How to make maps from CMB data without losing information

The next generation of CMB experiments can measure cosmological parameters with unprecedented accuracy - in principle. To achieve this in practice when faced with such gigantic data sets, elaborate data analysis methods are needed to make it computationally feasible. An important step in the data pipeline is to make a map, which typically reduces the size of the data set my orders of magnitude. We compare ten map-making methods, and find that for the Gaussian case, both the method used by the COBE DMR team and various variants of Wiener filtering are optimal in the sense that the map retains all cosmological information that was present in the time-ordered data (TOD). Specifically, one obtains just as small error bars on cosmological parameters when estimating them from the map as one could have obtained by estimating them directly from the TOD. The method of simply averaging the observations of each pixel (for total-power detectors), on the contrary, is found to generally destroy information, as does the maximum entropy method and most other non-linear map-making techniques. Since it is also numerically feasible, the COBE method is the natural choice for large data sets. Other lossless (e.g. Wiener-filtered) maps can then be computed directly from the COBE method map.Comment: Minor revisions to match published version. 12 pages, with 1 figure included. Color figure and links at http://www.sns.ias.edu/~max/mapmaking.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/mapmaking.html (faster from Europe) or from [email protected]

Note on the air forces on a wing caused by pitching.

The following contains information on the air forces on a wing produced by it's pitching at a finite rate of angular velocity. The condition of smooth flow at the region of the trailing edge is maintained. The wing then experiences the same lift as if moving with the momentary velocity of the rear edge

Notes on aerodynamic forces 1 : rectilinear motion

The study of the motion of perfect fluids is of paramount importance for the understanding of the chief phenomena occurring in the air surrounding an aircraft, and for the numerical determination of their effects. The author recently successfully employed some simple methods for the investigation of the flow of a perfect fluid that have never been mentioned in connection with aeronautical problems. These methods appeal particularly to the engineer who is untrained in performing laborious mathematical computations, as they do away with these and allow one to obtain many interesting results by the mere application of some general and well-known principles of mechanics. Discussed here are the kinetic energy of moving fluids, the momentum of a body in a perfect fluid, two dimensional flow, three dimensional flow, and the distribution of the transverse forces of very elongated surfaces of revolution

Linguistics Landscape: a Cross Culture Perspective

This paper was to aim in discussing the linguistic landscape. It was the visibility and salience of languages on public and commercial signs in a given territory or region (Landry and Bourhis 1997). The linguistic landscape has been described as being somewhere at the junction of sociolinguistics, sociology, social psychology, geography, and media studies. It is a concept used in sociolinguistics as scholars study how languages are visually used in multilingual societies, from large metropolitan centers to Amazonia. For example, some public signs in Jerusalem are in Hebrew, English, and Arabic (Spolsky and Cooper 1991, Ben-Rafael et al., 2006). Studies of the linguistic landscape have been published from research done around the world. The field of study is relatively recent; the linguistic landscape paradigm has evolved rapidly and while it has some key names associated with it, it currently has no clear orthodoxy or theoretical core

Note on vortices on their relation to the lift of airfoils

This note, prepared for the NACA, contains a discussion of the meaning of vortices, so often mentioned in connection with the creation of lift by wings. The action of wings can be more easily understood without the use of vortices

The twisted wing with elliptic plan form

A method for computing the aerodynamic induction of wings with elliptic plan form if arbitrarily twisted

Non-Gaussianity in Two-Field Inflation

We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the \delta N formalism and the transfer function formalism to express the bispectrum almost entirely in terms of model-independent physical quantities. Similarly, we calculate the trispectrum and show that the trispectrum parameter \tau NL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to the initial conditions, and that the amount of sourcing must be moderate in order to avoid excessive fine-tuning. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn slightly (but not too sharply) in field space. Therefore, it follows that two-field scenarios with attractor solutions necessarily produce small non-Gaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models like hybrid inflation and certain product potentials where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize qualitatively to general multi-field inflation.Comment: Discussion improved, gNL formula and extra figure included, typos corrected, references added. 18 pages, 2 figure

Notes on propeller design IV : general proceeding in design

The choice of the numbers of revolutions and of the diameter, the distribution of thrust, and the values of the constants in the aerodynamical equations of the propeller are discussed

Elements of the Wing Section Theory and of the Wing Theory

Results are presented of the theory of wings and of wing sections which are of immediate practical value. They are proven and demonstrated by the use of the simple conceptions of kinetic energy and momentum only

The velocity distribution caused by an airplane at the points of a vertical plane containing the span

A formula for the computation of the vertical velocity component on all sides of an airplane is deduced and discussed. The formation is of value for the interpretation of such free flight tests where two airplanes fly alongside each other to facilitate observation