Evolution models with extremal dynamics.

Archaeologists can learn from models of evolution as a self-organized critical phenomenon. Self-organized critical systems are large, interactive systems that organize into a critical state where minor events can trigger chain reactions. Such systems demonstrate power-law distributions in the size of changes, or “avalanches,” that occur. The theory of self-organized criticality is important in that it implies that the evolution of complex systems may be driven more by interactions between agents than by external events or natural selection. Stylistic changes may be examples of avalanches of interconnected events. Evidence for self-organized criticality is shown for stylistic evolution in historical pottery styles from New York State and is used to evaluate the nature of a prehistoric pottery typology from the Southwest.

We study a simple model of spin network evolution motivated by the hypothesis that the emergence of classical spacetime from a discrete microscopic dynamics may be a self-organized critical process. Self-organized critical systems are statistical systems that naturally evolve without fine tuning to critical states in which correlation functions are scale invariant. We study several rules for evolution of frozen spin networks in which the spins labeling the edges evolve on a fixed graph. We find evidence for a set of rules which behaves analogously to sand pile models in which a critical state emerges without fine tuning, in which some correlation functions become scale invariant.

Extremal dynamics in random replicator ecosystems

The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks—external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input—the case studied in the companion paper to this article). The system displays avalanche dynamics in the form of cascades of neuronal firing separated by periods of silence. We observe partial scale-free behaviour in the distribution of avalanche size for low levels of external input. We analytically derive the distributions of waiting times and investigate their temporal behaviour in relation to different levels of external input, showing that the system’s dynamics can exhibit partial long-range temporal correlations. We further show that as the system approaches the critical state by two alternative ‘routes’, different markers of criticality (partial scale-free behaviour and long-range temporal correlations) are displayed. This suggests that signatures of criticality exhibited by a particular system in close proximity to a critical state are dependent on the region in parameter space at which the system (currently) resides.

Persistent dynamic correlations in self-organized critical systems away from their critical point

Calving margins are highly sensitive to changes in climate and glacier terminus geometry. Numerical modelling suggests that calving glacier termini are self-organized critical systems that are fluctuating between states of advance and retreat. Over the next century, one of the largest contributions to sea level rise will come from ice sheets and glaciers calving ice into the ocean1. Factors controlling the rapid and nonlinear variations in calving fluxes are poorly understood, and therefore difficult to include in prognostic climate-forced land-ice models. Here we analyse globally distributed calving data sets from Svalbard, Alaska (USA), Greenland and Antarctica in combination with simulations from a first-principles, particle-based numerical calving model to investigate the size and inter-event time of calving events. We find that calving events triggered by the brittle fracture of glacier ice are governed by the same power-law distributions as avalanches in the canonical Abelian sandpile model2. This similarity suggests that calving termini behave as self-organized critical systems that readily flip between states of sub-critical advance and super-critical retreat in response to changes in climate and geometric conditions. Observations of sudden ice-shelf collapse and tidewater glacier retreat in response to gradual warming of their environment3 are consistent with a system fluctuating around its critical point in response to changing external forcing. We propose that self-organized criticality provides a yet unexplored framework for investigations into calving and projections of sea level rise.

Flow and mass balance of the Greenland Ice Sheet are largely controlled by marine-terminating glaciers that deliver large quantities of ice into fjords and coastal seas. The interaction of these glaciers with the ocean is crucial because heat and circulation in fjords drive high rates of melting. However, the links between warm ambient fjord water, subaqueous melting and iceberg calving are poorly understood. Here, we report a detailed record of surface circulation in Ikerasak Fjord, West Greenland, by tracking the displacements of icebergs in radar imagery acquired with a terrestrial radar interferometer, which also produced a detailed record of iceberg calving from Store Glacier. With images captured every three minutes, we derived fjord circulation and calving rates with unusually high temporal resolution. In the first of three periods, we observed low-speed surface currents (<0.15 m/s) together with high calving activity (around 50 events per hour) as a response to the break-up of proglacial winter melange. We subsequently observed faster surface currents (up to 0.57 m/s) but much less calving (<20 icebergs per hour). Later, as currents intensified and a large eddy formed, we observed a combination of fast fjord circulation (around 0.4 m/s) and high calving activity (20-40 events per hour). The record shows that calving is a self-organised critical system, with small icebergs produced continuously in a critical state, whereas large icebergs were produced mostly when calving becomes super-critical. A super-critical state was reached when the melange broke up and later as the eddy formed in front of the glacier. In this state, we found stronger fjord circulation to drive more frequent calving events, while more frequent calving in general caused a higher flux of ice to the ocean.

