics. Frontiers in Computational Neuroscience. 5/Article 5, 2011. What to make of all these findings? If to imagine these many research and reports as part of and achieved by a worldwide collaborative brain learning on her/his own, what philosophical implications might accrue? That is to say, how does our evolved cerebral anatomy know to take upon itself this certain form of self-organized, scale-invariant networks, as in every other realm of nature and society? As scientists increasingly note, an independent, universally applicable mathematical source seems to be at implicate creative work.

Modern anatomical tracing and imaging techniques are beginning to reveal the structural anatomy of neural circuits at small and large scales in unprecedented detail. When examined with analytic tools from graph theory and network science, neural connectivity exhibits highly non-random features, including high clustering and short path length, as well as modules and highly central hub nodes. These characteristic topological features of neural connections shape non-random dynamic interactions that occur during spontaneous activity or in response to external stimulation. (1)

However, modern circuit mapping and neural recording studies unequivocally show that the brain is not a random network. Instead, at different levels of scale, network studies have identified a number of specific non-random structural attributes, particularly the existence of network communities interlinked by hub regions. The modular small world of brain networks simultaneously promotes their economy and efficiency, by enabling their physical realization at low cost of wiring volume and metabolic energy, while also allowing efficient information flow. Non-random structure leads to the emergence of complex dynamics, generating a diverse repertoire of brain states that are differentially engaged during ongoing neural activity as well as in response to stimulation and task demands. (11)

Sporns, Olaf and Christopher Honey. Small Worlds Inside Big Brains. Proceedings of the National Academy of Sciences. 103/19219, 2006. This note comments on a research report by Bassett, Danielle, et al. Adaptive Reconfiguration of Fractal Small-World Human Brain Functional Networks. in the same issue which finds and verifies the presence of a consistent nest of structure and system.

Perhaps the most remarkable finding of the study by Bassett, et al is the relative invariance of the network topology across all physiologically relevant frequency bands, forming a self-similar or fractal architecture. (19219) Thus it appears that brain networks preserve global topological characteristics (continually maintaining the balance of efficient local and global processing) while flexibly adapting the specifics of the topology to satisfy changing task demands. (19220)

Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters. (Bassett, et al, 19518) We have shown that there is a scale-invariant or fractal organization of large scale brain functional networks in the resting state, which consistently demonstrate small-world properties in the scaling regime 2-37.5 Hz. (Bassett, et al, 19522)

Sporns, Olaf, et al. Organization, Development and Function of Complex Brain Networks. Trends in Cognitive Systems. 8/9, 2004. The same scale-free principles found in every natural and social realm are equally present in the human brain. Cortical systems in their intricate connectivity exhibit a robust small world, scale-free architecture.

We suggest that network analysis offers new fundamental insights into global integrative aspects of brain function, including the origin of flexible and coherent cognitive state within the neural architecture. (418)

Stam, Cees and Elizabeth van Straaten. The Organization of Physiological Brain Networks. Clinical Neurophysiology. 123/1067, 2012. VU University Medical Center, Amsterdam, neurophysicians describe and attest well to how much of a natural microcosm are actually we, especially in the anatomy and cogitation of our cerebral endowment.

There is an urgent need to understand the brain as a complex structural and functional network. Interest in brain network studies has increased strongly with the advent of modern network theory and increasingly powerful investigative techniques such as "high-density EEG", MEG, functional and structural MRI. Modern network studies of the brain have demonstrated that healthy brains self-organize towards so-called "small-world networks" characterized by a combination of dense local connectivity and critical long-distance connections. In addition, normal brain networks display hierarchical modularity, and a connectivity backbone that consists of interconnected hub nodes. This complex architecture is believed to arise under genetic control and to underlie cognition and intelligence. (Abstract)

Stephen, Damian, et al. The Dynamics of Insight: Mathematical Discovery as a Phase Transition. Memory & Cognition. 37/8, 2011. With coauthors Rebecca Boncoddo, James Magnuson, and James Dixon, University of Connecticut research psychologists add another take upon the scientific witness of a universally self-organizing materiality, which can be see arising from the “physical” cosmos to human cognitive faculties. And might our whole earth learn as its sequential trajectory now ascends to a global sphere? See also Stephen’s web publications page, and Dixon, et al, below for on-going work.

In recent work in cognitive science, it has been proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Furthermore, it has been unclear whether dynamics could effectively address the emergence of abstract concepts (e.g., language, mathematics). Here, we provide evidence that a quintessentially cognitive phenomenon — the spontaneous discovery of a mathematical relation — emerges through self-organization. (Abstract, 1132)

Attempts to understand how such networks change during learning has revealed that many of these models operate under the principles of self-organization from nonlinear dynamics. The same higher order relations that govern self-organization in a wide variety of other domains, such as fluids, lasers, and ferromagnets, are exhibited by a class of connectionist models that learn via Hebbian and SOM algorithms. (1134) The present study suggests that the reach of self-organization extends to the spontaneous formation of new structures at the conceptual level. Even quite abstract concepts, such as mathematical relation, emerge according to the principles of self-organization. (1144)

Stoop, Ralph, et al. Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains. Physical Review Letters. 110/108105, 2013. By way of sophisticated theory and experiment, Swiss neurophysicists add insight to the nonlinear topologies and thoughtful dynamics that grace cerebral anatomy and activity. To wit, it’s not dots, or neuronal columns, that matter as much as the relational connections between them. And this surmise seems to equally apply throughout nature and society from genomes to communities. This clever work was highlighted online by the journal sponsor, the American Physical Society APS, an excerpt of its notice is below.


We study to what extent cortical columns with their particular wiring boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic—intercolumnar—scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks. (Article Abstract)

Synopsis: A Double Power Law Powers Brain. The extraordinary complexity of the brain makes it hard to identify its underlying organizational principles. Ralph Stoop, at the University of Basel, Switzerland, and colleagues used computational models of neural networks to deduce that the details of the organization within individual columns are not very important. Instead, what counts is how different columns are interconnected. To study the importance of the “wiring” configuration within columns, the team arranged mathematical models of neurons into networks and compared configurations with different connectivities. Interestingly, the ability of these simulated columns to carry out a computational task, such as the classification of Arabic digits, did not significantly improve when the connection strengths or the layered arrangement were chosen to mimic those often seen in biological columns.

In contrast, the researchers found that the connections between columns in a side-by-side sheet made a big difference to the speed with which information propagated laterally to coordinate activity across the simulated cortex. The authors compared networks with different spatial distributions of connections between simplified columns. For example, in “scale-free” networks—including many real-world networks—the number of connections decreases with their length as a single power law, so there are few relatively long links. But Stoop and his colleagues found that, for the same total length of “wires,” signals spread more quickly in a network described by two power laws. This distribution, which was suggested by microscopy investigations in lab animals, includes a larger number of very long connections that help information to propagate quickly between distant columns. (Don Monroe, APS)

Stuart, Susan and Gordana Dodig Crnkovic, eds. Computation, Information, Cognition: The Nexus and the Liminal. Newcastle: Cambridge Scholars Publishing, 2007. Some 25 chapters engage these technical domains of neural net nodes and links and their biosemiotic activities. (Web definitions of iminal: ambiguity, openness, and indeterminacy, poised between two states.) Typical papers are Meaning and Self-Organization in Cognitive Science by Arturo Carsetti and The Informational Architectures of Biological Complexity by Pedro Marijuan and Raquel del Moral. Heavy slogging which may yet imply that our reality in inherently textual in kind, if we could only learn together to translate and read its salutary message.

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