Jean M. Carlson

Fire in the Earth system.

Burn, Baby, Burn Wildfires can have dramatic and devastating effects on landscapes and human structures and are important agents in environmental transformation. Their impacts on nonanthropocentric aspects of the environment, such as ecosystems, biodiversity, carbon reserves, and climate, are often overlooked. Bowman et al. (p. 481) review what is known and what is needed to develop a holistic understanding of the role of fire in the Earth system, particularly in view of the pervasive impact of fires and the likelihood that they will become increasingly difficult to control as climate changes. Fire is a worldwide phenomenon that appears in the geological record soon after the appearance of terrestrial plants. Fire influences global ecosystem patterns and processes, including vegetation distribution and structure, the carbon cycle, and climate. Although humans and fire have always coexisted, our capacity to manage fire remains imperfect and may become more difficult in the future as climate change alters fire regimes. This risk is difficult to assess, however, because fires are still poorly represented in global models. Here, we discuss some of the most important issues involved in developing a better understanding of the role of fire in the Earth system.

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes—flexibility and selection—must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.

HIGHLY OPTIMIZED TOLERANCE : A MECHANISM FOR POWER LAWS IN DESIGNED SYSTEMS

We introduce a mechanism for generating power law distributions, referred to as highly optimized tolerance (HOT), which is motivated by biological organisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. We suggest that power laws in these systems are due to tradeoffs between yield, cost of resources, and tolerance to risks. These tradeoffs lead to highly optimized designs that allow for occasional large events. We investigate the mechanism in the context of percolation and sand pile models in order to emphasize the sharp contrasts between HOT and self-organized criticality (SOC), which has been widely suggested as the origin for power laws in complex systems. Like SOC, HOT produces power laws. However, compared to SOC, HOT states exist for densities which are higher than the critical density, and the power laws are not restricted to special values of the density. The characteristic features of HOT systems include: (1) high efficiency, performance, and robustness to designed-for uncertainties; (2) hypersensitivity to design flaws and unanticipated perturbations; (3) nongeneric, specialized, structured configurations; and (4) power laws. The first three of these are in contrast to the traditional hallmarks of criticality, and are obtained by simply adding the element of design to percolation and sand pile models, which completely changes their characteristics.

Conserved and variable architecture of human white matter connectivity

Whole-brain network analysis of diffusion imaging tractography data is an important new tool for quantification of differential connectivity patterns across individuals and between groups. Here we investigate both the conservation of network architectural properties across methodological variation and the reproducibility of individual architecture across multiple scanning sessions. Diffusion spectrum imaging (DSI) and diffusion tensor imaging (DTI) data were both acquired in triplicate from a cohort of healthy young adults. Deterministic tractography was performed on each dataset and inter-regional connectivity matrices were then derived by applying each of three widely used whole-brain parcellation schemes over a range of spatial resolutions. Across acquisitions and preprocessing streams, anatomical brain networks were found to be sparsely connected, hierarchical, and assortative. They also displayed signatures of topo-physical interdependence such as Rentian scaling. Basic connectivity properties and several graph metrics consistently displayed high reproducibility and low variability in both DSI and DTI networks. The relative increased sensitivity of DSI to complex fiber configurations was evident in increased tract counts and network density compared with DTI. In combination, this pattern of results shows that network analysis of human white matter connectivity provides sensitive and temporally stable topological and physical estimates of individual cortical structure across multiple spatial scales.

Structural foundations of resting-state and task-based functional connectivity in the human brain

Magnetic resonance imaging enables the noninvasive mapping of both anatomical white matter connectivity and dynamic patterns of neural activity in the human brain. We examine the relationship between the structural properties of white matter streamlines (structural connectivity) and the functional properties of correlations in neural activity (functional connectivity) within 84 healthy human subjects both at rest and during the performance of attention- and memory-demanding tasks. We show that structural properties, including the length, number, and spatial location of white matter streamlines, are indicative of and can be inferred from the strength of resting-state and task-based functional correlations between brain regions. These results, which are both representative of the entire set of subjects and consistently observed within individual subjects, uncover robust links between structural and functional connectivity in the human brain.

