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A complete study of the modulation equations for the Benjamin–Bona–Mahony equation is performed. In particular, the boundary between the hyperbolic and elliptic regions of the modulation equations is found. When the wave amplitude is small, this boundary is approximately defined by , where k is the wave number. This particular value corresponds to the inflection point of the linear...
We leveraged IDH wild-type glioblastomas, derivative neurospheres, and single-cell gene expression profiles to define three tumor-intrinsic transcriptional subtypes designated as proneural, mesenchymal, and classical. Transcriptomic subtype multiplicity correlated with increased intratumoral heterogeneity and presence of tumor microenvironment. In silico cell sorting identified macrophages/microglia,...
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