6,266 research outputs found
The Equivariant Chow rings of quot schemes
We give a presentation for the (integral) torus-equivariant Chow ring of the
quot scheme, a smooth compactification of the space of rational curves of
degree d in the Grassmannian. For this presentation, we refine Evain's
extension of the method of Goresky, Kottwitz, and MacPherson to express the
torus-equivariant Chow ring in terms of the torus-fixed points and explicit
relations coming from the geometry of families of torus-invariant curves. As
part of this calculation, we give a complete description of the torus-invariant
curves on the quot scheme and show that each family is a product of projective
spaces.Comment: Revised slightly. Clarifed some statements and remove one
straightforward proof. 26 pages, many .eps figure
Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques.
BACKGROUND:How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10(11) mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages. RESULTS:While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs. CONCLUSIONS:Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation
Noiseless Gravitational Lensing Simulations
The microphysical properties of the DM particle can, in principle, be
constrained by the properties and abundance of substructures in DM halos, as
measured through strong gravitational lensing. Unfortunately, there is a lack
of accurate theoretical predictions for the lensing signal of substructures,
mainly because of the discreteness noise inherent to N-body simulations. Here
we present Recursive-TCM, a method that is able to provide lensing predictions
with an arbitrarily low discreteness noise, without any free parameters or
smoothing scale. This solution is based on a novel way of interpreting the
results of N-body simulations, where particles simply trace the evolution and
distortion of Lagrangian phase-space volume elements. We discuss the advantages
of this method over the widely used cloud-in-cells and adaptive-kernel
smoothing density estimators. Applying the new method to a cluster-sized DM
halo simulated in warm and cold DM scenarios, we show how the expected
differences in their substructure population translate into differences in the
convergence and magnification maps. We anticipate that our method will provide
the high-precision theoretical predictions required to interpret and fully
exploit strong gravitational lensing observations.Comment: 13 pages, 13 figures. Updated fig 12, references adde
- …