Red squares denote observations with the target on ACIS-S and blue disks denote observations with the target on ACIS-I.
Red triangles indicate the locations of major quaternary volcanoes (Figure 1); white dots denote observation sites.
where ∆z k and ∆θ k denote observation residual and heading change; φ k is the angle between the observation vector z k and the state estimate vector, while ϕk - 1 is the angle between the state estimate vector and the state estimate vector ; and the superscript T denotes transpose.
We denote observation or measurement data,, for at time as: (1) where is the observation noise at time for -th gene.
Additionally, the outputs scores matrix U is linearly regressed against the inputs scores matrix T: (3c) where B holds the regression coefficients determined by minimising the residuals E U. Finally, the explained variance in target data (which in our case is flux data, R) by the model is given by the following equation: (4) with indexes i and j denoting observation and flux indexes respectively.
for, where and denote the observations and noise components, respectively.
Given consecutive video frames, let denote the observations (silhouette) from that frame.
For the moment, denoting the observations, (y_{t},t=1,...,T), we will consider the decomposition begin{aligned} y_{t} =P_{t}+S_{t}+I_{t}, end{aligned} (2.1 respectively the permanent, seasonal and irregular components but on TICD we will use another decomposition.
Given gene expression time series data over m genes at n time points, we denote the observations as the matrix, where, the column vector of expression levels for each of the m genes at time point j.
○ denotes state and □ denotes observation variable.
