Tootfinder

An interview with Phil Spencer on bringing Xbox to handhelds via hardware or software, how Valve, Lenovo, and Asus "innovated in a new form factor", and more (Chris Plante/Polygon)
https://www.polygon.com/24108660/xbox-handheld-console-phil-…

A handheld Xbox is the dream, says Microsoft gaming chief Phil Spencer
Phil Spencer, the CEO of Microsoft Gaming, shared his thoughts on a handheld Xbox console in this interview with Polygon during the 2024 Game Developers Conference.

Mist, ich habe Fang getroffen und ihre Bewerbung nicht angenommen - ich dachte, sie wäre überqualifiziert. Verdammt 🥹
Aber das ist ziemlich genau das, was bei Dragon‘s Dogma Spaß macht - das und REISEN und dabei Sachen entdecken.
Toller, herziger Artikel von Chris Plante.
https://www.

🚩🚩🚩
Fintech giant Stripe announced on Thursday that it would let customers accept cryptocurrency payments, starting with USDC stablecoins, initially only on Solana, Ethereum and Polygon.
https://techcrunch.com/2024/04/25/afte

After 6-year hiatus, Stripe to start taking crypto payments, starting with USDC stablecoin | TechCrunch
The company announced that it would start to let customers accept cryptocurrency payments, starting with USDC stablecoins, initially only on Solana, Ethereum and Polygon

🕶️ The Meta Quest 2 and its accessories are cheaper than ever
#technology

The Meta Quest 2 and its accessories are cheaper than ever
The Quest 2 VR headset is more inviting than ever with a price drop to $199.99 at Amazon, Walmart, and Best Buy. Even its accessories are discounted.

Google updates Search to start showing crypto wallet balances across bitcoin and the EVM networks Arbitrum, Avalanche, Fantom, Optimism, and Polygon (Abner Li/9to5Google)
https://9to5google.com/2024/03/28/google-bitcoin-balance/

Google now indexing Bitcoin’s blockchain to show wallet balances
Google Search is home to various tools and the latest lets you look up Bitcoin addresses to show the balance of any wallet...

Maximum Polygon Packing: The CG:SHOP Challenge 2024
S\'andor P. Fekete, Phillip Keldenich, Dominik Krupke, Stefan Schirra
https://arxiv.org/abs/2403.16203

Maximum Polygon Packing: The CG:SHOP Challenge 2024
We give an overview of the 2024 Computational Geometry Challenge targeting the problem \textsc{Maximum Polygon Packing}: Given a convex region $P$ in the plane, and a collection of simple polygons $Q_1, \ldots, Q_n$, each $Q_i$ with a respective value $c_i$, find a subset $S \subseteq \{1, \ldots,n\}$ and a feasible packing within $P$ of the polygons $Q_i$ (without rotation) for $i \in S$, maximizing $\sum_{i \in S} c_i$. Geometric packing problems, such as this, present significant computation…

This https://arxiv.org/abs/1706.08152 has been replaced.
link: https://scholar.google.com/scholar?q=a

An algorithm to find maximum area polygons circumscribed about a convex polygon
A convex polygon Q is circumscribed about a convex polygon P if every vertex of P lies on at least one side of Q. We present an algorithm for finding a maximum area convex polygon circumscribed about any given convex n-gon in O(n^3) time. As an application, we disprove a conjecture of Farris. Moreover, for the special case of regular n-gons we find an explicit solution.

Discord wants to void your right to sue them, but you can opt out.
https://www.polygon.com/2024/4/20/24134970/discord-arbitration-how-to-opt-out
Or you can just delete your account which is what I did.
"We have received a (dare we say, terrifying) request to permanently delete your account. Your account has
been deactivated and will be permanently deleted after 14 days.
Just in case you change your mind (or were a bit too curious with pushing buttons), or did not request to
permanently delete your account, please login to Discord to cancel this request."
Fuck 'em.

