# Christian Rohrsen

View Profile## Nonlinearity is present the fast timescales

After performing EMD to 6 fly traces of 20000 data points (that is 1000 sec flight) for each group (tntXwtb; c105;c232>tnt; c105;c232Xwtb). This data size was chosen to reduce computing time of the SMAP procedure. The EMD decomposes the trace into different time scales in nonstationary data. It seems that the nonlinear behavior occurs at the first IMF (the fastest time scale) and a bit in the second IMF. The potential conclusion to this is that the behavior of the the fly is only unpredictable at the fast movements whereas slow movements are very predictable. Nevertheless, to be cautious it could be that this fastest timescale is just noise, and that this noise is nonlinear. I would say that there is no difference at any time scale between groups (pay attention to the different ranges in the Y-axes), so the ring neurons R1, R3, R4d do not have any effect.

As a groundtruth I have used the same analysis pipeline for the traces in the uniform arena from Maye et al. 2007. Here the effect is even more pronounced at the fastest time scales. So I will conclude that this is real fly behavior and not noise that is shared among both setups: the Ping pong ball machine and the torquemeter.In order to gain more insights into the underlying flight structure I took one random flight trace to explain a few observations. The x-axis is the theta (that actually goes from 0-4 in steps of 0.2 and therefore we see the 21 points), in the y-axis is the correlation of the prediction to groundtruth. We see that IMF has a bigger slope, but not only that, also that its prediction correlation is around 0.88, whereas lower timescales prediction is basically perfect. That is, fast time scales are not only more nonlinear but also less unpredictable. This pattern is repeated in every fly measured

To have an impression of how these IMF resultant traces look like: IMF1, IMF2 and IMF8

## Just creating cartesian traces from polar coordinates

This is for the sake of playing and curiosity. I made out of these two traces a modelling of their flying trace in a 2D world. Direction is right wing amplitude – left wing amplitude and distance flown is dependent on the sum of both (more amplitude of both, more forward thrust). Funny enough, the second one looks kind of fractal, which is characteristic of chaotic behaviors. If there is any comment to add to this new visualization, all ears!

## EMD with ICA to one sample of torque trace

Trace segment from Maye et al. 2007 in the uniform arena

Trace after filtering by selecting the first 8 IMFs (intrinsic mode functions) from EMD (empirical mode decomposition). Since the signal should be quite clean I do not take out the first IMFs. The last IMFs, however, are too slow and change the baseline to much

Some examples of the IMFs obtained from EMD:

Since this is separating behavior adapting to the data intrinsic time scales I am now thinking of analysing with the SMAP algorithm to see if the behavior is more or less nonlinear at certain time scales.

In addition, I have thought of using ICA (Independent component analysis), that is an algorithm famous for the blind source separation problem by extracting the most independent signals from the input signals (in this case the IMFs which are different time scales of the behavior). So the ICs should consist of mixes of different time scales that are correlated together and thus belong (but not necessarily) to the same action/movement module/… Here a few ICs (from 10). My idea is that muscles might coordinate independently between ICs but coordinated within ICs. However to prove that is not that easy I guess

## quality test before strokelitude experiments

Some traces from this week just so that you have an idea how do they look like. To me they are not the optimal traces I expected. But one can see some signal there. I will start the screen hoping to get enough good traces without too much work.

what do you think is the best quality control for accepting a trace for the analysis or not. I was thinking the 3D mapping gives a good hint but without quantification.

In addition I was writting to Andi Straw to solve the issue of running two cameras in the same computers, but now answer

## Better analysis of slope dependence on flight length and further insights in the SMAP code

This is another way of showing how the slope of the SMAP analysis varies with length. I have choped the time series in 4 chunks and saw what was the slope for the chunks and for the whole time series. I think this is the best statistical way of doing it, it should not depend on what line was tested. I cannot see any effect.

Here below is just to show what I found out in the code. What I thought that theta was controlling for nonlinearity in the model, for me it seems rather a control for under- overfitting in the model. So I might need to read the paper and see what do they say, and if it is the same as what I found out in the code.

## Do not agree with Sathish?

So this is the final graph assuming that 20Hz is the sampling rate. Sathish was not sure what it was and he said he will check.

To have a better overview how the length of the flight compares with the slope obtained from the SMAP. There is no big correlation whatsoever with around 100 flies. Sathish found this in his thesis with data from seventy something WTB, but to me it seems like an anecdotal result.

Here the same as above, just for showing the fit line.

## Thornlabs spectrometer working!

After getting a new spectrometer, we confirmed that the first one was faulty. Comparison of old (1st and 3rd measures) and new (2nd and 4th) spectrometer. Now much more sensitive and the right spectrum measured for the green LED present in the spectrometer itself and for the light comming out of the light guide coupled with the red LED (whose spectrum does not seem to change after travelling through the light guide)

## Sathish data

I have analyzed the c105+c232 > tnt data from Sathish. There are a total of 43 flies, although many of them only flew for a few minutes, and therefore should be discarded. Below all of the individual fly scores. I need to analyse now the other groups. This is btw the modified data set, whatever that means for Sathish.

This is a video of the projection from the torque data from Maye et al. 2007. The spikes are not that well sorted in this case as in the Strokelitude. I guess this is because the spikes do not look so smooth.

## Recurrence quantitative analysis

This is an example of a recurrence plot analysis. In the first graph is shown in single point in time in the optimal embedding dimension and the distance to the other points. For the recurrence plot analysis it is needed to put a threshold to make it binary. This is the second graph. From this second graph one can count many parameters like determinism, laminarity and so on. From what I see, the plots from the Strokelitude as well as Bjoern´s flight simulator in Maye et al 2007 show similar pattern (kind of crosses with vertical and horizontal lines).

This is a measure of the Recurrence Quantitative Analysis of different groups. Recurrence threshold is a tricky and to some extent subjective measure, so this is why I tried two different ones.

DET: recurrence points that form a diagonal line of minimal length, the more diagonal, the more deterministic.

LMAX: Max diagonal line length or divergence. Sometimes considered as an estimator of max. Lyapunov exponent

ENT: Shannon entropy reflects the complexity of the system

TND: info about stationarity (trend)

LAM: Laminarity is related to laminar phases in the system (intermittency). It is tallied as vertical lines over a threshold.

TT: Trapping time, measuring the average length of vertical lines. Related to laminarity.

Automat

Openloop

Uniform