## 2 Materials and Methods
### Entropy Measures  
The FEn was proposed as a measure of time-series complexity, providing the conditional probability that two vectors recognized as similar for \(m\) samples remain similar for the next \(m+1\) samples as well [16]. Given a \(N\)-length time-series \(\boldsymbol{x}(i)\) and an embedding dimension \(m\), (\(N-m\)) embedding vectors are constructed as follows:  
\[\boldsymbol{z}_{i}^{m}=\left[x(i),x(i+1),\ldots,x(i+m-1)\right]-x_{0}(i)\quad i =1,\ldots,N-m+1 \tag{1}\]  
where \(x_{0}(i)\) is a scalar value representing the baseline:  
\[x_{0}(i)=\frac{1}{m}\sum_{j=0}^{m-1}x(i+j) \tag{2}\]  
Each embedding vector \(\boldsymbol{z}_{i}^{m}\) contains \(m\) consecutive samples of the original time-series \(\boldsymbol{x}(i)\) and the distance value \(d_{i,j}\) is computed as the distance between \(\boldsymbol{z}_{i}^{m}\) and \(\boldsymbol{z}_{j}^{m}\), using the Chebyshev metric [16]:  
\[d_{i,j}=max|\boldsymbol{z}^{m}(i)-\boldsymbol{z}^{m}(j)|\quad i\geq 1\quad j \leq N-m+1 \tag{3}\]  
The degree of similarity \(\Gamma_{i,j}^{m}\) between \(\boldsymbol{z}_{i}\) and \(\boldsymbol{z}_{j}\) is derived through an exponential function \(\psi(d_{i,j},r,n)\):  
\[\Gamma_{i,j}^{m}=\psi(d_{i,j},r,n)=\exp\left(-\frac{(d_{i,j})^{n}}{r}\right) \tag{4}\]  
Through the \(\Gamma_{i,j}^{m}\), the \(\Phi_{m}(r,n)\) is defined as follows:  
\[\Phi_{m}(r,n)=\frac{1}{N-m}\sum_{i=1}^{N-m}\left(\frac{1}{N-m-1}\sum_{j=1}^{N- m}\Gamma_{i,j}^{m}\right)\quad j\
eq i \tag{5}\]  
Figure 2: Myo armband worn by a representative subject. Then, when constructing the embedding vectors for an embedding dimension of \(m+1\), the \(\Phi_{m+1}(r,n)\) function is derived according to (5) and the FEn is finally obtained as the natural logarithm of the ratio between \(\Phi_{m}(r,n)\) and \(\Phi_{m+1}(r,n)\):  
\[FEn(m,r,n)=\ln\Phi_{m}(r,n)-\ln\Phi_{m+1}(r,n) \tag{6}\]  
It is clear from (1) and (4) that the FEn depends upon three parameters: the embedding dimension \(m\), which defines the lengths of the embedding vectors to be compared, and the width and the gradient of the \(\psi(\cdot)\) function boundary [16], i.e., \(r\) and \(n\). The main difference between FEn and more classical time-series complexity measures (approximate and sample entropy) is the function used for assessing similarity, which in the latter case is the Heaviside step function [27] while for the FEn it is the exponential function (4). The use of (4) allows one to avoid abrupt changes in similarity, due to the continuous property of the exponential, ensuring the maximum degree of self-similarity, since the exponential function is convex [16]. The above-mentioned entropy measures are all based on evaluating the distances between subseries, using a certain distance metric. In more recent years, different measures for evaluating time-series complexity have been proposed, relying on mappings of ordinal or probability patterns of neighboring points [29; 30]. In particular, the PEn [30] uses ordinal descriptors instead of distance metrics. Considering a \(N\)-length time series \(\boldsymbol{x}(i)\), its embedding representation has the following form:  
\[\boldsymbol{z}_{j}^{d,\tau}=\left[x(j),x(j+\tau),\ldots,x(j+(d-1)\tau)\right] \quad j=1,2,\ldots,(N-(d-1)\tau) \tag{7}\]  
where \(d\) is the embedding dimension and must be \(\geq 2\), and \(\tau\in\mathbb{N}\) is the embedding delay--i.e., the time separation between time-series samples--and is commonly set to \(1\). The elements of each subseries of length \(d\) are mapped into an ordinal pattern, based on their ranks. For instance, by choosing \(d=3\) and with an embedding vector equal to \(\left(7,\quad 2,\quad 9\right)\), its ordinal pattern results \(\left(1,\quad 0,\quad 2\right)\).