IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

1. Network Physics: A Vital Interlinked Anatomy and Physiology

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.

Vidal-Saez, Maria, et al. Biological computation through recurrence.. arXiv:2402.05243. As scientific “megatrends” proceed apace, Universitat Pompeu Fabra and Universitat Autònoma de Barcelona biologists propose a further finesse of multiplex network capabilities as a better way to study and explain how organisms are able to get along and survive.

One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial informative features to compute the appropriate response. A growing body of work from machine learning and neuroscience has shown that such complex information processing can be performed by recurrent networks from interactions between incoming stimuli and internal dynamics. Here we review understandings of how recurrent networks are used by biological systems from cells to brains for this purpose. We focus on simpler networks and learning algorithms that have been found by evolution. We go on to discuss some relevant aspects concerning the emergence of this natural computation paradigm. (Abstract)

Living organisms are faced with the ongoing challenge of processing signals coming from their environment. The dynamical nature of recurrent networks allows the integration of the present conditions faced by the organism with its (recent) past, making the concept of recurrence-based computation an initial step towards a conceptual model for temporal information processing in living beings. The synergistic merger between applied mathematics, neuroscience and machine learning in this review can provide us with a general principle of biological information processing that has so far been elusive. (13-14)

Vidiella, Blai, et al. Networks: The Visual Language of Complexity. arXiv:2410.16158. Institute of Evolutionary Biology, CSIC-UPF, Barcelona system theorists including Sergi Valverde post this chapter to appear in Nonlinear Dynamics for Biological Systems from Springer, Switzerland next year.

Network theory has emerged as an intuitive framework to represent inter-dependencies among many system components, with both local and global properties. While basic growth mechanisms, like preferential attachment, can have a power-law degree distribution, they lack other uses. Different network extensions, like hypergraphs, have been developed to integrate exogenous factors in evolutionary models, as pairwise interactions are insufficient to capture environmentally-mediated species associations. As we confront societal and climatic challenges, the study of network and hypergraphs will aid in understanding and managing complexity. (Excerpt)

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)

Wang, Yafeng, et al. Growth, Collapse, and Self-Organized Criticality in Complex Networks. Nature Scientific Reports. 6/24445, 2016. Shaanxi Normal University, Zhejiang University, and Arizona State University physicists describe how the tendency of nonlinear phase transitions to be poised between order and chaos can similarly characterize network dynamics. Since this is phenomena now known to occur everywhere in nature and society, such an independent representation is increasingly possible and important.

Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. (Abstract)

Wang, Zhen, et al. Evolutionary Games on Multilayer Networks. arXiv:1504.04359. An introduction to a special issue of the European Physical Journal B, by an international team, including Matjaz Perc, with postings in China, Hungary, Slovenia, and Saudi Arabia. In regard, the paper surveys the progress of complexity science from the late 1980s to today. As the quote advises, nature’s creative course by which many discrete agents arrange into viable collectives is seen as most distinguished by interlinking network topologies. A novel reality is thus revealed and quantified of organically nested systems which repeat the same patterns and dynamics at every strata and species. It is then stated that keen insights can be gained if this developmental phenomena is seen as a strategic, decision-making game activity.

Wellnitz, David, et al. A Network Approach to Atomic Spectra.. Journal of Physics: Complexity. July, 2023. University of Strasbourg, Heidelberg and Konstanz, along with MPI Intelligent Systems researchers report that even these quantum material depths can be found to exhibit and hold to nature's common node/link netwise dynamic animations.

Network science provides a universal framework for modeling complex systems, contrasting the reductionist approach generally adopted in physics. In a prototypical study, we utilize network models created from spectroscopic data of atoms to predict microscopic properties of the underlying physical system. For simple atoms such as helium, an a posteriori inspection of spectroscopic network communities reveals the emergence of quantum numbers and symmetries. For more complex atoms such as thorium, finer network hierarchies suggest additional microscopic symmetries or configurations. Our work promotes a genuine bi-directional exchange of methodology between network science and physics, and presents new perspectives for the study of atomic spectra.

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