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No abstract

We consider an exclusion process, with particles injected with rate α at the origin and removed with rate β at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of α = β = 1 the model was solved previously by Derrida et al. Here we extend the solution to general α, β. The phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation.

This study provides first clinical evidence for the implication of a "glioma stem cell" or "self-renewal" phenotype in treatment resistance of glioblastoma. Biologic mechanisms identified here to be relevant for resistance will guide future targeted therapies and respective marker development for individualized treatment and patient selection.