we can also damp the heat equation:

\begin{equation} \pdv{u}{t} + ku = \pdv[2]{u}{x} \end{equation}

we note that substituting \(u(t,x) = e^{-kt}w(t,x)\) into the expression, we yield:

\begin{equation} \pdv{w}{t} = \pdv[2]{w}{t} \end{equation}

therefore, we simply have to solve the system normally on \(w\), then multiply the solution by \(e^{-kt}\) to obtain our solution for the damped equation.

darkpools are non-exchange, non-published exchange which doesn’t have the same reporting obligations of a stock market. The only thing they have to report is the actual filled transactions after 90 seconds.

darkpools are used because the order book/bid-ask spread is not leaked, which means large transactions will not be able to influence the market as much.

For data inference tasks, categorical data

Given \(\geq 2\) points, we can then start creating interpolations for missing data.

See polynomial interpolation

nearest neighbor method and data interpolation

you can think of nearest neighbor method as piecewise-constant interpolation

MAGIC

initialize a symmetric, positive definite matrix \(Q\). Then, run the update expressions given in the book.

optimize for a Secant Method equation which satisfies the Curvature Condition.