Stripe will let customers accept crypto payments, starting with USDC on Solana, Ethereum, and Polygon, the first time it has taken crypto payments since 2018 (Ingrid Lunden/TechCrunch)
https://techcrunch.com/2024/04/25/afte

After 6-year hiatus, Stripe to start taking crypto payments, starting with USDC stablecoin | TechCrunch
The company announced that it would start to let customers accept cryptocurrency payments, starting with USDC stablecoins, initially only on Solana, Ethereum and Polygon

How MrBeast dominates this ostentatious YouTube era, using a fast, frantic, and omnipresent editing style, as his videos slowly evolve to focus on storytelling (Patricia Hernandez/Polygon)
https://www.polygon.com/24093399/end-of-mrbeast-youtube-era

MrBeast may never quit YouTube, but his game is changing
Jimmy Donaldson warped YouTube with viral giveaway videos. While Jacksepticeye claims it hurt creators, YouTube Shorts is now challenging MrBeast’s success.

Deviations for generalized tiling billiards in cyclic polygons
Magali Jay
https://arxiv.org/abs/2402.15765 https://arxiv.org/pdf/2402…

Deviations for generalized tiling billiards in cyclic polygons
This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asympto…

Stripe will let customers accept crypto payments, starting with USDC on Solana, Ethereum, and Polygon, the first time it has taken crypto payments since 2018 (Ingrid Lunden/TechCrunch)
https://techcrunch.com/2024/04/25/afte

After 6-year hiatus, Stripe to start taking crypto payments, starting with USDC stablecoin | TechCrunch
The company announced that it would start to let customers accept cryptocurrency payments, starting with USDC stablecoins, initially only on Solana, Ethereum and Polygon

I'm pleased with myself. I'm trying to fake animation in Beamer slides using overlays. Fiddly, 1 line per each of multiple images. In org-mode.
But I've discovered org-mode macros, which can handle arbitrary emacs-lisp, so I can do it with one macro and a single invocation (with the number of images as a parameter).
Layering 3-ish languages (org-mode, e-lisp, Beamer-latex) isn't ideal, but it works. I just put
{{{oxeast 14}}}
in my org file and get t…

🥊 The end of the MrBeast era
#youtube

MrBeast may never quit YouTube, but his game is changing
Jimmy Donaldson warped YouTube with viral giveaway videos. While Jacksepticeye claims it hurt creators, YouTube Shorts is now challenging MrBeast’s success.

This https://arxiv.org/abs/2402.13197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Polygonal surfaces in pseudo-hyperbolic spaces
A polygonal surface in the pseudo-hyperbolic space H 2,n is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein 1,n with finitely many vertices. In this article, we give several characterizations of them. Polygonal surfaces are characterized by finiteness of their total curvature, by asymptotic flatness, and also by the fact of having parabolic type and polynomial quartic differential. Our result relies on a comparison between three ideal boundaries associated…

Avail, a modular blockchain project spun out of Polygon in 2023 to streamline the rollup experience, raised a $27M seed co-led by Founders Fund and Dragonfly (Yogita Khatri/The Block)
https://www.theblock.co/post/279095/peter-thiel-founders-fund-avail-f…

This https://arxiv.org/abs/1804.05105 has been replaced.
link: https://scholar.google.com/scholar?q=a

Recognizing Visibility Graphs of Polygons with Holes and Internal-External Visibility Graphs of Polygons
Visibility graph of a polygon corresponds to its internal diagonals and boundary edges. For each vertex on the boundary of the polygon, we have a vertex in this graph and if two vertices of the polygon see each other there is an edge between their corresponding vertices in the graph. Two vertices of a polygon see each other if and only if their connecting line segment completely lies inside the polygon, and they are externally visible if and only if this line segment completely lies outside the…

🥊 The end of the MrBeast era
#youtube

MrBeast may never quit YouTube, but his game is changing
Jimmy Donaldson warped YouTube with viral giveaway videos. While Jacksepticeye claims it hurt creators, YouTube Shorts is now challenging MrBeast’s success.

“After conducting interviews with over 60 players for this article, it’s clear that the propaganda of Helldivers 2 inherently encourages people to band together. But some are acting in bad faith, spinning the clear satire into an overly serious military role-play — one that extends beyond acts like consecrating someone as public enemy number one.”

A month in, Helldivers 2 is tangled in bigotry and witch hunting
Helldivers 2’s theme of fighting a war together is, for better or worse, resounding in the community beyond the game itself.

