A wavelet analysis on digital microstructure in microbumps

© 2015 IEEE. Heterogeneous three-dimensional system integration is the ultimate goal for packaging and integration, where materials are pushed to their physical limits. In this context, the microstructure of packaging materials, which exhibits a multi-scale nature, will be carefully designed and tightly controlled in both manufacturing and in-service conditions to ensure long-term reliability of the electronic products. A multi-level discrete wavelet transform using the haar wavelet is conducted on the dendritic structures, simulated with a phase field model, during solidification in microbumps with different sizes and geometries. The statistical data, e.g. the mean, standard deviation and energy, of the detail coefficients from the wavelet analysis reveal a wealthy of information on the features of the dendritic structure and its evolution during solidification at multiple resolutions. The size and geometry effects on the microstructure formed in the microbumps can thus be quantified by such data. Further studies using techniques such as principle component analysis and Radon transform can be conducted to evaluate the consistence of the result

Heat map of the real-time quantitative PCR (qRT-PCR) analysis results of PeDREB genes in leaves and roots under drought, low-temperature and high salinity treatments, with three biological and technical replicates.

<p>The expression levels of genes are presented using fold-change values transformed to log₂ format compared to controls. The log₂ (fold-change values) and the color scale are shown at the right of the heat map.</p

Comparison of group/subgroup size between moso bamboo, Arabidopsis and rice AP2/ERF families.

<p>The subclassification was by Nakano et al. (2006) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126657#pone.0126657.ref007" target="_blank">7</a>].</p

The ERF subfamily genes in moso bamboo.

<p>Note: The groups I to IV genes were DREB subfamily genes, the groups V, VI, VI-L, and VII to X genes were ERF subfamily genes.</p><p>The ERF subfamily genes in moso bamboo.</p

Ks and Ka/Ksvalue distributions of the AP2/ERF genes in the genomes of rice and moso bamboo viewed through the frequency distribution of relative Ks and Ka/Ks modes.

<p>Distribution of Ks and Ka/Ks values were obtained from orthologous gene-pairs (A and B) between the moso bamboo and rice genomes, and paralogous gene-pairs (C and D) in the moso bamboo genome. Ka/Ks = 1 indicates neutral selection, Ka/Ks > 1 indicates positive selection and Ka/Ks < 1 indicates purifying selection [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126657#pone.0126657.ref079" target="_blank">79</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126657#pone.0126657.ref080" target="_blank">80</a>].</p