Tootfinder

Der Cube-Look lebt: Harman/Kardon legt Soundsticks in Version 5 auf
Immer wieder hat Harman/Kardon die einst gut zum Power Mac G4 Cube passenden Lautsprecher aufgelegt. Nun kommt eine neue Runde für die Soundsticks.

When I was little, I felt there was something massive and cosmic about the Hampster Dance song, like a hymn still sung centuries later, like the seasonal chants of an uncontacted tribe. My first exposure to it was its use in the Scratch platformer series "Cube World", this game where important characters go to space and tragically die, this game that no longer functions due to all the updates since Scratch 1.4.

Decentralised self-organisation of pivoting cube ensembles using geometric deep learning
Nadezhda Dobreva, Emmanuel Blazquez, Jai Grover, Dario Izzo, Yuzhen Qin, Dominik Dold
https://arxiv.org/abs/2509.03140

Decentralised self-organisation of pivoting cube ensembles using geometric deep learning
We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its local neighborhood, trained using reinforcement learning. Furthermore, using geometric deep learning, we include the grid symmetries of the cube ensemble in the neural network architecture. We find that even the most localized versions succeed in reconfiguring…

Cube Height, Cube Width and Related Extremal Problems for Posets
Paul Bastide, J\k{e}drzej Hodor, Hoang La, William T. Trotter
https://arxiv.org/abs/2510.00928 https://

Cube Height, Cube Width and Related Extremal Problems for Posets
Given a poset $P$, a family $\mathcal{S}=\{S_x:x\in P\}$ of sets indexed by the elements of $P$ is called an inclusion representation of $P$ if $x\leqslant y$ in $P$ if and only if $S_x\subseteq S_y$. The cube height of a poset is the least non-negative integer $h$ such that $P$ has an inclusion representation for which every set has size at most $h$. In turn, the cube width of $P$ is the least non-negative integer $w$ for which there is an inclusion representation $\mathcal{S}$ of $P$ such tha…

Replaced article(s) found for cs.DC. https://arxiv.org/list/cs.DC/new
[1/1]:
- SGEMM-cube: Emulating FP32 GEMM on Ascend NPUs Using FP16 Cube Units with Precision Recovery
Weicheng Xue, Baisong Xu, Kai Yang, Yongxiang Liu, Dengdeng Fan, Pengxiang Xu, Yonghong Tian

Learning to Assemble the Soma Cube with Legal-Action Masked DQN and Safe ZYZ Regrasp on a Doosan M0609
Jaehong Oh, Seungjun Jung, Sawoong Kim
https://arxiv.org/abs/2508.21272 ht…

Learning to Assemble the Soma Cube with Legal-Action Masked DQN and Safe ZYZ Regrasp on a Doosan M0609
This paper presents the first comprehensive application of legal-action masked Deep Q-Networks with safe ZYZ regrasp strategies to an underactuated gripper-equipped 6-DOF collaborative robot for autonomous Soma cube assembly learning. Our approach represents the first systematic integration of constraint-aware reinforcement learning with singularity-safe motion planning on a Doosan M0609 collaborative robot. We address critical challenges in robotic manipulation: combinatorial action space expl…

The Application of Virtual Environments and Artificial Intelligence in Higher Education: Experimental Findings in Philosophy Teaching
Adel Vehrer, Zsolt Palfalusi
https://arxiv.org/abs/2509.00110

The Application of Virtual Environments and Artificial Intelligence in Higher Education: Experimental Findings in Philosophy Teaching
This study explores how virtual environments and artificial intelligence can enhance university students' learning experiences, with particular attention to the digital preferences of Generation Z. An experiment was conducted at the Faculty of Pedagogy, Humanities, and Social Sciences at University of Gyor, where Walter's Cube technology and a trained AI mediator were integrated into the instruction of ten philosophical topics. The curriculum was aligned with the official syllabus and enriched …

🇺🇦 #NowPlaying on KEXP's #Expansions
I:Cube:
🎵 Troglo Dance
#I:Cube
https://icube.bandcamp.com/track/troglo-dance
https://open.spotify.com/track/5oI27FYx7e585ZXA26Png4

Investigations of MWISP Clumps: 13CO Clump Source Catalog and Physical Properties
Yu Jiang, Qing-Zeng Yan, Ji Yang, Sheng Zheng, Xuepeng Chen, Yang Su, Zhibo Jiang, Zhiwei Chen, Xin Zhou, Yao Huang, Xiaoyu Luo, Haoran Feng, De-Jian Liu
https://arxiv.org/abs/2509.01955

Investigations of MWISP Clumps: 13CO Clump Source Catalog and Physical Properties
We present the first comprehensive catalogs of $^{13}$CO clumps from the Milky Way Imaging Scroll Painting (MWISP) project. By developing an equivalent global detection scheme integrated with the FacetClumps algorithm, we successfully extract 71,661 molecular clumps across a high-resolution $^{13}$CO data cube spanning 2310 deg$^2$ from the MWISP Phase I survey. To determine accurate distances, we design an automatic hierarchical distance decision method using signal regions as fundamental obje…

from my link log —
Rubik's cube perfect scramble.
https://www.solutionslookingforproblems.com/post/the-rubik-s-cube-perfect-scramble
saved 2025-08-02