Optimal Reeb graphs on two- and three-connected planar polygon
Oleksandr Pryshliak, Karolina Haieva
https://arxiv.org/abs/2404.07193 https://

Optimal Reeb graphs on two- and three-connected planar polygon
To investigate the topological structure of planar polygon decomposition on trapezoids, which is formed by height functions. We use the oriented Reeb graph of the function with a marked vertex. We describe all possible optimal Reeb graphs in the case of polygon in general position with one local minimum and one local maximum. By optimal Reeb graph we mean Reeb graph, which cann't be obtaned from other Reeb graph by subdivision of an edge or a leaf attaching. In this case polygon is a triangle w…

⛐ GTA Online’s community is in limbo while hype builds for GTA 6
#games

GTA Online’s community is in limbo while hype builds for GTA 6
Grand Theft Auto Online started as a part of GTA 5 and has become a wildly successful beast in its own right, but fans aren’t sure what the arrival of GTA 6 means for their hobby.

GPolylla: Fully GPU-accelerated polygonal mesh generator
Sergio Salinas-Fern\'andez, Nancy Hitschfeld-Kahler, Roberto Carrasco
https://arxiv.org/abs/2403.14723

GPolylla: Fully GPU-accelerated polygonal mesh generator
This work presents a fully GPU-accelerated algorithm for the polygonal mesh generator known as Polylla. Polylla is a tri-to-polygon mesh generator, which benefits from the half-edge data structure to manage any polygonal shape. The proposed parallel algorithm introduces a novel approach to modify triangulations to get polygonal meshes using the half-edge data structure in parallel on the GPU. By changing the adjacency values of each half-edge, the algorithm accomplish to unlink half-edges that …

lol. lmao https://techhub.social/@Techmeme/112102620968049364

WB media doing some bs again. At this point, I wonder if this would be enough for an animators union or writers union, hell even the actors union, to sue its CEO for defrauding shareholders. Y'know, since only shareholders matter in this late-stage capitalist dystopia
https://www.

Warner Bros. to delist Adult Swim-published games from Steam
Warner Bros. Discovery is telling indie devs it’s “retiring” games published by its Adult Swim Games label, game makers who worked with the publisher tell Polygon.

Symmetric Power L-functions of the hyper-Kloosterman Family
C. Douglas Haessig, Steven Sperber
https://arxiv.org/abs/2402.13051 https://

Symmetric Power L-functions of the hyper-Kloosterman Family
The symmetric power L-function of the hyper-Kloosterman family is a rational function over the integers. Its degree and complex absolute values of its zeros and poles are now known through the work of Fu and Wan. The purpose of this paper is to study the p-adic absolute value of these zeros and poles. In particular, we give a uniform lower bound, independent of the symmetric power, of the q-adic Newton polygon of this $L$-function under suitable conditions. We also give similar results for any …

⛐ GTA Online’s community is in limbo while hype builds for GTA 6
#games

GTA Online’s community is in limbo while hype builds for GTA 6
Grand Theft Auto Online started as a part of GTA 5 and has become a wildly successful beast in its own right, but fans aren’t sure what the arrival of GTA 6 means for their hobby.

Bicolored point sets admitting non-crossing alternating Hamiltonian paths
Jan Soukup
https://arxiv.org/abs/2404.06105 https://arxiv.o…

Bicolored point sets admitting non-crossing alternating Hamiltonian paths
Consider a bicolored point set $P$ in general position in the plane consisting of $n$ blue and $n$ red points. We show that if a subset of the red points forms the vertices of a convex polygon separating the blue points, lying inside the polygon, from the remaining red points, lying outside the polygon, then the points of $P$ can be connected by non-crossing straight-line segments so that the resulting graph is a properly colored closed Hamiltonian path.

How MrBeast dominates this ostentatious YouTube era, using a fast, frantic, and omnipresent editing style, as his videos slowly evolve to focus on storytelling (Patricia Hernandez/Polygon)
https://www.polygon.com/24093399/end-of-mrbeast-youtube-era

MrBeast may never quit YouTube, but his game is changing
Jimmy Donaldson warped YouTube with viral giveaway videos. While Jacksepticeye claims it hurt creators, YouTube Shorts is now challenging MrBeast’s success.

