@TonyVladusich@mathstodon.xyz
@TonyVladusich@mathstodon.xyz avatar

TonyVladusich

@TonyVladusich@mathstodon.xyz

I'm a computational neuroscientist & software engineer. Colors, photos, brains, nature, science, software & chess, preferably all at the same time!

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dave, to random
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deleted_by_author

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    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dave @OneSadCookie

    Thx! We just need to reshape the whole internet into Structs.

    johncarlosbaez, (edited ) to random
    @johncarlosbaez@mathstodon.xyz avatar

    Category theory meets AI!

    Former Tesla engineer George Morgan has started a company called Symbolica to improve machine learning using category theory:

    https://www.symbolica.ai/

    When Musk and Tesla's AI head Karpathy didn’t listen to his concern that current techniques in deep learning couldn't “scale to infinity and solve all problems,” Morgan left Tesla and started Symbolica. OpenAI investor Vinod Khosla gave Morgan $2 million to prove that ideas from category theory could help.

    “He delivered that, very credibly,” Khosla says. “So we said, ‘Go hire the best people in this field of category theory.’” He says that while he still believes in OpenAI’s continued success building large language models, he is “relatively bullish” on Morgan’s idea and that it will be a “significant contribution” to AI if it works as expected. So he's invested $30 million more.

    Symbolica has hired some category theorists, and here are job ads for 6 more:

    https://jobs.gusto.com/boards/-67195a74-31b4-4052-ba18-e859d461808c

    For more on the math, check out these papers, including the one shown below:

    https://categoricaldeeplearning.com/

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez @dougmerritt

    I think you likely dodged a dodgy bullet there, John!

    TonyVladusich, to random
    @TonyVladusich@mathstodon.xyz avatar

    Has anybody used Swift Numerics in anger? Specifically interested in the ComplexModule part.

    https://github.com/apple/swift-numerics

    tomkindlon, to mecfs
    @tomkindlon@disabled.social avatar

    🧵
    "ME/CFS Isn't Just Misunderstood, It's Actively Neglected"

    https://www.popsugar.com/fitness/mecfs-post-covid-49344168

    'Beth Pardo is among the people who developed ME/CFS after contracting COVID.' 'Pardo went from running ultramarathons to being unable to leave her bed'

    @mecfs

    @longcovid

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @tomkindlon @mecfs @longcovid

    I would be willing to bet a lot of money that long covid is primarily a disorder of the mitachondria and there’s some evidence to support that idea. Tbh I hadn’t thought about the cause before, but it fits

    https://www.news-medical.net/news/20240104/Study-identifies-mitochondrial-dysfunction-as-cause-of-long-COVID-fatigue.aspx

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @catsnfats @tomkindlon @mecfs @longcovid

    I’m embarrassed it took me this long to think about the problem. It only took 30 secs of thought to identify mitachondrial malfunction as the likely cause of long Covid. Hopefully the problem will get well funded over the next decades because folks will need to understand and treat it.

    johncarlosbaez, (edited ) to random
    @johncarlosbaez@mathstodon.xyz avatar

    So you wake up one day wanting to invent a 2-dimensional number system. This requires a new number 𝑖 that's at right angles to 1. So you figure multiplying by 𝑖 must rotate numbers by 90°. So multiplying by 𝑖² rotates by 180°, so

    𝑖² = -1

    Cool!

    Then you notice something else. The derivative of a function in the 𝑦 direction must be 𝑖 times its derivative in the 𝑥 direction, because the derivative is linear and you get the 𝑦 direction by rotating the 𝑥 direction by 90°: that is, multiplying it by 𝑖. So you get this equation:

    [ \frac{\partial f}{\partial y} = i \frac{\partial f}{\partial x} ]

    Cool!

    Then you notice something else. If you use this equation twice you get

    [ \frac{\partial^2 f}{\partial y^2} = i \frac{\partial f}{\partial x\partial y} = i^2 \frac{\partial^2 f}{\partial x^2} = - \frac{\partial^2 f}{\partial x^2} ]

    so

    [ \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} = 0 ]

    Wow! Every function with a second derivative obeys the Laplace equation!

    You decide this one is a keeper.

    https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez

    Haha, that’s terrific! Now that is how to make math not dull!

    dave, to random
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    deleted_by_author

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    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dave

    Lol, crushed it. Have a celebratory curry!

    dougmerritt, to random
    @dougmerritt@mathstodon.xyz avatar

    Why Mathematics is Boring; John Baez (@johncarlosbaez); 2024 Mar 28

    "I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my enthusiasm slowly but remorselessly crushed by pages and pages of bad writing. There are many ways math writing can be bad. But here I want to focus on just one: it can be dull."

    https://golem.ph.utexas.edu/category/2024/03/why_mathematics_is_boring_1.html

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dougmerritt @johncarlosbaez

    omg yes! I was thinking exactly this yesterday while skimming a paper whose title seemed like exactly the sort of thing I was looking for. but then without preamble, it launched into pages and pages of dull proofs. I was left aching for the punchline, the main idea, the raison d'etre that never arrived. so frustrating.

    a few years I crossed field boundaries from computational neuroscience to computer graphics and was positively stunned by the high quality of papers published in the ACM's flagship journal, Transactions on Graphics: New ideas were explained at the outset, the scene set with background material on the state of the art, all accompanied by a "money shot" figure on the first page at the level of the abstract. I wish math journals (indeed all journals) required these types of elements.

