## 2 Materials and Methods
### Data Acquisition and Signal Processing  
Walking tests of 9 meters long (4.5-meters-long for F.) in an open area are performed by the three AT patients, while 8-meter-long walking tests in a hallway are performed by healthy subjects. A network of 13 wearable lightweight sensors of the Movit System G1 is used. The sensors are located on the principal body parts (head, Arm, forearm, chest, hip, thigh, leg and foot). Further details are reported hereafter.  
* Head: the sensor is centered on the upper half of the head front (parallel to the coronal plane);
* Arm: the sensor is located near the biceps brachii, oriented to the back (parallel to the coronal plane) [arm sensor position is relative to the body standing in the T position, with palm in parallel with the transverse plane];
* Forearm: the sensor is located on the lower forearm, oriented to the top (parallel to the transverse plane) [forearm sensor position is relative to the body standing in the T position, with palm in parallel with the transverse plane];
* Chest: the sensor is centered between the shoulder blades on the back (parallel to the coronal plane);
* Hip: the sensor is located on the back of the hip line (parallel to the coronal plane);
* Thigh: the sensor is located on the upper thigh, oriented to the outside (parallel to the median plane);
* Leg: the sensor is located under the calf thigh,h oriented to the outside (parallel to the median plane); and
* Foot: the sensor is located at the middle of the back of the foot (parallel to the transverse plane).  
The temporal analysis concerns one portion of gaits in the middle of the straight path. The sequence of time instants corresponding to the right heel strike, left toe off, left heel strike, and right toe off fortwo subsequent gaits is derived using an ad hoc extraction algorithm processing the acquisitions provided by the aforementioned sensor system (see Figure 3 for details). Data from three different measurement sessions are collected for each healthy subject (and then the mean values for each quantity involved in the computation of the indices are derived) and from one single measurement session for the pathological subjects.  
Figure 3: Flow chart. The wearable wireless sensors start to acquire and record the movement data in their internal memory with a sample rate of 200 Hz after the recording button is pressed on the userinterface of the Motion Studio software. The movement data (_c_sv file) for each sensor are downloaded using the Motion Studio software by connecting all the sensors to the PC via the USB cable. The data file contains: device name, bone name, timestamp, 3-axis accelerometer data in unit \"g\", 3-axis gyroscope data in unit \"dps\", accelerometer/gyroscope range, and sample rate. The sensor data file is loaded in the Motion Analyzer software for data fusion and processing to generate the time instants of the heel strike and toe off for the left and right feet, in addition to the anatomical angles. The aforementioned information coming from data processing is loaded in a dedicated MATLAB algorithm that recognizes the time instants for the gait cycle and the adjoint gait cycle subphases, involved in the computation of the \(\Phi\)-bonacci gait number.