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

4. Universality Affirmations: A Critical Complementarity

Guszejnov, David, et al. Universal Scaling Relations in Scale-Free Structure Formation. arXiv:1707.05799. As a good example of the sophistication of mid 2017 cosmic science compared with a decade ago, Cal Tech astrophysicists including Philip Hopkins proceed to affirm a pervasive, natural interstellar self-similarity. And in regard, here is worldwide proof of the perennial tradition of a macrocosm and microcosm correspondence, by which both universe and human realms could be known. See also Star Cluster Structure from Hierarchical Star Formation by this extended group at arXiv:1708.09065.

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dlnM∝M−2 which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M−2 and a column density distribution with a power law tail of dA/dlnΣ∝Σ−1. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a ρ∝R−3 density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases. (Abstract)

Finally, in a somewhat different approach, one can notice that the apparent similarity in the slopes of the mass functions could be explained by a fractal-like, self-similar ISM out of which structures like stars, cores and GMCs form. An important property of these models is that they tie structures of different sizes together (stars, cores, clumps) as their mass distribution is the result of the same fractal ISM structure. The density structure predicted by these fractal ISM models is in agreement with simulations of supersonic turbulence. In general these inherently imply an underlying self-similar process, which serves as the main motivation for this paper. (2)

In this paper we showed that there are universal scaling relations that generally arise in scale-free models of structure formation with a large but finite dynamic range and no correlation between scales. These relations are shared between very different phenomena, including the formation of stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. Despite their differences all these processes can be approximately described by the dimensionless version of the pressure-free Euler equation with self-gravity. Thus a hierarchical structure building process would follow the same equation for all these systems on a wide range of scales. This means that (to first order) the formation of these (very different) gravitationally bound structures produces the same scaling relations for a wide range of physical quantities. (8)

Hastings, Harold, et al. Challenges in the Analysis of Complex Systems. European Physical Journal Special Topics. 226/15, 2017. For some context, I have been tracking nonlinear CS sciences since the 1980s, e.g. visiting the Santa Fe Institute in August 1987. As this large chapter and sections report, the past decades were an intense phase of technical studies which widely fanned out, ramified, clarified, and lately are melding into a common synthesis. In this special issue introduction, Bard College and University of Calgary theorists affirm that the same far-from-equilibrium patterns and processes have been found to occur from astronomy to seismology, chemistry, neural and cardiac dynamics, and even climatology. Since the 2000s, network phenomena, as affine with statistical physics and phase transitions, has become a significant addition. Similar to Jordi Vallverdu, et al 2017, it is noted that nature’s mathematical source is in generative play prior to and “in the absence of selection.”

One of the main challenges of modern physics is to provide a systematic understanding of systems far from equilibrium exhibiting emergent behavior. Prominent examples of such complex systems include, but are not limited to the cardiac electrical system, the brain, the power grid, social systems, material failure and earthquakes, and the climate system. Due to the technological advances over the last decade, the amount of observations and data available to characterize complex systems and their dynamics, as well as the capability to process that data, has increased substantially. The present issue discusses a cross section of the current research on complex systems, with a focus on novel experimental and data-driven approaches to complex systems that provide the necessary platform to model the behavior of such systems. (Abstract)

Helmrich, Stephan, et al. Signatures of Self-Organized Criticality in an Ultracold Atomic Gas. Nature. 577/481, 2020. In a paper appropriately published in the first month of this binocular year, University of Heidelberg, Cal Tech, and University of Koln physicists contribute to the ubiquitous occurrence of self-similar, critically poised states everywhere. The subject case here is elemental gases where such exemplary features appear even at these frigid, quantum extremes. See also Singular Charge Fluctuations at a Magnetic Quantum Critical Point and Quantum Spin Liquids in Science for January 17, 2020. Two decades into the 21st century, a Worldwide Discovery of a Organic, Procreative UniVerse does seem well underway, if we might be of a mind to ask and see.

Self organisation provides an elegant explanation for how complex structures emerge and persist throughout nature with remarkably similar scale-invariant properties. While this can be captured by simple models, the connection to real-world systems is difficult to test. Here we identify three key signatures of self-organised criticality in the dynamics of a dissipative gas of ultracold atoms and provide a first characterisation of its universal properties. We show that population decay drives the system to a stationary state that is independent of the initial conditions and exhibits scale invariance and a strong response to perturbations. This establishes a practical platform for investigating self-organisation phenomena and non-equilibrium universality with much experimental access to the microscopic details of the system. (Abstract)

