IV. Ecosmomics: Independent, UniVersal, Complex Network Systems and a Generative Code-Script Source
5. Common Code: A Further Report of Reliable, Invariant Principles
Center for Fractal Design. www.fractal.org. Julius Ruis, the Director of this Netherlands based Fractal Design and Consultancy, has emailed me (March 2008) his compliments and to notify about his own many-faceted website. We are pleased to list as a portal to visually appreciate a nested, creative self-similarity which enlivens every aspect of a natural genesis from cosmos to cauliflowers to civilizations. The site requires some negotiation, but is filled with treasures.
, . Fractals: Hunting the Hidden Dimension. www.pbs.org/wgbh/nova/fractals. This luminous Nova program aired on October 28, 2008 muses at its close that Galileo’s mathematical book of nature is at last legible via an intrinsic geometry not of Euclidean forms but of an infinitely variegated self-similarity. The presentation dutifully engages leading contributors over the years such as Ralph Abraham, James Brown, Ron Eglash, Brian Enquist, Ary Goldberger, Geoffrey West, and so on. But a prime distinction is an extended visit with its renowned founder Benoit Mandelbrot. As one example, a research team led by ecologist Enquist is shown measuring tree branches in a Costa Rican forest and concludes that one plant and a whole biota share a common, recurrent structure, verily that a tree recapitulates its forest. A nested natural iteration is thus revealed as creation’s mathematical basis now takes on a fractal form.
Agnati, Luigi, et al. Mosaic, Self-Similarity Logic and Biological Attraction Princples. Communicative & Integrative Biology. 2/6, 2009. With co-authors Peter Barlow, Frantisek Baluska, and Diego Guidolin, Italian, German, and British theorists contribute to the growing witness of an independent, genome-like, natural topology and its constant dynamics. The quotes seem to evince a grand genesis discovery, if we could only allow ourselves and imagine.
From a structural standpoint, living organisms are organized like a nest of Russian matryoshka dolls, in which structures are buried within one another. From a temporal point of view, this type of organisation is the result of a history comprised of a set of time backcloths which have accompanied the passage of living matter from its origins up to the present day. The aim of the present paper is to indicate a possible course of this passage through time and suggest how today’s complexity has been reached by living organisms. (552)
Ahn, Yong-Yeol, et al. Link Communities Reveal Multiscale Complexity in Networks. Nature. 466/761, 2010. Researchers from the Center for Complex Network Research, Northeastern University; Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard University; Institute for Quantitative Social Science, Harvard; and the College of Computer and Information Science, Northeastern, resolve a conceptual issue about how to allocate, describe, and understand such omnipresent relational form and fluidity. However then by such interdisciplinarity might it dawn that a grand genesis universe is revealed with a once and future, above and below, replication that we might avail for a better world? What time is it, whom altogether is learning, in translation are we reading a cosmic to child genetic code?
Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of networks is to identify communities: groups of related nodes that correspond to functional subunits such as protein complexes or social spheres. (761) Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy. In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization. (761) Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon. (761)
Alon, Uri. Simplicity in Biology. Nature. 446/497, 2007. Although life, from proteins to genes, bacteria and metabolic organisms, epitomizes dynamic complexity, recent studies find shared principles which engender motifs and networks that repeat at every phase. These convergent, modular patterns and processes constantly recur as they take on this universal mathematical form.
Amaral, L. and J. Ottino. Augmenting the Framework for the Study of Complex Systems. European Physics Journal B. 38/2, 2004. An introduction to a special issue on the ubiquitous presence of scale-free dynamic networks from food webs and epidemics to neural phenomena and especially the worldwide Internet. In this regard a generic definition of complex systems is attempted, see the quote below. These elemental units and interactions then self-organize into a universal, nested self-similarity.
A complex system is a system with a large number of elements, building blocks or agents, capable of interacting with each other and with their environment. The common characteristic of all complex systems is that they display organization without any external organizing being applied. The whole is much more than the sum of its parts. (148)
Ambika, G. and Jurgen Kurths. Tipping in Complex Systems. European Physical Journal Special Topics. 230/3177, 2021. Indian Institute of Science Education and Research and Potsdam Institute for Climate Research scholars introduce a topical issue with this subject title. A typical entry is Critical Transition Influenced by Dynamic Quorum Sensing in Nonlinear Oscillators by Paul Asir, et al. (search) From late 2021, one ought to note the worldwise extent to which such hyper-active nonlinear phenomena has become well quantified, yet an organic genesis reality that it implies has not been considered or brought into full benefit.
