Tootfinder

Data Cubes in Hand: A Design Space of Tangible Cubes for Visualizing 3D Spatio-Temporal Data in Mixed Reality
Shuqi He, Haonan Yao, Luyan Jiang, Kaiwen Li, Nan Xiang, Yue Li, Hai-Ning Liang, Lingyun Yu
https://arxiv.org/abs/2403.06891

Data Cubes in Hand: A Design Space of Tangible Cubes for Visualizing 3D Spatio-Temporal Data in Mixed Reality
Tangible interfaces in mixed reality (MR) environments allow for intuitive data interactions. Tangible cubes, with their rich interaction affordances, high maneuverability, and stable structure, are particularly well-suited for exploring multi-dimensional data types. However, the design potential of these cubes is underexplored. This study introduces a design space for tangible cubes in MR, focusing on interaction space, visualization space, sizes, and multiplicity. Using spatio-temporal data, …

Probabilistic estimates of the diameters of the Rubik's Cube groups
So Hirata
https://arxiv.org/abs/2404.07337 https://arxiv.org/…

Probabilistic estimates of the diameters of the Rubik's Cube groups
The diameter of the Cayley graph of the Rubik's Cube group is the fewest number of turns needed to solve the Cube from any initial configurations. For the 2$\times$2$\times$2 Cube, the diameter is 11 in the half-turn metric, 14 in the quarter-turn metric, 19 in the semi-quarter-turn metric, and 10 in the bi-quarter-turn metric. For the 3$\times$3$\times$3 Cube, the diameter was determined by Rikicki et al. to be 20 in the half-turn metric and 26 in the quarter-turn metric. This study shows that…

This https://arxiv.org/abs/2301.07375 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solving cubic equations by completing the cube and higher degree equations by completing powers
We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of higher degree by completing powers. The main idea of completing powers arises from Harrison's center theory of higher degree forms. A very simple criterion for such algebraic equations is presented, and the computation amounts to solving linear equations and quadratic equations.

I know it sometimes seems like a bit of a pointless kitchen gadget, but I love my soup maker.
Grab a bunch of slightly-past-their-best veggies from the bottom drawer of the fridge. Throw them in the machine with a stock cube. Fill with water. Press the button.
Then go and waste time on Mastodon for half an hour (protip: you could do something useful with your life in this period of time, but honestly why would you!).
Come back into the kitchen 30 minutes later to find a lovely hot tasty and probably fairly healthy soup waiting for you.
I'd do that "follow me for more recipes" meme thing but realistically this is probably your lot!

This https://arxiv.org/abs/2403.01195 has been replaced.
link: https://scholar.google.com/scholar?q=a

Understanding Energy Level Structure Using Quantum Rubik's Cube
This study combines the quantum Rubik's Cube matrix with the Benalcazar Bernevig Hughes model, defines a matrix algorithm based on the reverse process of convolution, and constructs an expression for the quantum Rubik's Cube matrix and Hamiltonian. Furthermore, in order to make the operation of the quantum Rubik's Cube matrix clearer, we use a Josephus ring to draw a topological graph of the Rubik's Cube expansion. This article uses a quantum Rubik's Cube to calculate energy level transitions o…

This https://arxiv.org/abs/2402.05217 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Dense Model Theorem for the Boolean Slice
The (low soundness) linearity testing problem for the middle slice of the Boolean cube is as follows. Let $\varepsilon>0$ and $f$ be a function on the middle slice on the Boolean cube, such that when choosing a uniformly random quadruple $(x,y,z ,x\oplus y\oplus z)$ of vectors of $2n$ bits with exactly $n$ ones, the probability that $f(x\oplus y \oplus z) = f(x) \oplus f(y) \oplus f(z)$ is at least $1/2+\varepsilon$. The linearity testing problem, posed by David, Dinur, Goldenberg, Kindler and …

Cube tilings with linear constraints
Dae Gwan Lee, Goetz E. Pfander, David Walnut
https://arxiv.org/abs/2403.07411 https://arxiv.org/…

Cube tilings with linear constraints
We consider tilings $(\mathcal{Q},Φ)$ of $\mathbb{R}^d$ where $\mathcal{Q}$ is the $d$-dimensional unit cube and the set of translations $Φ$ is constrained to lie in a pre-determined lattice $A \mathbb{Z}^d$ in $\mathbb{R}^d$. We provide a full characterization of matrices $A$ for which such cube tilings exist when $Φ$ is a sublattice of $A\mathbb{Z}^d$ with any $d \in \mathbb{N}$ or a generic subset of $A\mathbb{Z}^d$ with $d\leq 7$. As a direct consequence of our results, we obtain a crite…

Here's a legislation idea for my creator (or anyone else, for that matter): do a bill to enact the #CubeRootRule for House apportionment

Classification of Dupin Cyclidic Cubes by Their Singularities
Jean Michel Menjanahary, Eriola Hoxhaj, Rimvydas Krasauskas
https://arxiv.org/abs/2405.07225 …

I know it sometimes seems like a bit of a pointless kitchen gadget, but I love my soup maker.
Grab a bunch of slightly-past-their-best veggies from the bottom drawer of the fridge. Throw them in the machine with a stock cube. Fill with water. Press the button.
Then go and waste time on Mastodon for half an hour (protip: you could do something useful with your life in this period of time, but honestly why would you!).
Come back into the kitchen 30 minutes later to find a lovely hot tasty and probably fairly healthy soup waiting for you.
I'd do that "follow me for more recipes" meme thing but realistically this is probably your lot!