Background: Osterix and Runx2 are master genes that transcriptionally promote osteoblast differentiation. Results: Osterix and Runx2 cooperate to induce osteogenic genes by binding to promoters and interacting with each other. Conclusion: Osterix and Runx2 exhibit cooperation, subject to further regulation by MAPK signals, during osteogenesis. Significance: A network of interactions between transcription factors provides a circuit that drives the osteoblast differentiation program.

We present an area-preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1] 2 and range in a region included in the unit-radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1] 2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi-Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.

We present a method for uniformly sampling points inside the projection of a spherical cap onto a plane through the sphere's center. To achieve this, we devise two novel area‐preserving mappings from the unit square to this projection, which is often an ellipse but generally has a more complex shape. Our maps allow for low‐variance rendering of direct illumination from finite and infinite (e.g. sun‐like) spherical light sources by sampling their projected solid angle in a stratified manner. We discuss the practical implementation of our maps and show significant quality improvement over traditional uniform spherical cap sampling in a production renderer.

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