A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a statistical physics approach, based on the string landscape. We present a dynamical selection mechanism for hospitable vacua based on search optimization. Instead of focusing on stationary probability distributions, we are interested in the approach to equilibrium. This is particularly relevant if cosmological evolution has occurred for a time shorter than the exponentially-long mixing time for the landscape. This imposes a strong selection pressure among hospitable vacua, favoring those in regions where the search algorithm is efficient. Specifically, the mean first passage time is minimized for hospitable vacua lying at the bottom of funnel-like regions, akin to the smooth folding funnels of proteins and the loss functions of well-trained deep neural networks. The optimality criterion is time-reparametrization invariant and defined by two competing requirements: search efficiency, which requires minimizing the mean first passage time, and sweeping exploration, which requires that random walks are recurrent. Optimal landscape regions reach a compromise by lying at the critical boundary between recurrence and transience, thereby achieving dynamical criticality. Remarkably, this implies that the optimal lifetime of vacua coincides with the de Sitter Page time. Our mechanism makes concrete phenomenological predictions: 1. The expected lifetime of our universe is $10^{130}$ years, which is ~$2\sigma$ from the Standard Model metastability estimate; 2. The SUSY breaking scale should be high, $>10^{10}$ GeV. The present framework suggests a correspondence between the near-criticality of our universe and non-equilibrium critical phenomena on the landscape.

Self-Organized Criticality

Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the possibility of very high connectivity degree. Here we study a recent model based on self-organized criticality, which consists of an electrical network with threshold firing and activity-dependent synapse strengths. We study the model on a scale-free network, the Apollonian network, which presents many features of neuronal systems. The system exhibits a power law distributed avalanche activity. The analysis of the power spectra of the electrical signal reproduces very robustly the power law behaviour with the exponent 0.8, experimentally measured in electroencephalograms (EEG) spectra. The exponents are found to be quite stable with respect to initial configurations and strength of plastic remodelling, indicating that universality holds for a wide class of brain models.

Modelling the brain as a n Apollonian network

We introduce the standard distribution width of fitness to characterize the global and individual features of an ecosystern described by the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, the w(0) avalanche, is observed. The corresponding gap equation and the self-organized threshold w(c) are obtained. The critical exponents tau, gamma and rho, which describe the behaviour of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated by numerical simulation. The exact master equation and gamma equation are derived, and the scaling relations are established among the critical exponents of this new avalanche.

Avalanche dynamics in the Bak-Sneppen evolution model observed with a standard distribution width of fitness

We have studied the mechanisms generating 1/f (flicker) noise (FN). Recently, it has been suggested that FN in biological ion channels is caused by “the equilibrium conductance fluctuations related to the conformational flexibility of the channel pore structural constituents” [1]. It has also been claimed that FN results from the switching of the channels between their different conducting states [2], and is not an “inherent property of ion transport” [1]. To check those conjectures we nanofabricated synthetic pores of similar dimensions to those of biological channels and studied their transport characteristics [3,4]. We have examined the pores produced in two different polymeric materials: polyethylene terephthalate and polyimide. The pore in polyimide has smooth walls, while in PET there remain — sticking from the pore walls — charged, loose ends of cleaved polymer strands, so‐called “dangling ends”, which move continuously in a more or less random fashion. By comparing the synthetic and biological (BK channel) channels we show that the FN noise indeed originates from the channel’s opening‐closing process, related in turn to the underlying motions of channel wall constituents. The polyimide pore does not produce FN. Moreover, we have shown the non‐Markovianity of the ion transport through the biological and PET nanopores. On the basis of these findings and several recent literature reports we propose the following tentative mechanism for FN: a necessary but not sufficient condition for appearance of the FN noise in a given process is its coupling to another — deterministic or/and stochastic ‐ background process.

1/f Noise in Ion Transport through Nanopores: Origins and Mechanism

The history of the Universe started about 145 Ga ago, when the period known as the Big Bang took place Its evolution in space and time went on, and in the region where we live, about 35 Ga ago, the first manifestations of the phenomena we call Life were already taking place Today living things (human beings) are capable of asking meaningful questions about the origin, evolution and even the future of the Universe and its organization [1], all the way from apparently less “complicated” structures to structures as complex as living organisms and ecologies (Figs 211 and 212) The science that describes such interpolation is Astrobiology Perhaps, Astrobiology will be for Biology in the future what Cosmology is for Astronomy today

/pdf/scaling-phenomena-and-the-emergence-of-complexity-in-3gqv3wemaa.pdf

Self-Organized Criticality

Citations

Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape

Modelling the brain as a n Apollonian network

Avalanche dynamics in the Bak-Sneppen evolution model observed with a standard distribution width of fitness

1/f Noise in Ion Transport through Nanopores: Origins and Mechanism

Scaling phenomena and the emergence of complexity in astrobiology

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