While we validated this approach by voxel pattern simulations, the analysis hinges critically on the assumption that activity in independent neuronal populations within a single voxel combine additively in the observed BOLD signal.
Image and diffraction pattern simulations are based on data provided by Wang et al. [27].
Stationary, oscillating- and travelling axial-pulses are shown to emerge, in agreement with the experimentally observed axial patterns, and simulations, backed by linear analysis, show that transversal patterns may emerge as well.
In order to determine the pattern that might be seen with specific spatial scales of clustering, we conducted further simulations by imposed patterns with specific scales on the spatial coordinates of the homesteads, in varying proportions with random noise using a gamma distribution.
The radiation pattern is calculated from the simulations by placing an x-polarized electric dipole source at the feed gap of the dipole antenna.
Because of these phenotypic properties, we anticipate that under hypoxic and acidic conditions, MCF-7 cells will evolve phenotypes with constitutive upregulation of glycolysis, and that growth of these populations will exhibit a distinctive pattern predicted by model simulations with focal nodules of glycolytic cells growing in the normoxic region of the spheroid.
Simulations by Dr. Harrowell and his co-workers have been able to predict, based on the pattern of vibration frequencies, which areas were likely to be jammed and which were likely to continue moving.
We assessed the sensitivity of the results to this assumed mixing pattern by running simulations with a well-mixed population (no difference between within-group and between-group mixing) and a population with highly assortative mixing (between-group mixing rate that was 25% of the within-group mixing rate) (Web Figures 4 and 5).
The SAED pattern shows a systematic array of white spots of orthorhombic phase of Sb2S3 single crystal, corresponding to the diffraction pattern obtained by simulation [30].
Pattern formation simulations are then performed.
