The dopamine circuitry in NF1.

Genetically encoded “sensors” to measure circuits.

There is extreme noise in the patient annotations: for instance, in their health rhythm labels there’s around 20% contradictions in the dataset.

1. accurate diagnosis
2. limiting “domain rule violations”

approach

1. take your dataset, and validate rules
2. IF validation is successful, train model normally with that sample
3. IF the validation is unsuccessful, then use the output samples as negative examples

The dot product is a property of real vector spaces which is a simplified version of an inner product; specifically, it obviates the need to complex-conjugate anything because, well, \(\bar{n} = n, n \in \mathbb{R}\). The dot-product also yield a real number.

constituents

• \(x, y \in \mathbb{R}^{n}\) (NOTE the realness)
  • where, \(x = (x_1, \dots, x_{n})\) and \(y = (y_1, …, y_{n})\)

requirements

As we are familiar with, element-wise product and sum

\begin{equation} x\cdot y = x_1y_1 + \dots + x_{n}y_{n} \end{equation}

One envelope has 10 times the money in the other money.

WLOG let \(x\) be the envelope in Cary’s hand. The money in \(y\), then, \(y = \frac{1}{2}\qty(\frac{1}{10}x)+\frac{1}{2}\qty (10x) = 0.05x+5x = 5.05x\). Wat.

Basically; regardless if Cary took the envelope \(x\) or \(y\), the other envelope is expected to have \(5\times\) more money. What.

Why?

There’s a bug in this:

\begin{equation} y = \frac{1}{2}\qty(\frac{1}{10}x)+\frac{1}{2}\qty (10x) \end{equation}

is not true! There is a human PRIOR BELIEF!! Its very unlikely that mykel/chris put 10000 dollars into an envelope; so each individual amount in an envelope has an exogenous probability of it happening!