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Tissue boundaries were found using SPM5 segmentation algorithm and the SUIT toolbox [28,29].
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The outer boundary is found using local kurtosis which has near-zero values at the boundary.
A similar location for this boundary was found using mtDNA (Haig et al. 2004a; Barrowclough et al. 2005).
These functions were found using the boundary conditions, shown below in equation set (35), comparing the coefficients and solving simultaneous equations.
Many applied problems of mathematical physics require the study of spectral problems with a polynomial appearance of a parameter in the boundary conditions [1 3], while, in corresponding inverse problems, the unknown coefficients appearing in the equation and boundary conditions are found using known spectra [4 6].
Assuming that the core/shell piezoelectric structure exhibits spherically-hexagonal anisotropy, an exact solution is obtained through the eigenvalue decomposition method and the analytical expressions of the electroelastic fields are found using appropriate boundary and continuity conditions.
The boundary of the object enclosed by the ROI was found using two morphological operators; namely erosion and dilation.
Finally, geodesic active contours use the probability map of the tumor to shrink the ROI until optimal tumor boundaries are found.
Use of the alternative boundary was observed (i.e. alternative splicing) for 4 out of 15 cases for which multiple spliced cDNA transcripts were available, and an additional out-of-frame 3' boundary was found to have been used in a single cDNA for one additional case.
The final ILM boundary is then found using piecewise cubic spline interpolation.
Additional evidence of Zr grain boundary segregation was found by using high-angle annular dark-field TEM imaging (see Supplementary Fig. 1 for details).
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