Empirical evidence suggests that the hippocampus constructs maps of spatial environments based on the relative locations of places (i.e., topology), rather than absolute distances and coordinates (i.e., geometry).
Mathematical methods based on geometry that directly embody the developmental concepts of competency, commitment, and determination provide succinct descriptions of morphogenesis and allow quantitative predictions from fits to sparse genetic data in Caenorhabditis elegans.
Quantitative analyses associating the morphology of developing organs with dynamic gene expression patterns can reveal biological phenomena that cause malformations and malfunction but remain elusive to traditional qualitative assessments.
The geometry selection rules of dynamic Min protein patterns are determined in fully confined fluidic chambers, showing that both oscillations and running waves are derivatives of spiral rotations that are established as the majority pattern.
A mathematical model that combines stochasticity and spatial structure describes the dynamics of the viral population during an infection cycle, and fitting the model to RNA and virus abundances over time shows that poliovirus follows a geometric replication mode.