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Detect collisions between each possible pair of trajectories, and derive a risk estimate based on the overall chance of collision.
Detect collisions between each possible pair of trajectories, and derive a risk estimate based on the overall chance of collision. .
The next step is to calculate the correlation between each possible pair of trajectories, resulting in correlation values, where is the number of partials.
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Pairs of trajectories which lead to an unavoidable collision are penalized in the matching process, and as a result safe trajectories are always considered to be more likely than hazardous ones.
The alignment is performed using pairs of trajectories acquired simultaneously with two labeled proteins: Abp1-mCherry serving as a reference, and a protein of interest tagged with GFP.
Pairs of trajectories were further investigated to explore the coupled coordinated relationships between different temporal patterns based on the three dependency metrics in Section 2.5.
A similarity measure was performed on all pairs of trajectories using the Levenshtein Edit Distance (LED) [ 32], which enables comparison of chains of characters of different lengths using identical cost operations.
Because insulin resistance is highly correlated with current BMI, we specifically compared risk factors within pairs of trajectories with similar 14-year-old BMI (1 vs. 2, and 3 vs. 4) but different gradients (Table 3).
For this purpose we developed an algorithm that finds the translation, rotation and temporal shift minimizing the weighted mean square displacement between the time points of all pairs of trajectories, where the weights are the fluorescence intensities at each time point (see 'Materials and methods').
Each alignment was computed using 100 pairs of virtual trajectories each of which was generated with σ p = 16 nm, for the trajectory of the target protein, and σ r = 19 nm, for the trajectory of the reference protein.
Figure 7 shows pairs of flux trajectories of several metabolic processes included in the model, where the large green and red dots respectively represent the wild-type phenotype and the LXR activated phenotype.
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