VII. Our Earthuman Ascent: A Major Evolutionary Transition in Twndividuality

2. Systems Neuroscience: Multiplex Networks and Critical Function

Shin, Chang-Woo and Seunghwan Kim. Self-organized Criticality and Scale-free Properties in Emergent Functional Neural Networks. www.arxiv.org/abs/cond-mat/0408700. Published November 9, 2004 online as Condensed Matter 0408700, the paper argues that rather than learning by Hebbian rules, the brain acts as a dynamic nonlinear system.

We show that the functional structures in the brain are self-organized to both the small-world and the scale-free networks by synaptic re-organization by the spike timing dependent synaptic plasticity.

Singh, Soibam, et al. Scaling in Topological Properties of Brain Networks. Nature Scientific Reports. 6/24926, 2016. This work at the frontiers of systems neuroscience by an eight person team based at Jawaharlal Nehru University and McGill University can exemplify, as the Abstract conveys, how much nature’s universal dynamic lineaments are present in our cerebral crown.

The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure, which reveals the self-similar rules governing the network structure. Further, the calculated fractal dimensions of brain networks of different species are found to decrease when one goes from lower to higher level species which implicates the more ordered and self-organized topography at higher level species. The sparsely distributed hubs in brain networks may be most influencing nodes but their absence may not cause network breakdown, and centrality parameters characterizing them also follow one parameter scaling law indicating self-similar roles of these hubs at different levels of organization in brain networks. The local-community-paradigm decomposition plot and calculated local-community-paradigm-correlation co-efficient of brain networks also shows the evidence for self-organization in these networks. (Abstract)

Sizemore, Ann, et al. The Importance of the Whole: Topological Data Analysis for the Network Neuroscientist. Network Neuroscience. 3/3, 2019. In this special geometry issue, University of Pennsylvania researchers including Danielle Bassett provide a tutorial review of understandings about how our bicameral brains are graced by a dynamic array of multiplex webworks. The presence of an algebraic topology and a persistent homology, aka homological algebra, is seen to provide mathematical explanations. Simplical complexes are also identified as they serve to organize and inform. Some eight decades after C. S. Sherrington famous enchanted loom metaphor, the field of brain studies has finally reached a full quantification. See also Topological Gene Expression Networks Recapitulate Brain Anatomy and Function by Alice Patania, et al, and Columnar Connectome by Ana Wang Roe in the same issue.

Data analysis techniques have fundamentally improved our understanding of neural systems and the complex behaviors they support. Yet the restriction of network techniques to pairwise interactions does not take into account intrinsic topological features that are crucial for system function. To detect and quantify these topological features, we turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We also provide an introduction to persistent homology that builds a global descriptor of system structure. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. (Abstract excerpt)

Sperber, Dan. In Defense of Massive Modularity. Dupoux, E., ed. Language, Brain and Cognitive Development. Cambridge: MIT Press, 2001. Sperber wades into the debate on the side of a specialized, modular brain. As an observation, it would be expected from the recurrent course of self-organization that semi-autonomous modules similarly occur in cerebral form and function.

Spitzer, Manfred. The Mind within the Net. Cambridge: MIT Press, 1999. A good introduction to self-organizing neural networks. As so composed, the human brain engages in information processing and most of all pattern recognition. This function has mostly been excluded in mechanistic science because in its left-hemisphere emphasis, integrative patterns are not expected, so are not seen.

Spivey, Michael. The Continuity of Mind. Oxford: Oxford University Press, 2007. A Cornell University neuroscientist proposes that the limited computational model be set aside in favor of how dynamic system trajectories infuse our continually flowing cerebral activities.

The cognitive and neural sciences have been on the brink of a paradigm shift for over a decade. The traditional information-processing framework in psychology, with its computer metaphor of the mind, is still considered to be the mainstream approach. However, the dynamical systems perspectives on mental activity are now receiving a more rigorous treatment, allowing it to more beyond trendy buzzwords. The Continuity of the Mind will help to galvanize the forces of dynamical systems theory, cognitive and computational neuroscience, connectionism, and ecological psychology that are needed to complete this paradigm shift. (book jacket)

Finally, another hallmark property of self-organizing recurrent systems, like the logistic map, is fractal structure. Note the self-similar nature of how the shape of each tiny bifurcation resembles the shape of the larger ones. Fractal structure like this can be seen all over nature by looking at multiple spatial scales of coastlines, mountain ranges, trees, even the human vascular system. (89)

Sporns, Olaf. Brain Networks and Embodiment. Mesquita, Batja, et al, eds. The Mind in Context. New York: Guilford Press, 2010. An exemplary paper to date by the Indiana University systems neuroscientist of how everything neural and cognitive is being reconceived in terms of a similar self-organizing, scalar, systemic complexities. An aspect to be noted, as per the quote, is another instance of a mutual reciprocity of divergence and convergence, diversity and unity.

In summary, network interactions can be formally described by using concepts from statistical information theory, for example, mutual information, integration, and complexity. Some of these measures allow us to characterize statistical integrations in a network as a whole. When structural connections are arranged in such a way as to maximize some of these informational quantities, it appears that complexity is uniquely associated with structural patterns that resemble those of brain networks. This result is consistent with the theoretical idea that brain networks balance segregation and integration, which we defined as complexity. High complexity allows networks to integrate efficiently large amounts of information, a capacity that has been linked to consciousness. (54)

Many complex systems comprise large numbers of components that engage in dynamic interactions and give rise to emergent phenomena. The brain is no exception: One could argue that the nested hierarchical structure of brain systems, their propensity for spontaneous and exogenously driven nonlinear dynamics, and their embeddedness within a behaving organism, presents unique challenges to our attempts to understand how the brain/mind works. (58-59)

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.

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