E2E Program

United States Department of Homeland Security University of Alaska Anchorag

Nitrate regulates floral induction in Arabidopsis, acting independently of light, gibberellin and autonomous pathways

The transition from vegetative growth to reproduction is a major developmental event in plants. To maximise reproductive success, its timing is determined by complex interactions between environmental cues like the photoperiod, temperature and nutrient availability and internal genetic programs. While the photoperiod- and temperature- and gibberellic acid-signalling pathways have been subjected to extensive analysis, little is known about how nutrients regulate floral induction. This is partly because nutrient supply also has large effects on vegetative growth, making it difficult to distinguish primary and secondary influences on flowering. A growth system using glutamine supplementation was established to allow nitrate to be varied without a large effect on amino acid and protein levels, or the rate of growth. Under nitrate-limiting conditions, flowering was more rapid in neutral (12/12) or short (8/16) day conditions in C24, Col-0 and Laer. Low nitrate still accelerated flowering in late-flowering mutants impaired in the photoperiod, temperature, gibberellic acid and autonomous flowering pathways, in the fca co-2 ga1-3 triple mutant and in the ft-7 soc1-1 double mutant, showing that nitrate acts downstream of other known floral induction pathways. Several other abiotic stresses did not trigger flowering in fca co-2 ga1-3, suggesting that nitrate is not acting via general stress pathways. Low nitrate did not further accelerate flowering in long days (16/8) or in 35S::CO lines, and did override the late-flowering phenotype of 35S::FLC lines. We conclude that low nitrate induces flowering via a novel signalling pathway that acts downstream of, but interacts with, the known floral induction pathways

Singular systems of geometric partial differential equations

In this thesis we study the local solvability of a class of real analytic singular systems of nonlinear partial differential equations in a neighborhood of a singular point; the particular applications that we consider are (i) existence of a diffeomorphism, between two Riemannian manifolds, with prescribed nondistinct eigenvalues (ii) existence of Riemannian metrics with prescribed Ricci tensor whose rank is not locally constant. A system of partial differential equations is called singular if its principal symbol does not have locally constant rank, and every covector based at a singular point is characteristic. The partial differential operators associated with such systems may be smooth. Singular systems of partial differential equations appear often in the description of problems in geometry and physics, but there has been very little progress in their understanding. For every system in the class that we study the set of singular points is a submanifold of codimension one. We prove sufficient conditions for local solvability in a neighborhood of a singular point, and apply the developed theory to: (i) solve the eigenvalue problem when precisely two of the eigenvalues coincide to order zero at a point, (ii) prove the necessary and sufficient conditions for the existence of a Riemannian solution g of Ric(g) = $R\in{\cal R}$, where ${\cal R}$ is a generic class of analytic tensor fields of covariant symmetric 2-tensors such that the rank of each tensor field drops by one on a hypersurface

Geometric Integrability and Consistency of 3D Point Clouds

Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and differential geometric properties. Normal estimates are notoriously noisy, the errors propagate and may lead to flawed, inaccurate, and inconsistent curvature estimates. Frankot-Chellappa introduced the use of integrability constraints in normal estimation. Their approach deals with graphs z = f(x, y). We present a newly discovered General Orientability Constraint (GOC) for 3D point clouds sampled from general surfaces, not just graphs. It provides a tool to quantify the confidence in the estimation of normals, topology, and geometry from a point cloud. Furthermore, similarly to the Frankot-Chellappa constraint, the GOC can be used directly to extract the topology and the geometry of the manifolds underlying 3D point clouds. As an illustration we describe an automatic Cloud-to-Geometry pipeline which exploits the GOC. 1

Shape invariantsand principal directions from 3D points and normals

A new technique for computing the differential invariants of a surface from 3D sample points and normals is presented. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential invariants are computed directly from the points and the normals without prior recovery of a 3D surface model and an approximate surface parameterization. The technique is stable computationally