Mapping the CMB III: combined analysis of QMAP flights

We present results from the QMAP balloon experiment, which maps the Cosmic Microwave Background (CMB) and probes its angular power spectrum on degree scales. In two separate flights, data were taken in six channels at two frequency bands between 26 to 46 GHz. We describe our method for mapmaking (removal of 1/f-noise and scan-synchronous offsets) and power spectrum estimation, as well as the results of a joint analysis of the data from both flights. This produces a 527 square degree map of the CMB around the North Celestial Pole, allowing a wide variety of systematic cross-checks. The frequency dependence of the fluctuations is consistent with CMB and inconsistent with Galactic foreground emission. The anisotropy is measured in three multipole bands from l~40 to l~200, and the angular power spectrum shows a distinct rise which is consistent with the Saskatoon results.Comment: 4 pages, with 3 figures included. Submitted to ApJL. Window functions are available at http://pupgg.princeton.edu/~cmb/welcome.html and color figures and links at http://www.sns.ias.edu/~angelica/skymap.html#qma

Removing point sources from CMB maps

For high-precision cosmic microwave background (CMB) experiments, contamination from extragalactic point sources is a major concern. It is therefore useful to be able to detect and discard point source contaminated pixels using the map itself. We show that the sensitivity with which this can be done can often be greatly improved (by factors between 2.5 and 18 for the upcoming Planck mission) by a customized hi-pass filtering that suppresses fluctuations due to CMB and diffuse galactic foregrounds. This means that point source contamination will not severely degrade the cleanest Planck channels unless current source count estimates are off by more than an order of magnitude. A catalog of around 40,000 far infra-red sources at 857 GHz may be a useful by-product of Planck.Comment: 4 pages, with 2 figures included. Minor revisions to match accepted version. Color figure and links at http://www.sns.ias.edu/~max/cleaning.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/cleaning.html (faster from Europe) or from [email protected], and Angelica's foreground links at http://www.sns.ias.edu/~angelica/foreground.htm

POLAR: Instrument and Results

We describe the design, performance, and results of a polarimeter used to make precision measurements of the 2.7 K cosmic microwave background. In the Spring of 2000 the instrument searched for polarized emission in three microwave frequency bands spanning 26–36 GHz. The instrument achieved high sensitivity and long-term stability, and has produced the most stringent limits to date on the amplitude of the large angular scale polarization of the cosmic microwave background radiation

Discrete and continuous SIS epidemic models: A unifying approach

550030/2010-7.The susceptible-infective-susceptible (SIS) epidemiological scheme is the simplest description of the dynamics of a disease that is contact-transmitted, and that does not lead to immunity. Two by now classical approaches to such a description are: (i) the use of a mass-action compartmental model that leads to a single ordinary differential equation (SIS-ODE); (ii) the use of a discrete-time Markov chain model (SIS-DTMC). While the former can be seen as a mean-field approximation of the latter under certain conditions, it is also known that their dynamics can be significantly different, if the basic reproduction number is greater than one. The goal of this work is to introduce a continuous model, based on a partial differential equation (SIS-PDE), that retains the finite populations effects present in the SIS-DTMC model, and that allows the use of analytical techniques for its study. In particular, it will reduce itself to the SIS-ODE model in many circumstances. This is accomplished by deriving a diffusion-drift approximation to the probability density of the SIS-DTMC model. Such a diffusion is degenerated at the origin, and must conserve probability. These two features then lead to an interesting consequence: the biologically correct solution is a measure solution. We then provide a convenient representation of such a measure solution that allows the use of classical techniques for its computation, and that also provides a tool for obtaining information about several dynamical features of the model. In particular, we show that the SIS-ODE gives the most likely state, conditional on non-absorption. As a further application of such representation, we show how to define the disease-outbreak probability in terms of the SIS-PDE model, and show that this definition can be used both for certain and uncertain initial presence of infected individuals. As a final application, we compute an approximation for the extinction time of the disease. In addition, we present many numerical examples that confirm the good approximation of the SIS-DTMC by the SIS-PDE.preprintpublishe