The Rubik's Cube Perfect Scramble
The ChallengeI was playing with my son’s Rubik’s Cubes and tried to scramble a cube randomly so that no two squares with the same color were side by side. Here’s one way to do it: But I wanted a scramble that looked like a random scramble. No matter how many different moves I made, I couldn’t do it. Every time I separated two squares with the same color, two other squares of the same color would touch somewhere else.Looking for an easy answer, I went to puzzling.stackexchange.com and fo…

Ice Cube Sounds Off About the Raiders https://www.si.com/nfl/raiders/ice-cube-sounds-off-on-las-vegas-raiders-pete-carroll

Conditional Cube Attack on Round-Reduced ASCON
Zheng Li, Xiaoyang Dong, Xiaoyun Wang
https://arxiv.org/abs/2508.15172 https://arxiv.org/pdf/2508.15172

Conditional Cube Attack on Round-Reduced ASCON
This paper evaluates the secure level of authenticated encryption \textsc{Ascon} against cube-like method. \textsc{Ascon} submitted by Dobraunig \emph{et~al.} is one of 16 survivors of the 3rd round CAESAR competition. The cube-like method is first used by Dinur \emph{et~al.} to analyze Keccak keyed modes. At CT-RSA 2015, Dobraunig \emph{et~al.} applied this method to 5/6-round reduced \textsc{Ascon}, whose structure is similar to Keccak keyed modes. However, for \textsc{Ascon} the non-linear l…

On the wall-normal velocity variance in canonical wall-bounded turbulence
Michael Heisel, Rahul Deshpande, Gabriel G. Katul
https://arxiv.org/abs/2510.00363 https://

On the wall-normal velocity variance in canonical wall-bounded turbulence
The variance and spectra of wall-normal velocities are investigated for direct numerical simulations of turbulent flow in a channel, pipe, and zero-pressure-gradient (ZPG) boundary layer, across a decade of wall friction Reynolds numbers. Spectra along the spanwise wavenumber have a pronounced peak at intermediate wavenumbers that is proportional to the turbulent kinetic energy dissipation rate and the cube of the local shear stress throughout the bottom half of the boundary layer for all flow …

Quantitative improvements of functional inequalities under concavity properties
Andreas Malliaris, Francisco Mar\'in Sola
https://arxiv.org/abs/2510.00645 https://

Quantitative improvements of functional inequalities under concavity properties
A classical result of Hensley provides a sharp lower bound for the functional $\int_\mathbb{R} t^2f$, where $f$ is a non-negative, even log-concave function. In the context of studying the minimal slabs of the unit cube, Barthe and Koldobsky established a quantitative improvement of Hensley's bound. In this work, we complement their result in several directions. First, we prove the corresponding upper bound inequality for $s$-concave functions with $s\geq 0$. Second, we present a generalization…

Second order interlaced polynomial lattice rules for integration over $\mathbb{R}^s$
Tiangang Cui, Josef Dick, Friedrich Pillichshammer
https://arxiv.org/abs/2509.26624 https://…

Second order interlaced polynomial lattice rules for integration over $\mathbb{R}^s$
We study numerical integration of functions $f: \mathbb{R}^{s} \to \mathbb{R}$ with respect to a probability measure. By applying the corresponding inverse cumulative distribution function, the problem is transformed into integrating an induced function over the unit cube $(0,1)^{s}$. We introduce a new orthonormal system: \emph{order~2 localized Walsh functions}. These basis functions retain the approximation power of classical Walsh functions for twice-differentiable integrands while inheriti…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Ice Cube:
🎵 It Was A Good Day
#IceCube
https://drewdiamond.bandcamp.com/track/ice-cube-it-was-a-good-day
https://open.spotify.com/track/3dN0re4Ux685ZzJdBjM4Wq

Ice Cube Sounds Off About the Raiders https://www.si.com/nfl/raiders/ice-cube-sounds-off-on-las-vegas-raiders-pete-carroll

Fine Grain 3D Integration for Microarchitecture Design Through Cube Packing Exploration
Yongxiang Liu, Yuchun Ma, Eren Kurshan, Glenn Reinman, Jason Cong
https://arxiv.org/abs/2508.13158

Fine Grain 3D Integration for Microarchitecture Design Through Cube Packing Exploration
Most previous 3D IC research focused on stacking traditional 2D silicon layers, so the interconnect reduction is limited to inter-block delays. In this paper, we propose techniques that enable efficient exploration of the 3D design space where each logical block can span more than one silicon layers. Although further power and performance improvement is achievable through fine grain 3D integration, the necessary modeling and tool infrastructure has been mostly missing. We develop a cube packing…

Co-periods and central symmetric cube L-values
Cai Li, Fan Yangyu, She Dongming
https://arxiv.org/abs/2507.15279 https://arxiv.org/pd…

