Wyatt Milgrim
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View article: VC-Dimension of Hyperplanes Over Finite Fields
VC-Dimension of Hyperplanes Over Finite Fields Open
Let $$\mathbb {F}_q^d$$ be the d -dimensional vector space over the finite field with q elements. For a subset $$E\subseteq \mathbb {F}_q^d$$ and a fixed nonzero $$t\in \mathbb {F}_q$$ , let $$\mathcal {H}_t(E)=\{h_y: y…
View article: VC-Dimension of Hyperplanes over Finite Fields
VC-Dimension of Hyperplanes over Finite Fields Open
Let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field with $q$ elements. For a subset $E\subseteq \mathbb{F}_q^d$ and a fixed nonzero $t\in \mathbb{F}_q$, let $\mathcal{H}_t(E)=\{h_y: y\in E\}$, where $h_y$ is the …
View article: Towards the Gaussianity of Random Zeckendorf Games
Towards the Gaussianity of Random Zeckendorf Games Open
Zeckendorf proved that any positive integer has a unique decomposition as a sum of non-consecutive Fibonacci numbers, indexed by $F_1 = 1, F_2 = 2, F_{n+1} = F_n + F_{n-1}$. Motivated by this result, Baird, Epstein, Flint, and Miller defin…
View article: VC-Dimension and Distance Chains in $\mathbb{F}_q^d$
VC-Dimension and Distance Chains in $\mathbb{F}_q^d$ Open
Given a domain $X$ and a collection $\mathcal{H}$ of functions $h:X\to \{0,1\}$, the Vapnik-Chervonenkis (VC) dimension of $\mathcal{H}$ measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical…