Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical properties of the stable configuration for three classes of acyclic preferences: node-based preferences, distance-based preferences, and random acyclic systems. Using random overlay graphs, we prove by means of a mean-field assumption and a fluid-limit technique that these systems have an asymptotically continuous independent rank distribution for a proper scaling, and the analytical solution is compared to simulations. These results provide a theoretical ground for validating the performance of bandwidth-based or proximity-based unstructured systems.

In this paper, we propose a novel method for the registration of volumetric images of the brain that optimizes the alignment of both cortical and subcortical structures. In order to achieve this, relevant geometrical information is extracted from a surface-based morph and diffused into the volume using the Navier operator of elasticity, resulting in a volumetric warp that aligns cortical folding patterns. This warp field is then refined with an intensity driven optical flow procedure that registers noncortical regions, while preserving the cortical alignment. The result is a combined surface and volume morph (CVS) that accurately registers both cortical and subcortical regions, establishing a single coordinate system suitable for the entire brain.