Co-periods and central symmetric cube L-values
In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the cent…

On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube
Rongshuan Geng, Wantao Ning
https://arxiv.org/abs/2508.07174 https://arxiv.org/pdf/…

On the fault diameter and wide diameter of the exchanged 3-ary $n$-cube
Fault diameter and wide diameter are two critical parameters for evaluating communication performance in interconnection networks. They measure the fault tolerance and transmission efficiency of networks. The exchanged 3-ary $n$-cube is a recently proposed variant of the hypercube, denoted by $E3C(r, s, t)$. In this work, we obtain that the $(2r + 1)$-fault diameter and $(2r + 2)$-wide diameter of $E3C(r, s, t)$ are bounded between $n + 3$ and $n + 5$ for $1 \leq r \leq s \leq t$.

H2SGEMM: Emulating FP32 GEMM on Ascend NPUs using FP16 Units with Precision Recovery and Cache-Aware Optimization
Weicheng Xue, Baisong Xu, Kai Yang, Yongxiang Liu, Dengdeng Fan, Pengxiang Xu, Yonghong Tian
https://arxiv.org/abs/2507.23387

H2SGEMM: Emulating FP32 GEMM on Ascend NPUs using FP16 Units with Precision Recovery and Cache-Aware Optimization
Low-precision matrix engines, such as FP16 cube, offer high throughput but lack support for full-precision computation. In this work, we propose H2SGEMM, a high-performance algorithm for emulating FP32 general matrix-matrix multiplication (GEMM) using only FP16 computation units on a representative AI accelerator. The method decomposes each FP32 operand into two FP16 values and compensates for numerical errors through a tunable scaling strategy. A detailed analysis of numerical errors, includin…

How not to scramble a Rubik's cube
Thomas Fernique
https://arxiv.org/abs/2509.12134 https://arxiv.org/pdf/2509.12134

How not to scramble a Rubik's cube
We model the scrambling of a Rubik's cube by a Markov chain and introduce a stopping time $T$ which is a quite natural candidate to be a strong uniform time. This may pave the way for estimating the number of moves required to scramble a cube. Unfortunately, we show that $T$ is not this is not strongly uniform.

A Generalisation of Sperner's Theorem Using Weighted Chains
Ya\"el Dillies, Matthew Johnson, Aleksandra Kowalska
https://arxiv.org/abs/2509.26493 https://

A Generalisation of Sperner's Theorem Using Weighted Chains
We find the (unique) largest subset of $\{0, 1, 2\}^n$ such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most $k$ coordinates. To do so, we decompose the cube into weighted chains. In Appendix B we present a new proof of Sperner's theorem we found while working on this problem.

Borel Polychromatic Number of Grids
Katalin Berlow, Edward Hou
https://arxiv.org/abs/2508.18559 https://arxiv.org/pdf/2508.18559

Borel Polychromatic Number of Grids
We study Borel polychromatic colorings of grid graphs arising from free Borel actions of $\mathbb{Z}^d$. A polychromatic coloring is one in which every unit $d$-dimensional cube sees all available colors. In the classical setting, every grid admits a $2^d$-polychromatic coloring, while in the Borel setting this fails. Our main result shows that every free $\mathbb{Z}^d$-action admits a Borel $(2^d-1)$-polychromatic coloring. This result is sharp: any action where the generators act ergodically …

#movies #criticism

🇺🇦 #NowPlaying on KEXP's #AfternoonShow
Ice Cube:
🎵 Ghetto Bird
#IceCube
https://mentalhygienemusic.bandcamp.com/album/ice-cube-ghetto-bird-kill-the-computer-dusbtep-remix-vip-version
https://open.spotify.com/track/6M3lqzrkzSKrBehkeAxTXc

Kann es sein das manjaro zur zeit nicht brauchbar ist ? Ich wollte manjaro kde installieren, kannst vergessen und der pc ist ein cube von tuxedo. Ich glaube werde das original von tuxedo nehmen

“This Is My Favorite Team”—Rap Icon Ice Cube on Raiders Fandom https://raiderramble.com/2025/07/17/this-is-my-favorite-team-rap-icon-ice-cube-on-raiders-fandom/

Sitting on the porch at the cabin. A solitary loon calls out across the lake.
"What are you doing!?"
"Huh?" <dips cheese cube in the spinach dip>
"That's for the Vegetables!"
"You're not the boss of me!" <holds dip tighter>
"The vegan can't have it anyway cause it's not plant based so.... Stay. In your lane, loon."

