Michael Alexander Waddell

arXiv2018

Using Ramsey theory to measure unavoidable spurious correlations in Big Data

Given a dataset we quantify how many patterns must always exist in the dataset. Formally this is done through the lens of Ramsey theory of graphs, and a quantitative bound known as Goodman's theorem. Combining statistical tools with Ramsey theory of graphs gives a nuanced understanding of how far away a dataset is from random, and what qualifies as a meaningful pattern. This method is applied to a dataset of repeated voters in the 1984 US congress, to quantify how homogeneous a subset of congressional voters is. We also measure how transitive a subset of voters is. Statistical Ramsey theory is also used with global economic trading data to provide evidence that global markets are quite transitive.

math.CO↗

arXiv2015

A Solution for the Open Abelian Sandpile Problem of Distributing k Items in N Vertices, where k = N

This paper outlines a closed solution to an open problem in Graph Theory concerning the classification of the successful initial distributions of k items in N vertices, where $k = N$, that lead to the terminal set $N_k = \{ n_i\} $, where $n_i=1$ and $i=1,2,3,...,k$. First, each successful initial distribution is enumerated using an algorithm. The closed solution classifies the terminal set in terms of its modulus, and proves that each successful initial distribution can be classified by the same modulus.

math.GM↗