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if and only if

Last edited: August 8, 2025

to prove that something goes both ways: given \(A\Rightarrow B\), and \(A \Leftarrow B\), \(A \Leftrightarrow B\).

If P != NP, then BPP in P

Last edited: August 8, 2025

We really really want to prove:

\begin{equation} \text{BPP} \subseteq \text{P} \end{equation}

which will give \(\text{P} = \text{BPP}\).


How about we replace the truly random bits on the random tape \(r \in \qty {0,1}^{\text{poly}\qty(|x|)}\) with “pseudo-randomness” bits and prove that \(M\) can’t tell the difference.

Namely, a thing that is “pseudo-random” is easier to brute force over. So, we ideally can brute force over \(\text{poly}\qty(n)\) many outcomes instead of \(2^{\text{poly}\qty(n)}\) in the case of true randomness.

immoral v-structure

Last edited: August 8, 2025

v-structure whose parents are unconnected are immoral

This is immoral:

This is moral

Immunogen Design

Last edited: August 8, 2025

Using a bunch of signals to create a 3d representation of the system

features

  • cyro-EM
  • x-ray
  • tomo
  • glynomics/libidomics
  • genetics

studying large-scale viron behavior

Misc. Discoveries bydoing a bunch of MD

  • proteins of specific virons “breath”: oning and closing an entire backbone group; this is not yet quantified in physical modeling
  • when its open, the “breathing open” motion causes the virus to be vunerable
  • *we don’t *
  • “we are so biased by what we can see experimentally”

Immunogen Design

Last edited: August 8, 2025

Using a bunch of signals to create a 3d representation of the system

features

  • cyro-EM
  • x-ray
  • tomo
  • glynomics/libidomics
  • genetics

studying large-scale viron surface protein behavior using MD

“we are so biased by what we can see experimentally, so do MD”

“breathing” motion

  • proteins of specific virons “breath”: oning and closing an entire backbone group; this is not yet quantified in physical modeling
  • when its open, the “breathing open” motion causes the virus to be vunerable
  • so some antibodies jam into the open position

“head tilting” motion

  • when its tilted, there is an epitope that becomes exposed
  • this is a site that’s possible for introduction of what’s needed

overall architecture

  • use conventional MD
  • discover regions of instability (see above for examples) for possible binding surfaces
  • bam inhibition!

maybe at some point run a cyro-EM to experimentally run some