Nathan Dalaklis

activity

20212026

collaborators

7 papers

cs.CC2026

Riftbound is Turing Complete

Nathan Dalaklis, Beckett Fields

Riftbound: League of Legends Trading Card Game is a trading card game about capturing and holding locations in a king-of-the-hill style contest. Originally released in China in Aug…

math.DS2026

Complex Diophantine Approximations and Cusp Excursions

Nathan Dalaklis, Yan Mary He

We study the Hausdorff dimension spectrum of asymptotic approximation rates of complex Diophantine approximation and that of the asymptotic average excursion time of cusp excursion…

math.DS2025

Multifractal Analysis of Equilibrium States of Endomorphisms of $P^{k}$

Nathan Dalaklis, Yan Mary He

Let $f$ be a holomorphic endomorphism of $C P^{k}$ of algebraic degree at least $2$ and let $X \subseteq C P^{k}$ be an uniformly expanding set. In th…

math.CA2025

The higher order partial derivatives of Okamoto's function with respect to the parameter

Pieter Allaart, Nathan Dalaklis, Kiko Kawamura +2

Let ${F_{a} : a \in (0, 1)}$ be Okamoto's family of continuous self-affine functions, introduced in [{\em Proc. Japan Acad. Ser. A Math. Sci.} {\bf 81} (2005), no. 3, 47--50]. This fam…

math.GN2024

The $D$ -Variant of Transfinite Hausdorff Dimension

Bryce Decker, Nathan Dalaklis

We assign every metric space $X$ the value $t_{D} H D (X)$ , an ordinal number or one of the symbols $- 1$ or $Ω$ , and we call it the $D$ -variant of transfinite Hausdorff dimension of $…

math.DS2024

Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems

Nathan Dalaklis

Let $Φ = {ϕ_{e}}_{e \in E}$ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation $E_{A}^{\infty}$ and limit set $J$ . Under a mild condi…

math.CA2021

The partial derivative of Okamoto's functions with respect to the parameter

Nathan Dalaklis, Kiko Kawamura, Tobey Mathis +1

The differentiability of the one parameter family of Okomoto's functions as functions of $x$ has been analyzed extensively since their introduction in 2005. As an analogue to a sim…