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IV. Ecosmomics: An Independent Source Script of Generative, Self-Similar, Complex Network Systems

1. Network Physics: A Vital Anatomy and Physiology

Sreedharan, Jithin, et al. Inferring Temporal Information from a Snapshot of a Dynamic Network. Nature Scientific Reports. 9/3057, 2019. Purdue University and University of Michigan (Abram Magner) computer researchers finesse nature’s pervasive webwork anatomy and physiology by showing that a small segment can serve in some way as an invariant capsule. The paper opens with the standard litany that the same such phenomena has been found in kind from cells to brains to economies (second quote). See also Network Archaeology by J. Young, et al at arXiv:1803.09191.


The problem of reverse-engineering the evolution of a dynamic network, known broadly as network archaeology, is of much importance in diverse applications. In an analysis of infection spread, it discerns the underlying spatial and temporal processes. For biomolecular interaction networks (e.g., protein interaction networks), it reveals early molecules that are implicated in diseases. In economic networks, it shows the flow of capital and associated actors. It can further help describe the structural and functional evolution of the human brain connectome. In this paper, we model, formulate, and analyze the arrival order of nodes in a dynamic network from a single snapshot. (Abstract)

Complex systems are comprised of interacting entities; e.g., cellular processes are comprised of interacting genes, proteins, and biomolecules; social systems, of individuals and organizations; and economic systems, of financial entities. These systems are modeled as networks, with nodes as entities and edges as their interactions. Typical systems continually evolve to optimize various criteria, including function (e.g., flow of information in social networks, evolution of brain connectomes to specialize function), structure (e.g., evolution of social network structures to minimize sociological stress while maximizing information flow), and survivability (e.g., redundant pathways in genic interactions as evidenced by synthetic lethality screens). (1)

Stone, Lewi, et al. Network Motifs and Their Origins. PLoS Computational Biology. April, 2019. As the Abstracts notes, LS, Tel Aviv University, Yael Artzy-Randrup, University of Amsterdam and the veteran ecologist Daniel Simberloff, University of Tennessee provide a once and present review of this common feature of life’s dynamic physiology and anatomy.

Modern network science is a new and exciting research field that has transformed the study of complex systems over the last 2 decades. Of much interest is the identification of small “network motifs” embedded in a larger network and that indicate the presence of evolutionary design principles or have an overly influential role on system-wide dynamics. Motifs are patterns of interconnections, or subgraphs that appear in an observed network more often than in compatible randomized networks. Here, we argue that the same concept and tools for the detection of motifs were well known in the ecological literature into the last century, a fact that is generally not recognized. We review the early history of network motifs, their evolution in the mathematics literature, and their recent rediscoveries. (Abstract)

Straka, Mika, et al. From Ecology to Finance (and Back?). arXiv:1710.10143. As nature’s anatomy and physiology becomes increasingly evident, IMT School for Advanced Studies, Lucca, Italy theorists including Guido Caldarelli and Fabio Saracco proceed with an emphasis on bipartite networks which enables their recurrent notice from ecosystems to social media and economies. See also On Economic Complexity and the Fitness of Nations by Greg Morrison, et al at Nature Scientific Reports (7/15332, 2017) for another take on iterative bipartite nets.

A prominent network type found in many real-world systems is the so-called bipartite network, which is characterized by the presence of two different types of nodes. Although purely data-based analyses provide valuable insight into the mechanisms of networks, recent results have shown that such structures contain more information than is apparent at first sight. In particular, several techniques have been designed based on statistical physics and information theory, which provide the possibility to filter statistically relevant signals from the network that otherwise remain hidden when the data is take at face value. Network theory is by nature interdisciplinary and has created a vast vocabulary and a plethora of tools. Due to the interaction patterns of many biological systems, the analysis of bipartite networks has been very popular in ecology and its methodologies have spread to other areas of research. We present a brief review of insights that have been gained in the areas of ecological networks, economic and financial networks. (2)

Suvakov, Milovan, et al. Hidden Geometries in Networks Arising from Cooperative Self-Assembly. Nature Scientific Reports. 8/1987, 2018. In these later 2010s of daily global scientific discourse, Jozef Stefan Institute, Slovenia physicists including Bosiljka Tadic (search) delve deeper into nature’s phenomenal, generative topologies so as to find further dimensions. We seek to report this frontier work, along with companion studies, as growing evidence of an independent, mathematical source code in creative, exemplary effect everywhere. As a result, relatively inorganic and living systems are found to organize or assemble themselves into similarly quickening scales and activities. By these perceptions, a universal reciprocity via a particulate nodal component and a relational connectivity mode or phase, which altogether carry vital information and form a triune whole, can be identified. See also Functional Geometry of Human Connectomes in this journal (9/12060, 2019), and Simplicial Complexes and Complex Systems by Vsevolod Salnikov, et al in the European Journal of Physics (40/014001, 2018).