Mechanical Automation with Vision: A Design for Rubik's Cube Solver
Abhinav Chalise, Nimesh Gopal Pradhan, Nishan Khanal, Prashant Raj Bista, Dinesh Baniya Kshatri
https://arxiv.org/abs/2508.12469 …

Mechanical Automation with Vision: A Design for Rubik's Cube Solver
The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the development of a user-friendly graphical user interface (GUI) designed in Unity. The initial state after detection from real-time YOLOv8 model (Precision 0.98443, Recall 0.98419, Box Loss 0.42051, Class Loss 0.2611) is virtualized on GUI. To get the solution…

Cubical small-cancellation quotients of non-products
Macarena Arenas, Kasia Jankiewicz, Daniel T. Wise
https://arxiv.org/abs/2509.13447 https://arxiv.org/p…

Cubical small-cancellation quotients of non-products
We show that if $X$ is a compact nonpositively curved cube complex which is a non-product, then $π_1 X$ has a proper quotient that is $π_1$ of a cube complex with these same properties.

Not to be alarmist but the Power Mac G4 Cube is now a quarter of a century old

🇺🇦 #NowPlaying on #BBC6Music's #CraigCharles
Ice Cube:
🎵 It Was a Good Day
#IceCube
https://drewdiamond.bandcamp.com/track/ice-cube-it-was-a-good-day
https://open.spotify.com/track/2MuJbBWAVewREJmB8WdGJ3

The 21 Worst Things About the Worst Movie of the Year, ‘War of the Worlds’ https://flip.it/2eHWai
I don’t know — this kinda makes me want to see it…

The 21 Worst Things About the Worst Movie of the Year, ‘War of the Worlds’
Everyone involved should be embarrassed, including me for watching this

from my link log —
A polyhedron without Rupert’s property.
https://johncarlosbaez.wordpress.com/2025/08/28/a-polyhedron-without-ruperts-property/
saved 2025-08-28

Rupert’s Property
You can cut a hole in a cube that’s big enough to slide an identical cube through that hole! Think about that for a minute—it’s kind of weird. Amazingly, nobody could prove any co…

Crosslisted article(s) found for stat.CO. https://arxiv.org/list/stat.CO/new
[1/1]:
- Learning to Assemble the Soma Cube with Legal-Action Masked DQN and Safe ZYZ Regrasp on a Doosan ...
Jaehong Oh, Seungjun Jung, Sawoong Kim

🧑‍🤝‍🧑 Modular robots assemble into bridges, shelters and tools for outdoor tasks
#robots

Modular robots assemble into bridges, shelters and tools for outdoor tasks
Modular robots built by Dartmouth researchers are finding their feet outdoors. Engineered to assemble into structures that best suit the task at hand, the robots are pieced together from cube-shaped robotic blocks that combine rigid rods and soft, stretchy strings whose tension can be adjusted to deform the blocks and control their shape.

Fermion mass ratios from the exceptional Jordan algebra
Tejinder P. Singh
https://arxiv.org/abs/2508.10131 https://arxiv.org/pdf/2508.10131

Fermion mass ratios from the exceptional Jordan algebra
We revisit the "three generations" problem and the pattern of charged-fermion masses from the vantage of octonionic and Clifford algebra structures. Working with the exceptional Jordan algebra J3(OC) (right-handed flavor) and the symmetric cube of SU(3) (left-handed charge frame), we show that a single minimal ladder in the symmetric cube, together with the Dynkin Z2 swap (the A2 diagram flip), leads to closed-form expressions for the square-root mass ratios of all three charged families. The u…

You probably heard of mac and cheese. But have you tried crack and cheese? It comes in cube form.

Canonical Frames for Bracket Generating Rank 2 Distributions which are not Goursat
Nicklas Day, Igor Zelenko
https://arxiv.org/abs/2508.09307 https://arxiv…

Canonical Frames for Bracket Generating Rank 2 Distributions which are not Goursat
We complete a uniform construction of canonical absolute parallelism for bracket generating rank $2$ distributions with $5$-dimensional cube on $n$-dimensional manifold with $n\geq 5$ by showing that the condition of maximality of class that was assumed previously by Doubrov-Zelenko for such a construction holds automatically at generic points. This also gives analogous constructions in the case when the cube is not $5$-dimensional but the distribution is not Goursat through the procedure of it…

Spotted at the therapist.

I'm putting water out for the birds but they're ignoring it. I've used shallow bowls and an old ice cube tray and put them in various parts of the garden that I see the birds in most often. What am I doing wrong? I really want them to drink, bathe etc as they are undoubtedly suffering in these conditions.

There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Pranay Gorantla, Abhinav Prem, Nathanan Tantivasadakarn, Dominic J. Williamson
https://arxiv.org/abs/2509.19440

There and Back Again: A Gauging Nexus between Topological and Fracton Phases
Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases, the X-Cube model in 3+1D can be realized via such a construction by starting with a stack of 2+1D Toric Codes and turning on a coupling which condenses a composite "particle-string" object. In a recent work [arXiv:2505.13604], we have demonstrated that in fact,…

A perfect matching reciprocity method for embedding multiple hypercubes in an augmented cube: Applications to Hamiltonian decomposition and fault-tolerant Hamiltonicity
Da-Wei Yang, Hongyang Zhang, Rong-Xia Hao, Sun-Yuan Hsieh
https://arxiv.org/abs/2507.12834