Just debugged a polygon screwup where I'd passed (tlx,tly, width, height) where the box creator actually took two points rather than point size. Blech!

Convex Polygon Containment: Improving Quadratic to Near Linear Time
Timothy M. Chan, Isaac M. Hair
https://arxiv.org/abs/2403.13292 https://

Convex Polygon Containment: Improving Quadratic to Near Linear Time
We revisit a standard polygon containment problem: given a convex $k$-gon $P$ and a convex $n$-gon $Q$ in the plane, find a placement of $P$ inside $Q$ under translation and rotation (if it exists), or more generally, find the largest copy of $P$ inside $Q$ under translation, rotation, and scaling. Previous algorithms by Chazelle (1983), Sharir and Toledo (1994), and Agarwal, Amenta, and Sharir (1998) all required $Ω(n^2)$ time, even in the simplest $k=3$ case. We present a significantly fas…

Robot Navigation in Unknown and Cluttered Workspace with Dynamical System Modulation in Starshaped Roadmap
Kai Chen, Haichao Liu, Yulin Li, Jianghua Duan, Lei Zhu, Jun Ma
https://arxiv.org/abs/2403.11484

Robot Navigation in Unknown and Cluttered Workspace with Dynamical System Modulation in Starshaped Roadmap
This paper presents a novel reactive motion planning framework for navigating robots in unknown and cluttered 2D workspace. Typical existing methods are developed by enforcing the robot staying in free regions represented by the locally extracted ellipse or polygon. Instead, we navigate the robot in free space with an alternate starshaped decomposition, which is calculated directly from real-time sensor data. Additionally, a roadmap is constructed incrementally to maintain the connectivity info…

This https://arxiv.org/abs/2306.17742 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Blockchain scaling and liquidity concentration on decentralized exchanges
Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from adverse selection risk by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liquidity concentration around the market price, using the entry of blockchain scaling solutions, Arbitrum and Polygon, as our instruments. Lower gas fees on scaling solutions allow LPs to update more f…

🕹️ Overwatch 2 Season 10 shakes up the game a ton this week
https://www.polygon.com/overwatch-2-guide/24128435/season-10-start-time-release-date-battle-pass

When does Overwatch 2 season 10 start, and what’s included?
Overwatch 2 season 10 starts mid-April and adds new hero Venture, new game mode Clash, new map Hanaoka, and more. Here’s when you can start playing OW2 season 10.

@… @… Nochmal eine Beståtigung von anderer Stelle:

New #MechanicalKeyboard day! It's a #Kiser Monorail 45% #keyboard which I recently bought from @…

PitchBook: in 2021, 223 male-founded video game startups raised $4.1B, five women-founded startups raised $1.2M, and 62 mixed-gender startups raised $400.9M (Nicole Carpenter/Polygon)
https://www.polygon.com/24058266/video-game-industry-funding-gap

The video game funding gap: How investors are failing marginalized developers
‘There is a massive disparity on how funding is allocated in the industry,’ according to industry experts. Companies led by marginalized leaders get way, way less funding.

Strong collapsibility of the arc complexes of orientable and non-orientable crowns
Pallavi Panda
https://arxiv.org/abs/2402.10530 https://

Strong collapsibility of the arc complexes of orientable and non-orientable crowns
We prove that the arc complex of a polygon with a marked point in its interior is a strongly collapsible combinatorial ball. We also show that the arc complex of a Möbius strip, with finitely many marked points on its boundary, is a simplicially collapsible combinatorial ball but is not strongly collapsible.

Cyclic Polygon Plots
Maksim Schreck, Peter Albers, Filip Sadlo
https://arxiv.org/abs/2403.05296 https://arxiv.org/pdf/2403.05296

Cyclic Polygon Plots
In this paper, we introduce the cyclic polygon plot, a representation based on a novel projection concept for multi-dimensional values. Cyclic polygon plots combine the typically competing requirements of quantitativeness, image-space efficiency, and readability. Our approach is complemented with a placement strategy based on its intrinsic features, resulting in a dimensionality reduction strategy that is consistent with our overall concept. As a result, our approach combines advantages from di…

Starbucks is shutting Odyssey, which launched in December 2022 in closed beta offering NFT-based rewards minted on the Polygon blockchain, on March 31, 2024 (Andrew Hayward/Decrypt)
https://decrypt.co/221967/starbucks-shutting-down-odyssey-nft-rewards…

Starbucks Is Shutting Down Its Odyssey NFT Rewards Program—Will It Return?
Starbucks Odyssey is shutting down this month, and it's unclear whether the Polygon-based NFT rewards program will be revived.