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to novel functional materials with a sophisticated architecture. In addition to inter-particle forces, the geometrical shapes are decisive factors. A comprehensive understanding of these processes is thus vital for the design of assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with the attachment of structured groups of particles described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) within a growing network. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to geometric factors alone and that it can be efficiently modulated by changing the chemical potential and the polydispersity of the binding simplexes. (Abstract excerpt)

Tadic, Bosiljka and Needima Gupta. Hidden Geometry and Dynamics of Complex Networks. arXiv:2012.07506. Josef Stefan Institute, Slovenia and Indian Institute of Technology, Madras mathematicians provide these latest insights into nature’s endemic intricate formations and processes, which continue to prove their greater procreative presence. By so doing, they contribute further evidence of optimum self-organized critical vitalities at every scale and instance. Two women scholars thus move closer to an ecosmic discovery of a genesis uniVerse. However and whenever, as attributed to a global progeny, can these findings gain an actual validity in this decade?

Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, higher cliques). Current research aims at quantifying these hidden geometries by the algebraic topology and deep graph theory. Here, we use the recent model for self-assembly of cliques to grow nano-networks. In summary, our results become robust indicators of self-organized criticality, which is induced by the network geometry alone without any magnetic disorder. (Abstract excerpt)

Testolin, Alberto, et al. Deep Learning Systems as Complex Networks. Journal of Complex Networks. Online June, 2019. University of Padova physicists including Samir Suweis exemplify this historic synthesis, two decades into the 21st century, whence many diverse fields come together and reinforce each other. Herein self-organizing complexities are present in both cerebral architectures and physical substrates and thus serve to unite the disparate phases. See also Emergence of Network Motifs in Deep Neural Networks by this group in Entropy (22/204, 2020).

Thanks to the availability of large digital datasets and much computational power, deep learning algorithms can learn representations of data over multiple levels of abstraction. These machine-learning methods have aided challenging cognitive tasks such as visual object recognition, speech processing, natural language understanding and automatic translation. Deep belief networks (DBNs) can also discover intricate structures in large datasets in an unsupervised way. While these self-organizing systems apply within the framework of statistical mechanics, their internal functioning and emergent dynamics remains opaque. In this article, we propose to study DBNs using complex network techniques to gain insights into the structural and functional properties of the computational graph resulting from the learning process. (Abstract edits)


Vespignani, Alessandro. Twenty Years of Network Science. Nature. 558/528, 2018. A Northeastern University, Network Science Institute biophysicist reviews how studies of a nature, life, and society suffused and structured by such topologies have advanced since the Collective Dynamics of ‘Small-World’ Networks paper by Duncan Watts and Steven Strogatz in Nature (393/440, 1998). It could also be dated, from concurrent work by Albert-Laszlo Barabasi and Reka Albert on scale-free networks – publication lists on their websites chronicle how the field has flourished over the two decades.

Vivaldo, Gianna, et al. The Network of Plants Volatile Organic Compounds. Nature Scientific Reports. 7/11050, 2017. After noting the total degree that network phenomena are being found to distinguish all manner of natural and neural realms, five Italian systems biophysicists including Guido Calderelli proceed to find their similar, vital presence across botanical flora.

Plants emission of Volatile Organic Compounds (VOCs) is involved in a wide class of ecological functions, as VOCs play a crucial role in plants interactions with biotic and abiotic factors. In this paper, VOCs spontaneously emitted by 109 plant species (56 different families) have been qualitatively and quantitatively analysed in order to provide an alternative classification of plants species. In particular, by using bipartite networks methodology from Complex Network Theory, and through the application of community detection algorithms, we show that is possible to classify species according to chemical classes such as terpenes and sulfur compounds. Such complex network analysis allows to uncover hidden plants relationships related to their evolutionary and adaptation to the environment story. (Abstract)

In this paper we apply complex networks analyses to identify community structures in plants species network, on the basis of their similarities in terms of VOCs emissions. Complex Network theory has been already successfully used in ecology to determine, for example, the stability and robustness of food webs with respect to the removal of one or more individuals from the network, or in biology to study the structure of protein interactions in the cell by the so-called protein interaction networks, similarly metabolic networks are used to study the biochemical reactions which take place into living cells. Furthermore, biological networks found important applications in medicine, where they are applied as a solution to human diseases comorbidity analyses, or to study the structural and functional aspects of human brain, by defining the reciprocal interactions of the cerebral areas. (1)
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Voitalov, ivan, et al. Scale-free Networks Well Done. arXiv:1811:02071. Northeastern University theorists including Dmitri Krioukov provide a further theoretical basis for the common, iterative presence of mathematical relation across all manner of natural and social networks.