We suggest a generalized definition of self-organized criticality (SOC) systems: SOC is a critical state of a nonlinear energy dissipation system that is slowly and continuously driven towards a critical value of a system-wide instability threshold, producing scale-free, fractal-diffusive, and intermittent avalanches with powerlaw-like size distributions. We develop here a macroscopic description of SOC systems that provides an equivalent description of the complex microscopic fine structure, in terms of fractal-diffusive transport (FD-SOC). Quantitative values for the size distributions of SOC parameters (length scales $L$, time scales $T$, waiting times $\Delta t$, fluxes $F$, and energies $E$) are derived from first principles, using the scale-free probability conjecture, $N(L) dL \propto L^{-d}$, for Euclidean space dimension $d$. We apply this model to astrophysical SOC systems, such as lunar craters, the asteroid belt, Saturn ring particles, magnetospheric substorms, radiation belt electrons, solar flares, stellar flares, pulsar glitches, soft gamma-ray repeaters, black-hole objects, blazars, and cosmic rays. The FD-SOC model predicts correctly the size distributions of 8 out of these 12 astrophysical phenomena, and indicates non-standard scaling laws and measurement biases for the others.

Near universal values of social inequality indices in self-organized critical models

The evolution of an experimental braided river produced in our laboratory has been monitored and analyzed. It has been shown that in addition to the spatial scaling revealed by Sapozhnikov and Foufoula‐Georgiou [1996a], braided rivers also exhibit dynamic scaling. This implies that a smaller part of a braided river evolves identically (in the statistical sense) to a larger one provided the time is renormalized by a factor depending only on the ratio of the spatial scales of those parts. The small value of the estimated dynamic exponent z is interpreted as an indication that the evolution of small channels in a braided river system is to a large extent forced by the evolution of bigger channels. The presence of dynamic scaling is further interpreted as indicating that braided rivers may be in a critical state and behave as self‐organized critical systems.

Abstract. The dissipation power and size of auroral blobs are investigated in detail to examine the possible analogy between the dynamic magnetosphere and a forced and/or self-organized critical system. The distributions of these auroral parameters are sorted in terms of different levels of activity, namely substorms, pseudo-breakups, and quiet conditions. A power law (scale-free) component is seen in all these distributions. In addition, a peak distribution is found for substorm intervals and a hump for pseudo-breakup intervals. The peak distribution is present prominently during magnetic storms, i.e. when the magnetosphere is strongly driven by the solar wind. It is interpreted that the scale-free component is associated with the activity of the diffuse aurora, corresponding to disturbances at all permissible scales within the plasma sheet. Ionospheric feedback appears to be essential for the presence of two components in the distribution for auroral dissipation power. These results are consistent with the concept that the magnetosphere is in a forced and/or self-organized critical state, although they do not constitute conclusive evidence for the analogy.