Hidalgo, Jorge, et al. Cooperation, Competition and the Emergence of Criticality in Communities of Adaptive Systems. arXiv:1510.05941. The Spanish, Italian, and American team including Jayanth Banavar and Amos Maritan follow up their 2014 paper (search) with further theoretical explanations for nature’s propensity to seek and reach a balance between relative order or conflict. This “metastable” state (Kelso) is lately being verified from many quarters, for example At the Edge of Chaos by Christian Rossert, et al, (PLoS One October 2015) and Adaptation to Sensory Input Tunes Visual Cortex to Criticality by Woodrow Shew, et al (Nature Physics 11/8, 2015).
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The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between exceedingly ordered and too noisy states. We here present a model, based on information theory and statistical mechanics, illustrating how and why a community of agents aimed at understanding and communicating with each other converges to a globally coherent state in which all individuals are close to an internal critical state, i.e. at the borderline between order and disorder. We study --both analytically and computationally-- the circumstances under which criticality is the best possible outcome of the dynamical process, confirming the convergence to critical points under very generic conditions. Finally, we analyze the effect of cooperation (agents try to enhance not only their fitness, but also that of other individuals) and competition (agents try to improve their own fitness and to diminish those of competitors) within our setting. (Abstract)

Hidalgo, Jorge, et al. Information-based Fitness and the Emergence of Criticality in Living Systems. Proceedings of the National Academy of Sciences. 111/10095, 2014. We cite this entry by senior system theorists JH, Jacopo Grilli, Samir Suweis, Miguel Munoz, Jayanth Banavar and Amos Maritan (search each) as an early perception of life’s universal propensity to seek and reside at an optimum self-organized criticality. By 2020, a few years later, this section can now document its robust worldwide affirmation. In this time of great need, if we might mindfully allow and witness, here is a vital finding that a phenomenal nature prefers an active reciprocity of conserve/create, person/group and ever so on. Rather than totalitarian or anarchic extremes, me individual vs. We together politics, a salutary resolve going forward would be a middle way complementarity.

Recently, evidence has been mounting that biological systems might operate at the borderline between order and disorder, i.e., near a critical point. A general mathematical framework for understanding this common pattern, explaining the possible origin and role of criticality in living adaptive and evolutionary systems, is still missing. We rationalize this apparently ubiquitous criticality in terms of adaptive and evolutionary functional advantages. We provide an analytical framework, which demonstrates that the optimal response to broadly different changing environments occurs in systems organizing spontaneously—through adaptation or evolution—to the vicinity of a critical point. Furthermore, criticality turns out to be the evolutionary stable outcome of a community of individuals aimed at communicating with each other to create a collective entity. (Significance)

Horstmeyer, Leonhard, et al. Network Topology near Criticality in Adaptive Epidemics. arXiv:1805.09358. Just as every other area from quantum to neural has become defined by the universally prevalent self-organized complex network systems, here LH and Stefan Thurner, Medical University of Vienna and Christian Kuehn, Technical University of Munich theorists describe how even human disease vectors among variegated populations similarly hold, as they mathematically must,Just as every other area from quantum to neural has become defined by the universally prevalent self-organized complex network systems, here LH and Stefan Thurner, Medical University of Vienna and Christian Kuehn, Technical University of Munich theorists describe how even human disease vectors among variegated populations similarly hold and exhibit, as they mathematically must, to predictable, critical principles.

We study structural changes of adaptive networks in the co-evolutionary susceptible-infected-susceptible (SIS) network model along its phase transition. We clarify to what extent these changes can be used as early-warning signs for the transition at the critical infection rate λc at which the network collapses and the system disintegrates. We analyze the interplay between topology and node-state dynamics near criticality. Several network measures exhibit clear maxima or minima close to the critical threshold that could potentially serve as early-warning signs. For the SI link density and triplet densities the maximum is found to originate from the co-existence of two power laws. (Abstract)

Iyer-Biswas, Srividya, et al. Universality in Stochastic Exponential Growth. Physical Review Letters. 113/028101, 2014. University of Chicago and LBNL (Gavin Crooks) physicists consider a common mathematical recurrence for ecosmos to economic developments. See also 1409.7068 for more work by the authors on bacterial cells.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth. (Abstract)

Jagielski, Maciej, et al. Theory of Earthquakes Interevent Times Applied to Financial Markets. arXiv:1610.08921. With Ryszard Kutner and Didier Sornette, European theorists describe an inherent mathematical correspondence between these disparate geological and societal realms, which is then seen as a universal quality of abrupt dynamic phenomena.

We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses. (Abstract)

The activity of many complex systems in social and natural sciences can be characterized by sporadic bursts followed by long periods of low activity. To quantitatively describe this kind of dynamics, we can use the interevent times defined as times between two consecutive events of high (suitably defined) activity of the system. It was shown in many research papers that the probability density distribution (PDF) of interevent times plays the role of a universal characteristic of dynamical complex systems. Examples include anomalous transport, pattern discovery, earthquakes and rock fractures, extreme events and long-memory processes, email communications, web browsing, library visits, stock trading, human dynamics, social dynamics, finance risks, letter correspondences, and financial markets. (1, bold added)

Jofre, Paula, et al. Cosmic Phylogeny: Reconstructing the Chemical History of the Solar Neighborhood with an Evolutionary Tree. arXiv:1611.02575. Cambridge University, Universidad Diego Protales, Chile, and Oxford University scientists, including Robert Foley, explore promising ways to apply life’s developmental topologies across chemical and stellar realms. An allusion is made to an analogous celestial genome, whose resultant webworks suggest an “astrocladistics.”

