# Thinks: Symbolic Dynamics for Categorising Rally Stage Wiggliness?

Many years ago, i had the privilege of attending a month long complex systems summer school organised by the Santa Fe Institute. One of the lecture series presented was by Michael Jordan and from it I remember a couple of really werful concepts, if not the detail. One was the Bayes Ball, and the other was symbolic dynamics.

I’ve briefly tinkered with a very simple symbolic dynamics representatio before in an attempt to come up with signatures for identifying different sorts of simple dynamics for summarisingdriver’s performance in rally stages (e.g. Detecting Features in Data Using Symbolic Coding and Regular Expression Pattern Matching) and I’ve started wondering again about whether the approach might also be useful in trying to capture something of the wiggliness of rally stage routes.

To this end, the following quote looks relevant, even if it does come from a paper on heart rate dynamics in rats:

Symbolic Dynamics

The symbolic dynamics method, proposed by Porta, aims to convert the CI and SAP series in a sequence of symbols and evaluates the dynamics of each three consecutive symbols (words). First, a procedure known as uniform quantization is applied to the CI or SAP series, where the full range of values is divided into six equal levels. Each quantization level is represented by a symbol (0 to 5) and all points within the same level will be assigned the same symbol. Next, sequences of three consecutive symbols (words) are evaluated and classified according to its variation pattern: zero variation (0V), one variation (1V), two like variations (2LV) or two unlike variations (2UV).

The 0V family comprises words where there is no variation between symbols, i.e., all symbols are equal. The sequences {0,0,0} and {3,3,3} are examples of sequences from this class. The 1V family represents words that have only one variation from one symbol to another, i.e. sequences with two consecutive equal symbols and one different. Examples of sequences of this family are {5,2,2} and {0,0,1}. The 2LV family is composed of words containing three different symbols but with the same variations direction, i.e. in ascending or descending order. Examples of sequences of this family are {1,2,5} and {3,2,1}. Lastly, 2UV family comprises sequences that form a peak or a valley, i.e. with two different variations, in opposite directions. The sequences {2,4,2} and {3,0,1} are examples of this family.

Once this classification is made for the entire series, the percentage of patterns classified in each family is used for analysis.

Silva, L.E.V., Geraldini, V.R., de Oliveira, B.P. et al. Comparison between spectral analysis and symbolic dynamics for heart rate variability analysis in the rat. Sci Rep 7, 8428 (2017). https://doi.org/10.1038/s41598-017-08888-w

So, something to play with there: three tuple sequences and the changes within them, which could perhaps be useful for identifying right-left-right / left-right-left sections in a route etc. Hmm…

## Author: Tony Hirst

I'm a Senior Lecturer at The Open University, with an interest in #opendata policy and practice, as well as general web tinkering...

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