Current training methods for interns and residents in teaching hospitals do not adequately raise spatial perception about geometry and topology changes of skeletal morphology. Two reasons for the inability are trainees can only observe an operation before he participates in a surgery and preoperative rehearsal usually involves 2D (two dimensional) paper surgical simulations based on X-ray images. Moreover, surgery visiting doctors may also fail in real operations even after evaluating topology and geometry changes on rigid bones, prostheses and bone grafts of all procedures by 2D paper simulations. The failure rates were reported as 10-20% for setting-bone surgery. Computer-based surgery simulation represents a rapidly emerging and increasingly important area of research that combines a number of disciplines for the common purpose of improving health care. Generally, the goal of computer-based surgery simulation is to enable a surgeon to experiment with different surgical procedures in an artificial environment. We are developing a virtual surgical simulator specifically for HIT-RAOS, the robot-assisted setting-bone surgery system, which involves both various robots modeling and patients modeling. To satisfy requires on surgery programming and surgery rehearse based on special patient, a novel method of biological tissue model and simulation based special CT images includes 10 series is proposed in this article. Biological tissue geometry model, physical model and mechanical equilibrium equation based on strain energy function are built. Biomechanical equations are solved by finite element method. To make sure the simulator can be available in diverse operation systems, Java3D and VRML are chosen as the main developing tools. Based all the works above, As application examples, femur models and simulation are given and a cutting skin experiment was conducted, the results are contented. This validity of method and mathematics model is tested to compare simulation outcome with biomechanical experimentation

The causes of major and rapid transitions observed in biological macroevolution as well as in the evolution of social systems are a subject of much debate. Here we identify the proximate causes of crashes and recoveries that arise dynamically in a model system in which populations of (molecular) species coevolve with their network of chemical interactions. Crashes are events that involve the rapid extinction of many species, and recoveries the assimilation of new ones. These are analyzed and classified in terms of the structural properties of the network. We find that in the absence of large external perturbation, "innovation" is a major cause of large extinctions and the prime cause of recoveries. Another major cause of crashes is the extinction of a "keystone species." Different classes of causes produce crashes of different characteristic sizes.

Swept and delta wings maneuvering at moderate and high angles of attack produce highly nonlinear and often discontinuous aerodynamic forces and moments that are difficult to model. The nonlinear indicial response (NIR) methodology and the concept of critical states accompanied by changes in the flow structure and topology could provide a rational framework for the analyses and modeling of these flows. The analysis of surface oil-flow photographs and laser light sheet high-speed video images of smoke flow has been performed. The correlation of the structural and topological changes in the flow with force and moment data follows. Critical states are often accompanied by changes in the flow topology and not all topological changes produce measurable changes hi the forces and moments, however, a useful relationship may exist.

We develop a statistical analytical model that predicts the occurrence frequency distributions and parameter correlations of avalanches in nonlinear dissipative systems in the state of a slowly-driven self-organized criticality (SOC) system. This model, called the fractal-diffusive SOC model, is based on the following four assumptions: (i) The avalanche size $L$ grows as a diffusive random walk with time $T$, following $L \propto T^{1/2}$; (ii) The instantaneous energy dissipation rate $f(t)$ occupies a fractal volume with dimension $D_S$, which predicts the relationships $F = f(t=T) \propto L^{D_S} \propto T^{D_S/2}$, $P \propto L^{S} \propto T^{S/2}$ for the peak energy dissipation rate, and $E \propto F T \propto T^{1+D_S/2}$ for the total dissipated energy; (iii) The mean fractal dimension of avalanches in Euclidean space $S=1,2,3$ is $D_S \approx (1+S)/2$; and (iv) The occurrence frequency distributions $N(x) \propto x^{-\alpha_x}$ based on spatially uniform probabilities in a SOC system are given by $N(L) \propto L^{-S}$, which predicts powerlaw distributions for all parameters, with the slopes $\alpha_T=(1+S)/2$, $\alpha_F=1+(S-1)/D_S$, $\alpha_P=2-1/S$, and $\alpha_E=1+(S-1)/(D_S+2)$. We test the predicted fractal dimensions, occurrence frequency distributions, and correlations with numerical simulations of cellular automaton models in three dimensions $S=1,2,3$ and find satisfactory agreement within $\approx 10%$. One profound prediction of this universal SOC model is that the energy distribution has a powerlaw slope in the range of $\alpha_E=1.40-1.67$, and the peak energy distribution has a slope of $\alpha_P=1.67$ (for any fractal dimension $D_S=1,...,3$ in Euclidean space S=3), and thus predicts that the bulk energy is always contained in the largest events, which rules out significant nanoflare heating in the case of solar flares.