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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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IV. Ecosmomics: An Independent, UniVersal, Source Code-Script of Generative Complex Network Systems

5. Common Code: A Further Report of Reliable, Invariant Principles

Figueiredo, P. H., et al. Self-Affine Analysis of Protein Energy. Physica A. 389/2682, 2010. In a similar theoretical fashion as everywhere else across a procreative nature and nurture, Universidade Federal Rural de Pernambuco, Programa de Modelagem Computacional - SENAI - Cimatec, Universidade Federal do Rio de Janeiro, Universidade Federal da Bahia, physicists find life’s fertile biochemical milieu to abide in and fluoresce by webwork dances of enfolded molecules and relational partners.

In recent years, there has been a growing evidence that many complex physical, economical, and biological systems manifest self-affinity characterized by long-range power-law correlations. In such a context, the detrended fluctuation analysis (DFA) was recently proposed [1] to analyze long-range power-law correlations in nonstationary systems. One advantage of the DFA method is that it allows the long-range power-law correlations in signals with embedded polynomial trends that can mask the true correlations in the fluctuations of a noise signal. The DFA method has been applied to analyze the DNA and its evolution [1,2], file editions in computer diskettes [3], economics [4,5], climate temperature behavior [6], phase transition [7], astrophysics sources [8,9] and cardiac dynamics [10,11], among others. (2682)

The study of fractal characteristics of the proteins provides countless results. The fractal analysis uncovered self-similarity in many research fields such as cluster dimension of proteins [12], anomalous temperature dependence of the Raman spin–lattice relaxation rates [13], relation between the fractal dimension and the number of hydrogen bridges [14], multifractality in the energy hypersurface of the proteins [15], packing of small protein fragments [16], surface volume [17], degree of compactness of the proteins [18], measurement of the average packing density [19] as well as a hydrophobicity scale [20] among others. Furthermore, the fractal methods identify different states of the same system according to its different scaling behaviors, e.g., the fractal dimension is different for structures with (without) hydrogen bonds [14,15]. In this sense, the correct interpretation of the scaling results obtained by the fractal analysis is crucial to understand the intrinsic geometry (and sometimes dynamics) of the systems under study.

Fortunato, Santo and Claudio Castellano. Scaling and Universality in Proportional Elections. Physical Review Letters. 99/138701, 2007. As Galileo famously noted, nature’s philosophy is written with a mathematical quill. In this paper, scientists from Torino and Roma quantify that underlying and informing our seemingly chaotic political elections is a constantly recurrent, systematic geometry. A proposal of this website is that a persistent gridlock thus occurs along archetypal lines of so-called right conservative and left liberal poles, when their resolve is an obvious complementarity.

We show that, in proportional elections, the distribution of the number of votes received by candidates is a universal scaling function, identical in different countries and years. This finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical, political, and/or economical context where voters operate. (Abstract, 138701)

Many social nontrivial phenomena emerge spontaneously out of the mutual influence of a large number of individuals, similarly to large-scale thermodynamic behavior resulting from the interaction of a huge number of atoms or molecules. However, human interactions are neither purely mechanical nor reproducible, both typical requirements for a physical description of a process. Nevertheless the collective behavior of large groups of individuals may be independent of the details of social interactions and individual psychological attributes, and be instead the consequence of generic properties of the elementary interactions, allowing for a simple ‘‘statistical physics’’ modeling. (138701)

Frank, Steven. All of Life is Social. Current Biology. 17/16, 2007. An introduction to a special section on Social Biology which records that the complementary interplay of selfish or selfless behavior found from bees to baboons occurs across an expanded spectrum from genomes, viruses, bacteria, to human cognitive and linguistic discourse.

For example, multicellularity originated through a complex evolutionary history of cellular aggregations, in which the opposing social forces of conflict and cooperation likely played a key role. Similarly, genomes arose through social histories of genetic aggregations and organelle symbioses. Several aspects of multicellularity, of genomes, of societies, and of cognition can be understood only within the social history of conflict and cooperation. (R648)

Frank, Steven. The Common Patterns of Nature. Journal of Evolutionary Biology. Online July 17, 2009. The University of California, Irvine ecologist contends that a realm of mathematical formulae underlies animate activity from “amino acid substitutions to ecological communities” with the result that generic forms and functions can be found in occurrence everywhere.

