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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

Ishikawa, Masumi, et al, eds. New Developments in Self-Organizing Systems. Neural Networks. 17/8-9, 2004. A large edition dedicated to advances in understanding the brain’s dynamic, hierarchical formation and performance.

Kahn, D., et al. Dreaming and the Self-Organizing Brain. Journal of Conscious Studies. 7/7, 2000. The authors contend that conceiving the brain as a fractally scaled, critically poised system can bring new understandings and explanations for dream activity and content.

Kaiser, Marcus. A Tutorial in Connectome Analysis: Topological and Spatial Features of Brain Networks. NeuroImage. 57/3, 2011. In an issue on Educational Neuroscience, a Newcastle University neuroinformatics specialist provides an overview of this systems turn to study pervasive interconnections from local neuron and net to global cerebration. And we enter as an example, mid 2011, of how much this “–omics” view is accepted across every natural, organismic, and social realm. However might we imagine a “cosmic connectome” whence the whole genesis uniVerse, or “cosmome” (putting “mom” back again), be rightly appreciated as the animate, generative essence it is?

High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organizations of the connectome at the macroscopic level of connectivity between brain regions as well as the microscopic level of connectivity between neurons. We will describe topological features at three different levels: the local scale of individual nodes, the regional scale of sets of nodes, and the global scale of the complete set of nodes in a network. Such features can be used to characterize components of a network and to compare different networks, e.g. the connectome of patients and control subjects for clinical studies. At the global scale, different types of networks can be distinguished and we will describe Erdös–Rényi random, scale-free, small-world, modular, and hierarchical archetypes of networks. Finally, the connectome also has a spatial organization and we describe methods for analyzing wiring lengths of neural systems. As an introduction for new researchers in the field of connectome analysis, we discuss the benefits and limitations of each analysis approach. (Abstract)

Kaiser, Marcus, et al. Hierarchy and Dynamics of Neural Networks. Frontiers in Neurodynamics. 4/Article 112, 2010. Amongst this burst of cyberscience communications, an Introduction to a special collection that adds further mature credence to how our cerebral anatomy and cognition is formed and functions by self-organizing complexities.

Kanai, Ryota, et al. Cerebral Hierarchies: Predictive Processing, Precision and the Pulvinar. Philosophical Transactions of the Royal Society B. 370/20140169, 2015. In an issue on Cerebral Cartography: A Vision of the Future edited by Semir Zeki, Japanese and British neuroscientists, including Karl Friston, opine that if a brain might best be appreciated as made to predict and plan, then its neural architecture should reflect this. This is a Bayesian brain view which seeks a good enough inference from past experience so as to deal with future happenstance. See also The BRAIN Initiative: A Review by Lyric Jorgenson, et al, Cerebral Cartography and Connectomics by Olaf Sporns, the publication of Cosnciousness: Here, There and Everywhere? by Giulio Tononi and Christof Koch.

The Bayesian Brain: Recent advances in theoretical neuroscience have inspired a paradigm shift in cognitive neuroscience. This shift is away from the brain as a passive filter of sensations towards a view of the brain as a statistical organ that generates hypotheses or fantasies which are tested against sensory evidence. In this formulation, the brain is, literally, a fantastic organ (fantastic: from Greek phantastikos, the ability to create mental images). This perspective can be traced back to Helmholtz and the notion of unconscious inference. This notion has been generalized to cover deep or hierarchical Bayesian inference—about the causes of our sensations—and how these inferences induce beliefs, movement and behaviour. (2) The pulvinar is the largest nucleus in the primate thalamus and has expanded in size during primate evolution—in parallel with other visual structures. The pulvinar has long been thought to play a role in mediating visual attention perhaps by registering the saliency of a visual scene.

Kello, Christopher. Critical Branching Neural Networks. Psychological Review. Online February, 2013. In a lengthy paper that exemplifies the current interdisciplinary reach of science studies from the big bang to big brains, a University of California, Merced, neuroscientist and Acting Dean of Graduate Studies, applies principles from statistical physics to help reveal dynamic cerebral topologies. By this synthesis, a steady scale-invariance from neurons to behavior can be demonstrated. Since cognitive anatomy and process is often poised at a phase transition self-organized criticality, multifractal spikings and webwork geometries are found to result.