This https://arxiv.org/abs/2404.09835 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto, Inf. Process. Lett., 1981], but the version without holes was conjectured to be polynomial-time solvable more than two decades ago~[Baur and Fekete, Algorithmica, 2001]. Our reduction reli…

Flip graphs of coloured triangulations of convex polygons
Karin Baur, Diana Bergerova, Jenni Voon, Lejie Xu
https://arxiv.org/abs/2402.06546 https://

Flip graphs of coloured triangulations of convex polygons
A triangulation of a polygon is a subdivision of it into triangles, using diagonals between its vertices. Two different triangulations of a polygon can be related by a sequence of flips: a flip replaces a diagonal by the unique other diagonal in the quadrilateral it defines. In this paper, we study coloured triangulations and coloured flips. In this more general situation, it is no longer true that any two triangulations can be linked by a sequence of (coloured) flips. In this paper, we study t…

Robot Navigation in Unknown and Cluttered Workspace with Dynamical System Modulation in Starshaped Roadmap
Kai Chen, Haichao Liu, Yulin Li, Jianghua Duan, Lei Zhu, Jun Ma
https://arxiv.org/abs/2403.11484

Robot Navigation in Unknown and Cluttered Workspace with Dynamical System Modulation in Starshaped Roadmap
This paper presents a novel reactive motion planning framework for navigating robots in unknown and cluttered 2D workspace. Typical existing methods are developed by enforcing the robot staying in free regions represented by the locally extracted ellipse or polygon. Instead, we navigate the robot in free space with an alternate starshaped decomposition, which is calculated directly from real-time sensor data. Additionally, a roadmap is constructed incrementally to maintain the connectivity info…

Hecke-Farey coordinates for Bring's curve that gives Bring's surface
Doha Kattan, David Singerman
https://arxiv.org/abs/2402.08782 https://<…

Hecke-Farey coordinates for Bring's curve that gives Bring's surface
The modular group $Γ$ (which is the Hecke group $H_3$) can be used to study triangular maps. Here we use the Hecke group $H_4$ to study the regular map that underlies Bring's surface of genus 4. Our main result is the determination of the 20-sided hyperbolic polygon that gives Bring's surface.

A note on Seshadri constants, Gromov widths of toric surfaces and lattice widths of polygons
Atsushi Ito
https://arxiv.org/abs/2404.06026 https://

A note on Seshadri constants, Gromov widths of toric surfaces and lattice widths of polygons
In this note, we study Seshadri constants and Gromov widths of toric surfaces via lattice widths of their moment polygons. We give the sharp lower bound of the ratio between the Gromov width of a symplectic toric $4$-fold and the lattice width of the moment polygon, which answers to a question raised by Codenotti, Hall and Hofscheier.

Polygonal surfaces in pseudo-hyperbolic spaces
Alex Moriani
https://arxiv.org/abs/2402.13197 https://arxiv.org/pdf/2402.13197<…

Polygonal surfaces in pseudo-hyperbolic spaces
A polygonal surface in the pseudo-hyperbolic space H 2,n is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein 1,n with finitely many vertices. In this article, we give several characterizations of them. Polygonal surfaces are characterized by finiteness of their total curvature, by asymptotic flatness, and also by the fact of having parabolic type and polynomial quartic differential. Our result relies on a comparison between three ideal boundaries associated…

This https://arxiv.org/abs/2312.13778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Progressive Evolution from Single-Point to Polygon for Scene Text
The advancement of text shape representations towards compactness has enhanced text detection and spotting performance, but at a high annotation cost. Current models use single-point annotations to reduce costs, yet they lack sufficient localization information for downstream applications. To overcome this limitation, we introduce Point2Polygon, which can efficiently transform single-points into compact polygons. Our method uses a coarse-to-fine process, starting with creating and selecting anc…