A perfect matching reciprocity method for embedding multiple hypercubes in an augmented cube: Applications to Hamiltonian decomposition and fault-tolerant Hamiltonicity
This paper focuses on the embeddability of hypercubes in an important class of Cayley graphs, known as augmented cubes. An $n$-dimensional augmented cube $AQ_n$ is constructed by augmenting the $n$-dimensional hypercube $Q_n$ with additional edges, thus making $Q_n$ a spanning subgraph of $AQ_n$. Dong and Wang (2019) first posed the problem of determining the number of $Q_n$-isomorphic subgraphs in $AQ_n$, which still remains open. By exploiting the Cayley properties of $AQ_n$, we establish a l…

Input-Sensitive Reconfiguration of Sliding Cubes
Hugo Akitaya, Matias Korman, Frederick Stock
https://arxiv.org/abs/2507.04170 https://

Input-Sensitive Reconfiguration of Sliding Cubes
A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes …

Modeling Scintillation Photon Transport and Reconstruction Algorithms for the Time-of-Flight Detector in the T2K Neutrino Experiment
C. Alt, A. Blanchet, S. Bordoni, P. Collard, T. H. Bui, M. H. Bui, G. Ha, C. Jes\'us-Valls, V. S. Kasturi, A. Klustov\'a, A. Korzenev, T. A. Le, T. Lux, A. D. Nguyen, D. T. Nguyen, H. Nguyen, S. Samani, F. S\'anchez, M. Ta, T. Tha\'iduc, E. Villa

Modeling Scintillation Photon Transport and Reconstruction Algorithms for the Time-of-Flight Detector in the T2K Neutrino Experiment
The T2K ND280 upgrade aims to reduce the systematic uncertainty of the CP-violating phase, $δ_{CP}$, to reject non-CP violation hypothesis at $3σ$ confidence level. A crucial component of the ND280 upgrade, alongside the Super Fine Grained Detector (SuperFGD) and two High-Angle Time Projection Chambers (TPCs), is the Time-of-Flight (ToF) detector, which significantly enhances background rejection and particle identification capabilities. The ToF detector features six modules in a cube configu…

On certain root number $1$ cases of the cube sum problem
Shamik Das, Somnath Jha
https://arxiv.org/abs/2508.05361 https://arxiv.org/pdf/2508.05361

On certain root number $1$ cases of the cube sum problem
We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{-432n^2}: Y^2=X^3-432n^2$ is $1$ for every $n$, however a given $n$ may or may not be a sum of two rational cubes. We give explicit criteria in terms of the $2$-parts and $3$-parts of the ideal class groups of certain cubic number fields to determine whether such an $n$ is a cube sum. In particular, we study integers $n$ divisible by $3$ such that the …

Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
Daiki Kawabe
https://arxiv.org/abs/2507.13126 https://

Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
This note provides a detailed proof of Conner--Gesmundo--Landsberg--Ventura's result that the border rank of the Kronecker square of the little Coppersmith--Winograd tensor is $(q+2)^{2}$.We also indicate how the same ideas seem to extend to the case of the Kronecker cube, pointing toward the conjectural value $(q+2)^{m}$ for $m\ge 4$, although a full proof is left for future work.

Tonight's mission: boldly stream #STO from my #Linux powered PC! Prepare for warp speed, questionable tactical decisions, and probably me getting blown up by a Borg cube. Beam aboard the live stream! #StarTrekOnline

#ShamelesslyStolenFromTheOtherSite

Lipshitz--Sarkar stable homotopy type for certain planar trivalent graphs with perfect matchings
Nilangshu Bhattacharyya
https://arxiv.org/abs/2508.12272 https://

Lipshitz--Sarkar stable homotopy type for certain planar trivalent graphs with perfect matchings
We develop a space-level refinement of the $2$-factor homology by constructing a stable homotopy type associated to a certain family $\mathscr{G}$ of planar trivalent graphs equipped with perfect matchings. Specifically, we define a cover functor from the $2$-factor flow category $\mathscr{C}(Γ_{M})$ to the cube flow category $\mathscr{C}_{C}(n)$, where the perfect matching graph $Γ_{M}$ represents a planar trivalent graph $G$ together with a perfect matching $M$, such that $(G,M) \in \mathsc…

A notion of quasi-convex subgroups in acylindrically hyperbolic groups
Ping Wan
https://arxiv.org/abs/2509.20532 https://arxiv.org/pdf/2509.20532

A notion of quasi-convex subgroups in acylindrically hyperbolic groups
In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off cusped spaces. We also prove that this notion of quasiconvexity is preserved under sufficiently long Dehn filling. As an application, we generalize a theorem of Groves-Manning on groups acting on $\operatorname{CAT}(0)$ cube complexes.

from my link log —
Rupert's snub cube and other math holes.
http://tom7.org/ruperts/
saved 2025-09-16 https://dotat.at/:/AHLA1.html

President of Raider Nation Gives His Take on Upcoming Season https://www.si.com/nfl/raiders/las-vegas-ice-cube-pete-carroll-geno-smith-training-camp

