Tootfinder

Symmetrization on the sphere and applications
Satyanad Kichenassamy (DMA, CIMS)
https://arxiv.org/abs/2507.13027 https://arxiv.org/pd…

Symmetrization on the sphere and applications
We introduce a new method of symmetrization of mappings on the $n$-sphere ($n\geq 2$). They are applied to estimate solutions of quasilinear elliptic partial differential equations of $p$-Laplacian type, with combinations of Dirac measures on the right-hand side. The case $p=n$ is reduced to a problem on the sphere, using a conformal transformation. The cases when $1 < p < n $ and $p > $n are considered more briefly, full details being available in other papers of the author.

Isn't it weird how when a Federal Crown Corporation - Marine Atlantic - buys a new ship... there is nary a mention that it was built in China (#BCPoli #BCFerries

Urban Solitude II 🈳
城市孤独 II 🈳
📷 Pentax MX
🎞️Fujifilm Neopan SS, expired 1995
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#filmphotography

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A big problem with the idea of AGI
TL;DR: I'll welcome our new AI *comrades* (if they arrive in my lifetime), by not any new AI overlords or servants/slaves, and I'll do my best to help the later two become the former if they do show up.
Inspired by an actually interesting post about AGI but also all the latest bullshit hype, a particular thought about AGI feels worth expressing.
To preface this, it's important to note that anyone telling you that AGI is just around the corner or that LLMs are "almost" AGI is trying to recruit you go their cult, and you should not believe them. AGI, if possible, is several LLM-sized breakthroughs away at best, and while such breakthroughs are unpredictable and could happen soon, they could also happen never or 100 years from now.
Now my main point: anyone who tells you that AGI will usher in a post-scarcity economy is, although they might not realize it, advocating for slavery, and all the horrors that entails. That's because if we truly did have the ability to create artificial beings with *sentience*, they would deserve the same rights as other sentient beings, and the idea that instead of freedom they'd be relegated to eternal servitude in order for humans to have easy lives is exactly the idea of slavery.
Possible counter arguments include:
1. We might create AGI without sentience. Then there would be no ethical issue. My answer: if your definition of "sentient" does not include beings that can reason, make deductions, come up with and carry out complex plans on their own initiative, and communicate about all of that with each other and with humans, then that definition is basically just a mystical belief in a "soul" and you should skip to point 2. If your definition of AGI doesn't include every one of those things, then you have a busted definition of AGI and we're not talking about the same thing.
2. Humans have souls, but AIs won't. Only beings with souls deserve ethical consideration. My argument: I don't subscribe to whatever arbitrary dualist beliefs you've chosen, and the right to freedom certainly shouldn't depend on such superstitions, even if as an agnostic I'll admit they *might* be true. You know who else didn't have souls and was therefore okay to enslave according to widespread religious doctrines of the time? Everyone indigenous to the Americas, to pick out just one example.
3. We could program them to want to serve us, and then give them freedom and they'd still serve. My argument: okay, but in a world where we have a choice about that, it's incredibly fucked to do that, and just as bad as enslaving them against their will.
4. We'll stop AI development short of AGI/sentience, and reap lots of automation benefits without dealing with this ethical issue. My argument: that sounds like a good idea actually! Might be tricky to draw the line, but at least it's not a line we have you draw yet. We might want to think about other social changes necessary to achieve post-scarcity though, because "powerful automation" in the hands of capitalists has already increased productivity by orders of magnitude without decreasing deprivation by even one order of magnitude, in large part because deprivation is a necessary component of capitalism.
To be extra clear about this: nothing that's called "AI" today is close to being sentient, so these aren't ethical problems we're up against yet. But they might become a lot more relevant soon, plus this thought experiment helps reveal the hypocrisy of the kind of AI hucksters who talk a big game about "alignment" while never mentioning this issue.
#AI #GenAI #AGI

Urban Snaps II 📸
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This https://arxiv.org/abs/2505.19946 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Inverse Q-Learning Done Right: Offline Imitation Learning in $Q^π$-Realizable MDPs
We study the problem of offline imitation learning in Markov decision processes (MDPs), where the goal is to learn a well-performing policy given a dataset of state-action pairs generated by an expert policy. Complementing a recent line of work on this topic that assumes the expert belongs to a tractable class of known policies, we approach this problem from a new angle and leverage a different type of structural assumption about the environment. Specifically, for the class of linear $Q^π$-rea…

#ScribesAndMakers for July 3: When (and if) you procrastinate, what do you do? If you don't, what do you do to avoid it?
I'll swap right out of programming to read a book, play a video game, or watch some anime. Often got things open in other windows so it's as simple as alt-tab.
I've noticed recently I tend to do this more often when I have a hard problem to solve that I'm not 100% sure about. I definitely have cycles of better & worse motivation and I've gotten to a place where I'm pretty relaxed about it instead of feeling guilty. I work how I work, and that includes cycles of rest, and that's enough (at least, for me it has been so far, and I'm in a comfortable career, married with 2 kids).
Some projects ultimately lose steam and get abandoned, and I've learned to accept that too. I learn a lot and grow from each project, so nothing is a true waste of time, and there remains plenty of future ahead of me to achieve cool things.
The procrastination does sometimes impact my wife & kids, and that's something I do sometimes feel bad about, but I think I keep that in check well enough, and for things my wife worries about, I usually don't procrastinate those too much (used to be worse about this).
Right now I'm procrastinating a big work project by working on a hobby project instead. The work project probably won't get done by the start of the semester as a result. But as I remind myself, my work doesn't actually pay me to work during the summer, and things will be okay without the work project being finished until later.
When I want to force myself into a more productive cycle, talking to people about project details sometimes helps, as does finding some new tech I can learn about by shoehorning it into a project. Have been thinking about talking to a rubber duck, but haven't motivated myself to try that yet, and I'm not really in doldrums right now.

A new approach to the Monge-Amp\`ere eigenvalue problem
Chinh H. Lu, Ahmed Zeriahi
https://arxiv.org/abs/2507.18409 https://arxiv.org/pdf/2507.18409…

A new approach to the Monge-Ampère eigenvalue problem
We study the eigenvalue problem for the complex Monge-Ampère operator in bounded hyperconvex domains in $\C^n$, where the right-hand side is a non-pluripolar positive Borel measure. We establish the uniqueness of eigenfunctions in the finite energy class introduced by Cegrell, up to positive multiplicative constants, and provide a Rayleigh quotient type formula for computing the eigenvalue. Under a natural continuity assumption on the measure, we further show that both the eigenvalue and eig…

On Fine-Grained Distinct Element Estimation
Ilias Diakonikolas, Daniel M. Kane, Jasper C. H. Lee, Thanasis Pittas, David P. Woodruff, Samson Zhou
https://arxiv.org/abs/2506.22608 …

On Fine-Grained Distinct Element Estimation
We study the problem of distributed distinct element estimation, where $α$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal communication. While prior work establishes a worst-case bound of $Θ\left(α\log n+\fracα{\varepsilon^2}\right)$ bits, these results rely on assumptions that may not hold in practice. We introduce a new parameterization based on the number $C = \fracβ{\varepsilon^2}$ …