Linear Programs Where Every Shadow Simplex Path is Exponentially Long
Alexander E. Black
https://arxiv.org/abs/2403.04886 https://arx…

Linear Programs Where Every Shadow Simplex Path is Exponentially Long
It remains open whether there is a version of the simplex method guaranteed to run in strongly polynomial time. One variant, the shadow simplex method, has been shown to have strongly polynomial expected run-time both for random linear programs and in the smoothed analysis model. The shadow simplex method solves a linear program by implicitly projecting the feasible region onto a two dimensional polygon. The choice of projection is not canonical, so for each method of choosing a projection one …

This https://arxiv.org/abs/2402.01257 has been replaced.
link: https://scholar.google.com/scholar?q=a

Polygonal corona limit on multigrid dual tilings
The growth pattern of an invasive cell-to-cell propagation (called the successive coronas) on the square grid is a tilted square. On the triangular and hexagonal grids, it is an hexagon. It is remarkable that, on the aperiodic structure of Penrose tilings, this cell-to-cell diffusion process tends to a regular decagon (at the limit). In this article we generalize this result to any regular multigrid dual tiling, by defining the characteristic polygon of a multigrid and its dual tiling. Exploiti…

Fixed points of generalized contractions on O-metric spaces
Hallowed O. Olaoluwa, Aminat O. Ige, Johnson O. Olaleru
https://arxiv.org/abs/2403.09655 https:…

Fixed points of generalized contractions on O-metric spaces
The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and establish in the setting, fixed point theorems of contractions and generalized contractions. The proofs of the theorems rely heavily on polygon O-inequalities which are a natural generalization of the triangle inequality, and the construction of which leads to the…

📉 Riot is cutting off its most inviting entry point to League lore
(… nice game you’ve got there, sorry it’s so toxic.)
https://www.polygon.com/24090199/riot-forge-league-of-legends-universe-lore

Closing Riot Forge is a big disservice to new League of Legends fans
The end of Riot Forge means the end of League of Legends Story stand-alone games, which cuts off the best entry point for understanding the lore.

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
Jack Stade, Mikkel Abrahamsen
https://arxiv.org/abs/2404.09835 https://

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto, Inf. Process. Lett., 1981], but the version without holes was conjectured to be polynomial-time solvable more than two decades ago~[Baur and Fekete, Algorithmica, 2001]. Our reduction reli…

This https://arxiv.org/abs/2311.14819 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On a Fiber Conjecture of Wan
For a prime $p$ and $p$-power $q$, let $f(x)\in\mathbb{F}_q[x]$ with $\textrm{deg}\ f$ coprime to $p$. As $λ$ varies in $\overline{\mathbb{F}_p^\times}$, Wan has conjectured that the $p$-adic Newton polygon of the corresponding Artin-Schreier curve given by $λf$ is constant. That is, \[ \textrm{NP}(f) = \textrm{NP}(λf). \] In this paper, we prove this conjecture when $λ\in\mathbb{F}_p^\times$ and provide a detailed counterexample showing it is false in general.

🃏 Balatro is the perfect example of a game that wants you to break it
#games

Balatro wants you to break it
Destroy everything! Balatro, a roguelite card game from developer LocalThunk, is a game that’s designed to be broken.

This https://arxiv.org/abs/2305.03095 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture
We prove that the billiard claimed to be a possible counterexample to the Birkhoff-Poritsky conjecture is actually not a counterexample. We also show that for a billiard in a table obtained by the string construction over any convex polygon, this polygon is a core of the billiard dynamics.

🎥 MSCHF’s new project turns your code terminal into a ASCII movie streaming app
https://www.polygon.com/24055971/mschf-ascii-theater-barbie-command-prompt-terminal

MSCHF’s new project turns your code terminal into a streaming app
MSCHF is known for attention-grabbing stunts, and ASCII Theater might get the attention of copyright holders of big films, such as Barbie.

