To fully understand animal transcription networks, it is essential to accurately measure the spatial and temporal expression patterns of transcription factors and their targets. We describe a registration technique that takes image-based data from hundreds of Drosophila blastoderm embryos, each costained for a reference gene and one of a set of genes of interest, and builds a model VirtualEmbryo. This model captures in a common framework the average expression patterns for many genes in spite of significant variation in morphology and expression between individual embryos. We establish the method's accuracy by showing that relationships between a pair of genes' expression inferred from the model are nearly identical to those measured in embryos costained for the pair. We present a VirtualEmbryo containing data for 95 genes at six time cohorts. We show that known gene-regulatory interactions can be automatically recovered from this data set and predict hundreds of new interactions.

No abstract

A method for computing isovalue or contour surfaces of a trivariate function is discussed. The input data are values of the trivariatefunctwn, F+, at the cuberille grid points (Xi, yj, zk) and the output is a collection of triangles representing the surface consisting of all points where F(x, y, z) is a constant value. The method described here is a modification that is intended to correct a problem with a previous method. marked indicates Fijk > a. While there are 28 = 256 possible configurations, there are only 15 shown in Figure 2. This is because some configurations are equivalent with respect to certain operations. First off, the number can be reduced to 128 by assuming two configurations are equivalent if marked grid points and unmarked grid points are switched. This means that we only have to consider cases where there are four or fewer marked grid points. Further reduction to the 15 cases shown is possible by equivalence due to rotations.

We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.