Frank, Steven. The Invariances of Power Law Distributions. arXiv:1604.04883. The UC Irvine mathematical biologist continues his insightful articulation of intrinsic natural patterns and processes across evolutionary nature. Search here and the e-print site for more papers. In this entry, scaling relations from trees to forests are seen to reveal a universal invariance similar to form and function phenomena found in kind everywhere else. Once again we seem to be closing on a grand genesis vista from universe to human by way of some such genomic influence just waiting to be discovered. See also his Common Probability Patterns Arise from Simple Invariances at 1602.03559.

Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here, I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances. (Abstract)

Frank, Steven and Jordi Bascompte. Invariance in Ecological Pattern. arXiv:1906.06979. UC Irvine and University of Zurich system theorists join their common studies across life’s evolutionary and environmental species to presently be able to advance and affirm nature’s infinite propensity to repeat self-similar forms and processes in kind at each and every creaturely and communal scale and instance.

The abundance of different species in a community often follows the log series distribution. Why does the complexity and variability of ecological systems reduce to such simplicity? This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. By bringing this unifying invariance approach into ecology, one can see that the log series pattern of species abundances dominates when the consequences of density dependent processes are invariant to addition or multiplication. Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches. (Abstract excerpt)

Frey, Erwin, et al. Protein Pattern Formation. arXiv:1801.01365. Ludwig Maximilian University and MPI Biochemistry researchers continue to articulate how life’s biomolecular substance and sustenance arises from and exemplifies nature’s dynamical self-organization processes. That is to say, besides all the biochemical reactions, an independent universal source of formative topologies seems at generative work.

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in E. coli whose biological function is to ensure precise cell division. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms. (Abstract)

In summary, protein pattern formation plays key roles in many essential biological processes from bacteria to animals, including cell polarisation and division. Combined theoretical and experimental approaches have established important principles of pattern-forming protein systems. Perhaps the most crucial feature that has emerged from these research efforts is the identification of the cytosol as a depot. This depot enables the system to store proteins and redistribute them throughout the system. Cytosolic diffusion is the key process that detects the local shape of the membrane, and it is this explicit dependence on geometry that is imprinted on membrane-bound protein patterns. (15)

Friedman, Eric and Adam Landsberg. Hierarchical Networks, Power Laws, and Neuronal Avalanches. Chaos. 23/1, 2013. University of California, Berkeley, and Scripps College, Claremont, mathematicians illustrate three tiers or aspects of nature’s ubiquitous complex systems. The paper describes the above phenomena with reference to an independent, universal source and activity. Its presence in critically self-organized, nested brain dynamics is then exemplary evidence. With this in place, it is recorded that similarly everywhere else in cosmos and civilization can be found this repetitive manifestation. In the second decade of this century and millennium, we seem to be reaching a revolutionary veracity throughout the worldwide literature of a genesis uniVerse, whence all this natural appearance results from and expresses its own iterative genetic source code.

We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions—even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws. (Abstract)

Many real-world networks are hierarchically organized into layers of modules and submodules, one prominent example being the neuronal network of the human brain. A central but still largely unexplored question is how an underlying hierarchical structure can affect a network's dynamical behavior. In this paper, we develop a renormalization analysis to uncover some important implications of hierarchical architecture in a network. Our main result reveals the interesting role of hierarchy in generating robust power-law behavior in networks, a fact which helps explain recent results on neuronal cascades in human brains. In addition, we show that other properties of these networks are consistent with the experimental data on brain networks and suggest new experiments to improve our understanding of brain networks and behavior. The ideas developed in this paper should be broadly applicable to many other network settings which exhibit a hierarchical modular (HM) structure, ranging from engineered to biological to social systems. (Lead Paragraph)

Friston, Karl. A Free Energy Principle for a Particular Physics. arXiv:1906.10184. The Wellcome Centre for Human Neuroimaging, London collegial neurotheorist posts a 148 page draft manuscript which seeks to join his self-composing and cognizing Bayesian brain theories with a conducive, natural, cosmic affinity. Search KF as this view gains a growing number of supporters. Akin to Integrated Information theory (Tononi) and other entries, these fluid perceptions take on their own iterative course in quest of better explanations, albeit in arcane terms which ought to gain a common clarity.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing independencies, mediated by Markov blankets (see below), speak to a recursive composition of ensembles (things) at increasingly higher spatiotemporal scales. This decomposition provides a broad description of small things via quantum mechanics and the Schrodinger equation, then statistical mechanics and related fluctuation theorems, and through to big things in classical mechanics. Our main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In so doing, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states as they represent and infer external states. (Abstract edits)