On harmonic maps from the complex plane to hyperbolic 3-space
Subhojoy Gupta, Gobinda Sau
https://arxiv.org/abs/2404.06354 https://ar…

On harmonic maps from the complex plane to hyperbolic 3-space
For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane. Our proof uses the harmonic map heat flow. We also show that such a harmonic map is unique once we prescribe the principal part of its Hopf differential.

A Coreset for Approximate Furthest-Neighbor Queries in a Simple Polygon
Mark de Berg, Leonidas Theocharous
https://arxiv.org/abs/2403.04513 https://…

A Coreset for Approximate Furthest-Neighbor Queries in a Simple Polygon
Let $\mathcal{P}$ be a simple polygon with $m$ vertices and let $P$ be a set of $n$ points inside $\mathcal{P}$. We prove that there exists, for any $\varepsilon>0$, a set $\mathcal{C} \subset P$ of size $O(1/\varepsilon^2)$ such that the following holds: for any query point $q$ inside the polygon $\mathcal{P}$, the geodesic distance from $q$ to its furthest neighbor in $\mathcal{C}$ is at least $1-\varepsilon$ times the geodesic distance to its further neighbor in $P$. Thus the set $\mathcal{C…

Flip Graphs of Pseudo-Triangulations With Face Degree at Most 4
Maarten L\"offler, Tamara Mchedlidze, David Orden, Josef Tkadlec, Jules Wulms
https://arxiv.org/abs/2402.12357

Flip Graphs of Pseudo-Triangulations With Face Degree at Most 4
A pseudo-triangle is a simple polygon with exactly three convex vertices, and all other vertices (if any) are distributed on three concave chains. A pseudo-triangulation~$\mathcal{T}$ of a point set~$P$ in~$\mathbb{R}^2$ is a partitioning of the convex hull of~$P$ into pseudo-triangles, such that the union of the vertices of the pseudo-triangles is exactly~$P$. We call a size-4 pseudo-triangle a dart. For a fixed $k\geq 1$, we study $k$-dart pseudo-triangulations ($k$-DPTs), that is, pseudo-tri…

Random approximation of convex bodies in Hausdorff metric
Joscha Prochno, Carsten Sch\"utt, Mathias Sonnleitner, Elisabeth M. Werner
https://arxiv.org/abs/2404.02870

Random approximation of convex bodies in Hausdorff metric
While there is extensive literature on approximation, deterministic as well as random, of general convex bodies $K$ in the symmetric difference metric, or other metrics arising from intrinsic volumes, very little is known for corresponding random results in the Hausdorff distance when the approximant $K_n$ is given by the convex hull of $n$ independent random points chosen uniformly on the boundary or in the interior of $K$. When $K$ is a polygon and the points are chosen on its boundary, we de…

Newton polygons and B\"{o}ttcher coordinates near infinity for polynomial skew products
Kohei Ueno
https://arxiv.org/abs/2404.05154 https://

Newton polygons and Böttcher coordinates near infinity for polynomial skew products
Let $f(z,w)=(p(z),q(z,w))$ be a polynomial skew product such that the degrees of $p$ and $q$ are grater than or equal to $2$. Under one or two conditions, we prove that $f$ is conjugate to a monomial map on an invariant region near infinity. The monomial map and the region are determined by the degree of $p$ and a Newton polygon of $q$. Moreover, the region is included in the attracting basin of a superattracting fixed or indeterminacy point at infinity, or in the closure of the attracting basi…

Probability that $n$ points are in convex position in a regular $\kappa$-gon : Asymptotic results
Ludovic Morin
https://arXiv.org/abs/2401.16207 https://…

Probability that $n$ points are in convex position in a regular $κ$-gon : Asymptotic results
Let $\mathbb{P}_κ(n)$ be the probability that $n$ points $z_1,\ldots,z_n$ picked uniformly and independently in $\mathfrak{C}_κ$, a regular $κ$-gon with area $1$, are in convex position, that is, form the vertex set of a convex polygon. In this paper, we give an equivalent of $\mathbb{P}_κ(n)$ for all $κ\geq 3$, which improves on a famous result of Bárány. A second aim of the paper is to establish a limit theorem which describes the fluctuations around the limit shape of a $n$-tuple of p…

