CMB mapping experiments: a designer's guide

We apply state-of-the art data analysis methods to a number of fictitious CMB mapping experiments, including 1/f noise, distilling the cosmological information from time-ordered data to maps to power spectrum estimates, and find that in all cases, the resulting error bars can we well approximated by simple and intuitive analytic expressions. Using these approximations, we discuss how to maximize the scientific return of CMB mapping experiments given the practical constraints at hand, and our main conclusions are as follows. (1) For a given resolution and sensitivity, it is best to cover a sky area such that the signal-to-noise ratio per resolution element (pixel) is of order unity. (2) It is best to avoid excessively skinny observing regions, narrower than a few degrees. (3) The minimum-variance mapmaking method can reduce the effects of 1/f noise by a substantial factor, but only if the scan pattern is thoroughly interconnected. (4) 1/f noise produces a 1/l contribution to the angular power spectrum for well connected single-beam scanning, as compared to virtually white noise for a two-beam scan pattern such as that of the MAP satellite.Comment: 28 pages, with 13 figures included. Minor revisions to match accepted version. Color figures and links at http://www.sns.ias.edu/~max/strategy.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/strategy.html (faster from Europe) or from [email protected]

Nagata compactification for algebraic spaces

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes.Comment: 49 pages, various clarifications and bugfixe

Reformulating Space Syntax: The Automatic Definition and Generation of Axial Lines and Axial Maps

Space syntax is a technique for measuring the relative accessibility of different locations in a spatial system which has been loosely partitioned into convex spaces.These spaces are approximated by straight lines, called axial lines, and the topological graph associated with their intersection is used to generate indices of distance, called integration, which are then used as proxies for accessibility. The most controversial problem in applying the technique involves the definition of these lines. There is no unique method for their generation, hence different users generate different sets of lines for the same application. In this paper, we explore this problem, arguing that to make progress, there need to be unambiguous, agreed procedures for generating such maps. The methods we suggest for generating such lines depend on defining viewsheds, called isovists, which can be approximated by their maximum diameters,these lengths being used to form axial maps similar to those used in space syntax. We propose a generic algorithm for sorting isovists according to various measures,approximating them by their diameters and using the axial map as a summary of the extent to which isovists overlap (intersect) and are accessible to one another. We examine the fields created by these viewsheds and the statistical properties of the maps created. We demonstrate our techniques for the small French town of Gassin used originally by Hillier and Hanson (1984) to illustrate the theory, exploring different criteria for sorting isovists, and different axial maps generated by changing the scale of resolution. This paper throws up as many problems as it solves but we believe it points the way to firmer foundations for space syntax

Monte Carlo Estimation for Imprecise Probabilities: Basic Properties

We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly practical techniques for proving strong consistency of the estimators and use these to prove the consistency of an example in the literature. We also provide an example where there is no consistency

Upscaling carbon fluxes from towers to the regional scale: Influence of parameter variability and land cover representation on regional flux estimates

Quantifying the current carbon cycle of terrestrial ecosystems requires that we translate spatially sparse measurements into consistent, gridded flux estimates at the regional scale. This is particularly challenging in heterogeneous regions such as the northern forests of the United States. We use a network of 17 eddy covariance flux towers deployed across the Upper Midwest region of northern Wisconsin and Michigan and upscale flux observations from towers to the regional scale. This region is densely instrumented and provides a unique test bed for regional upscaling. We develop a simple Diagnostic Carbon Flux Model (DCFM) and use flux observations and a data assimilation approach to estimate the model parameters. We then use the optimized model to produce gridded flux estimates across the region. We find that model parameters vary not only across plant functional types (PFT) but also within a given PFT. Our results show that the parameter estimates from a single site are not representative of the parameter values of a given PFT; cross-site (or joint) optimization using observations from multiple sites encompassing a range of site and climate conditions considerably improves the representativeness and robustness of parameter estimates. Parameter variability within a PFT can result in substantial variability in regional flux estimates. We also find that land cover representation including land cover heterogeneity and the spatial resolution and accuracy of land cover maps can lead to considerable uncertainty in regional flux estimates. In heterogeneous, complex regions, detailed and accurate land cover maps are essential for accurate estimation of regional fluxes