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What is the best way to pixelize a sphere? This question occurs in many practical applications, for instance when making maps (of the earth or the celestial sphere) and when doing numerical integrals over the sphere. This package consists of source code and documentation for a method which involves inscribing the sphere in a regular icosahedron and then equalizing the pixel areas.
Understanding diffuse Galactic radio emission is interesting both in its own right and for minimizing foreground contamination of cosmological measurements. Cosmic Microwave Background experiments have focused on frequencies > 10 GHz, whereas 21 cm tomography of the high redshift universe will mainly focus on < 0.2 GHz, for which less is currently known about Galactic emission. Motivated by this, we present a global sky model derived from all publicly available total power large-area radio surveys, digitized with optical character recognition when necessary and compiled into a uniform format, as well as the new Villa Elisa data extending the 1.4 GHz map to the entire sky. We quantify statistical and systematic uncertainties in these surveys by comparing them with various global multi-frequency model fits. We find that a principal component based model with only three components can fit the 11 most accurate data sets (at 10, 22, 45 & 408 MHz and 1.4, 2.3, 23, 33, 41, 61, 94 GHz) to an accuracy around 1%-10% depending on frequency and sky region. The data compilation and software returning a predicted all-sky map at any frequency from 10 MHz to 100 GHz are publicly available in the archive file at the link below.
Mangle deals accurately and efficiently with complex angular masks, such as occur typically in galaxy surveys. Mangle performs the following tasks: converts masks between many handy formats (including HEALPix); rapidly finds the polygons containing a given point on the sphere; rapidly decomposes a set of polygons into disjoint parts; expands masks in spherical harmonics; generates random points with weights given by the mask; and implements computations for correlation function analysis. To mangle, a mask is an arbitrary union of arbitrarily weighted angular regions bounded by arbitrary numbers of edges. The restrictions on the mask are only (1) that each edge must be part of some circle on the sphere (but not necessarily a great circle), and (2) that the weight within each subregion of the mask must be constant. Mangle is complementary to and integrated with the HEALPix package (ascl:1107.018); mangle works with vector graphics whereas HEALPix works with pixels.
AI-Feynman fits analytical expressions to data sets via symbolic regression, mapping the target variable to different features supplied in the data array. Using a neural network with constraints in the number of parameters utilized, the code provides the ability to obtain analytical expressions for normalized features that are used to predict a Pareto-optimal target. AI-Feynman is robust in handling noisy data, recursively generating multidimensional symbolic expressions that match data from an unknown functions.