Structured Task Solving via Modular Embodied Intelligence: A Case Study on Rubik's Cube
Chongshan Fan, Shenghai Yuan
https://arxiv.org/abs/2507.05607 h…

Structured Task Solving via Modular Embodied Intelligence: A Case Study on Rubik's Cube
This paper presents Auto-RubikAI, a modular autonomous planning framework that integrates a symbolic Knowledge Base (KB), a vision-language model (VLM), and a large language model (LLM) to solve structured manipulation tasks exemplified by Rubik's Cube restoration. Unlike traditional robot systems based on predefined scripts, or modern approaches relying on pretrained networks and large-scale demonstration data, Auto-RubikAI enables interpretable, multi-step task execution with minimal data req…

Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain
Mohab Safey El Din (PolSys), Georgy Scholten (LJLL), Emmanuel Tr\'elat (LJLL)
https://arxiv.org/abs/2507.13071

Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain
Let K be the unit-cube in Rn and f\,: K $\rightarrow$ R^n be a Morse function. We assume that the function f is given by an evaluation program $Γ$ in the noisy model, i.e., the evaluation program $Γ$ takes an extra parameter $η$ as input and returns an approximation that is $η$-close to the true value of f . In this article, we design an algorithm able to compute all local minimizers of f on K . Our algorithm takes as input $Γ$, $η$, a numerical accuracy parameter $ε$ as well as some ext…

Nontrivial Solutions to a Cubic Identity and the Factorization of $n^2 n 1$
Hajrudin Fejzi\'c
https://arxiv.org/abs/2508.14937 https://arxiv.org/pdf/25…

Nontrivial Solutions to a Cubic Identity and the Factorization of $n^2+n+1$
We investigate a variation of Nicomachus's identity in which one term in the cubic sum is replaced by a different cube. Specifically, we study the Diophantine identity \[ \sum_{j=1}^{n} j^3 + x^3 - k^3 = \left( \sum_{j=1}^{n} j + x - k \right)^2 \] and classify all integer solutions $(k,x,n)$. A full parametric family of nontrivial solutions was introduced in a 2005 paper, along with a conjectural condition for when such solutions exist. We provide a complete proof of this characterization and …

$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes
Michel Mollard (IF)
https://arxiv.org/abs/2507.16387 https://

$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes
The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive 1s. We study a one parameter generalization, p-th order Fibonacci cubes $Γ^{(p)}_n$, which are subgraphs of $Q_n$ induced by strings without p consecutive 1s. We show the link between vertices of $Γ^{(p)}_n$ and compositions of integers with parts in $\{1, 2, \ldots , p\}$. Among other eumerative properties, we study the order, size and cube polynomial of $Γ^{(p)}_n$ as well as their gene…

Crosslisted article(s) found for cs.ET. https://arxiv.org/list/cs.ET/new
[1/1]:
- Fine Grain 3D Integration for Microarchitecture Design Through Cube Packing Exploration
Yongxiang Liu, Yuchun Ma, Eren Kurshan, Glenn Reinman, Jason Cong

At #burningman this year, I brought a small 1200 lumen projector that I could mount on my bike. Would it be feasible to do some quick on the fly projection mapping? It seems that yes, for somewhat small (about 6m x 3m max for reasonable brightness) and not very bright pieces, it works.
I may experiment with this more in the future.

The inverse of the star discrepancy of a union of randomly digitally shifted Korobov polynomial lattice point sets depends polynomially on the dimension
Josef Dick, Friedrich Pillichshammer
https://arxiv.org/abs/2509.15877

The inverse of the star discrepancy of a union of randomly digitally shifted Korobov polynomial lattice point sets depends polynomially on the dimension
The star discrepancy is a quantitative measure of the uniformity of a point set in the unit cube. A central quantity of interest is the inverse of the star discrepancy, $N(\varepsilon, s)$, defined as the minimum number of points required to achieve a star discrepancy of at most~$\varepsilon$ in dimension~$s$. It is known that $N(\varepsilon, s)$ depends only linearly on the dimension~$s$. All known proofs of this result are non-constructive. Finding explicit point set constructions that achiev…

Galois' Professor's Revenge
M. Damele, A. Loi, M. Mereb, L. Vendramin
https://arxiv.org/abs/2509.09662 https://arxiv.org/pdf/2509.09662

Galois' Professor's Revenge
We prove that the groups associated with the Revenge Cube and the Professor's Cube can be realized as Galois groups over the rationals.