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez @oantolin @dougmerritt

    Lol. I knew a leading researcher in my field who held a similar philosophy. He could not understand my paper (he was a reviewer) so my mentor had to have a long phone conversation to convince him to accept it. It didn’t work, he never did come to understand the paper, but he was gracious enough to allow it to be published nevertheless. My mentor later told me this is a big thing, as getting the first paper for a big new idea published is always the hardest. In the end I published 5 follow up papers in quick succession in top journals. He was spot on that the first one paved the way for the others (as he called it, legitimatising the whole research program.)

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dougmerritt @johncarlosbaez @oantolin

    Here is the first paper in the series.

    https://www.sciencedirect.com/science/article/pii/S0042698912002489

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dougmerritt @johncarlosbaez @oantolin

    The program itself I called “gamut relativity”. You can follow the paper trail easily with that search term.

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez @dougmerritt @oantolin

    Thanks for the link, I didn't know that paper! The idea that colour space can be modelled as a Riemann surface/manifold is certainly intriguing, although I think the jury is still out in terms of evidence supporting the idea.

    Another interesting mathematical approach related to this idea -- one that I use in my Colors photo editing app in order to decompose hue into a map of selectable components (red, yellow, orange, lime, green etc) -- is to model the hue domain as an atlas of charts mapping arcs around the hue circle into orthogonal 2D subspaces.

    Each subspace "captures" the points bounded by contiguous radii. The vector decomposition of each point onto the 2D subspace axes gives us a projection that allows the user to adjust each hue component independently.

    The adjusted charts are reassembled into the atlas via transition maps, et voila the image is recomposed with specific hue adjusted.

    For example, in the figures below I've used the app to remove the green (10GY) patch from the circle!

    image/png

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dougmerritt @johncarlosbaez

    this is the sort of paper that drives me to distraction. I mean, wtf is your idea even? I really want to learn more about the screened Poisson equation, but this sort of writing makes the barrier too high.

    https://arxiv.org/pdf/2403.03076.pdf

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dougmerritt @johncarlosbaez

    their notation also sucks. I mean who in their right mind writes this?

    denote ( \mathbf{n} = (n, m) ), and use ( u(\mathbf{n}) ) and ( u(n, m) ) interchangeably

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez @dougmerritt

    Thanks for the feedback guys! I myself would generally eschew using the same symbol for a bold vector as one of the elements of the vector. But having defined the vector why then continue to use the clumsier element-based notation? I’m probably just rationalising my own irritation when reading the paper though. As John says, he reads a lot of math paper. I don’t. I was particularly interested in this one though because my app uses the discrete screened Poisson equation. I simply struggled to comprehend the nature of the advance, which is exactly what bugs me about a lot of math papers.

    Now, the real question is: what can I do to capture John’s interest in the relationship between computational vision science and physics?! 😉

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez

    Haha, yes you’re right, and you’ve neatly swerved my question about how to pique your interest.

    As an attempt, did you know that the visual system has a topographical map of the visual field, and that that map is a conformal map: namely, it is a complex logarithmic map! This map models quite exactly how the resolution of vision varies from high in the fovea to low in the periphery. If our visual system had equally high resolution as the centre, our brains would need to weigh thousands of pounds!

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @johncarlosbaez @dougmerritt

    Haha, any math remotely connected to Grothendieck has me running away like being chased by a jaguar! It’s fascinating but way beyond my training. I assume this sort of math gets taught in advanced graduate seminars and the like?

    TonyVladusich, to random
    @TonyVladusich@mathstodon.xyz avatar

    Dave! @dave

    dave, to random
    @dave@social.lightbeamapps.com avatar

    deleted_by_author

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    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @dave

    hey, I have to hold boss Dave and Ali-G Dave in my head simultaneously!

    cocoaphony, to random
    @cocoaphony@mastodon.social avatar

    Watched the first ep of Netflix’s 3 Body Problem, and my concern “how are they going to fit this into 8 episodes?” is warranted. It’s just going too fast, to the point of frantic. I think they’ve made a lot of very good cuts to simplify parts of the book, and the 30 episode Tencent series was honestly very slow, but good grief that’s too much to put into one episode. If you’re going to add this many extra characters (and I like the extra characters), we need a little time to meet them.

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @cocoaphony

    Do we know if this series covers all 3 books? Agree it went really fast.

    j_bertolotti, to random
    @j_bertolotti@mathstodon.xyz avatar

    "Please fill this anonymous survey"
    Proceed to ask enough personal questions that anyone with two working neurons can uniquely identify me 🤦‍♂️

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @j_bertolotti

    Tbf it is quite hard to find people with 2 whole working neurons these days

    demofox, to random
    @demofox@mastodon.gamedev.place avatar

    Here's a meme I made for another site

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @demofox

    Now why didn’t I think of that?!

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @demofox

    I want to combine this meme with the one where the fella doesn’t want kids and plans to tell them at dinner time.

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @demofox

    Just a joke I saw https://stream.digio.space/item/0ba36333-7d7e-4d32-9494-2d14017ec622

    kcarruthers, to random
    @kcarruthers@mastodon.social avatar

    Uh oh 😧 for neurospicy folks: People with hypermobility may be more prone to long , study suggests

    https://www.theguardian.com/society/2024/mar/19/people-with-hypermobility-may-be-more-prone-to-long-covid-study-suggests

    TonyVladusich,
    @TonyVladusich@mathstodon.xyz avatar

    @kcarruthers

    Oh fantastic!

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