Many real-world complex systems are observed to undergo sudden transitions in their dynamical states or pattern of behavior and then they are said to tip from one emergent state to another. A few such transitions that can affect humanity in many ways are global changes in climate, earthquakes, hurricanes, abrupt shifts in ecosystems, blackouts in power systems, crashing of financial markets, psychological breakdowns, and surge of epidemics. They happen mostly due to small perturbations in the critical values of the system’s parameters or variables leading to large qualitative changes. (Abstract)
Amgalan, Anar, et al. Unique Scales Preserve Self-Similar Integrate-and-Fire Functionality of Neuronal Clusters. arXiv:2002.10568. SUNY Stony Brook and UM Amherst computational neuroscientists including Hava Siegelmann post a strongest statement to date of the actual presence of a “functional scale-invariance or fractality” which spans its dynamic multiplex architecture. In regard, here is another current affirmation of a microcosmic instantiation of nature’s universal genetic complexities in our very own cerebral faculty.
Identifying the brain's neuronal cluster size as nodes in a network computation is critical to both neuroscience and artificial intelligence. Experiments support many forms and sizes of neural clustering, while neural mass models (NMM) assume scale-invariant functionality. Here, we use simulations within a fMRI network to show that a brains stay structurally self-similar continuously across scales. As such, we propose a coarse-graining of network of neurons to ensemble-nodes, with multiple spikes making up its ensemble-spike, and time re-scaling factor defining its ensemble-time step. The fractal-like spatiotemporal structure and function that emerges allows strategic choices across experimental scales for computational modeling, along with regulatory constraints on developmental and/or evolutionary "growth spurts" in brain size. (Abstract excerpt)
Anteneodo, Celia and M. G. E. da Luz. Complex Dynamics of Life at Different Scales: From Genomic to Global Environmental Issues. Philosophical Transactions of the Royal Society A. 368/5561, 2010. Brazilian biophysicists introduce a special issue that exemplifies the scientific verification across nature’s nested realms of life’s vital, inherent, ascendant, bountiful intricacy. The issue is available online with full, free access. Typical papers of note are Rudolf, Hanel, et al, “Living on the Edge of Chaos: Minimally Nonlinear Models of Genetic Regulatory Dynamics;” Pablo Gleiser and Victor Spoormaker on “Modelling Hierarchical Structure in Function Brain Networks;” and “Complex Dynamics of Our Economic Life on Different Scales” by Tobais Preis, Daniel Reith and Eugene Stanley.
In very general terms, complexity arises from relatively simple interactions among numerous mutually interacting parts. Despite the simplicity of the governing rules, a rich collective dynamic emerges which is quite distinct from that of the individual elements. (5562)
Arnold, Carrie. Ants Swarm Like Brains Think. Nautilus. Issue 23, 2015. A report on the decade-long field and laboratory project of the Stanford University biologist Deborah Gordon to study the intelligent behavior, organization, and ecology of ant colonies in the Arizona desert. These intricate insect societies are lately seen as an archetypal example of a complex system which exhibits robust communality along with integral cognitive qualities. Recently the dynamic phenomena she found was noted by the UC Davis computational neuroscientist Mark Goldman as inherently similar to layered neural network activities. Both instances involve many, interconnected entities whether ants or neurons, from which emerges a coherent, intelligent response. Thus in 2015, still another confirmation of nature’s grand, infinitely reiterated, genetic universality is achieved.
Ashish, George and James O’Dwyer.. Universal abundance fluctuations across microbial communities, tropical forests, and urban populations. PNAS. 120/44, 2023. We highlight late this year an entry from the Carl Woese Institute for Genomic Biology, University of Illinois as an exemplary observation across a widest span from microbes to ecosystems to a metropolis of a consistent recurrence in kind of one same pattern and process. Such a scenario then seen as akin to, and by implication rooted in, a conducive natural source. Another iconic instance is thus reported of a whole scale commonality which altogether well presages an epochal 2024 discovery event.
Large fluctuations in complex populations, such as microbial communities and urban populations can trigger catastrophic ecological and economic collapse. Understanding these fluctuations is crucial for mitigating these such events. However, models of these systems are often very detailed to analyze. Here, we study time-series data from three disparate complex populations — gut microbial species, employees in US cities, and forest tree species — to demonstrate that emergent behavior in all these populations is described by a single simplified model, resembling the universality observed in many physical systems. (Significance)
Bagrow, James and Eric Bolit. An Information-Theoretic, All-Scales Approach to Comparing Networks. Applied Network Science. 4/45, 2019. University of Vermont complexity researchers conceive a common pictorial image as an effective way to represent nature’s ubiquitous propensity to join discrete elements or entities into viable communal assemblies. The novel approach is thus dubbed a Network Portrait.
As network studies proceed, it is more common to move beyond a single network to analyze multiple arrays. An important task then becomes network comparisons by way of a similarity or distance measure in between. Here we introduce a new measure as a Network Portrait Divergence which is mathematically principled, incorporates the topological characteristics at all structural scales, and is generally applicable to all types of networks. An important feature that enables many of its useful properties is that it is based on a graph invariant. We test our measure on both synthetic graphs and real world networks taken from protein interaction data, neuroscience, and computational social science applications. (Abstract edits)