🇺🇦 #NowPlaying on KEXP's #AfternoonShow
Ice Cube:
🎵 Friday
#IceCube
https://djtramaine713.com/track/ice-cube-friday-chopped-slowed
https://open.spotify.com/track/13AvIMuWOBUWGBhWGIHb6N

A Near-Optimal Polynomial Distance Lemma Over Boolean Slices
Prashanth Amireddy, Amik Raj Behera, Srikanth Srinivasan, Madhu Sudan
https://arxiv.org/abs/2507.03193

A Near-Optimal Polynomial Distance Lemma Over Boolean Slices
The celebrated Ore-DeMillo-Lipton-Schwartz-Zippel (ODLSZ) lemma asserts that n-variate non-zero polynomial functions of degree d over a field $\mathbb{F}$ are non-zero over any "grid" $S^n$ for finite subset $S \subseteq \mathbb{F}$, with probability at least $\max\{|S|^{-d/(|S|-1)},1-d/|S|\}$ over the choice of random point from the grid. In particular, over the Boolean cube ($S = \{0,1\} \subseteq \mathbb{F}$), the lemma asserts non-zero polynomials are non-zero …

learn 👇

A Crystallographic Metric for Continuous Quantification of Unit Cell Deformation
Shannon Bernier, Gregory Bassen, Matthew Brem, Davor Tolj, Quentin Simmons, Tyrel M. McQueen
https://arxiv.org/abs/2508.01177

A Crystallographic Metric for Continuous Quantification of Unit Cell Deformation
Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit cell distortion relative to a cube, called the cubic deviation metric. This enables continuous comparisons between unit cells of different geometries. We demonstrate the potential of this tool with four separate case study applications to real material system…

Counting sums of two powers
Anand Patel
https://arxiv.org/abs/2507.08337 https://arxiv.org/pdf/2507.08337

Counting sums of two powers
We generalize two well-known enumerative facts. The first, due to Clebsch, says that a general binary sextic form is expressible as the sum of a cube and a square in 40 different ways. The second, due to Zariski and later Vakil, states that a general pencil of binary 12-ics contains exactly 3762 cubes plus squares, ignoring scaling.

An ${\mathfrak S}_3$-cover of $K_4$ and integral polyhedral graphs
Taizo Sadahiro
https://arxiv.org/abs/2508.18593 https://arxiv.org/pdf/2508.18593

An ${\mathfrak S}_3$-cover of $K_4$ and integral polyhedral graphs
We show that the star graph defined as the Cayley graph of Sn+1 generated by the star transpositions is an Sn -cover of the complete graph Kn+1 , which is known to have fine spectral properties. In the case n = 3, the star graph also has fine geometric properties: it em- beds into the honeycomb lattice and has a spectrum computable via both representation theory and an explicit Fourier formula. Inter- mediate covers correspond to the cube and truncated tetrahedron, offering a new interpretation…

Search for Z/2 eigenfunctions on the sphere using machine learning
Andriy Haydys, Willem Adriaan Salm
https://arxiv.org/abs/2507.13122 https://

Search for Z/2 eigenfunctions on the sphere using machine learning
We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we implemented it using the JAX library. We found Z/2 eigenfunctions for three cases: In the first two cases we fixed the branch points at the vertices of a tetrahedron and at a cube respectively. In a third case, we allowed the AI to move the branch points around and, in the end, it positioned the branch points at the vertices…

Electromagnetic energy calibration of the SoLid detector with horizontal muons
SoLid collaboration
https://arxiv.org/abs/2507.05180 https://

Electromagnetic energy calibration of the SoLid detector with horizontal muons
SoLid is a neutrino experiment at very-short baseline searching for active-to-sterile oscillations of reactor antineutrinos. The detection principle is based on the pairing of two types of solid scintillators: polyvinyl toluene and $^6$Li:ZnS(Ag), which is a new technology used in this field of Physics. In addition to good neutron-gamma discrimination, this setup allows the detector to be highly segmented; the basic detection unit is a 5 cm cube. High segmentation provides numerous advantages i…

🇺🇦 #NowPlaying on #BBC6Music's #TheMorningAfterMix
Ice Cube:
🎵 It Was a Good Day
#IceCube
https://drewdiamond.bandcamp.com/track/ice-cube-it-was-a-good-day
https://open.spotify.com/track/2GrOq1y5gksYrqkc8Jzl9T

The structure of the double discriminant
Theresa C. Anderson, Adam Bertelli, Evan M. O'Dorney
https://arxiv.org/abs/2507.16138 https://

The structure of the double discriminant
For a polynomial $f(x) = \sum_{i=0}^n a_i x^i$, we study the double discriminant $DD_{n,k} = \operatorname{disc}_{a_k} \operatorname{disc}_x f(x)$, which appears in the proof of the van der Waerden--Bhargava theorem. We conjecture that $DD_{n,k}$ is the product of a square, a cube, and possibly a linear monomial and we prove this when $k=0$. We also investigate the (typically large and smooth) outlying integer constant in the factorization of $DD_{n,k}$.

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes
Hajime Tanaka, Norihide Tokushige
https://arxiv.org/abs/2508.17559 https://

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes
We give lower and upper bounds on the burning number of Hamming graphs, Johnson graphs, and halved cube graphs. For the lower bounds, we use the fact that $1$-skeletons of the eigenpolytopes of these graphs are isomorphic to the original graphs. Then, we present a dynamic search algorithm performed on the eigenpolytope to find an unburned vertex. This idea was originally used by Alon (Discrete Appl.\ Math.,\ 1992), who determined the burning number of the hypercube graphs.

