Tootfinder

A note on the spectral radius and $[a,b]$-factor of graphs
Dandan Fan, Huiqui Lin, Yinfen Zhu
https://arxiv.org/abs/2509.00769 https://arxiv.org/pdf/2509.0…

A note on the spectral radius and $[a,b]$-factor of graphs
The investigation of eigenvalue conditions for the existence of an $[a,b]$-factor originates in the work of Brouwer and Haemers (2005) on perfect matchings. In the decades since, spectral extremal problems related to $[a,b]$-factors have attracted considerable attention. In this paper, we establish a spectral radius condition that ensures the existence of an $[a,b]$-factor in a graph $G$ with minimum degree $δ(G) \geq a$, where $b > a \geq 1$. This result resolves a problem posed by Hao and Li…

Pedestrians and cyclists eager to get back on the Lower Don Trail are heartbroken to learn that much of the trail will remain barricaded until next spring — almost two years later than the city originally promised.
https://www.

I saw this blooming today downtown by the Cayuga Lake Inlet, my wife thinks it is a tree that's supposed to bloom in the Spring that's blooming in late August instead
#photo #photography #flowers

SLIM: Subtrajectory-Level Elimination for More Effective Reasoning
Xifeng Yao, Chengyuan Ma, Dongyu Lang, Yinhao Ni, Zhiwei Xu, Huarui Xie, Zihao Chen, Guang Shen, Dandan Tu, Yi Bai, Changzheng Zhang
https://arxiv.org/abs/2508.19502

SLIM: Subtrajectory-Level Elimination for More Effective Reasoning
In recent months, substantial progress has been made in complex reasoning of Large Language Models, particularly through the application of test-time scaling. Notable examples include o1/o3/o4 series and DeepSeek-R1. When responding to a query, these models generate an extended reasoning trajectory, during which the model explores, reflects, backtracks, and self-verifies before arriving at a conclusion. However, fine-tuning models with such reasoning trajectories may not always be optimal. Our …

🇺🇦 #NowPlaying on BBCRadio3's #ClassicalMixtape
Johann Sebastian Bach, Danusha Waskiewicz, Simone Jandl, Rainer Zipperling, Sabina Colonna-Preti, Enrico Bronzi, Alois Posch, Ottavio Dantone, Claudio Abbado & Orchestra Mozart:
🎵 Brandenburg Concerto No 6 in B flat major, BWV 1051 (1st mvt)

Neutralizing Optical Defects in GeSn
Nirosh M. Eldose, Dinesh Baral, Diandian Zhang, Fernando Maia de Oliveira, Hryhorii Stanchu, Mohammad Zamani-Alavijeh, Yuriy I. Mazur, Wei Du, Shui-Qing Yu, Gregory J. Salamo
https://arxiv.org/abs/2508.13027

Neutralizing Optical Defects in GeSn
Reports of photoluminescence from GeSn grown on Ge substrates by molecular beam epitaxy have been limited. We find that one limiting factor to observing photoluminescence is due to localized defect states marked by photoluminescence at 2400 nm and originating from the Ge substrate and buffer layer. In this study, we report on an optical study utilizing doped Ge(001) substrates to effectively suppress defect-related photoluminescence in GeSn layers by filling localized defect trap states. For th…

A look at Ross Ulbricht's return to public life after receiving a pardon in January, including speaking at Bitcoin 2025 and accepting millions in donations (New York Times)
https://www.nytimes.com/2025/09/07/technol

The Spectacular Comeback Tour of Ross Ulbricht, the Founder of Silk Road
Ross Ulbricht, who created the Silk Road dark web marketplace and was serving a life sentence for drug distribution, has embarked on a strange and unexpected comeback after President Trump pardoned him in January.

On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid
Sourabhashis Das, Wentang Kuo, Yu-Ru Liu
https://arxiv.org/abs/2508.12648

On the distribution of the total number of generators of $h$-free and $h$-full elements in an abelian monoid
Let $\mathfrak{m}$ be an element of an abelian monoid, with $Ω(\mathfrak{m})$ denoting the total number of prime elements generating $\mathfrak{m}$. We study the moments of $Ω(\mathfrak{m})$ over subsets of $h$-free and $h$-full elements, establishing the normal order of $Ω(\mathfrak{m})$ within these subsets. This work continues the study on the distribution of generalized arithmetic functions over $h$-free and $h$-full elements in abelian monoids as introduced in the authors' previous work.

🇺🇦 #NowPlaying on BBCRadio3's #Breakfast
Johann Sebastian Bach, Brian Bannatyne‐Scott, Dunedin Consort & John Butt:
🎵 Matthew Passion, BWV 244, Pt. 2: 58. Aria "Mache dich, mein Herze, rein" (Bass)
#DunedinConsort
https://open.spotify.com/track/5mMtYHdCEzgd1sOlPUMTQU