Using 17 chemical elements as a proxy for stellar DNA, we present a full phylogenetic study of stars in the solar neighbourhood. This entails applying a clustering technique that is widely used in molecular biology to construct an evolutionary tree from which three branches emerge. These are interpreted as stellar populations which separate in age and kinematics and can be thus attributed to the thin disk, the thick disk, and an intermediate population of probable distinct origin. Combining the ages of the stars with their position on the tree, we are able to quantify the mean rate of chemical enrichment of each of the populations, and thus show in a purely empirical way that the star formation rate in the thick disk is much higher than in the thin disk. Our method offers an alternative approach to chemical tagging methods with the advantage of visualising the behaviour of chemical elements in evolutionary trees. This offers a new way to search for `common ancestors' that can reveal the origin of solar neighbourhood stars. (Abstract)

Kalinin, Nikita, et al. Self-organized Criticality and Pattern Emergence through the Lens of Tropical Geometry. Proceedings of the National Academy of Sciences. I115/E8135, 2018. National Research University, St. Petersburg, IBM Watson Research Center, University of Toulouse, Institute of Science and Technology, Austria, and CINVESTAV, Mexico system mathematicians provide another way to perceive and quantify nature’s constant propensity to reach an a balance beam of more or less relative order in every topological form and function. In actuality, each instantiated complement of the dual, reciprocal condition then resides in both modes at once (particle/wave). See also Introduction to Tropical Series by the authors at arXiv:1706.03062.

A simple geometric continuous model of self-organized criticality (SOC) is proposed. This model belongs to the field of tropical geometry and appears as a scaling limit of the classical sandpile model. We expect that our observation will connect the study of SOC and pattern formation to other fields (such as algebraic geometry, topology, string theory, and many practical applications) where tropical geometry has already been successfully used. (Significance)

Klamser, Pascal and Pawel Romanczuk. Collective Predator Evasion: Putting the Criticality Hypothesis to the Test. PLoS Computational Biology. March, 2021. Humboldt University, Berlin, computational neuroscientists conduct analytical studies of how and why animal groupings as they cope with survival issues seem to tend toward a dynamic critical state. Their work goes on to study the role that self-organizing forces play in facilitating this optimum viability.

Collective intelligence relies on efficient processing of information. Complex systems theory suggests that this activity is optimal at the border between order and disorder, i.e. at a critical point. However, for animal collectives fundamental questions remain open regarding self-organization towards criticality. Using a spatially explicit model of collective predator avoidance, we show that schooling prey performance is indeed optimal at criticality, but is not due to a collective response. Rather it occurs because of the emergent dynamical group structure. More importantly, this structural sensitivity makes the critical state evolutionary highly unstable in the context of predator-prey interactions, and demonstrates the decisive importance of spatial self-organization in collective animal behavior. (Author summary)

Kolodrubetz, Michael. Quenching Our Thirst for Universality. Nature. 563/191, 2018. A UT Dallas systems physicist introduces three papers in this issue: Observation of Universal Dynamics in a Spinor Bose Gas Far from Equilibrium (Prufer, 217), Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity (Eiger, 221) and Universal Dynamics in an Isolated One-Dimensional Bose Gas Far from Equilibrium (Erne, 225), that verify in different places and ways the natural presence of ubiquitous, infinitely iterated, formative patterns and active processes.

Although we live in a world of constant motion, physicists have focused largely on systems in or near equilibrium. In the past few decades, interest in non-equilibrium systems has increased, spurred by developments that are taking quantum mechanics from fundamental science to practical technology. Physicists are therefore tasked with an important question: what organizing principles do non-equilibrium quantum systems obey? Herein Prüfer et al, Eigen et al, and Erne et al report experiments that provide a partial answer to this question. The studies show, for the first time, that ultracold atomic systems far from equilibrium exhibit universality, in which measurable experimental properties become independent of microscopic details. (MK)
While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium universality is identified through the scaling of the spatio-temporal evolution of the system. This has been studied in the reheating process in inflationary cosmology, the dynamics of nuclear collision described by quantum chromodynamics, and the post-quench dynamics in dilute quantum gases in non-relativistic field theory. Here we observe the emergence of universal dynamics by spatially resolved spin correlations in a quasi-one-dimensional spinor Bose–Einstein condensate. (Prufer)

Understanding the behaviour of isolated quantum systems far from equilibrium and their equilibration is one of the most pressing problems in quantum many-body physics. There is strong theoretical evidence that sufficiently far from equilibrium a wide variety of systems — including the early Universe after inflation, quark–gluon matter generated in heavy-ion collisions, and cold quantum gases — exhibit universal scaling in time and space during their evolution, independent of their initial state or microscale properties. (Erne)

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