Tootfinder

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Rinaldo B. Schinazi
https://arxiv.org/abs/2506.13662

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Consider an $n\times n$ matrix $P$ with the following properties. All entries in $P$ are positive or $0$, the sum of each row is 1 and for all $i$ and $j$ in $\{1,\dots,n\}$ there exists a natural number $k$ such that the $(i,j)$ entry of the matrix $P^k$ is strictly positive. Then, there exists a unique row vector $v$ with only strictly positive entries, whose sum of entries is 1 and such that $vP=P$. We present a proof of this well-known result that uses only basic algebra and the Bolzano-Wei…

Vision-driven River Following of UAV via Safe Reinforcement Learning using Semantic Dynamics Model
Zihan Wang, Nina Mahmoudian
https://arxiv.org/abs/2508.09971 https://

Vision-driven River Following of UAV via Safe Reinforcement Learning using Semantic Dynamics Model
Vision-driven autonomous river following by Unmanned Aerial Vehicles is critical for applications such as rescue, surveillance, and environmental monitoring, particularly in dense riverine environments where GPS signals are unreliable. We formalize river following as a coverage control problem in which the reward function is submodular, yielding diminishing returns as more unique river segments are visited, thereby framing the task as a Submodular Markov Decision Process. First, we introduce Ma…

YES!
GDP growth is effectively dead.The motor is broken.
Now it's time to face reality and share the wealth that is so evidently present.
An economy for life!
#degrowth
Blow to Chancellor as UK economy shrank unexpectedly in May

Blow to Chancellor as UK economy shrank unexpectedly in May
The UK economy contracted unexpectedly in May, marking the second month in a row of falling output and heaping further pressure on Chancellor Rachel Reeves. The Office for National Statistics (ONS) said gross domestic product (GDP) contracted by 0.1% in May, following a 0.3% drop in April. Most economists had expected the economy to rebound […]

UK economy saw zero growth in July
https://www.bbc.com/news/articles/c203edl1zq3o
"Faced with economic stagnation the elites are panicking. Wild eyed in the control room, they thrash around seeking to fix the unfixable, pushing all the buttons, pulling all the levers, to n…

UK economy saw zero growth in July
The economy failed to grow following the biggest contraction in manufacturing output for a year.

Interesting that some who replied to my post on tax and GDP growth yesterday missed the point.
The point isn't to debate whether tax -> growth (it might, with a tail wind).
The point is that
1) Growth won't happen like it used to.
2) That is good because GDP growth is ecologically and socially lethal.
3) So our leaders (sic) had better adapt to the new reality and use taxation and other measures to build a better, fairer future.
More here:

Getting Real about the Crises Facing the UK | Stop the Damage! Build a Better Future!
Britain and the rest of the world face a set of almost intractable challenges, ecological (including climate), economic and social. Yet political leaders with few exceptions are failing to propose the actions and policies that could address the scale of this pancrisis. Here though is an alternative initiative, a kind of alternative manifesto with a portfolio of illustrative policies...

#Microsoft finishes swallowing #Github, the largest repository of #OpenSource software.
GitHub just got less independent at Microsoft after CEO resignation | The Verge

GitHub just got less independent at Microsoft after CEO resignation
Microsoft is bringing GitHub into its AI engineering team. It’s part of an AI shakeup, following the GitHub CEO resigning.

The progressive Honduran government declares the country free from illiteracy following a mass literacy campaign.
https://www.nodal.am/2025/09/el-gobierno-declaro-al-pais-territorio-libre-de-analfabetismo/

El Gobierno declaró al país territorio libre de analfabetismo – NODAL
NODAL - Noticias de América Latina y el Caribe

"The UK’s actual record in the 1930s is far from good, but no doubt if Nigel Farage had been in power he would have eagerly sent every Jewish refugee fleeing from the Nazis back to Germany."
mainly macro: Key myths on asylum, immigration and how to take on the far right
https://

On the day the UK parliament voted to proscribe the citizen peaceful direct action group Palestine Action as supposedly terrorist, Channel 4 showed the searing Basement Films documentary "Gaza doctors under attack". It showed the actions of the Israeli terrorist State in destroying Gaza's healthcare system, murdering civilians of all kinds and targeting health workers some of whom have died following torture. Sprinkled throughout were the repetitive lies of the occupation.

“A returns deal with France that makes access to safety in the UK — even for those with close family or connections here — dependent on someone else risking their life to cross the Channel only cements the role of smugglers in how people fleeing war and persecution must seek asylum in the UK."
'A grubby trade in human lives' | Morning Star
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