⬇️⬇️⬇️ The "Math" of Fear
As it is Thursday, I have a post for you today in anticipation of Gov. DeWine's new Maps of Fear which he has tried to phase in. I have previously discussed both the new red and blue maps and their issues -
The first is a hyper-simplistic (and unrealistic) but illustrative example of the calculations that the new blue map goes through to arrive at its numbers.
But that's not how Gov. DeWine would present this situation to us. Instead of looking at the total available beds, they look only at the beds in use.
By manipulating the numbers, they have increased the real percentage by a third.
More from Maths
OK, I may be guilty of a DoS attack attempt on mathematicians' brains here, so lest anyone waste too much precious brain time decoding this deliberately cryptic statement, let me do it for you. •1/15
First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15
Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15
Maybe a tad clearer again by writing “P(u)” for “u∈y” and leaving out the quantifier on y, viꝫ: “∀x.((∀z∈x.(((∀t∈x.((t∈z) ⇒ P(t)))) ⇒ P(z))) ⇒ (∀z∈x.P(z)))” [✯]. Now it appears as an induction principle: namely, … •4/15
… “in order to prove P(z) for all z∈x, we can assume, when proving P(z), that P(t) is already known for all t∈z∩x” (n.b.: “(∀z.(Q(z)⇒P(z)))⇒(∀z.P(z))” can be read “in order to prove P(z) for all z, we can assume Q(z) known when proving P(z)”). •5/15
\u2200x.\u2200y.((\u2200z.((z\u2208x) \u21d2 ((\u2200t.((t\u2208x) \u21d2 (t\u2208z) \u21d2 (t\u2208y)))) \u21d2 (z\u2208y))) \u21d2 (\u2200z.((z\u2208x) \u21d2 (z\u2208y))))
— Gro-Tsen (@gro_tsen) February 12, 2021
First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15
Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15
Maybe a tad clearer again by writing “P(u)” for “u∈y” and leaving out the quantifier on y, viꝫ: “∀x.((∀z∈x.(((∀t∈x.((t∈z) ⇒ P(t)))) ⇒ P(z))) ⇒ (∀z∈x.P(z)))” [✯]. Now it appears as an induction principle: namely, … •4/15
… “in order to prove P(z) for all z∈x, we can assume, when proving P(z), that P(t) is already known for all t∈z∩x” (n.b.: “(∀z.(Q(z)⇒P(z)))⇒(∀z.P(z))” can be read “in order to prove P(z) for all z, we can assume Q(z) known when proving P(z)”). •5/15
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Keep dwelling on this:
Further Examination of the Motif near PRRA Reveals Close Structural Similarity to the SEB Superantigen as well as Sequence Similarities to Neurotoxins and a Viral SAg.
The insertion PRRA together with 7 sequentially preceding residues & succeeding R685 (conserved in β-CoVs) form a motif, Y674QTQTNSPRRAR685, homologous to those of neurotoxins from Ophiophagus (cobra) and Bungarus genera, as well as neurotoxin-like regions from three RABV strains
(20) (Fig. 2D). We further noticed that the same segment bears close similarity to the HIV-1 glycoprotein gp120 SAg motif F164 to V174.
https://t.co/EwwJOSa8RK
In (B), the segment S680PPRAR685 including the PRRA insert and highly conserved cleavage site *R685* is shown in van der Waals representation (black labels) and nearby CDR residues of the TCRVβ domain are labeled in blue/white
https://t.co/BsY8BAIzDa
Sequence Identity %
https://t.co/BsY8BAIzDa
Y674 - QTQTNSPRRA - R685
Similar to neurotoxins from Ophiophagus (cobra) & Bungarus genera & neurotoxin-like regions from three RABV strains
T678 - NSPRRA- R685
Superantigenic core, consistently aligned against bacterial or viral SAgs
Further Examination of the Motif near PRRA Reveals Close Structural Similarity to the SEB Superantigen as well as Sequence Similarities to Neurotoxins and a Viral SAg.
The insertion PRRA together with 7 sequentially preceding residues & succeeding R685 (conserved in β-CoVs) form a motif, Y674QTQTNSPRRAR685, homologous to those of neurotoxins from Ophiophagus (cobra) and Bungarus genera, as well as neurotoxin-like regions from three RABV strains
(20) (Fig. 2D). We further noticed that the same segment bears close similarity to the HIV-1 glycoprotein gp120 SAg motif F164 to V174.
https://t.co/EwwJOSa8RK
In (B), the segment S680PPRAR685 including the PRRA insert and highly conserved cleavage site *R685* is shown in van der Waals representation (black labels) and nearby CDR residues of the TCRVβ domain are labeled in blue/white
https://t.co/BsY8BAIzDa
Sequence Identity %
https://t.co/BsY8BAIzDa
Y674 - QTQTNSPRRA - R685
Similar to neurotoxins from Ophiophagus (cobra) & Bungarus genera & neurotoxin-like regions from three RABV strains
T678 - NSPRRA- R685
Superantigenic core, consistently aligned against bacterial or viral SAgs