Kolomogorov Complexity is a “universal theory of information”. “how much information is contained in a string”

The Kolomogorov Complexity of a string \(x\) is the length of the shortest description, \(|d(x)|\)

information as description

Key idea: the more we can compress a string, the more information it contains. The amount of information in a string \(x\) is the length of the shortest description of \(x\).

aside

For some \((M,w)\), we are about to write short strings of it; how do we encode it?

Where:

\begin{equation} ||X-Y||_{\infty} = \max \{| x_{i} - y_{i} |, x \in X, y \in Y} \} \end{equation}

Want mechanics? No. You get energy.

First, recall the stationary-action principle. To define a system in Lagrangian Mechanics, we define a smooth function \(L\), called the “Lagrangian”, and some configuration space (axis) \(M\).

By convention, \(L=T-V\). \(T\) is the kinetic energy in the system, and \(V\) is the potential energy in the system.

By the stationary-action principle, then, we require \(L\) to remain at a critical point (max, min, saddle.) This fact allows us to calculate the equations of motion by hold \(L\) at such a point, and evolving the \((T,V)\) pair to remain at that point.

DOI: 10.3389/fcomp.2021.624694

One-Liner

Proposed a large multimodal approach to embed auditory info + biomarkers for baseline classification.

Novelty

Developed a massively multimodal audio-to-embedding correlation system that maps audio to biomarker information collected (mood, memory, respiratory) and demonstrated its ability to discriminate cough results for COVID. (they were looking for AD; whoopsies)

Notable Methods

• Developed a feature extraction model for AD detection named Open Voice Brain Model
• Collected a dataset on people coughing and correlated it with biomarkers

Key Figs

Figure 2

This is MULTI-MODAL as heck