9,720 research outputs found
Intersection Cohomology of S1-Actions on Pseudomanifolds
For any smooth free action of the unit circle S1 on a smooth manifold M, the
Gysin sequence of M is a long exact sequence relating the DeRham Cohomology of
M and the orbit space M/S1. If the action is not free then M/S1 is not a smooth
manifold but a stratified pseudomanifold, the lenght of M/S1 depending on the
number of orbit types; and there is a Gysin sequence relating their
intersection cohomologies. The links of the fixed strata in M/S1 are
cohomological complex projective spaces, so the conecting homomorphism of this
sequences is the multiplication by the Euler class.
In this article we extend the above results for any action of S1 on a
stratified pseudomanifold X of lenght 1. We use the DeRham-like intersection
cohomology defined by means of an unfolding. If the action preserves the local
structure, then the orbit space X/S1 is again a stratified pseudomanifold of
lenght 1 and has an unfolding. There is a long exact sequence relating the
intersection cohomology of X and X/S1 with a third complex , the
Gysin Term, whose cohomology depends on basic cohomological data of two
flavours: global and local. Global data concerns the Euler class induced by the
action; local information depends on the cohomology of the fixed strata with
values on some presheaves.Comment: AMSTeX Article, 23 pages. Keywords and phrases: Intersection
Cohomology, Stratified Pseudomanifold
Peculiar Velocities and the Mean Density Parameter
We study the peculiar velocity field inferred from the Mark III spirals using
a new method of analysis. We estimate optimal values of Tully-Fisher scatter
and zero-point offset, and we derive the 3-dimensional rms peculiar velocity
() of the galaxies in the samples analysed. We check our statistical
analysis using mock catalogs derived from numerical simulations of CDM models
considering measurement uncertainties and sampling variations. Our best
determination for the observations is . We use the
linear theory relation between , the density parameter , and
the galaxy correlation function to infer the quantity where is the linear bias parameter
of optical galaxies and the uncertainties correspond to bootstrap resampling
and an estimated cosmic variance added in quadrature. Our findings are
consistent with the results of cluster abundances and redshift space distortion
of the two-point correlation function. These statistical measurements suggest a
low value of the density parameter if optical galaxies are
not strongly biased tracers of mass.Comment: Accepted for publication in MNRAS. 8 pages latex (mn.sty), including
7 figure
Equivariant intersection cohomology of the circle actions
In this paper, we prove that the orbit space B and the Euler class of an
action of the circle S^1 on X determine both the equivariant intersection
cohomology of the pseudomanifold X and its localization. We also construct a
spectral sequence converging to the equivariant intersection cohomology of X
whose third term is described in terms of the intersection cohomology of B.Comment: Final version as accepted in RACSAM. The final publication is
available at springerlink.com; Revista de la Real Academia de Ciencias
Exactas, Fisicas y Naturales. Serie A. Matematicas, 201
Tensor decomposition with generalized lasso penalties
We present an approach for penalized tensor decomposition (PTD) that
estimates smoothly varying latent factors in multi-way data. This generalizes
existing work on sparse tensor decomposition and penalized matrix
decompositions, in a manner parallel to the generalized lasso for regression
and smoothing problems. Our approach presents many nontrivial challenges at the
intersection of modeling and computation, which are studied in detail. An
efficient coordinate-wise optimization algorithm for (PTD) is presented, and
its convergence properties are characterized. The method is applied both to
simulated data and real data on flu hospitalizations in Texas. These results
show that our penalized tensor decomposition can offer major improvements on
existing methods for analyzing multi-way data that exhibit smooth spatial or
temporal features
- …