In statistics and machine learning, the Markov blanket for a node in a graphical model contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node and its children. In a Bayesian network, the values of the parents and children of a node evidently give information about that node. In a Bayesian network, the Markov blanket of node A includes its parents, children and the other parents of all of its children. (WikiPedia)

Gagler, David, et al. Scaling Laws in Enzyme Function Reveal a New Kind of Biochemical Universality. PNAS. 119/9, 2022. Arizona State University bioscientists including Sara Walker, Chris Kempes and Hyunju Kim enter a good example of novel Earthuman abilities which can now find life’s deeper phases to also be distinguished by common, recurrent, self-similar patterns as everywhere else. A further implication is that such a result can be traced to and rooted in physical phenomena. A section heading is Universal Scaling Laws Define the Behavior of Enzyme Classes Across Diverse Biochemical Systems. A graphic depicts how the same forms hold from Archaea and Bacteria to Eukaryotes and Metagenomes, independently of specific components. We wonder again at our emergent EarthWise faculty whom can just now come to these discoveries.

All life on Earth uses a shared set of chemical compounds and reactions which provides a detailed model for universal biochemistry. Here, we introduce a more generalizable concept that is more akin to the kind of universality found in physics. We show how enzyme functions form universality classes with common scaling behavior. Together, our results establish the existence of a new kind of biochemical universality, independent of the details of life on Earth’s component chemistry. (Abstract excerpt)

In physics, the notion of coarse-graining is critical to identifying universality classes, because it allows ignoring most details of individual systems in favor of uncovering systematic behavior across different systems. (3)

Gallos, Lazaros, et al. Scaling Theory of Transport in Complex Biological Networks. Proceedings of the National Academy of Sciences. 104/7746, 2007. Biophysicists at CCNY Levich Institute and Bar-Ilan University develop a theoretical framework for this ubiquitous property invariantly found from proteins to people.

We study transport in real-world biological networks and via a model, which possess both self-similar properties and the scale-free character in their degree distribution. We explain our results with theoretical arguments and simulation analysis. We use approaches from renormalization theory in statistical physics that enable us to exploit the self-similar characteristics of the fractal networks and develop a scaling theory of transport, which we use to address the effects of the modularity and the degree inhomogeneity of the substrate.

Garcia-Ruiz, Ronald and Adam Vernon. Emergence of Simple Patterns in Many-Body Systems from Macroscopic Objects to the Atomic Nucleus. arXiv:1911.04819. . R. Garcia Ruiz is posted at CERN Geneva and MIT, while A. Vernon is with KU Leuven, Belgium and the University of Manchester. Among an increasing number of reports, this entry with 175 references is a good example to date of a global scientific endeavor now able to quantify a substantial nature that everywhere gives rise to common forms and flows by its own propensities. With a root basis in nuclear shell clusters, a recurrent regularity spreads in kind across micro-physical and macro-biological realms. As the second quote cites, iconic mathematical shapes can found throughout, aka “magic numbers.” See also Underlying Structure of Collective Bands and Self-Organization in Quantum Systems by Takaharu Otsuka, et al at arXiv:1907.10759, and Magic Number Colloidal Clusters as Minimum Free Energy Structures by Junwei Wang, et al in Nature Communications (9/5259, 2018.)

Strongly correlated many-body systems often display the emergence of simple patterns and regular behavior of their global properties. Phenomena such as clusterization, collective motion and shell structures are commonly observed across different size, time, and energy scales in our universe. Although at the microscopic level their individual parts are described by complex interactions, the collective behavior of these systems can exhibit strikingly regular patterns. This contribution provides an overview of the experimental signatures that are used to identify the emergence of structures and collective phenomena in distinct physical systems, along with macroscopic examples. (Abstract)

Throughout nature, driving forces give rise to the arrangement of constituents in many-body systems at almost every size. On biological scales, this manifests in collective phenomena and pattern formation such as the phyllotaxis of plants, where growth patterns appear in the leaves or flowers around a plant stem. A striking example is observed in the seeds in a sunflower head, which follows the Fibonacci sequence. Complex many-body systems often form clusters to minimise their energy by interactions between neighbours and their mean field. This can form “magic” numbers, as in the atomic nucleus, where certain integer numbers of constituents of a given system result in greater stability of its collective whole. Another instance is the abundance distribution of isotopes in the universe following nucleosynthesis. (2, edits)

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126. For protons, this corresponds to the elements helium, oxygen, calcium, nickel, tin, and lead. (Wikipedia)

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