power utility, or isoelastic utility, is a financial econometric is a utility that results absolute, constant relative risk aversion. i.e.: you tell me how risk averse you are exogenously, I tell you how much utility some consumption is.

constituents

• some relative risk coefficient \(\gamma \in (0,1)\), higher more risk averse
• consumption of some asset \(C\)

requirements

Utility \(U( C)\) is defined by:

\begin{equation} U( C) = \frac{c^{1-\gamma}-1}{1-\gamma} \end{equation}

additional information

As you can see, the higher \(\gamma\), the lower utility some consumption brings.

a predicate or a property is a function whose range is true/false.

a relation is a property whose domain is a set of \(k\) tuples, which we call a $k$-ary relation.

We use interrupts to implement preemption, “preempting” threads in order to swap on another thread to CPU. This enables scheduling to happen.

preempting into a brand new thread

IMPORTANT: because interrupts are disabled at the beginning of the interrupt handler, and re-enabled by the end, new threads (which starts not at the interrupt handle) will not re-enable interrupts.

void interrupt_handler() {
    /* disables interupts, automatically by timer handler */

    // future spawns start here
    context_switch(...);

    /* enables interupts, automatically by timer handler */
}

void threadfunc_wrapper() {
    // manually enable interrupts before first run
    intr_enable(true);
    // start thread's actual business
    threadfunc();
}

For for instance, we need to figure a \(w\) such that:

\begin{equation} f = w^{\top}\mqty[f_1 \\ \dots\\f_{N}] \end{equation}

where weight \(w \in \triangle_{N}\).

To do this, we essentially infer the weighting scheme by asking “do you like system \(a\) or system \(b\)”.

1. first, we collect a series of design variables \((a_1, a_2, a_3 …)\) and \((b_1, b_2, b_3…)\) and we ask “which one do you like better”
2. say our user WLOG chose \(b\) over \(a\)
3. so we want to design a \(w\) such that \(w^{\top} a < w^{\top} b\)
4. meaning, we solve for a \(w\) such that…

\begin{align} \min_{w}&\ \sum_{i=1}^{n} (a_{i}-b_{i})w^{\top} \\ \text{such that}&\ \bold{1}^{\top} w = 1 \\ &\ w \geq 0 \end{align}

Goal: minimize cognitive load for the audience to communicate your ideas. Running examples tend to be good helpful for people.

resist the urge to tell people too much

reasonable checklist

• time
• prior knowledge
• av constraints

notice: unrelated text could be subdued.

Mykel’s Research Tips

1. don’t jump directly to an outline (open with something)
2. number the slides
3. try to have some humor

Some techniques

• To emphasize a single idea, put them in isolation in a single sentence
• Introduce naive solutions, then show how your solution is better
• Iteratively build up the problem while showing what’s hard