Pupillometric evidence for the decoupling of attention from perceptual input during offline thought

Accumulating evidence suggests that the brain can efficiently process both external and internal information. The processing of internal information is a distinct “offline” cognitive mode that requires not only spontaneously generated mental activity; it has also been hypothesized to require a decoupling of attention from perception in order to separate competing streams of internal and external information. This process of decoupling is potentially adaptive because it could prevent unimportant external events from disrupting an internal train of thought. Here, we use measurements of pupil diameter (PD) to provide concrete evidence for the role of decoupling during spontaneous cognitive activity. First, during periods conducive to offline thought but not during periods of task focus, PD exhibited spontaneous activity decoupled from task events. Second, periods requiring external task focus were characterized by large task evoked changes in PD; in contrast, encoding failures were preceded by episodes of high spontaneous baseline PD activity. Finally, high spontaneous PD activity also occurred prior to only the slowest 20% of correct responses, suggesting high baseline PD indexes a distinct mode of cognitive functioning. Together, these data are consistent with the decoupling hypothesis, which suggests that the capacity for spontaneous cognitive activity depends upon minimizing disruptions from the external world.

Patterns of seismic activity preceding large earthquakes

We analyze the patterns of seismic activity which precede large events in a mechanical model of a fault. The model generates a statistical distribution of events similar to that observed for a single fault, with a scaling region consistent with the Gutenberg-Richter law at small and moderate magnitudes, and an excess of events at large magnitudes. We find only slight variation in the scaling behavior during a loading cycle. However, we do observe systematic variations in space and time of the overall rate of activity. In the model, the activity accelerates dramatically preceding a large event and is usually a maximum hi the neighborhood of the future epicenter. These results are compared to California seismicity data, where we find that activity patterns vary regionally. Looking at patterns of activity in the San Francisco Bay Area since 1948, we find an increase of activity on the Calaveras fault near San Jose beginning in the 1980s which, if our model is relevant, would forecast a large earthquake in that region. The 1989 Loma Prieta earthquake occurred on the San Andreas fault within 30 km of the section of the Calaveras fault showing increased activity.

Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of shear transformation zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi [Phys. Rev. Lett. 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

Constraining earthquake source inversions with GPS data: 1. Resolution-based removal of artifacts

[1] We present a resolution analysis of an inversion of GPS data from the 2004 Mw 6.0 Parkfield earthquake. This earthquake was recorded at thirteen 1-Hz GPS receivers, which provides for a truly coseismic data set that can be used to infer the static slip field. We find that the resolution of our inverted slip model is poor at depth and near the edges of the modeled fault plane that are far from GPS receivers. The spatial heterogeneity of the model resolution in the static field inversion leads to artifacts in poorly resolved areas of the fault plane. These artifacts look qualitatively similar to asperities commonly seen in the final slip models of earthquake source inversions, but in this inversion they are caused by a surplus of free parameters. The location of the artifacts depends on the station geometry and the assumed velocity structure. We demonstrate that a nonuniform gridding of model parameters on the fault can remove these artifacts from the inversion. We generate a nonuniform grid with a grid spacing that matches the local resolution length on the fault and show that it outperforms uniform grids, which either generate spurious structure in poorly resolved regions or lose recoverable information in well-resolved areas of the fault. In a synthetic test, the nonuniform grid correctly averages slip in poorly resolved areas of the fault while recovering small-scale structure near the surface. Finally, we present an inversion of the Parkfield GPS data set on the nonuniform grid and analyze the errors in the final model.

Influence of friction and fault geometry on earthquake rupture

We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridge-Knopoff model in which radiation effects are approximated by viscous dissipation.