A Method to Reclaim Multifractal Statistics from Saturated Images

The CompuMAINE lab has developed a patented computational cancer detection method utilizing the 2D Wavelet Transform Modulus Maxima (WTMM) method to help predict disrupted, tumor-associated breast tissue from mammography. The lab has a database of mammograms in which some of the image subregions contain artefacts which are excluded from the analysis, image saturation is one such artefact. To maximize statistical power in our clinical analyses, our goal is therefore to minimize the rejection of image subregions containing artefacts. The goal of this particular project is to explore the effects of image saturation on the resulting multifractal statistics from the 2D WTMM method. Groups of numerically simulated (monofractal) fractional Brownian motion (fBm) surfaces with varying roughness exponents were generated and saturated at the 1\%, 5\%, 10\% and 20\% levels. We find that image saturation reduces the range of available statistical order moments relative to an unsaturated image. By assessing the effects of image saturation on the 2D WTMM calculations, we developed a filtering approach where we nearly regained the entire range of statistical order moments thus limiting the impacts of image saturation

A comparison of zero and minimal intelligence agendas in majority-rule voting models

Emergent behavior in repeated collective decisions of minimally intelligent agents -- who at each step in time invoke majority rule to choose between a status quo and a random challenge -- can manifest through the long-term stationary probability distributions of a Markov Chain. We use this known technique to compare two kinds of voting agendas: a zero-intelligence agenda that chooses the challenger uniformly at random, and a minimally-intelligent agenda that chooses the challenger from the union of the status quo and the set of winning challengers. We use Google Co-Lab's GPU accelerated computing environment to compute stationary distributions for some simple examples from spatial-voting and budget-allocation scenarios. We find that the voting model using the zero-intelligence agenda converges more slowly, but in some cases to better outcomes