We have an expression:

\begin{equation} B = \frac{FL^{3}}{3EI} = \frac{N m^{3}}{3 p m^{4}} = \frac{Nm^{3}}{\frac{N}{m^{2}}m^{4}} = m \end{equation}

With constants:

• \(B\): \(m\), deflection at the point of force application
• \(F\): \(N\), force applied
• \(L\): \(m\), distance between fixed point and point of force application
• \(E\): \(p=\frac{N}{m^{2}}\), elastic modulus
• \(I\): \(m^{4}\), second moment of area

As per measured:

• \(B\): \(9.15 \cdot 10^{-4} m\)
• \(F\): \(20N\)
• \(L\): \(9.373 \cdot 10^{-2} m\)
• \(I\): \(1.37 \cdot 10^{-10} m^{4}\) = \(\frac{WH^{3}}{12}\) = \(\frac{(6.25 \cdot 10^{-3})(6.4 \cdot 10^{-3})^{3}}{12}\)

Theoretical:

For elements with large possible future state space, we can’t just iterate over all states to get a value function for every state, and THEN go about using the greedy policy to perform actions.

Therefore, we employ a technique called receding horizon planning: planning from the current state upwards to a maximum horizon \(d\), figure out what the best SINGLE action would be given that information for only this state, and then replan.

These are basically MDP methods but tweaked. We make some changes:

1. for everywhere that we need a state, we use a belief
2. to sample the next state given an action (random next step), we call our generative model to get a new observation, and call update(b,a,o) with our filter to propegate our belief forward
3. if we need an action-value, we use the one-step lookahead in POMDP:

\begin{equation} Q(b,a) = R(b,a)+\gamma \qty(\sum_{o}^{}P(o|b,a) U^{\Gamma}(update(b,a,o))) \end{equation}

where,

\begin{equation} R(b,a) = \sum_{s}^{} R(s,a)b(s) \end{equation}

The Open Voice Brain Model is a audio processing architecture proposed by Laguarta 2021 for audio/biomarker correlation work.

Here’s a fairly self-explanatory figure:

The model outputs an AD diagnoses as well as a longitudinal correlation with Memory, Mood, and Respiratory biomarkers.

This is then the embedding that they are proposing for use by other tasks.