The neural dynamics of stimulus and response conflict processing as a function of response complexity and task demands.

Both stimulus and response conflict can disrupt behavior by slowing response times and decreasing accuracy. Although several neural activations have been associated with conflict processing, it is unclear how specific any of these are to the type of stimulus conflict or the amount of response conflict. Here, we recorded electrical brain activity, while manipulating the type of stimulus conflict in the task (spatial [Flanker] versus semantic [Stroop]) and the amount of response conflict (two versus four response choices). Behaviorally, responses were slower to incongruent versus congruent stimuli across all task and response types, along with overall slowing for higher response-mapping complexity. The earliest incongruency-related neural effect was a short-duration frontally-distributed negativity at ~200 ms that was only present in the Flanker spatial-conflict task. At longer latencies, the classic fronto-central incongruency-related negativity 'N(inc)' was observed for all conditions, but was larger and ~100 ms longer in duration with more response options. Further, the onset of the motor-related lateralized readiness potential (LRP) was earlier for the two vs. four response sets, indicating that smaller response sets enabled faster motor-response preparation. The late positive complex (LPC) was present in all conditions except the two-response Stroop task, suggesting this late conflict-related activity is not specifically related to task type or response-mapping complexity. Importantly, across tasks and conditions, the LRP onset at or before the conflict-related N(inc), indicating that motor preparation is a rapid, automatic process that interacts with the conflict-detection processes after it has begun. Together, these data highlight how different conflict-related processes operate in parallel and depend on both the cognitive demands of the task and the number of response options.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.