The key to teaching division to young students who have only been introduced recently to more complicated mathematics forms is to make the student feel involved with the process, while finding it pleasant at the same time.
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Ok, it's time for a #FUNctionalAnalysis thread! Let's talk about Hilbert spaces. (I hope you like linear algebra, because that's what we're
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
— syzygay (@syzygay1) August 9, 2020
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
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@EricTopol @NBA @StephenKissler @yhgrad B.1.1.7 reveals clearly that SARS-CoV-2 is reverting to its original pre-outbreak condition, i.e. adapted to transgenic hACE2 mice (either Baric's BALB/c ones or others used at WIV labs during chimeric bat coronavirus experiments aimed at developing a pan betacoronavirus vaccine)
@NBA @StephenKissler @yhgrad 1. From Day 1, SARS-COV-2 was very well adapted to humans .....and transgenic hACE2 Mice
@NBA @StephenKissler @yhgrad 2. High Probability of serial passaging in Transgenic Mice expressing hACE2 in genesis of SARS-COV-2
@NBA @StephenKissler @yhgrad B.1.1.7 has an unusually large number of genetic changes, ... found to date in mouse-adapted SARS-CoV2 and is also seen in ferret infections.
https://t.co/9Z4oJmkcKj
@NBA @StephenKissler @yhgrad We adapted a clinical isolate of SARS-CoV-2 by serial passaging in the ... Thus, this mouse-adapted strain and associated challenge model should be ... (B) SARS-CoV-2 genomic RNA loads in mouse lung homogenates at P0 to P6.
https://t.co/I90OOCJg7o
@NBA @StephenKissler @yhgrad 1. From Day 1, SARS-COV-2 was very well adapted to humans .....and transgenic hACE2 Mice
1. From Day 1, SARS-COV-2 was very well adapted to humans .....and transgenic hACE2 Mice
— Billy Bostickson \U0001f3f4\U0001f441&\U0001f441 \U0001f193 (@BillyBostickson) January 30, 2021
"we generated a mouse model expressing hACE2 by using CRISPR/Cas9 knockin technology. In comparison with wild-type C57BL/6 mice, both young & aged hACE2 mice sustained high viral loads... pic.twitter.com/j94XtSkscj
@NBA @StephenKissler @yhgrad 2. High Probability of serial passaging in Transgenic Mice expressing hACE2 in genesis of SARS-COV-2
1. High Probability of serial passaging in Transgenic Mice expressing hACE2 in genesis of SARS-COV-2!
— Billy Bostickson \U0001f3f4\U0001f441&\U0001f441 \U0001f193 (@BillyBostickson) January 2, 2021
2 papers:
Human\u2013viral molecular mimicryhttps://t.co/irfH0Zgrve
Molecular Mimicryhttps://t.co/yLQoUtfS6s https://t.co/lsCv2iMEQz
@NBA @StephenKissler @yhgrad B.1.1.7 has an unusually large number of genetic changes, ... found to date in mouse-adapted SARS-CoV2 and is also seen in ferret infections.
https://t.co/9Z4oJmkcKj
@NBA @StephenKissler @yhgrad We adapted a clinical isolate of SARS-CoV-2 by serial passaging in the ... Thus, this mouse-adapted strain and associated challenge model should be ... (B) SARS-CoV-2 genomic RNA loads in mouse lung homogenates at P0 to P6.
https://t.co/I90OOCJg7o