## 3 Results
### Results of Periodicity Intensity in _Call Movements_  
Our final in-depth discussion is of the periodicity intensity algorithm applied to accelerometer data from new-born calves. The 24 calves used in the calf movement study had different dates of birth, and their sensor data thus started on different dates. For the oldest calf (sensor ID 20714), the accelerometer data began on 2 nd March at 09:00, and for the youngest calf, the accelerometer data began on 5 April at 10:00. Though start dates varied, all calves in the herd were contributing accelerometer data by 5 th April. Thus it is from that date onwards that we obtain a picture of the full herd's periodicity. Of the 24 calves, 5 are considered outliers and did not contribute to the analysis of the overall herd because their collars had fallen off at some point during the data logging, and if reattached, it would have created a gap in the data, which would have impacted the calculation of periodicity intensity for a period of more than 2 weeks. The 19 remaining calves were used in the analysis. The graphs of periodicity intensity for individual calves can be seen in Figure 5, and their \(x\)-axes are time-aligned. For these, the periodicity frequency was set to 24 h, the window size was 7 days and the stride length or shift of the time-lagged overlapping windows was 15 min.  
Figure 5 shows the 24 individual periodicity intensity graphs, and the first 4 in the left column and the 3 rd in the right column were discarded for reasons mentioned earlier. The vertical green lines in the graph indicate the dates of disbudding, a process of the surgical removal of horn buds before the calves grow and cause danger to other calves and to the farmer [37].  
Looking across the set of 19 graphs, it is difficult to discern any coordinated pattern across the herd. When we generate a stacked graph of the time-aligned periodicity intensities in the same way as was performed for the student VLE accesses, we get the graph shown in Figure 6, where each colour represents periodicity intensity for a different calf.  
The staked line graph of periodicity intensities shows a peak at around the beginning of May followed by a clear drop in 24 h periodicity intensity across the herd, indicating a synchronous dis-improvement in herd welfare. This reached its low point after about 1 week, around 9 May and was followed by a return to better herd welfare, although not as high at around 2 May. Because of the 7-day windowing in our calculations, the drop-off, which reached its minimum point around 9 May, was most likely caused by a stressful or traumatic event at around 2 May, which is the time window during which the disbudding process took place.  
As with the use case of student learning habits from a VLE, we divided the calves into random sub-groups and plotted a stacked line graph for each sub-group. These show the same shape as the stacked line graph for the whole herd. Thus there is no artificial boost or trough from a sub-group of calves, and the pattern is generalised across the herd.  
The result of this analysis of periodicity intensity is similar to that from the analysis of student accesses to their VLE. We have individual feedback on a well-being indicator for each calf based on their movements with deeper insights into the well-being of the overall herd, and this is of interest to the farmer.  
Figure 5: Line graphs of calf periodicity intensities for each of the 24 calves. Frequency is 24 h, window size is 7 days and window shift is 15 min. The vertical green lines indicate the dates of disbudding.  
Figure 6: Stacked line chart of cumulative calf periodicity intensity from 19 of the 24 calves, from [31]. \(y\)-axis values have been normalised to the range 0 to 1.