Hong Kong

Banff NP

Pinnacles NP

Yosemite NP

Singapore

NYC

Shanghai

Grand Canyon NP

We need to figure out good aways of modeling/representing uncertainty.

unifying principle

• data: samples / distribution
• representation: simplify / keep what matters
• control: convex / gradient / MPC

Different things requires different techniques but broadly the structure.

contributions

• factor models of covariance
• 1d projections of distributions and distribution shaping
• informational representation: conditioning + shrinking horizon reoptimization

factor model

Suppose someone hands you a model for returns:

\begin{equation} r \approx F_{\text{base}} s + \varepsilon, s \sim \mathcal{N}\qty(0, \Omega_{\text{base}}), \epsilon \sim \mathcal{N}\qty(0, D_{\text{base}}) \end{equation}

Igneous Rocks

right and left lateral

right lateral

if the side opposite you move to the right

left lateral

if the side opposite you move to the lfet

Igneous Rocks

location

Volcanic Rocks

“extrusive rock.”

Rocks that solidifed upon eruptive in a volcano. fast cooling, small crystals

Plutonic Rocks

Rocks that solidified underground

“Intrusive rocks.”

Intrusive locks slowly cool and crystallize inside the earth. slow cooling, large crystals

plumbing network

dikes, etc. lubing between

Bowen’s Reaction Series

Since different minerals melt at different tempreatures (as in above), we have a…

Melting Point

REREMEMBERRR

• (denser) mafic rocks crystalize at higher temperatures
• (lighter) felsic rocks crystalize at lower temperaturers

Partial Melting

Partial Melting! This results in the felsic runoff first, and then mafic runoff.

Spreeading centers are ultramafic, which emans that this process mostyl contirbutes a dyversity of tho utputs.

“will it flow or will it blow?”

flow

Mafic magmas is low in sillica and hot; this results in low viscocity, runny magma, low gass content (gas rises faster than magma).