(under construction)

Supported by NASA through  an Applied Information Research grant NAG5-10750

Period:

04/15/01-04/14/02

Personnel:

Principal Investigator: Istvan Szapudi
Collaborators: Simon Prunet, Stephane Colombi (AIP, Paris)

Objectives:

The aim of this proposal is to develop an array
of techniques for statistical characterization
of the CMB based on fast clustering algorithms,
which will be used for estimation of the
angular power spectrum, polarization power
spectrum, cross correlations with large scale
structure and foregrounds, and constraining higher order
(non-Gaussian) statistics of the CMB.
The proposed novel methods enable the analysis of MAP
in minutes on a typical present day workstation,
allowing Monte Carlo studies hitherto impossible.
 

Status:

We have  performed the basic algorithmic research underlying
the goals of our project.  This resulted in new correlation function engine,
SpICE, (Spatially Inhomogenous Correlation Estimator), which can
produce correlation functions and the angular power spectrum
of the CMB in much shorter times then previously was possible.
For the first time, accurate analysis of megapixel CMB maps is
possible under very general assumptions on a simple workstation
(or even notebook).

Comparitive Timings:
 

N	COBE	LDB	MAP	PLANCK
Max Likelihood	1 day	1 year	1600 years	1.6 million years
OSH			80 hours
Szapudi \etal (2001)	0.08 sec	85 sec	23 hours	96 days
SpICE			300sec	46 minutes

In the above, Max Likelihood timings are estimated from Borill  (1999) and Bond, Jaffe \&
Knox (2000), OSH is  the experiment specific technique of Oh, Spergel \& Hinshaw.
The scaling is N^3, N^2, N^2, and N^1.6 for the four methods.

Publications:

The theory of the method is published in

Szapudi, Prunet, Pogosyan, Bond, & Szalay (2001) ApJLett, 548, 11L.

The new algorithm and latest results for MAP simulations can be found in

Szapudi, Prunet, & Colombi (2001) ApJLett., 561,11L.

Preview:

Presently our team is working on incorporating our  CMB analysis software into the Planck level 2 pipeline. We are also working on the public release of SpICE 1.0, a HEALPix compatible
implementation of our algorithm with basic CMB analysis functionality.

 Version 1.0  of SpICE is available now! Please read the README
message to compile, and then run

spice -help

This version will calculate C_l's from CMB maps, with quite a few options already
concerning noise, etc. Check it out! (See also eSpICE)

Plans for the near and not so near future:

We are working on generalization of our technique and algorithms for vector
and tensor correlations for lensing and polarization,  higher order statistics,
N-point correlation functions/N-1 spectra to constrain non-Gaussianity.
Our method is also being adapted for point processes for surveys such as
the SDSS, and a Euclidean version is under development for mission with
smaller field of view, like the HST ACS.  We are developing  code for 3 dimensional
distribution including the effects of red shift distortions. Of course, the final goal of all
these planned generalizations is scientific application, which will follow
immediately after code development and testing.