If anyone in the #Seattle area wants to get into #chinafake #collecting or is generally just into #vintage

If anyone in the #Seattle area wants to get into #chinafake #collecting or is generally just into #vintage

🇺🇦 #NowPlaying on #BBC6Music's #LaurenLaverne
Ice Cube:
🎵 It Was a Good Day
#IceCube
https://drewdiamond.bandcamp.com/track/ice-cube-it-was-a-good-day
https://open.spotify.com/track/2GrOq1y5gksYrqkc8Jzl9T

Extending edge colorings of distance-2 matchings in the hypercube
P\'al B\"arnkopf
https://arxiv.org/abs/2509.15764 https://arxiv.org/pdf/2509.157…

Extending edge colorings of distance-2 matchings in the hypercube
Casselgren, Markstörm, and Pham conjectured that any precolored distance-2 matching in the $d$-dimensional cube $Q_d$ can be extended to a proper $d$-edge coloring. In this paper, we prove this conjecture and some related theorems. Especially, our result establishes that if $G$ is a bipartite graph, then a precolored distance-2 matching in the Cartesian product $G \square K_{2m}$ can be extended to an edge coloring using at most $Δ(G)+1$ colors. As another generalization, we establish the sam…

Hyperfiniteness of the boundary action of virtually special groups
Koichi Oyakawa
https://arxiv.org/abs/2509.04613 https://arxiv.org/pdf/2509.04613

Hyperfiniteness of the boundary action of virtually special groups
We prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite. This can be considered as a generalization of hyperfiniteness of the boundary action of cubulated hyperbolic groups by Huang-Sabok-Shinko.

On the optimization of discrepancy measures
Fran\c{c}ois Cl\'ement, Nathan Kirk, Art B. Owen, T. Konstantin Rusch
https://arxiv.org/abs/2508.04926 https://

On the optimization of discrepancy measures
Points in the unit cube with low discrepancy can be constructed using algebra or, more recently, by direct computational optimization of a criterion. The usual $L_\infty$ star discrepancy is a poor criterion for this because it is computationally expensive and lacks differentiability. Its usual replacement, the $L_2$ star discrepancy, is smooth but exhibits other pathologies shown by J. Matoušek. In an attempt to address these problems, we introduce the \textit{average squared discrepancy} whi…

🇺🇦 #NowPlaying on #BBC6Music's #LaurenLaverne
Ice Cube:
🎵 It Was a Good Day
#IceCube
https://drewdiamond.bandcamp.com/track/ice-cube-it-was-a-good-day
https://open.spotify.com/track/2GrOq1y5gksYrqkc8Jzl9T

On the cubic Shimura lift to $PGL(3)$: Hecke correspondences
Solomon Friedberg, Omer Offen
https://arxiv.org/abs/2507.06963 https://a…

On the cubic Shimura lift to $PGL(3)$: Hecke correspondences
In this paper we establish a new Fundamental Lemma for Hecke correspondences. Let $F$ be a local field containing the cube roots of unity. We exhibit an algebra isomorphism of the spherical Hecke algebra of $PGL_3(F)$ and the spherical Hecke algebra of anti-genuine functions on the cubic cover $G'$ of $SL_3(F)$. Then we show that there is a matching (up to a specific transfer factor) of distributions on the two groups for all functions that correspond under this isomorphism. On $PGL_3(F)$ the d…

Maximal sets of a given diameter in Hamming cubes
Boris Bukh, Aleksandre Saatashvili
https://arxiv.org/abs/2507.10828 https://arxiv.o…

Maximal sets of a given diameter in Hamming cubes
A subset of the Hamming cube over $n$-letter alphabet is said to be $d$-maximal if its diameter is $d$, and adding any point increases the diameter. Our main result shows that each $d$-maximal set is either of size at most $(n+o(n))^d$ or contains a non-trivial Hamming ball. The bound of $(n+o(n))^d$ is asymptotically tight. Additionally, we give a non-trivial lower bound on the size of any $d$-maximal set and show that the number of essentially different $d$-maximal sets is finite.

🇺🇦 #NowPlaying on #BBC6Music's #6MusicsRaveForever
Joey Beltram:
🎵 Flash Cube
#JoeyBeltram
https://traxrecords.bandcamp.com/track/flash-cube-joey-beltram
https://open.spotify.com/track/7zjgokzU4TBrxJSNhYak6H

🇺🇦 #NowPlaying on #BBC6Music's #6MusicsRaveForever
Rubini:
🎵 Easyleft Henri (Original Mix)
#Rubini
https://degustibus.bandcamp.com/track/easyleft-henri-i-cube-remix
https://open.spotify.com/track/13LhiMD5rpN9ujTh24p7b3

🇺🇦 #NowPlaying on #BBC6Music's #LaurenLaverne
Yo‐Yo:
🎵 You Can't Play with My Yo-Yo (feat. Ice Cube)
#YoYo