Capacitor charging:

\begin{equation} Q = Q_0 (1-e^{-\frac{t}{RC}}) \end{equation}

where \(Q\) is capacitor change at time \(t\), and \(Q_0\) initial change, and \(RC\) the resistance and capacitance.

Where, \(RC\) is called the “time constant”.

\begin{equation} I = \frac{V}{R} (e^{-\frac{t}{RC}}) \end{equation}

Note! these are inverse relationships: as a capacitor CHARGE, the current DROPS.

Dyson’s Model of Life is a theory of origin of life:

1. cells form as machines that perform tasks
2. genes show up later as parasites, eventually forming symbiosis with cells

Read: and so, we can essentially ditch trying to find things characteristics of “cells” per-se like RNA, instead we can go about finding generic boxes of containers called “cells” and see how they evolve.

See also: high chemical activity, metabolism, Stepwise Evolution, and Two Main Functions of Life

It a constant.

\begin{equation} \lim_{n \to \infty} \qty(1- \frac{\lambda}{n})^{n} = e^{-\lambda} \end{equation}

see error-correction code

We want to solve huge POMDP in the real world, but the belief states are huge. Notably, reachable beliefs are very small given an initial belief.

Why is vanilla PCA bad

PCA as a denoising procedure: the underlying data is some data which is normally noised. This is not strictly true, the points don’t have normal noise.

Better PCA: E-PCA

Instead of Euclidean distance, we use

\begin{equation} L(U,V) = \mid X-UV\mid^{2} \end{equation}