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Prikvačeni tweet
An irrational point x0 iterated on the tent map each day.https://twitter.com/anthoknees/status/1158091351289761792 …
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So in personal news today, Amazon delivered a textbook I ordered by putting the box in my recycling bin.
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Ty proslijedio/la je Tweet
I will never master balancing a “professional twitter presence” and also being a part of gay twitter
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*Addendum: By "nothing is changing," I mean "the number of people going into a class is the same as the number going out," so the total number in the classes is unchanging. Not "no one is moving through the classes."
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Once last time for the day crowd since most of the med types on here have earlier schedules than us mathy weirdos.https://twitter.com/NeuroOscillator/status/1223821590485446656 …
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Ty proslijedio/la je Tweet
Congratulations! A milestone in scientific publishing!https://twitter.com/SRBR_Outreach/status/1223353553496035329 …
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I just realized this bit totally has the same vibe as
@tpwky and their "quarantini" thing but I wasn't trying to step on any toes. At least this one already has an accepted name - the Manchancho.
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Now I also get why people who do this a lot have ko-fi accounts and shit because if you do that all the time, it's probably helpful to have someone paying for your theorem-juice.
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Anyway if I do a follow up soon, it will be on the local stability for the equilibria (pre-req - some matrix algebra on a 3x3 matrix) and maaaaaaybe a comment on global stability and Lyapunov functions? Then probably just some handwavy qualitative stuff with some other models.
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An aside on this: the Ancho Reyes substitution for the normal sweet vermouth is probably my favorite quick and easy substitution on the classic Manhattan without going slightly more exotic like the Brooklyn. That little bit of heat and richness it adds is really the best.
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In which I really just went all fucking in on a first day mathematical epidemiology lecture. That was more work that I expected.https://twitter.com/NeuroOscillator/status/1223821590485446656 …
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For a dynamical systems epidemiologist, an R0 takes on a meaning slightly different than just case counting. It's a number that tells us about the birth and death of equilibrium points in a dynamical model - about watching dance between hills and valleys. And that's kinda cool.
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Now, actually showing in this SIR model the stability profile takes a little work, and I'll have to save it for another night - it will involve a little linear algebra - but the main takeaway is this:
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This is a technical point because in more advanced models we might have a still-locally-stable DFE but also an EE popping up further away. I might go over one of these a little a later night.
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And in this model it makes our DFE unstable, and the EE is the stable one. As a technical matter of fact, the change in the local stability of the DFE is how we define the R0 in this context.
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But if the R0 is greater than one, suddenly we see the birth of a new equilibrium - a "forward bifurcation" if I'm being really technical here - and suddenly we have two equilibria.
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... so of course the disease dies out. It can't maintain itself. And our population eventually goes back to all susceptibles over (a really long) time.
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For our little SIR model that could, we're in the straightforward case where everything is either globally stable or unstable. Our DFE is globally stable if the R0 is less than one. You can interpret this as each case producing fewer subsequent cases than itself...
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Now contrast this with a wavy laminate floor where spilled water ends up in several distinct pools as an analogy to local stability. Where your spilled drink hit the floor determines where it will settle in.
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Contrast this with global stability, which is the idea that (almost) everything get pulls into it no matter where it starts. Think of a shower or tub drain as analogous to globally stable - everything slopes down into it.
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What does stable and unstable mean? Well, we have a couple of concepts about stability. We have what we call local stability and global stability. Essentially, an equilibrium is locally stable if stuff immediately around it gets pulled into it.
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