**7. Uncertainty and accuracy of mDFA computation**

### **7.1. Physics/mathematics**

Readers of this article might have questions about the uncertainty and accuracy when it comes to the acquisition of the data points.

We must identify all R-peaks (R-peak within a single heartbeat of EKG trace) to construct a heartbeat-interval time series. Firstly, we put a red-mark sign on top of each and every R-peak. Unfortunately, our computer does miss some R-peaks due to the movement of subjects (animals). There are two major reasons for that. One is inevitable drift of baseline of EKG trace. The other is electric-originated or muscle-movement-originated spike-like noises. Therefore, secondly in our study, we always check/repair each and every R-peak by eyes on a PC screen. This is NOT easy tasks but must-do tasks for us; we decided so in the beginning of


**Figure 15.** mDFA results during **a** 13-h overseas flight.

**Figure 14** shows two examples of iPod-mDFA screen view. This might give convincing evidence for the idea that 'stressfulness decreases SI'. We would like to emphasise that iPod-

In conclusion, stress decreases SI down to a lower value. We would like to emphasise that three examples, SI = 0.64, and SI = 0.53, SI = 0.77, are great results of iPod-mDFA gadget, and read-out time after 2000 heartbeat detections is only 1–2 s. All SI monitoring were instanta-

A volunteer (a male aged 66) travelled by air from the Narita-Tokyo Airport to the Washington Dulles International Airport in order to attend a conference held in the USA. Using the iPod device, we recorded his EKGs and computed the scaling exponents as shown in **Figure 15**. Twenty-four SI measurements during the flight were documented and plotted, from which we found that mDFA accomplished understandable results similar to that

We confirmed that the SI values can represent the internal world of the subject (see **Figure 15**). For example, when the subject was at an aroused state such as in the waiting lounge (see 1 in **Figure 15**), watching an exciting documentary (note: highly personalised expression), and preparing for landing (see 24 in **Figure 15**), the SI is near 1.0. In turn, when watching a movie which has an emotional involvement (note: highly personalised expression), the heartbeat of subject shows a lower SI values (see 18–20 in **Figure 15**). Finally, when the subject is at asleep condition,

In conclusion, a happy life could fundamentally guarantee a healthy exponent. Anxiety and stress lowered the scaling exponent. mDFA might reflect psychological and physical internal bodily state. mDFA might look at the internal state through the heart. The heart is the window

Readers of this article might have questions about the uncertainty and accuracy when it comes

We must identify all R-peaks (R-peak within a single heartbeat of EKG trace) to construct a heartbeat-interval time series. Firstly, we put a red-mark sign on top of each and every R-peak. Unfortunately, our computer does miss some R-peaks due to the movement of subjects (animals). There are two major reasons for that. One is inevitable drift of baseline of EKG trace. The other is electric-originated or muscle-movement-originated spike-like noises. Therefore, secondly in our study, we always check/repair each and every R-peak by eyes on a PC screen. This is NOT easy tasks but must-do tasks for us; we decided so in the beginning of

mDFA is beneficial more than we have expected.

the SI decreases significantly (see 7–9 in **Figure 15**).

**7. Uncertainty and accuracy of mDFA computation**

**6. Case study 2: overseas flight**

18 Time Series Analysis and Applications

shown in **Figure 13**.

of the mind.

**7.1. Physics/mathematics**

to the acquisition of the data points.

neously computed by iPod-mDFA system as shown in **Figure 13**.

this study. As a result, our time series obtained from any subjects are a 100% accurate. It is a perfectly captured R-R interval data: prematured ventricular contractions, atrial fibrillations, whatever it is.

mDFA computes SI values. For a given time series data, mDFA returns only one SI. If you repeat this procedure for a given time series, you get an exactly the same SI value. Readers can imagine an artificial time series that is, for example, a white noise-like fluctuation data, it gives a scaling exponent of 0.5. A random-walk-like time series data give a scaling exponent of 1.5. However, 1/f time series (SI = 1.0) is very difficult to make artificially, definitely because 1/f-spectrum-like fluctuation is an outcome from natural dynamic phenomena. In short, a structure of a time series gives a single SI. It is mathematically accurate.