It is now well-established that intrinsic variations in human neural and behavioral activity tend to exhibit scaling laws in their fluctuations and distributions. The meaning of these scaling laws is an ongoing matter of debate between isolable causes versus pervasive causes. A spiking neural network model is presented that self-tunes to critical branching and, in doing so, simulates observed scaling laws as pervasive to neural and behavioral activity. These scaling laws are related to neural and cognitive functions, in that critical branching is shown to yield spiking activity with maximal memory and encoding capacities when analyzed using reservoir computing techniques. The model is also shown to account for findings of pervasive 1/f scaling in speech and cued response behaviors that are difficult to explain by isolable causes. Issues and questions raised by the model and its results are discussed from the perspectives of physics, neuroscience, computer and information sciences, and psychological and cognitive sciences. (Abstract)

In many different studies of neural and behavioral activity, intrinsic variations have been reported to resemble scaling laws across a wide range of scales (Kello et al., 2010), which are decidedly unlike white noise. (230) These findings add to a vast literature on scaling laws found throughout nature, but their general meaning is an ongoing matter of debate. (230) The same basic debate between domain-specific versus domain-general explanations of scaling laws has been unfolding throughout the sciences for decades, suggestive of a deep issue at stake. If scaling laws are expressions of general principles, then those principles may illuminate relations between neural and behavioral scales of analysis. Relating these scales is a central issue in the psychological and cognitive sciences, and connectionist theories are perhaps the most explicit and formal in addressing this issue to date. (231)

Pervasive Scaling Laws and Criticality Based on results discussed thus far, let us accept for now that scaling laws of various kinds are widely associated with intrinsic variations in neural and behavioral activity and are pervasive to them. If intrinsic variations always reflect inherent component interactions, then what kind of interactions would lead to pervasive scaling laws? Physics provides us with a ready answer in critical phenomena studied in statistical mechanics. The field of statistical mechanics describes how the macroscopic quantities of systems arise statistically from their microscopic components and interactions among them. For some simple systems, interactions can be disregarded because macroscopic quantities are simple aggregates of component quantities, such as heat being an aggregate of particle energies in a gas. (233)

Kello, Christopher, et al. Scaling Laws in Cognitive Sciences. Trends in Cognitive Sciences. Online in Press,, 2010. Senior neuroscientists from the USA, UK, Spain, and Holland find a constant recurrence across neural, behavioral, and linguistic realms to such a degree as to imply a constant, fundamental order in living, complex systems. The same iteration occurs, e.g., in perception, action, memory, and word frequencies. As a consequence, this phenomena must be rooted in and spring from statistical physics principles such as criticality and phase transitions.

Scaling laws are ubiquitous in nature, and they pervade neural, behavioral and linguistic activities. A scaling law suggests the existence of processes or patterns that are repeated across scales of analysis. Although the variables that express a scaling law can vary from one type of activity to the next, the recurrence of scaling laws across so many different systems has prompted a search for unifying principles. In biological systems, scaling laws can reflect adaptive processes of various types and are often linked to complex systems poised near critical points. The same is true for perception, memory, language and other cognitive phenomena. Findings of scaling laws in cognitive science are indicative of scaling invariance in cognitive mechanisms and multiplicative interactions among interdependent components of cognition.

Kelso, J. A. Scott. An Essay on Understanding the Mind. Ecological Psychology. 20/2, 2008. The Florida Atlantic University cognitive systems wizard always has something to say, and this paper in the “Life and the Sciences of Complexity” series in honor of Arthur Iberall, is no exception. Starting with an historical glimpse at the early 1980s, one can glimpse a growing articulation of a deep affinity and synthesis of human and universe.

The central thesis of this article can be stated bluntly: Minds, brains, and bodies, yours and mine, immersed as they are in their own worlds, both outside and inside, share a common underlying dynamics. (183) The remarkable developments of quantum mechanics demonstrating the essential complementarity of both light and matter should have ushered in not just a novel epistemology but a generalized complementary science. (185)

Kelso, Scott. Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge: MIT Press, 1995. A comprehensive theory of cerebral development and cognitive function by way of nonlinear science with an emphasis on synergetic principles.

Kelso, Scott and Emmanuelle Tognoli. Toward a Complementary Neuroscience: Metastable Coordination Dynamics of the Brain. Murphy, Nancey, et al, eds. Downward Causation and the Neurobiology of Free Will. Berlin: Springer, 2009. The Florida Atlantic University complexity scientist, with FAU research professor Tognoli, contribute to understandings of our cerebral faculty as a self-organizing system from local, semi-autonomous neural areas to their reciprocal integration into mindwide cognitive activity. To the corpus of work in this regard by Kelso and colleagues over some twenty years (search for writings) is added a “metastability” quality so as connect and root such phenomena with the latest physical theories.

