## 3 Results  
### Results of Periodicity Intensity in the Homes of Older Adults  
We first examine and discuss the results of periodicity intensity calculation on sensor data from the homes of older citizens. The output from periodicity detection on data from the NEX project participants was calculated in real-time and made available online. These visualisations were used in debriefings with participants by their clinical carers and project researchers and supported by a short-form informative YouTube video to explain the graphs and to ensure the participants understood how to interpret them.  
Three example outputs are shown in Figure 2, where the values in each graph are normalised to a [0, 1] range as actual periodicity intensity values will vary considerably across participants, and each participant is interested in the relative changes in their own graph rather than in absolute values or in comparison to others. Following experimentation to determine the best parameters to use for each of the graphs, the frequency for periodicity calculation is 24 h, reflecting interest in the circadian rhythm. The window is 7 days, thus eliminating changes between weekends/weekdays, and the overlap or stride length is 1 h, making the computation fast. Each graph represents a periodicity intensity over a 3-month period.  
The first graph in Figure 2 shows a participant with a relatively stable and regular lifestyle and only small variations in periodicity intensity. The gradual rise in periodicity intensity towards the end of the 3 months shows a slight improvement in lifestyle regularity, and there are no major perturbations throughout the 3 months. This participant is known to have a healthy, regular and comfortable lifestyle.  
In the second graph in Figure 2, we see a participant with much more ups-and-downs in lifestyle. The increase in lifestyle regularity in the middle of the period corresponds to a constant presence at home due to catching COVID-19, self-isolating and recovering with regular behaviour and habits. For this period, the volume of sensor activations was much lower than in the earlier period as the participant was not doing much at home except spending time in bed, but it is not the number of sensor activations but their timing that contributes to periodicity intensity. Towards the end of the 3-month monitoring period,  
Figure 2: Normalised periodicity intensity from three sample ARC trial participants for a three-month duration. The frequency is 24 h, the window size is 7 days, and the window shift is 1 h. \(x\)-axis values span 3 months, and \(y\)-axis values have been normalised to the range 0 to 1.  
this participant moved out of the home to recuperate with family, hence the flatlining at the end.  
The third graph in Figure 2 shows a participant who also caught COVID-19 during the early part of the 3-month recording period and then soon afterwards also moved out of their home to recuperate with family, which was indicated by the flatlining in the graph. The slight rise in periodicity intensity during the second half of the 3 months indicates family calling to the home on a semi-regular basis to collect mail and check it for security.  
The result of this analysis is a form of self-monitoring of the individual but with deeper insights into overall behaviour and activities. This may be used to promote or sustain long-term behaviour change as the subject seeks to maintain high levels of rhythmicity in their lives.