Because cursed languages work best together. Repo is here.

Some Motivation

We wanted an Emacs OS, but that required implementing libc syscalls and also just getting glib to compile, which is obviously not happening. Instead we are going for the second-best thing, which is to be able to interactively write an OS in Emacs.

And thus this project essentially involves enabling the process of incremental development of an operating system kernel. That is, beyond the bare basics and the important, atomic things, everything else should be able to be written and interpreted as they are written (e.g., instead of being compiled into the kernel before).

Jax stuff news!

“Feel the API”

jit -> sharding hints -> explicit sharding -> shard_map collectives -> pallas -> FFI

Refs

There are refs now! Dynamics slicing! Plumbing out metrics is hard! Batch-norms! How do we express things in Jax.

“I want to keep this thing in memory at the same place.”

For stuff like gradient accumulation / sparse updating this is very good.

history

• we can’t express mutability
• and we think the change

fine.

There’s refs now!

CAPM, a Review

Note that we will be using the Sharpe-Linter version of CAPM:

\begin{equation} E[R_{i}-R_{f}] = \beta_{im} E[(R_{m}-R_{f})] \end{equation}

\begin{equation} \beta_{im} := \frac{Cov[(R_{i}-R_{f}),(R_{m}-R_{f})]}{Var[R_{m}-R_{f}]} \end{equation}

Recall that we declare \(R_{f}\) (the risk-free rate) to be non-stochastic.

Let us begin. We will create a generic function to analyze some given stock.

Data Import

We will first import our utilities

import pandas as pd
import numpy as np

Let’s load the data from our market (NYSE) as well as our 10 year t-bill data.

The fact that DFAs are limited, it allows us to optimize a DFA. Specifically, we ask: “does this DFA have a minimal number of states?”

Formally: can we accept the same language with a particular DFA with another DFA with less states?

For every language \(L\), there is a unique (up to state relabeling) minimal-state DFA \(M^{*}\) such that \(L(M^{*}) = L\).

Furthermore, there exists an efficient algorithm which, given DFA \(M\), will produce this unique \(M^{*}\).

Foreword

Hi there, internet traveler.

The time is 2015/2016, I was either in 5th or 6th grade. At that time, I was barely beginning to be actually comfortable using the language of English.

One of the ways I practiced English, which is also a habit I continue to do today, is to write. I write mostly expository prose now, but, back then, shining with childish naïvete, I decided to write a multi-part story as a means of practicing English.