The Gaussian, in general, gives:

\begin{equation} e^{-\frac{ax^{2}}{2}} \end{equation}

which is a Bell-Shaped curve. It’s pretty darn important

solving heat equation without boundary

for general expression:

\begin{equation} \pdv{U}{t} = \alpha \pdv[2]{U}{x} \end{equation}

\begin{equation} U(t,x) = \frac{1}{\sqrt{4\pi \alpha t}}\int_{\mathbb{R}} f(y) e^{-\frac{(x-y)^{2}}{4\alpha t}} \dd{y} \end{equation}

where,

\begin{equation} \hat{U}(t,\lambda) = \hat{f}(\lambda)e^{-\alpha t \lambda^{2}} \end{equation}

\begin{equation} \hat{U}(t,\lambda) = \hat{f}(\lambda)e^{-\lambda^{2}(t)} \end{equation}

Heat Equation and Gaussian

\begin{equation} H(t,x) = \frac{1}{\sqrt{2\pi} t}e^{-\frac{x^{2}}{2t}} \end{equation}

You will note that \(H\) does satisfy the heat equation:

The point of Gaussian elimination is to solve/identiy-ify a linear equation. Take, if you have a matrix expression:

\begin{equation} Ax = b \end{equation}

We can apply \(A^{-1}\) to both side, we then have:

\begin{equation} A^{-1}Ax = A^{-1} b \end{equation}

Applying the definition of the identity:

\begin{equation} Ix = A^{-1}b \end{equation}

Therefore, to solve for some \(A^{-1}\), which would yield \(x\).

GDB is gnu’s very own debugger

• b main or b 72 (set breakpoint on main function or line 72)
• r args (run with args)
• p thingname or p 3+5 (print a variable or return value)
  • p/t print as binary
  • p/x print as hex
• info (get args, locals)
• n s continue next, step, continue

int test;
short lsb = 0xff;
test |= lsb

printf("%d\n",lsb);

int test;

Here’s a list of gears that I like and stuff that I use.

clothing

t-shirt

MUJI Washed Heavy Weight Crew Neck

If you ever have the pleasure of buying these in China, you should. It’s cheaper there. This is a white T-Shirt, its 100% cotton, its heavy, you can wipe your glasses with it, why not?

shorts

Amazon Essential Inseam Drawstring

They are like very basic shorts; they are a nice quality, don’t seem to break, and is drawstring instead of rubber band which makes them nice to adjust.

See inference.

In general, the joint probability distribution tables are very hard to solve because it requires—for instance for binary variables—requries \(2^{n}\) entires, which is a lot.

1. how do you define very large models?
2. how do you perform inference with very large models
3. what about the data can we use to inform the design process

“If you can tell me a generative story, we can compress our joint probability distribution”. Get ready for…… inference with causality with Baysian Network.