Individualist tendencies for diverse regions of the brain to express themselves coexist with coordinate tendencies to couple and cooperate as a whole. In the metastable brain, local and global processes coexist as a complementary pair, not as conflicting theories. (107-108)

Kelso, Scott, et al. Outline of a General Theory of Behavior and Brain Coordination. Neural Networks. 37/1, 2013. Kelso, with coauthors Guillaume Dumas and Emmanuelle Tognoli, are Florida Atlantic University, Center for Complex Systems & Brain Sciences, researchers who explain how human brains are so dynamically self-composed, poised and intelligent. As neuroscientists Danielle Bassett, Stephen Grossberg, and others also aver, a prime cerebral quality is a reciprocal interplay between whole brain or area module coherences and nested scales of semi-autonomous neural nets. Several themes might then be gleaned. At the outset, a “neural choreography” motif is cited to express both dancers and score. A multi-level model is then deployed from single neurons and local field potentials to disparate regions, global integrations, and even inter-personal synchronies (search Dumas). Again this balance repeats at every range – independent in the small and a necessary lucidity in the large. A “Metastable Brain” is thus conceived, soon to be a 2014 book by the authors. Scott Kelso’s 2006 The Complementary Nature, with Dennis Engstrom (whom emailed me to say my review was one of the best appreciations of their work) offers a luminous survey. See also “Enlarging the Scope: Grasping Brain Complexity” by Tognoli and Kelso at arXiv: 1310.7277 (October 2013). So akin to Scott Gilbert’s symbiotic organisms and everywhere else, nature’s “me + We = US” mutual viability holds once more.


Much evidence suggests that dynamic laws of neurobehavioral coordination are sui generis: they deal with collective properties that are repeatable from one system to another and emerge from microscopic dynamics but may not (even in principle) be deducible from them. Nevertheless, it is useful to try to understand the relationship between different levels while all the time respecting the autonomy of each. We report a program of research that uses the theoretical concepts of coordination dynamics and quantitative measurements of simple, well-defined experimental model systems to explicitly relate neural and behavioral levels of description in human beings. Our approach is both top-down and bottom-up and aims at ending up in the same place: top-down to derive behavioral patterns from neural fields, and bottom-up to generate neural field patterns from bidirectional coupling between astrocytes and neurons. Much progress can be made by recognizing that the two approaches—reductionism and emergentism—are complementary. A key to understanding is to couch the coordination of very different things—from molecules to thoughts—in the common language of coordination dynamics. (Abstract)

According to the present theory, the normal brain realizes its complexity at all scales not in its most ordered form (integration qua synchronization) or disordered form (segregation qua desynchronization), but in a subtle blend of both tendencies. Dual tendencies for integration and segregation constitute a complementary pair very much along the lines proposed by Stephen Grossberg, one of the pioneers of the field of Neural Networks: the brain is organized to obey principles of complementarity. (129) The two “forces” that constitute the general theory deal fundamentally with (mostly bidirectional) information exchange. One force is the strength of coupling between the elements; this allows information to be distributed to all participating elements and is a key to integrative, collective action. The other is the ability of individual elements to express their autonomy, and thereby minimize the influence of others. Self-organization in the metastable regime is the interplay of both. (129)

Kiebel, Stefan, et al. A Hierarchy of Time-Scales and the Brain. PLoS Computational Biology. 4/11, 2008. With Jean Daunizeau and Karl Friston, Wellcome Trust Centre, University College London, neuroscientists quantify the presence of direct structural parallels between us “ontogenetic adaptive agents,” and a person’s dynamic, scalar (phylogenetic) environment. Compare, for example, with Altamura, et al (2012) above for evidences that we ourselves, our very cerebral, cognitive faculty, again seems a human epitome of the genesis universe.

In this paper, we suggest that cortical anatomy recapitulates the temporal hierarchy that is inherent in the dynamics of environmental states. Many aspects of brain function can be understood in terms of a hierarchy of temporal scales at which representations of the environment evolve. The lowest level of this hierarchy corresponds to fast fluctuations associated with sensory processing, whereas the highest levels encode slow contextual changes in the environment, under which faster representations unfold. (Abstract) We then review empirical evidence that suggests that a temporal hierarchy is recapitulated in the macroscopic organization of the cortex. This anatomic-temporal hierarchy provides a comprehensive framework for understanding cortical function: the specific time-scale that engages a cortical area can be inferred by its location along a rostro-caudal gradient, which reflects the anatomical distance from primary sensory areas. (Abstract)

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