The Complexity of Geodesic Spanners using Steiner Points
Sarita de Berg, Tim Ophelders, Irene Parada, Frank Staals, Jules Wulms
https://arxiv.org/abs/2402.12110

The Complexity of Geodesic Spanners using Steiner Points
A geometric $t$-spanner $\mathcal{G}$ on a set $S$ of $n$ point sites in a metric space $P$ is a subgraph of the complete graph on $S$ such that for every pair of sites $p,q$ the distance in $\mathcal{G}$ is a most $t$ times the distance $d(p,q)$ in $P$. We call a connection between two sites in the spanner a link. In some settings, such as when $P$ is a simple polygon with $m$ vertices and a link is a shortest path in $P$, links can consist of $Θ(m)$ segments and thus have non-constant comple…

Robustly Guarding Polygons
Rathish Das, Omrit Filtser, Matthew J. Katz, Joseph S. B. Mitchell
https://arxiv.org/abs/2403.11861 https://

Robustly Guarding Polygons
We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees.

This https://arxiv.org/abs/2111.05778 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theoretical and Empirical Analysis of a Fast Algorithm for Extracting Polygons from Signed Distance Bounds
Recently there has been renewed interest in signed distance bound representations due to their unique properties for 3D shape modelling. This is especially the case for deep learning-based bounds. However, it is beneficial to work with polygons in most computer-graphics applications. Thus, in this paper we introduce and investigate an asymptotically fast method for transforming signed distance bounds into polygon meshes. This is achieved by combining the principles of sphere tracing (or ray mar…

Super Guarding and Dark Rays in Art Galleries
MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg, Anna Lubiw, Jayson Lynch, Joseph O'Rourke, Frederick Stock
https://arxiv.org/abs/2404.04613

Super Guarding and Dark Rays in Art Galleries
We explore an Art Gallery variant where each point of a polygon must be seen by k guards, and guards cannot see through other guards. Surprisingly, even covering convex polygons under this variant is not straightforward. For example, covering every point in a triangle k=4 times (a 4-cover) requires 5 guards, and achieving a 10-cover requires 12 guards. Our main result is tight bounds on k-covering a convex polygon of n vertices, for all k and n. The proofs of both upper and lower bounds are non…

This https://arxiv.org/abs/2103.01215 has been replaced.
link: https://scholar.google.com/scholar?q=a

Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil
Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal family naturally arise in the analysis of the numerical range and Blaschke products. We examine the behaviour of such polygons when the inscribed conic varies through a confocal pencil and discover cases when each conic from the confocal family is inscribed in an $n$-polygon, which is inscribed in the circle, with the same $n$. Complete geometric characterization of such cases for $n\in\{4,6\}$ is given and p…

This https://arxiv.org/abs/2303.14555 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Area formula for spherical polygons via prequantization
We present a formula for the signed area of a spherical polygon via prequantization. In contrast to the traditional formula based on the Gauss-Bonnet theorem that requires measuring angles, the new formula mimics Green's theorem and is applicable to a wider range of degenerate spherical curves and polygons.

This https://arxiv.org/abs/2111.05778 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theoretical and Empirical Analysis of a Fast Algorithm for Extracting Polygons from Signed Distance Bounds
Recently there has been renewed interest in signed distance bound representations due to their unique properties for 3D shape modelling. This is especially the case for deep learning-based bounds. However, it is beneficial to work with polygons in most computer-graphics applications. Thus, in this paper we introduce and investigate an asymptotically fast method for transforming signed distance bounds into polygon meshes. This is achieved by combining the principles of sphere tracing (or ray mar…

Shadoks Approach to Knapsack Polygonal Packing
Guilherme D. da Fonseca, Yan Gerard
https://arxiv.org/abs/2403.20123 https://arxiv.org…

Shadoks Approach to Knapsack Polygonal Packing
We describe the heuristics used by the Shadoks team in the CG:SHOP 2024 Challenge. Each instance consists of a convex polygon called container and a multiset of items, where each item is a simple polygon and has an associated value. The goal is to pack some of the items inside the container using translations, in order to maximize the sum of their values. Our strategy consists of obtaining good initial solutions and improving them with local search. To obtain the initial solutions we used integ…