Understanding cell types and mechanisms of dental growth is essential for reconstruction and engineering of teeth. Therefore, we investigated cellular composition of growing and non-growing mouse and human teeth. As a result, we report an unappreciated cellular complexity of the continuously-growing mouse incisor, which suggests a coherent model of cell dynamics enabling unarrested growth. This model relies on spatially-restricted stem, progenitor and differentiated populations in the epithelial and mesenchymal compartments underlying the coordinated expansion of two major branches of pulpal cells and diverse epithelial subtypes. Further comparisons of human and mouse teeth yield both parallelisms and differences in tissue heterogeneity and highlight the specifics behind growing and non-growing modes. Despite being similar at a coarse level, mouse and human teeth reveal molecular differences and species-specific cell subtypes suggesting possible evolutionary divergence. Overall, here we provide an atlas of human and mouse teeth with a focus on growth and differentiation.

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The relation between coherent risk measures, valuation bounds, and certain classes of portfolio optimization problems is established. One of the key results is that coherent risk measures are essentially equivalent to generalized arbitrage bounds, named "good deal bounds" by Cerny and Hodges (1999). The results are economically general in the sense that they work for any cash stream spaces, be it in dynamic trading settings, one-step models, or deterministic cash streams. They are also mathematically general as they work in (possibly infinitedimensional) linear spaces.The valuation theory presented seems to fill a gap between arbitrage valuation on the one hand and utility maximization (or equilibrium theory) on the other hand. "Coherent" valuation bounds strike a balance in that the bounds can be sharp enough to be useful in the practice of pricing and still be generic, i.e., somewhat independent of personal preferences, in the way many coherent risk measures are somewhat generic.