## 2 Materials and Methods
### The Algorithm for the JT/ST Algebraic Relationship  
The duration of the JT interval and the ST amplitude is continuously and synchronously recorded throughout the experiment and denoted as vectors \(x=(x_{1},x_{2},\ldots,x_{n})\) and \(y=(y_{1},y_{2},\ldots,y_{n})\) accordingly; where \(n\) is the total number of heartbeats recorded during the whole experiment. The algebraic relationship between time series \(x\) and \(y\) is reconstructed using the algorithm presented in [12]. This algorithm comprises three basic parts.  
Step #1. Six elements \(x_{k-\delta}\), \(x_{k}\), \(x_{k+\delta}\), \(y_{k-\delta}\), \(y_{k}\), \(y_{k+\delta}\) are mapped into a two-dimensional perfect matrix of Lagrange differences (the concept of perfect matrices of Lagrange differences is introduced in [12], where \(\delta\) is the time lag; \(k=(1+\delta),(2+\delta),\ldots,(n-\delta)\). Altogether, 18 different perfect matrices of Lagrange differences exist [8]. For example, the first perfect matrix of Lagrange differences \(L^{(1)}_{\delta,k}=\left[\begin{array}{cc}x_{k}&x_{k+\delta}-y_{k+\delta}\\ x_{k-\delta}-y_{k-\delta}&y_{k}\end{array}\right]\) is used in [13]. In general, one could choose one of the 18 different matrices in accordance with the optimal architecture of the matrix (the optimality of the matrix architecture is defined in the further steps of the algorithm).  
Step #2. The sequence of matrices \(L^{(\beta)}_{\delta,k}\) is transformed into a scalar sequence using a mapping \(\mathcal{F}:\mathbb{R}^{2\times 2}\rightarrow\mathbb{R}^{1}\), where \(\beta\in\{1,2,\ldots,18\}\). The mapping \(\mathcal{F}\) is defined as the maximal modulus of the two eigenvalues of \(L^{(\beta)}_{\delta,k}\) in [12] and [13]. We generalize the mapping by setting \(\mathcal{F}=\|L^{(\beta)}_{\delta,k}\|\) in this paper. The norm of the matrix \(\|A\|=sup_{z\in\mathbb{R}^{2}}\left(\frac{\|A\|_{2}}{\|z\|_{2}}\right)=sup_{z,\|z\|_{2}=1}(\|Az\|_{2})\geq max(|\lambda_{1}|,|\lambda_{2}|)\) where \(\lambda_{1}\) and \(\lambda_{2}\) are two eigenvalues of \(A\), and 2-norm is the Euclidian norm [17]. Note that the inequality becomes equality when matrix is symmetric. Therefore, we increase the sensitivity of the method by replacing the maximal modulus of the eigenvalues with the norm in the definition of the mapping.  
Step #3. Finally, internal and external smoothing is applied for the scalar sequence \(\|L_{\delta,k}^{(\beta)}\|\). If the radius of the internal smoothing is denoted by \(R_{i}\) and the radius of the external smoothing is denoted by \(R_{e}\), then the smoothed sequence depicting the algebraic relationship between time series \(x\) and \(y\) reads as follows:  
\[s_{k}(R_{i},R_{e},\beta)=\frac{1}{R_{i}(2R_{e}+1)}\sum_{j=k-R_{e}}^{k+R_{e}} \sum_{\delta=1}^{R_{i}}\|L_{\delta,j}^{(\beta)}\| \tag{1}\]  
where \(k=(1+R_{i}+R_{e}),(2+R_{i}+R_{e}),\ldots,(n-R_{i}-R_{e})\). A well-posed optimization problem in respect of the smoothing parameters is formulated in [8] for the whole cohort of persons resulting into \(R_{i}=3\), \(R_{e}=4\) and \(\beta=1\). These values of the parameters are kept fixed in this paper as well. All further numerical computations are based on \(s_{k}(3,4,1)\).