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Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalization
TLDR
It is shown that graph convolution extends the regime in which the data is linearly separable by a factor of roughly 1/ √ D, where D is the expected degree of a node, as compared to the mixture model data on its own.
Decision Algorithms for Ostrowski-Automatic Sequences
In this thesis, we extend the notion of k-automatic sequences to Ostrowski-automatic sequences. We develop a procedure for computationally deciding certain combinatorial and enumeration questions
Repetitions in infinite palindrome-rich words
TLDR
Lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets are addressed, and a candidate infinite rich word over the alphabet is constructed with a small critical exponent of $2+\sqrt{2}/2$.
Critical exponent of infinite balanced words via the Pell number system
TLDR
This work proves that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is $3/2$ using a formulation of first-order logic, the Pell number system, and a machine computation based on finite-state automata.