Tootfinder

"In order to make an apple pie from scratch, you must first create the
universe."
-- Carl Sagan, Cosmos

🇺🇦 #NowPlaying on KEXP's #DriveTime
Night Moves:
🎵 Carl Sagan
#NightMoves
https://nightmoves.bandcamp.com/track/carl-sagan
https://open.spotify.com/track/24GCf1A4pOTEDDcBponpjn

Coloquei uns quadrinhos para decorar a parede da mesa de trabalho do quarto-biblioteca. Não sei se ficou bonito, mas eu gosto muito dessas frases. Especialmente a do quadro do meio.

Information-computation trade-offs in non-linear transforms
Connor Ding, Abhiram Rao Gorle, Jiwon Jeong, Naomi Sagan, Tsachy Weissman
https://arxiv.org/abs/2506.15948

Information-computation trade-offs in non-linear transforms
In this work, we explore the interplay between information and computation in non-linear transform-based compression for broad classes of modern information-processing tasks. We first investigate two emerging nonlinear data transformation frameworks for image compression: Implicit Neural Representations (INRs) and 2D Gaussian Splatting (GS). We analyze their representational properties, behavior under lossy compression, and convergence dynamics. Our results highlight key trade-offs between INR'…

Found the Cosmos book from 1980 (made about the show) at thrift for a couple bucks, this thing is incredible.
#CarlSagan #Cosmos #bookstodon #books

"Science is more than a body of knowledge. It's a way of thinking, a way of skeptically interrogating the universe with a fine understanding of human fallibility. If we are not able to ask skeptical questions -- to interrogate those who tell us something is true -- to be skeptical of those in authority, then we're up for grabs for the next charlatan, political or religious, who comes ambling along."
-- Carl Sagan (Charlie Rose interview)

"Em algum lugar, algo incrível estš esperando para ser descoberto."
Usando minha camisa com esta frase do Carl Sagan que tem tanto significado para mim.

Ordered set partition posets
Bruce E Sagan (Michigan State University), Sheila Sundaram (University of Minnesota)
https://arxiv.org/abs/2506.23355 https://…

Ordered set partition posets
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and respresentation-theoretic properties. An ordered set partition is a set partition where the subsets are listed in a specific order. Ordered set partitions appear in combinatorics, number theory, permutation polytopes, and the study of coinvariant algebras. The ordered set partitions of {1,...,n} can be partially ordered by refinement and then a unique minimal el…

An exceptional equinumerosity of lattice paths and Young tableaux
Liam Ayres, Evan Bialo, Aidan Cook, Alwin Chen, Matteus Froese, Erica Liu, Maryam Mohammadi Yekta, Oliver Pechenik, Benjamin Wong
https://arxiv.org/abs/2506.03116

An exceptional equinumerosity of lattice paths and Young tableaux
We consider families $\mathcal{P}_n$ of plane lattice paths enumerated by Guy, Krattenthaler, and Sagan (1992). We show by explicit bijection that these families are equinumerous with the set $\mathrm{SYT}(n+2,2,1^n)$ of standard Young tableaux.

The superspace coinvariant ring of type B
Sutanay Bhattacharya
https://arxiv.org/abs/2505.24122 https://arxiv.org/pdf/2505.24122

The superspace coinvariant ring of type B
Given the rank $n$ superspace $Ω_n$, the ring of polynomial-valued differential forms on $\mathbb C^n$, one can define an action of hyperoctahedral group $\mathfrak B_n$ on it. This leads to a superspace coinvariant ideal $SR_n^B$, defined as the quotient of $Ω_n$ by two-sided ideal generated by all $\mathfrak B_n$ invariants with vanishing constant terms. We derive the Hilbert series of $SR^B_n$ conjectured by Sagan and Swanson, and prove an operator theorem that yields a concrete descriptio…