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a definition of power-law distributions, equivalent to the definition of regularly varying distributions in statistics. This result allows the distribution to deviate from a pure power law arbitrarily but without affecting the power-law tail exponent. We identify three estimators of these exponents that are statistically consistent. Finally, we apply these estimators to a representative collection of synthetic and real-world data. (Abstract excerpt)

A power law is a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities. (New England Complex Systems Institute)

Voutsa, Venetia, et al. Two Classes of Functional Connectivity in Dynamical Processes in Networks. Journal of the Royal Society Interface. October, 2021. Twenty-five senior researchers from Germany, France, the UK, Austria, and the Netherlands including Brian Fath and Andrea Brovelli post a 26 page, 290 reference entry as an especial instance of the of the 2020s universal complex code synthesis. As the Abstract notes, a consistent presence in kind can be averred as multiplex node/link and modular network topologies are found to form and animate life’s many biospheric, cerebral, societal and environmental phases. Once again, an evidential occurrence of an ecosmic genotype and phenotype occurs in exemplary effect as a common code-script nstantiates itself at every UniVerse to Earthuman Verse occasion. From our natural genesis view, these integral findings are coincident with our EarthKinder moment. In such regard, they can compose a necessary geonomic basis for a super-organic viability.

The relationship between network structure and dynamics is a well investigated aspect of complex system phenomena with relevance to a wide range of instances from neuroscience to geomorphology. A major strategy is the quantitative comparison of evident network architecture (structural connectivity, SC) with network representations of temporal forms (functional connectivity, FC). Here we show that one can distinguish two classes of functional connectivity—one based on simultaneous activity (co-activity) of nodes, the other on sequential activity of nodes. We expand the theoretical view of SC instances and the two FC classes for various scenarios in ecology, systems biology, socio-ecological realms and elsewhere. (Abstract excerpt)

In conclusion, we have attempted to unify the broad range of SC/FC approaches within a common framework. We have reproduced key findings from the literature and extended them towards additional variations of network topology and dynamical characteristics in order to see common properties and underlying principles and offer a deep mechanistic understanding of the major contributors to SC/FC correlation. (15)

Wang, Wei, et al. Coevolution Spreading in Complex Networks. arXiv: 1901.02125. In a 115 page paper with 334 references, informatics researchers based at the University of Electronic and Technology of China apply the latest complexity theories to further quantify this vital phase of composite social behavior, disease, health, and other aspects. The paper now appears in Physics Reports. (Online July 29, 2019).

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, for they coevolve with strong interactions. The study of dynamic spatiotemporal patterns and critical phenomena of networked coevolution spreading can provide theoretical foundations to control epidemics, predict collective behaviors in social systems, and so on. In this review, we draw upon the perspectives of statistical mechanics and network science such as critical phenomena, phase transitions, interacting mechanisms, and network topology for four representative types of biological contagions, social contagions, epidemic–awareness, and epidemic–resources. (Abstract excerpt)

Wang, Wen-Xu, et al. Universal Dynamics on Complex Networks. EPL Europhysics Letters. 87/18006, 2009. An important distinction can be made with regard to complex system phenomena, whose study can be seen to take two approaches. The majority of efforts consider their manifest evidence across nature from galaxies to genomes to global societies. Their other mode, as increasingly noted in physics journals in sections such as Interdisciplinary Studies or Soft Matter, is to distill common features which seem to be in similar effect everywhere. As a latter example, Chinese American scientists at Arizona State University report how a generic pattern and process can be gleaned from “real-world networks, whether biological, physical, technological or social.” One may then muse that these dual implicate or explicate phases exemplify the independent presence and phenotype impression of a genetic code.

In particular, given networks from different contexts, is there a universal class of dynamics that absolutely has no dependence on structural details of the network? Here we provide a surprising but an affirmative answer to the above question. In particular, we find the existence of weighting schemes for which the details of various real-world networks, whether biological, technological or social, have little influence on typical dynamical processes such as synchronization, epidemic spreading, and percolation. (18006)

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