Mm
This page is still under construction…
Recent posts
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The Phase Space Formulation (Part I)
In the first of two expository posts, we will discuss the connection between classical and quantum mechanics through the what is known as the phase space formulation. Specifically, we will focus on the Weyl-Wigner transform and introduce an analogue of the Poisson bracket used in classical mechanics. Furthermore, we briefly discuss how the theory depends on the parameter $\hbar$, introducing the notion of deformation quantization... -
A Geometric Interpretation of Linear Sketching
Consider a data stream $\{q_i\}_{i=1}^{\infty}$ of elements $q_i$ each belonging to some finite set of outcomes $\mathcal{O} = \{o_1, \ldots, o_N\}$. Then at each moment $t$, one may define a count vector $\mathbf{x}(t) \in \R^N$ defined by \begin{equation*} x_n(t) = \abs{\{i \leq t \mid q_i = o_n\}}. \end{equation*} The count sketch structure allows one to produce a good approximation to $\mathbf{x}(t)$, referred to as a sketch, using space sublinear in $t$. We describe the structure from a different, but equivalent, perspective than discussed in the original document introducing the sketching algorithm... -
Differential Forms and Foliations
This post is somewhat of a rigorous extension to Dan Piponi’s document on an intuitive visualization of differential forms... -
Solmization
In this short post I describe briefly some ways to visualize pitch perception, tuning and temperaments, and speculate on how the process of solmization occurs...